The volume of a cube depends on the length of its sides. This can be written
in function notation as v(s). What is the best interpretation of v(4) = 64?
A. 4 sides of the cube have a total length of 64 feet.
B. A cube with side lengths of 4 feet has a volume of 64 cubic feet.
C. 4 of these cubes will have a total volume of 64 cubic feet.
OD. A cube with a volume of 4 cubic feet has side lengths of 64 feet.

Answer:

Both sides are equal, and are equvalent to 5 square root of 2

Step-by-step explanation:

This is a special right angled triangle known as the 45-45-90 triangle

The hypotenuse of a 45-45-90 triangle is x square root 2, with x being both sides of the triangle

10=x square root of 2 (Divide both sides by square root of 2)

10/square root of 2=x (Rationalize)

x=5 square root of 2

The area of each circle would be given below:

Circle A= 153.86 in²

Circle B = 314in²

Circle C = 615.44in²

Circle D = 452.16 in²

To calculate the area of a circle, the formula that should be used is given below such as follows:

Area of circle = πr²

For circle A;

radius = 7 in

area = 3.14×7×7 = 153.86 in²

For circle B;

radius = 3+7 = 10in

area = 3.14×10×10 = 314in²

For circle C;

radius = 10+4 = 14 in

area = 3.14×14×14

= 615.44in²

For circle D;

radius = 14-2 = 12in

radius = 3.14×12×12

= 452.16 in²

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Scaled version means adjusted value from the original size. For example, 3:5 could be a scaled version of 6:10.

Scale Version of an object is a replica or model of the original object that has been proportionally reduced or enlarged in size. The scale of a model is the ratio of the size of the model to the size of the original object. For example, if a model of a building is one-tenth the size of the actual building, then the scale of the model is 1:10, which means that every measurement on the model is one-tenth of the corresponding measurement on the actual building.

Scale versions of objects are often used in engineering, architecture, and design to create smaller or larger versions of objects that can be studied, tested, or used for other purposes. For example, architects might create scale models of buildings to study their design and appearance, while engineers might create scale models of machines or structures to test their performance under different conditions.

Scale versions can also be used in maps, where the scale is used to indicate the relationship between the size of the map and the size of the area it represents. In this case, the scale might be represented as a ratio, such as 1:10,000, or as a statement of the size of a unit of measurement on the map, such as 1 inch equals 1 mile.

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part a.

The equation that has the variable in the correct place to match the given situation is: Sunday's mile

part b

the Mansour family drove 210 miles on Sunday.

An equation is described as a formula that expresses the equality of two expressions, by connecting them with the equals sign =..

We have that the equation that has the variable in the correct place to match the given situation is: Sunday's mile

Sunday's miles = Total miles - Friday's miles - Saturday's miles

Sunday's miles = 687 - 313 - 164

Sunday's miles = 210

In conclusion, the Mansour family drove 210 miles on Sunday.

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Answer:

the 2 angles are 169.1° and 10.9°

Step-by-step explanation:

Supplementary angles add to 180

x = first angle

y = second angle = x - 158.2

x + y = 180

x + (x - 158.2) = 180

2x = 180 + 158.2

2x = 338.2

x = 338.2/2 = 169.1

y = 169.1 - 158.2 = 10.9

x + y = 169.1 + 10.9 = 180

Answer:

Naida's statement is true

Step-by-step explanation:

Since the elevation of Lima, Peru is a positive number, you can automatically tell that it is above sea level since sea level is zero

Answer:

Step-by-step explanation:

[tex]\left \{ {{x+y=0} \atop {-3x+4y=14}} \right.[/tex] ⇔ [tex]\left \{ {{y=-x} \atop {y=\frac{3}{4} x+ \frac{7}{2} }} \right.[/tex]

The value of x in the polygon is 5 centimetres.

A polygon is a two-dimensional geometric figure that has a particular number of sides.

Two polygons are similar if their corresponding angles are congruent and the corresponding sides have a constant ratio .

Therefore, using the ratio of the similar polygon, let's find the value of x as follows:

35 / x = 42 / 6

cross multiply

35 × 6 = 42x

210 = 42x

divide both sides of the equation by 42

x = 210 / 42

x = 5 cm

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The probability that the water will run out on a given day is  0.0038.

To find the probability that the demand for water on a given day exceeds the supply of 380 million gallons, we use the standard normal distribution to standardize the value of 380 million gallons as follows:

where;

x = of 380 million gallons,

µ is the mean daily demand of water = 300 million gallons,

σ is the standard deviation = 30 million gallons.

Substituting the given values:

z = (380 - 300) / 30

z = 2.67

Using a calculator, the probability that a standard normal random variable is greater than 2.67 is 0.0038.

Therefore, the probability that the water will run out on a given day is  0.0038.

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(a) The shape of sampling distribution is not too close to 0 or 1 (b) The mean of standard deviation = 0.033

(c) [tex]P(Z > (P-P + 0.03) / 0.033) = P(Z > 0.91)[/tex]

(a) The sampling distribution of p-p is approximately normal by the Central Limit Theorem because both sample sizes are large enough (n₁ = n₂ = 240) and the sample proportions of orange candies are not too close to 0 or 1.

(b) The mean of the sampling distribution of p-p is equal to the difference between the population proportions, which is 0.20 - 0.23 = -0.03. The standard deviation of the sampling distribution of p-p is given by:

sqrt[(p₁q₁/n₁) + (p₂q₂/n₂)]

= sqrt[(0.200.80/240) + (0.230.77/240)]

= 0.033

The standard deviation represents the amount of variation we expect to see in the differences between sample proportions of orange candies from multiple random samples of the same size.

(c) To find P(P-P>0), we need to standardize the difference between the sample proportions and the population difference and then find the probability that the standardized difference is greater than 0. That is:

(P-P - (p₁ - p₂)) / sqrt[(p₁q₁/n₁) + (p₂q₂/n₂)]

= (P-P - (-0.03)) / 0.033

= (P-P + 0.03) / 0.033

Using a standard normal distribution table or calculator, we can find the probability that a standard normal variable is greater than this value. For example, if we use a calculator, we get:

P(Z > (P-P + 0.03) / 0.033) = P(Z > 0.91)

where Z is a standard normal variable. The probability is approximately 0.18. This means that if we take many random samples of 240 M&M's milk chocolate candies and 240 peanut M&M's and calculate the difference between the sample proportions of orange candies, about 18% of the time we would expect to see a difference of 0.03 or greater (favoring M&M's milk chocolate candies).

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Answer:

Total amount of becomes after 16 year is $93649 .

The slope of the relation with the equation 5x - 3y = 4 is 5/3

To find the slope of the line whose equation is 5x - 3y = 4, we need to rearrange the equation to be in slope-intercept form, y = mx + b, where m is the slope of the line.

First, we'll subtract 5x from both sides:

-3y = -5x + 4

Next, we'll divide both sides by -3 to isolate y:

y = (5/3)x - 4/3

Now we can see that the slope of the line is 5/3.

So the correct answer is: 5/3

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The graph of the solution set for the inequality -14 ≥ k > -20 is on the image at the end.

To do this we just need to isolate the variable k in the middle.

We start with:

0 ≥ (k+14)/3 > – 2

We can multiply both sides by 3:

3*0 ≥ (k+14) > – 2*3

0 ≥ (k+14) > - 6

Now subtract 14 in both sides:

-14 ≥ k > -6 - 14

-14 ≥ k > -20

Then we need to draw an open circle at k = -20 and a closed circle at k = -14, and connect them with a line, like in the image below.

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The inequality that represents the range of prices of winter coats the shopper can buy as 175 ≤ p ≤ 430

To write the inequality, we can use the variable p to represent the price of the coat. The inequality we can write is:

p ≥ 175

This inequality means that the price p of the coat must be greater than or equal to $175.

Now, we also know that the shopper has a budget of $430 to spend on a winter coat. This means that the price p of the coat must be less than or equal to $430. We can represent this inequality as:

p ≤ 430

This inequality means that the price p of the coat must be less than or equal to $430.

To find the range of prices that the shopper can buy, we need to find the values of p that satisfy both of these inequalities. We can do this by finding the intersection of the two inequality regions on a number line, or by solving the system of inequalities:

p ≥ 175

p ≤ 430

To solve this system, we simply need to find the values of p that satisfy both inequalities simultaneously. We can do this by taking the intersection of the two inequality regions:

175 ≤ p ≤ 430

This means that the price p of the winter coat must be greater than or equal to $175 and less than or equal to $430. Therefore, the shopper can buy any winter coat with a price in this range.

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Julieta's claim about the quadrilateral is false.

The statement is given as:

It is impossible to draw a quadrilateral that is not a trapezoid and not a parallelogram.

The condition for a shape to be a quadrilateral is that the shape must have four sides.

An irregular shape that has four sides is a quadrilateral, but neither a quadrilateral nor a parallelogram

Therefore, Julieta's claim is false

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Answer:

Step-by-step explanation:

x^2 = 8

x=+-√8

The tangent secant exterior angle measure theorem indicates that the measure of the arc DG, m[tex]\widehat{DG}[/tex] is 85°, the correct option is the option B.

B. m[tex]\widehat{DG}[/tex] = 85°

The tangent secant exterior angles theorem states that if two secant or tangent or a secant and tangent intersect on the exterior to a circle, the measure of the angle formed is half the difference of the arcs they intercept.

The possible options in the question indicates that the possible drawing in the consists of a tangent and a secant, with the angle m∠DBG, being external to the circle.

The tangent secant exterior angle measure theorem indicates that we get;

m∠DBG = (1/2) × (m[tex]\widehat{GFE}[/tex] - m[tex]\widehat{DG}[/tex])

The question indicates; m[tex]\widehat{GFE}[/tex] = 149°

m∠DBG = 32°

Therefore;

32 = (1/2) × (149° - m[tex]\widehat{DG}[/tex])

149° - m[tex]\widehat{DG}[/tex] = 2 × 32° = 64°

m[tex]\widehat{DG}[/tex] = 149° - 64° = 85°

The measure of the arc DG, m[tex]\widehat{DG}[/tex] is 85°

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The probability of surveying 100 randomly selected households and getting 4 or fewer tuned to 60 minutes is only 0.02%.

P(X <= 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)

P(X = k) = (100 choose k) * 0.078^k * (1 - 0.078)^(100-k)

P(X <= 4) = (100 choose 0) * 0.078^0 * (1 - 0.078)^(100-0) + (100 choose 1) * 0.078^1 * (1 - 0.078)^(100-1) + (100 choose 2) * 0.078^2 * (1 - 0.078)^(100-2) + (100 choose 3) * 0.078^3 * (1 - 0.078)^(100-3) + (100 choose 4) * 0.078^4 * (1 - 0.078)^(100-4)

Using a calculator or software, we can find that:

P(X <= 4) = 0.000203

This means that the probability is 0.02%.

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Charges for TV advertising on a TV show are based on the number of viewers, which is measured by the rating. The rating is the percentage of population of 110 million TV households.The CBS television show 60 minutes recently had a rating of 7.8, indicating that 7.8% of the household were tuned to that show.An advertiser conducts an independent survey of 100 households and finds that only 4 were tuned to 60 minutes. Assuming that the 7.8 rating is correct, find the probability of surveying 100 randomly selected households and getting 4 or fewer tuned to 60 minutes.Does the result suggest that the rating of 7.8 is too high?

From the graph attached below, the solution to the system of linear inequalities are (1, 4)

A system of linear inequalities is a collection of linear inequalities in the same variables. The solution is any ordered pair that satisfies each of the inequalities.

In the problem given;

y < - x + 5 ...eq(i)

y ≥ 3x + 1 ...eq(ii)

To determine the solution to the system of linear inequalities, it is easier for us to use graphical method. This is simply done by plotting the points and determine the coordinate at which both inequalities intersect.

From the graph of the system of linear inequalities, the solution to this is (1, 4) which is option E

Kindly find attached graph below

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When w = 10 and z = 2, the value of expression 2w⁻²z⁰ is equal to 1/50. So, correct option is A.

The expression 2w⁻²z⁰ can be simplified as follows:

2w⁻²z⁰ = 2/w² * z⁰

Since z⁰ = 1 for any non-zero value of z, we can simplify further:

2w⁻²z⁰ = 2/w² * 1

Now we can substitute w = 10 into the expression:

2(10)⁻² * 1 = 2/100 = 1/50

In general, when we have a negative exponent in an expression, we can rewrite it as a positive exponent in the denominator. In this case, w⁻² can be rewritten as 1/w². Additionally, any number raised to the power of 0 is always 1, so z⁰ = 1. By simplifying the expression, we can easily substitute the given values of w and z to evaluate the expression.

So, correct option is A.

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The image of point R by rotation is equal to R'(x, y) = (- 4, 7).

The statement of the problem asks us to find the image of point by a kind of rigid transformation known as rotation, whose formula is:

(x, y) → (x · cos θ - y · sin θ, x · sin θ + y · cos θ)

Where:

If we know that x = 4, y = 7 and θ = - 180°, then the coordinates of the image of point R are:

R'(x, y) = (4 · cos 180° - 7 · sin 180°, 4 · sin 180° + 7 · cos 180°)

R'(x, y) = (- 4, 7)

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Answer:

A.) Newly married couples tend to have two earners.

Step-by-step explanation:

When newly married couples first start off marriage, they tend to both work to make stable income since they recently had to work to make money for only their selves, which is why they both tend to have two earners.

The equations that represent circles that have a diameter of 12 units and a center that lies on the y-axis are:

A. x² + (y - 3)² = 36.

D. x² + (y + 8)² = 36.

In Mathematics and Geometry, the standard form of the equation of a circle is represented by the following mathematical equation;

(x - h)² + (y - k)² = r²

Where:

Note: A center that lies on the y-axis simply means the value of h on the x-axis is equal to 0.

Based on the information provided above, we have the following parameters:

Radius, r = diameter/2 = 12/2 = 6 units.

Center, (h, k) = (0, 3).

By substituting the given parameters into the equation of a circle formula, we have the following;

(x - h)² + (y - k)² = r²

(x - 0)² + (y - 3)² = 6²

x² + (y - 3)² = 36.

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The ratio of the two arc lengths is equal to a / b. (Correct choice: B)

In this problem we must determine the ratio of two arc lengths, that is, the ratio between two circular arcs. The length of a circular arc is described by the following expression:

s = θ · r

Where:

s - Arc length

θ - Angle, in radians.

r - Radius

And the ratio of the length JK to the length MN is:

JK / MN = (θ · a) / (θ · b)

JK / MN = a / b

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The numeric value of the expression 3c + 4d when c = 56 and d = 10 is given as follows:

208.

To calculate the numeric value of a function or of an expression, we substitute each instance of any variable or unknown on the function by the value at which we want to find the numeric value of the function or of the expression presented in the context of a problem.

The expression for this problem is given as follows:

3c + 4d.

Hence the numeric value of the expression is given as follows:

3 x 56 + 4 x 10 = 208.

The expression is:

3c + 4d.

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The number of ways to pick 3 astronauts from 10 candidates can be found using the combination formula, which is:

nCk = n! / (k!(n-k)!)

where n is the total number of candidates, k is the number of candidates to be chosen, and "!" denotes the factorial function.

In this case, we want to choose 3 astronauts from a pool of 10 candidates, so we can plug these values into the formula:

10C3 = 10! / (3!(10-3)!)

= (10 x 9 x 8) / (3 x 2 x 1)

= 120

Therefore, there are 120 ways to pick 3 astronauts to go to the moon out of 10 candidates.

Answer:

120 or 220

Step-by-step explanation:

The value of five ordered-pair solutions of this equation by using a table are,

x           y

- 6        - 1

- 3        - 2

0            3

3          - 4

6          - 5

We have to given that;

The graph of an equation is sketched in the figure.

Hence, From graph we get;

The value of five ordered-pair solutions of this equation by using a table are,

x           y

- 6        - 1

- 3        - 2

0            3

3          - 4

6          - 5

Thus, The value of five ordered-pair solutions of this equation by using a table are,

x           y

- 6        - 1

- 3        - 2

0            3

3          - 4

6          - 5

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Answer:

e = 3

Step-by-step explanation:

Use the property of the proportion to find e (cross-multiply):

[tex]10 \times e = 6 \times 5[/tex]

[tex]10e = 30[/tex]

Divide both sides of the equation by 10 to make e the subject:

[tex]e = 3[/tex]

Answer:

3

Step-by-step explanation:

6 x 10 = 60

6 x 5 = 30

5/10 = 30/60

30/ 10= 3

60/ 10 = 6

E/6 = 3/6

E=3

Answer:

2x+9y=18

Step-by-step explanation: