d.
a.
b.
12
8
Which triangles are similar?
8
3
25
(25
25
25
6
6
16
Ос
od
Оа
O
b

Using the formula of volume of a sphere and hemisphere, the volume of the figures are given as;

1. 2144.57 m³

2. 696.6 m³

3. 20569.1m³

4. 2637ft³

5. 56.5km³

6. 6381.79 in³

The volume of a sphere is given as 4/3πr³

Where π is a constant whose value is equal to 3.14 approximately. “r” is the radius of the hemisphere.

1. The volume of the sphere is;

v = 4/3 * 3.14 * 8³ = 2144.57m³

2. The volume of the sphere is;

v = 4/3 * 3.14 * (11/2)³ = 696.6m³

3. The volume of the sphere is;

v = 4/3 * 3.14 * 17³ = 20569.1m³

4. The volume of the hemisphere is;

v = 2/3 * 3.14 * 10.8³ = 2637ft³

5. The volume of the hemisphere is;

v = 2/3 * 3.14 * 3³ = 56.5km³

6. The volume of the hemisphere is;

v = 2/3 * 3.14 * (29/2)³ = 6381.79in³

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Answer:

$90

Step-by-step explanation:

To find out how much money he can save by paying the total amount at the time of purchase, first you have to determine the total amount that Jackson would pay if he can agree to pay $250 down and $130 a month for 18 months:

$250+(130*18)=$2590

Then, you need to find the difference:

$2590-$2500=$90

According to this, the answer is that you will save $90 by paying the total amount at the time of purchase.

This question is based on the simply math calculation. Therefore, the money can he save is $90 by paying the total amount at the time of purchase.

Given:

Jackson wants to purchase a home theater system that sells for $2500. Either he can pay the total amount at the time of purchase or he can agree to pay $250 down and $130 a month for 18 months.

We need to determined money can he save by paying the total amount at the time of purchase.

According to the question,

To find out,  money he can save by paying the total amount at the time of purchase, first you have to determine the total amount that Jackson would pay if he can agree to pay $250 down and $130 a month for 18 months:

⇒ $250+(130 \(\times\) 18)=$2590

Now, calculating the difference:

⇒ $2590 - $2500 = $90

Therefore, the money can he save is $90 by paying the total amount at the time of purchase.

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Answer:

i think b, because when an ucharged object touches/combines with another object that's uncharged.. the uncharged object will become charged. so by bringing a charged object into contact with an uncharged object, some electrons will migrate to even out the charge on both objects.

Step-by-step explanation:

hope this helps!

Answer:

B

Step-by-step explanation:

opposites attract

The values of x for which f(x) = 7 are x = 61 and x = 21.

To find the values of x for which f(x) = 7, we can set up the equation and solve for x.

The given function is f(x) = 0.5|x - 41| - 3.

Setting f(x) equal to 7, we have:

0.5|x - 41| - 3 = 7.

First, let's isolate the absolute value term:

0.5|x - 41| = 7 + 3.

0.5|x - 41| = 10.

To remove the absolute value, we can consider two cases:

Case: (x - 41) is positive or zero:

0.5(x - 41) = 10.

Multiplying both sides by 2 to get rid of the fraction:

x - 41 = 20.

Adding 41 to both sides:

x = 61.

So x = 61 is a solution for this case.

Case: (x - 41) is negative:

0.5(-x + 41) = 10.

Multiplying both sides by 2:

-x + 41 = 20.

Subtracting 41 from both sides:

-x = -21.

Multiplying both sides by -1 to solve for x:

x = 21.

So x = 21 is a solution for this case.

Therefore, the values of x for which f(x) = 7 are x = 61 and x = 21.

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Rhys will have to pay £6 interest after the first year.

To calculate the interest, we can use the formula:

Interest = Principal x Rate

Where:

Principal = £200

Rate = 3% = 0.03 (in decimal form)

So, the interest Rhys will have to pay after the first year is:

Interest = £200 x 0.03 = £6

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If the value of sin x = 0.2, then the values for sin(π - x) is 0.2.

Given that,

the value of sin x = 0.2

We have to find the value of sin(π - x).

We know the trigonometric rule that,

sin(π - x) = sin (x)

for any value of x.

So here whatever the value of x, the value of  sin(π - x) is sin (x) itself.

So here sin x = 0.2.

So, by the rule,

sin(π - x) = sin (x) = 0.2

Hence the value is 0.2.

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To solve the savings plan balance, we have to calculate the interest for 19 months. The formula for calculating interest for compound interest is given below:$$A = P \left(1 + \frac{r}{n} \right)^{nt}$$where A is the amount, P is the principal, r is the rate of interest, t is the time period and n is the number of times interest compounded in a year.

The given interest rate is 11% per annum, which will be converted into monthly rate and then used in the above formula. Therefore, the monthly rate is $r = \frac{11\%}{12} = 0.0091667$.

The monthly payment is $PMT = $250. We need to find out the amount after 19 months. Therefore, we will use the formula of annuity.

$$A = PMT \frac{(1+r)^t - 1}{r}$$where t is the number of months of the plan and PMT is the monthly payment. Putting all the values in the above equation, we get:

$$A = 250 \times \frac{(1 + 0.0091667)^{19} - 1}{0.0091667}$$$$\Rightarrow

A = 250 \times \frac{1.0091667^{19} - 1}{0.0091667}$$$$\Rightarrow

A =250 \times 14.398$$$$\Rightarrow A = 3599.99$$

Therefore, the savings plan balance after 19 months with an APR of 11% and monthly payments of $250 is $3599.99 (approx).

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The system has an infinite number of solutions, but the only solution is (a, b) = (0, 0).

The given system of equations can be solved using the substitution method. We can begin by solving the first equation,\(a^2 + b^2\), for either a or b. Let's solve for a:

\(a^2 + b^2 = 0\)

\(a^2 + b^2 = 0\)

\(a^2 = -b^2\)

\(a = \pm\sqrt(-b^2)\)

We can substitute this expression for a into the second equation, \(3a^2 - 2ab - b^2 = 0\), and simplify:

\(3(\pm\sqrt(-b^2))^2 - 2(\pm\sqrt(-b^2))b - b^2 = 0\)

\(3b^2 - 2b^2 - b^2 = 0\)

0 = 0

Since 0 = 0, this means that the system of equations has an infinite number of solutions. In other words, any values of a and b that satisfy the equation \(a^2 + b^2 = 0\) will also satisfy the equation \(3a^2 - 2ab - b^2 = 0\)

However, the equation \(a^2 + b^2 = 0\) only has a single solution, which is a = b = 0. Therefore, the solution to the system of equations is (a, b) = (0, 0).

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Answer:

99x78=7722

123x56=6888

98x172=16856

900x38=34200

Step-by-step explanation:

Answer:

Step-by-step explanation:

The line segment's slope represents the period during which the speed decreases is b. The slope is -10.

The slope of a line segment measures the steepness of the line segment.

The slope is the ratio of the rise (the change in vertical height, y, between the endpoints) over the run (the difference in horizontal length, x, between the endpoints.

Elapsed Time (sec)     Speed (mph)

1                                        45

2                                       35

3                                       25

4                                       15

5                                       15

6                                       15

The Slope of the line segment during speed decreases = y₂ - y₁ ÷ x₂ - x₁.

= (35 - 45) / (2 - 1)

= -10/1

= -10

Thus, b. The slope is -10.

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To determine when the total cost of each health club will be the same, we can set up an equation and solve for the number of months.

Let's assume the number of months is represented by 'x'.

For Club A, the total cost is given by:

Total cost of Club A = $13 (one-time fee) + $28x (monthly fee)

For Club B, the total cost is given by:

Total cost of Club B = $19 (one-time fee) + $27x (monthly fee)

To find the number of months when the total cost is the same, we set the two equations equal to each other:

$13 + $28x = $19 + $27x

Simplifying the equation, we get:

$28x - $27x = $19 - $13

$x = 6

Therefore, after 6 months, the total cost of each health club will be the same.

To find the total cost for each club after 6 months, we substitute the value of 'x' back into the equations:

Total cost of Club A after 6 months = $13 + $28(6) = $13 + $168 = $181

Total cost of Club B after 6 months = $19 + $27(6) = $19 + $162 = $181

So, the total cost for both Club A and Club B will be $181 after 6 months.

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Answer:

t - (-2,-1)

q - (1,-3)

r - (3,3)

s - (0,2)

Step-by-step explanation:

Answer:

The scale factor represents a proportional relationship between the scale drawing and the building’s dimensions. If the dimensions change, then the scale factor must also change to preserve the relationship.

Step-by-step explanation:

Answer:

The scale factor is a proportional relationship.   The scale factor represents a proportional relationship between the scale drawing and the building’s dimensions. If the dimensions change, then the scale factor must also change to preserve the relationship. Enlargements have a scale factor greater than 1.  Reductions have a scale factor between 0 and 1. The proportion should be preserved.

Hope this Helps!

Answer: -4/15

Step-by-step explanation: To add these two fractions together,

we start by finding their Least Common Denominator (LCD).

Since our denominators of 5 and 3 have no factors in common,

our least common denominator is 5 · 3 or 15.

In order to get a denominator of 15 in each fraction,

we multiply top and bottom of the first fraction by 3

and top and bottom of the second fraction by 5.

That gives us -9/15 + 5/15 which simplifies to -4/15.

As your last step, make sure that the fraction

that you end up with doesn't reduce.

In this case, -4/15 does not reduce but watch out for this last step.

The value of line RS is 23

From the diagram shown, we have that line PS, line PQ, line QR and line RS form a square.

Note that the sides of a square are equal to each other.

The relationship is represented as;

Line PS = Line PQ = Line QR = Line RS

We have that;

Substitute the expressions

6x - 5 = 9x - 4

Now, collect like terms

6x - 9x = - 4 - 5

Subtract the like terms

-3x = -9

Make 'x' the subject of formula

-3x/-3 = -9/-3

x = 3

Then, RS = 9x - 4 = 9(3) - 4 = 27 - 2 = 23

Hence, the value is 23

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(a) The errors made by the student are:

Incorrectly expanding 49(2) as 24 instead of 98.

Mistakenly factoring the quadratic equation as (y - 8)(y - 1) instead of

\(y^{2} - 9y + 8.\)

(b) The exact solution to the equation is x = 7/11.

(a) The student made two errors in their solution:

Error 1: In the step \("22x + 49(2) = 0,"\) the student incorrectly expanded 49(2) as 24 instead of 98. The correct expansion should be 49(2) = 98.

Error 2: In the step \("y^{2} - 9y + 8 = 0,"\) the student mistakenly factored the quadratic equation as (y - 8)(y - 1) = 0. The correct factorization should be \((y - 8)(y - 1) = y^{2} - 9y + 8.\)

(b) To find the exact solution to the equation, let's correct the errors made by the student and solve the equation:

Starting with the original equation: \(22x + 4 - 9(2) = 0\)

Simplifying: 22x + 4 - 18 = 0

Combining like terms: 22x - 14 = 0

Adding 14 to both sides: 22x = 14

Dividing both sides by 22: x = 14/22

Simplifying the fraction: x = 7/11

Therefore, the exact solution to the equation is x = 7/11.

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Answer:

D

Step-by-step explanation:

A and D are both equidistant from the x- axis, that is

A is 3 units above the x- axis and D is 3 units below the x- axis

then the x- axis is the line of symmetry

Answer:

6

Step-by-step explanation:

cause 3+3 is 6

thanks for the easy points :3

Answer:

id.kkkkk.. maybe 5.. maybe 6...

:O

The value of n(AUB) i.e. union of A and B is 53.

What are Intersections and Unions in Probablity?

The union of two sets results in a new set that contains all of the items from both sets. The union is abbreviated as A∪B or "A or B." The intersection of two sets yields a new set containing all of the members from both sets. The junction is denoted by the letters A∩B or "A and B."

Solution:

Given that,

n(A) = 14

n(B) = 51

n(A∩B) = 12

We know that thee formula is n(AUB) = n(A) + n(B) - n(A∩B)

Putting the values,

n(AUB) = 14 + 51 - 12 = 53

So, the answer for the value of n(AUB) = 53

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To simplify this expression we need to follow this procedure:

It means that the correct answer is:

Answer:

0.167

Step-by-step explanation:

if you divide 30/180 it will get you a decimal of 0.166666667 but if you were to divide 180 by 30 you will get 6

technecaly your answer would be 0.166666667 but you only take the first number in the decimal which is 0.1 then take six 0.16 then add the 7 0.167

that should end up being your answer if i did the math right

Answer:

Step-by-step explanation:

5/12 * 6/15 =30/180

1/6=1/6

which is true, Right-hand side is equal to left-hand side

Answer:

Step-by-step explanation:

1.values of x at y=0 are 1

2.5

3.

(3,-4)

4.

it is a minimum.

5.

axis of symmetry is x=3

∠LMN is an obtuse angle.

==========================================

Explanation

Let's go through the answer choices to see which are true, and which are false.

Answer:

Step-by-step explanation:

The data is incorrect. The correct data is:

Deluxe standard

39 27

39 28

45 35

38 30

40 30

39 34

35 29

Solution:

Deluxe standard difference

39 27 12

39 28 11

45 35 10

38 30 8

40 30 10

39 34 5

35 29 6

a) The mean difference between the selling prices of both models is

xd = (12 + 11 + 10 + 8 + 10 + 5 + 6)/7 = 8.86

Standard deviation = √(summation(x - mean)²/n

n = 7

Summation(x - mean)² = (12 - 8.86)^2 + (11 - 8.86)^2 + (10 - 8.86)^2 + (8 - 8.86)^2 + (10 - 8.86)^2 + (5 - 8.86)^2 + (6 - 8.86)^2 = 40.8572

Standard deviation = √(40.8572/7

sd = 2.42

For the null hypothesis

H0: μd = 10

For the alternative hypothesis

H1: μd ≠ 10

This is a two tailed test.

The distribution is a students t. Therefore, degree of freedom, df = n - 1 = 7 - 1 = 6

2) The formula for determining the test statistic is

t = (xd - μd)/(sd/√n)

t = (8.86 - 10)/(2.42/√7)

t = - 1.25

We would determine the probability value by using the t test calculator.

p = 0.26

Since alpha, 0.05 < than the p value, 0.26, then we would fail to reject the null hypothesis.

b) Confidence interval is expressed as

Mean difference ± margin of error

Mean difference = 8.86

Margin of error = z × s/√n

z is the test score for the 95% confidence level and it is determined from the t distribution table.

df = 7 - 1 = 6

From the table, test score = 2.447

Margin of error = 2.447 × 2.42/√7 = 2.24

Confidence interval is 8.86 ± 2.24

Given,

The expression of the inequality is,

Adding 3 to both sides then,

Substracting 3x to both sides then,

The value of x is greater than 2.

The interval of the inequality is (2, inf)

Hence, option d is correct.

Answer:

16/1000000

Step-by-step explanation: