A blizzard at Dairy Queen costs $3.00. Identify the independent and dependent variables.

The dimensions of the rectangular box are length (L), width (W), and height (H). The radius of the sphere inscribing the rectangular box is 8.

Let's assume the dimensions of the rectangular box are length (L), width (W), and height (H). Since the box is inscribed in a sphere, its longest diagonal will be equal to the diameter of the sphere, which is 2r (r is the radius of the sphere).

The surface area of the rectangular box can be calculated by summing the areas of its six faces: 2(LW + LH + WH) = 384.

The sum of the lengths of the 12 edges of the box is given as 4(L + W + H) = 112.

From these equations, we can solve for L + W + H = 28.

To find the radius of the inscribing sphere, we need to find the longest diagonal of the rectangular box. Using the Pythagorean theorem, the longest diagonal is √(L^2 + W^2 + H^2).

Since we have L + W + H = 28, we can substitute L + W = 28 - H into the equation for the longest diagonal: √((28 - H)^2 + H^2) = 2r.

By solving this equation, we find that H = 8.

Substituting this value into the equation L + W + H = 28, we get L + W = 20.

Finally, substituting L + W = 20 into the equation for the longest diagonal, we find √(20^2 + 8^2) = 2r.

Simplifying, we find r = 8.

Therefore, the radius of the sphere inscribing the rectangular box is 8.

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Answer:

294 square meters

Step-by-step explanation:

The surface area of a certain pyramid is 54 square meters. Its volume is 648 cubic meters. If a similar pyramid has a volume of 8232 cubic meters, what is its surface area?

We solve the above question using Proportion

The surface area of a certain pyramid

= 54 square meters.

Volume of certain pyramid =

648 cubic meters.

Surface area of similar pyramid = x

Volume of similar pyramid = 8232 cubic meters.

Hence,

Surface area : Volume

= Surface area/ Volume

= 54 m²/648 m³ = x/8232 m³

Cross Multiply

54 × 8232 = 648 × x

x = 54 × 8232/648

x = 294 square meters

The probability of getting 2 the same color is 9/11.

What is probability?

  According to the probability formula, the probability of an event occurring, or P(E), is equal to the proportion of positive outcomes to all outcomes. P(E) is defined mathematically as favorable outcomes divided by total outcomes. Mathematical branch known as probability deals with determining the possibility of an event occurring. Here using probability we can also calculate combination .

Here the total number of marbles are,

=>Total marbles = Blue + Red + Green

=>Total marbles = 5 + 4 + 3

=>Total marbles = 12

Then, Probability of a green = 3/12

=> Probability of not green = 1 - 3/12 = 9/12=3/4

To get exactly one green in two draws, we either get a green, not green, or a not green, green

=>First Draw Green, Second Draw Not Green

=> 1st draw: Probability of a green = 3/12

In 2nd draw: Probability of not green = 9/11 <-- 11 since we did not replace the first marble

To get the probability of the event, since each draw is independent, we multiply both probabilities

=> Probability of the event is (5/12) * (9/11) = 45/132

First Draw Not Green, Second Draw Not Green

=>1st draw: Probability of not a green = 9/12

=>2nd draw: Probability of not green = 7/11 <-- 11 since we did not replace the first marble

To get the probability of the event, since each draw is independent, we multiply both probabilities

=>Probability of the event is (9/12) * (7/11) = 63/132

To get the probability of exactly one green, we add both of the events:

First Draw Green, Second Draw Not Green + First Draw Not Green, Second Draw Not Green

=> 45/132 + 63/132 = 108/132=9/11.

Hence the probability of getting 2 the same color is 9/11.

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The phrases that are inequalities are:

B) -2 < 2

D) 7w > 5.6

E) f - 4 - 7 > 7 - 4 - f

First, we define an equation as:

\(P = Q\)

Where P and Q are two expressions.

On the other hand, an inequality can be:

\(P > Q\\P < Q\\P \neq Q\\P \geq Q\\P \leq Q\)

These are inequalities because now the expressions P and Q can (and in some cases must) be different.

With that in mind, the phrases that are inequalities are:

B) -2 < 2

D) 7w > 5.6

E) f - 4 - 7 > 7 - 4 - f

As you can see, in these 3 we have the "lower than" or "larger than" symbols used, so these represent inequalities.

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However, I can explain the process of simplifying the given functions using the Karnaugh Map (K-Map) method and provide you with the minimized SOP and POS forms.

1. For Function 1, we have the following grouped and labeled K-Maps:
  - K-Map for variables a, b, and e (4x4 grid)
  - K-Map for variable d (2x2 grid)
2. To obtain the minimized SOP forms of Function 1, we need to analyze the grouped cells in the K-Maps and write the corresponding Boolean expressions. By applying the K-Map method, we can obtain six possible minimized SOP forms for Function 1.

3. For Function 2, we have the following grouped and labeled K-Maps:
  - K-Map for variables a, b, c, and e (4x4 grid)
  - K-Map for variable d (2x2 grid)
4. To obtain the minimized POS forms of Function 2, we need to analyze the grouped cells in the K-Maps and write the corresponding Boolean expressions. By applying the K-Map method, we can obtain three possible minimized POS forms for Function 2.

Please note that the specific expressions and grouped cells for each function can be obtained by visually examining the K-Maps. It would be best to refer to a resource that allows you to draw and label the K-Maps to get the accurate results for Function 1 and Function 2.

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1. We can use the subset A = R as the domain of the function f.

2. The data support a well-defined function.

3.  (a) f(x) = x^2 -- The function is well-defined.

(b) g(a) = 1/a --The function is not well-defined on R.

(c) h(x) = √(x-2) + 42 -- The function is not defined for any input x less than 2, so it is not well-defined on the entire domain of R.

1. To make f(x) = 3 - 7x a well-defined function, we need to ensure that the output of the function is a real number for every input in the domain.

Since the function is defined for all real numbers x, the domain of the function can also be all real numbers.

2. The data { (1,3), (2,4), (3,2), (4,1)} support a well-defined function from (1,2,3,4) to (1,2,3,4).

For a function to be well-defined, each input in the domain must correspond to exactly one output in the range.

In this case, we can see that each input in the domain (1,2,3,4) has exactly one corresponding output in the range (1,2,3,4).

3.

(a) f(x) = x^2 is a well-defined function on the domain of all real numbers, R. For every input x, the output x^2 is a real number, so the function is well-defined.

(b) g(a) = 1/a is not a well-defined function on the domain of all real numbers, R. The function is undefined at a = 0 because division by zero is not allowed. Therefore, the function is not well-defined on R.

(c) h(x) = √(x-2) + 42 is a well-defined function on the domain x ≥ 2. For every input x greater than or equal to 2, the output √(x-2) + 42 is a real number, so the function is well-defined.

However, the function is not defined for any input x less than 2, so it is not well-defined on the entire domain of R.

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Answer:

I'm sorry I don't know

Step-by-step explanation

Pickles are pretty tasty, though!

The system of linear inequalities to represent Jackson's workout is: 6.9x + 10.4y ≥ 400; x ≤ 45.

Let x be the number of minutes Jackson uses the light stair stepper.

Let y be the number of minutes Jackson uses the vigorous stair stepper.

The calories burned during x minutes of light effort on the stair stepper are 6.9x.

The calories burned during x minutes of vigorous effort on the stair stepper are 10.4y

To burn at least 400 calories, we can write the inequality:

6.9x + 10.4y ≥ 400

To ensure that Jackson has at most 45 minutes to exercise, we can write the inequality: x + y ≤ 45

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Answer:

15 Cents each

Step-by-step explanation:

3.60 Divided by 24

Answer:

3rd option

Step-by-step explanation:

(5y - 16) and (3y + 20) are a linear pair and sum to 180° , that is

5y - 16 + 3y + 20 = 180

8y + 4 = 180 ( subtract 4 from both sides )

8y = 176 ( divide both sides by 8 )

y = 22

then

5y - 16 = 5(22) - 16 = 110 - 16 = 94°

3y + 20 = 3(22) + 20 = 66 + 20 = 86°

The measurement that gives you the difference between the points on the scatterplot and the prediction line for the same value of x is the residual. Therefore, the correct answer is C. Residual.

In regression analysis, the residual represents the vertical distance between the observed data points and the corresponding predicted values on the regression line. It is calculated by taking the difference between the actual observed value and the predicted value for a specific value of the independent variable (x). The residuals provide a measure of how well the regression line fits the data, with smaller residuals indicating a better fit.

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Answer:

the first one

Step-by-step explanation:

absolute value is a number's distance from zero, so distance from zero can not possibly be negative. Therefore, |4x-2|=-6 has no solution.

Answer:

It would be the first one because there is no value of x that makes the equation be true since an absolute value can never be negative.

Step-by-step explanation:

Hope this helps:)....if don't help then sorry for wasting your time and may God bless you:)

18% of the milk mixture and how much of the cream mixture should he use.

A dairyman wants to combine milk with 5 percent butterfat and cream with 75 percent butterfat to create a 56-liter combination. Butterfat should make up 53% of the final combination.

Let x represent the volume of MILK required for the combination, in liters.

Consequently, x/56 is the PROPORTION of milk in the mixture. [because the final mixture has 56 liters in total]

We require 56 - x liters of CREAM in the mixture because we have 56 liters overall in the mixture.

The PROPORTION of cream in the combination is therefore equal to (56 - x)/56.

Our goal is for the final mixture to have 75% butterfat.

Fill in the equation with each of these values to obtain:

50 = (x/60)(5) + ((60 - x)/60) (75)

Add 56 to both sides to get: 3000 = (5)(x) + (56 - x)(75)

The formula is:

Multiply both sides by 56 to get: 3000 = (5)(x) + (56 - x)(75)

Expand: 3000 = 5x + 4200 - 75x

Simplify: 3000 = 4200 - 70x

Subtract 4500 from both sides: -1300 = -70x

Solve: x = (-1300)/(-70) = (1300)/(70) = 130/7

If you don't want to divide 130 by 7, you can evaluate this quickly by first realizing that 30/7 = 18.

Consequently, 130/7 must be a little larger than 18.

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The given set H is not a subspace of M2x4.

To prove that H is a subspace of M2x4, we need to show that it satisfies the following conditions:

H contains the zero vector

H is closed under addition

H is closed under scalar multiplication

Condition 1:The zero matrix in M2x4 is not in H because FM3x2 multiplied by the zero matrix will not equal the zero matrix in M3x4.

Condition 2:Let A and B be matrices in H. We need to show that A + B is also in H.

FA = 0 and FB = 0

F(A + B) = FA + FB (distributivity of matrix multiplication)

F(A + B) = 0 + 0 = 0

Therefore, A + B is in H and H is closed under addition.

Condition 3:Let A be a matrix in H and c be a scalar.

FA = 0

F(cA) = c(FA) (associativity of scalar multiplication)

F(cA) = c(0) = 0

Therefore, cA is in H and H is closed under scalar multiplication.

Since H does not satisfy Condition 1, it is not a subspace of M2x4.

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Answer:  1. Mary Ann has saved $2 more than Carlos

Step-by-step explanation: At 3 hours...

Carlos has $26 according to chart

Mary Ann has...

y=6(3)+10

y=18+10

y=28

so

28-26=2

she has 2 more dollars than him

The difference in their savings after 3 hours of working is option 1. Mary Ann has saved $2 more than Carlos.

A linear function can be defined as the function whose graph is a straight line. It can also be defined as the function with one or more variables and the exponent of the variable is 1.

Given are two linear functions.

Let x represent the number of hours each person works y represent the total earnings in dollars.

Savings of Mary Ann is represented as,

y = 6x + 10

Savings of Carlos is represented in the graph shown.

After working 3 hours,

Savings of Mary Ann = (6 × 3) + 10 = $28

From the graph,

Savings of Carlos = $26

Difference in the savings = $28 - $26 = $2

Hence Mary Ann has saved $2 more than Carlos.

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The price of one donuts, if you can buy 6 donuts and two kolaches for $8.84 and one kolache and 4 donuts would cost $5.36 is  $0.94.

Let's represent the price of one donut with "d" and the price of one kolache with "k". Then we can write two equations based on the information given:

6d + 2k = 8.84 (equation 1)

4d + 1k = 5.36 (equation 2)

We can use equation 2 to solve for k:

k = 5.36 - 4d

Now we can substitute this expression for k into equation 1:

6d + 2(5.36 - 4d) = 8.84

Simplifying and solving for d:

6d + 10.72 - 8d = 8.84

2d = 1.88

d = 0.94

Therefore, the price for one donut is $0.94.

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Answer:

112

Step-by-step explanation:

Everything is multiplied by 8

Answer:112

Step-by-step explanation:

Took quiz

Answer:

$41.40

Step-by-step explanation:

36 divided by 100 is 0.36 so 1% is 0.36. times by 15 to get 15% is 5.4.

So the 15% tip is $5.40 so overall the price would be $41.40

Answer:

$5.40

Step-by-step explanation:

$36.00 is the amount that you need to find 15% of

First, you can do 36 x 0.15 = $5.40 (15% is 0.15 in decimal form)

The amount of the tip is $5.40

Jose has 3/5 lb

Maria = 3/5 - 1/2 = 1/10 lb

Atul has 2/3 lb

Pounds of candy Autul have than Maria:-

2/3 —3/5 = 4/15

Answer:- 4/15

Answer:

the answer your looking for is 2 2/8 pies

Answer:

\(9^{4}\)

Step-by-step explanation:

9^-5 = 9^4  x  9^-9

4-9 = -5

The derivative of F(x) is \(F'(x) = x^{(1/3)\).

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.

To find the derivative of the given function F(x), we will apply the fundamental theorem of calculus and differentiate the integral with respect to x.

Let's compute F'(x):

F(x) = ∫[0 to x] \(t^{(1/3)} dt\)

To differentiate the integral with respect to x, we'll use the Leibniz integral rule:

F'(x) = d/dx ∫[0 to x] \(t^{(1/3)} dt\)

According to the Leibniz integral rule, we have to apply the chain rule to the upper limit of the integral.

\(F'(x) = x^{(1/3)} d(x)/dx - 0^{(1/3)} d(0)/dx\)   [applying the chain rule to the upper limit]

Since the upper limit of the integral is x, the derivative of x with respect to x is 1, and the derivative of 0 with respect to x is 0.

\(F'(x) = x^{(1/3)} (1) - 0^{(1/3)} (0)\)

\(F'(x) = x^{(1/3)\)

Therefore, the derivative of F(x) is \(F'(x) = x^{(1/3)\).

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Answer:

So I believe you are supposed to find the common denominator between the two so we know that 2 times 2 is 4 and 3 times 3 is nine, and when you multiply 2 and three you get 6. I believe the answer is (6).

Step-by-step explanation: A=6

Answer: 1957.5

Step-by-step explanation: We provide you with the result of the division 7830 by 4 straightaway:

7830 divided by 4 = 1957.5

The result of 7830/4 is a terminating decimal with 1 digit to the right of the decimal point.

7830 divided by 4 in decimal = 1957.5

7830 divided by 4 in fraction = 7830/4

7830 divided by 4 in percentage = 195750%

Note that you may use our state-of-the-art calculator above to obtain the quotient of any two integers or decimals, including 7830 and 4, of course.

Repetends, if any, are denoted in ().

The conversion is done automatically once the nominator, e.g. 7830, and the denominator, e.g. 4, have been inserted.

No need to press the button, unless you want to start over.

Give it a try now with a similar division by 4.

Answer:

Step-by-step explanation:

If S is the midpoint of R and S and the coordinate R(-9, 4) and S(2, -1), we are to find T.

Usimg the midpoint formula;

\(M(X, Y) = (\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})\\ where; X = \frac{x_1+x_2}{2}\\Y = \frac{y_1+y_2}{2}\)

Given \(x_1 = -9, y_1 = 4, X = s \ and \ Y = -1\), to get the other coordinate T (x2, y2), we will use the formula above as shown;

\(X = \frac{x_1+x_2}{2}\\2 = \frac{-9+x_2}{2}\\cross \ multiply\\2*2 = -9+x_2\\4 = -9+x_2\\x_2 = 4+9\\ x_2 = 13\)

Similarly to get y2;

Y = y1+y2/6

-1 = 4+y2/2

cross multiply

-1*2 = 4+y2

-2 = 4+y2

y2 = -2-4

y2 = -6

Hence the coordinate T is (13, -6)

Answer:

2.6 x 10 ^4

Step-by-step explanation:

Answer:

2.6 x 10 to the power of 4

Step-by-step explanation:

hope this helps! :)

Answer:

1: b

2: c

Step-by-step explanation:

Answer:

Step-by-step explanation:

1-D

2-B

Answer: amount of variation

Step-by-step explanation:

The mean is a measure of the center whereas the standard deviation measures the variation of data about the mean.

The mean of the values is the ratio of the total sum of values to the number of values.

Here,
The mean is a measure of the center in the data set, whereas the standard deviation measures the variation of data about the mean in the data set.

Thus, the mean is a measure of the center whereas the standard deviation measures the variation of data about the mean.

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Answer:

The answer is 1 over 3.

Step-by-step explanation:

All you had to do was simplify it.