Solve for z.


z² = 16

Enter your answer in the box.

Answer:

14

Step-by-step explanation:

all you have to do to find difference is subtract the small number from the bigger number, 18 - 4 = 14

Answer:

14

Step-by-step explanation:

The difference of 18 and 4

18 - 4

14

The middle 50% of the distribution for X, or the IQR, lies between 87 acres and 261 acres.

A measurement of the dispersion or variability of a dataset is the interquartile range (IQR). The 75th and 25th percentiles of the data, or the difference between the upper and lower quartiles, are used to define it. The range of the middle 50% of the data is represented by it, in other words.

The IQR is a reliable indicator of the spread of the data that, in comparison to the range or standard deviation, is less susceptible to outliers or extreme values. For this reason, it is valuable in statistics. It is frequently employed as a measure of variability when the data contains extreme values or when the distribution is not normal.

Given that, mean = 174 and standard deviation = 58 acres.

Using the quartile values we have:

Q1 = mean - (1.5 * standard deviation)

Q1 = 174 - (1.5 * 58) = 87 acres

Q3 = mean + (1.5 * standard deviation)

Q3 = 174 + (1.5 * 58) = 261 acres

Hence, the middle 50% of the distribution for X, or the IQR, lies between 87 acres and 261 acres.

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The complete question is:

Answer:

Step-by-step explanation:

(g * h)(24)

gh*24

24gh

Answer:

a

Step-by-step explanation:

I just did the test

Answer:

The effect on the graph of the function f(x) = 2^x when f(x) is replaced with f(x − 3) is that it translates horizontally 3 units right.

When a function is replaced with f(x - c), where c is a positive constant, the graph of the function shifts horizontally c units to the right. Similarly, if c is negative, the graph shifts horizontally c units to the left.

Therefore, replacing f(x) with f(x - 3) in the function f(x) = 2^x shifts the graph of the function horizontally by 3 units to the right.

Please mark this answer as Brainliest!!

Answer: 2+ 2

Step-by-step explanation:

no problem

The coordinates for the dilated triangle is obtained as A'(-1, 8), B'(-7, 6), and C'(-7, -4).

What is dilation?

Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. The initial shape should be stretched or contracted during a dilatation.

The coordinates point of the triangle is given as -

A (-1,6)

B (-4,5)

C (-4,0)

To dilate triangle ABC by a scale factor of 2 about the point (-1, 4), we can follow these steps -

Translate the triangle so that the center of dilation is at the origin.

We can do this by subtracting (-1, 4) from each vertex -

A' = (-1, 6) - (-1, 4) = (0, 2)

B' = (-4, 5) - (-1, 4) = (-3, 1)

C' = (-4, 0) - (-1, 4) = (-3, -4)

Dilate the translated triangle by multiplying the coordinates of each vertex by the scale factor of 2 -

A'' = 2(0, 2) = (0, 4)

B'' = 2(-3, 1) = (-6, 2)

C'' = 2(-3, -4) = (-6, -8)

Translate the dilated triangle back to its original position by adding (-1, 4) to each vertex -

A'B'C' = A'' + (-1, 4) = (-1, 8)

B'' + (-1, 4) = (-7, 6)

C'' + (-1, 4) = (-7, -4)

Therefore, the coordinates of the dilated triangle A'B'C' are (-1, 8), (-7, 6), and (-7, -4).

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The probability that a specific fire engine is not available when needed is 0.04 (since the probability of it being available is 0.96).

The question asks for two probabilities related to the availability of fire engines in a town. The first part asks for the probability that neither engine is available when needed, and the second part asks for the probability that a fire engine is available when needed.

To calculate the probability that neither engine is available when needed, we need to use the multiplication rule for independent events. We know that the probability that one specific engine is not available when needed is 0.04 (1 - 0.96). Since the two engines operate independently, the probability that both are not available when needed is the product of their individual probabilities:

P(neither available) = P(engine 1 not available) * P(engine 2 not available)

P(neither available) = 0.04 * 0.04

P(neither available) = 0.0016

Therefore, the probability that neither fire engine is available when needed is 0.0016.

To calculate the probability that a fire engine is available when needed, we can simply use the given probability of 0.96:

P(available) = 0.96

Therefore, the probability that a fire engine is available when needed is 0.96.

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Answer: 1287

Step-by-step explanation:

The given statement "Adding together all the residuals from a regression plot will always sum to 0" is False. A residual is defined as the difference between the observed value and the predicted value for each data point in a regression plot. The sum of residuals is not always equal to 0.

In a linear regression plot, the predicted values for each data point are calculated using the line of best fit. The residual for each data point is calculated as the difference between the observed value and the predicted value. The residuals are a measure of how well the line of best fit predicts the observed data. Ideally, the residuals should be randomly distributed around 0.

The sum of the residuals will be 0 only if the line of best fit perfectly predicts the observed data. However, this is not always the case. In fact, a good regression plot will have some residuals that are positive and some that are negative, resulting in a sum that is not equal to 0. This is because the line of best fit is only an estimate of the relationship between the variables being studied and will never perfectly predict the observed data.

Therefore, the statement "Adding together all the residuals from a regression plot will always sum to 0" is False. The sum of residuals may be close to 0 in some cases, but it will not always be exactly equal to 0.

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Philip puts 8 ounces of snack mix in each bag. To get this answer, we found the total weight of the mix by adding the weights of the three ingredients and converted it to ounces.

First, we need to find the total weight of the mix. Since Philip mixes 2 pounds of each ingredient and he has three ingredients, the total weight of the mix is:

2 pounds + 2 pounds + 2 pounds = 6 pounds

Since there are 16 ounces in a pound, the total weight of the mix in ounces is:

[6 pounds] 16 ounces/pound = 96 ounces

To find how many ounces of mix Philip puts in each bag, we divide the total weight of the mix by the number of bags:

96 ounces / 12 bags = 8 ounces per bag

Therefore, Philip puts 8 ounces of snack mix in each bag.

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the speed of the bus in meters per second is 8.33 m/s. If a bus travels a distance of 1 kilometer in 2 minutes, we can use the formula for speed to calculate its speed in meters per second (m/s).

The formula for speed is:

Speed = Distance ÷ Time

Here, the distance is 1 kilometer, which is equal to 1000 meters (since 1 kilometer = 1000 meters), and the time is 2 minutes, which is equal to 120 seconds (since 1 minute = 60 seconds).

So, we can plug these values into the formula:

Speed = 1000 meters ÷ 120 seconds

Simplifying this expression, we get:

Speed = 8.33 meters per second (rounded to two decimal places)

Therefore, the speed of the bus in meters per second is 8.33 m/s.

To put this into context, it's important to understand that speed is the rate at which an object moves, while velocity is the rate at which it moves in a specific direction. So, in this case, we have only calculated the speed of the bus, not its velocity. However, knowing the speed of the bus can be useful for a variety of applications, such as determining how long it will take to travel a certain distance, or calculating the fuel efficiency of the vehicle

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Answer: The cost of each small candle is $3 and the cost of each large candle is $6.

Step-by-step explanation:

Let's use variables to represent the cost of each small candle and each large candle. Let's call the cost of each small candle "x" and the cost of each large candle "y".

We can set up two equations based on the information given:

4x + 1y = 18 (equation 1)

5x + 2y = 27 (equation 2)

We can solve for one variable in terms of the other by using one equation to eliminate one variable. Let's solve for "y" in terms of "x" by multiplying equation 1 by 2 and subtracting it from equation 2:

5x + 2y = 27

(8x + 2y = 36)

-3x = -9

Dividing both sides by -3, we get:

x = 3

Now that we know the cost of each small candle is $3, we can substitute that value into one of the equations to solve for the cost of each large candle. Let's use equation 1:

4x + 1y = 18

4(3) + 1y = 18

12 + y = 18

y = 6

Therefore, the cost of each small candle is $3 and the cost of each large candle is $6.

The distance between the two people is changing at a rate of 24.884 mi/h after 15 minutes.

We can use the Pythagorean theorem to determine the distance between the two people as a function of time. Let x be the distance traveled by the person walking east, and y be the distance traveled by the person walking northeast. Then, after 15 minutes (or 0.25 hours), we have:

x = (9 mi/h) * (0.25 h) = 2.25 mi

y = (8 mi/h) * (0.25 h) = 2 mi

The distance between the two people is given by:

[tex]d = sqrt(x^2 + y^2)[/tex]

Taking the derivative with respect to time t, we get:

[tex]d' = (2x dx/dt + 2y dy/dt) / (2sqrt(x^2 + y^2))[/tex]

Substituting the values we found earlier, we get:

[tex]d' = (2(2.25)(9) + 2(2)(8)) / (2sqrt((2.25)^2 + (2)^2))= 24.884 mi/h[/tex]

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Answer:

B. 15

Step-by-step explanation:

its right on edge

the center of dilation for the triangle is (0,0)

The center of dilation is a point in a plane about which a dilation, a type of transformation, is performed. A dilation is a transformation that changes the size of a geometric figure, while preserving its shape and orientation. The center of dilation is the fixed point that serves as the reference for the scaling or shrinking of the figure.

In a dilation, each point of the original figure is moved away from or towards the center of dilation, by a certain factor called the scale factor.  

The coordinate of yellow triangle and scaled triangle both passes through center of axes.

So, the center of dilation is (0,0).

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The percent error for Jason's measurement is 7.14%. This means that his measurement was off by 7.14% compared to the actual value.

Percent error is a measure of the difference between an actual value and an estimated or measured value, expressed as a percentage of the actual value. It is used to evaluate the accuracy of measurements or calculations.

To calculate the percent error for Jason's measurement, we first need to find the absolute error, which is the difference between his measurement and the actual value:

Actual value minus measured value equals absolute error.

Absolute error = |14 - 13|

Absolute error = 1 inch

Next, we can use the formula for percent error:

(Absolute error / Actual Value) x 100% equals the percent of error.

Percent error = (1 / 14) x 100%

Percent error = 0.0714 x 100%

Percent error = 7.14%

Therefore, the percent error for Jason's measurement is 7.14%. This means that his measurement was off by 7.14% compared to the actual value.

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The quadratic function to represent the total area of the park and its path is given by: f(x) = 2x² + 18x + 36.

In this problem, we are given that the length of a rectangular park is twice its width, and it is surrounded by a 3-foot wide path.

We are required to write a quadratic function to represent the total area of the park and its path.

The rectangular park can be represented as follows:

Length = 2x (twice the width)

Width = x

Therefore, the total length of the park including the 3-foot wide path can be represented as (2x + 2*3),

and the total width of the park including the 3-foot wide path can be represented as (x + 2*3).

The area of the park is given by the product of its length and width.

Thus, the area of the park can be represented as follows: Area of the park = (2x + 6)(x + 6)

To represent this as a quadratic function,

we can simplify the above expression using the distributive property.

Area of the park = 2x² + 6x + 12x + 36 = 2x² + 18x + 36.

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Answer:

35

Step-by-step explanation:

Change the percent to decimal form and of means multiply.

25% of 140

.25 * 140

35

Answer:

35

Step-by-step explanation:

Step-by-step explanation:

[tex]{ \tt{h(x) = {x}^{2} + 4x - 7 }}[/tex]

Substitute for x as -2;

[tex]{ \tt{h( - 2) = {( - 2)}^{2} + 4( - 2) - 7}} \\ \\ { \tt{h( - 2) = 4 - 8 - 7}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ { \tt{h( - 2) = - 11}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

Answer:-9

Step-by-step explanation:

h(-2)=h(x)

it symbolize that x=-2;

so, we'll replace every x with -2:

-2^2+3*(-2)-7=4-6-7=-9

The answer choice that is the most appropriate is B. A one-sample z-interval for estimating a population proportion

This is the most appropriate method because you are trying to estimate the proportion of all registered voters who have a favorable impression of Candidate A based on the sample data.

A one-sample z-interval is used when you want to estimate a population proportion using a sample proportion.

To calculate the one-sample z-interval for estimating a population proportion, you can use the following formula:

Confidence Interval = p ± Z * sqrt((p * (1 - p)) / n)

where:

Using this method, you will calculate a confidence interval that estimates the true proportion of registered voters who have a favorable impression of Candidate A, based on the sample data.

This is the most appropriate method because it focuses on estimating a single population proportion and incorporates the sample data and sample size into the calculation.

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The simplified form of the expression the sum of 6. 6 and 3. 2 all divided by 5 times the quantity of the squared difference of 2 minus 5 plus 6 is -0.3267

To simplify this expression, we'll work from the inside out, using the order of arithmetic operation

First, we'll evaluate the expression inside the parentheses:

(2 - 5 + 6) = 3

Next, we'll calculate the squared difference of 2 and 5:

(2 - 5)^2 = (-3)^2 = 9

Then, we'll subtract the result from step 2 from the result of step 1:

3 - 9 = -6

Next, we'll calculate the sum of 6.6 and 3.2:

6.6 + 3.2 = 9.8

Finally, we'll divide the result from step 4 by 5 times the result from step 3:

9.8 / (5 × -6) = 9.8 / -30

= -0.3267 (rounded to four decimal places)

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The missing value is approximately 64.12 degrees, which is closest to option D: 21.25 using inverse cos.

The inverse cosine (or arccosine) of both sides of the equation must be taken in order to locate the missing value in the equation cos = 7/18 to the closest tenth. We will then be able to convert the value of to degrees and round it to the closest hundredth using the value of the radian that is produced.

cos θ = 7/18

= arccos(7, 18, 7)

A 1.1181 radian angle

We can use the conversion factor /180 to convert radians to degrees.

θ = 1.1181 × 180/π

64.12 degrees.

As a result, the figure that is lacking is roughly 64.12 degrees, which is closest to choice D: 21.25.

Due to the periodic nature of the cosine function, there are often two solutions when determining the inverse cosine of a value. But, since the problem states that we should round to the closest hundredth, which suggests a single answer, we can disregard the second option in this instance. By reinserting the value we discovered into the original equation and making sure it equals 7/18, we can further confirm that the result is accurate.

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Answer:  The area of the smaller circle is [tex]65.6cm^{2}[/tex].

Step-by-step explanation:

A = [tex]\pi r^{2}[/tex], r is the radius.

1. Find out the diameter of the small circle.

[tex]\frac{1}{3}(27)= 9[/tex]

2) Find out the radius, r.

[tex]radius = \frac{diameter}{2} =\frac{9}{2} =4.5[/tex]

3) We plugin r = 4.5 into the formula to solve the area of the smaller circle.

[tex]A=\pi r^{2}=\pi (4.5)^{2} =65.6cm^{2}[/tex]

Answer:

To find the vertex and x-intercepts for the quadratic function f(x)=4.9x^2-28x+40:

First, we can find the x-coordinate of the vertex using the formula x = -b/2a, where a, b, and c are the coefficients of the quadratic function.

In this case, a = 4.9 and b = -28, so:

x = -(-28)/2(4.9) = 2.86

Next, we can find the y-coordinate of the vertex by plugging in this x value into the original function:

f(2.86) = 4.9(2.86)^2 - 28(2.86) + 40 = 6.65

So the vertex is at (2.86, 6.65).

To find the x-intercepts, we can set the function equal to zero and solve for x:

4.9x^2 - 28x + 40 = 0

We can use the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

Plugging in the coefficients, we get:

x = (28 ± sqrt(28^2 - 4(4.9)(40))) / 2(4.9)

Simplifying:

x = (28 ± sqrt(144.4)) / 9.8

x = 5.36 or 1.43

So the x-intercepts are (5.36, 0) and (1.43, 0).

The missing side length for the triangle is given as follows:

[tex]x = \frac{16\sqrt{3}}{3}[/tex]

The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:

For the angle of 60º on the triangle, we have that:

The tangent of 60º is equals to the square root of 3, hence the value of x is obtained as follows:

tan(60º) = 16/x

[tex]\sqrt{3} = \frac{16}{x}[/tex]

[tex]x = \frac{16}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}}[/tex]

[tex]x = \frac{16\sqrt{3}}{3}[/tex]

The triangle is given by the image presented at the end of the answer.

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To find the surface area of the volume generated when the curve y = x^2 revolves around the y-axis from x = 0 to x = 2, we will use the surface area formula for revolution:

Surface Area = 2 * pi * ∫[x * sqrt(1 + (dy/dx)^2)] dx from x = 0 to x = 2.

First, find the derivative dy/dx:
y = x^2
dy/dx = 2x

Now, plug in the derivative and simplify the expression inside the integral:
sqrt(1 + (2x)^2) = sqrt(1 + 4x^2)

Now, set up the integral with the surface area formula:
Surface Area = 2 * pi * ∫[x * sqrt(1 + 4x^2)] dx from x = 0 to x = 2.

Next, we will approximate the integral using a calculator:
Approximate Integral ≈ 9.8433

Finally, multiply by 2 * pi:
Surface Area ≈ 2 * pi * 9.8433 ≈ 61.9362

So, the surface area of the volume generated when the curve revolves around the y-axis is approximately 61.9362 (rounded to four decimal places).

Part A: The theoretical probability of drawing a red card is 0.32 or 32%.

Part B: The experimental probability of drawing a red card is 0.38 or 38%, and it is 6% greater than the theoretical probability.

Part A: The theoretical probability of drawing a red card from the hat is the number of red cards divided by the total number of cards in the hat:

[tex]P_{red}[/tex] = 8 ÷ (8 + 6 + 7 + 4)

= 8 ÷ 25

= 0.32 or 32%.

Part B: The experimental probability of drawing a red card can be calculated by dividing the number of times a red card was drawn by the total number of trials:

[tex]P_{red}[/tex] = 437 ÷ 1150

= 0.38 or 38%.

The difference between the experimental probability and the theoretical probability can be calculated as follows:

0.38 - 0.32

= 0.06 or 6%

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The constant of proportionality is calculated as:

Option D: 8.5

The constant of proportionality is defined as the constant value of the ratio between two proportional quantities.

Now, we are given a table of values and as such, we can find the constant of proportionality from the formula:

k = y/x

From the table, we have:

k = 25.50/3

k = 8.5

k = 42.5/5

k = 8.5

k = 59.50/7

k = 8.5

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The solution of the system of equations:

2x+2y+ 6z = 8

5x+6y + 5z = 3

5x + 6y + 3z = 5

Is the one in option a.

(x= 34, y = -27,z = -1)

Here we have the system of equations:

2x+2y+ 6z = 8

5x+6y + 5z = 3

5x + 6y + 3z = 5

If we subtract the third equation from the second one we will get:

(5x + 6y + 5z) - (5x + 6y + 3z) = 3 - 5

5z - 3z = -2

We just removed two of the variables, so we can now solve this linear equation for z so we get:

2z = -2

z = -2/2

z = -1

We know that the value of z is -1, that is enough to identify the correct option because only one of these has z = -1  which is the first one, so that is the correct option.

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a) Check the graph for normality as small sample sizes can affect normality tests. b) The hypothesis is inconclusive; the mean may not be less than 40.

c) To reduce margin of error, increase sample size or decrease confidence level. One-tailed hypothesis with t-score = -1.073, df = 9, sig level = 0.5.

a) It is necessary to inspect the graph of the sample data because the normality tests like K-S Test or Anderson Darling test or any test aren't very powerful when it comes to the small sample data. That is why we always need to examine the plot and use our own judgement to whether it is normal or not rather than relying solely on the hypothesis tests. Smallest deviations in the dataset can generate the statistically significant p-value which is not good for the small sample data and these tests are robust against the making of decision like normality due to the certain effects of central limit theorem.

b) The hypothesis would be as followed:

H o: μ=40

H₁: μ<40

t = (X-μ)/(s/√n)

t = (X-μ)/(s/√n) = (37.4 - 40)/(7.662/√10)

t = -2.6/2.423

t = -1.073

p-value= 0.1556

Based on the above calculation, p-value> alpha value which shows that we have insignificant results and we fail to reject the hypothesis. There is no sufficient evidence that the average number of pepperonis is less than 40.

c) Current margin of error would be:

M.E = (t₀.₉₅,₉)(s/√n)

M.E = (2.262)(7.662/√10)

M.E = 5.481

Two ways to reduce the margin error would be:

1) Increase the sample size, margin of error will be reduced as the sample size is inversely proportional.

2) Reduce the confidence level like instead of 95% use 90% or less.

T-Score: -1.073

DF: 9

Significance Level: 0.5

One-tailed or two-tailed hypothesis: One-tailed

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Complete question is below