part one is -3 and 7
part two is -3

The distance between two opposite corners of the given floor is 17 feet.

Pythagoras's theorem states that in a right-angled triangle, the square of one side is equal to the sum of the squares of the other two sides.

Given that the floor of a storage unit is 15 feet long and 8 feet wide.

Let x would be the distance between two opposite corners of the floor

As per the figure, We have a right triangle with legs 15 and 8 and with hypotenuse x.

According to Pythagoras's theorem,

x² = 15² + 8²

x² = 225 + 64

x² = 289

x = √289

x = 17

Thus, the distance is 17 feet between two opposite corners.

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Answer:

30ft

Step-by-step explanation:

1530ft2 divided by 51ft.

Answer:

3/9

Step-by-step explanation:

3/9 because it goes up 3 right 9

Answer:

13½ kilometers

Step-by-step explanation:

If Nina runs 4½ km in ⅓ of an hour, at this pace, the number of km she'd run in an hour can be calculated as follows.

Let x be the number of km to run in an hour.

4½km => ⅓ hr

x km => 1 hr

Cross multiply

\( 1*4\frac{1}{2} = \frac{1}{3}*x \)

\( 4\frac{1}{2} = \frac{x}{3} \)

Multiply both sides by 3

\( 4\frac{1}{2}*3 = \frac{x}{3}*3  \)

\( \frac{9}{2}*3 = x  \)

\( \frac{27}{2} = x \)

\( 13\frac{1}{2} = x \)

x = number of km Nina runs in 1 hour = 13½ kilometers

The number of minutes required to wash 12 windows is 8 4/7 minutes.

According to the given question.

You can wash one window in 15 minutes, so each minute you can wash 1/15.

Your sister can wash one window in 20 minutes, so each minute the sister can wash 1/20.

If working together you can wash 1/15 + 1/20 = 7/60.

Hence, the time required to wash 12 windows together

= 12 × 7/60

= 8 4/7 minutes.

Therefore, the number of minutes required to wash 12 windows is 8 4/7 minutes.

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Answer:

3920 - 36x ≤ 500

Step-by-step explanation:

Calista worked all summer to save for spending money while she is away for college. She goes off to college with $3920 in her savings account. She wants to have at least $500 left in her account at the end of her 36-week school year. Write an inequality to represent this situation.

Let the amount of money spent in 36 weeks = x

At least = Less than or equal to = ≤

$3920 - 36x ≤ $500

Hence, the inequality to represent this situation is written as:

3920 - 36x ≤ 500

Note that the line of reflection that reflects quadrilateral ABCD onto quadrilateral A'B'C'D' is given as attached. Note that when a shape is reflected, it must be reflected over a line. In this case, the line of reflection is y = -3.

A line of reflection is a line that acts as a mirror, reflecting a figure across the line so that the image is a mirror image of the original.

When a shape is reflected, it must be reflected over a line. The line of reflection of quadrilateral ABCD onto quadrilateral A'B'C'D is

From the given graph, we have the following observations

ABCD was flipped over to form A'B'C'D'

The line of reflection is between both shapes.

Using points C and C' as references;

We have:

C = (-3, -1)

C" = (-3, -5)

Notice that both points have the same x-coordinate

This means that the line of reflection is parallel to the x-axis and passes through the y-axis.

The point at which it passes through the y-axis is calculated using the mid-point formula.

Therefore, we have:

y = (y1+y2)/2

y = (-1-5)/2

y = -6/2

y = -3

Hence, the line of reflection is y = -3
See the attachment for the line of reflection.

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Answer:

Step-by-step explanation:

Answer:

C (is greater than it equal to) 31

Step-by-step explanation:

Isolate the c by adding 11 to both sides (cancels out the 11 and turns 20 into 31). Keep the sign the same!! Hope this helped! <33

Answer:

Ông sáu sẽ mất 4281000 đồng

The equation that relates the y-displacement to the acceleration in the y-direction, the initial velocity in the y-direction, and the time is:\(y = (1/2)at^2 + v_{i}t\)

where y is the vertical displacement, a is the acceleration in the y-direction, t is time, and \(v_{i}\) is the initial velocity in the y-direction.

This equation is derived from the kinematic equations of motion, specifically the one that relates the displacement, velocity, acceleration, and time for motion in one dimension. The first term of the equation represents the displacement due to the acceleration, while the second term represents the displacement due to the initial velocity. The equation can be used to calculate the vertical displacement of an object with a known initial velocity and acceleration in the y-direction after a certain amount of time has passed.

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Answer:

8 adults

Step-by-step explanation:

78-6 for the child is 72 and tben since each adult is $9 so $72 divide by $9

The nails produced in this factory with lengths less than or equal to 5.0706 centimeters are in the bottom 8%, and nails produced with lengths greater than or equal to 5.1894 centimeters are in the top 8%.

According to the given information, the mean length of nails produced in a factory is 5.13 centimeters and the standard deviation is 0.04. We need to find the two lengths that separate the top 8% and bottom 8% of the nails produced.

To solve this problem, we need to use the z-score formula which is given by:

z = (x - μ) / σ

Where x is the observed value, μ is the mean, and σ is the standard deviation.

For the top 8%, we need to find the z-score such that the area under the normal curve to the right of it is 0.08. Using a standard normal table or calculator, we can find that the z-score is approximately 1.405.

So,

1.405 = (x - 5.13) / 0.04

x - 5.13 = 0.04 * 1.405

x = 5.1894

Therefore, the length separating the top 8% of nails produced is 5.1894 centimeters.

Similarly, for the bottom 8%, we need to find the z-score such that the area under the normal curve to the left of it is 0.08. Using a standard normal table or calculator, we can find that the z-score is approximately -1.405.

So,

-1.405 = (x - 5.13) / 0.04

x - 5.13 = -0.04 * 1.405

x = 5.0706

Therefore, the length separating the bottom 8% of nails produced is 5.0706 centimeters.

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Consider a situation where we are typing data it in to an Excel worksheet and accidentally type 762 instead of 726. This type of inaccuracy is referred to as "transposing."

A vertical range containing cells is converted into a horizontal range, alternatively vice versa, via the TRANSPOSE function.

Consider a situation where we are typing data it in to an Excel worksheet and accidentally type 762 instead of 726.

Thus, this type of inaccuracy is referred to as "transposing."

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As per linear equation, within 2.5 months, Rusty's hair will grow over  \(\frac{5}{8}\) inches.

"A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. When this equation is graphed, it always results in a straight line."

Given, the growth rate of Rusty's hair is \(\frac{1}{4}\) inches per month.

Let, within 'x' months, her hair will grow \(\frac{5}{8}\) inches.

Therefore, x ×  \(\frac{1}{4}\)  =  \(\frac{5}{8}\)

⇒ x = ( \(\frac{5}{8}\) × 4)

⇒ x = 2.5

Therefore, within 2.5 months, Rusty's hair will grow over  \(\frac{5}{8}\) inches.

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Answer: 34

Step-by-step explanation:

since the line is cut in half the sides equal

therefore

4x-7 = 2x+5

solve for x

4x = 2x + 12

2x = 12

x = 6

plug into either equation as they are both the same

4(6) - 7 = 17

if one half is 17 then the other half is 17

add the halves for the full line segment AT

AT = 17 + 17 = 34

The point (9, -7) is the only solution to the system of linear inequalities given.

To determine which point would be a solution to the system of linear inequalities, let's substitute the given points into the inequalities and see which point satisfies both inequalities.

The system of linear inequalities is:

y > -4x + 6

y > (1/3)x - 7

Let's test each given point:

For the point (9, -7):

Substituting the values into the inequalities:

-7 > -4(9) + 6

-7 > -36 + 6

-7 > -30 (True)

-7 > (1/3)(9) - 7

-7 > 3 - 7

-7 > -4 (True)

Since both inequalities are true for the point (9, -7), it is a solution to the system of linear inequalities.

For the point (-12, -2):

Substituting the values into the inequalities:

-2 > -4(-12) + 6

-2 > 48 + 6

-2 > 54 (False)

-2 > (1/3)(-12) - 7

-2 > -4 - 7

-2 > -11 (False)

Since both inequalities are false for the point (-12, -2), it is not a solution to the system of linear inequalities.

For the point (12, 1):

Substituting the values into the inequalities:

1 > -4(12) + 6

1 > -48 + 6

1 > -42 (True)

1 > (1/3)(12) - 7

1 > 4 - 7

1 > -3 (True)

Since both inequalities are true for the point (12, 1), it is a solution to the system of linear inequalities.

For the point (-12, -7):

Substituting the values into the inequalities:

-7 > -4(-12) + 6

-7 > 48 + 6

-7 > 54 (False)

-7 > (1/3)(-12) - 7

-7 > -4 - 7

-7 > -11 (True)

Since one inequality is true and the other is false for the point (-12, -7), it is not a solution to the system of linear inequalities.

In conclusion, the point (9, -7) is the only solution to the system of linear inequalities given.

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With this query, no effort is necessary. measure the tbsp. of all items.

A great source of both phosphorus and calcium, which are essential for the growth and upkeep of strong, strong teeth and bones, is milk. They lower the chance of developing osteoporosis and suffering broken bones later in life. Milk encourages strong bones.

1. Measure \(8\) tbsp. chocolate sauce and add \(2\frac{1}{2}\) cups of milk.

No work is required for this question. It is a simple instruction to measure out 8 tbsp. of chocolate sauce and add it to \(2\frac{1}{2}\) cups of milk.

2. Start with \(1\frac{3}{4}\) cups of milk and add \(2\frac{1}{2}\) tbsp. chocolate sauce.

No work is required for this question. It is a simple instruction to start with \(1\frac{3}{4}\) cups of milk and add \(2\frac{1}{2}\) tbsp. of chocolate sauce.

3. Add \(3\frac{1}{3}\) tbsp. chocolate sauce to \(1\frac{1}{4}\) cups milk.

No work is required for this question. It is a simple instruction to add  \(3\frac{1}{3}\)tbsp. of chocolate sauce to \(1\frac{1}{4}\) cups of milk.

4. For every 1 cup of milk add \(2\frac{1}{2}\) tbsp. of chocolate sauce.

No work is required for this question. It is a simple instruction to add \(2\frac{1}{2}\) tbsp. of chocolate sauce for every \(1\) cup of milk.

5. Stir \(1\) tbsp. chocolate sauce into \(\frac{2}{3}\) cup milk.

No work is required for this question. It is a simple instruction to stir 1 tbsp. of chocolate sauce into \(\frac{2}{3}\) cup of milk.

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Answer:

27

Step-by-step explanation:

4.5*3*2 = 27

hi,

You just have to multiply the three measures.  

So :  

2*3*4.5 =  27 cm³

Easy, is it not ?  

The difference lies in the comparison made: critical values in the z-test using rejection region(s) and the P-value in the z-test using a P-value. The choice between the two approaches depends on the nature of the population and the specific hypothesis being tested.

The correct answer is (d): In the z-test using rejection region(s), the test statistic is compared with critical values. The z-test using a P-value compares the P-value with the level of significance alpha.

The z-test is a statistical test used to assess whether a sample mean or proportion significantly differs from a hypothesized population mean or proportion. The difference between the z-test for mu (population mean) using rejection region(s) and the z-test for p (population proportion) using a P-value lies in the approach used to make the inference.

In the z-test using rejection region(s), the test statistic (calculated from the sample) is compared with critical values based on the chosen level of significance alpha. The critical values are determined from the standard normal distribution or a z-table, and if the test statistic falls within the rejection region (beyond the critical values), the null hypothesis is rejected.

On the other hand, in the z-test for p using a P-value, the test statistic is compared with the P-value. The P-value represents the probability of observing a test statistic as extreme or more extreme than the one obtained, assuming the null hypothesis is true. If the P-value is smaller than the chosen level of significance alpha, the null hypothesis is rejected.

Therefore, the difference lies in the comparison made: critical values in the z-test using rejection region(s) and the P-value in the z-test using a P-value. The choice between the two approaches depends on the nature of the population and the specific hypothesis being tested.

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Answer:

Average Speed

C.) 19.6 m/s

Instantaneous Speed

D.) 39.2 m/s

Step-by-step explanation:

Given the function to represent the distance traveled by the object in \(t\) seconds:

\(y = 4.9t^2\)

To find:

Object's average speed during the first 4 seconds ?

Instantaneous speed at t = 4 seconds

Solution:

Average speed of a moving object is given by, Total Distance covered divided by Total time taken.

\(\text{Average Speed = }\dfrac{\text{Total Distance traveled}}{\text{Total Time Taken}}\)

Let us find the distance traveled in 4 seconds by putting t = 4 in the equation \(y = 4.9t^2\)

\(y = 4.9\times 4^2 = 78.4\ m\)

Now, let us put the values in the formula:

\(\text{Average Speed = }\dfrac{78.4}{4} = \bold{19.6\ m/s}\)

For instantaneous speed, we need to differentiate y w.r.to t:

\(Speed = \dfrac{d}{dt}y = 4 \times 4.9 t^{2-1}\\\Rightarrow Speed = \dfrac{d}{dt}y = 4 \times 4.9 t\)

Now, let us put t = 4 seconds

Speed = \(4\times 4.9\times 4\) = 39.2 m/s

The answers are:

Average Speed

C.) 19.6 m/s

Instantaneous Speed

D.) 39.2 m/s

Answer:

The third one

Step-by-step explanation:

Answer:

y = –3x + 4 and y = –3x – 4 and y = –3x + 4 and y = –6x + 8

Step-by-step explanation:

Answer:

x = 3

Step-by-step explanation:

3(x−5)+4x−2=4

Step 1: Simplify both sides of the equation.

3(x−5)+4x−2=4

(3)(x)+(3)(−5)+4x+−2=4(Distribute)

3x+−15+4x+−2=4

(3x+4x)+(−15+−2)=4(Combine Like Terms)

7x+−17=4

7x−17=4

Step 2: Add 17 to both sides.

7x−17+17=4+17

7x=21

Step 3: Divide both sides by 7.

7x

7

=

21

7

x=3

f(x) is increasing on the intervals (−∞, π/4) and (5π/4, ∞), and decreasing on the interval (π/4, 5π/4).

To determine the intervals on which f(x) = 3sin(x) + 3cos(x) is increasing and decreasing, we need to find the derivative of f(x) and examine its sign.

f'(x) = 3cos(x) - 3sin(x)

To find where f'(x) = 0, we set the derivative equal to zero and solve:

3cos(x) - 3sin(x) = 0

cos(x) - sin(x) = 0

From this equation, we can see that it is satisfied when x = π/4 and x = 5π/4.

Now, we analyze the sign of f'(x) in different intervals:

For x < π/4: f'(x) > 0, so f(x) is increasing.

For π/4 < x < 5π/4: f'(x) < 0, so f(x) is decreasing.

For x > 5π/4: f'(x) > 0, so f(x) is increasing.

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Answer:

M= 4.5

Step-by-step explanation:

take 5m+11 = 9m - 7

add seven to each side to get

5m + 18 = 9m

then subtract 5m from each side

18= 4m

then divide by 4

18÷4= 4.5

Answer:

The girl who completed 42 push-ups in 6 minutes did more push-ups than the girl who completed 24 push-ups in 3 minutes.

Step-by-step explanation:

Answer:

The hikers each receive 2 1/3 cups of trail mix.

1. Multiply 8 by 3 1/4 to get how much cups of trail mix they have in total which  will come out as 28.

2. Then divide the 28 cups by the 12 hikers, and you will get 2 1/3 as your answer.