A large box of chocolates has a width that is 2 times the height of the box and a length that is 1. 5 times the width of


the box. Each of the 48 chocolates rests in a cube with a side length of 1 inch

Answer:

120 pounds

Step-by-step explanation:

65% of y= 78 pounds

\(\frac{65}{100}\) × y = 78 pounds

65y = 78  × 100=7800

y= 7800/65= 120 pounds

Answer:

NOT nets = A, C, D, F
Nets = B, E, G, H

Figure B (Triangular prism)

SA: 3 rectangles + 2 triangles

Rectangles: (20·8) + (20·10) + (20·6) = 480 ft²

Triangles: (8·6)/2 + (8·6)/2 = 48 ft²

Total SA: 528 ft²

Figure E (Square pyramid)

SA: 1 square + 4 triangles

Square: 10·10 = 100 yd²
Triangles: (12·10)/2 + (12·10)/2 + (12·10)/2 + (12·10)/2 = 240 yd²

Total SA: 340 yd²

Figure G (Rectangular prism)

SA = 2 wide rectangles + 4 narrow rectangles

Wide: (7·11) + (7·11) = 154 cm²

Narrow: (2·7) + (2·7) + (11·3) + (11·3) = 94 cm²

Total SA: 248 cm²

Figure H (Cube)

SA = 6 squares

Squares: 6 x (1·1) = 6 m²

Total SA: 6 m²

I hope this helps and God bless!

Answer:

8

Step-by-step explanation:

x= 3

21-6/3 + 6/2

15/3 + 3/1

5+3=8

Answer:

8

Step-by-step explanation:

plug in 3 for all the x's

7(3)-6/3= 21-6/3=15/3=5

2(3)/2=6/2=3

5+3=8

An ellipsoid is a three-dimensional geometric shape that resembles a stretched or flattened sphere. It is defined by two axes of different lengths and a third axis that is perpendicular to the other two. The equation for the flattening factor is given by \(\(f = \frac{a - b}{a}\),\)where \(a\) represents the length of the major axis and \(b\) represents the length of the minor axis.

An ellipsoid is a geometric shape that is obtained by rotating an ellipse around one of its axes. It is characterized by three axes: two semi-major axes of different lengths and a semi-minor axis perpendicular to the other two. The ellipsoid can be thought of as a generalized version of a sphere that has been stretched or flattened in certain directions. It is used to model the shape of celestial bodies, such as the Earth, which is approximated as an oblate ellipsoid.

An ellipse, on the other hand, is a two-dimensional geometric shape that is obtained by intersecting a plane with a cone. It is defined by two foci and a set of points for which the sum of the distances to the foci is constant. An ellipse differs from a sphere in that it is a flat, two-dimensional shape, while a sphere is a three-dimensional object that is perfectly symmetrical.

The flattening factor (\(f\)) of an ellipsoid represents the degree of flattening compared to a perfect sphere. It is calculated using the equation\(\(f = \frac{a - b}{a}\),\\\) where \(a\) is the length of the major axis (semi-major axis) and \(b\) is the length of the minor axis (semi-minor axis). The flattening factor provides a quantitative measure of how much the ellipsoid deviates from a spherical shape.

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The correct option  a.) 63%, is the percentage of children have a cholesterol level lower than 199.

For the stated question-

Percentage  P(X < 199)

For the given normal distribution :

Z = (score - mean) / SD

Z = (199 - 194) / 15

Z = 5 / 15

Z - score = 0.3333

P(Z < 0.33) :

Use the z - table ;

P(Z < 0.33) = 0.6293

0.6293 * 100% = 62.93%

= 63% (nearest whole percent)

Thus, the percentage of children have a cholesterol level lower than 199 is 63%.

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The plot of y(t) will show how the mass oscillates with time, starting from the equilibrium position and gradually coming to rest due to the damping effect of the friction.

The given equation represents the motion of a mass connected to a spring with viscous friction. To plot the displacement, y(t), we need to solve the differential equation. With initial conditions y(0) = 0, we can find the solution using the Laplace transform. After solving the equation, we can plot y(t) for t < 0 and t ≥ 0 separately. For t < 0, the applied force, f(t), is zero, so the mass will not experience any external force and will remain at rest. For t ≥ 0, the applied force is 10, and the mass will respond to this force and undergo oscillatory motion around the equilibrium position.

To solve the given differential equation, we can start by finding the characteristic equation by setting the coefficients of y, its derivative, and its second derivative to zero:

s^2 + 18s + 102 = 0.

Solving this quadratic equation gives us the roots s1 = -3 + 3i and s2 = -3 - 3i. These complex roots indicate that the mass will undergo damped oscillations.

Using the Laplace transform, we can solve the differential equation and obtain the expression for Y(s), the Laplace transform of y(t):

(s^2 + 18s + 102)Y(s) = F(s),

where F(s) is the Laplace transform of f(t). Since f(t) = 10 for t ≥ 0, its Laplace transform is F(s) = 10/s.

Solving for Y(s) gives us:

Y(s) = 10 / [(s^2 + 18s + 102)].

To find y(t), we need to inverse Laplace transform Y(s). Using partial fraction decomposition, we can express Y(s) as:

Y(s) = A / (s - s1) + B / (s - s2),

where A and B are constants to be determined. After finding A and B, we can inverse Laplace transform Y(s) to obtain y(t).

With the given initial condition y(0) = 0, we can solve for A and B by setting up equations using the initial value theorem:

A / (s1 - s1) + B / (s1 - s2) = 0,

A / (s2 - s1) + B / (s2 - s2) = 0.

Solving these equations will give us the values of A and B. Finally, we can substitute these values back into the inverse Laplace transform of Y(s) to obtain y(t).

For t < 0, since the applied force f(t) is zero, the mass will not experience any external force. Therefore, y(t) will remain at its initial position, y(0) = 0.

For t ≥ 0, the applied force f(t) is 10, and the mass will respond to this force and undergo oscillatory motion around the equilibrium position. The displacement, y(t), will depend on the properties of the mass, the spring, and the viscous friction. The plot of y(t) will show how the mass oscillates with time, starting from the equilibrium position and gradually coming to rest due to the damping effect of the friction.

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The df value for the t statistic computed for the corresponding hypothesis test is 38.

To calculate the degrees of freedom (df) for a t-test in an independent-measures research study, you need to know the sample size of each group.

Since the study compares two treatment conditions and uses a total of 40 participants, we need to assume that the sample size is equal in each group.

Therefore, each treatment condition has 20 participants (40 participants / 2 conditions).

The formula to calculate df for an independent t-test is:

df = (n1 + n2) - 2

where n1 and n2 are the sample sizes for each group.

Substituting the values, we get:

df = (20 + 20) - 2

df = 38

Therefore, the df value is 38

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The unit rate represented by the information is  6/5 mile per hour

The given parameters are

Distance = 2/5 mile

Time = 1/3 hour

The ratio of distance in time is calculated as

Ratio = Distance : Time

This gives

Ratio = 2/5 mile : 1/3 hour

Divide both ratio by 1/3

So, we have

Ratio = 6/5 mile : 1 hour

Express as fraction

Ratio = 6/5 mile/1 hour

This gives

Ratio = 6/5 mile per hour

Hence, the unit rate represented by the information is  6/5 mile per hour

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Answer:

x < 6

Step-by-step explanation:

There is an open circle ( no equals) at 6   and the line goes to the left

This means that it is less than 6

x < 6

Answer:

y = \(\frac{3}{2}\)x + \(\frac{7}{2}\)

Step-by-step explanation:

The base form of the slope-intercept form is y = mx + b. We need to think of this as a system of linear equations problem, where we are solving for m and x using 2 equations. Substituting the x and y coordinates of the 2 points, we have 5 = m + b and -1 = -3m + b.

Let's now solve the system by elimination. We first subtract to eliminate the variable b and we get 6 = 4m, so m = \(\frac{3}{2}\). Then we substitute \(\frac{3}{2}\) for m in any of the equations and we get b = \(\frac{7}{2}\). Thus, the equation of the line that goes through (1, 5) and (-3, -1) is y = \(\frac{3}{2}\)x + \(\frac{7}{2}\).

The percentage of the sheets with no air bubbles is given as follows:

13.53%.

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following mass probability function:

\(P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}\)

The parameters are listed and explained as follows:

The mean for this problem is given as follows:

\(\mu = 2\)

The proportion of these sheets with no air bubbles is P(X = 0), hence it is given as follows:

P(X = 0) = e^-2 = 0.1353 = 13.53%.

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Answer:

6.28

Step-by-step explanation:

2×3.14 because this is just simple multiple

Answer:

C

Step-by-step explanation:

\(42 + 120 = 2 + 160\)

Answer:

third option (7.5, 8)

this option (6, 5, -3)

Step-by-step explanation:

you eliminate one variant by expressing it through the other(s) until you have one equation with one variable.

that you solve, and then you go back to the other elimination expressions to calculate the others.

2x - y = 7

-2x + 3y = 9

since the terms with x are already so similar, we could now simply add both equations and solve that result :

2x + (-2x) -y + 3y = 7+9 = 16

0×x + 2y = 16

2y = 16

y = 8

=>

2x - 8 = 7

2x = 15

x = 7.5

x - 2y - 3z = 5

x + 2y + 3z = 7

x + z = 3

the same trick by adding the first 2 equations

x + x -2y + 2y -3z + 3z = 5 + 7 = 12

2x + 0y + 0z = 12

2x = 12

x = 6

=>

6 + z = 3

z = -3

and then

6 + 2y + 3(-3) = 7

6 + 2y - 9 = 7

2y - 3 = 7

2y = 10

y = 5

Answer:

negative reciprocals

Step-by-step explanation:

The probability that Walmart's quality standard will be satisfied by average weight of a random sample of 10 bags of the Frito-Lay Fiery Mix Variety Pack is calculated using the properties of normal distribution.

The average weight of a random sample of 10 bags from the Frito-Lay Fiery Mix Variety Pack follows a normal distribution with the same mean as the individual bags (556.8g) but with a standard deviation equal to the original standard deviation divided by the square root of the sample size \(\(\frac{{1.2g}}{{\sqrt{10}}}\)\). To find the probability that the average weight falls within Walmart's demanded range (556g to 558g), we need to calculate the area under the normal curve between these two values.

To do this, we can standardize the values by subtracting the mean from each limit and dividing by the standard deviation of the sample mean. This will give us the z-scores for each limit. Using a standard normal distribution table or a statistical calculator, we can find the corresponding probabilities for each z-score. The probability between these two limits represents the chance that Walmart's quality standard will be satisfied.

Please note that the specific decimal value for the probability may vary depending on the z-table or calculator used, but it will typically be a small probability since the demanded range is relatively narrow.

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15625=295.80x is the expression for the given condition.

An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms. In mathematics, an expression is a phrase that has at least two numbers or variables and at least one arithmetic operation. Addition, subtraction, multiplication, or division are all examples of math operations. A number, a variable, or a combination of numbers, variables, and operation symbols constitutes an expression. An equation consists of two expressions joined by an equal sign. Example of a word: the sum of 8 and 3. Example of a word: The product of 8 and 3 equals 11. 8 + 3 is an expression.

Here,

Let x be the number of month to payout.

15625=295.80x

x=52.82

The expression for given condition is 15625=295.80x.

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There are two local minima which are: x = sqrt(12/5), x = -sqrt(12/5)

To find the x-coordinates of all local minima using the second derivative test;

1. Find the first derivative of f(x): f'(x)
2. Set f'(x) to 0 and solve for x to find critical points
3. Find the second derivative of f(x): f''(x)
4. Evaluate f''(x) at the critical points
5. If f''(x) > 0 at a critical point, it is a local minimum

Find the first derivative of f(x) = x^5 - 4x³ + 10:
f'(x) = 5x^4 - 12x²

Set f'(x) to 0 and solve for x:
0 = 5x^4 - 12x²
x² (5x² - 12) = 0

Solutions: x = 0, x = sqrt(12/5), x = -sqrt(12/5)

Find the second derivative of f(x):
f''(x) = 20x³ - 24x

Evaluate f''(x) at the critical points:
f''(0) = 0
f''(sqrt(12/5)) = 20(sqrt(12/5))³ - 24(sqrt(12/5))
f''(-sqrt(12/5)) = -20(sqrt(12/5))³ - 24(-sqrt(12/5))

Determine if the critical points are local minima:
f''(0) = 0, inconclusive
f''(sqrt(12/5)) > 0, local minimum
f''(-sqrt(12/5)) > 0, local minimum

So, there are two local minima: x = sqrt(12/5), x = -sqrt(12/5)

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Answer:

2/5

Step-by-step explanation:

total possibilities = 10

red = 4

4/10

(4:2)/(10:2)

2/5

The area of the regular 12-sided polygon with a radius of 4 units is approximately 31.28 square units.

What is polygon?

A polygon is a two-dimensional geometric shape that is made up of straight lines connecting a sequence of points, which are called vertices.

To find the area of a regular polygon with 12 sides and a radius of 4 units, we can use the formula:

Area = (1/2) * perimeter * apothem

The perimeter of the polygon can be found by multiplying the number of sides by the length of each side. Since the polygon is regular, all sides are of equal length. Let's call this length "s".

s = 2 * r * sin(π/n) where r is the radius and n is the number of sides

s = 2 * 4 * sin(π/12)

s = 1.38 (rounded to two decimal places)

The perimeter of the polygon is:

P = 12 * s

P = 16.56 (rounded to two decimal places)

To find the apothem, we can use the formula:

apothem = r * cos(π/n)

apothem = 4 * cos(π/12)

apothem = 3.77 (rounded to two decimal places)

Now we can calculate the area of the polygon:

Area = (1/2) * P * apothem

Area = (1/2) * 16.56 * 3.77

Area = 31.28 square units (rounded to two decimal places)

Therefore, the area of the regular 12-sided polygon with a radius of 4 units is approximately 31.28 square units.

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The sum of the angle measures of the polygon is 540°, the value of x is 5.

The sum of the angle measures of the polygon is 540°.

We know that the sum of the interior angles of a polygon of n sides = (n – 2) × 180°. = 3× 180°= 540°

If a polygon has x sides, then the sum of its angle measures can be found using the formula:

Therefore, for a polygon with x sides, the equation becomes:

⇒(x-2) * 180° = 540°

Solving for x, we get:

⇒x = (540° + 360°) / 180° + 2

⇒x = 3 + 2

⇒x = 5

So, the polygon has 5 sides.

Therefore, the value of  x is 5.

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The time waveform for f(t) = cos(cot[u(t+T)−u(t−T)]) is a periodic waveform with a duration of 2T. For f(t) = A[u(t+3T)-u(t+T)+"(t-T)-n(t-3T)], the time waveform is a combination of step functions and a linear ramp.

In the first part, the function f(t) = cos(cot[u(t+T)−u(t−T)]) involves the cosine function and two unit step functions. The unit step functions, u(t+T) and u(t-T), are responsible for switching the cosine function on and off at specific time intervals. The cotangent function determines the frequency of the cosine waveform. Overall, the waveform exhibits a periodic nature with a duration of 2T.

In the second part, the function f(t) = A[u(t+3T)-u(t+T)+"(t-T)-n(t-3T)] combines step functions and a linear ramp. The unit step functions, u(t+3T) and u(t+T), control the presence or absence of the linear ramp. The ramp is defined by "(t-T)-n(t-3T)" and represents a linear increase in amplitude over time. The negative term, n(t-3T), ensures that the ramp decreases after reaching its maximum value. This waveform has different segments with distinct behaviors, including steps and linear ramps.

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The linear formula to depict the change in altitude as a function of time (in minutes) is: altitude (in feet) = -25 × time (in minutes) + 3000.

The change in altitude is a linear function of time, with a slope of -500 feet per 20 minutes, since the hiker is descending. To find the y-intercept, we can use the initial altitude of 3000 feet.

Let y be the altitude in feet and x be the time in minutes. Then the formula is:

y = mx + b

where m is the slope and b is the y-intercept.

Substituting the given values, we get:

y = -25x + 3000

Therefore, the linear formula to depict the change in altitude as a function of time (in minutes) is:

altitude (in feet) = -25 × time (in minutes) + 3000.

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Answer

y = f(x) = 3x - 1

Explanation

The general form of the equation in point-slope form is

y - y₁ = m (x - x₁)

where

y = y-coordinate of a point on the line.

y₁ = This refers to the y-coordinate of a given point on the line

m = slope of the line.

x = x-coordinate of the point on the line whose y-coordinate is y.

x₁ = x-coordinate of the given point on the line

Two lines that are parallel to each other have the same slope.

If the equation of a straight line is written in the form of y = 3x - 6,

,The slope and y-intercept form of the equation of a straight line is given as

y = mx + c

where

y = y-coordinate of a point on the line.

m = slope of the line.

x = x-coordinate of the point on the line whose y-coordinate is y.

c = y-intercept of the line.

So, in y = 3x - 6, the slope = m = 3

So, using the point-slope form,

y - y₁ = m (x - x₁)

m = 3

(x₁, y₁) = (2, 5)

x₁ = 2, y₁ = 5

y - y₁ = m (x - x₁)

y - 5 = 3 (x - 2)

y - 5 = 3x - 6

y = 3x - 6 + 5

y = 3x - 1

In function notation, y = f(x)

So, the equation of the line required is

y = f(x) = 3x - 1

Hope this Helps!!!

There are several tests that use the chi-squared distribution, including the chi-square goodness-of-fit test, chi-square test of independence, and chi-square test for homogeneity.

These tests are used to analyze categorical data and determine if there is a significant association or difference between variables.

1. Chi-square Goodness-of-Fit Test:

  This test is used to determine if observed data fits a specific theoretical distribution. It compares the observed frequencies in different categories with the expected frequencies based on a hypothesized distribution.

2. Chi-square Test of Independence:

  This test is used to examine the relationship between two categorical variables. It determines if there is a significant association between the variables by comparing the observed frequencies in a contingency table with the expected frequencies assuming independence.

3. Chi-square Test for Homogeneity:

  This test is used to compare the distribution of a categorical variable across different groups or populations. It determines if there is a significant difference in the proportions of the variable between the groups by comparing the observed frequencies in multiple contingency tables.

In each of these tests, the chi-square test statistic is calculated by summing the squared differences between observed and expected frequencies, divided by the expected frequencies. The resulting test statistic follows a chi-square distribution with degrees of freedom determined by the number of categories or groups.

To make a conclusion, the test statistic is compared to the critical value from the chi-square distribution with a given significance level. If the test statistic exceeds the critical value, we reject the null hypothesis and conclude that there is evidence of a relationship or difference between the variables.

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Answer:

\(\displaystyle \frac{3\sqrt{230}}{5}\)

Step-by-step explanation:

Use the Pythagorean Theorem:

\(\displaystyle a^2 + b^2 = c^2 \\ \\ 9,7^2 + b^2 = 13,3^2; \sqrt{82,8} = \sqrt{b^2} \\ \\ \frac{3\sqrt{230}}{5}\:[or\:9,0994505329...] = b\)

So, you have this:

\(\displaystyle 9,1 ≈ b\)

I am joyous to assist you at any time.

The sample size should be taken so that the margin of error does not exceed 5 is 829.

The term confidence interval is known as the probability that a population parameter will fall between two set values.

Here we have given that it is known that the population variance is 144.

And we need to find . at 95% confidence, what sample size should be taken so that the margin of error does not exceed 5

While we looking into the given question, we know that the variance is 144.

And the confidence interval is 95%.

Now, as per the formula of margin of error, the sample size is calculated as,

=> SE = σ / √n

Apply the given values on it, then  we get,

=> 5 = 144/√n

=> √n = 144/5

=> n = (28.8)²

=> n = 829.44

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To check whether the sequence converges or diverges, we examine the behaviour of the sequence as n approaches infinity. Here the sequence converges to the value 13/14.

Let's analyze the given sequence: an = \((4 + 13n^2) / (n + 14n^2).\)

As n approaches infinity, the dominant terms in both the numerator and denominator become the highest power of n. In this case, it is the term 13n² in the numerator and the term 14n² in the denominator.

Dividing both the numerator and denominator by n², we get:

an = \((4/n^2 + 13) / (1/n + 14).\)

As n approaches infinity, \(4/n^2\)tends to 0, and 1/n tends to 0. Therefore, we have:

an = (0 + 13) / (0 + 14) = 13/14.

The sequence converges to the constant value 13/14 as n goes to infinity.

In conclusion, the sequence converges to the value 13/14.

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