Sara’s hair was 25 inches long. Three years later it was 43 inches long. What was the percent increase?

Answer:

- [tex]\frac{8}{13}[/tex]

Step-by-step explanation:

let n be the other rational number , then

- [tex]\frac{26}{3}[/tex] n = [tex]\frac{16}{3}[/tex]

[a number × its reciprocal = 1 ]

multiply both sides by the reciprocal - [tex]\frac{3}{26}[/tex]

n = [tex]\frac{16}{3}[/tex] × - [tex]\frac{3}{26}[/tex]  ( cancel the 3 on numerator/ denominator )

n = - [tex]\frac{16}{26}[/tex] = - [tex]\frac{8}{13}[/tex]

Therefore, we have the values of:

a = -g(x) for -10 < x < -8

b = lower limit of the range where g(x) = -6

c = -C for -1 < x < 1

d = upper limit of the range where g(x) = 4

e = we cannot determine the value of e based on the given information.

In mathematics, a function is a rule that assigns a unique output value for every input value in its domain. It is a relation between a set of inputs and a set of possible outputs with the property that each input is related to exactly one output. Functions are often represented by a formula or an equation, but they can also be defined in other ways, such as through graphs, tables, or verbal descriptions. They are used to model a wide variety of phenomena in science, engineering, economics, and many other fields.

Here,

We can find the values of a, b, c, d, and e by examining the given information:

For -15 < x < -10: g(x) = -(-10) = 10

For -10 < x < -8: g(x) = -a

For -1 < x < 1: g(x) = -C

For b < x < l: g(x) = -(-6) = 6

For 10 < x < 15: g(x) = -8

For d < x < e: the value of g(x) is not specified in the given information, so we cannot determine the value of e based on this.

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Answer:

64 sq cm

Step-by-step explanation:

triangle area = 1/2*b*h (×4 because 4 triangles)

square area = lw

Answer:

x=33

Step-by-step explanation:

all angles in a triangle sum to 180 degrees

x+2x+(2x+15) = 180 <---- simplify this

5x+15 = 180

5x=165

x = 33

The power of the test to detect an average increase in height of 1 inch could be increased by d. giving the drug to 25 randomly selected students instead of 50.

The power of a test is the probability of correctly rejecting the null hypothesis when it is false. In this case, the null hypothesis is that the drug does not cause people to grow taller, and the alternative hypothesis is that the drug causes an average increase in height of 1 inch.

To increase the power of the test, we want to increase the probability of correctly rejecting the null hypothesis when it is false. One way to do this is to increase the sample size, which will reduce the standard error of the mean and increase the t-statistic, making it more likely to reject the null hypothesis.

However, in this case, we can increase the power of the test by giving the drug to a smaller sample size of 25 instead of 50. This is because the effect size of the drug is not known, and giving the drug to a larger sample size will increase the variance of the data, making it harder to detect a significant difference. By reducing the sample size, we can increase the power of the test while still maintaining a reasonable sample size.

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The sum of the geometric series is 3904/3125.

By using the formula for the sum of a geometric series, we'll have to identify the first term, the common ratio, and the number of terms.

Let's identify the first term, the common ratio, and the number of terms in the given series as shown below;

The first term, a = 4³/5³

Common ratio, r = 4/5

The number of terms, n = 3

We have identified the values of a, r, and n, we can now substitute them into the formula for the sum of a geometric series, shown below;

S_n = a(1 - rⁿ) / (1 - r)

S₃ = {(4³/5³) [1 - (4/5)³]} / [1 - (4/5)]

S₃ = {(64/125) [1 - (64/125)]} / [1/5]

S₃ = (64/125) [(125-64)/125] [5/1]

S₃ = (64/125) (61/125) (5)

Therefore, S₃ = 3904/3125.

Thus, the sum of the geometric series (4³/5³) + (4⁴/5⁴) + (4⁵/5⁵) is equal to 3904/3125.

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Answer:

uh I don't even know what this is

Answer: x = 500

Step-by-step explanation:

Use the Pythagorean Theorem

a²+b²=c²

300² + 400² = x²

90000 + 160000 = x²

250000 = x²

√250000 = √x²

500 = x

hope i explained it :)

If the cost price of the goods is R200 and they are sold at a mark-up of 100%, then the selling price is equal to the cost price plus the mark-up, or:

Selling price = Cost price + Mark-up

Mark-up = 100% x Cost price

= 100% x R200

= R200

So the mark-up is R200.

Selling price = Cost price + Mark-up

= R200 + R200

= R400

Therefore, the selling price of the goods is R400.

Answer:

We can simplify the expression as follows:

5^(2000) + 5^(1999)

5^(1999) - 5^(1997)

= 5^(1999) * (1 + 1/5)

5^(1997) * (1 - 1/25)

= (5/4) * (25/24) * 5^(1999)

= (125/96) * 5^(1999)

Therefore, the value of the expression is (125/96) * 5^(1999).

Step-by-step explanation:

a) Biker A follows the hypotenuse of the triangle on a straight path.

It is probable that the bikers will meet at the vertex located at the base of the triangle.

The bikers have created a triangle with sides measuring 12, 21, and 24 miles and angles measuring 61, 89, and 30 degrees, respectively.

a) Biker A follows the hypotenuse of the triangle on a straight path.

It is probable that the bikers will meet at the vertex located at the base of the triangle.

They cover almost equal distances from their starting points:

24 miles ≈ √12²+21² miles

b) They encounter each other.

c) The angle at one vertex measures 30 degrees.

d) e) As shown in the attached picture, it is an almost right triangle.

f) Together, they cover a total distance of 57 miles (12+21+24).

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The possible echelon forms of the given matrix are:

A matrix is in echelon form when it has leading nonzero entries in each row, with each row starting further to the right than the row above it. In the given matrix, the first row does not have any nonzero entries, so it does not meet this criterion. The second row does have a nonzero entry (x) so it can meet the criterion, provided that it is the leading entry.

This is the case for b. 0 x
0 0, c. x *
0 0, and d. x *
0 x.
The other criterion for echelon form is that all starred entries (*) may have any value including zero. This criterion is met in all three cases.

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Answer:

V = (4y³ + 6y² - 4y - 6) ft³

Step-by-step explanation:

Its a rectangular prism so its Volume is its lenght * its width* its height:

V = l * w * h

V = (4y - 3) ft * (y + 2) ft * (y + 1) ft

V = (4y² + 8y - 6y - 6) ft² * (y + 1) ft

V = (4y² + 2y - 6) ft² * (y + 1) ft

V = (4y³ + 2y² - 6y + 4y² + 2y - 6) ft³

V = (4y³ + 6y² - 4y - 6) ft³

Answer:

  see attached

Step-by-step explanation:

You want the given triangle dilated by a factor of -3 about point A.

To find the image point corresponding to a pre-image point, multiply the pre-image point's distance from A by the dilation factor. The negative sign means the distance to the image point is measured in the opposite direction.

In the attached figure, the chosen point is 4 units up and 5 units right of A. Its image in the dilated figure is 3·4 = 12 units down, and 3·5 = 15 units left of A.

This same process can be used to locate the other vertices of the triangle's image.

If a random variable is normally distributed, and has a mean of 228 and

a standard deviation of 16. If a sample of size 12 is taken, then the shape

of the sampling distribution for the sample mean is normally distributed

since the variable is normally distributed. Hence, option B is correct.

A normal distribution is a type of probability distribution in which the

value of the mean, standard deviation, and random variables are well

known. Sampling distribution refers to the probability distribution of the

statistics that have been derived from a sample taken from a population.

As per the Central Limit Theorem, if the sample size is large enough,

then the sampling distribution of the sample means will be normally

distributed, no matter how the population looks. If the random variable is

normally distributed, then the sampling distribution of the sample mean

will also be normally distributed, no matter what the size of the sample is.

Hence, option B is the correct answer as the sampling distribution of the

sample mean is normally distributed since the variable is normally distributed.

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Check the picture below.

[tex]11^2=(x+3)(3)\implies 121=3x+9\implies 112=3x \\\\\\ \cfrac{112}{3}=x\implies 37.3\approx x[/tex]

Answer:

by similarity

as these questions are usually solve by similarity

Answer:

576 books.

Step-by-step explanation:

134+254+188=576 books in total.

Answer:

576

Step-by-step explanation:

This is literally easy!

Checked books are 134 + 254 + 188 = 576

Answer:

Step-by-step explanation:

To calculate the time it will take a car to travel 140km at an average speed of 35km/h, we can use the formula:

time = distance ÷ speed

Plugging in the given values, we get:

time = 140km ÷ 35km/h

time = 4 hours

Therefore, it will take a car 4 hours to travel 140km at an average speed of 35km/h.

Answer:

ㅤ

Car will take 4 hours

ㅤ

Step-by-step explanation:

ㅤ

[tex]\large{\blue{\star} \: {\underline{\boxed{\pmb{\tt{Time = \dfrac{Distance}{Speed}}}}}}}[/tex]

ㅤ

[tex]\large{\leadsto{\sf{Given_{(Distance)} = 140 \: km}}}[/tex]

ㅤ

[tex]\large{\leadsto{\sf{Given_{(Speed)} = 35 \: km/hr}}}[/tex]

ㅤ

[tex]\large{\underline{\underline{\sf{Applying \: Formula:-}}}}[/tex]

ㅤ

[tex]\large{\leadsto{\sf{Required_{(Time)} = \bigg(\dfrac{\cancel{140}}{\cancel{35}}\bigg)} \: hr}}[/tex]

ㅤ

[tex]\large{\purple{\boxed{\leadsto{\sf{Required_{(Time)} = 4 \: hr}}}}}[/tex]

ㅤ

━━━━━━━━━━━━━━━━━━━━━━

[tex]\star \: {\large{\underline{\underline{\pink{\mathfrak{More:-}}}}}} \: \star[/tex]

ㅤ

[tex]\large{\dashrightarrow{\sf{Time = \dfrac{Distance}{Speed}}}}[/tex]

ㅤ

[tex]\large{\dashrightarrow{\sf{Speed = \dfrac{Distance}{Time}}}}[/tex]

ㅤ

[tex]\large{\dashrightarrow{\sf{Distance = Speed \times Time}}}[/tex]

The function f represents the 1000 revenue in dollars the school can 800 expect to receive if it sells 220 – 12x coffee mugs for x dollars 600 each.

The statements that accurately describe this situation are:

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Juanita's approximate monthly Social Security benefit is $1,844.90 to the nearest dollar.

The age at which a person is qualified to receive their full retirement payment under Social Security is determined by their lifetime earnings history. The complete retirement age for anybody born in 1960 or later is 67. The complete retirement age is steadily lowered for people born before 1960, and is 65 for those born in 1937 or before.

Given that, Juanita started collecting benefits at age 65.

Thus, her benefits reduced by 13.3%.

0.133 x $2,128 = $283.10

Deducting the reduction amount from the total:

$2,128 - $283.10 = $1,844.90

Hence, Juanita's approximate monthly Social Security benefit is $1,844.90 to the nearest dollar.

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The true statement is, Parameter values can be used within the method code block. (option e).

In computer programming, methods are used to group a set of instructions together that can be executed repeatedly. Parameters are used to pass values to a method so that the method can perform specific actions based on the values passed. Let's discuss the given statements one by one to determine which ones are true.

Parameter values can be used within the method code block.

This statement is true. Parameter values can be used within the method code block to perform specific actions. The parameter values can be manipulated or combined with other values to produce the desired result.

In summary, methods can be written with any number of parameters, and parameter values can be used within the method code block to perform specific actions. The number of parameters needed will depend on the specific task the method is designed to perform.

Hence the option (e) is correct.

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The y-intercept for this situation shows that the speed of the ship sailing is 0 miles per second during the time t = 4 seconds, after that the speed keeps on decreasing.

Look into the fact that the vector of acceleration points in the same general direction as the vector of velocity change. This indicates that whether you add to or subtract from the velocity depends on the direction of the acceleration.

The graph is shown for the distance travelled by the ship with time by Clare.

Thus, the y-intercept for this situation shows that the speed of the ship sailing is 0 miles per second during the time t = 4 seconds, after that the speed keeps on decreasing.

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Answer:

301.733% increase

Step-by-step explanation:

Answer:

The equation of a line perpendicular to y=3 that goes through the point (-5, 3) is: x = -5.

Step-by-step explanation:

To find the equation of a line perpendicular to y=3 that goes through the point (-5, 3), we need to remember that the slope of a line perpendicular to another line is the negative reciprocal of the slope of the original line.

The equation y=3 is a horizontal line that goes through the point (0,3), and its slope is zero. The negative reciprocal of zero is undefined, which means that the line perpendicular to y=3 is a vertical line.

To find the equation of this vertical line that goes through the point (-5, 3), we can start with the point-slope form of a linear equation:

y - y1 = m(x - x1)

where m is the slope of the line and (x1, y1) is a point on the line. Since the line we want is vertical, its slope is undefined, so we can't use the point-slope form directly. However, we can still write the equation of the line using the point (x1, y1) that it passes through. In this case, (x1, y1) = (-5, 3).

The equation of the vertical line passing through the point (-5, 3) is:

x = -5

This equation tells us that the line is vertical (since it doesn't have any y term) and that it goes through the point (-5, 3) (since it has x=-5).

So, the equation of a line perpendicular to y=3 that goes through the point (-5, 3) is x = -5.

Answer:

x= -5

Step-by-step explanation:

The perpendicular line is anything with x= __.

x= -5 however, will go through the point (-5, 3) and that is our answer.

We can obtain 6 different numbers by multiplying 2 distinct integer divisors of 10.

The divisors of 10 are 1, 2, 5, and 10.

To determine how many different numbers can be obtained from multiplying 2 distinct integer divisors.

We need to select 2 distinct divisors and find their product.

The possible pairs are:

Therefoore, we can obtain 6 different numbers.

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Answer:

I'm sorry, but the given expressions QRT and TRS do not seem to correspond to angles. They appear to be algebraic expressions involving variables x. Without further information or context, it is not possible to determine any angles or measures of angles.

Please provide additional information or clarify the question.

The expected count for women for the presence of aortic stenosis is 57.7. The correct option is D.

Aortic stenosis is a cardiovascular ailment that causes the aortic valve in the heart to narrow, reducing blood flow from the heart to the rest of the body. Aortic stenosis usually progresses gradually and, in the beginning, may not produce any symptoms.

The severity of aortic stenosis is divided into four categories, ranging from mild to severe. People who are asymptomatic may require monitoring, whereas those who are symptomatic may need to undergo surgery or other procedures.

The expected count for women for the presence of aortic stenosis in this question refers to the number of women who have this condition according to a particular study or statistic.

Therefore, the correct option is D.

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The degree measure of the largest angle is 72° in the triangle.

We have, The sum of two angles of a triangle is 6/5 of a right angle.

One of these two angles is 30° larger than the other.

Let A and B be the two angles of the triangle such that A = B + 30°.

We know that the sum of three angles in a triangle is 180°.

⇒ A + B + C = 180°

⇒ B + 30° + B + C = 180°

⇒ 2B + C = 150°

We also know that the sum of two angles of a triangle is 6/5 of a right angle.

⇒ A + B = 6/5 × 90°

⇒ B + 30° + B = 108°

⇒ 2B = 78°

⇒ B = 39°

C = 150° - 2B ⇒ 72°

A = B + 30° ⇒ 39° + 30° ⇒ 69°

Therefore, the degree measure of the largest angle in the triangle is 72°.

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