50 Points! Multiple choice algebra question. Photo attached. Thank you!

Answer:

----------------------

Use the compound interest formula:

Where:

Plugging in the values, we get:

The statement that there are approximately as many boys between 167 and 169 as there are between 169 and 170 is false.

In statistics, understanding and interpreting data is an essential skill. One way to interpret data is by analyzing the distribution of values within a certain range.

To determine whether the statement is true or false, we need to analyze the distribution of boy's heights between the two ranges. Assuming the heights of boys are normally distributed, we can use the empirical rule, also known as the 68-95-99.7 rule, to estimate the percentage of boys within each range.

The empirical rule states that in a normal distribution:

68% of the values fall within one standard deviation of the mean

95% of the values fall within two standard deviations of the mean

99.7% of the values fall within three standard deviations of the mean

We can use this rule to estimate the percentage of boys within each range as follows:

Between 167 and 169: This range is one standard deviation below the mean. Therefore, approximately 68% of boys' heights fall within this range.

Between 169 and 170: This range is between one and two standard deviations below the mean. Therefore, approximately 27% of boys' heights fall within this range.

Based on this analysis, we can see that there are not approximately as many boys between 167 and 169 as there are between 169 and 170. In fact, there are significantly more boys between 167 and 169 than there are between 169 and 170.

The statement that there are approximately as many boys between 167 and 169 as there are between 169 and 170 is false.

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The solution of expression after subtraction is,

⇒ 8249 L 860 ml

We have to given that;

Subtract measurements 450l 890ml from 8700l 750ml​

Now, WE can simplify as,

⇒ L      ml

8700    750

- 450     890

---------------------------

8249     860

Therefore, After subtraction we get;

⇒ 8249 L 860 ml

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Answer: 10xy³ - x²y + 3xy

Step-by-step explanation:

To simplify the expression (3xy³ + 8x²y - 3xy) + (7xy³ - 9x²y + 6xy), we can combine like terms.

Adding the corresponding terms together, we have:

3xy³ + 7xy³ = 10xy³

8x²y - 9x²y = -x²y

-3xy + 6xy = 3xy

Combining these terms, the simplified expression becomes:

10xy³ - x²y + 3xy

Therefore, the correct option is:

O 10xy³ - x²y + 3xy

The numerical value of side length x in the right triangle is 8.

The figures in the image are two similar right triagles.

Since the two right triangles are similar, we equate the ratio of the sides of the two triangles.

x/6 = (x + 4)/9

Cross multiply and solve for x:

6( x + 4 ) = x × 9

Apply distributive property:

6 × x + 6 × 4 = x × 9

Simplifying, we get:

6x + 24 = 9x

Subtract 6x from both sides:

6x - 6x + 24 = 9x - 6x

24 = 9x - 6x

24 = 3x

3x = 24

Divide both sides by 3:

x = 24/3

x = 8

Therefore, the value of 8.

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Answer:

Store A

Step-by-step explanation:

If an item is 20% off, then you pay 80% of the price.

If an item is 10% off, then you pay 90% of the price.

Store A

80% of $1640 = 0.8 × $1640 = $1312

Store B

90% of $1500 = 0.9 × $1500 = $1350

Answer: Store A

Answer:

Store A

Step-by-step explanation:

Store A offers a 20% discount which is equivalent to 0.20 x $1,640 = $328.

The laptop is therefore sold for $1,640 - $328 = $1,312 at Store A.

Store B offers a 10% discount which is equivalent to 0.10 x $1,500 = $150.

The laptop is therefore sold for $1,500 - $150 = $1,350 at Store B.

Therefore, Store A offers a better deal at $1,312 compared to Store B at $1,350.

The expected value for a person buying a ticket is $0.35 rounded to the nearest cent.

The expected value is calculated considering the probabilities of winning each prize and the corresponding values of each prize.

Assuming:

P($25) as the probability of winning the $25 prize

P($10) as the probability of winning the $10 prize

There are 100 tickets sold, therefore, the probabilities can be found as follows:

P($25) = 1/100 (since there is only 1 $25 prize)

P($10) = 1/100 (since there is only 1 $10 prize)

The expected value (E), will then be:

E = P($25) * $25 + P($10) * $10

E = (1/100) * $25 + (1/100) * $10

E = $0.25 + $0.10

E = $0.35

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Answer: the height of the equilateral triangle is 6√3 inches.

Step-by-step explanation:

To find the height of an equilateral triangle, we can use the formula:

height = (√3/2) * side

In this case, we are given the perimeter of the triangle, which is 36 inches.

Since an equilateral triangle has three equal sides, each side would be 36 inches divided by 3, which is 12 inches.

Now we can substitute the side length into the formula:

height = (√3/2) * 12

Simplifying:

height = (√3/2) * 12

height = (√3 * 12)/2

height = (12√3)/2

height = 6√3

Therefore, the height of the equilateral triangle is 6√3 inches.

Answer:

RG

Step-by-step explanation:

Answer: false

Step-by-step explanation:

All the equations which are equivalents are,

⇒ 2 + x = 5

⇒ x + 1 = 4

⇒ Negative 5 + x = negative 2

We have to given that;

All expressions are,

2 + x = 5

x + 1 = 4

9 + x = 6

x + (-4) = 7

-5 + x = -2

Now, We can simplify all the expressions as;

⇒ 2 + x = 5

⇒ x = 5 - 2

⇒ x = 3

⇒ x + 1 = 4

⇒ x = 4 - 1

⇒ x = 3

⇒ 9 + x = 6

⇒ x = 6 - 9

⇒ x = - 3

⇒ x + (-4) = 7

⇒ x = 7 + 4

⇒ x = 11

⇒ -5 + x = -2

⇒x = - 2 + 5

⇒ x = 3

Thus, All the equations which are equivalents are,

⇒ 2 + x = 5

⇒ x + 1 = 4

⇒ Negative 5 + x = negative 2

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As Jim has $30 more than Max, as per this, Max has $270.

Let's assume Max's savings as 'x' dollars.

We have:

2/5 of Jim's savings is equal to 4/9 of Max's savings.

(2/5) * Jim's savings = (4/9) * Max's savings

We also know that Jim has $30 more than Max.

Jim's savings = Max's savings + $30

So,

(2/5) * Jim's savings = (4/9) * Max's savings

(2/5) * (Max's savings + $30) = (4/9) * Max's savings

To solve for Max's savings, we can solve this equation:

(2/5) * (x + $30) = (4/9) * x

So, for x:

(2/5) * (x + $30) = (4/9) * x

Multiplying both sides by 45 (the least common denominator of 5 and 9) to eliminate the fractions:

18(x + $30) = 20x

18x + 540 = 20x

540 = 20x - 18x

540 = 2x

x = 270

Therefore, Max has $270.

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The required angles (corresponding, vertical and alternate) in relation to the Parallel lines are attached accordingly.

Parallel lines are coplanar infinite straight lines that do not cross at any point in geometry. Parallel planes are planes that never intersect in the same three-dimensional space.

When two parallel lines cross by any other line (i.e. the transversal), corresponding angles are generated in matching corners or corresponding corners with the transversal.

When two parallel lines are sliced by a transversal, the resulting alternate exterior angles are congruent, according to the Alternate Exterior Angles Theorem.

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If rectangular prism with a square base has a height of 17.2 cm and a volume of 24.768 cm², the side length of the square base is 1.2 cm.

Let's denote the side length of the square base as x cm. Then, the volume of the rectangular prism can be expressed as V = x² * 17.2 cm³, and its surface area can be expressed as S = 2x² + 4x * 17.2 cm².

We are given that the volume of the rectangular prism is 24.768 cm³, so we can write the equation:

x² * 17.2 cm³ = 24.768 cm³

Simplifying this equation, we get:

x² = 24.768 cm³ / 17.2 cm² = 1.44 cm²

Taking the square root of both sides, we get:

x = 1.2 cm

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The graph of the function is attached and the amplitude and the period are 5 and 2π

From the question, we have the following parameters that can be used in our computation:

f(x) = 5cos(θ)

A sinusoidal function is represented as

f(x) = Acos(B(x + C)) + D

Where

So, we have

A = 5

Period = 2π/1

Evaluate

A = 5

Period = 2π

Hence, the amplitude is 5 and the period is 2π

The graph of the function is attached

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The expected value of the car 7 years after it was purchased is $47,029.12.

To solve this problem, we need to calculate the expected value of the car after 7 years. To do this, we need to use the formula for calculating the value of a depreciating asset:

Value after n years = Initial Value - (Initial Value × (Depreciation Rate/100)×n)

In this case, the initial value of the car is $54792, the depreciation rate is 19%, and n = 7. Thus, the expected value of the car 7 years after it was purchased is:

Value after 7 years = 54792 - (54792 × (19/100)×7)

Value after 7 years = 54792 - (54792 × 0.19×7)

Value after 7 years = 54792 - 7762.88

Value after 7 years = $47,029.12

Therefore, the expected value of the car 7 years after it was purchased is $47,029.12.

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The approximate height difference between the birdhouse and the tree house is 3 ft.

It is less than the approximate difference in height between the swing set and the tree house.

A fraction represents the parts of a whole or collection of objects e.g. 3/4 shows that out of 4 equal parts, we are referring to 3 parts.

We have:

height of birdhouse = 14[tex]\frac{9}{16}[/tex] ft

height of tree house = 11[tex]\frac{13}{16}[/tex] ft

Thus, the approximate height difference between the birdhouse and the tree house will be:

14[tex]\frac{9}{16}[/tex] ft - 11[tex]\frac{13}{16}[/tex]  = 2[tex]\frac{3}{4}[/tex] ft

                   = 2.75 ft

                  = 3 ft

To determine if it is greater than or less than the approximate difference in height between the swing set and the tree house, we have to find the approximate difference in height between the swing set and the tree house. That is:

height of swing set = 8[tex]\frac{1}{4}[/tex] ft

height of tree house = 11[tex]\frac{13}{16}[/tex] ft

difference = 11[tex]\frac{13}{16}[/tex] - 8[tex]\frac{1}{4}[/tex]

                    = 3[tex]\frac{1}{2}[/tex]

                    = 3.5

                    = 4 ft

Therefore, it is less than the approximate difference in height between the swing set and the tree house

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Answer:

6/MN = 8/9

8MN = 54

MN = 6 3/4

The correct answer is B.

given that m is parallel to n,

the angle opposite (2x + 16)° is also (2x + 16)° as vertically opposite angles are equal.

using the corresponding angle rule we know that:

2x + 16 = 96

2x = 80

so x = 40

a. Jason will receive the strongest signal from BTS-4 because he is located in the Voronoi cell of BTS-4.

b. The coordinates of BTS-4 are (−8,4).

a. Jason will receive the strongest signal from BTS-4 because he is located in the Voronoi cell of BTS-4. A Voronoi cell is a region of space that is closer to a given point than any other point. In this case, the given point is BTS-4. The Voronoi diagram is a partitioning of the plane into Voronoi cells, one for each point.

b. The edge connecting vertices P and Q has the equation y=4, which means that it is a horizontal line that intersects the y-axis at 4. The coordinates of BTS-2 are (−8,6), which means that it is located 8 units to the left of the origin and 6 units above the origin. Therefore, BTS-4 must be located 8 units to the left of the origin and 4 units above the origin, which gives it the coordinates (−8,4).

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If y varies directly as x, when x = 15, the value of y is equal to 5.

If y varies directly as x, we can express this relationship using the formula y = kx, where k is the constant of proportionality.

Given that y = 9 when x = 27, we can substitute these values into the equation:

9 = k x 27

To solve for k, we divide both sides of the equation by 27:

k = 9 / 27

k = 1/3

Now that we know the value of k, we can use it to find y for any other value of x.

Let's find y when x = 15:

y = (1/3) x 15

y = 5

Therefore, when x = 15, y is equal to 5.

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The complete question:

Y varies directly as x, and y=9 when x = 27.

Find the value of y, when x =15.

The triangles are similar and

Yes , ΔPSQ ≅ ΔRST because ∠S ≅ ∠S and PS / RS = QS / TS . Thus the triangles are similar by the SAS theorem

Given data ,

Let the first triangle be ΔPSQ

Let the second triangle be ΔRST

Now , the corresponding sides are

PS / RS = QS / TS

where the corresponding sides of similar triangles are in the same ratio

And , the common angle to both the triangles is m∠S

So , ∠S ≅ ∠S and PS / RS = QS / TS

Two sides are equal and the angle between the two sides is equal (SAS: side, angle, side)

Hence , the triangles are similar

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The 91-day T-bill that Nadeen bought at an interest rate of 4.30% p.a. and face value of $5,000 indicates;

a) Nadeen paid about $4,946.24 for the T-bill

b) Barbara's selling price for the T-bill is about $4,962.74

A Treasury bill (T-bill), is a short-term obligation that is issued by the U.S. Department of Treasury and which is backed by the United States government, and has a maturity of less than a year. T-bills are low risk investment as they are backed by the credit and full faith of the U.S. government.

The formula for the price of the T-bill can be calculated with the formula;

Price = Face Value/(1 + (Interest Rate × Days to Maturity/360))

Plugging in the value from the question, we get;

Price = 5000/(1 + (0.043 × 91/360)) ≈ 4946.24

b) The formula for the selling price can be presented as follows;

Selling Price = Face Value/(1 + (Interest Rate × Remaining Days to Maturity/360))

Plugging in the known values, we get;

Selling Price = 5,000/(1 + (0.053 × (91 - 40)/360)) ≈ $4,962.74

Therefore, Barbara sold the T-bill to her friend for $4,962.74

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Mrs. Bright has worked for 8 years, and Mr. Oswald has already worked for 24 years, which is more than Twice the number of years Mrs. Bright has worked.

The number of years Mrs. Bright has worked for the company. We know that Mr. Oswald has been in the company for 24 years, which is three times the number of years Mrs. Bright has worked.

So, Mrs. Bright has worked for 24 / 3 = 8 years in the company.

Now, let's find the number of years Mr. Oswald needs to work for the company to make it twice the number of years Mrs. Bright has worked.

Twice the number of years Mrs. Bright has worked is 2 * 8 = 16 years.

Since Mr. Oswald is already employed for 24 years, we need to find the additional years he needs to work to reach 16 more years.

16 more years - 24 years = -8 years.

The result of -8 years indicates that Mr. Oswald has already worked for more than twice the number of years Mrs. Bright has worked. Therefore, it is not possible for Mr. Oswald to work for more years in order to make it twice the number of years Mrs. Bright has worked.

Mrs. Bright has worked for 8 years, and Mr. Oswald has already worked for 24 years, which is more than twice the number of years Mrs. Bright has worked.

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The probability that a random adult has a high school degree or some college, but has no college degree is 53. 50 % .

The number of adults with some high school degree or some college would be :

= 3, 561 + 6, 058

= 9, 619 people

The probability that a random adult would have high school degree or some college is therefore :

= Adults with high school degree or some college / Total adults in the town

= 9, 619 / 17, 981

= 53. 50 %

In conclusion, the probability is 53. 50%.

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The mean score of a random student (YY) is 574.5. the standard deviation of the random student's score (YY) is 8.

Given:

- Each correct question is worth 10 points.

- Every student receives an additional 555 bonus points.

Let's calculate the mean and standard deviation of YY:

Mean of YY:

The mean score, denoted as μY, can be calculated using the mean of XX (μX) and the scoring scheme:

μY = μX * 10 + 555

Substituting the value of μX from the given information:

μY = 1.95 * 10 + 555

μY = 19.5 + 555

μY = 574.5

Therefore, the mean score of a random student (YY) is 574.5.

Standard Deviation of YY:

The standard deviation of YY, denoted as σY, can be calculated using the standard deviation of XX (σX) and the scoring scheme:

σY = σX * 10

Substituting the value of σX from the given information:

σY = 0.8 * 10

σY = 8

Therefore, the standard deviation of the random student's score (YY) is 8.

Complete question: Mr. Gupta gave his students a quiz with three questions on it. Let X represent the number of questions

that a randomly chosen student answered correctly. Here is the probability distribution of X along with

summary statistics:

0

1

2

2.

3

X = # correct

P(X)

0.05

0.20

0.50

0.25

Mean: Hex = 1.95

Standard deviation: Ox 0.8

Mr. Gupta decides to score the tests by giving 10 points for each correct question. He also plans to give

every student 5 additional bonus points. Let Y represent a random student's score.

What are the mean and standard deviation of Y?

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Determine Joy's annual income tax liability. If the amount is significantly different from the R4000 monthly deduction, she may need to consult a tax advisor to ensure accurate tax planning.

To assess whether the monthly income tax deduction of R4000 is too much for Joy, we need to calculate her annual income tax liability and compare it to the deduction.

First, let's calculate the amount Joy contributes to her pension fund annually:

Pension fund contribution = 7% of annual salary

Pension fund contribution = 7/100 * R286,500

Pension fund contribution = R20,055

Next, we need to determine Joy's taxable income by subtracting her pension fund contribution from her annual salary:

Taxable income = Annual salary - Pension fund contribution

Taxable income = R286,500 - R20,055

Taxable income = R266,445

Now, we can calculate the income tax liability based on the South African income tax brackets for the 2023 tax year. Please note that tax brackets are subject to change, so it's essential to verify with the latest tax regulations.

According to the current tax brackets, the tax rates for the 2023 tax year are as follows:

18% on the first R216,200 of taxable income

26% on the portion of taxable income between R216,201 and R337,800

31% on the portion of taxable income between R337,801 and R467,500

36% on the portion of taxable income between R467,501 and R613,600

39% on the portion of taxable income above R613,601

Using these tax rates, we can calculate the income tax liability:

Tax liability = (18% * amount within first bracket) + (26% * amount within second bracket) + (31% * amount within third bracket) + (36% * amount within fourth bracket) + (39% * amount within fifth bracket)

First, let's calculate the amounts within each tax bracket:

Amount within first bracket = min(Taxable income, R216,200)

Amount within second bracket = min(max(Taxable income - R216,200, 0), R337,800 - R216,201)

Amount within third bracket = min(max(Taxable income - R337,800, 0), R467,500 - R337,801)

Amount within fourth bracket = min(max(Taxable income - R467,500, 0), R613,600 - R467,501)

Amount within fifth bracket = max(Taxable income - R613,600, 0)

Now, let's substitute the values and calculate the income tax liability:

Tax liability = (18% * min(Taxable income, R216,200)) + (26% * min(max(Taxable income - R216,200, 0), R337,800 - R216,201)) + (31% * min(max(Taxable income - R337,800, 0), R467,500 - R337,801)) + (36% * min(max(Taxable income - R467,500, 0), R613,600 - R467,501)) + (39% * max(Taxable income - R613,600, 0))

By calculating this equation, you can determine Joy's annual income tax liability. If the amount is significantly different from the R4000 monthly deduction, she may need to consult a tax advisor to ensure accurate tax planning.

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The measure of Angle 2 is 17 degrees.

The measure of angle 2,  the relationships between the given angles formed by the parallel lines and transversals.

1. The angles formed by lines s, t, and y, clockwise from top left, are:

  - Blank

  - Blank

  - (10x + 5) degrees

  - Blank

  - (4x - 7) degrees

  - Blank

2. The angles formed by s and z are:

  - 65 degrees

  - 1

  - Blank

  - Blank

3. The angles formed by z and t are:

  - 2

  - Blank

  - Blank

  - Blank

From the given information, we can deduce the following:

- Angle 1 is congruent to the angle formed by z and t (corresponding angles).

- Angle (10x + 5) degrees is congruent to angle 65 degrees (alternate interior angles).

- Angle (4x - 7) degrees is congruent to angle 2 (alternate interior angles).

Therefore, we can set up the following equations:

65 = 10x + 5     (Equation 1)

2 = 4x - 7       (Equation 2)

Solving Equation 1:

65 - 5 = 10x

60 = 10x

x = 6

Substituting x = 6 into Equation 2:

2 = 4(6) - 7

2 = 24 - 7

2 = 17

Hence, the measure of angle 2 is 17 degrees.

Therefore, the correct answer is:Angle 2 = 17 degrees.

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The area of the sector with an angle of 285 degrees and a radius of 6 units is 28.5π square units.

To find the area of a sector, we can use the formula:

Area of Sector = (Central Angle / 360 degrees) × π ×  (Radius²)

Given that the central angle is 285 degrees and the radius is 6, we can substitute these values into the formula:

Area of Sector = (285 degrees / 360 degrees) ×  π ×  (6²)

Area of Sector = (19/24) ×  π × 36

Area of Sector = (19/24) ×  36π

Area of Sector = (19 × 36π) / 24

Area of Sector = 684π / 24

Area of Sector = 28.5π

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Answer:

(x - 3)² + (y + 4)² = 29

Step-by-step explanation:

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r is the radius

we have the coordinates of the centre but require to find the radius r

the radius is the distance from the centre to a point on the circle.

using the distance formula to find r

r = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = (3, - 4 ) centre and (x₂, y₂ ) = (8, - 2) point on circle

r = [tex]\sqrt{(8-3)^2+(-2-(-4))^2}[/tex]

  = [tex]\sqrt{5^2+(-2+4)^2}[/tex]

  = [tex]\sqrt{25+2^2}[/tex]

  = [tex]\sqrt{25+4}[/tex]

  = [tex]\sqrt{29}[/tex]

then equation with centre (3, - 4 ) and r = [tex]\sqrt{29}[/tex] , is

(x - 3)² + (y - (- 4) )² = ([tex]\sqrt{29}[/tex] )² , that is

(x - 3)² + (y + 4)² = 29