The diagram shows a cuboid
What is the surface area of the cuboid?
4cm,5cm and 9cm

Using Pascal's triangle the expansion of the expression \((5x+5)^3\) is \(125x^3+375x^2+375x+125\).

What is Pascal's triangle?

The triangle can be used to calculate the coefficients of the expansion of  \((a+b)^n\) by taking the exponent n and adding 1. The coefficient will correspond with line n+1 of the triangle.

Here for \((5x+5)^3\) , n= 3 so the coefficient of the expansion will correspond with line 4.

The expansion follow the rule ,

\((a+b)^n=c_{0}a^nb^0+c_{1}a^{n-1}b^1+c_{n-1}a^1b^{n-1}+c_{n}a^0b^n\)

The values of the coefficients, from the triangle, are 1-3-3-1.

=> \(1a^3b^0+3a^2b+3a^1b^2+1a^0b^3\)

Here substitute a=5x and b=5 then,

=> \(1(5x)^35^0+3(5x)^25+3(5x)^25^2+1(5x)^15^3\)

=> \(125x^3+375x^2+375x+125\)

Hence the expansion of the expression \((5x+5)^3\) is \(125x^3+375x^2+375x+125\).

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Answer:

22

Step-by-step explanation:

is 22 because 3 times 22 ut maie us 68

Answer:

Let Dad = Y, Son = X

Mathematically, from your statement:

Y = 3X, and (Y+10) + (X+10) = 68

Solving for X in 2nd equation, X = 48-Y

Insert this into first equation and solve for Y:

Y = 3(48-Y)

Y= 144 - 3Y

4Y = 144

Y = 36

Now, solve for X using either equation. I rearranged the 1st equation for X:

X = Y/3

X = 36/3 = 12

The boy is 12 and the dad is 36

Step-by-step explanation:

Hope this helps u

Crown me as brainliest:)

we know that

speed = distance/time

speed = dx/dt

Let x = the distance from the base of the ladder to the base of the wall

y = the distance from the tip of the ladder to the base of the wall, we have:

x^2+y^2 = 13^2

y^2=13^2-12^2 = 169 - 144 = 25 => y = 5 ft

2x dx/dt + 2y dy/dt = 0

2*5* dx/dt + 2*5*(-4) = 0

10 dx/dt = 40

dx/dt = (40/10) ft/sec

dx/dt = 4 ft/sec

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Answer:

X= 1.8

Step-by-step explanation:

If I’m not mistaken then this is how to work it out. X^2 + 4x -9 =0. X^2 + 4x would be 5x. 5x - 9 = 0. +9 on both sides. 5x=9. Divide by 5 on each side. X= 1.8

The x-intercept is the x value at which the graph intercects the x-axis. This happens when y = 0, so, to find it without graphing, we just need to input y = 0 and solve for x:

So, the x-intercept is at x = 0.75 and y = 0, that is, at point:

The y-intercept is similar but is the y value at which the graph intercepts the y-axis, that is, when x = 0.

So, we can input x = 0 and solve for y:

Thus, the y-intercept is at x = 0 and y = -1.5, that is, at point:

The expression with the greater value is the second one:

log₀.₅(4)

Here we have two logarithms whose base are 0.5.

Remember that a logarithm of base a can be rewritten as follows:

logₐ(x) = ln(x)/ln(a)

In this case, we have the expressions:

log₀.₅(6)

log₀.₅(4)

We can rewrite these as:

ln(6)/ln(0.5)

lon(4)/ln(0.5)

Remember that ln(x) < 0  if 0 < x < 1

Because the denominator is negative in both cases, the greater number will be the one with the smallest numerator, which is the second option.

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Answer:

i just wanted to say god bless yall and im sry for not answerinng the question

Step-by-step explanation:

A major disadvantage of correlations is that they cannot make a cause-and-effect statement.

Correlations are statistical measures that describe the size and direction of a relationship between variables.

Correlations are expressed as numbers. Correlations establish that relationships exist but do not explain if the change in one variable is caused by the change in another variable's value.

The disadvantages of correlations include:

Thus, a major disadvantage of correlations is that they cannot make a cause-and-effect statement.

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The ratio of the final surface charge density (ηf) to the initial surface charge density (ηi) is given by 3.68 * \(Q_i / (A_i \times A_i).\)

To understand the concept and solve this problem, we need to consider the relationship between surface charge density, area, and charge. Surface charge density (σ) is defined as the charge (Q) per unit area (A). Mathematically, we can express this relationship as σ = Q/A.

Let's assume the initial area of the irregular shape is \(A_i\), and the final area after each dimension is reduced is \(A_f\). Since each dimension (x and y) is reduced by a factor of 3.68, we can write the relationship between the initial and final areas as:

\(A_f = (1/3.68) \times A_i\)

Now, let's consider the relationship between charge and area. Since the charge remains constant for a given area, we can express it as \(Q_i = Q_f\), where \(Q_i\) is the initial charge and \(Q_f\) is the final charge.

Since the charge remains constant, the ratio of the surface charge densities can be expressed as:

ηf/ηi = \(\sigma _f/\sigma _i = Q_f/A_f / Q_i/A_i\)

Substituting the expressions for area into the equation, we have:

ηf/ηi = \(Q_f/A_f / Q_i/A_i = Q_f / (A_f * Q_i) * (A_i / Q_i)\)

Canceling out the \(Q_i\) terms, we get:

ηf/ηi = \(Q_f / (A_f * Q_i) * (A_i / Q_i) = Q_f / (A_f * A_i)\)

Since \(Q_i = Q_f\), we can simplify further:

ηf/ηi = \(Q_f / (A_f * A_i) = Q_i / (A_f * A_i)\)

Now, substituting the expressions for area into the equation, we have:

ηf/ηi = \(Q_i / (A_f * A_i) = Q_i / ((1/3.68) * A_i * A_i)\)

Simplifying, we find:

ηf/ηi = 3.68 x \(Q_i / (A_i \times A_i).\)

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Complete Question:

The irregularly shaped area of charge in the figure has surface charge density ηi. Each dimension (x and y) of the area is reduced by a factor of 3.68.

What is the ratio ηf/ηi where ηf is the final surface charge density?

Answer:

-11

Step-by-step explanation:

Lets rewrite the equation with the values

-(-3) - 2³ + ab

3 - 8 + (-3*2)

-5 + -6 = -11

-11

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

-11

Step-by-step explanation:

Simply plug in a=-3 and b=2 into the equation provided. Remember the signs (+/-) and be careful with your calculations.

-(-3) - (2)^3 + (-3)(2)  = -11

The z score associated with the highest 10% is closest to: option (c) 1.28

-To find the z score associated with the highest 10%, first determine the percentage that corresponds to the lower 90%, since the z score table typically represents the area to the left of the z score.

- Look up the 0.90 (90%) in a standard normal distribution  (z score) table, which will give you the corresponding z score.

-The z score closest to 0.90 in the table is 1.28, which corresponds to the highest 10% of values.

Therefore, the z score associated with the highest 10% is closest to 1.28.

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Answer:

the mean is 46.

Step-by-step explanation:

The total is 460 and divided by the amount of numbers(10) is 46.

Answer:

y=90x−410

Step-by-step explanation:

in point-slope form, this would be...

y−130=90⋅(x−6)<-----

If you convert this to slope-intercept form this would be...

y=90x−410

Answer:

The prepaid phone plan will have a steeper line and lower y-intercept.

I hope this is right

Step-by-step explanation:

prepaid phone plan y = .20x

contracted phone plan y = .02x + 50

Answer:

A (The prepaid phone plan will have a steeper line and lower y-intercept.)

Step-by-step explanation:

The general equation for a circle is \((x-h)^2+(y-k)^2=r^2\), where \((h,k)\) is the centre of the circle and \(r\) is the radius.

First, we can determine the centre of the circle.

( _ , _ )

The point directly on top is (4,7). Because it lies on the same vertical line as the centre, they have the same x-coordinate.

(4, _ )

The point directly to the right of it is (7,4). Because it lies on the same horizontal line as the centre, they have the same y-coordinate.

(4,4)

Therefore, the centre of the circle is (4,4). Plug this into the general equation:

\((x-h)^2+(y-k)^2=r^2\\(x-4)^2+(y-4)^2=r^2\)

Now, we can determine the radius of the circle.

To do this, we can calculate the distance between the centre of the circle and one of the given points that lie on the circumference.

The centre is (4,4), and one of the points is (4,7). Because they only have a difference of 3 units in the y-direction (and none in the x-direction), this means that the radius is 3 units. Plug this into the general equation:

\((x-4)^2+(y-4)^2=r^2\\(x-4)^2+(y-4)^2=3^2\\(x-4)^2+(y-4)^2=9\)

\((x-4)^2+(y-4)^2=9\)

Answer:

6

Step-by-step explanation:

(2)/((6)√(8))*√(2)-((18)/√81))-2)

(6)sqrt√8 = 6sqrt √2³= 2^3/6=2^1/2= √2

(2√2)/√2 -(-18/√9²)-2)

2-(-18/9 -2)

2-(-2-2)=2+4=6

Answer:

55 boxes of ice cream

Step-by-step explanation:

Tubs of ice cream : boxes of ice cream = 3 : 1

If the factory makes 165 tubs of ice cream in a day, how many boxes of ice cream bars were made?

Boxes of ice cream made in a day = x

Tubs of ice cream : boxes of ice cream = 165 : x

Equate both ratios to find x

3 : 1 = 165 : x

3/1 = 165/x

Cross product

3 * x = 1 * 165

3x = 165

x = 165/3

x = 55

Boxes of ice cream made in a day = 55

Answer:

C

Step-by-step explanation:

A - Incorrect because it is bigger than -0.5

B - Incorrect because it is bigger than -0.5

D - Incorrect because it is bigger than -0.5

C- Correct!

The value of the given expression [\(87^3+ 13^3/87^2 -87 * 13 + 13^2\)] by simplifying the numerator and denominator using suitable identities is 100.

We will first calculate the numerator:

As  (\(a^3\) + \(b^3\)) = (a + b)(\(a^2\) - ab + \(b^2\)) :

\(87^3\) + \(13^3\) = (87 + 13)(\(87^2\) - \(87 * 13\) + \(13^2\))

= 100(\(87^2\) - 87 * 13 + \(13^2\))

Now, calculate the denominator:

\(87^2 - 87 * 13 + 13^2\)

As,(\(a^2 -2ab +b^2\)) =\((a - b)^2\):

\(87^2 - 87 * 13 + 13^2 = (87 - 13)^2\)

\(= 74^2\)

So by solving the equation further:

\((87^3+13^3) / (87^2- 87 * 13+13^2) = 100*(87^2- 87 *13 + 13^2)/(87^2 - 87 * 13 + 13^2)\)

As we can see the numerator and denominator are the same expressions (\(87^2 - 87 * 13 + 13^2\)). so, they cancel each other:

\((87^3 + 13^3) / (87^2 - 87 * 13 + 13^2) = 100\)

So, the value of the given expression is 100.

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Answer:

\(40 + 37 + 30 + 40 + 39 + 41 + 38 + n = 265 + n\)

1)

\( \frac{265 + n}{8} = 43\)

\(265 + n = 344\)

\(n = 79\)

2)

\( \frac{265 + n}{8} = 40\)

\(265 + n = 320\)

\(n = 55\)

3)

\( \frac{265 + n}{8} = 38\)

\(265 + n = 304\)

\(n = 39\)

The Spearman rank-order correlation coefficient is a measure of the direction and strength of the linear relationship between two ordinal variables.

Spearman's rank-order correlation is used when two variables are measured on an ordinal scale.

What is the Spearman Rank-Order Correlation Coefficient?

The Spearman Rank-Order Correlation Coefficient is a non-parametric statistical measure that estimates the relationship between two variables using ordinal data.

It evaluates the strength and direction of a relationship between two variables by rank-ordering the data.

The Spearman correlation coefficient, named after Charles Spearman, calculates the association between two variables' rankings.

The correlation coefficient ranges from -1 to +1. A value of +1 indicates that there is a perfect positive relationship between the variables, whereas a value of -1 indicates that there is a perfect negative relationship between the variables.

In contrast, a value of 0 indicates that there is no correlation between the variables.

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There would be a 1/36 chance of rolling a 6 then a 3 consecutively on a 6-sided die

Because the chance of rolling each of the numbers individually would be 1/6, and you are trying to roll 2 specific numbers in a row on a single die, you can simply multiply 1/6 by 1/6 to get your answer.

Answer:

Answer down below!

Step-by-step explanation:

We have 25 squares in total, and 14 of them are fill, we can figure out it's percentage with division

25/14 = 0.56

We can do 0.56 *100 to get the percentage!

Which that will give you 56%

Where the above conditions are given,  the correct option is: Plan 1 is a better deal for more than 5 cards purchased.

To determine   which pricing plan is a better deal,we need to compare the total cost for a certain number of game cards purchased.

Let's calculate the   total cost for different numbers  of game cards.

For Plan 1  -

- Admission fee  - $5 (fixed)

- Cost per game card  - $1

For Plan 2  -

- Admission fee  - $2.50 (fixed)

- Cost per game card  - $1.50

Now, let's compare the total cost for different numbers of game cards  -

1. If you purchase 1 game card  -

  - Plan 1  - $5 (admission fee) + $1 (cost per game card) = $6

  - Plan 2  - $2.50 (admission fee) + $1.50 (cost per game card) = $4

2. If you purchase 5 game cards  -

  - Plan 1  - $5 (admission fee) + $5 (cost for 5 game cards) = $10

  - Plan 2  - $2.50 (admission fee) + $7.50 (cost for 5 game cards) = $10

3. If you purchase 8 game cards  -

  - Plan 1  - $5 (admission fee) + $8 (cost for 8 game cards) = $13

  - Plan 2  - $2.50 (admission fee) + $12 (cost for 8 game cards) = $14.50

Based on these calculations, we can conclude that  -

- Plan 1 is a better deal for more than 5 cards purchased.

- Plan 2 is a better deal for more than 8 cards purchased.

Therefore, the correct option is  - Plan 1 is a better deal for more than 5 cards purchased.

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Answer:

a) 2 * 8 = 16

b) (-2.5)(-2.5) = 6.25 = \(\frac{625}{1000} = \frac{5}{8}\)

Step-by-step explanation:

Answer:

Domain of (cd)(x) is all real numbers values except 2.

The value of (f/g)(5) is 270

Step-by-step explanation:

To determine if the bolts vary by more than the required variance, we can conduct a hypothesis test. The null hypothesis (H₀) states that the variance of the bolts is equal to or less than the required variance (σ² ≤ 0.025), while the alternative hypothesis (H₁) states that the variance is greater than the required variance (σ² > 0.025).

Next, we need to determine the critical value(s) of the test statistic. Since we are testing for variance, we will use the chi-square distribution. For a one-tailed test with α = 0.01 and 14 degrees of freedom (n-1), the critical value is 27.488.

Now, we can compare the test statistic to the critical value. The test statistic is calculated as (n-1) * s² / σ², where n is the sample size (15), s² is the sample variance (0.1587²), and σ² is the required variance (0.025).

If the test statistic is greater than the critical value, we reject the null hypothesis and conclude that the bolts vary by more than the required variance. Otherwise, we fail to reject the null hypothesis.

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To determine if the bolts vary by more than the required variance, we can conduct a hypothesis test. The null hypothesis (H₀) states that the variance of the bolts is equal to or less than the required variance (σ² ≤ 0.025), while the alternative hypothesis (H₁) states that the variance is greater than the required variance (σ² > 0.025).

Next, we need to determine the critical value(s) of the test statistic. Since we are testing for variance, we will use the chi-square distribution. For a one-tailed test with α = 0.01 and 14 degrees of freedom (n-1), the critical value is 27.488.

Now, we can compare the test statistic to the critical value. The test statistic is calculated as (n-1) * s² / σ², where n is the sample size (15), s² is the sample variance (0.1587²), and σ² is the required variance (0.025).

If the test statistic is greater than the critical value, we reject the null hypothesis and conclude that the bolts vary by more than the required variance. Otherwise, we fail to reject the null hypothesis.

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The median number of faculty in departments in the college of arts and science is 12.

The median is a measure of central tendency that represents the middle value of a dataset when the values are sorted in ascending or descending order. Its purpose is to give a single representative value for the dataset, offering a way to understand the center of the data distribution. Unlike the mean, which can be affected by extreme values, the median is resistant to outliers and gives us a better understanding of what a typical value in the data set might be.

To find the median number of faculty in the College of Arts and Science at Delta University, first, arrange the department faculty numbers in ascending order:

7, 8, 9, 11, 12, 13, 14, 15, 17.

Since there are nine departments, which is an odd number, the median will be the middle value in the sorted list. So the middle number is the fifth number, which is 12

The median number of faculty in departments in the College of Arts and Science at Delta University is 12, as it is the middle value in the sorted list.

Note: The question is incomplete. The complete question probably is: The college of arts and science at delta university has nine departments. The number of faculty in each department is shown below. What is the median number of faculty in departments in the college of arts and science? 8, 12, 9, 15, 17, 11, 13, 14, 7.

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