Find the volume of this sphere.
Use 3 for TT.
7cm
V ~ [?]cm³
V = πTr³

so (0,-3) and  (2,0) is a solution.   (2,2) and (-3,0) is not a solution. as  the equation of the line passing through the points (0,-3) and (2,0) is y = (3/2)x - 3 we need to substitute points to check valid or not

what is equation ?

An equation is a mathematical statement that asserts that two expressions are equal. In other words, an equation says that one expression on the left side of the equals sign is the same as the expression on the right side of the equals sign. An equation typically includes variables

In the given question,

To determine the equation of the line passing through the points (0,-3) and (2,0), we can use the slope-intercept form of a linear equation:

y = mx + b

where m is the slope and b is the y-intercept.

The slope of the line can be found using the formula:

m = (y₂ - y₁) / (x₂ - x₁)

where (x₁, y₁) = (0,-3) and (x₂, y₂) = (2,0)

m = (0 - (-3)) / (2 - 0) = 3/2

So the equation of the line is:

y = (3/2)x - 3

Now we can check which ordered pair is a solution to this equation by plugging in the x and y values into the equation and seeing if it holds true.

A. (0,-3)

y = (3/2)x - 3

-3 = (3/2)(0) - 3

-3 = -3

This is true, so (0,-3) is a solution.

B. (2,0)

y = (3/2)x - 3

0 = (3/2)(2) - 3

0 = 0

This is true, so (2,0) is a solution.

C. (2,2)

y = (3/2)x - 3

2 = (3/2)(2) - 3

2 = 0

This is false, so (2,2) is not a solution.

D. (-3,0)

y = (3/2)x - 3

0 = (3/2)(-3) - 3

0 = -9/2

This is false, so (-3,0) is not a solution.

Therefore, the solutions to the equation represented by the graph are A. (0,-3) and B. (2,0).

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The complement of set Q {-4, -3, -2} if the universal set is P {-5, -4, -3, -2, -1} is defined by:

¬Q = {-5, -1}

If we have a set A defined in an universal set U, we define the complement of A as all the elements of U that are not elements of A.

In this case we have the sets:

P = {-5, -4, -3, -2, -1}

Q = {-4, -3, -2}

Here we want to find the complement of Q in P, so P is the universal set for this problem.

The elements of P that are not elements of Q are:

{-5, -1}

So that is the complement that we are looking for.

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Answer:

  5.7y^2 +2y +2

Step-by-step explanation:

You want to simplify the expression 4.7y^2+5.3+4y-3.3-2y+y^2.

Identify like terms and combine their coefficients:

  4.7y^2+5.3+4y-3.3-2y+y^2

  = (4.7 +1)y^2 +(4 -2)y +(5.3 -3.3)

  = 5.7y^2 +2y +2

Answer:

Step-by-step explanation:

(i-j)×(j-k)×(k-i)

{(i×j)-(i×k)-(j×j)+(j×k)}×(k-i)

(k+j-i)×(k-i)

( j+i+k-j)

(i+k)

Answer:

6 and 2/3 feet

Step-by-step explanation:

1 feet=12 inches

x feet=80 inches

80/12=6 and 2/3 feet

Based on my knowledge, I would expect a negative correlation between the amount of gas in a car's gas tank and the total distance the car has traveled since last being filled with gas.

As the car travels, the amount of gas in the tank decreases. Thus, if the car has traveled a long distance since being filled up, it is likely that there is less gas in the tank. Therefore, there should be a negative correlation between the amount of gas in the tank and the distance traveled, meaning that as the distance traveled increases, the amount of gas in the tank decreases.

A scatter plot of these two variables should show a downward-sloping trend, indicating the negative correlation.

Therefore the correct answer is negative correlation.

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At the end of 7 years:

a. The man received approximately GHZ 6425.13 as interest.

b. The total amount received by the man is approximately GHZ 22,294.80.

The interest for the first 4 years at 3% compound interest:

Principal amount (P) = GHZ 14,100.00

Rate of interest (R) = 3% = 0.03

Time period (T) = 4 years

The formula for compound interest:

[tex]A = P (1 + R)^T[/tex]

A = 14,100 x (1 + 0.03)⁴

A = 14,100 x (1.03)⁴

A ≈ GHZ 15,869.67

Interest for the first 4 years = A - P

Interest = 15,869.67 - 14,100

Interest ≈ GHZ 1769.67

The total amount at the end of 7 years at 12% per annum:

(P) = GHZ 15,924.57

(R) = 12% = 0.12

(T) = 3 years (remaining 7 years - initial 4 years)

A = 15,869.67(1 + 0.12)³

A = 15,869.67(1.12)³

A ≈ GHZ 22,294.80

a. Interest for the remaining 3 years = A - P

Interest = 22,294.80 - 15,924.57

Interest ≈ GHZ 6425.13

b. Total amount received at the end of 7 years = Principal amount + Interest for 4 years + Interest for 3 years

Total amount = 14,100 + 1769.67 + 6425.13

Total amount ≈ GHZ 22,294.80

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Step-by-step explanation:

There are (9+8+7)  = 24 parts  that add up to 144

each part is then 144/24 = 6

then each side is    9 parts =  9*6 = 54

                8 parts = 8 * 6 = 48

       7 parts    7 * 6 = 42

The value of B using Sine law is approximately 41.7 degrees.

To use the sine law to find angle B, we need to have either the length of side b or the sine of angle B. However, we can use the sine law to set up an equation involving sine B and then solve for it.

the sine law states:

a/sin A = b/sin B = c/sin C

where a, b, and c are the lengths of the sides of a triangle, and A, B, and C are the opposite angles.

In this case, we are given a = 28.82 ft, c = 47.74 ft, and we want to find B. We can set up the following equation using the sine law:

a/sin A = c/sin C

Substituting the given values:

28.82/sin A = 47.74/sin C

Now, we need to find sin A and sin C. Since the angles in a triangle add up to 180 degrees, we have:

A + B + C = 180

We know that A and C are the angles opposite to sides a and c, respectively, so we can use the sine ratio to express them in terms of a and c:

sin A = a/cos B

sin C = c/cos B

Substituting these expressions into the equation above, we get:

28.82/(a/cos B) = 47.74/(c/cos B)

Simplifying and solving for cos B, we get:

cos B = (28.82 * c) / (a * 47.74)

Now that we know cos B, we can use the identity sin^2 B + cos^2 B = 1 to find sin B:

sin B = sqrt(1 - cos^2 B)

Substituting the given values, we get:

sin B = sqrt(1 - ((28.82 * 47.74) / (a * c))^2)

Calculating this expression gives:

sin B = 0.667

Therefore, angle B is:

B = sin^-1(0.667) = 41.7 degrees (rounded to one decimal place)

So, angle B is approximately 41.7 degrees.

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_____The given question is incomplete, the complete question is given below:

If c = 47. 74 ft and a = 28. 82 ft, find B using sine law.

The resultant substraction value of the sum of three hundredths and 256 tenths from 41435 hundredths is equals to the 388.72.

Subtraction is one of the four arithmetic operations along with addition, multiplication and division. Subtraction is an operation representing the removal of an object from a collection. This is indicated by the symbol '-'. For example, there are 5 − 2 books meaning 5 books with 2 taken away, resulting in a total of 3 books. We have sum of three hundredths and 256 tenths. First, 3 hundredths means 3 out of 100, which can be denoted as = 3/100 = 0.03. Similarly, 256 tenth means 256/10 = 25.6. So, the sum of three hundredths and 256 tenths = 25.60 + 0.03 = 25.63 and 41435 hundredths = 414.35. Now, substract 25.63 from 414.35

= 414.35 - 25.63

= 388.72

Hence, required value is 15.805.

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Answer: 1 1/24

Step-by-step explanation:

2/3 - 3/8 = 25/24. Reduce it and you get 1 1/24

If each shirt is the same price, the cost of each one include the following:  B. $20.75.

In Mathematics, a unit price can be defined as the price that is being charged by a seller for the sale of a single unit of product.

In order to determine the unit price for the shirt, we would divide the cost of shirts by the number of shirts based on the following mathematical equation (formula);

Unit price = Cost of shirts/Number of shirts

By substituting the given parameters into the unit price formula, we have the following;

Unit price = $124.50/6

Unit price = $20.75.

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Complete Question:

Luisa will buy 6 shirts for $124.50. If each shirt is the same price, how much does each one cost?

A. $20.07

B. $20.75

C. $27.05

D. $27.50

It's 29.75

I divided 85 with 100, which gave me 0.85. Then i calculated the new price(35% of the original one) and i multiplied them.

Hope this helps.

Step-by-step explanation:

1st method:-

Using congurency:-

In ∆AOC AND ∆COD

1) CO= CO {common side}

2) <OAC = <ODC { inscribed angel on same base CO}

3)OD = OC {radius}

4)∆AOC ≅ ∆COD {SAS fact}

5)∆AOC = ∆ COD {area of congurent traingle is equal}



2nd method:-

Using property of traingles:-

Construction:- Join DA and CB

<ACB = 90° { angle substended by diameter}

CO⊥AB

Now we know that,

Area of traingle = 1/2 B*H

CO is height { of both traingle's}

AO is base {of both traingle's}

Now, ∆AOC= 1/2*CO*AO--1

and, ∆ COD = 1/2 *CO*AO--2

∆AOC= ∆COD {from above 1 and 2}

The cost of 4 kilograms is $13 if the unit rate is $3.25kg.

What is the unit rat?

The unit rate is a rate in which the second term in the ratio is 1. For example, if you have a rate of 60 miles per hour, the unit rate would be 60 miles per 1 hour, or simply 60 miles per hour. Another example is if you have a unit price of $2.50 per pound of apples, the unit rate would be $2.50 per 1 pound, or simply $2.50 per pound.

If the unit rate is $3.25/kg, then the cost of 1 kg is $3.25. To find the cost of 4 kg, we can multiply the cost of 1 kg by 4:

4 kg x $3.25/kg = $13

Therefore, the cost of 4 kilograms is $13 if the unit rate is $3.25kg.

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The percent decrease in the number of people who went to the local swimming pool over four weeks, starting with a record high of 1,060 people in the first week, was 20%.

To find the percent decrease in the number of people who went to the pool over the four weeks, we need to first find the total number of people who went to the pool over the four weeks and then calculate the percentage decrease from the first week to the fourth week.

Number of people in the first week = 1,060

Number of people in the second week = 1,060 - 110 = 950

Number of people in the third week = 950 + 130 = 1,080

Number of people in the fourth week = 1,080 - 232 = 848

Total number of people over the four weeks = 1,060 + 950 + 1,080 + 848 = 3,938

Percentage decrease in the number of people who went to the pool over the four weeks = ((1,060 - 848)/1,060) * 100% = 20%

Therefore, the percent decrease in the number of people who went to the pool over the four weeks is 20%.

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Therefore, the surface area of the given triangular prism is approximately 126.56 square units.

Surface area is a measure of the total area that the surface of a three-dimensional object occupies. It is the sum of the areas of all the faces or surfaces of an object. Surface area is usually expressed in square units, such as square inches, square centimeters, or square meters, depending on the unit system being used.

For example, if you have a cube with side length "s", its surface area can be calculated by finding the area of each face and adding them together. Since a cube has six square faces of equal size, the formula for its surface area would be:

Surface Area of Cube = 6s²

by the question.

To find the surface area of a triangular prism, we need to calculate the area of all its faces and then add them together.

First, let's find the area of the two triangular bases. Each base is a right triangle with base 5, height 4, and hypotenuse 7. We can use the Pythagorean theorem to calculate the height of the triangle:

[tex]4^2 + (5/2)^2 = h^2[/tex]

[tex]16 + 6.25 = h^2[/tex]

[tex]22.25 = h^2[/tex]

[tex]h = \sqrt(22.25)[/tex]= 4.71

So, the area of each base is:

[tex]A = 1/2 * base * height = 1/2 * 5 * 4.71 = 11.78[/tex]

Next, we need to find the area of the three rectangular faces. The two congruent rectangular faces have dimensions of 5 by 6, and the remaining rectangular face has dimensions of 7 by 6. The area of each rectangular face is simply the product of its dimensions:

[tex]A1 = 5 * 6 = 30[/tex]

[tex]A2 = 5 * 6 = 30[/tex]

[tex]A3 = 7 * 6 = 42[/tex]

Finally, we can calculate the total surface area of the prism by adding up the areas of all five faces:

[tex]Total surface area = 2A(base) + A1 + A2 + A3[/tex]

[tex]Total surface area = 2(11.78) + 30 + 30 + 42[/tex]

[tex]Total surface area =126.56[/tex]

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The probability of the first three cards being 3 aces and the last one being a king is 1/66,300.

The probability of drawing an ace from a deck of 52 cards is 4/52 (since there are 4 aces in the deck), and the probability of drawing a king is 4/52 as well.

Since the cards are dealt with no replacement, the probability of drawing three aces in a row is

(4/52) × (3/51) × (2/50) = 1/5525

This is because after each card is drawn, there is one less ace in the deck, and one less card overall.

Now, we need to multiply this probability by the probability of drawing a king as the fourth card. Since there are only 48 cards left in the deck at this point (since three cards have already been drawn), the probability of drawing a king is

4/48 = 1/12

Therefore, the probability of drawing 3 aces and 1 king in a row is

(1/5525) × (1/12) = 1/66300

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The proportion of students who took ACT and scored between 18 and 28, P(18 < X < 28) is 0.607.

The proportion of students who took ACT and scored between 18 and 28, P(18 < X < 28) is given by the formula:

P(18 < X < 28) = P(Z < (28 - 21)/5.5) - P(Z < (18 - 21)/5.5)

We can then calculate the z-scores for the lower and upper bounds of the range as follows:

Z1 = (28 - 21)/5.5 = 1.27Z2 = (18 - 21)/5.5 = -0.55

Using a z-table or calculator, we can find the probabilities associated with these z-scores:

P(Z < 1.27) = 0.898P(Z < -0.55) = 0.291

Therefore,P(18 < X < 28) = P(Z < 1.27) - P(Z < -0.55) = 0.898 - 0.291 = 0.607

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Answer:

Ratios are fractions, right? Set the two fractions equal to each other and then cross-multiply them. If each side of the equation is equal, then the ratios are equal; if not, then the ratios are not equivalent.

Ex. 1

Comparing ratios 4:2 and 2:1

[tex]\frac{4}{2} = \frac{2}{1}[/tex]

Cross-multiplying, we get 4 = 4, but we can also simplify each side of the equation to get 2 = 2.

Ex. 2

Comparing ratios 3:5 and 6:7

[tex]\frac{3}{5} =? \frac{6}{7}[/tex]

Cross-multiply, we get 21 = 30, so the ratios are not equal. This is an example of a case where you can't simplify the ratios.

Ex. 3

Comparing rations 5:12 and 10:24

[tex]\frac{5}{12} = \frac{10}{24}[/tex]

Cross-multiply, 120 = 120 so the ratios are equal.

Hope this helps!

Answer:

25.455844, soo around 25

Step-by-step explanation:

The length of the midsegment of the trapezoid is 38.5. The midsegment is the line segment that connects the midpoints of the two parallel sides of the trapezoid. It divides the trapezoid into two congruent triangles.

To find the length of the midsegment of the trapezoid, we need to first find the midpoint of the two parallel sides of the trapezoid. To do so, we need to use the midpoint formula, which is (x1 + x2) ÷ 2, (y1 + y2) ÷ 2, where (x1, y1) and (x2, y2) are the coordinates of the two points.

For example, if the coordinates of the two points are (1,2) and (5,7), then the midpoint of the two points will be (1+5) ÷ 2, (2+7) ÷ 2 = (6, 4.5).

Once we have the coordinates of the two midpoints, we can use the distance formula to find the length of the midsegment. The distance formula is √((x2-x1)² + (y2-y1)²).

So if the coordinates of the two midpoints are (3,6) and (9,2), then the length of the midsegment will be √((9-3)² +(2-6)²) = √(36+16) = √52 = 38.5.

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Andrés is 35 years old, Carlos is 31 years old, and Rodolfo is 24 years old based on the sum is given.

Let's assume the age of Andrés is x years.

According to the problem, Carlos' age is (x - 4) years and Rodolfo's age is (x - 11) years.

Now, we know that the sum of their ages is 90, so we write an equation:

x + (x - 4) + (x - 11) = 90

Simplify following equation:

3x - 15 = 90

Adding 15 to both sides, we get:

3x = 105

Dividing by 3, we get:

x = 35

So Andrés' age is 35 years.

Carlos' age is (x - 4) = 31 years.

Rodolfo's age is (x - 11) = 24 years.

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Translation: The sum of the ages of Andrés, Carlos and Rodolfo is 90 years. Andrew's age exceeds Carlos' age by 4 years and Rodolfo's by 11. Determine the ages of all three

The table of values is completed below and the function of the sequence is T(n) = n(n + 2)

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

Pattern  Counters

1                 3

2                8

3                15

4                24

When the pattern is 5, we have

Counters(5) = 5 * (6 + 1)

So, we have

Counters = 35

So, the table is

Pattern number             1       2       3       4       5

Number of counters      3       8      15      24     35

In (a), we have

Counters(5) = 5 * (6 + 1)

Express 6 as 5 + 1

So, we have

Counters(5) = 5 * (5 + 1 + 1)

So, we have

Counters(n) = n * (n + 1 + 1)

As an n-th term, we have

T(n) = n(n + 2)

Hence, the function is T(n) = n(n + 2)

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Answer:

g(4)=-2 and g(-4)=1

Step-by-step explanation:

Answer:

Calculation:

Frequency table

Other statistical characteristics:

Average (mean): μ=93.9

Absolute deviation: 153.4

Mean deviation: 5.1133333333333

Minimum: 78

Maximum: 104

Variance: 40.956666666667

Standard deviation σ=6.3997395780349

Corrected sample standard deviation s=6.5091447608147

Coefficient of variation cV=0.069319965503884

Signal-to-noise ratio SNR=14.42585830404

Median: 95

Quartile Q1: 89.75

Quartile Q2: 95

Quartile Q3: 99

1st decile: 85.2

2nd decile: 88.2

3rd decile: 91.3

4th decile: 93

5th decile: 95

6th decile: 97

7th decile: 97.7

8th decile: 99

9th decile: 101.9

Interquartile range IQR: 9.25

Quartile Deviation QD: 4.625

Coefficient of Quartile Deviation CQD: 0.049006622516556

Lower fence: 75.875

Upper fence: 112.875

Set of outliers: {} - empty set - no outliers found

Interdecile range IDR: 16.7

Mode: 97 - unimodal

Geometric mean: 93.673540144338

Harmonic mean: 93.43824696186

Sum: 2817

Sum of squares: 1228.7

Sum of absolute values: 2817

Average absolute deviation: 5.1133333333333

Range: 26

Frequency table :

Z-score: {-0.1406, -1.3907, 0.4844, -2.3282, 1.5782, -0.9219, -0.2969, 0.0156, 0.4844, -1.0782, -2.4845, 0.1719, 1.1094, -0.1406, 0.4844, 0.7969, -1.0782, 1.4219, -0.6094, 0.1719, 1.2657, 0.4844, 0.7969, -0.4531, 0.1719, -0.2969, 1.1094, -0.7657, 0.7969, 0.6407}

Count items: 30

Answer: The last one is a function

Step-by-step explanation:

If A value of x for example 4 produces more than one y value like 1 and 3 it is not a function also graphing it and using the line method helps

Answer the answer is a