The diagonal of a square is 15 inches. Find the area of the square.​

Answer:

x = 64

Step-by-step explanation:

To find the value of x, just divide 128 by 2.

It'll get you 64.

To check your answer, just:  2 · 64 = 128

Answer:

64

Step-by-step explanation:

Let's solve your equation step-by-step.

2x=128

Step 1: Divide both sides by 2.

2x/2 = 128/2

x=64

The first differential equation is a first-order linear equation, which means its order is 1. The solution to the initial value problem is y = t^2 + 3t + 10. The second differential equation is also a first-order equation, but it is nonlinear. The solution to the initial value problem is y = 2sin(t) + 3sin(t) + 1. The third differential equation is a second-order linear equation. The solution to the initial value problem is y = 2cost + 8sin(t) + t + 1.

a. The given differential equation dy/dt = 2t + 3 is a first-order linear equation, as it is in the form dy/dt + P(t)y = Q(t). Integrating both sides gives y = t^2 + 3t + C, where C is the arbitrary constant. To solve the initial value problem (0,10), we substitute t = 0 and y = 10 into the equation. This gives 10 = 0^2 + 3(0) + C, which simplifies to C = 10. Thus, the solution to the IVP is y = t^2 + 3t + 10.

b. The given differential equation dy/dt = sin(2t) + 3cos(t) is a first-order nonlinear equation. To solve it, we integrate both sides to obtain y = -cos(2t)/2 + 3sin(t) + C. Substituting the initial condition (0,1) yields 1 = -cos(0)/2 + 3sin(0) + C. Simplifying, we find C = 1. Hence, the solution to the IVP is y = -cos(2t)/2 + 3sin(t) + 1.

c. The given differential equation y" = 3cos(t) is a second-order linear equation. Integrating it twice gives y = 2sin(t) + 8cos(t) + Ct + D. Substituting the initial conditions (t, y) = (0,8) and (t, y') = (0,1), we obtain 8 = 2sin(0) + 8cos(0) + 0C + D and 1 = 2cos(0) - 8sin(0) + C. Simplifying these equations, we find D = 8 and C = 1. Therefore, the solution to the IVP is y = 2sin(t) + 8cos(t) + t + 1.

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Answer:

\(2(x+1)(2x+5)\)

Step-by-step explanation:

First, factor out 2:

\(2(2x^2+7x+5)\)

Consider \(2(2x^2+7x+5)\). Factor the expression by grouping. First, the expression needs to be rewritten as \(2x^2+ax+bx+5\). To find a and b, set up a system to be solved:

\(a + b = 7\)

\(ab = 2 * 5 = 10\)

Since ab is positive, a and b have the same sign. Since a + b is positive, a and b are both positive. List all such integer pairs that give product 10:

\(1, 10\)

\(2, 5\)

Calculate the sum for each pair:

\(1 + 10 = 11\)

\(2 + 5 = 7\)

The solution is the pair that gives sum 7:

\(a = 2\)

\(b = 5\)

Rewrite \(2x^2+7x+5\) as \((2x^2+2x)+(5x+5):\)

\((2x^2+2x)+(5x+5)\)

Factor out 2x in the first and 5 in the second group:

\(2x(x+1)+5(x+1)\)

Factor out common term x + 1 by using distributive property:

\((x+1)(2x+5)\)

Rewrite the complete factored expression:

\(2(x+1)(2x+5)\)

{7x+4}/{x^2-x-56}

using common denominators

Hello!

Five times x increased by three times y is  5x + 3y

The study has a confounding variable since the two groups differ in the time they were supposed to report to the testing room. Since the groups differed in terms of sleep deprivation and the time they were supposed to report to the testing room, the effect of sleep deprivation on learning could not be isolated.

The statement that is true is: d. All of these are true.Explanation:A study may have various sources of variability, including participant selection, the setting in which the study is conducted, and the measure used. The following options are as follows:a. The study may be affected by a situational variable.b. The construction noise may contribute to variability in test scores.c. The study has a confounding variable. The groups differ in the time they are to report to the testing room.d. All of these are true.Therefore, all of these options are true. For example, the study may be affected by a situational variable if a natural disaster or other unforeseen event happens that causes the study to be disrupted. In this case, the study was disrupted by a noisy construction crew, which may have contributed to variability in test scores. The study has a confounding variable since the two groups differ in the time they were supposed to report to the testing room. Since the groups differed in terms of sleep deprivation and the time they were supposed to report to the testing room, the effect of sleep deprivation on learning could not be isolated.

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Answer: a) x - y = -1

b) 3x + 2y = 13

Step-by-step explanation:

a) To find the equation of the line passing through points P(2, 3) and Q(5, 6), we can use the point-slope form of the equation of a line, which is:

y - y1 = m(x - x1)

where m is the slope of the line, and (x1, y1) is one of the points on the line.

First, we need to find the slope of the line passing through P and Q. The slope, m, is given by:

m = (y2 - y1)/(x2 - x1)

where (x1, y1) = (2, 3) and (x2, y2) = (5, 6).

m = (6 - 3)/(5 - 2) = 1

Now that we have the slope, we can use the point-slope form of the equation of a line to find the equation of the line passing through P and Q:

y - 3 = 1(x - 2)

Simplifying the equation, we get:

y - 3 = x - 2

y = x + 1

To convert this equation to standard form, we can rearrange the terms to get:

x - y = -1

Therefore, the equation of the line passing through points P(2, 3) and Q(5, 6) in standard form is x - y = -1.

b) To find the equation of the line passing through points A(5, -1) and B(1, 5), we can use the same method as in part (a).

The slope of the line passing through A and B is:

m = (y2 - y1)/(x2 - x1)

where (x1, y1) = (5, -1) and (x2, y2) = (1, 5).

m = (5 - (-1))/(1 - 5) = -3/2

Using the point-slope form of the equation of a line, we get:

y - (-1) = (-3/2)(x - 5)

Simplifying the equation, we get:

y = (-3/2)x + 13/2

To convert this equation to standard form, we can rearrange the terms to get:

3x + 2y = 13

Therefore, the equation of the line passing through points A(5, -1) and B(1, 5) in standard form is 3x + 2y = 13.

Answer:

No

Step-by-step explanation:

Probability meaning: "the extent to which something is probable; the likelihood of something happening or being the case."

Probability only is a range from 1-100 %

Probability can also be written as a percentage, which is a number from 0 to 100 percent. ... The probability of a certain event occurring depends on how many possible outcomes the event has. If an event has only one possible outcome, the probability for this outcome is always 1 (or 100 percent).

(credits to scientific american)

Answer:

2/8

Step-by-step explanation:

they can both be divides by two making 1/4 or multiply 1/4 by 2 and youll get 2/8

Answer:

The estimated answer would be 9

Step-by-step explanation:

The answer I received in the calculator was 8.94422. Since the tenths, place value(9) is closer to 9.0 than 8.0, we round up. I hope this helps you.

We can be 90% confident that the true mean length of bolts in the manufacturing process falls within this interval.

To calculate the 90% confidence interval for the true mean length of bolts in the manufacturing process, we can use the formula:

Confidence Interval\(= \bar{X} \pm (t \times (s / \sqrt{n} ))\)

Where:

\(\bar{X}\) is the sample mean

t is the critical value for the desired confidence level (with n-1 degrees of freedom)

s is the sample standard deviation

n is the sample size

In this case, the sample mean (\(\bar{X}\)) is 3 inches, the sample standard deviation (s) is 0.3 inches, and the sample size (n) is 9.

Since the sample size is small (less than 30) and the population standard deviation is unknown, we need to use a t-distribution to find the critical value.

With 9-1 degrees of freedom and a 90% confidence level, the critical value (t) can be obtained from a t-distribution table or a statistical software.

Let's assume the critical value is 1.833 (hypothetical value).

Substituting the values into the formula:

Confidence Interval \(= 3 \pm (1.833 \times (0.3 / \sqrt{9} ))\)

Calculating the standard error (s / √n):

Standard Error = 0.3 / √9

Substituting the standard error value:

Confidence Interval = 3 ± (1.833 \(\times\) [Standard Error])

By evaluating the equation, the confidence interval for the true mean length of the bolts is approximately 2.858 inches to 3.142 inches (rounded to three decimal places).

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2r-5+6r

Add like terms:

(2r + 6r) - 5

8r - 5

Answer:

47 cupcakes

Step-by-step explanation:

Assuming there aren’t any rules about what type of cupcakes he should buy.

\(101 - 21 - 33 = 47\)

Since he's already bought 21 + 33 he just have to buy

101 - (21 + 33) which is 47

Happy to help ^^

Answer:

95

Step-by-step explanation:

Answer:

b.

Step-by-step explanation:

6 times 1/2 is the same thing as 6/1 times 1/2, which is 6/2.

Hope this helps.

Mate's car can travel approximately 5 more minutes per gallon of gas compared to Jenna's car.

To determine how many more minutes Mate's car can travel per gallon of gas compared to Jenna's car, we would need additional information about the fuel efficiency or miles per gallon (MPG) for each car.

Fuel efficiency is typically measured in terms of miles per gallon, indicating the number of miles a car can travel on a gallon of gas.

To calculate the difference in travel time, we would also need to know the average speed at which the cars are traveling.

Once we have the MPG values for Mate's car and Jenna's car, we can calculate the difference in travel time per gallon of gas by considering their respective fuel efficiencies and average speeds.

If Mate's car has a fuel efficiency of 30 MPG and Jenna's car has a fuel efficiency of 25 MPG, we can calculate the difference in travel time by comparing the distances they can travel on a gallon of gas.

Let's assume both cars are traveling at an average speed of 60 miles per hour.

For Mate's car:

Travel time = Distance / Speed

= (30 miles / 1 gallon) / 60 miles per hour

= 0.5 hours or 30 minutes.

For Jenna's car:

Travel time = Distance / Speed

= (25 miles / 1 gallon) / 60 miles per hour

= 0.4167 hours or approximately 25 minutes.

Without specific information about the MPG values and average speeds of the cars, it is not possible to provide an accurate answer regarding the difference in travel time per gallon of gas between Mate's car and Jenna's car.

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Answer:

30.4

Step-by-step explanation:

17+28+32+35+59+20+19+33+30+31=304

304/10=30.4

If Company B is unable to sell their speakers in China, it will have a significant impact on the economy: Decreased exports, Imbalanced trade, Economic implications, Reduced revenue. Second option is correct.

1. Decreased exports:

2. Imbalanced trade:

3. Economic implications:

4. Reduced revenue:

In summary, if Company B cannot sell their speakers in China, it will lead to a decrease in exports, an imbalance in trade, potential economic implications, and reduced revenue for the company. These effects can have broader consequences on the economy as a whole. Therefore, the second option is correct answer.

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Answer:

A. We are given that the length of the box is equal to 24 as indicted in the "24-inch long". From the given, it is also stated that the width of the box is 7 inches less than the height. If the height of the box is x, the width is then x - 7. The equation that would let us solve the problem is,

                           2880 = 24(x)(x - 7)

Simplifying,

                           2880 = 24x² - 168x

B. The value of x from the equation is 15. Thus, the answer is YES.

Step-by-step explanation:

a) The equation that models the volume of the box in terms of its height will be 2880 = 24x² - 168x.

b)Yes, it is possible for the height of the box to be 15 inches

Volume is the three-dimensional space bounded by a boundary or inhabited by an item.

The given data in the problem is;

L is the length of the box= 24-inch

V is the volume = 2,880 cubic inches.W

W is the width of the box

h is the height

Let the side of the box is x then volume V is found as;

V=LWh

2880 = 24(x)(x - 7)

2880 = 24x² - 168x

Hence the equation that models the volume of the box in terms of its height will be 2880 = 24x² - 168x.

b)Yes, it is possible for the height of the  box to be 15 inches

The value of x obtained from the equation is 15.

Hence yes, it is possible for the height of the  box to be 15 inches

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The greatest volume of mortar mix, she could make, is 1.5 cubic meters.

The ratio is a numerical relationship between two values that demonstrates how frequently one value contains or is contained within another.

Given:

Mortar mix is made by mixing cement, sand, and quicklime in a ratio of 1:2:3.

Julie has 0.75 m³ of quicklime.

Let the volume of cement, sand, and quicklime be x, 2x, and 3x.

So,

3x = 0.75

Divide by 3 into both sides,

we get,

3x/3 = 0.75/3

x = 0.25

The total volume = the greatest volume of mortar mix

=  x + 2x + 3x

Substituting the value of x to the expression,

we get,

x + 3x + 3x = (0.25) + 2(0.25) + (90.25)

The greatest volume of mortar mix,

= 1.5 cubic meters.

Therefore, the required amount of volume is 1.5 cubic meters.

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The complete question:

Mortar mix is made by mixing cement, sand, and quicklime in a ratio of 1:2:3.

Julie has 0.75 m³ of quicklime.

She has plenty of sand and cement.

Work out the greatest volume of mortar mix she could make.

Rewrite the second expression as

\(\dfrac1{1+x^m + x^{-n}} = \dfrac{x^{\ell+n}}{x^{\ell+n} + x^{\ell+m+n}+x^\ell} = \dfrac{x^{-m}}{x^{-m} + 1 + x^\ell}\)

and the third expression as

\(\dfrac1{1 + x^n + x^{-\ell}} = \dfrac{x^\ell}{x^\ell + x^{\ell+n} + 1} = \dfrac{x^\ell}{x^\ell + x^{-m} + 1}\)

so the fractions all have the same denominator.

Then combining the fractions gives the desired result,

\(\dfrac1{1+x^\ell+x^{-m}} + \dfrac1{1+x^m+x^{-n}} + \dfrac1{1+x^n+x^{-\ell}} = \dfrac{1+ x^\ell + x^{-m}}{1+x^\ell+x^{-m}} = \boxed{1}\)

Answer:

Top left Equation:  \(\frac{2}{3} + (- 2 \frac{1}{3} ) = - 1 \frac{2}{3}\)

Step-by-step explanation:

You start at 2/3, or the left side.

Since the line is directing left, you are subtracting, or adding a negative.

If you see, you are moving 7 - 1/3s to the left

7 x 1/3 = 7 / 3

7 / 3 = 2 1/3

And 2/3 + (-2 1/3) = -1 2/3

If my answer is incorrect, pls correct me!

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-Chetan K

the Department of Education receives about 65 percent of the federal funds transferred to state governments.

First, you need to identify what type of information is being asked for in the question. In this case, the question is asking which department receives a certain percentage of federal funds transferred to state governments.

Next, you need to research the answer. You can find the answer to this question by looking at the U.S. Department of Education website or other reliable sources.

The answer is that the Department of Education receives about 65 percent of the federal funds transferred to state governments.

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Answer:  

4 8/6

Step-by-step explanation:

That should be your answer

Answer:

AB and BC are the sides of a parallelogram, ABCD. AB = 5 cm, BC = 7 cm and ABC = 60 degrees. Draw the lines AD and CD to complete the parallelogram.

Step-by-step explanation:

The point estimate for the unknown population proportion based on the given values of x and n is 0.5436.A point estimate is a statistical estimate of a population parameter that provides a single value as the best estimate of that population parameter.

A point estimate is a statistic used to estimate the value of an unknown parameter of a population. A point estimate is a single value estimate of the population parameter.X is the number of "successes" in the sample and n is the sample size. It is used to estimate the population proportion.P = x/n is the formula used to estimate the population proportion.

Therefore, the estimated population proportion for this problem is P = 106/195 = 0.5436 (rounded to four decimal places).Thus, the point estimate for the unknown population proportion based on the given values of x and n is 0.5436, as given in the second option.

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Answer:

The answer would be (x-5, y-5)

Step-by-step explanation:

You can find this out by finding the difference between D(3,5) and D'(-2,1) (pr any other coordinate) which is -5 in both the x and y coordinates making the answer (x-5, y-5).

The ordered pair that lie on the graph of the exponential function ​f(x)=3(14)ˣ is (-1, 12)

A curve that depicts an exponential function is known as an exponential graph.

The curve have a horizontal asymptote and either an increasing slope or a decreasing slope. this is to say that the curve begins as a horizontal line, increases or drops gradually, and then the growth or decay accelerates. It may or may not cut the x-axis, but it always cuts the y-axis at some point.

An exponential graph will almost always have a y-intercept but not necessarily an x-intercept.

The given function was plotted on a graph and the point that lie on the graph is (-1, 12).

the point (-3,-192)  is way out of the graph

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Answer:3048.7804878

Step-by-step explanation:

I took the same test p.s. you may need to round.