A rectangular prism with a 8-centimeter length, a 4-centimeter width,
and a 5-centimeter height is placed on a rectangular prism with a 14-
centimeter length, a 8-centimeter width, and a 1-centimeter height.
6 cm
4 cm
5 cm
14 cm
1 cm
8 cm
What is the volume of the composite solid?
The volume is cubic centimeters.

There are 35 different committees that can be formed, each consisting of one man and one woman.

To form the committee consisting of one man and one woman, we need to choose one man from the available seven men and one woman from the available five women.

Number of choices for selecting one man = 7

Number of choices for selecting one woman = 5

To find the total number of different committees that can be formed, we multiply these numbers together:

Total number of committees = 7 × 5

Total number of committees = 35

Therefore, there are 35 different committees that can be formed, each consisting of one man and one woman.

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Answer:

1 mile : 2 cm

Step-by-step explanation:

ratio is 4.5 miles : 9

Which, if you want simplified, 1:2

Answer:

2 cm is 1 mile

or 1 cm is 1/2 mile

Step-by-step explanation:

We are going  from 9 cm to 4.5 miles

9 cm * scale factor = 4.5 miles

scale factor = 4.5 miles / 9 cm

scale factor = 1/2 mile per cm

The scale is 2 cm is 1 mile

or 1 cm is 1/2 mile

The value of the principal is $10,000.

The equation A = P(1 + 0.043t) represents the amount of money earned on a savings account with 4.3% annual simple interest A is the account balance after t years P is the principal amount, and 0.043 is the interest rate per year.

The account balance is $15,160 after 12 years.

Substituting these values into the equation, we get:

15,160 = P(1 + 0.043(12))

Simplifying the right-hand side, we get:

15,160 = P(1 + 0.516)

15,160 = P(1.516)

Dividing both sides by 1.516, we get:

P = 10,000

This means that the account was initially opened with a principal of $10,000 and it earned simple interest of 4.3% per year for 12 years resulting in an account balance of $15,160.

The principal and it does not take into account the interest that is earned on the interest itself.

In contrast compound interest takes into account the interest that is earned on both the principal and the previously earned interest.

The account in question had been earning compound interest instead of simple interest the final account balance after 12 years would have been higher than $15,160.

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From the calculation, she can't carry all but she can carry her suitcase with clothes in it and three out of the four gift items.

We know that we have to consider the restriction that the airline has placed. We have been told that the luggage that have to be packed in this case would have to be less than 22.7 kg.

We would now have to look at all the things that Haley would need to pack so as to determine what can be packed and what can not be packed.

Total luggage  that she has to pack;

Mass of empty suitcase + mass of her clothes + mass of 4 gifts

Total luggage = 5.1 Kg + 14.8 Kg + 4(0.87) = 23.38 Kg

This implies that she can't carry all but she can carry her suitcase with clothes in it and three out of the four gift items.

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The measure of <BED = 135 degrees

To determine the value, we need to know the following;

From the information given, we have that;

Angle AED + Angle ACD are on a straight line

Now, susbtitute the values, we have that;

135 + ACD = 180

collect like terms

ACD = 180 - 135

subtract the values

ACD = 45

Then, we have that;

<BED = <ACD + <BEC

Substitute the values

<BED = 45 + 90

<BED = 135 degrees

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The cosine value is given as follows:

[tex]\cos{\theta} = \frac{4\sqrt{23}}{23}[/tex]

The tangent value is given as follows:

[tex]\tan{\theta} = -\frac{\sqrt{7}}{4}[/tex]

First we must obtain the secant value, according to the identity presented as follows:

[tex]\sec^2{\theta} = 1 + \tan^{2}{\theta}[/tex]

Replacing the tangent into the expression, we have that:

[tex]\sec^2{\theta} = 1 + \frac{7}{16}[/tex]

[tex]\sec^2{\theta} = \frac{23}{16}[/tex]

[tex]\sec{\theta} = \frac{\sqrt{23}}{4}[/tex]

The secant is positive, as the angle is in the fourth quadrant, where the cosine is positive.

The cosine is then given as follows:

[tex]\cos{\theta} = \frac{1}{\sec{\theta}}[/tex]

[tex]\cos{\theta} = \frac{4}{\sqrt{23}} \times \frac{\sqrt{23}}{\sqrt{23}}[/tex]

[tex]\cos{\theta} = \frac{4\sqrt{23}}{23}[/tex]

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1. f(x) =  (2x² + 4x + 4) / x³ = 0; as lim x→∞, and lim x→-∞

2. g(x)  = (2x²  +  4x  + 4)/x² = ∞; as lim x→∞, and lim x→-∞]

3.  h(x)  = (2x²  +  4x  + 4)/x = ∞ as lim x→∞, and -∞ as lim x→-∞.

To find the end behavior of each of the functions, we can take the limit as x approaches infinity and negative infinity.

For  f(x)  = (2x²  +  4x  + 4)/x³;

lim x→∞ (2x² + 4x + 4) / x³ = 0

lim x→-∞ (2x² + 4x + 4) / x³ = 0

f(x) approaches zero as x approaches positive or negative infinity.

For  g(x)  = (2x²  +  4x  + 4)/x²;

lim x→∞ (2x² + 4x + 4) / x² = ∞

lim x→-∞ (2x² + 4x + 4) / x² = ∞

g(x) approaches infinity as x approaches positive or negative infinity.

For  h(x)  = (2x²  +  4x  + 4)/x

lim x→∞ (2x² + 4x + 4) / x = ∞

lim x→-∞ (2x² + 4x + 4) / x = -∞

h(x) approaches infinity as x approaches positive infinity, and negative infinity as well, but with a negative sign.

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The measure of angle QRS in triangle QRS is 56.8 degrees.

To find the measure of angle QRS in triangle QRS, we can use the fact that the sum of the measures of the angles in a triangle is always 180 degrees.

We know that:

- The measure of angle RSQ is 48.2 degrees

- The measure of angle SQR is 75 degrees

Let x be the measure of angle QRS. Then, we can write:

RSQ + SQR + QRS = 180

Substituting the known values, we get:

48.2 + 75 + x = 180

Simplifying and solving for x, we get:

x = 180 - 48.2 - 75x = 56.8

Therefore, the measure of angle QRS in triangle QRS is 56.8 degrees.

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The variables for this problem are given as follows:

a = 16, [tex]b = 16\sqrt{2}[/tex] , c = 16, d = 16.

The three trigonometric ratios are the sine, the cosine and the tangent, and they are obtained according to the rules presented as follows:

For side lengths a and c, we have a right triangle with angles of 45º, hence using the 45-45-90 Triangle Rule, with the hypotenuse of [tex]16\sqrt{2}[/tex], the lengths a and c are given as follows:

a = c = 16.

The length a is also the geometric mean of the lengths c and d, hence:

16² = 16d

d = 16.

Then the length b is obtained applying the Pythagorean Theorem as follows:

b² = 16² + 16²

[tex]b = \sqrt{2 \times 16^2}[/tex]

[tex]b = 16\sqrt{2}[/tex]

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The given table represents a linear function with a constant rate of change of 2. Option D is the right answer.

To determine if the table represents a linear function and calculate the rate of change, let's examine the given values:

x   | y

-----------

1   | 3

2   | 5

3   | 7

4   | 9

By looking at the y-values, we can observe that for every increase of 1 in x, the corresponding y-value increases by 2. This indicates a constant rate of change, suggesting that the table represents a linear function.

To calculate the rate of change, we can use the formula:

[tex]\[\text{{Rate of Change}} = \frac{{\text{{Change in y}}}}{{\text{{Change in x}}}}\][/tex]

Taking any two points from the table, let's choose (1, 3) and (2, 5):

[tex]\[\text{{Rate of Change}} = \frac{{5 - 3}}{{2 - 1}} = \frac{2}{1} = 2\][/tex]

The table provided exhibits a linear function with a constant rate of change. As the x-values increase by 1 from [tex]1[/tex] to [tex]4[/tex], the corresponding y-values increase by [tex]2[/tex] from [tex]3[/tex] to [tex]9[/tex]. This consistent change in y for each unit change in x indicates a linear relationship between the variables.

The rate of change, also known as the slope of the function, is determined by the ratio of the change in y to the change in x. In this case, the rate of change is [tex]2[/tex], meaning that for every increase of [tex]1[/tex] in [tex]x[/tex], the y-value increases by 2.

Thus, the table represents a linear function with a rate of change of [tex]2[/tex].

Therefore, the correct answer is D) Yes; rate of change = [tex]2[/tex].

NOTE: The given question is incomplete. The complete question is:

Determine if the table below represents a linear function. If so, what's the rate of change?

options:

A)  Yes; rate of change = 4

B)  No; it's a non-linear function.

C)  Yes; rate of change = 3

D)  Yes; rate of change = 2​

Table:

x   | y

-----------

1   | 3

2   | 5

3   | 7

4   | 9

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Answer:

1?

Step-by-step explanation:

9 1/4 is the longest distance

2 times

According to the chart, the mile that she ran the fastest was [tex]9 \frac{1}{2}[/tex] miles. 1 dot equals 1 minute so her fastest mile was [tex]9 \frac{1}{2}[/tex].

I hoped this helped if not please tell me what I did wrong ૮ ˶ᵔ ᵕ ᵔ˶ ა

Answer:

28 in²

Step-by-step explanation:

Area of parallelogram = base X vertical height

= 7 X 4

= 28 in²

Shakira needs to rent a car for one day and she is trying to decide which car rental company to use. Alpha Car Rental offers a Porsche for $29.17 per day, plus 57 cents per mile. Beta Car Rental also offers the same car for $50.23 per day, plus 44 cents per mile.

To determine which car rental is a better deal, Shakira needs to calculate at what number of miles the prices for both Alpha and Beta Car Rental are the same. To do this, she can use the following equation:

The variable of x is the number of miles. This equation simplifies to x = 21.06 miles. Therefore, at 21.06 miles, Alpha and Beta Car Rental will be the same price.

The graph of the inequality y ≤ (5/2)x - 5 is a downward-sloping line with shading below the line.

To graph the inequality 5x - 2y ≥ 10, we need to convert it to slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept. Let's go step by step:

Step 1: Start with the original inequality:

5x - 2y ≥ 10

Step 2: Move the 5x term to the other side of the inequality by subtracting 5x from both sides:

-2y ≥ -5x + 10

Step 3: Divide the entire inequality by -2 (since we want to isolate y and have a positive coefficient for y):

y ≤ (5/2)x - 5

Now we have the inequality in the desired form. The graph of y ≤ (5/2)x - 5 represents all the points below or on the line y = (5/2)x - 5.

To graph this inequality, follow these steps:

Step 1: Plot the y-intercept, which is -5. This point is (0, -5).

Step 2: Find a second point by using the slope (5/2). The slope is the ratio of the change in y to the change in x. Starting from the y-intercept, move up 5 units (numerator of the slope) and move right 2 units (denominator of the slope). This gives us the point (2, 0).

Step 3: Draw a solid line passing through the two points (0, -5) and (2, 0). This line represents the equation y = (5/2)x - 5.

Step 4: Since the inequality is "y ≤ (5/2)x - 5," we need to shade the region below the line (including the line itself) to represent all the points that satisfy the inequality.

The graph should resemble a downward-sloping line passing through the points (0, -5) and (2, 0), with the shaded region below the line.

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The radius of the circle is [tex]\sqrt{59[/tex] and the coordinates are (6,8).

The given equation of the circle is:

[tex]x^2+Y^2-12x-16y+51=0[/tex]

To find the center and radius of the given circle, we need to rewrite the equation in the standard form [tex](x-a)^2 + (y-b)^2 = r^2[/tex],

where (a,b) is the center of the circle and r is the radius.

We can start by completing the square for the x and y terms. For the x terms, we add and subtract (12/2)² = 36 to get:

[tex]x^2 - 12x + 36 + y^2 - 16y = -51 + 36 + 0[/tex]

Similarly, for the y terms, we add and subtract (16/2)² = 64 to get:

[tex]x^2 - 12x + 36 + y^2 - 16y + 64 = -51 + 36 + 64[/tex]

Simplifying:

[tex](x - 6)^2 + (y - 8)^2 = 59[/tex]

Now we can see that the center of the circle is at (6, 8), and the radius is [tex]\sqrt{59[/tex].

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The statement "When added, the sum of the y-intercepts must be 1" and "f(x) could have a rate of change equal to 1 and g(x) could have a rate of change of 2" can be used to describe the original functions f(x) and g(x).

Within mathematical study, we encounter various types of relations between objects – but none quite so distinctive as a function. These relations are essentially collections or sets composed solely from ordered pairs – pairings containing precisely two distinct elements each.

The defining trait for functions lies in how they operate with regards to these paired elements: specifically that every element comprising the domain – representing all potential inputs – correspond with absolute exclusivity to just one solitary member within the codomain – signifying all possible outputs.

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The line of symmetry for the above figure is attached accordingly.

In mathematics, symmetry with regard to a reflection is known as reflection symmetry, line symmetry, mirror symmetry, or mirror-image symmetry.

That is, a figure with reflectional symmetry does not alter when it is reflected. A line/axis of symmetry exists in 2D, while a plane of symmetry exists in 3D.

After inserting the symmetry lines, the above resulted in a kite.

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The reflection rule that maps triangle DEF onto triangle D'E'F' is a reflection across the line that passes through (2,2) and (−1.25,2.75).

A translation is a type of transformation that moves all the points of a figure the same distance and in the same direction.

The shape and size of the figure do not change, only its position in the plane.

(3, 6)--->(1,6)

3-x=1

x=-2

(x-2, y)

To find the reflection rule that maps the triangle D(3, 6), E(-4,-3), F(6, 1) onto its image D'(1, 6), E(8, -3), F'(-2, 1), we need to determine the line of reflection.

In triangle the point where the perpendicular bisectors intersect will be the center of the reflection.

We find that the midpoint of DE is (−0.5,1.5), the midpoint of DF is (4.5,3.5), and the midpoint of EF is (1,−1).

The perpendicular bisectors of DE and DF intersect at (2,2), and the perpendicular bisectors of DE and EF intersect at (−1.25,2.75).

Therefore, the reflection rule that maps triangle DEF onto triangle D'E'F' is a reflection across the line that passes through (2,2) and (−1.25,2.75).

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(a) The distribution of X ~ N(7.08, 2.29)

(b) The probability of a patron's lunch cost is 0.049

(b) The probability of a group patron's lunch cost is 0.049

(d) The assumption of normal distribution is not necessary

Given that

Mean = 7.08

Standard deviation = 2.29

The distribution of X is represented as

X ~ N(Mean , Standard deviation)

So, we have

X ~ N(7.08, 2.29)

The z-score is calculated as

z = (x - Mean)/Standard deviation

So, we have

z = (6.9379  - 7.08)/2.29 and z = (7.2186 - 7.08)/2.29

Evaluate

z = -0.062 and z = 0.061

So, we have

P = P(-0.062 < z < 0.061)

Evaluate

P = 0.049039

Approximate

P = 0.049

This is same as part (b)

i.e. the probability that the average lunch is between $6.9379 and $7.2186 is 0.049

No, the assumption is not necessary

This is because

The distribution has a sample size less than 25 as required by the central limit theorem

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The interquartile range for the average of 15 cities is 1.8.

a) X ~ N(9.6, 1.3)

b) X bar ~ N(9.6, 0.13)

c) The probability that one randomly selected city's waterway will have less than 9.3 ppm pollutants can be calculated using the z-score formula: P(X < 9.3) = P(Z < (9.3 - 9.6) / 1.3) = 0.338.

d) The probability that the average amount of pollutants is less than 9.3 can be calculated using the z-score formula: P(Xbar < 9.3) = P(Z < (9.3 - 9.6) / 0.13) = 0.819.

e) The assumption that the distribution is normal is indeed necessary for part d.

f) The IQR for the average of 15 cities can be calculated as follows: Q1 = 8.7 and Q3 = 10.5. IQR = 10.5 - 8.7 = 1.8.

Therefore, the interquartile range for the average of 15 cities is 1.8.

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Answer:  A. 32

Step-by-step explanation:

Rule:  That if an angle is created on the end of circle The arc that it creates is 2 times the angle.

arc AX = 2 (<B)

arc AX = 2(56)

arc AX = 112

Rule:  The angle of 2 secants = 1/2 (outer arc - inner arc)

<C =  1/2 (arc AB - arc AX)

<C = 1/2 ( 176 - 112)

<C = 1/2 (64)

<C = 32     >A

Answer:

1. An ordered pair in polar coordinates (r, θ) represents a point in the plane with a distance of r from the origin and an angle of θ with respect to the positive x-axis. When r < 0, this means that the point is located on the opposite side of the origin from the positive x-axis. In other words, the angle θ is shifted by 180 degrees.

2. In polar coordinates, a point can be represented by infinitely many ordered pairs because the distance r and the angle θ are not unique. For example, the point (1, π/4) and the point (1, 9π/4) both represent the same point in the plane.

3. The component form of a vector (a, b) represents the horizontal and vertical displacement of the vector from its initial point to its terminal point. The graph of a vector in standard position is a line segment from the origin to its terminal point. The horizontal and vertical components of the vector correspond to the x- and y-coordinates of the terminal point, respectively.

4a. The velocity of the plane Vp relative to the air can be expressed as Vp = (450 cos(60°), 450 sin(60°)) - (30, 0) = (225 - 30, 389.71) = (195, 389.71) mph.

4b. The velocity of the wind V can be expressed as V = (-30, 0) mph.

4e. The true velocity of the plane vr can be expressed as vr = Vp + V = (195 - 30, 389.71) = (165, 389.71) mph. The true speed of the plane is the magnitude of the true velocity, which is approximately 414.7 mph.

Jeremy is wrong as I explained below.

As we know,

Thus, as we can see from the figure figure 1 is a rectangle and Figure 2 is a square so,

I do not agree with Jeremy.

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Complete question:

a. Materials price variance: U$990  and Materials quantity variance: F$198

b. Labor rate variance: F$248

Labor efficiency variance: U$752

a. Materials price and quantity variances:

Materials price variance:

The materials price variance measures the difference between the actual cost of materials purchased and the standard cost of materials.

Actual quantity purchased = 77,000 microns

Actual cost per micron = $0.30 per micron

Standard quantity allowed for production = (7 microns per toy) x (4,700 toys) = 32,900 microns

Standard cost per micron = $0.33 per micron

Materials price variance = (Actual quantity purchased x Actual cost per micron) - (Standard quantity allowed x Standard cost per micron)

Materials price variance = (77,000 x $0.30) - (32,900 x $0.33)

Materials quantity variance:

The materials quantity variance measures the difference between the actual quantity of materials used and the standard quantity allowed for production.

Actual quantity used = (77,000 microns purchased) - (35,875 microns in ending inventory)

Standard quantity allowed = (7 microns per toy) x (4,700 toys)

Materials quantity variance = (Actual quantity used - Standard quantity allowed) x Standard cost per micron

Materials quantity variance = ((77,000 - 35,875) - (7 x 4,700)) x $0.33

b. Labor rate and efficiency variances:

Labor rate variance:

The labor rate variance measures the difference between the actual labor rate paid and the standard labor rate.

Actual labor hours worked = 6,040 hours

Actual labor cost per hour = $45,904 / 6,040 hours

Standard labor hours allowed for production = (1.2 hours per toy) x (4,700 toys)

Standard labor cost per hour = $7.10 per hour

Labor rate variance = (Actual labor hours worked x Actual labor cost per hour) - (Standard labor hours allowed * Standard labor cost per hour)

Labor rate variance = (6,040 x Actual labor cost per hour) - (5,640 x $7.10)

Labor efficiency variance:

The labor efficiency variance measures the difference between the actual labor hours used and the standard labor hours allowed for production.

Labor efficiency variance = (Actual labor hours worked - Standard labor hours allowed) x Standard labor cost per hour

Labor efficiency variance = (6,040 - (1.2 x 4,700)) x $7.10

Please note that the actual labor cost per hour and the actual labor cost per micron need to be calculated before computing the variances.

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Answer:If the Diameter of a circle is 22 inches, the area will be 380.13in².

Step-by-step explanation:

These are the formulas you use:

Area=pi*Radius^2  or A=pi*Radius*Radius

Diameter=2*Radius

A=1

4*pi*Diameter*2=1 2

4*pi*222=380.13271in

380.13271in is approximately 380.13in².

Step-by-step explanation:

OK, 'Brainless'....  the triangle side length rule states that any two sides of a triangle must sum to greater than the remaining side length...

42 + 20 > x        then  12 , 20, 22, 32, 42, 50     will work here

42+x > 20            all of the possibles work here

20 + x > 42         32, 42, 50, 62 and 70 work here

   so   32 and 42 are in all of the lists ....that is your answer

Answer:

To many questions, and too many numbers

Step-by-step explanation: