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Answer:

Step-by-step explanation:

The dimension the  a box with a square end the largest possible volume is 10 ×10 × 23.3

First, we will need to complete the question.

Let us assume that its dimensions are h by h by w and its girth is 2h + 2w.

Volume = h²w

Where h is the length

w is the girth

From the information given, we have;

Length + girth = 90

w+(2h+2w) = 90

2h + 3w = 90

Make 'w' the subject

w = 90- 2h/3

w = 30 - 2h/3

Substitute the values

Volume = h²(30 - 2h/3)

expand the bracket

Volume = 30h² - 2h³/3

Find the differential value

Volume = 60h - 6h²

h = 10

Substitute the values

w =  30 - 2h/3

w = 30 - 2(10)/3

w = 30 - 20/3

w = 23.3 in

The dimensions are 10 ×10 × 23.3

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Answer:

Answer is C hope this helps

Step-by-step explanation:

the probability that the claim will be rejected assuming the manufacturer's claim is true is approximately 0.2489.

To find the probability that the claim will be rejected assuming the manufacturer's claim is true, we need to calculate the probability of having 70 or fewer patients cured out of 100.

First, we need to determine the mean (μ) and standard deviation (σ) of the binomial distribution.

For a binomial distribution, the mean (μ) is given by μ = n * p, where n is the number of trials (100 patients) and p is the probability of success (0.73).

μ = 100 * 0.73 = 73

The standard deviation (σ) of a binomial distribution is given by σ = sqrt(n * p * (1 - p)).

σ = sqrt(100 * 0.73 * (1 - 0.73)) = sqrt(100 * 0.73 * 0.27) = sqrt(19.71) ≈ 4.44

Next, we will use the normal distribution to approximate the binomial distribution. Since the sample size is large (n = 100) and both np (100 * 0.73 = 73) and n(1 - p) (100 * 0.27 = 27) are greater than 5, the normal approximation is valid.

We want to find the probability of having 70 or fewer patients cured, which is equivalent to finding the cumulative probability up to 70 using the normal distribution.

Using the z-score formula:

z = (x - μ) / σ

For x = 70:

z = (70 - 73) / 4.44 ≈ -0.6767

Now, we can use a standard normal distribution table or a calculator to find the cumulative probability up to z = -0.6767.

The cumulative probability P(X ≤ 70) is approximately 0.2489.

Therefore, the probability that the claim will be rejected assuming the manufacturer's claim is true is approximately 0.2489.

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Answer:

x=19

3x+123= 180

3x =180-123

3x =57

x=57/3

x=19

Answer:

It will take Eric 10 weeks to save £1200

Step-by-step explanation:

He makes £14 per hour, since he works for 38 hours per week,

That means that he makes (14)(38) = £532 per week

Since he saves 1/4 of his earnings, that gives us,

Savings per week = (1/4)(weekly earnings)

Savings per week = 1/4(532)

Savings per week = £133 (per week)

Now, we need to find the number of weeks till he saves £1200,

we have,

Total savings = (number of weeks)(Savings per week)

let n = number of weeks,

Total savings = n(Savings per week)

so,

1200 = n(133)

n = 1200/133

n = 9.0225

Now, since he will have less than 1200 in 9 weeks (the number is greater than 9 i.e 9.0225 > 9)

So, we round up to 10,

Hence it will take Eric 10 weeks to save £1200

Answer:

he can make 6 because 2 and 1/2 plus 1/2 = 3 and 3 divided by 2 is 6

Step-by-step explanation:

The probability that one of two selected unit cubes will have exactly two painted faces while the other unit cube has no painted faces will be 0.0714.

We have,

Total number of smaller cubes = 64

Side of larger cube = 4 units,

And,

Two faces of the larger cube that share an edge are painted blue,

And the cube is disassembled into 64 unit cubes.

Now,

If two faces of the larger cube that share and edge are painted blue, it means that 28 of the 64 unit cubes are painted in at least one side and 36 cubes have no painting faces.

And,

Also, from the 28 cubes painted only 4 have exactly two painted faces.

So,

Using combination formula,

\(^n}C_{r}=\frac{n!}{r!(n-r)!}\)

Now,

Ways to select 2 cubes from the 64 = ⁶⁴C₂ ,

And,

Ways to select one cube with exactly two painted faces and one cube with no painted faces = ⁴C₁ × ³⁶C₁

So,

The probability that one of two selected unit cubes will have exactly two painted faces while the other unit cube has no painted faces,

i.e.

Probability = \(\frac{ ^{4}C_{1}* ^{36}C_{1}}{ ^{64}C_{2}}\)

On solving we get,

Probability = 0.0714

So,

The Probability of two selected unit cubes is 0.0174.

Hence we can say that the probability that one of two selected unit cubes will have exactly two painted faces while the other unit cube has no painted faces will be 0.0714.

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\(~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$530\\ r=rate\to 8.4\%\to \frac{8.4}{100}\dotfill &0.084\\ t=years\dotfill &1 \end{cases} \\\\\\ I=(530)(0.084)(1)\implies I=44.52 \\\\[-0.35em] \rule{34em}{0.25pt}\)

\(~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$530\\ r=rate\to 8.4\%\to \frac{8.4}{100}\dotfill &0.084\\ t=years\dotfill &3 \end{cases} \\\\\\ I=(530)(0.084)(3)\implies I=133.56\)

Answer:

A) She pays $44.52 in one year.

B) She pays $133.56 in three years.

Step-by-step explanation:

Ken’s sister borrowed $530 from the bank at 8.4% per year.

A) how much interest did she pay in one year

Here's the required formula to find the interest :

\(\longrightarrow{\tt{I = \dfrac{PRT}{100}}}\)

Substituting all the given values in the formula to find the interest for one year :

\(\begin{gathered} \qquad\longrightarrow{\sf{I = \dfrac{PRT}{100}}} \\ \\ \qquad\longrightarrow{\sf{I = \dfrac{P \times R \times T}{100}}} \\ \\ \qquad\longrightarrow{\sf{I = \dfrac{530 \times 8.4 \times 1}{100}}} \\ \\ \qquad\longrightarrow{\sf{I = \dfrac{530 \times 8.4}{100}}} \\ \\ \qquad\longrightarrow{\sf{I = \dfrac{4452}{100}}} \\ \\ \qquad\longrightarrow{\sf{\underline{\underline{\red{I = \$44.52}}}}} \end{gathered}\)

Hence, the interest is $44.52.

\(\begin{gathered}\end{gathered}\)

b) how much interest did she pay in three years

Here's the required formula to find the interest :

\(\longrightarrow{\tt{I = \dfrac{PRT}{100}}}\)

Substituting all the given values in the formula to find the interest for three years :

\(\begin{gathered} \qquad\longrightarrow{\sf{I = \dfrac{PRT}{100}}} \\ \\ \qquad\longrightarrow{\sf{I = \dfrac{P \times R \times T}{100}}} \\ \\ \qquad\longrightarrow{\sf{I = \dfrac{530 \times 8.4 \times 3}{100}}} \\ \\ \qquad\longrightarrow{\sf{I = \dfrac{530 \times 25.2}{100}}} \\ \\ \qquad\longrightarrow{\sf{I = \dfrac{13356}{100}}} \\ \\ \qquad\longrightarrow{\sf{\underline{\underline{\red{I = \$133.56}}}}} \end{gathered}\)

Hence, the interest is $133.56.

\(\rule{300}{2.5}\)

Answer:

a = -√3/3

b = 2√3/3

Step-by-step explanation:

Finding the slope of the tangent at C  by finding the derivative:

x^2 + y^2 = 1

2x + 2y y' = 0

2y y' = -2x

y' = -2x / 2y = -x/y

So the slope = - 1/2 / √3/2

= -1/2 * 2/√3

= -1/√3

= -√3/3

Using the point-slope form of a straight line

y - y1 = m(x - x1)

y - √3/2 = -√3/3(x - 1/2)

y - √3/2 =  -√3/3 x +√3/6

y =  -√3/3 x + √3/6 +√3/2

y =  -√3/3 x + 4√3/6

y = -√3/3x +  2√3/3

Answer:

Option B

Step-by-step explanation:

Average rate of change of a function between x = a and x = b will be,

Average rate of change = \(\frac{f(b)-f(a)}{b-a}\)

We have to calculate average rate of change of the given quadratic function between x = 0 and x = 2.

From the given graph,

f(2) = 6

f(0) = 10

Therefore, average rate of change = \(\frac{f(2)-f(0)}{2-0}\)

                                                          = \(\frac{10-6}{2-0}\)

                                                          = 2

Option B will be the answer.

The closest option to the reorder point is 71.40 pounds.

To determine the reorder point, we need to find the demand during the lead time and the safety stock.

First, let's calculate the demand during the lead time. The mean daily rate is 15 pounds, and it takes 4 days for the order to arrive. So, the mean demand during the lead time is 15 pounds/day * 4 days = 60 pounds.

Next, let's calculate the safety stock. The pizza shop wants to limit the probability of a stockout to 7 percent. We can find this value using the z-score table.

Looking up the z-score corresponding to a 7 percent probability, we find that it is approximately 1.89.

The standard deviation is given as 6 pounds.

So, the safety stock is calculated as 1.89 * 6 pounds = 11.34 pounds.

Finally, the reorder point is the sum of the mean demand during the lead time and the safety stock.

Reorder point = 60 pounds + 11.34 pounds = 71.34 pounds.

Therefore, the closest option to the reorder point is 71.40 pounds.

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Based on the given mean and standard deviation of the stock XYZ's daily returns, there is a 22.66% probability of experiencing a loss that exceeds 1.5 standard deviations from the mean on any given day.

To find the probability of facing a loss that amounts to more than 1.5 standard deviations from the mean on any given day, we need to calculate the area under the normal distribution curve beyond this threshold.

First, we calculate the value corresponding to 1.5 standard deviations below the mean:

1.5 * 40 basis points = 60 basis points.

Next, we find the z-score associated with this value by using the formula:

\(z = (X - \mu) / \sigma,\)

where X is the threshold value, μ is the mean, and σ is the standard deviation.

z = (60 - 20) / 40 = 0.75.

Using a standard normal distribution table or calculator, we can find the area under the curve beyond the z-score of 0.75. This corresponds to the probability of facing a loss greater than 1.5 standard deviations from the mean.

The probability of facing a loss greater than 1.5 standard deviations from the mean on any given day is approximately 1 - 0.7734 = 0.2266, or 22.66%.

In conclusion, based on the given mean and standard deviation of the stock XYZ's daily returns, there is a 22.66% probability of experiencing a loss that exceeds 1.5 standard deviations from the mean on any given day.

This implies that such losses, although relatively rare, can occur in a normal distribution of the stock's returns. It is important for investors to be aware of the potential for larger losses and to manage their risk accordingly.

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The LU factorization of matrix A is A = LU, where L = [[1, 0, 0], [-2, 1, 0], [1.5, -3, 1]] and U = [[4, -8, 10], [0, 24, -27], [0, 0, -12.5]].

Let's go step by step to find the LU factorization of matrix A.

Matrix A:

A =

[4, -8, 10]

[-8, 8, -7]

[6, -7, 3]

Step 1:

Initialize the L matrix as an identity matrix of the same size as A.

L =

[1, 0, 0]

[0, 1, 0]

[0, 0, 1]

Step 2:

Perform Gaussian elimination to obtain U.

- Multiply the first row of A by (1/4) and replace the first row of A with the result.

A =

[1, -2, 2.5]

[-8, 8, -7]

[6, -7, 3]

- Subtract 8 times the first row of A from the second row of A and replace the second row of A with the result.

A =

[1, -2, 2.5]

[0, 24, -27]

[6, -7, 3]

- Subtract 6 times the first row of A from the third row of A and replace the third row of A with the result.

A =

[1, -2, 2.5]

[0, 24, -27]

[0, 5, -12.5]

Step 3:

Update the L matrix based on the operations performed during Gaussian elimination.

L =

[1, 0, 0]

[0, 1, 0]

[0, 0, 1]

Step 4:

The resulting matrix A is the upper triangular matrix U.

U =

[1, -2, 2.5]

[0, 24, -27]

[0, 5, -12.5]

Therefore, the LU factorization of matrix A is:

L =

[1, 0, 0]

[0, 1, 0]

[0, 0, 1]

U =

[1, -2, 2.5]

[0, 24, -27]

[0, 5, -12.5]

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Answer:

8x - 28y

Step-by-step explanation:

-2(-1x + 5y) + 3(2x - 6y)

2x - 10y + 6x - 18y

collect like terms

2x + 6x - 10y - 18y

8x - 28y

\((8.1 + 7.4) - 25 \div 2.5 \\ = 15.5 - 25 \div 2.5 \\ = 15.5 - 10 \\ = 5.5\)

5.5

Hope it helps.

Do comment if you have any query.

\(\huge\text{Hey there!}\)

\(\large\boxed{\mathsf{(8.1 + 7.4) - 25 \div 2.5}}\\\large\boxed{= \mathsf{\bold{15.5} - 25\div2.5}}\\\large\boxed{\mathsf{= 15.5 - \bf 10}}\\\large\boxed{\mathsf{= \bf 5.5}}\\\\\huge\boxed{\text{Therefore, your answer is: \textsf{5.5}}}}\huge\checkmark\)

\(\huge\text{Good luck on your assignment \& enjoy your day!}\)

~\(\frak{Amphitrite1040:)}\)

The order of values in ascending order will be -4<-2<2<2.64<4<16 as the definition of ascending order says, "When numbers are arranged in ascending order, they are done so from smallest to largest".

When numbers are arranged in ascending order, they are done so from smallest to largest. Climbing down the stairs of numbers starting with their highest value is another way to think of descending. The slide is descended while moving down it. Ascending order, in which the numbers are arranged from lower value to higher value, is the opposite of descending order. A number can be arranged in ascending order by going from smallest to largest from left to right.

Here,

4²=16

-√4=-2

√4²=4

-2√4=-4

6-4=2

√7=2.64

-4<-2<2<2.64<4<16

According to the definition of ascending order, "When numbers are arranged in ascending order, they are done so from smallest to largest," the order of values in ascending order will be -4<-2<2<2.64<4<16.

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Answer:

Yes, you showed your work.

Step-by-step explanation:

Answer:

y=-4

Step-by-step explanation:

The answer is going to be -4 as when y=-16 x=8.

Answer:

B because it is a single digit number with added decimals

Step-by-step explanation:

Answer:

C. It is 2/9 and 0.2 with a line over it.

Step-by-step explanation:

Answer:

The answer to the question provided is possibly 2.

Step-by-step explanation:

\( \: \: \: \: \: \: \: \: \: \: \: \: 3y + 77 = 2y + 79 \\ \frac{ - 2y \: \: \: \: \: \: = - 2y}{1y + 77 = 79} \\ \frac{ \: \: \: \: \: \: \: \: - 77 = - 77}{ \frac{1y}{1} = \frac{2}{1} } \\ \\ y = 2\)

Answer:

16an - 19an + 9an + 8b + 12b

6an + 20b

Answer:

6an+20b I believe

Step-by-step explanation:

Answer:

96 school days

Step-by-step explanation:

i hope this is right but tell me if its wrong

The polynomial expression that represents AB + C in simplest form is: x³ + 3x² + 3x  - 1.

Polynomials are algebraic expressions having variables and constants, and may include exponents.

AB + C would be expressed as:

(x + 1)(x² + 2x - 1) + 2x

Expand

x(x² + 2x - 1) +1(x² + 2x - 1) + 2x

x³ + 2x² - x + x² + 2x - 1 + 2x

x³ + 3x² + 3x  - 1 (simplest form)

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Answer:

The x value of a is 5

Step-by-step explanation:

The directions right and left on the grid is equal to the x-axis while the directions up and down is equal to the y-axis

Answer:

5

Step-by-step explanation:

the answer is 5

Answer: 10077696

Step-by-step explanation:

6x6x6x6x6x6x6x6x6

Answer: 10077696

Step-by-step explanation:

1. Add All The Ones. Which is equal to 6

2. Multiply 6x6x6x6x6x6x6x6x6

3. And You’ve got your answer..

make me brainliest!

Answer:

Only can do the first one

Let's call the measures of the angles in the triangle x, 3x, and 4x.

According to the ratio, we have:

x : 3x : 4x = 8 : 3 : 4

To find the value of x, we can set up a proportion:

8/x = 3/(3x) = 4/(4x)

Cross multiplying, we get:

8x = 12

So, x = 12/8 = 3

Therefore, the measures of the angles in the triangle are 3x, 3(3x), and 4(3x).

The measure of the largest angle is 4x = 4(3) = 12.

A diagonal through the interior of a cube is a line segment that connects two opposite vertices of the cube. In this case, the cube has top face vertices A, B, D, and C, and bottom face vertices E, F, H, and G. There are four possible diagonals through the interior of the cube: AD, BC, AE, and CG.

- Diagonal AD connects vertex A from the top face to vertex D, also on the top face. This diagonal does not pass through the interior of the cube.
- Diagonal BC connects vertex B from the top face to vertex C, also on the top face. This diagonal does not pass through the interior of the cube.
- Diagonal AE connects vertex A from the top face to vertex E on the bottom face. This diagonal passes through the interior of the cube.
- Diagonal CG connects vertex C from the top face to vertex G on the bottom face. This diagonal passes through the interior of the cube.
Thus, the diagonals AE and CG are diagonals through the interior of the cube.

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