7.
Here is a fair 6-sided spinner.


Liz is going to spin the spinner 120 times.
(b) Work out an estimate for the number of times the spinner will land on 7

The option that would have the same value as required is option A.

Equivalent exponents are any two or more exponents that, when added to a base number, produce the same value or result. In other words, equivalent exponents are various ways of expressing the same exponentiation-based mathematical action.

We now have that;

[tex](49^2/5) (7^- 3/4)\\(7^2)^2/5 (7^-3/4)\\(7^4/5) (7^-3/4)\\7^ (4/5 - 3/4)\\7^ 1/20[/tex]

Thus the correct expression is the one that is shown in option A above here.

Learn more about equivalent exponents:https://brainly.com/question/28611407

#SPJ1

The light should be placed in the middle of the triangle parkway in order to meet the aim of having it at the same distance from each of the three roadways.

Since we want the light to be equally far from all three streets in this scenario, that means we want it to be equally far from each side of the triangle parkway.

In light of this requirement, the lamppost ought to be put in the middle of the triangle parkway. This is due to the incenter's equidistant location from all three sides, which ensures that the distance between the lamppost and each side of the triangle is equal.

More about the triangle link is given below.

https://brainly.com/question/25813512

#SPJ1

The statement that explains why Oliver is incorrect is  1 - (-1) tan(x) simplifies to 2tan(x), not 1 + tan(x).

We can show that Oliver is incorrect in his simplification of the expression tan 4 as -1 by simplifying it as follow:

Oliver's work:

tan = 3 T tan +x3π

1 - tan = -1 + tan(x)

tan(x) 3 T 4 - 1 + tan(x)

1 - (-1) tan(x) - 1 + tan(x)

1 + tan(x) +X

We notice that Oliver has incorrectly assumed that 1 - (-1) is equal to 1+tan(x), which lead him to incorrectly conclude that tan 4 simplifies to -1.

Learn more about  simplification at: https://brainly.com/question/28595186

#SPJ1

The exponential regression of the data is  y = 3.143 * 6.064ˣ

Exponential regression is a statistical technique used to model and analyze data that follows an exponential trend. It involves finding the equation of an exponential function that best fits a set of data points. The exponential regression equation has the general form:

y = abˣ

where y is the dependent variable, x is the independent variable, and a and b are the regression coefficients to be determined.

From the given data;

The regression equation is y = 3.143 * 6.064ˣ

The correlation of the data (r) = 0.9941

The r-squared of the data (r²) = 0.9883

Learn more on exponential regression here;

https://brainly.com/question/9302810

#SPJ1

Thus, the equation of tangent line y(x) to the curve r(t) = ⟨7t, 4t⟩ at the point t=1.

To find the equation of the tangent line y(x) to the parametric curve r(t) = ⟨7t, 4t⟩ at the point t=1, we'll first need to find the coordinates of the point and the slope of the tangent line.

At t=1, the coordinates of the point are:
x = 7(1) = 7
y = 4(1) = 4

So the point is (7, 4).

Now we need to find the derivatives of x(t) and y(t) with respect to t:
dx/dt = 7 (since x(t) = 7t)
dy/dt = 4 (since y(t) = 4t)

At t=1, the slope of the tangent line is given by the ratio dy/dx:
slope = (dy/dt) / (dx/dt) = 4 / 7

Now we can use the point-slope form of the equation of a line:
y - y1 = m(x - x1)

where m is the slope and (x1, y1) is the point (7, 4). Plugging in our values, we get:
y - 4 = (4/7)(x - 7)

This is the equation of the tangent line y(x) to the curve r(t) = ⟨7t, 4t⟩ at the point t=1.

Know more about the equation of tangent line

https://brainly.com/question/30162650

#SPJ11

The expression that represents the perimeter of the triangle is 5x - 2.

Writing an expression

From the question, we are to write an expression that represents the perimeter of the triangle

From the given information,

"The length of the base of the triangle is represented by x"

and

"The legs are 1 unit less than twice the length of the base"

∴ One leg of the triangle = 2x - 1

The perimeter of a rectangle is the sum of all the sides

Thus,

Perimeter of the isosceles triangle = 2x - 1 + 2x - 1 + x

Perimeter of the isosceles triangle = 2x +2x + x - 1 - 1

Perimeter of the isosceles triangle = 5x - 2

Hence, the expression that represents the perimeter of the triangle is

5x - 2

Learn more on Writing an expression here: brainly.com/question/24382052

#SPJ1

complete question:

In an isosceles triangle (a triangle where two of the three sides called legs are equal), the legs

are 1 unit less than twice the length of the base. If the length of the base of the triangle is

represented by x, create an expression that represents the perimeter of the triangle.

The solution to the initial value problem is y(t) = -1 + e^t, y(0) = 0.

To solve the initial-value problem using the Laplace transform, we first apply the transform to both sides of the differential equation, using the linearity and derivative properties of the transform:

L{dy/dt} - L{y} = L{1}

sY(s) - y(0) - Y(s) = 1/s

sY(s) - Y(s) = 1/s

Next, we solve for Y(s):

Y(s) = 1/(s(s-1))

We can simplify this expression using partial fractions:

Y(s) = A/s + B/(s-1)

1/(s(s-1)) = A/(s) + B/(s-1)

Multiplying both sides by s(s-1), we get:

1 = As - A + Bs - B

Setting s=0, we get:

1 = -A

A = -1

Setting s=1, we get:

1 = B

B = 1

Therefore, the Laplace transform of the solution y(t) is:

Y(s) = (-1/s) + (1/(s-1))

Taking the inverse Laplace transform, we get:

y(t) = -1 + e^t

Therefore, the solution to the initial-value problem is:

y(t) = -1 + e^t, y(0) = 0

Learn more about initial value here

https://brainly.com/question/2546258

#SPJ11

When testing the goodness of fit for the logistic regression model, if the obtained chi-square is less than the critical value, one would " Accept the null hypothesis". The correct option is c.

In the goodness of fit test for the logistic regression model, the null hypothesis states that there is no significant difference between the observed and expected values. If the obtained chi-square value is less than the critical value, it means that the difference between the observed and expected values is not significant, and hence, we fail to reject the null hypothesis. Therefore, we accept the null hypothesis and conclude that the model fits the data well. On the other hand, if the obtained chi-square value is greater than the critical value, we reject the null hypothesis and conclude that the model does not fit the data well.

The correct option is c.

You can learn more about null hypothesis at

https://brainly.com/question/4436370

#SPJ11

The value of the complementary angle of 54° is determined as  B = 36°.

Two angles are called complementary when their measures add to 90 degrees. Two angles are called supplementary when their measures add up to 180 degrees.

So if the measure of one angle is 54°, the value of its complementary angle is calculated as follows;

Mathematically, the formula for calculating the complementary angle of 54° is given as;

B + 54° = 90

B = 90 - 54°

B = 36°

Thus, the value of the complementary angle of 54° is determined as 36° since both angles will add up to 90 degrees.

Learn more about complementary angles here: https://brainly.com/question/16281260

#SPJ1

The complete question is below:

Use your knowledge of complementary and vertical angles to hit

this shot.

If angle A is 54° and angle B is its complementary angle. Angle B = ?

For Lamar's free-throw attempts, we can find the proportion of shots he made as 4/10 or 0.4. We can use this proportion to estimate how many of his next 20 free-throw attempts he would expect to make by multiplying the proportion by the number of attempts:

Expected number of missed free-throws = (1 - 0.4) x 20 = 12

Therefore, we would expect Lamar to miss 12 of his next 20 free-throw attempts based on his recent performance.

For the trains at Castroville Station, we can find the proportion of trains that were full as 12/18 or 0.67. We can use this proportion to estimate how many of the next 12 trains we would expect to be full by multiplying the proportion by the number of trains:

Expected number of full trains = 0.67 x 12 = 8

Therefore, we would expect 8 of the next 12 trains to be full based on the recent pattern of trains at Castroville Station.

Learn more about Proportion here: brainly.com/question/31548894

#SPJ11

The frequency of the rotor currents on no-load is fr = 0.033 * 60 = 1.98 Hz.

The synchronous speed of the motor is given by

Ns = (120f) / P,

where Ns is the synchronous speed in revolutions per minute (RPM), f is the supply frequency in hertz (Hz), and P is the number of poles.

For the given motor, the synchronous speed is

Ns = (120 * 60) / (6 * 2) = 1200 RPM

On no-load, the rotor speed is equal to the synchronous speed, i.e., N = Ns = 1200 RPM.

The slip of the motor is given by

s = (Ns - N) / Ns,

where N is the rotor speed in RPM.

Thus, the slip of the motor is

s = (1200 - 1160) / 1200 = 0.033 or 3.3%

The frequency of the rotor currents on no-load is given by

fr = s * f,

where f is the supply frequency.

Thus, the frequency of the rotor currents on no-load is

fr = 0.033 * 60 = 1.98 Hz

Learn more about frequency here

https://brainly.com/question/254161

#SPJ11

The term that best describes the disorder that Ahmed has is given as follows:

c. major depression.

What differs depression from the other disorders cited in this problem is the length of the duration of the symptoms.

Ahmed has been feeling the symptoms for the past three weeks, which is a large time, as the other disorders such as anxiety and panic attacks have an alternance of time where the person feel the symptoms with times where the people is feeling good, without the symptoms.

More can be learned about depression at https://brainly.com/question/27643530

#SPJ1

To construct a confidence interval, we need to determine the critical value based on the confidence level and sample size. For a 95% confidence level and a sample size of 7, the critical value is 2.571.

The critical value is used to calculate the margin of error for a confidence interval. It is based on the confidence level and sample size, and it is determined from a t-distribution table or a calculator.

For a 95% confidence level and a sample size of 7, we can find the critical value by looking at the t-distribution table with 6 degrees of freedom (df = n - 1). The 95% confidence level corresponds to a two-tailed test with an alpha level of 0.05, and the critical value for a t-distribution with 6 degrees of freedom and an alpha level of 0.025 (half of 0.05) is 2.571.

Therefore, to construct a 95% confidence interval for a sample size of 7, we can use the formula:

sample mean ± (critical value) x (standard error of the mean)

where the standard error of the mean is calculated as the sample standard deviation divided by the square root of the sample size.

Learn more about Sample Size:

brainly.com/question/25894237

#SPJ11

The probability of a penny falling out is,

⇒ 3 / 11

We have to given that;

A cup has some coins in it.

And, The cup tips over and 1 coin falls out.

Here, By given table;

Total number of coins are,

⇒ 3 + 5 + 2 + 1

And, Number of penny coins are,

⇒ 3

Hence, The probability of a penny falling out is,

⇒ P = number of penny / total number of coins

⇒ P = 3 / 11

So, The probability of a penny falling out is,

⇒ 3 / 11

Learn more about the probability visit:

https://brainly.com/question/13604758

#SPJ1

We often take information from a sample from the population in the process of a statistical investigation because it is often impractical or impossible to collect data from the entire population.

In statistical investigation, a sample is a subset of a population that is selected for study. Collecting data from an entire population can be impractical or impossible due to cost, time, or other constraints. By studying a representative sample, statistical inferences can be made about the entire population with a certain degree of confidence.

The size and selection of the sample are important factors that affect the accuracy of the statistical inference. Generally, larger samples are more representative of the population and lead to more accurate estimates of population parameters.

You can learn more about population at

https://brainly.com/question/29885716

#SPJ11

The volume formula for a pyramid is V = (1/3)bh where b is the base area and h is the height. We are given the volume and base measurements (remember that area for squares and rectangles is length * width), so plug the values into the equation and solve for the height:

8477.3 = (1/3)*34*34h

8477.3=(1156/3)h

25431.9/1156 = h

h is approximately 22 meters

The term that best describes the type of data collected specifically for a particular research project is derived from primary data.

This type of data is collected directly from the source, such as through surveys or experiments, and is tailored to answer specific research questions that have not been satisfactorily addressed by existing secondary data sources. Derived primary data is typically more expensive and time-consuming to collect than secondary data, but it can provide valuable insights that are not available elsewhere.
It is important to note that derived primary data should be collected using sound research methods to ensure its validity and reliability. This includes careful consideration of sampling methods, data collection techniques, and data analysis procedures. Researchers should also be transparent about the limitations of their data and any potential sources of bias or error that could affect their findings.
In contrast, referential data refers to data that are collected from existing sources, such as databases or published reports, and syndicated data refers to data that are collected by third-party research firms and sold to multiple clients. Cohort data refers to data that are collected from a specific group of individuals over time to track changes and trends. While each of these types of data can be useful for research, derived primary data is often the most valuable for answering specific research questions and generating new insights.

Learn more about satisfactorily here:

https://brainly.com/question/5813955

#SPJ11

Answer:

Step-by-step explanation:

For every product sold, the employee's earnings increase by $225.

Option C is the correct answer.

We have,

The expression for the amount of money an employee earns monthly after selling n products is given as:

$1,500 + $225n.

Here,

$1,500 is the fixed monthly earning, and $225n represents the earning from selling n products.

Thus,

For every product sold, the earning increases by $225.

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ1

A sample size of at least 139 should be taken to ensure that the margin of error does not exceed 5, with a population variance of 144 and a 95% confidence level.

Margin of error = Z-score * (σ / √n)
where Z-score is the critical value for the level of confidence (in this case, 95%), σ is the population standard deviation (which is equal to the square root of the variance, so σ = 12), and n is the sample size.

We want the margin of error to be less than or equal to 5, so we can set up the following inequality:
5 ≥ Z-score * (σ / √n)

To find the value of the Z-score for 95% confidence, we can use a standard normal distribution table or calculator. The Z-score for 95% confidence is approximately 1.96.

Substituting the values we have into the inequality, we get:
5 ≥ 1.96 * (12 / √n)

Solving for n, we get:
n ≥ ((1.96 * 12) / 5)²
n ≥ 138.2976

Since we cannot have a fractional sample size, we need to round up to the nearest whole number:
n = 139

Therefore, a sample size of at least 139 should be taken to ensure that the margin of error does not exceed 5, with a population variance of 144 and a 95% confidence level.

In summary, the long answer to your question is that we used the formula for the margin of error, substituted the given values, solved for n, and rounded up to get a sample size of 139.

Know more about sample size here:

https://brainly.com/question/28583871

#SPJ11

The Lagrange form of the polynomial that fits the given data is L(x) = (1/4)*x^3 - (3/2)*x^2 + (17/4)*x - 3.

To find the Lagrange form of the polynomial that fits the given data, we can use the following formula:

Lagrange form:

L(x) = ∑ [y * l_i(x)], i=0 to n

where

l_i(x) = ∏ [(x - x_j)/(x_i - x_j)], j=0 to n, j ≠ i

In this formula, x and y are the given data points, n is the number of data points (n+1 is the degree of the polynomial), and L(x) is the polynomial that fits the data.

Using the given data x = {1, 2, 3, 5} and y = {0, 5, 26, 164}, we can compute the Lagrange form as follows:

l_0(x) = (x - 2)(x - 3)(x - 5)/(1 - 2)(1 - 3)(1 - 5) = -(x^3 - 10x^2 + 31x - 30)/4
l_1(x) = (x - 1)(x - 3)(x - 5)/(2 - 1)(2 - 3)(2 - 5) = (x^3 - 9x^2 + 23x - 15)/2
l_2(x) = (x - 1)(x - 2)(x - 5)/(3 - 1)(3 - 2)(3 - 5) = -(x^3 - 8x^2 + 13x - 6)/2
l_3(x) = (x - 1)(x - 2)(x - 3)/(5 - 1)(5 - 2)(5 - 3) = (x^3 - 6x^2 + 11x - 6)/4

L(x) = 0l_0(x) + 5l_1(x) + 26l_2(x) + 164l_3(x)
= (1/4)*x^3 - (3/2)*x^2 + (17/4)*x - 3

Therefore, the Lagrange form of the polynomial that fits the given data is L(x) = (1/4)*x^3 - (3/2)*x^2 + (17/4)*x - 3.

Learn more about Lagrange here:brainly.com/question/31637769

#SPJ11

Answer:

See below!

Step-by-step explanation:

Hypotenuse = 20

Opposite = 16

Adjacent = 12

Using trigonometric ratios to solve this question.

sin θ = opposite / hypotenuse

sin Z = 16 / 20

sin Z = 4 / 5

We know that,

tan θ = opposite / adjacent

tan Z = 16 / 12

tan Z = 4 / 3

[tex]\rule[225]{225}{2}[/tex]

The probability that at least one die is showing 2 and the sum of the two dice is 6 is 1/18

A probability is a number that reflects the chance or likelihood that a particular event will occur. The certainty of an event to occur is 1 and it equivalent to 100% in percentage.

Probability = sample space /total outcome

The possible total out come for rolling two dice is 36.

For two dice two have a sum of 6 and at least one must show 2, the result must either be 2,4 or 4,2. Therefore the sample space is 2

Therefore the probability of at least one die showing 2 and sum of 6 = 2/36 = 1/18

learn more about probability from

https://brainly.com/question/24756209

#SPJ1

(a) Event "X and Y": F

(b) Event "X or Y": A, B, C, D, F

(c) The complement of the event X: E, F, G

(a) Event "X and Y": F

The letter "F" satisfies both conditions: it comes before "E" (Event X) and it is found in the word "FACE" (Event Y).

(b) Event "X or Y": A, B, C, D, F

The letters A, B, C, D, and F satisfy either condition: they come before "E" (Event X) or they are found in the word "FACE" (Event Y).

(c) The complement of the event X: E, F, G

The complement of Event X includes all the letters that do not come before "E". In this case, the letters E, F, and G do not satisfy the condition of coming before "E".

To learn more about the set;

https://brainly.com/question/8053622

#SPJ1

Answer:

1.5.1 : constant difference is 8

1.5.2: When there are 10 chairs stacked, it's 127 cm tall.

Step-by-step explanation:

There is a linear relationship between the height of the stack and the number of chairs.

1 chair = 55 cm + 0 extra cm = 55cm

2 chairs = 55cm + 8cm = 63 cm

3 chairs = 55cm + 8(2)cm = 71 cm

4 chairs = 55cm + 8(3)cm = 79 cm

1.5.1 the constant difference between all the underlined numbers above is 8.

1.5.2 You could just keep calculating above until you get 127 cm. (Your teacher might not like that, but it's an option!)

You can find the equation & either solve for the number of chairs OR graph it.

So if we let C = the number of stacked chairs, our equation for H (height) would be:

H = 55 + 8(C-1)

If we substitute H = 127, solve for C.

127 = 55+ 8(c-1)

127 = 55+ 8c-8

127 = 47 + 8c

127 -47 = 8c

80 = 8c

10=c

When there are 10 chairs stacked, it's 127 cm tall.

Check that the answer works:

55 cm (1st chair) + 8*9 (8cm for each additional chair) = 55+ 72 = 127 cm

Answer:

[B] 3

Step-by-step explanation:

We can set up a proportion to solve for x:

[tex]\frac{15}{10} =15+\frac{x}{12}[/tex]

[tex]10(15 + x) = 15(12)[/tex]         >> Distribute

[tex]150 + 10x = 180[/tex]               >> Subtract 150 from both side

[tex]10x = 30[/tex]                          >> Divide both side by 10

[tex]x=3[/tex]                               >> Solution

~ Lenvy ♥~

Let's denote the radius of both the hemisphere and the cylinder as "r" and the height of the cylinder as "h".

The volume of the solid is given as 792π cm^3.

The volume of the hemisphere is (2/3)πr^3, and the volume of the cylinder is πr^2h. Since the solid is made up of a hemisphere and a cylinder, we can write the equation:

(2/3)πr^3 + πr^2h = 792π

We can simplify the equation by dividing both sides by π:

(2/3)r^3 + r^2h = 792

Given that the ratio of the radius to the height is 1:3, we can write r = 3h.

Substituting this value into the equation, we get:

(2/3)(3h)^3 + (3h)^2h = 792

Simplifying further:

(2/3)(27h^3) + 9h^3 = 792

18h^3 + 9h^3 = 792

27h^3 = 792

Dividing both sides by 27:

h^3 = 792/27

h^3 = 29.333...

Taking the cube root of both sides:

h ≈ 3.080

Therefore, the height of the solid is approximately 3.080 cm.

Consider the sample mean in random samples of size n from a given population to be a random variable because the outcome of the sample mean is unpredictable.

Outcome of the sample mean can vary from one random sample to another.

The sample mean is computed as the sum of the values in the sample divided by the sample size.

And since the sample is a random sample, the values in the sample are random variables themselves.

This implies, the sample mean is a function of those random variables and, as a result, it is also a random variable.

In other words, the sample mean is not a fixed quantity.

But rather a value that varies depending on the particular random sample that is chosen from the population.

This randomness in the value of the sample mean makes it a random variable.

Therefore, sample mean from a random sample can be random variable because the outcome is unpredictable.

learn more about sample mean here

brainly.com/question/30543966

#SPJ4