If a fruit cake needs 3 4 of a carton of all-purpose cream and 2 3 of a carton of condensed milk to make, how many cartons of all purpose cream does Grandma need to buy to make 5 fruit cakes?

It can be concluded that the mean cholesterol level after treatment is less than the mean before treatment.

Let the hypothesis be:

H₀: The difference in the mean is less than or equal to 0.

H₁: The difference in the mean is greater than 0.

Here, the sample size, n = 8.

Assume, α = 0.05.

First, find the mean of the differences.

\(\bar{d}=\frac{(283-215)+(299-206)+...+(277-196)}{8}\)

  \(=79.375\)

Now, the standard deviation of the difference is:

\(s_d=\sqrt{\frac{(68-79.375)^2+...+(81-79.375)^2}{8-1}}\)

   \(=13.3838\)

The t value is:

\(t=\frac{\bar{d}}{\frac{s_d}{\sqrt{n}}}\)

 \(=16.7745\)

Now, the degree of freedom is 8 - 1 = 7.

The p-value corresponding to this is 0.0005, which is less than the value of 0.05.

So, reject H₀.

Hence, it can be concluded that the mean cholesterol level after treatment is less than the mean before treatment.

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Answer:

11/21

Step-by-step explanation:

1/3=7/21

1/7=3/21

(7+3)/21=10/21

21/21-10/21=11/21

Thus 11/21 of the circle is shaded.

The interest for Part 1 is approximately $385.10.

The interest for Part 2 is approximately $709.31.

The formula is as follows:

Interest is calculated as follows: Principal * Rate * Time

Where

Part 1:

$132,000 is the principal.

(Decimal) Rate = 12% = 0.12

Time = 8 days/365 days.

How much interest is there in Part 1?

Interest is calculated as follows : $132,000 * 0.12 * (8/365) = $385.10

Therefore, the interest for Part 1 is approximately $385.10.

Part 2:

$106,750 as the principal

(Decimal) Rate = 12% = 0.12

Time = 20 days / 365 days.

How much interest will there be in Part 2

Interest is calculated as follows : $106,750 * 0.12 * (20/365) = $709.31

Therefore, the interest for Part 2 is approximately $709.31.

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Answer:

C    y≥3

Step-by-step explanation:

Range is the y values that a function can be ...this one can be as low as 3 and up to infinity

The value of the variable 'w' for the given equation 7 ( w + 7 )³ = 7(6³)  is equal to w = -1.

As given in the question,

Given equation is equal to :

7 ( w + 7 )³ = 7(6³)

Divide both the side of the equation by 7 we get,

⇒ 7 ( w + 7 )³ / 7 = 7(6³) /7

⇒( w + 7 )³ = (6³)  

Take cube root both the side of the equation we get,

⇒∛( w + 7 )³ = ∛(6³)  

⇒ w + 7 = 6

Now subtract 7 from both the side of the equation we get,

⇒w + 7 - 7 = 6 - 7

⇒ w = -1

Therefore, the value of the variable 'w' for the given equation is equal to w = -1.

The complete question is:

Solve this equation:

7 ( w + 7 )³ = 7(6³)

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Answer:

B) 11.8

Step-by-step explanation:

First write in 4 for x and 2 for y

Then multiply 1.3 times 6 (4+2) and subtract 2-6

Your expression should now be 7.8 +4

After adding these, it should be 11.8

Answer:

B. all of the money this is my answer

Answer:

40

Step-by-step explanation:

range is the difference between the highest and lowest number.

60 is the highest and 20 is the lowest

60-20=40

Answer and Step-by-step explanation:

To find out how many more yards of red fabric Reuben used, we need to subtract the amount of yellow fabric from the amount of red fabric. Since the two fractions have different denominators, we need to find a common denominator before subtracting them. The least common multiple of 8 and 4 is 8, so we can rewrite both fractions with a denominator of 8:

7/8 - 1/4 = 7/8 - (1/4) * (2/2) = 7/8 - 2/8 = (7 - 2)/8 = 5/8

So, Reuben used 5/8 yards more red fabric than yellow fabric.

Answer:5

Step-by-step explanation:

Answer:

large box: 18.75

small box: 13.5

Answer:

(a) Yes, E and F are independent events.

(b) P(E and F) = P(E)P(F) = (1/2)(1/2) = 1/4

Check the picture below.

\( {x}^{2} + {x}^{2} = {6}^{2} \: \: \: (by \: \: pythagoras \: \: \: theorem) \\ = > {2x}^{2} = 36 \\ = > {x}^{2} = \frac{36}{2} \\ = > {x}^{2} = 18 \\ = > x = \sqrt{18} \\ = > x = \sqrt{2 \times 3 \times 3} \\ = > x = 3 \sqrt{2 } \\ = > x = 4 .2\)

Answer:

Answer:The length of the leg is 4.2 units.

Hope you could get an idea from it.

Doubt clarification - use comment section.

Answer:

B) 4,700

Step-by-step explanation:

6000 - 4000 = 2000

2000 in 15 year, find how much for each year

2000/ 15 = 133.3333333

133.3333333 estimated = 133

133 approximately for each year

1975 to 1980 is five years

133 x 5 = 665

4000 + 665 = 4665

4665 rounded the the nearest hundred

4700

The volume of the prism is 97.425 in³.

The volume of the prism is 5280 in³.

We have,

A.

The prism is an equilateral triangle prism.

So,

The area of an equilateral triangle can be calculated using the formula:

Area = (√(3) / 4) x side²

Substituting the given side length of 5 inches into the formula, we have:

Area = (√(3) / 4) x 5²

= (√(3) / 4) x 25

= 25  √(3) / 4

= 10.825 inches²

Now,

The volume of the prism.

= 10.825 x 9

= 97.425 in³

B.

The prism is a right triangular prism.

So,

base² + 16² = 34²

base² = 1156 - 256

base² = 900

base = 30

Now,

Area of the triangle.

= 1/2 x base x height

= 1/2 x 30 x 16

= 15 x 16

= 240 in²

The volume of the prism.

= 240 x 22

= 5280 in³

Thus,

The volume of the prism is 97.425 in³.

The volume of the prism is 5280 in³.

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Answer:

19.2

Step-by-step explanation:

(32) 3/5

= 32 multiple 3/5

= 96/5 [ explanation: 32 multiple 3 = 96 ]

= 19.2 [ explanation: 96 divided by 5 = 19.2 ]

The amount of blue paint and red paint that you use will be 3 quarts and 2 quarts, respectively.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

You mix 1/2 quart of blue paint for every 1/3 quart of red paint to make 5 quarts of purple paint.

Let 'x' be the amount of blue paint and 'y' be the amount of red paint. Then the equations are given as,

x / y = (1/2) / (1/3)

x / y = 3/2                        ...1

x + y = 5                          ...2

From equations 1 and 2, then we have

(3/2) y + y = 5

(5/2) y = 5

y = 2 quart

Then the value of 'x' is given as

x + 2 = 5

x = 3 quart

The amount of blue paint and red paint that you use will be 3 quarts and 2 quarts, respectively.

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Answer:

Step-by-step explanation:

Let the exponential function given in the picture is,

f(x) = a(b)ˣ

Here, a = Initial value

b = Base value

x = Exponent

Since, the graph passes through the points (0, 1) and (1, 3)

For (0, 1),

1 = a(b)⁰

a = 1

For (1, 3),

3 = 1(b)¹

b = 3

Therefore, equation of the given function will be,

f(x) = (3)ˣ

Therefore, Initial value = 1

Base = 3

Asymptote (Horizontal) → y = 0

Vertical asymptote → None

Domain → (-∞, ∞) Or {x | x ∈ R}

Range → (0, ∞) Or {y | y > 0}

Therefore, answers given by Juan are incorrect.

1) Polynomial of 4 terms.

2) The rational roots of the function are,

x = - 2, 1

3) The zeroes of the function are,

x = - 2, - 3, 2

4) The zeroes of the function are,

x = 1, - 1, 2i, - 2i

5) The correct function which shows the cubic equation is, option 1.

We have to given that;

1) Function is,

⇒ 3x⁵ + 5x⁴ - 7x³ + 15

Clearly, There are 4 terms in function.

Hence, Polynomial of 4 terms.

2) Function is,

⇒ x⁴ + 5x³ + 7x² - 3x - 10 = 0

The correct rational roots are satisfy the function,

Hence, We get;

Plug x = 1,

⇒ x⁴ + 5x³ + 7x² - 3x - 10 = 0

⇒ 1⁴ + 5(1)³ + 7 (1)² - 3(1) - 10 = 0

⇒ 0 = 0

Plug x = - 2;

⇒ x⁴ + 5x³ + 7x² - 3x - 10 = 0

⇒ 2⁴ + 5(2)³ + 7 (2)² - 3(2) - 10 = 0

⇒ 0 = 0

Thus, The zeroes of the function are,

x = - 2, 1

3) Function is,

⇒ y = (x + 3) (x + 2) (x - 2)

Hence, The zeroes of the function are,

x = - 3

x = - 2

x = 2

4) Function is,

⇒ 3x² - 4 = - x⁴

⇒ x⁴ + 3x² - 4 = 0

⇒ x⁴ + 4x² - x² - 4 = 0

⇒ x² (x² + 4) - 1 (x² + 4) = 0

⇒ (x² - 1) (x² + 4) = 0

⇒ x² - 1 = 0

⇒ x² = 1

⇒ x = ±1

⇒ x² + 4 = 0

⇒ x² = - 4

⇒ x = ±2i

Hence, The zeroes of the function are,

x = 1, - 1, 2i, - 2i

5) By given graph the  correct function which shows the cubic equation is, Option 1.

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b) We have to define the distribution for the sample mean.

The mean for the sampling distribution will be the same as the population mean, but the standard deviation will be affected by the sample size:

Then, the distribution is N(8.6, 0.2562).

c) We have to calculate the probability that a randomly chosen city have less than 9.5 ppm pollutants.

In this case, we have to use the populations distribution.

We start by calculating the z-score:

Then, we use this z-score to find the probability in the standard normal variable:

d) We now have to calculate the probability for the average of the 39 cities to have less than 9.5 ppm.

In this case, we use the sampling distribution, so we calculate the corresponding z-score as:

Now we can express the probability as:

e) For sampling distributions, if the sample is large enough, we don't need to check for normality in the underlying distribution.

In this case, as the underlying distribution is normal, the sample size can be small and still have a normal distribution for the sampling distribution.

f) We have to calculate Q1, Q3 and IQR.

We can use the z-scores for this quartiles and convert them back to the sampling distribution parameters.

The z-scores are:

We then can calculate the quartiles as:

We can then calculate the IQR as:

Answer:

b) N(8.6, 0.2562)

c) 0.7131

d) 0.9998

e) No

f) Q1 = 8.4272, Q3 = 8.7728, IQR = 0.3456

Step-by-step explanation:

Slope 1/2    point    5,1  

  in point slope form would be

    (y-1) = 1/2 (x-5)

Answer:

X/4=3/6

Start off by cross multiplying the tops and bottoms, so X/4=3/6 turns into 6X=12. Now divide by 6 on both sides.

6X=12      X=2

Answer:

2

Step-by-step explanation:

Cross Multiple and Divide

X. 3

----. = ----

4. 6

So what you want to do is multiply diagonally:

(6)(X) = 6X

(3)(4) = 12

Now that we have our two answers, we put an equal sign between them.

6X = 12

Now to get X alone. Since it's being multiplied by 6, you want to do the opposite and divide.

So remember to divide on both sides to get rid of the 6.

6X divided by 6 is just X.

12 divided by 6 is 2

We got our answers, put the equal sign in-between

X = 2

The chance that you will get a heads or tails when you flip a coin once (option A) is not mutually exclusive.

Mutually exclusive events are events that cannot occur at the same time, or that do not have any overlap. In the case of flipping a coin, the possibility of getting a head and the possibility of getting tails are independent of each other, and both can occur simultaneously. Therefore, the chance that you will get heads or tails when you flip a coin once is not mutually exclusive.

On the other hand, the other events listed (B, C, and D) are mutually exclusive. The chance that you will only study for the test alone or with a friend cannot occur simultaneously, as you can either study alone or with a friend, but not both. Similarly, the chance that you will meet your friends for pizza or at a Chinese restaurant for dinner today at 6 cannot occur at the same time, as you can either go to the pizza place or the Chinese restaurant, but not both. And the chance that you will answer the ringing phone or take a walk cannot occur simultaneously, as you can either answer the phone or take a walk, but not both.

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The chance that you will get a heads or tails when you flip a coin once (option A) is not mutually exclusive.

this question is related to probability.

mutually exclusive

Mutually exclusive events are those events that do not occur at the same time.

For example, when a coin is tossed then the result will be either head or tail, but we cannot get both the results. Such events are also called disjoint events since they do not happen simultaneously.

probability

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.

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Answer:

(35/6) spoons of syrup would be needed.

Step-by-step explanation:

First, we make the conversion of the measures from mixed numbers to fractions.

3 1/2 spoons

3 3/5 gallons

Now, we make a rule of three.

For 7/2 spoons, we need 18/5 gallons.

How many spoons for 6 gallons?

7/2 spoons - 18/5 gallons

x spoons - 6 gallons.

Applying cross multiplication:

Now, we simplify by 3;

(35/6) spoons of syrup would be needed.

The constant of proportionality in the equation is 5/4

The constant connecting two given numbers in what is known in a proportional relationship is the constant of proportionality.

The constant of proportionality may also be referred to as the constant ratio, constant rate, unit rate, constant of variation, or even the rate of change.

In the problem, y = 5/4x

The constant term 5/4 as used in the equation is used t multiply the input x values to get the out put y values

The term helps in relating x to y

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Answer:

The solution is X=7.4 sin38°