Answer: it is b
Step-by-step explanation:
it is b bec if you do that by 10x9 90=a a x x =1 90/s
Answer:
C
Step-by-step explanation:
To determine the number of distinct triangles that can be made with the given measurements, we can use the Law of Sines, which states:
a/sin(A) = b/sin(B) = c/sin(C)
where a, b, c are the lengths of the sides opposite to the angles A, B, and C, respectively.
Using this formula, we can solve for sin(B) as follows:
sin(B) = b*sin(A)/a
sin(B) = 8*sin(42°)/3
sin(B) ≈ 0.896
Since sin(B) is a positive value, we know that there are two possible angles B that satisfy this equation: one acute angle and one obtuse angle. To find the acute angle B, we take the inverse sine of sin(B):
B = sin^(-1)(0.896)
B ≈ 63.8°
To find the obtuse angle, we subtract the acute angle from 180°:
B' = 180° - 63.8°
B' ≈ 116.2°
Now, we can use the fact that the sum of the angles in a triangle is 180° to find the possible values for angle C. For the acute triangle, we have:
C = 180° - A - B
C = 180° - 42° - 63.8°
C ≈ 74.2°
For the obtuse triangle, we have:
C' = 180° - A - B'
C' = 180° - 42° - 116.2°
C' ≈ 21.8°
Therefore, we have found two distinct triangles that can be made with the given measurements: one acute triangle with angles A = 42°, B ≈ 63.8°, and C ≈ 74.2°, and one obtuse triangle with angles A = 42°, B' ≈ 116.2°, and C' ≈ 21.8°. Thus, the answer is C. 2.
If Alyssa has 6 shirts, 4 skirts, and 10 pairs of shoes, how many possible outfits can she make?
Answer: 240
You multiply them. 6x4x10 :)
The number of different outfits made by Alyssa as per the given number of shirt , skirts and shoes is equal to 240 outfits.
To find the number of possible outfits Alyssa can make, you multiply the number of choices for each item of clothing:
Number of shirts = 6
Number of skirts = 4
Number of pairs of shoes = 10
Substitute the values and multiply with each other
Total number of possible outfits
= 6 (shirts) × 4 (skirts) × 10 (shoes)
= 240 outfits.
Therefore, Alyssa can make 240 different outfits using her 6 shirts, 4 skirts, and 10 pairs of shoes.
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A recent Health of Boston report suggests that 14% of female residents suffer from asthma as opposed to 6% of males (Boston Globe, August 16, 2010). Suppose 250 females and 200 males responded to the study.
Let p1 represent the population proportion of females with asthma and p2 the population proportion of males with asthma. Let females and males represent population 1 and population 2, respectively.
a. Develop the appropriate null and alternative hypotheses to test whether the proportion of females suffering from asthma is greater than the proportion of males.
H0: p1 − p2 ≤ 0; HA: p1 − p2 > 0
H0: p1 − p2 = 0; HA: p1 − p2 ≠ 0
H0: p1 − p2 ≥ 0; HA: p1 − p2 < 0
b. Calculate the value of the test statistic and its associated p-value. (Round intermediate calculations to 4 decimal places, "test statistic" value to 2 decimal places and "p-value" to 4 decimal places.)
Test statistic p-value c. At the 5% significance level, what is the conclusion? Do the data suggest that females suffer more from asthma than males?
No, since we reject H0
No, since we do not reject H0
Yes, since we reject H0
Yes, since we do not reject H0
The data suggest that females suffer more from asthma than males.
The null and alternative hypotheses for this problem are:
H0: p1 - p2 = 0; HA: p1 - p2 ≠ 0
The value of the test statistic is 3.7775 and its associated p-value is 0.0002. At the 5% significance level, the conclusion is that we reject the null hypothesis, and therefore we can say that the data suggest that females suffer more from asthma than males.
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A company that chipe crystal bowis claims that bowls anive undamaged in 95 percent of the shipments. Let the randomi variable represent the number of shipments with undamaged bowis in 25 randomly elected shipments, Fandom variable Grotows a binomial distribution with a mean of 23.75 shipments and a standard deviation of approximately 1.09 shipments. Which of the following is the best interpretation of the mean?A. Every shipment of 25 bowls will have 23.75 undamaged bowlsB. Every slypment of 25 bowls will have 23.75 damaged bowl.C. On average the company receives 23.25 is before receiving the first her with a damaged bowlD. For possible shipments of 25 average number of damaged shipment equal to 23.75E. for all possible shipment of size 25 the average number of undamaged shipment equal to 23.75
The best interpretation of the mean is A) "Every shipment of 25 bowls will have 23.75 undamaged bowls."
The question states that the company claims that 95% of their shipments arrive undamaged. This implies that the probability of a bowl being damaged in a shipment is 0.05.
Since the random variable G follows a binomial distribution with n=25 (number of shipments) and p=0.05 (probability of a shipment having a damaged bowl), the mean of G is given by np = 25 x 0.05 = 1.25.
However, the question asks about the number of undamaged bowls in a shipment, which is simply the number of bowls in a shipment minus the number of damaged bowls.
Therefore, the mean number of undamaged bowls in a shipment is 25 - 1.25 = 23.75. This means that on average, a shipment of 25 bowls will have 23.75 undamaged bowls.
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Describe the relationship between n and 4 that makes the equation 7 x n/4 greater that 7
An Inequality is a relationship between two expressions or values that aren't equal. The relationship between n and 4 is given by the inequality n> 4.
We want to find a relation between n and 4 similar that
7 *( n/ 4)> 7
still, we get
If we now divide both sides of the former inequality by 7.
7 *( n/ 4)/ 7>7/7
n/ 4> 1
So n/ 4 must be lesser than 1.
A better way to show the relationship is to multiply both sides of the inequality by 4.
4 *( n/ 4)> 4 * 1
n> 4
So the relationship between n and 4 is that n must be lesser than 4.
In mathematics, an inequality is a relationship that results in an unstable comparison of two figures or other fine expressions. It's frequently used to compare two figures on a number line grounded on their size.
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The prices of consumer goods do not always exactly follow the CPI. The following chart shows several consumer items, along with their respective prices in 1983 and today.ItemPrice in 1983 ($)Current Price ($)Pair of boots67.45126.85Hair dryer15.2529.95Box of tissues1.152.25Toaster22.8544.25Using the prices shown on this chart, which of the following is a reasonable estimate of the current CPI?a. 208b. 195c. 180d. 173
None of the given options (i.e. a, b, c, or d) is correct.
Given the prices of consumer items, we can find the estimate of the current CPI.
The percentage change in the price of the consumer item over time can be given as:
Percentage change = (Current Price − Price in 1983)/Price in 1983 × 100%
Now, using the percentage change we can find the average percentage change (increase or decrease) in prices. We calculate the average percentage change by finding the sum of the percentage change in prices of all items and then dividing it by the number of items.
Thus, we have:
Average percentage change = [(126.85−67.45)/67.45 + (29.95−15.25)/15.25 + (2.25−1.15)/1.15 + (44.25−22.85)/22.85]/4Average percentage change = 4.4188%
Now, the current CPI can be found using the following formula:
Current CPI = CPI in 1983 × [1 + (Average percentage change)/100]Current CPI = 100 × [1 + 4.4188/100] ≈ 104.42 ≈ 104
Therefore, the reasonable estimate of the current CPI is 104.
None of the given options (i.e. a, b, c, or d) is correct.
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Between which consecutive integer does the square root of 138 lie
The square root of 138 is between 11 and 12. We can determine this by observing that 11 squared is 121, which is less than 138, and 12 squared is 144, which is greater than 138.
Therefore, the square root of 138 must lie between 11 and 12. Another way to approach this problem is to use estimation. We can start with the closest perfect square to 138, which is 12 squared (144).
Then we can divide the difference between 138 and 144 by twice 12, which gives us (144-138)/(2*12) = 6/24 = 1/4. This means that the square root of 138 is approximately 12 - 1/4 = 11.75, which is between 11 and 12.
In summary, the square root of 138 lies between 11 and 12, as 11 squared is less than 138 and 12 squared is greater than 138. Alternatively, we can estimate the square root of 138 as 11.75, which is also between 11 and 12.
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Ben knows that a line passes through the point (-3, 8) and has a slope of -3/4, but he needs to find the equation of the line. Therefore, he should substitute 8 for_______
and he should substitute -3 for _________, and he should substitute -3/4 for __________ into the Point-Slope Formula. He will need to __________ and simplify before solving for y = mx + b form.
Answer:
Ben knows that a line passes through the point (-3, 8) and has a slope of -3/4, but he needs to find the equation of the line. Therefore, he should substitute 8 for_______
and he should substitute -3 for _________, and he should substitute -3/4 for __________ into the Point-Slope Formula. He will need to __________ and simplify before solving for y = mx + b form.
Step-by-step explanation:
To use the Point-Slope formula to find the equation of the line, Ben should substitute the following values:
Substitute 8 for y, since the point (-3, 8) has a y-coordinate of 8.
Substitute -3 for x, since the point (-3, 8) has an x-coordinate of -3.
Substitute -3/4 for m, since the line has a slope of -3/4.
The Point-Slope formula is:
y - y1 = m(x - x1)
Substituting the values, we get:
y - 8 = (-3/4)(x - (-3))
Simplifying the right-hand side, we get:
y - 8 = (-3/4)(x + 3)
To get the equation in y = mx + b form, we can start by distributing the (-3/4) to the x and the 3:
y - 8 = (-3/4)x - 9/4
Adding 8 to both sides, we get:
y = (-3/4)x + 23/4
So the equation of the line is y = (-3/4)x + 23/4.
What is the probability of
drawing a face card, then
drawing a heart with
replacement
Answer:
n(s) =52. n(f) = 12 n(h) = 13
p (f)= 13/52. p(f)= 12/52
A system of equations is graphed on the coordinate plane.
A student concludes that the solution of the system is (-0.5, 1.5).
Is this correct? Justify your response.
The correctness of the student's solution, we need to have the equations of the system.
A system of equations is graphed on the coordinate plane. A student concludes that the solution of the system is (-0.5, 1.5). Is this correct? Justify your response.To conclude that a system of equations has a solution in the coordinate plane, a set of ordered pairs (x, y) should satisfy both equations in the system of equations. That is, the system of equations should have a point (x, y) that is a solution of both equations.Only by testing the solution in the given system of equations can we know if the student's conclusion is correct. If the solution is satisfied by the system of equations, then the answer is true. Otherwise, it is false. However, since no system of equations is provided in the question, we cannot test the student's solution.To justify the correctness of the student's solution, we need to have the equations of the system.
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find the long leg: b =
Answer:
b ≈ 12.1
Step-by-step explanation:
using the tangent ratio in the right triangle
tan60° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{b}{7}[/tex] ( multiply both sides by 7 )
7 × tan60° = b , then
b ≈ 12.1 ( to the nearest tenth )
P(A) = 1/2 P(B) = 3/4 and P(A U B) = 3/8 Find P(A n B)
Answer:
P(A n B) = 1/4
Step-by-step explanation:
We know that:
P(A U B) = P(A) + P(B) - P(A n B)
Substituting the given values, we get:
3/8 = 1/2 + 3/4 - P(A n B)
Simplifying, we get:
P(A n B) = 1/4
Answer: P ( A n B ) = 7/8
Step-by-step explanation: P ( A U B ) = P(A) + P(B) - P( A n B )
3/8 = 1/2 + 3/4 - P( A n B )
3/8 = 5/4 - P ( A n B )
P ( A n B ) = 5/4 - 3/8
P ( A n B ) = 7/8
Question
Find the value of y
for the given value of x
.
y=1−2x;x=9
Answer:
y=-17
Step-by-step explanation:
1-2(9)=1-18=-17
Answer: y = -17
Step-by-step explanation:
Using PEMDAS, you need to do the multiplication first. 2 times x is 18, because the value of x is 9. You will then get 1 - 18. This is -17, so y = -17. I hope that this helped! :)
The number 2 is the first even counting number,4 is the second even number, 6 is the third even number, and so forth. What is the sum of the first 25th even counting numbers
The number 2 is the first even counting number,4 is the second even number, 6 is the third even number, and so forth. the sum of the first 25th even counting numbers is 650.
Since we are given that the first even counting number is 2 and each subsequent even counting number can be obtained by adding 2 to the previous one. so by using the formula for finding the 25th term of an arithmetic series which :
an=a+(n-1)d, where the nth term d is a common difference and a is the first term so, the 25th term is 2 + (25-1)*2 = 2 + 48 = 50. Now for finding the sum of the first 25 even counting numbers, we use the formula which is Sn = n /2 * (a1 + an), where Sn is the sum of the first n terms of the series, a1 is the first term, and an is the nth term. since in this n=25, a1=2 and an=50, so after substituting the values we get S25 = 25/2 * (2 + 50) = 25/2 * 52 = 650
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Use the following points to find the slope.
(1, -1)
(4, 8)
Use the slope and one of the points to find the y-intercept.
Write the final formula.
*
Answer:
the formula is -xcomma y because I there is y intercept then there x will be negative. not y
Use the quadratic formula to solve. Show work describe solution.
Answer:
Use the quadratic formula to solve. Show work describe solution.
Step-by-step explanation:
The quadratic formula is used to find the solutions (or roots) of a quadratic equation in the form ax^2 + bx + c = 0, where a, b, and c are constants.
The quadratic formula is:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
To use the quadratic formula, we need to plug in the values of a, b, and c from the given equation and solve for x.
For example, let's say we have the equation 2x^2 + 5x - 3 = 0.
Here, a = 2, b = 5, and c = -3.
Plugging these values into the quadratic formula, we get:
x = (-5 ± sqrt(5^2 - 4(2)(-3))) / 2(2)
Simplifying the expression inside the square root:
x = (-5 ± sqrt(49)) / 4
x = (-5 ± 7) / 4
We get two solutions:
x = (-5 + 7) / 4 = 1/2
x = (-5 - 7) / 4 = -3
So the solutions to the equation 2x^2 + 5x - 3 = 0 are x = 1/2 and x = -3.
These solutions represent the points where the quadratic curve intersects the x-axis. They can also be used to factor the quadratic equation or graph the quadratic function.
Solve each inequality (show work)
Answer:
5 less than or equal to x
Step-by-step explanation:
make x subject
How is pi and apple pie related to each other?
Answer: Pie is the unofficial food of Pi Day; its symbol, π, is often carved into pie crusts.
Step-by-step explanation:
Answer:
You can divide and divide, but with pi, you never reach the end of the digits after a decimal point.
Step-by-step explanation:
This is why most people know pie as 3.14. It also means that the circumference is a bit more than 3 times the size of the diameter. It doesn't matter what circle you measure—the relationship will always be the same.
Consider the circuit depicted in the diagram. Part (a) Write the equation which results from applying the loop rule to loop akledcba. Part (b) If the current going through the center of the loop is 65 A, what is the current going through the top, in amps?ξ = 24.0ν b 0.10Ω Β, 5.0Ω ε2, 48.0ν RS 20 Ω a τη: R w- 40 Ω e 0.50 Ω ΓΑ *0.20 Ω R 78 Ω 36.0V ξ: 6.0ν 9 10.05 Ω h
The equation which results from applying the loop rule to loop akledcba is Ia + Ik + Il + Ie + Id + Ic + Ib + Ia
The current going through the top is 2.71 A.
Itop = 65 A - (24.0 V/0.10 Ω) - (5.0 Ω * 2) - (48.0 V/20 Ω) - (40 Ω * 0.50 Ω) - (36.0 V/6.0 Ω) - (10.05 Ω * 0.20 Ω) - (78 Ω * 0.20 Ω) = 2.71 A.
For Part (a), the equation resulting from applying the loop rule to loop akledcba is:
Iakledcba = Ia + Ik + Il + Ie + Id + Ic + Ib + Ia
For Part (b), if the current going through the centre of the loop is 65 A, then the current going through the top in amps is:2.71 A.
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what is -0.33333333333 as a fraction
Answer:
-1/3
Step-by-step explanation:
Answer:
-1/3
Step-by-step explanation:
Find the product of (7-8x)(3x^3-2x^2+x)
Answer:
Step-by-step explanation:
To find the product of (7-8x)(3x^3-2x^2+x), we need to use the distributive property of multiplication over addition/subtraction.
First, let's distribute the 7 across the second factor:
(7)(3x^3) - (7)(2x^2) + (7)(x)
This simplifies to:
21x^3 - 14x^2 + 7x
Next, we need to distribute the -8x across the second factor:
(-8x)(3x^3) + (-8x)(-2x^2) + (-8x)(x)
This simplifies to:
-24x^4 + 16x^3 - 8x^2
Now, we can combine the two simplifications:
(7-8x)(3x^3-2x^2+x) = 21x^3 - 14x^2 + 7x - 24x^4 + 16x^3 - 8x^2
Finally, we can combine like terms to simplify the expression:
-24x^4 + 37x^3 - 22x^2 + 7x
Therefore, the product of (7-8x)(3x^3-2x^2+x) is -24x^4 + 37x^3 - 22x^2 + 7x.
Find the probability of
drawing a spade, then
drawing a face card out of a
deck
The likelihood of pulling a spade followed by a face card from a deck is 3/52, or roughly 0.0588. (rounded to four decimal places).
What is the probability?The probability of drawing a spade from a deck of 52 cards is 13/52, or 1/4, since there are 13 spades in the deck.
Once a spade has been drawn and not returned to the deck, there are now 51 cards left in the deck, of which 12 are face cards (the Jack, Queen, and King of each suit). Therefore, the probability of drawing a face card given that a spade has already been drawn is 12/51.
To find the probability of both events happening together (drawing a spade and then a face card), we can multiply the probabilities of each event:
P(drawing a spade, then drawing a face card) = P(drawing a spade) x P(drawing a face card given that a spade has been drawn)
= (1/4) x (12/51)
= 3/52
Therefore, the probability of drawing a spade, then drawing a face card out of a deck is [tex]3/52[/tex] , or approximately [tex]0.0588[/tex] (rounded to four decimal places).
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Let be a random variable with the following probability distribution:
Value (P(X=x)
x of X
10) (0.05)
20) (0.65)
30) (0.05)
40) (0.20
50) (0.05)
Find the expectation E (X) and variance Var (X) of X.
Answer:Let be a random variable with the following probability distribution
Value x of X / P (X=x)
20 / 0.05
30 / 0.05
40 / 0.35
50 / 0.20
60 / 0.35
Find the expectation of E(X) and variance Var (X) of X.
(A) E (x) = ?
(B) Var (X) =?
Step-by-step explanation:
Without dividing how can you decide which quotient is greater: 51 +31 or 5 1/4÷2 1/2
Answer:
51 + 31
Step-by-step explanation:
To compare which quotient is greater between 51+31 and 5 1/4 ÷ 2 1/2, we can use estimation.
First, we can estimate 51+31 to be around 80.
Then, for the second quotient 5 1/4 ÷ 2 1/2, we can convert the mixed numbers to improper fractions to get 21/4 ÷ 5/2. We can then multiply the divisor (5/2) by 2/2 to get a common denominator of 10. This gives us 21/4 ÷ 5/2 = 21/4 ÷ 5/10. We can then invert the divisor and multiply to get 21/4 x 10/5 = 21/2 or 10.5.
Since 80 is greater than 10.5, we can conclude that 51+31 is greater than 5 1/4 ÷ 2 1/2.
To save for retirement, Ed is investing 14.286 thousand dollars this year. Write the function R(t) that shows the stream of money flowing into Ed's investment account under each of the following circumstances. Assume a continuous income stream. Do NOT round any values (a) Ed continues to invest the same amount each year for the next 20 years. R(t)-14.286thousand dollars per year (b) Ed increases his investment by 3.75 thousand dollars per year over the next 20 years. A(t)-18.036 | X thousand dollars per year (c) Ed increases his investment by 3.75% each year over the next 20 years. R(t)- thousand dollars per year
(a) Since Ed continues to invest the same amount each year for the next 20 years, the function R(t) will be constant and equal to 14.286 thousand dollars per year:
R(t) = 14.286
(b) Since Ed increases his investment by 3.75 thousand dollars per year over the next 20 years, the function R(t) will be a linear function of time, with a slope of 3.75 and an initial value of 14.286:
R(t) = 14.286 + 3.75t
(c) Since Ed increases his investment by 3.75% each year over the next 20 years, the function R(t) will be a geometric sequence, with a common ratio of 1.0375 and an initial value of 14.286:
R(t) = 14.286 * (1.0375)^t
Note that since the function is continuous, we could also use the continuous growth formula [tex]R(t) = 14.286 * e^{0.0375t}[/tex] to model the investment stream.
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The research department at the home office of automobile accidents,the characterstics of the driver, and so an. A random sample 400 police written on single persons revealed 120 had at least one accident in previous three year period
The study collected data from a random sample of 400 police reports on single persons. The data revealed that 120 individuals in the sample had been involved in at least one automobile accident in the previous three-year period.
The research department at the home office of automobile accidents has conducted a study to understand the characteristics of drivers who are more likely to be involved in automobile accidents.
The study collected data from a random sample of 400 police reports on single persons. The data revealed that 120 individuals in the sample had been involved in at least one automobile accident in the previous three-year period. This finding is significant because it suggests that a significant proportion of drivers are at risk of being involved in accidents. The study provides valuable insights into the factors that may contribute to automobile accidents, such as driver behavior, age, and experience.
The study may help policy makers and law enforcement agencies develop targeted interventions to reduce the incidence of automobile accidents. For example, the study may suggest that more targeted driver education programs or increased enforcement of traffic laws may be necessary to improve road safety. Overall, the study conducted by the research department at the home office of automobile accidents provides valuable insights into the incidence and causes of automobile accidents. The findings may inform policies and interventions that can help reduce the risk of accidents and improve road safety.
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an aquarium has a rectangular base that measures 100 cm by 40 cm and has a height of 50 cm. the aquarium is filled with water to a depth of 37 cm. a rock with volume $1000 \text{cm}^3$ is then placed in the aquarium and completely submerged. by how many centimeters does the water level rise? express your answer as a decimal to the nearest 100th.
The water level in the aquarium rises by (A) 0.25.
The volume of water in the aquarium before the rock is added is:
100 cm x 40 cm x 37 cm = 148000 cm^3
When the rock is added, its volume is 1000 cm^3, so the total volume of water and the rock is:
148000 cm^3 + 1000 cm^3 = 149000 cm^3
To find the new water level, we need to divide the total volume by the base area of the aquarium:
149000 cm^3 ÷ (100 cm x 40 cm) = 37.25 cm
Therefore, the water level rises by:
37.25 cm - 37 cm = 0.25 cm
So the answer is (A) 0.25.
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Your question is incomplete, but probably the complete question is :
An aquarium has a rectangular base that measures 100 cm by 40cm and has a height of 50cm. The aquarium is filled with water to a depth of 37 cm. A rock with volume 1000cm^3 is then placed in the aquarium and completely submerged. By how many centimeters does the water level rise?
(A) 0.25
(B) 0.5
(C)
(D)1.25
(E) 2.5
Which equation could represent the shown graph below
Oy=√x-2
O y = √x+2
O y = -√x+2
O y = -√x-2
Solve for x and y.
8
7
X
y
By answering the presented question, we may conclude that Therefore, the solution to the system of equations is: x = 36/31 and y = 57/31.
What is equation?In mathematics, an equation is a statement stating the equivalence of two expressions. An equation generally made up of two sides delimited by a system of equations (=). For example, the argument "2x + 3 = 9" states that the word "2x Plus 3" equals the integer "9". The objective of equation solving is to identify the amount or amounts of the variables ( independent variables) that will allow this equation to really be true. Mathematics can be simple or complex, regular or quadratic, and contain one or more parts. In the equation "x2 + 2x - 3 = 0," for illustration, the variable x is elevated to the second power. Lines are employed in numerous different fields of mathematics, including arithmetic, calculus, and geometry.
From the given system of equations, we have:
[tex]8x + 7y = 17 ...(1)\\x - 3y = -5 ...(2)\\x = 3y - 5 ...(3)\\8(3y - 5) + 7y = 17\\24y - 40 + 7y = 17\\31y = 57\\y = 57/31\\x = 3(57/31) - 5\\x = 36/31[/tex]
Therefore, the solution to the system of equations is:
x = 36/31 and y = 57/31.
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The solution to the system of equations is: x = 36/31 and y = 57/31.
What is equation?In mathematics, an equation is a statement stating the equivalence of two expressions. An equation generally made up of two sides delimited by a system of equations (=). For example, the argument "2x + 3 = 9" states that the word "2x Plus 3" equals the integer "9". The objective of equation solving is to identify the amount or amounts of the variables ( independent variables) that will allow this equation to really be true. Mathematics can be simple or complex, regular or quadratic, and contain one or more parts. In the equation [tex]"x^2 + 2x - 3 = 0,[/tex]" for illustration, the variable x is elevated to the second power. Lines are employed in numerous different fields of mathematics, including arithmetic, calculus, and geometry.
From the given system of equations, we have:
[tex]$\begin{aligned} & 8 x+7 y=17 \ldots(1) \\ & x-3 y=-5 \ldots(2) \\ & x=3 y-5 \ldots(3) \\ & 8(3 y-5)+7 y=17 \\ & 24 y-40+7 y=17 \\ & 31 y=57 \\ & y=57 / 31 \\ & x=3(57 / 31)-5 \\ & x=36 / 31\end{aligned}$[/tex]
Therefore, the solution to the system of equations is:
x = 36/31 and y = 57/31.
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Solve for x in a triangle
In a right triangle, the trigonometric ratio x must be positive. There isn't an x solution that meets the requirements. The cosine and sine function values given are incompatible with a correct right triangle. x = -0.40
Which triangle is on the right?A right triangle is one with a 90 degree inner angle. The two arms of a right angle are made up of height and base.
The sum of the angles B and C's measurements in a right triangle is 90 degrees (since angle A is 90 degrees).
So we have:
B + C = 90
And since sin C = 3x + 0.31, we know that:
C = sin⁻¹(3x + 0.31)
B + sin⁻¹(3x + 0.31) = 90
Subtracting sin⁻¹(3x + 0.31) from both sides, we get:
B = 90 - sin⁻¹(3x + 0.31)
Now we can use the fact that cos B = x - 0.49:
cos(90 - sin⁻¹(3x + 0.31)) = x - 0.49
Using the identity cos(90 - θ) = sin(θ), we can rewrite this as:
sin(sin⁻¹(3x + 0.31)) = x - 0.49
Simplifying the left side using the inverse sine function, we get:
3x + 0.31 = x - 0.49
Subtracting x and 0.31 from both sides, we get:
2x = -0.80
Dividing both sides by 2, we get:
x = -0.40
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Please help it’s for tmr, I only have 0 minute left
Leo has a number of toy soldiers between 27 and 54. If he wants to group them four by four, there are none left, seven by seven, 6 remain, five by five, 3 remain. How many toy soldiers are there?
The answer is 48 but I need step by step explanation
Leo has 48 toy soldiers.
What is the key concept is used to solve the question ?
This problem involves finding a number that satisfies certain conditions related to division with remainders. Specifically, the number must be divisible by 4 with no remainder, must leave a remainder of 6 when divided by 7, and must leave a remainder of 3 when divided by 5.
Calculating the number of toy soldiers :
Let's start by using the first condition to narrow down the possibilities for the number of toy soldiers. We know that the number must be divisible by 4 with no remainder, and it must be between 27 and 54. The multiples of 4 in this range are 28, 32, 36, 40, 44, 48, and 52.
Next, we can use the second condition to eliminate some of these possibilities. If we divide each of these numbers by 7, we get the following remainders:
28 ÷ 7 = 4 remainder 0
32 ÷ 7 = 4 remainder 4
36 ÷ 7 = 5 remainder 1
40 ÷ 7 = 5 remainder 5
44 ÷ 7 = 6 remainder 2
48 ÷ 7 = 6 remainder 6
52 ÷ 7 = 7 remainder 3
The only number in our list that leaves a remainder of 6 when divided by 7 is 48, so we can tentatively conclude that this is the number of toy soldiers.
Finally, we can check the third condition to make sure that 48 leaves a remainder of 3 when divided by 5. Indeed, 48 ÷ 5 = 9 remainder 3, so all of the conditions are satisfied.
Therefore, we can confidently say that Leo has 48 toy soldiers.
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