1
5
x + 1
3
= −1
2
x + 8
3

The critical value for the left-tailed test is −2.0537.

For a left-tailed test, when α=0.02, the critical z-value is the value on the horizontal axis of the z- or standard normal distribution curve such that the area under the curve to the left of this critical value is 0.02.

Using a standard normal distribution table,

Z-Score, also known as the standard score, indicates how many standard deviations an entity is, from the mean.

There are two z-score tables which are:

Now 0.5-α=0.5-0.02

=0.48

So 0.48 is closest in z score table is z=2.05

The left-tailed critical value always negative(-).

So, the value is -2.05.

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Answer: B. statistic

Step-by-step explanation: A characteristic, usually a numerical value, which describes a sample, is called a statistic.

If the distribution of observations were perfectly symmetrical and unimodal, option B) The mean, median, and mode would be the same.

In a perfectly symmetrical and unimodal distribution, the mean, median, and mode would be equal. This is because in such a distribution, the data would be evenly spread around a central value. The mean is calculated by summing all the observations and dividing by the total number of observations. Since the distribution is symmetrical, the sum of the observations on one side of the central value would be equal to the sum on the other side, resulting in a balanced mean.

The median is the middle value when the observations are arranged in ascending or descending order. In a symmetrical distribution, the middle value would be the same as the central value, leading to the median being equal to the mean.

The mode represents the value that appears most frequently in the distribution. In a perfectly symmetrical and unimodal distribution, all values would occur with the same frequency, resulting in multiple modes. However, since the distribution is unimodal, meaning it has only one peak, all the modes would coincide, and the mode would also be equal to the mean and median. Therefore, in a perfectly symmetrical and unimodal distribution, the mean, median, and mode would all be the same value, leading to answer B) The mean, median, and mode would be the same.

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If the two prisms are stacked on top of each other then the height of the prism is 30 inches. Then the volume of the prism will be 1080 in³.

A rectangular prism is a closed solid that has two parallel rectangular bases connected by a rectangle surface.

A toy store is building a display with two rectangular prisms.

The base of each prism is a square with an edge length of 6 inches.

One prism is 10 inches tall and the other is twice as tall.

The two prisms are stacked on top of each other.

Then the total volume of the display will be

The volume of the prism will be

Volume = Base area × Height

Then the height of the second prism will be

h₂ = 2 × 10 = 20 inches

Then the volume of the prism will be

Volume = 6 × 6 × 10 + 6 × 6 × 20

Volume = 360 + 720

Volume = 1080 cubic inches

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To solve the given integro-differential equation, we can use the Laplace transform method.

First, we take the Laplace transform of both sides of the equation and solve for the transformed function Y(s). Then, we inverse Laplace transform Y(s) to obtain the solution y(t) in the time domain.

To convert the integro-differential equation into an initial value problem, we differentiate the equation with respect to t multiple times until the integral term disappears. This results in a differential equation involving derivatives of y(t) only. We can then solve this initial value problem by finding the solution that satisfies the given initial condition.

Finally, we compare the solution obtained from the initial value problem with the solution obtained using the Laplace transform method to verify that they are the same.

To solve part i), we apply the Laplace transform to both sides of the integro-differential equation. After solving for the transformed function Y(s), we take the inverse Laplace transform to obtain y(t).

For part ii), we differentiate the integro-differential equation with respect to t, removing the integral term. We continue differentiating until the equation involves only derivatives of y(t). This results in an initial value problem that can be solved by finding the solution that satisfies the given initial condition.

In part iii), we solve the initial value problem obtained in part ii) to find the solution y(t). We compare this solution with the one obtained from the Laplace transform method in part i) to ensure they are identical, thus confirming the correctness of the solution.

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Matilda have the following equation:

To proof:

So, the values of x and y are:

In the options available , the correct is x=10 and y =2 becuase:

The regression equation b₀b₁x algebraically describes the relationship between the two variables, x and y.

The dependent variable is predicted value in basic linear regression is given by the equation = b0 + b1x. In order to minimize the total sum of squared errors, the values of b0 and b1 are derived from the data using the equation line = b₀ + b₁X.

Given that, b₀+b₁x algebraically describes the relationship between the two variables, x and y.

Therefore, the regression equation b₀b₁x algebraically describes the relationship between the two variables, x and y.

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The table that represents a linear function is Table 1. Thus, the correct option is A.

A linear equation is an equation in which each term has at max one degree. Linear equation in variable x and y can be written in the form y = mx + c.

Linear equation with two variables, when graphed on a cartesian plane with axes of those variables, give a straight line.

We know that, slope m= (y2-y1)/(x2-x1)

Table 1:

Put (x1, y1)=(1, 5) and (x2, y2)=(2, 9) in slope formula

That is, (9-5)/(2-1)

= 4

Similarly, the slope between last two points is (9-5)/(4-1)

=4

Table 2:

Put (x1, y1)=(1, -5) and (x2, y2)=(2, 10) in slope formula

That is, (10+5)/(2-1)

= 15

Similarly, slope between last two points (20+15)/(4-3)

=35

Hence, the table that represents a linear function is Table 1. Thus, the correct option is A.

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Part a: Point D that partitions line segment AB in a 1:2 ratio: D(x,y) = (4, 3).

Part a: Point E that partitions segment AC in a 1:2 ratio: E(x,y) = (8/3, 5).

section formula:

(x,y ) = (m.x2 + n.x1 / (m + n) , m.y2 + n.y1 / (m + n) )

Part a: Point D that partitions segment AB in a 1:2 ratio.

m = 1 and n = 2

A(1, 3) and B(10,3)

D(x,y) = (1*10 + 2*1 / 1+2 , 1*3 + 2*3 / 1+2)

D(x,y) = (12/3 , 9/3)

D(x,y) = (4, 3)

Part a: Point E that partitions segment AC in a 1:2 ratio.

m = 1 and n = 2

A(1, 3) and C(6,9)

E(x,y) = (1*6 + 2*1 / 1+2 , 1*9 + 2*3 / 1+2)

E(x,y) = (8/3 , 15/3)

E(x,y) = (8/3, 5)

Triangle ADE is similar to the triangle ABC.

Triangle ADE is a dilation of triangle ABC by a scale factor of 1/2 using A as the center.

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According to CDC data as of 2021, the average height for adult men in the United States is around 5 feet 9 inches (69.2 inches or 175.7 cm), and the average height for adult women is around 5 feet 4 inches (64.2 inches or 162.5 cm).

Height is a measure of the distance between the base of an object and its highest point. Human height is commonly described as the vertical distance between the bottom of the feet and the top of the head. Height is generally measured in centimetres or feet and inches. Height is an important physical feature that can be influenced by both inherited and environmental factors such as nutrition and physical activity.

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Answer:

9/2 but you have to simplify it

Step-by-step explanation:

Answer:  3

Step-by-ste3p explanation:

Answer:

-1

Step-by-step explanation:

Answer in attachment.

Hope it helps :)

Answer:

40

Step-by-step explanation:

area of shaded region = area of whole figure - area of non shaded region

area of whole figure: The whole figure is a rectangle

The area of a rectangle can simply be calculated by multiplying the width by the length

The given width is 10ft and the given length is 8ft

Hence area of whole figure = 10 * 8 = 80ft²

Area of non shaded region: the non shaded region also creates a rectangle

Like stated previously the area of a rectangle can simply be calculated by multiplying the width by the length

The given width is 5ft and the given length is 8ft

Hence, area of non shaded region = 5 * 8 = 40ft²

Finally we can find the area of the shaded region.

We can easily do this my subtracting the area of the nonshaded region from the area of the whole figure

If we have identified that the area of the whole figure is 80 and the area of the non shaded region is 40

Then, area of shaded region = 80 - 40 = 40ft²

Answer: A (4, -7) B (9, -7)

Step-by-step explanation:

When it’s reflected over the x-axis, the y coordinates become negative but the x coordinates don’t change

x coordinates: 4, 9

y coordinates: 7, 7

Reflected over x-axis: (4, -7), (9, -7)

The percentage of people who do not like to listen to radio as well as watch the television is 65%.

It is important to note that a percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.

From the information, 36% like to listen to radio as well as watch the television.

Therefore, the percentage of the people who do not like to listen to radio as well as watch the television will be:

= 1 - 35%

= 65%

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In a survey of a community. 55% of the people like to listen the radio, 65% like to watch the television and 35% like to listen the radio as well as watch the television

Find the percentage of the people who do not like to listen radio as well as watch the television.

After considering the given data we conclude that there truth table is possible and is placed in the given figures concerning every sub question.

A truth table is a overview that projects  the truth-value of one or more compound propositions for each possible combination of truth-values of the propositions starting up the compound ones.
Every row of the table represents a possible combination of truth-values for the component propositions of the compound, and the count of rows is described by the range of possible combinations.
For instance, if the compound has just two component propositions, it comprises  four possibilities and then four rows to the table. The truth-value of the compound is projected on each row comprising the truth functional operator.
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11 + 55y = 2,981

Explanation:

To solve for y, we need to isolate it on one side of the equation. We can do this by subtracting 11 from both sides and then dividing both sides by 55:

11 + 55y = 2,981

55y = 2,981 - 11

55y = 2,970

y = 2,970/55

y = 54

Therefore, y = 54 is the solution to the equation 11 + 55y = 2,981.

Answer:

54

Step-by-step explanation:

55y+11=2981

55y=2970

-11      -11

55y/55=2970/55  

y=54

(a) The 95% confidence interval is approximately (908.32, 939.68), meaning we can be 95% confident that the true mean life span falls within this range. (b) The 90% lower confidence bound is approximately 920.58, representing the minimum likely value for the mean life span with 90% confidence.

To construct confidence intervals for the mean life span of high-performance halogen headlight bulbs, we use a random sample of 25 bulbs with an average life span of 924 hours and a sample standard deviation of 40 hours. For a 95% two-sided confidence interval, we calculate the margin of error and determine the range within which the true mean life span is likely to fall. Additionally, for a 90% lower confidence bound, we find the lower limit of the range representing the minimum likely value for the mean life span.

A. To construct a 95% two-sided confidence interval on the mean life span, we use the formula: x ± Z * (s / sqrt(n)), where x is the sample mean, s is the sample standard deviation, n is the sample size, and Z is the critical value corresponding to the desired confidence level. For a 95% confidence level, the critical value is approximately 1.96. Substituting the given values, we have x ± 1.96 * (40 / sqrt(25)), which simplifies to 924 ± 1.96 * 8. Therefore, the 95% confidence interval is approximately (908.32, 939.68), meaning we can be 95% confident that the true mean life span falls within this range.

B. To construct a 90% lower confidence bound on the mean life span, we calculate the lower limit using the formula: x - Z * (s / sqrt(n)). For a 90% confidence level, the critical value is approximately 1.645. Substituting the given values, we have 924 - 1.645 * (40 / sqrt(25)), which simplifies to 920.58. Therefore, the 90% lower confidence bound is approximately 920.58, representing the minimum likely value for the mean life span with 90% confidence.


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The return value of the function call round(3.14159, 3) is c. 3.14. The round function rounds the first argument (3.14159) to the number of decimal places specified in the second argument (3). In this case, it rounds to 3.14.

The function call in your question is round(3.14159, 3). The "round" function takes two arguments: the number to be rounded and the number of decimal places to round to. In this case, the number to be rounded is 3.14159 and the desired decimal places are 3.

The return value is the result of the rounding operation. In this case, rounding 3.14159 to 3 decimal places gives us 3.142.

So, the correct answer is:

b. 3.142

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The coefficient of the third term, \(-6xy^2\), in the expression \(5x^{(3y^4+7x^2y^3-6xy^2-8xy)}\), is -6.

The given expression is \(5x^{(3y^4+7x^2y^3-6xy^2-8xy)}\).

In the given expression, there are 4 terms. The third term in the expression is \(-6xy^{(2)}\).To find the coefficient of this third term, we need to isolate the term and see what multiplies the term.In the third term, \(-6xy^{(2)}\), the coefficient of \(xy{^(2)}\) is -6.

Therefore, the coefficient of the third term in the expression \(5x^{(3y^4+7x^2y^3-6xy^2-8xy)}\) is -6. The coefficient of a term in an expression is the number that multiplies the variables in the term.

In other words, it is the numerical factor of a term. In this case, the coefficient of the third term in the given expression is -6.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)

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Answer: yes because of what is given

Step-by-step explanation: Exactly.

Richard's net pay for the week, considering Social Security, Medicare, and FIT deductions, can be calculated by subtracting the total deductions from his gross earnings.

First, let's determine the amount deducted for Social Security. The Social Security rate is 6.2%, and the maximum earnings subject to this deduction are $118,500. Since Richard is $1,000 below the maximum level, the amount subject to Social Security deduction is $1,000. Therefore, the Social Security deduction is 6.2% of $1,000.

Next, we calculate the Medicare deduction. The Medicare rate is 1.45%, and it is applied to the entire earnings of $1,700.

To calculate the FIT deduction, we need additional information about Richard's taxable income, tax brackets, and exemptions. Without this information, we cannot provide an accurate calculation for the FIT deduction.

Finally, we subtract the total deductions (Social Security, Medicare, and FIT) from Richard's gross earnings of $1,700 to obtain his net pay for the week.

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False. A linear programming problem can include more than one decision variable. Linear programming is a mathematical method used to find the optimal solution for a problem with multiple constraints and objectives, often related to maximizing or minimizing a certain value.

Decision variables are the variables that determine the potential solutions, and their values can be changed to affect the outcomes.

In many practical situations, there are multiple decision variables involved. For instance, a company may need to determine the optimal production quantities for different products, subject to resource constraints and market demands. In this case, the decision variables would represent the production quantities for each product, and there would be more than one variable.

In conclusion, the statement that a linear programming problem cannot include more than one decision variable is false. Multiple decision variables can be present in a linear programming formulation to address complex problems that involve multiple choices and constraints.

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Using the formula for the closest integer, it is found that Alejandro is not correct, as the integer is of 48 and not 52.

The integer that has square root n is given by:

S(n) = n².

Hence the integer that has a square root closest to n is given by:

C(n) = n² - 1.

In this problem, we want the square root closest to n = 7, hence:

C(7) = 7² - 1 = 48.

Which is a different value than 52, hence Alejandro is not correct.

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The equation \(\pi d|n, d = n^{(d(n)/2)}\) can be proven using the concept of Euler's product formula and the properties of exponents.

Let's consider a positive integer n and its prime factorization: \(n = p_1 ^{a_1} * p_2 ^{a_2} * ... *p_k ^{a_k}\), where p₁, p₂, ..., pₖ are distinct prime numbers and α₁, α₂, ..., αₖ are positive integers. For any positive divisor d of n, we can write d = p₁^β₁ * p₂^β₂ * ... * pₖ^βₖ, where 0 ≤ β₁ ≤ α₁, 0 ≤ β₂ ≤ α₂, ..., 0 ≤ βₖ ≤ αₖ.

Now, let's examine the product ∏d|n, d, which represents the product of all positive divisors of n. According to Euler's product formula, this product can be expressed as \(\pi d|n, d = p_1^{0} * p_1^{1} * ... * p_1^{a_1}* p_2^{0} * p_2^{1} * ... * p_2^{a_2} * ... * p_k^{0] * p_k^{1} * ... * p_k^{a_k}\)

Simplifying this product, we obtain \(\pi d|n, d = p_1^{(0+1+...+a_1)} * p_2^{(0+1+...+a_2)} * ... * p_k^{(0+1+...+a_k)}\).

The sum of the exponents within each prime factor term is equal to the sum of the positive divisors of each prime factor raised to the power of β, where β ranges from 0 to α. Therefore, this sum can be written as d(n)/2, where d(n) is the Euler's totient function of n. Hence, we have \(\pi d|n, d = n^{(d(n)/2)}\), which proves the equation.

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Answer:

c.15 to 10

Step-by-step explanation:

The ration 12 to 8 means that for every 12 lions there are 8 tigers in the zoo.

Ratios have the quality of conservate their meaning when both values in the ratio are multiplied or divided by the same number.

For example:

a ratio of 2 to 4 is the same as a ratio of 3 to 6 (both values are multiplied by 1.5 (or in fraction by 3/2) ).

in the same way that the ratio 9 to 3 is the same as 3 to 1 (divide both values by 3).

In this case we are looking for an equivalent ratio to the 12 to 8 ratio, the answer is

c.15 to 10

because this results from multiplying the two original values by 1.25 or, in fraction, by 5/4. You can see this becase

12*1.25 = 15

and

8*1.25 = 10

we get that when we multiply the ratio 12 to 8 by 1.5 the equivalent ratio is option C.

Answer:

v=20π ft/s

Step-by-step explanation:

Given:

Distance from the security car to the movie theater, D=25 ft

Distance of the reflection from the car, d=30 ft

Speed of rotation of the strobe lights, 2 rev/s

To find the speed at which the reflection of the security strobe lights is moving along the wall of the movie theater, we need to calculate the linear velocity of the reflection when it is 30 ft from the car.

We can start by finding the angular velocity in radians per second. Since the strobe lights rotate at 2 revolutions per second, we can convert this to radians per second.

ω=2πf

=> ω=2π(2)

=> ω=4π rad/s

The distance between the security car and the reflection on the wall of the theater is...

r=30-25= 5 ft

The speed of reflection is given as (this is the linear velocity)...

v=ωr

Plug our know values into the equation.

v=ωr

=> v=(4π)(5)

∴ v=20π ft/s

Thus, the problem is solved.

The speed of the reflection of the security strobe lights along the wall of the movie theater is 2π ft/s.

To solve this problem, we can use the concept of related rates. Let's consider the following variables:

x: Distance between the security car and the movie theater wall

y: Distance between the reflection of the security strobe lights and the security car

θ: Angle between the line connecting the security car and the movie theater wall and the line connecting the security car and the reflection of the strobe lights

We are given:

x = 25 ft (constant)

y = 30 ft (changing)

θ = 2 revolutions per second (constant)

We need to find the speed at which the reflection of the security strobe lights is moving along the wall (dy/dt) when the reflection is 30 ft from the car.

Since we have a right triangle formed by the security car, the movie theater wall, and the reflection of the strobe lights, we can use the Pythagorean theorem:

x^2 + y^2 = z^2

Differentiating both sides of the equation with respect to time (t), we get:

2x(dx/dt) + 2y(dy/dt) = 2z(dz/dt)

Since x is constant, dx/dt = 0. Also, dz/dt is the rate at which the angle θ is changing, which is given as 2 revolutions per second.

Plugging in the known values, we have:

2(25)(0) + 2(30)(dy/dt) = 2(30)(2π)

Simplifying the equation, we find:

60(dy/dt) = 120π

Dividing both sides by 60, we get:

dy/dt = 2π ft/s

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