In ADEF, what is the length of segment DF?
F
60°
E
D
45

The hypotheses to test if this sample indicates a significant change in the average number of hours spent studying is:

0: µ = 14 (null hypothesis)

1: µ ≠ 14 (alternative hypothesis)

Option B is the correct answer.

We have,

The null hypothesis states that the population mean for the number of hours spent studying by full-time students at 4-year colleges in the United States is equal to 14 hours per week,

while the alternative hypothesis states that it is different from 14 hours per week.

By using a two-tailed test, we are checking for any significant change in either direction, whether the average number of hours spent studying has increased or decreased from 14 hours per week.

Thus,

The hypotheses to test if this sample indicates a significant change in the average number of hours spent studying is:

0: µ = 14 (null hypothesis)

1: µ ≠ 14 (alternative hypothesis)

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Answer:

•  Mean = 30.4

•  Median = 30

•  Mode = None

•  Range = 5

Step-by-step explanation:

To find the mean, we add all the numbers together and divide by the total number of numbers. In this case, we have 5 numbers: 28, 32, 29, 30, and 33. Adding them together gives us 152. Dividing by 5 gives us a mean of 30.4.

To find the median, we need to order the numbers from smallest to largest: 28, 29, 30, 32, and 33. The median is the middle number which is 30.

To find the mode, we look for the number that appears most frequently in the list. In this case, there is no number that appears more than once so there is no mode.

To find the range, we subtract the smallest number from the largest number. In this case, the smallest number is 28 and the largest number is 33 so the range is 5.

Therefore:

•  Mean = 30.4

•  Median = 30

•  Mode = None

•  Range = 5

I hope that helps!

The correct statement is B. After she had walked 2km along the trail, Erica's vertical distance from the top of the valley was equal to T kilometres.

A function assigns the value of each element of one set to the other specific element of another set.

Given that the function, V(d) models Erica's vertical distance from the top of the valley (in kilometres) after walking d kilometres along the trail.

Therefore, the statement V(2)=T means that after Erica had walked 2km along the trail, Erica's vertical distance from the top of the valley was equal to T kilometres.

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The complete question is:
Erica walked down a trail into a valley. V(d) models Erica's vertical distance from the top of the valley (in kilometres) after walking d kilometres along the trail. What does the statement V(2)=T mean?

A-Erica's vertical distance from the top of the valley was the same after she had walked 2km and after she had walked T kilometres.

B- After she had walked 2km along the trail, Erica's vertical distance from the top of the valley was equal to T kilometres.

C- After she had walked T kilometres along the trail, Erica's vertical distance from the top of the valley was equal to 2km.

As we have proved that PM = PN and Line l is a perpendicular bisector of line segment M N.

A perpendicular bisector is a line that is perpendicular to another line segment and passes through the midpoint of that line segment. In this context, we will prove that if point P is on the perpendicular bisector of line segment MN, then PM = PN.

To prove this, we need to use the properties of perpendicular bisectors. Let l be the perpendicular bisector of line segment MN, passing through its midpoint O. By definition, the line l intersects MN at right angles, and so angle POM and angle PON are both right angles.

Now, since point P lies on the perpendicular bisector l, it is equidistant from the endpoints of the line segment MN, which means that PM = PO and PN = PO. Therefore, PM = PO = PN, and we have proven that if P lies on the perpendicular bisector of MN, then PM = PN.

In summary, we have used the properties of a perpendicular bisector to show that if a point P lies on the perpendicular bisector of line segment MN, then it is equidistant from the endpoints of that segment.

Hence, PM = PN.

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The value of x is 20.

Given that a rectangle PQRS has diagonals PR = 4x - 15, and QS = 3x + 5, we need to find the value of x,
Since, we know that the diagonals of a rectangle are equal,

So,

PR = QS

4x-15 = 3x+5

x = 20

Hence the value of x is 20.

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The total surface area of the square pyramid is 99 cm²

An equation is an expression that can be used to show the relationship between two or more numbers and variables using mathematical operators.

The area of a figure is the amount of space it occupies in its two dimensional state.

To get the surface area:

Area of base = 10 cm * 2 cm = 20 cm²

Area of first triangle lateral face = (1/2) * 2 cm * 8 cm = 8 cm²

Area of second triangle lateral face = (1/2) * 10 cm * 6.3 cm = 31.5 cm²

Total surface area = 20 cm² + 2(8 cm²) + 2(31.5 cm²) = 99 cm²

The total surface area is 99 cm²

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Answer:

390

Step-by-step explanation:

The mean height of sunflowers on Constantin's farm is 210.33 centimetres, rounded to two decimal places.

To find the mean height of sunflowers on Constantin's farm, we need to sum up all the heights and divide by the total number of sunflowers.

Adding up all the heights, we get:

301 + 285 + 20 + 351 + 35 + 205 + 311 + 25 + 45 + 310 + 301 + 305 = 2524

There are 12 sunflowers in total, so we divide the sum by 12:

2524 / 12 = 210.33

This means that if we were to select a sunflower at random from Constantin's farm, on average, we would expect it to be about 210.33 centimetres tall.

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The interest is $293.88 in interest

The remaining balance is approximately $2793.88.

Monthly Interest Rate = 0.2 / 12

Monthly Interest Rate ≈ 0.01667 (rounded)

Month 1:

Interest: $4000 * 0.01667 ≈ $66.68 (rounded)

New Balance: $4000 + $66.68 = $4066.68

Payment: $300

Remaining Balance: $4066.68 - $300 = $3766.68

Month 2:

Interest: $3766.68 * 0.01667 ≈ $62.82 (rounded)

New Balance: $3766.68 + $62.82 = $3829.50

Payment: $300

Remaining Balance: $3829.50 - $300 = $3529.50

Month 3:

Interest: $3529.50 * 0.01667 ≈ $58.86 (rounded)

New Balance: $3529.50 + $58.86 = $3588.36

Payment: $300

Remaining Balance: $3588.36 - $300 = $3288.36

Month 4:

Interest: $3288.36 * 0.01667 ≈ $54.80 (rounded)

New Balance: $3288.36 + $54.80 = $3343.16

Payment: $300

Remaining Balance: $3343.16 - $300 = $3043.16

Interest: $3043.16 * 0.01667 ≈ $50.72 (rounded)

New Balance: $3043.16 + $50.72 = $3093.88

Payment: $300

Remaining Balance: $3093.88 - $300 = $2793.88

Total = $66.68 + $62.82 + $58.86 + $54.80 + $50.72

≈ $293.88 in interest

The remaining balance is approximately $2793.88.

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Using the Pythagoras theorem, the longest leg has the length of 24 feet.

Given that,

A ladder of length (2x+6) feet is positioned x feet from a wall.

Height of the ladder = (2x + 6) feet

Distance of ladder from the wall = x feet

Height of the wall that the ladder is placed = (2x + 4) feet

These three lengths form s right triangle where (2x + 6) feet is the hypotenuse.

Longest leg is (2x + 4) feet

Using the Pythagoras theorem,

(2x + 6)² = (2x + 4)² + x²

4x² + 24x + 36 = 4x² + 16x + 16 + x²

4x² + 24x + 36 = 5x² + 16x + 16

x² - 8x - 20 = 0

(x - 10) (x + 2) = 0

x = 10 or x = -2

x = 2 is not possible.

So x = 10

Longest leg = 2x + 4 = 20 + 4 = 24 feet

Hence the length of the longest leg is 24 feet.

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Answer: 2.4

Step-by-step explanation: obviously not anywhere close to 3 trust

The surface area of the larger can is approximately 674.375 square centimeters.

We have,

The ratio of the corresponding linear measures of two similar cans is 4 to 7.

The ratio of their surface areas will be the square of this ratio, which is (4/7)² = 16/49.

Let A be the surface area of the larger can.

(220 cm²) / A = 16/49

220 cm² x 49 = A x 16

10780 cm² = A x 16

A = 10780 cm² / 16

A = 674.375 cm²

Therefore,

The surface area of the larger can is approximately 674.375 square centimeters.

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A. 28% is the percent of the mixture is fruit juice.

First, we need to find the total amount of fruit juice in the mixture.

For Brand A juice: 6 L x 52% = 3.12 L of fruit juice

For Brand B juice: 9 L x 12% = 1.08 L of fruit juice

Total fruit juice in the mixture: 3.12 L + 1.08 L = 4.2 L

The total amount of the mixture is 6 L + 9 L = 15 L

The percent of the mixture that is fruit juice is:

(4.2 L / 15 L) x 100% = 28%

Therefore, the answer is A. 28%.

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Next all three balls toll after 60 minutes, that is 12:00 PM.

Given that, Three balls toll at an intervals of 10 minutes, 15 minutes and 20 minutes.

They toll together all 11:00 am.

Take LCM of three different intervals. That is,

10= 2×5

15=3×5

20=2×2×5

So, the LCM is 2×2×3×5= 60

Means all three balls toll after 60 minutes, which is 12:00 PM.

Therefore, next all three balls toll after 60 minutes, that is 12:00 PM.

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It could be feasible to accommodate the prism diagonally or by orienting it in a certain way, depending on the geometry of the container.

Given that:

Length, L = 2 and 1/2 = 2.5 cm

Width, W = 2 and 1/2 = 2.5 cm

Height, H = 5 cm

The volume of the rectangular prism is calculated as,

Volume = 2.5 x 2.5 x 5

Volume = 31.25 cubic centimeters

Therefore, the volume of the rectangular prism is 31.25 cubic centimeters.

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Answer:

The correct statement is: ΔJDC ≅ ΔYAM.

This is because the given statement ΔJCD ΣΔMAY tells us that ΔJCD is congruent to ΔMAY by the SAS (side-angle-side) postulate.

We can use this information to conclude that ΔJDC is congruent to ΔYAM by the CPCTC (corresponding parts of congruent triangles are congruent) theorem. Specifically, the corresponding parts that are congruent are:

Therefore, the correct congruency statement is ΔJDC ≅ ΔYAM. The other statements are not correct.

A ∩ B is the intersection of sets A and B, which is the set of elements that are in both A and B.

A = {2, 3, 5, 7} and B = {1, 2, 5, 10}, so A ∩ B = {2, 5}.

B ∩ D^c is the intersection of set B and the complement of set D, which is the set of elements in B that are not in D.

B = {1, 2, 5, 10} and D^c = {1, 4, 6, 8, 9, 10}, so B ∩ D^c = {1, 10}.

A^c is the complement of set A, which is the set of elements in U that are not in A.

U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and A = {2, 3, 5, 7}, so A^c = {1, 4, 6, 8, 9, 10}.

C ∩ D is the intersection of sets C and D, which is the set of elements that are in both C and D.

C = {1, 2, 3, 6} and D = {3, 5, 7}, so C ∩ D = {3}.

B u D^c is the union of set B and the complement of set D, which is the set of elements that are in B or in the complement of D, or both.

B = {1, 2, 5, 10} and D^c = {1, 4, 6, 8, 9, 10}, so B u D^c = {1, 2, 4, 5, 6, 8, 9, 10}.

Thus, this can be the universal set.

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Answer:

Step-by-step explanation:

18

18 is a mulitple of both 6 and 18

The expression (X - Y) 5 ÷ 8 - 1 ÷ 4 (X + Y) is equivalent to

(20X² - 20Y² - 1) / (4X + 4Y)

We have,

We can simplify the given expression as follows:

(X - Y) 5 ÷ 8 - 1 ÷ 4 (X + Y)

= (5X - 5Y) ÷ 8 - 1 ÷ (4X + 4Y)

[distributing the factors]

= (5X - 5Y) /8 - 1/(4X + 4Y)

[finding a common denominator]

= ((5X - 5Y)(4X + 4Y) - 1)/(4X + 4Y)

= (20X² + 20XY - 20XY - 20Y² - 1) / (4X + 4Y)

= (20X² - 20Y² - 1) / (4X + 4Y)

Therefore,

The expression (X - Y) 5 ÷ 8 - 1 ÷ 4 (X + Y) is equivalent to

(20X² - 20Y² - 1) / (4X + 4Y)

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The surface area of the triangular prism that is shown above is calculated as: 63.25 square yards. .

The surface area of a triangular pyramid is calculated using the formula below:

SA = A + 3a

where we have:

A = the area of the triangular base of the pyramid

a = the area of one of the pyramid's faces.

Area of one of the pyramid's face (a) = 1/2 * base * height = 1/2 * 5 * 7

a = 17.5 square yards

Area of triangular base (A) = 1/2 * base * height = 1/2 * 5 * 4.3

A = 10.75 square yards

Surface area (SA) = 10.75 + 3(17.5) = 63.25 square yards.

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The amount that the taxpayer is owing in taxes is $2,691.05.

We have,

Income tax payable refers to a business organization's tax liability to the government in the jurisdiction in which it operates. The amount of liability will be determined by the company's profitability over a given time period and the applicable tax rates. Tax payable is considered a current liability rather than a long-term liability because it must be settled within the next 12 months.

Based on the table, we are using the tax rate of 15% for the taxable income of $11,757.

The tax payable will equals to:

= 15%*$11,757 + $927.50

= $1,763.55 + $927.50

= $2,691.05

Hence, The amount that the taxpayer is owing in taxes is $2,691.05.

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complete question:

Based on this table, if someone had a taxable income of $11,757, how much would they owe in taxes?

Answer:

In the explanation

Hope this helps!

Step-by-step explanation:

1. 20: 1.3010

2. 25: 1.3979

3. 300: 2.4771

4. 500: 2.690 ( 2.6989700 )

5. 8000: 3.9031

6. 0.7: -0.1549

7. 0.04: -1.3979

( The blank for the question on the bottom is pq, refer to the product property in logarithms :) )

Answer:

Step-by-step explanation:

I explain 1 through 10 that should give you an idea of how this goes.

See image for explan

The area of the rectangle is 10 in².

We have,

Given,

Length = 5 inches

Width = 2 inches

Now,

Area of a rectangle.

= length x width

= 5 x 2

= 10 in²

Thus,

The area of the rectangle is 10 in².

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In pigs, the length of pregnancies varies according to a Normal distribution with mean 114 days and standard deviation 5 days, approximately 2.28% of pig pregnancies are longer than 124 days.

We can start by standardizing the value 124 using the formula:

z = (x - μ) / σ

where x is the value we want to standardize, μ is the mean, and σ is the standard deviation.

So in this case:

z = (124 - 114) / 5 = 2

Using a standard normal distribution table or calculator, we can find that the proportion of values greater than 2 is approximately 0.0228.

Therefore, approximately 2.28% of pig pregnancies are longer than 124 days.

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The total area of the path is 296 square feet, and the value of x is,

⇒ 64.2 feet.

Now, We know that;

To find the area of a rectangle, we multiply the length of the rectangle by the width of the rectangle.

Based on the screenshot provided, the rectangular vegetable garden has dimensions of (x+2) feet by (x+10) feet, and there is a stone path around the garden that is 3 feet wide on all sides.

To find the value of x, we need to set up an equation using the information given.

Hence, The total area of the garden and the path is equal to the area of the outer rectangle minus the area of the inner rectangle, which is:

(x+2+2) × (x+10+2) = (x+2) × (x+10) + 296

Simplifying and solving for x, we get:

x² + 16x + 48 = x² + 12x + 20 + 296

4x = 268

x = 67

Therefore, the value of x is, 67 feet.

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There are 3/20  pink tulips in the garden

By determining the percentage of the garden that is made up of pink tulips.

If 3/10 of the tulips are pink and tulips account for half of the garden, the percentage of the garden that is pink tulips is:

(3/10) x (1/2) = 3/20

So, 3/20 of the garden is pink tulips.

Hence, the answer is 3/20.

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Applying the Pythagorean theorem, the length of the unknown side in the right triangle is: a ≈ 13.2.

The Pythagorean theorem is expressed as:

c² = a² + b², given that a and b are small legs of the right triangle and c is the longest leg or hypotenuse facing the right angle in the triangle.

Given the following:

c = 16

b = 9

a = ?

Plug in the values:

16² = a² + 9²

a² = 16² - 9²

a = √(16² - 9²)

a ≈ 13.2

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Answer:

65.8

Step-by-step explanation:

to solve such equations u should use (PEMDAS)

parenthesis, exponents, multiplication, division, addition, subtraction

note that multiplication doesn't become always before division if the division is before in the equation we divide then multiply

same with addition and subtraction we add or subtract depnding on what first

other than that we follow the steps i mentioned before

parenthesis, exponents, multiplication, division, addition, subtraction

so solve the parantheses first

then the exponents (you may have not learned this yet)

then multiplication and division together start with the one that comes first

the addition and subtraction start with the one that comes first

so for example :5×5÷5×5

=25÷5×5

=5×5

=25

i started with the first multiplication cuz it came first then division cuz it was before the other multiplication

and then the other multiplication

now here is the answer for your equation 93+48÷(12-42)x17

using PEMDAS(don't write this it's just for explaining)

parantheses first

93+48÷-30×17

we don't have exponents so just skip it

now division and multiplication

93+(-1.6)×17

finally addition amd subtraction

because we don't have subtraction we won't use it too

93 +(-27.2)

=65.8

Based on the percentage of melons, Andres' fruit salad will taste more Melony than Sadie's.

The percentage is the quotient of the numerator and denominator.

Like ratios, percentages show the relative size of a value compared to another.

Percentages are expressed as the quotient multiplied by 100.

                           Sadie            Andres

Cups of melon       4                      7

Cups of apple        3                      5

Ratios                   4:3                   7:5

The sum of ratios   7                     12

Percentages of melon to apple:

                         Sadie              Andres

                 57.14% (4/7 x 100)  58.33% (7/12 x 100)

Thus, using the percentage of melon to apple, we can conclude that Andres' fruit salads tastes 58.33% more Melony than Sadie's.

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