If the expression 1/2x was placed in the form ax^b where a and b are real numbers, then a + b equal to option (4) -1/2
The given expression is 1/(2x), which can be rewritten as:
1/(2x) = 1/2 × (1/x)
Here, we can see that the expression can be written in the form of ax^b, where a = 1/2 and b = -1.
To see why a = 1/2, notice that 1/2 is the coefficient of (1/x). And to see why b = -1, note that x^(-1) is the exponent on the variable x
So, we have:
1/(2x) = (1/2) × x^(-1)
And, a + b = (1/2) + (-1)
Add the numbers
= -1/2.
Therefore, the correct option is (4) -1/2.
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Student A can solve 75% of problems, student B can solve 70%. What is the probability that A or B can solve a problem chosen at random?
The probability that student A or B can solve a problem chosen at random is 0.95.
Probability is calculated by dividing the number of favourable outcomes by the number of possible outcomes.
Random: An event is referred to as random when it is not possible to predict it with certainty. The probability that either student A or B will be able to solve a problem chosen at random can be calculated as follows:
P(A or B) = P(A) + P(B) - P(A and B) where: P(A) = probability of A solving a problem = 0.75, P(B) = probability of B solving a problem = 0.7, P(A and B) = probability of both A and B solving a problem. Since A and B are independent, the probability of both solving the problem is:
P(A and B) = P(A) x P(B) = 0.75 x 0.7 = 0.525
Now, using the above formula: P(A or B) = P(A) + P(B) - P(A and B) = 0.75 + 0.7 - 0.525 = 0.925
Therefore, the probability that student A or B can solve a problem chosen at random is 0.95 (or 95%).
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1. A 180-day simple interest loan in the amount of $16, 400 will be paid in full in the amount of $16, 851. Find the interest rate of
the loan. Use the banker's method, which uses 360 days in a year.
OR=5.5%
OR=5.0%
OR=4.5%
R= 6.0%
Answer:
Using the banker's method, we can use the following formula to find the interest:
Interest = (Principal x Rate x Days) / 360
Where,
Principal = $16,400
Amount = $16,851
Days = 180
We know that the interest plus the principal equals the amount, so we can set up the following equation:
Interest + Principal = Amount
Substituting the values:
(16,400 x Rate x 180) / 360 + 16,400 = 16,851
Multiplying both sides by 360:
16,400 x Rate x 180 + 5,904,000 = 6,066,360
16,400 x Rate x 180 = 162,360
Rate = 162,360 / (16,400 x 180)
Rate = 0.055 or 5.5%
Therefore, the interest rate of the loan is 5.5%.
how do i graph y=9-x
Answer:
We can rewrite the equation in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. To do this, we can rearrange the terms as follows:y = 9 - xy = -1x + 9
This gives us a slope of -1 and a y-intercept of 9. We can plot the y-intercept at (0, 9) and use the slope to find another point on the line. The slope tells us that for every increase of 1 in x, the value of y decreases by 1. So, starting from (0, 9), we can move one unit to the right and one unit down to get another point (1, 8). We can continue this process to find more points or connect the two points we already have to draw a line.
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The resulting graph should be a straight line that starts at the point (0, 9) on the y-axis and intersects the x-axis at the point (9, 0). The line slants downward from left to right.
Here, we have,
We can rewrite the equation in slope-intercept form,
y = mx + b,
where m is the slope and b is the y-intercept.
To do this, we can rearrange the terms as follows:
y = 9 - x
y = -1x + 9
This gives us a slope of -1 and a y-intercept of 9.
We can plot the y-intercept at (0, 9) and use the slope to find another point on the line.
The slope tells us that for every increase of 1 in x, the value of y decreases by 1.
So, starting from (0, 9), we can move one unit to the right and one unit down to get another point (1, 8).
We can continue this process to find more points or connect the two points we already have to draw a line.
To graph the equation y = 9 - x, you can follow these steps:
Step 1: Create a table of values. Choose some x-values and substitute them into the equation to find the corresponding y-values. For simplicity, let's choose three values for x:
x | y = 9 - x
0 | 9 - 0 = 9
3 | 9 - 3 = 6
6 | 9 - 6 = 3
Step 2: Plot the points. Use the x-values from the table and their corresponding y-values to plot the points on the graph. The points are (0, 9), (3, 6), and (6, 3).
Step 3: Draw the line. Connect the plotted points with a straight line. The line should pass through all the plotted points.
The resulting graph should be a straight line that starts at the point (0, 9) on the y-axis and intersects the x-axis at the point (9, 0). The line slants downward from left to right.
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suppose the mean income of firms in the industry for a year is 80 million dollars with a standard deviation of 13 million dollars. if incomes for the industry are distributed normally, what is the probability that a randomly selected firm will earn less than 96 million dollars? round your answer to four decimal places.
The probability that a randomly selected firm will earn less than 96 million dollars is 0.8907
The given data is that the mean income of firms in the industry for a year is 80 million dollars with a standard deviation of 13 million dollars. Now, it is required to find the probability that a randomly selected firm will earn less than 96 million dollars if incomes for the industry are distributed normally.
The probability is calculated by the Z-score formula which is given as below:
z = (x - μ) / σ
Where,μ = 80 (Mean), x = 96 (Randomly selected firm income), σ = 13 (Standard deviation)
Putting the values in the formula we have,
z = (96 - 80) / 13z = 1.23
Now we will use the Z-table to find the probability value. From the Z-table, we can say that the probability of Z-score = 1.23 is 0.8907.
Therefore, the probability that a randomly selected firm will earn less than 96 million dollars is 0.8907 (approx) when rounded off to four decimal places.
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Given: Triangle ABC is similar to triangle DEF, side BC = 19, angle ABC = 48, angle BCA = 73.
If the side DF = 15, then AB - EF = ?
Answer:
We are given two similar triangles, triangle ABC and triangle DEF, and some measurements of triangle ABC. We are also given that DF, one of the sides of triangle DEF, is equal to 15 units. Using this information, we are asked to find the difference between the lengths of sides AB and EF.
To solve the problem, we can first use the angle-angle similarity theorem to determine that the corresponding angles of the two triangles are equal. Therefore, angle DEF is equal to angle BCA, and angle ABE is equal to angle DFE.
Next, we can use the law of sines to find the length of side AB. The law of sines states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is equal for all sides and angles in the triangle. Applying this to triangle ABC, we have:
AB/sin(73) = BC/sin(48)
Substituting the value of BC as 19 units, we can solve for AB to get:
AB = 22.78 units
Similarly, we can use the law of sines to find the length of side EF. Since angle DFE is equal to angle ABE, we can use the same ratio as above to get:
EF/sin(73) = DF/sin(48)
Substituting the value of DF as 15 units, we can solve for EF to get:
EF = 18.20 units
Finally, we can subtract EF from AB to get:
AB - EF = 22.78 - 18.20 = 4.58 units
Therefore, the difference between the lengths of sides AB and EF is 4.58 units.
Benito made a wooden box to grow herbs on his patio. The box is 16 inches wide, 12 inches tall, and 28 inches long. He plans to fill the box exactly two-thirds full with potting soil. What volume of soil does Benito need? I know how to do this I just need to know if the two-thirds part is trying to throw me off
To fill the wooden box with potting soil precisely up to two-thirds of its capacity, Benito requires a volume of 3,584 cubic inches.
The volume of soil that Benito needs to fill the box two-thirds full can be calculated by finding two-thirds of the total volume of the box.
The volume of the box can be calculated by multiplying the width, height, and length:
16 inches (width) x 12 inches (height) x 28 inches (length) = 5,376 cubic inches.
Two-thirds of this volume can be found by multiplying the total volume by 2/3:
5,376 cubic inches x 2/3 = 3,584 cubic inches.
Therefore, Benito needs 3,584 cubic inches of potting soil to fill the box exactly two-thirds full.
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We revisit a probabilistic model for a fault diagnosis problem from an earlier homework. The class variable C represents the health of a disk drive: C = 0 means it is operating normally; and C = 1 means it is in failed state. When the drive is running it continuously monitors itself using temperature and shock sensor, and records two binary features, X and Y. X =lif the drive has been subject to shock (e.g;, dropped) , and X = 0 otherwise Y =1if the drive temperature has ever been above 70*C, and Y = 0 otherwise. The following table defines the joint probability mass function of these three random variables: pxyc(r,y, c) 0.1 0.2 0.2 0 0 0 0 0 0 0.05 0.25
The probability of the disk drive being in a normal state is 0.5, and the probability of the disk drive being in a failed state is 0.3.
The given table represents the joint probability mass function of the random variables, pxyc (r, y, c). r, y, and c denote the temperature, shock sensor, and health status of the disk drive. The values of r, y, and c are binary.The joint probability mass function of three random variables r, y, and c can be represented as follows:pxyc (r, y, c)= P(r, y, c)Here,P(r=0, y=0, c=0)= 0.1, P(r=0, y=1, c=0)= 0.2, P(r=1, y=0, c=0)= 0.2,P(r=0, y=0, c=1)= 0, P(r=0, y=1, c=1)= 0, P(r=1, y=0, c=1)= 0,P(r=0, y=0, c=0)= 0, P(r=0, y=1, c=0)= 0, P(r=1, y=1, c=0)= 0.05,P(r=0, y=0, c=1)= 0.25, P(r=0, y=1, c=1)= 0, P(r=1, y=0, c=1)= 0.From the given table, the probability of the disk drive being in a normal state, C=0, is P(C=0)=P(r=0, y=0, c=0)+P(r=0, y=1, c=0)+P(r=1, y=0, c=0)=0.1+0.2+0.2=0.5Hence, the probability of the disk drive being in a failed state, C=1, is:P(C=1)=P(r=0, y=0, c=1)+P(r=0, y=1, c=1)+P(r=1, y=0, c=1)+P(r=1, y=1, c=0)=0.25+0+0+0.05=0.3Therefore, the probability of the disk drive being in a normal state is 0.5, and the probability of the disk drive being in a failed state is 0.3.
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For what value of x, the fraction become undefined 6/x-3
Answer:
the value of x is 3
Step-by-step explanation:
6/3-3=6/0
which is undefinied
Answer:
3
Step-by-step explanation:
alexis created the two-way frequency table from information she gathered by asking 88 teenagers about their last online shopping experience. own money parents' money total completed purchase 16 34 50 just looked 22 16 38 total 38 50 88 about what percent of the teenagers purchased something with their parents' money?
The percentage of the teenagers who purchased something with their parents' money can be calculated from the two-way frequency table. About 38.64% of the teenagers purchased something with their parents' money.
There were a total of 88 teenagers who were surveyed by Alexis. 38 of them completed the purchase, and out of these 38 teenagers, 34 of them used their parents' money. So, the percentage of teenagers who purchased something with their parents' money can be calculated as follows:
Percent of teenagers who purchased something with their [tex]parents' money = \frac{Frequency of completed purchase}{Total Number of teenagers surveyed} *100[/tex]
Percent of teenagers who purchased something with their parents' money = [tex]\frac{34}{88} * 100%[/tex]%
Therefore percent of teenagers who purchased something with their parents' money = 38.64%
Therefore, about 38.64% of the teenagers purchased something with their parents' money.
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The market capitalization rate on the stock of Flexsteel Company is 12%. The expected ROE is 13% and the expected EPS are Rs. 3. 60. If the firm's plowback ratio is 75%, what will be the P/E ratio?
As per the given metrics, the P/E ratio for Flexsteel Company is 6.9.
The capitalization rate of Flexsteel Company = 12%
Plowback ratio of Flexsteel Company = 75% = 0.75
Return on equity of Flexsteel Company = 13% = 0.13
Expected EPS of Flexsteel Company = Rs. 3.60
Calculating the growth rate -
Growth rate = Plowback ratio x Return on equity
Growth rate = 0.75 x 0.13
= 0.0975
Calculating the price-to-earnings (P/E) ratio -
P/E ratio = (Market capitalization rate - Growth rate) / (Return on equity - Growth rate)
= (0.12 - 0.0975) / (0.13 - 0.0975)
= 0.0225/0.0325
= 0.69 or 6.9
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A spinner is divided into five colored sections that are not of equal size: red, blue, green, yellow, and purple. The spinner is spun several times, and the results are recorded below:
Spinner Results
Color Frequency
Red 20
Blue 9
Green 11
Yellow 7
Purple 16
Based on these results, express the probability that the next spin will land on red or green or purple as a decimal to the nearest hundredth.
Answer: 0.75
Step-by-step explanation:
The total frequency of all the colors is 20+9+11+7+16=63.
The probability of landing on red or green or purple is the sum of the frequencies of these three colors divided by the total frequency:
P(red or green or purple) = (20+11+16)/63
P(red or green or purple) ≈ 0.75(rounded to the nearest hundredth)
Therefore, the probability of the next spin landing on red or green or purple is approximately 0.75.
Answer:
0.75
Step-by-step explanation:
The total spins was 63. The total amount of spins for red, green or purple is 47.
Dividing, we get 47/63 ≈ 0.75.
Hope this helps!
Zoey needed to get her computer fixed. She took it to the repair store. The
technician at the store worked on the computer for 3. 25 hours and charged
her $59 for parts. The total was $205. 25. Write and solve an equation which
can be used to determine x, the cost of the labor per hour.
3.25x + 59 = 205.25 is an equation which can be used to determine x, the cost of the labor per hour.
Let's assume that the cost of labor per hour is x dollars.
The technician worked on the computer for 3.25 hours, so the cost of labor is 3.25x dollars.
In addition, Zoey was charged $59 for parts.
The total cost, including labor and parts, was $205.25.
Therefore, we can write the equation:
3.25x + 59 = 205.25
To solve for x, we need to isolate x on one side of the equation.
We can do this by subtracting 59 from both sides:
3.25x = 146.25
Finally, we can solve for x by dividing both sides by 3.25:
x = 45
Therefore, the cost of labor per hour is $45.
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b) Father is 30 years older than his son. After five years, he will be three times as old as his son will be. Find their present age.
Step-by-step explanation:
40 Years is the right answer
Answer:
son is 10 , father is 40
Step-by-step explanation:
let x be the sons age then father is x + 30
in 5 years
son is x + 5 and father is x + 30 + 5 = x + 35
at this time the father is three times as old as his son , then
x + 35 = 3(x + 5)
x + 35 = 3x + 15 ( subtract x from both sides )
35 = x + 15 ( subtract 15 from both sides )
20 = x
then sons age = x = 10 and fathers age = x + 30 = 10 + 30 = 40
Find the perimeter of the given figure. tb +b) 4cm 5cm 8cm 3cm. 1èm
The perimeter of the figure with dimensions (4cm, 5cm, 8cm, and 3cm) is 20 cm
What is the perimeter?
The entire length of a shape's boundary is referred to as the perimeter in geometry. A shape's perimeter is calculated by combining the lengths of all of its sides and edges. Its dimensions are expressed in linear measures like centimeters, meters, inches, and feet.
Why is a perimeter important?
They help you to quantify physical space and also provide a foundation for more advanced mathematics found in algebra, trigonometry, and calculus. Perimeter is a measurement of the distance around a shape and area gives us an idea of how much surface the shape covers.
What is the formula for the perimeter of a rectangle?
The formula for the perimeter of a rectangle is,
P = length + breadth + length + breadth.
Perimeter of given figure(4cm, 5cm, 8cm, and 3cm) = 4 + 5 + 8 + 3
= 20
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-2y=6. 6x+9y=9 in substitution form
Answer:
[tex]y=-3,\:x=6[/tex]
Step-by-step explanation:
hope this helped :P
Describe the translation of figure SPOT. Complete the sentence to explain your answer. Two squares plotted on the same coordinate plane. Square S P O T has vertices at (2, 3), (3, 2), (2, 1), and (1, 2). The corresponding vertices of square S prime P prime O prime T prime are at (5, 4), (6, 3), (5, 2), and (4, 3). Figure SPOT is translated unit(s) right and unit(s) up
Figure SPOT is translated unit(s) right and unit(s) up to the right move 8 and to the up move 9.
An effective method for beginning to make this idea clear for translating squares is to give them a slice-out shape to get across the page truly.
Afterward, kids need to figure out how to have the option to interpret a shape without this support.
while doing the above task, ideally, let's begin by putting the effective method for beginning making this idea clear for translating square is to give them a slice out shape to get across the page truly.
Afterward, kids need to figure out how to have the option to interpret a shape without this support.
while doing the above task, ideally, let's begin by putting the mark of your pencil on the upper left-hand corner of the shape and afterward dropping your pencil down 1 and right 2, then, at that point, plotting the primary place of your new shape with a dab.
You would then have to do likewise with the upper right-hand corner of the shape, the bottom left, and afterward the bottom right.
To respond to this, they would have to interpret the square and afterward give the directions of point An on the new shape, which would be (8, 9). mark your pencil on the upper left-hand corner of the shape and afterward drop your pencil down 5 and right 6, then, at that point, plot the primary place of your new shape with a dab.
You would then have to do likewise with the upper right-hand corner of the shape, the bottom left, and afterward the bottom right.
To respond to this, they would have to interpret the square and afterward give the directions of point An on the new shape, which would be (5, 4), (6, 3), (5, 2), and (4, 3).
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All the students in the sixth grade either purchased their lunch or brought their lunch from home on Monday.
* 24% of the students purchased their lunch
* 190 students brought their lunch from home.
How many students are in the sixth grade?
24% of the students bought their lunch on Monday. Therefore, the number of students in the 6th grade is 190
Step-by-step explanation:
how to calculate the product of two random variable that follows normal distribution with mean 0 and variance 1
The product of two random variables that follows the normal distribution with mean 0 and variance 1 is expected 0.
To compute the product of two random variables that are normal distributed with a mean of 0 and a variance of 1, the following procedure can be employed:
Since the mean of the normal distribution is 0 and the variance is 1, we can assume that the standard deviation is also 1.Thus, we can write the probability density function of the normal distribution as:
f(x) = (1/√2π) * e^(-x^2/2)
Using the definition of expected value, we can write the expected value of a random variable X as:E[X] = ∫x * f(x) dx, where the integral is taken over the entire range of X.
Similarly, we can write the expected value of a random variable Y as:E[Y] = ∫y * f(y) dy, where the integral is taken over the entire range of Y.
Since the two random variables are independent, the expected value of their product is the product of their expected values. Thus, we can write:E[XY] = E[X] * E[Y]
Substituting the probability density function of the normal distribution into the expected value formula, we can write:E[X] = ∫x * f(x) dx = ∫x * (1/√2π) * e^(-x^2/2) dx = 0
E[Y] = ∫y * f(y) dy = ∫y * (1/√2π) * e^(-y^2/2) dy = 0
Thus, the expected value of the product of two random variables that follow a normal distribution with mean 0 and variance 1 is:E[XY] = E[X] * E[Y]
= 0 * 0 ⇒ 0
Therefore, the product of two random variables that follow a normal distribution with mean 0 and variance 1 has an expected value of 0.
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a normal distribution is observed from the times to complete an obstacle course. the mean is 69 seconds and the standard deviation is 6 seconds. using the empirical rule, what is the probability that a randomly selected finishing time is greater than 87 seconds? provide the final answer as a percent rounded to two decimal places. provide your answer below: $$ %
The probability that a randomly selected finishing time is greater than 87 seconds is 14.08%. This can be calculated using the empirical rule.
The empirical rule states that for any data that is normally distributed, about 68% of the data will fall within one standard deviation of the mean (in this case, within 69 ± 6 seconds). Approximately 95% of the data will fall within two standard deviations (in this case, within 69 ± 12 seconds), and about 99.7% of the data will fall within three standard deviations (in this case, within 69 ± 18 seconds).Given the mean and standard deviation given, we can calculate the probability that a randomly selected finishing time is greater than 87 seconds.
We can do this by subtracting the area under the curve from the mean to the value we are interested in (in this case, 87 seconds). Since the total area under the curve is 1, subtracting the area from the mean to 87 seconds will give us the desired probability.To calculate the area under the curve, we need to calculate the Z-score, which is the number of standard deviations away from the mean a particular value is. In this case, the Z-score is (87 - 69) / 6, which is 2.16. Using a Z-table, the probability of a Z-score of 2.16 or higher is 0.8592. Therefore, the probability that a randomly selected finishing time is greater than 87 seconds is 1 - 0.8592, which is 0.1408. Rounding to two decimal places, this is 14.08%.
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Construct the first three Fourier approximations to the square wave function f(x) = {1 - pi lessthanorequalto x < 0 -1 0 lessthanorequalto x < pi F_1(x) = -(4/pi)*(sin(x)) F_2(x) = (4/pi)*(sin(x)) F_3(x) = (4/pi)*((sin(x))-(1/3)*(sin(3x)))
The Fourier series for f(x) is f(x) = (4/π) [sin(x) + (1/3) sin(3x) + (1/5) sin(5x) + ...].
The square wave function can be defined as:
f(x) = {1 -π ≤ x < 0
-1 0 ≤ x < π
To find the Fourier series for this function, we first need to determine the coefficients a_n and b_n.
a_n = (1/π) ∫_0^π f(x) cos(nx) dx
= (1/π) ∫_0^π (-1) cos(nx) dx + (1/π) ∫_(-π)^0 cos(nx) dx
= (2/π) ∫_0^π cos(nx) dx
= (2/π) [sin(nπ) - sin(0)]
= 0
b_n = (1/π) ∫_0^π f(x) sin(nx) dx
= (1/π) ∫_0^π (-1) sin(nx) dx + (1/π) ∫_(-π)^0 sin(nx) dx
= -(2/π) ∫_0^π sin(nx) dx
= -(2/π) [cos(nπ) - cos(0)]
= (2/π) [1 - (-1)^n]
Therefore, the Fourier series for f(x) is:
f(x) = (4/π) [sin(x) + (1/3) sin(3x) + (1/5) sin(5x) + ...]
To find the first three Fourier approximations, we truncate this series at the third term.
F_1(x) = -(4/π) sin(x)
F_2(x) = (4/π) sin(x) + (4/3π) sin(3x)
F_3(x) = (4/π) sin(x) + (4/3π) sin(3x) - (4/5π) sin(5x)
These are the first three Fourier approximations of the square wave function f(x). The more terms we include in the Fourier series, the closer the approximations will be to the original function.
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This table shows values that represent an exponential function.
X
0
1
23456
y
1
2
4
8
16
32
64
What is the average rate of change for this function for the interval from x = 3
to x = 5?
The average rate of change for the exponential function over the interval from x = 3 to x = 5 is 12.
Calculating the average rate of changeThe average rate of change for an exponential function can be found by dividing the change in y-values over the change in x-values for the given interval.
For the interval from x = 3 to x = 5, the change in x-values is 5 - 3 = 2.
The corresponding y-values for x = 3 and x = 5 are
y = 8 and y = 32, respectively.
Therefore, the change in y-values over the interval is 32 - 8 = 24.
The average rate of change for the exponential function over the interval from x = 3 to x = 5 is:
Average rate of change = Change in y-values / Change in x-values
Average rate of change = 24 / 2
Average rate of change = 12
Hence, the average rate of change for the exponential function over the interval is 12
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Determine it the two triangles are congruent. If they are. state how vou know. HL, SSS,ASA,AAS
Answer: The two triangles are congruent by axiom AAS as the opposite side of equal angles are also equal.
Use the unique factorization theorem to write the following integers in standard factored form. (a) 756 2^2.3^3.7. (b) 819 3^2.7.11 (c) 9,075 3^2.5^2.7
The factorizations of these integers above represent their factorizations into their respective prime numbers.
(a) 756 = 2^2.3^3.7, (b) 819 = 3^2.7.11, (c) 9,075 = 3^2.5^2.7The unique factorization theorem refers to an essential theorem in standard algebraic theory that characterizes the unique factorization properties of integers. Standard factored form, on the other hand, refers to an expression in which an integer is factored into its standard, irreducible components.In view of this, the three provided integers, 756, 819, and 9,075 can be factored as follows:756 = 2^2.3^3.7 (in standard factored form)819 = 3^2.7.11 (in standard factored form)9,075 = 3^2.5^2.7 (in standard factored form)Note that the factorizations of these integers above represent their factorizations into their respective prime numbers.
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555 centigrams = 55.5 ________
decigrams
grams
decagrams
hectograms
555 centigrams = 55.5 GRAMS
The metric system is based on multiples of 10, where each unit is 10 times larger or smaller than the previous one. In this system, "centi-" means one hundredth, so 1 centigram is one hundredth of a gram. Therefore, 555 centigrams is equal to 5.55 grams (since there are 100 centigrams in 1 gram).
On the other hand, "deci-" means one-tenth, so 1 decigram is one-tenth of a gram. Therefore, 555 centigrams is also equal to 55.5 decigrams (since there are 10 decigrams in 1 gram).
In summary, 555 centigrams is equal to:
55.5 decigrams
5.55 grams
555 centigrams is equal to = 55.5 decigrams
Solution:1 cg is equal to 10 dg, therefore 555 cg is equivalent to 55.5 dg.
1 Centigram = 1 x 10 = 10 Milligrams
555 Centigrams = 555 / 10 = 55.5 Decigrams
In ΔJKL, the measure of ∠L=90°, JK = 7. 3 feet, and KL = 4. 7 feet. Find the measure of ∠J to the nearest tenth of a degree
The measure of ∠J in ΔJKL is approximately 57.5 degrees.
The measure of ∠J in ΔJKL can be found using the trigonometric function tangent, which is defined as the ratio of the opposite side to the adjacent side.
The straight line that "just touches" the plane curve at a given point is called the tangent line in geometry. It was defined by Leibniz as the line that passes through two infinitely close points on the curve.
tan(∠J) = JK/KL
tan(∠J) = 7.3/4.7
∠J = arctan(7.3/4.7)
∠J = 57.5 degrees (rounded to the nearest tenth of a degree)
Therefore, the measure of ∠J in ΔJKL is approximately 57.5 degrees.
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the correlation coefficient may assume any value between : -1, and 1. 0 and 1. 0 and 8. -1, and 0. -infinity and infinity.
The correlation coefficient may assume any value between -1 and 1. Correct answer option A.
This means that the coefficient might be negative, zero, or positive, with -1 being a perfect negative correlation, 0 representing no connection, and 1 representing a perfect positive correlation.
The correlation coefficient is a numerical measure of two variables' linear connection. It is a measure of the strength of the link between two variables. A correlation coefficient of 1 indicates that there is a perfect positive connection, a coefficient of -1 indicates that there is a perfect negative correlation, and a coefficient of 0 shows that there is no correlation between the two variables.
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Select the correct answer.Adam constructed quadrilateral PQRS inscribed in circle O. How can he prove PQRS is a square?A.He needs to show only that the diagonals are perpendicular.B.He needs to show only that the diagonals are perpendicular and congruent.C.He needs to show only that the diagonals are perpendicular and bisect each other.D.He needs to show that the diagonals are perpendicular, congruent, and bisect each other.
Adam needs to show that the diagonals are perpendicular, congruent, and bisect each other.Therefore Option D is correct.
To prove that PQRS is a square, Adam needs to show that all four sides are congruent and that all four angles are right angles.
One way to do this is by showing that the diagonals of PQRS are perpendicular, congruent, and bisect each other.
If the diagonals are perpendicular, then opposite angles are congruent and the quadrilateral is a kite.
If the diagonals bisect each other, then opposite sides are congruent and the kite is a rhombus.
If the diagonals are also congruent, then all sides are congruent and the rhombus is a square.
Therefore, He needs to show that the diagonals of PQRS are perpendicular, congruent, and bisect each other to prove that PQRS is a square.
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6. The desks at Ryder Middle School are shaped
like a rectangle with an area of 2x²-3x - 2
square inches. The length of the desk is 2x + 1
inches. Write an expression to represent the
width of the desk. (Hint: A = lw)
The equation for the area of a rectangle is A = lw, where l is the length and w is the width. We are given the area (2x² - 3x - 2) and the length (2x + 1). To solve for the width, we can rearrange the equation to w = A/l.
Therefore, the expression to represent the width of the desk is w = (2x² - 3x - 2)/(2x +1).
1. y = (x - 5)(x + 1), Find y if x = - 3.
2. v= u + at
(a)
YEAR 7 HOME WORK
Work out v when u = 23, a = 4, and t = 3
(b)
Work out u when v= 30, a = 2 and t = 8
(c) Work out t when v = 40, u = 12 and a = 4
3. The circumference of a circle can be found using the formula C = 2nr or C = nd
Find the circumference of a circle with radius 8 cm.
Leave your answer to one decimal place.
4. Speed is calculated using the formula S=
Find the speed at which a car travelled if it took 2 hours to travel a distance of 100 km
D
T
where D is distance and T is time.
Answer:
1) y=-2, y=-8
2a) v=35
b) u=12
c) t=7
3) c=50.3
4) s=50
1 ]
Given:-
[tex] \tt{y = ( x - 5 ) ( x + 1 ) }[/tex][tex] \: [/tex]
[tex] \tt{x = - 3}[/tex][tex] \: [/tex]
To find:-
[tex] \tt \: y = ?[/tex][tex] \: [/tex]
Solution:-
[tex] \tt{y = ( x - 5 ) ( x + 1 )}[/tex][tex] \: [/tex]
now , put the value of x = -3 in equation
[tex] \tt \: y = ( -3 - 5 ) ( -3 + 1 )[/tex][tex] \: [/tex]
[tex] \tt \: y = ( - 8 ) ( - 2 )[/tex][tex] \: [/tex]
or
[tex] \tt \: y = 16 [/tex][tex] \: [/tex]
[tex] \texttt{The value of \boxed{ \tt \red{ y = ( -8 ) ( -2 )} } \: or \boxed{ \tt \red{ 16}} !}[/tex]
[tex] \: [/tex]
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2 ]
[tex] \texttt{v = u + at} \: - - - \texttt{given \: formula \: or \: eqn}[/tex]
a ) ----»
Given:-
[tex] \tt \: u = 23 [/tex][tex] \: [/tex]
[tex] \tt \: a = 4[/tex][tex] \: [/tex]
[tex] \tt \: t = 3[/tex][tex] \: [/tex]
To find:-
[tex] \tt \: v = ?[/tex][tex] \: [/tex]
Solution:-
[tex] \tt \: v = u + at[/tex][tex] \: [/tex]
now , put the given value in equation
[tex] \tt \: v = 23 + 4×3[/tex][tex] \: [/tex]
[tex] \tt \: v = 23 + 12[/tex][tex] \: [/tex]
[tex] \boxed{\tt \purple{ v = 35}}[/tex][tex] \: [/tex]
____________________________________
b )
Given:-
[tex] \tt \: v = 30[/tex][tex] \: [/tex]
[tex] \tt \: a = 2 [/tex][tex] \: [/tex]
[tex] \tt \: t = 8[/tex][tex] \: [/tex]
To find:-
[tex] \tt \: u = ?[/tex][tex] \: [/tex]
Solution:-
[tex] \tt \: v = u + at[/tex][tex] \: [/tex]
put the given value in equation
[tex] \tt \: 30 = u + 2×8[/tex][tex] \: [/tex]
[tex] \tt \: 30 = u + 16[/tex][tex] \: [/tex]
[tex] \tt \: 30 - 16 = u[/tex][tex] \: [/tex]
[tex] \tt \: 14 = u[/tex][tex] \: [/tex]
[tex] \boxed{ \tt \pink{ u = 14}}[/tex][tex] \: [/tex]
____________________________________
c )
Given:-
[tex] \tt \: v = 40[/tex][tex] \: [/tex]
[tex] \tt \: u = 12[/tex][tex] \: [/tex]
[tex] \tt \: a = 4[/tex][tex] \: [/tex]
To find:-
[tex] \tt \: t = ?[/tex][tex] \: [/tex]
Solution:-
[tex] \tt \: v = u + at[/tex][tex] \: [/tex]
now , put the given value in equation
[tex] \tt \: 40 = 12 + 4t[/tex][tex] \: [/tex]
[tex] \tt \: 40 - 12 = 4t[/tex][tex] \: [/tex]
[tex] \tt \: 28 = 4t[/tex][tex] \: [/tex]
[tex] \tt \cancel \frac{28}{4} = t[/tex][tex] \: [/tex]
[tex] \tt \: 7 = t[/tex][tex] \: [/tex]
[tex] \boxed{\texttt{ \green{t = 7}}}[/tex][tex] \: [/tex]
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3 ]
Given:-
[tex] \tt \: radius = 8[/tex][tex] \: [/tex]
To find:-
[tex] \texttt{circumference of circle = ?}[/tex][tex] \: [/tex]
By using given formula:-
[tex] \underline{ \tt \: \: C = 2πr \: \: }[/tex][tex] \: [/tex]
Solution:-
[tex] \tt \: C = 2πr [/tex][tex] \: [/tex]
[tex] \texttt{C = 2× 3.14× 8 [ as we know that the value of π = 3.14 constant ]}[/tex][tex] \: [/tex]
[tex] \tt{C = 16 × 3.14}[/tex][tex] \: [/tex]
[tex] \tt{C = 50.24}[/tex][tex] \: [/tex]
[tex] \texttt{The Circumference of the circle is { \blue{50.24}} !}[/tex]
[tex] \: [/tex]
━━━━━━━━━━━━━━━━━━━━━━━━━━━
4 ]
Given:-
[tex] \texttt{Time ( T ) = 2h}[/tex][tex] \: [/tex]
[tex] \texttt{Distance ( D ) = 100km}[/tex][tex] \: [/tex]
To find:-
[tex] \texttt{Speed ( S ) = ?}[/tex][tex] \: [/tex]
By using formula:-
[tex] \underline{\tt{ \: \: Speed= \frac{Distance}{Time} \: \: }}[/tex][tex] \: [/tex]
Solution:-
[tex] \tt \: S = \frac{D}{T} [/tex][tex] \: [/tex]
[tex] \tt \: S = \cancel\frac{100}{2} [/tex][tex] \: [/tex]
[tex] \tt \: S = 50[/tex][tex] \: [/tex]
[tex] \texttt{The Speed of the car is \color{green}50.}[/tex]
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hope it helps⸙
In ABC, D is a point on AB and E is a point
on AC such that DE is parallel to BC. If AE = 3,
EC = x, ED = x + 1, and CB = x + 5, find the
length of EC. [Only an algebraic solution will be
accepted.]
The required value of EC is 5 units.
How to find the value of EC?Since DE is parallel to BC, we can use the property of similar triangles to set up a proportion:
AD/DB = AE/EC
We know that AD + DB = AB = x + 5. Since D is a point on AB, we can express AD and DB in terms of x:
AD = x, DB = x + 5 - x = 5
We also know that AE = 3 and ED = x + 1. Using these values, we can express AD in terms of ED:
AD = ED - AE = (x + 1) - 3 = x - 2
Substituting these values into the proportion, we get:
(x - 2)/5 = 3/EC
Multiplying both sides by 5EC, we get:
x - 2 = 15/EC
Multiplying both sides by EC, we get:
EC(x - 2) = 15
Expanding the left side, we get:
ECx - 2EC = 15
Solving for EC, we get:
EC = 15/(x - 2)
We are given that EC = x, so we can set these expressions equal to each other:
x = 15/(x - 2)
Multiplying both sides by (x - 2), we get:
x(x - 2) = 15
Expanding the left side, we get:
x² - 2x = 15
Bringing all terms to one side, we get:
x² - 2x - 15 = 0
We can factor this quadratic equation:
(x - 5)(x + 3) = 0
Therefore, x = 5 or x = -3. We reject x = -3 since we are given that EC > 0. Thus, the length of EC is: EC = x = 5.
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