What is the volume of a hemisphere with a radius of
48 m ,rounded to the nearest tenth of a cubic meter?

The correct equation of the circle with center (0,0) that passes through the point (-6,-6) is:

(x + 6)² + (y + 6)² = 72

Please note that the equation represents the circle with center (0,0) and radius √72.[tex][/tex]

Answer:

The equation of a circle with center (0,0) that passes through the point (-6,-6) is:

(x - 0)² + (y - 0)² = r²

where r is the radius of the circle. Since the center of the circle is (0,0), we can use the distance formula to find the radius:

r = √(0 - (-6))² + (0 - (-6))² = √(6² + 6²) = √72

Therefore, the equation of the circle is:

x² + y² = 72

The graph shows that Rose's savings account balance increases by $20 each month.

The balance of her account after m months is 20m dollars. We want to find an inequality that shows when 20m>160, or when m>8.

Therefore, the inequality that shows when Rose will have more than 160 dollars in her savings account is m>8.

Here is a table of values that shows that Rose will have more than 160 dollars in her savings account after 8 months:

Month | Balance

------- | --------

1 | 20

2 | 40

3 | 60

4 | 80

5 | 100

6 | 120

7 | 140

8 | 160

In conclusion, the graph shows that Rose's savings account balance increases by $20 each month.

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According the given figure, angle Z is calculated using interesting secants and tangents to be

50 degrees

To find angle Z we follow the following procedures

first find angle he central angle

central angle = 180 - 2 * 25

central angle = 180 - 50

central angle = 130

Secondly

central angle is equal to the minor arc

Then using interesting secants and tangents

Angle Z = 1/2(major arc - minor arc)

major arc = 360 - 130 = 230

Angle Z = 1/2(230 - 130)

Angle Z = 1/2(100)

Angle Z = 50 degrees

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Answer:

Step-by-step explanation:

The surface area of the rectangular prism given the length, width and height is 1800 square cm.

Surface area of a rectangular prism = 2(LW + LH + WH)

Where,

Length, L = 40 cm

Width, W = 10 cm

Height, H = 10 cm

Surface area of a rectangular prism = 2(LW + LH + WH)

= 2(40×10 + 40×10 + 10×10)

= 2(400 + 400 + 100)

= 2(900)

= 1800 square cm

Therefore, 1800 square cm is the surface area of the rectangular prism.

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Answer: (x−a)^2 + (y−b)^2 = r^2

Step-by-step explanation:BC is tangent to circle A at B and to circle D at C (not drawn to scale). AB=7, BC= 18, and DC = 5. Find AD to the nearest tenth. B

The area of ΔEFG is approximately 916 square centimeters.

Given that,

In ΔEFG

f = 88 cm ,

g = 18 cm

∠E=68°

To find the area of ΔEFG,

Use the formula:

Area = (1/2)xfxgxsin(∠E)

First, we need to convert the angle from degrees to radians.

We can do this by multiplying by π/180.

∠E = 68° * π/180 ≈ 1.19 radians

Next, we can plug in the values we have:

Area = (1/2)x88x18xsin(1.19)

        ≈ 915.56 cm²

Rounding this to the nearest square centimeter,

we get,

Area ≈ 916 cm²

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Answer:

The number is divisible by 2, 3, 4, 5, 6, 10.

Step-by-step explanation:

Number ends in 40. It is even. It is divisible by 2.

Sum of digits is 15. It is divisible by 3.

Last two digits are 40. It is divisible by 4.

Last digit is 0. It is divisible by 5 and 10.

It is divisible by both 2 and 3. It is divisible by 6.

Answer: The number is divisible by 2, 3, 4, 5, 6, 10.

Answer:

To find the product of 74.57 and 0.006, you can follow these steps:

Step 1: Multiply the two numbers without considering the decimal points.

       7457 x 0.006 = 44.742

Step 2: Count the total number of decimal places in the original numbers. In this case, 74.57 has two decimal places, and 0.006 has three decimal places. Add these decimal places together to get a total of five decimal places.

Step 3: Place the decimal point in the product so that it is five places from the right.

       44.742 --> 0.44742

Therefore, the product of 74.57 and 0.006 is 0.44742.

Step-by-step explanation:

Answer:

0.44742

Step-by-step explanation:

multiply each inividual digit on the top number (74.57)

by each number seperately from the bottom number (0.006) and multiply from right to left

Answer:

t = 2 and t = 3.

Step-by-step explanation:

To solve the equation 2^(2t) - 12(2^t) + 32 = 0, we can use a substitution to simplify the equation. Let's set u = 2^t:Substituting u = 2^t, the equation becomes:u^2 - 12u + 32 = 0Now we have a quadratic equation in terms of u. We can solve it by factoring or using the quadratic formula. Let's try factoring:(u - 4)(u - 8) = 0Setting each factor equal to zero, we have:u - 4 = 0 or u - 8 = 0Solving for u:u = 4 or u = 8Now, substitute back u = 2^t:For u = 4:

2^t = 4Taking the logarithm base 2 of both sides:

t = log2(4)

t = 2For u = 8:

2^t = 8Taking the logarithm base 2 of both sides:

t = log2(8)

t = 3

The vertices of triangle P' Q ' R' , given the 90 degrees counterclockwise rotation about the origin is :

P' = (1, -2)

Q' = (-2, 1)

R' = (2, 2)

A 90 degree counterclockwise rotation about the origin can be performed by switching the x- and y-coordinates of each point and then negating the new x - coordinate.

This is :

( , ) → ( − , )

This means that P with vertices ( -2, - 1 ) would then become ( 1, - 2 ).

Q with  (1, 2) would then become (-2, 1)

And R would go from ( 2, - 2 ) to ( 2, 2 )

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The value of r is 5 cm.

Given that, a right triangle has a base of r cm and hypotenuse of 10 cm with an angle 60 degrees we need to find the value of r,

The trigonometric function cosine (cos) can be used to determine the value of the right triangle's base (r).

We are aware of the hypotenuse (10 cm) and angle (60 degrees) in this situation.

The ratio of a right triangle's neighboring side to hypotenuse is known as the cosine function.

The base (r) in this instance is the opposite side, and the hypotenuse measures 10 cm.

Using the formula for cosine:

cos(angle) = adjacent/hypotenuse

cos(60 degrees) = r/10

60 degrees has a cosine of 0.5.

So,

0.5 = r/10

To solve for r, we can multiply both sides of the equation by 10:

0.5 x 10 = r

5 = r

Therefore, the value of r is 5 cm.

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Answer:

1:4

Step-by-step explanation:

4/17=1/4

7/28=1/4

9/36=1/4

1. Volume of Water= 35.25 unit³

2. Volume of 1 ice = 1.4 unit³

3. Volume of 3 ice cubes submerged = 3.78 unit³

1. Volume of Water

= πR²H

= 3.14 x 3/2 x 3/2 x 5

= 3.14 x 45/4

= 35.25 unit³

2. Volume of 1 ice

= π(r2² - r1²)h

= 3.14 x [(4/6)² - (2/6)²] x 4/3

= 3.14 x 12/36 x 4/3

= 3.14 x 1/3 x 4/3

= 1.395

= 1.4 unit³

3. Volume of 3 ice cubes submerged

= 3 x (9/10 x 1.4)

= 3.78 unit³

4 . Total Height displacement

= 5 - 4/3

= 11/3 unit

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The correct option is the second one, the interval in which the function is decreasing is [-5, 0]

To identify in which intervals the function is decreasing, we need to find when the function is (when reading from left to right) going downwards.

And trivially, the function is increasing if it goes upwards (again, when reading from left to right).

Here we can see that the intervals in which the function is decreasing are:

[-5, 0] and [2, 4]

The only of thes that appears in the options is the first one, so that is the correct option.

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The area (A) of the trapezoid is 225 square kilometers.

The area of Figure #12 is 144 square centimeters.

Question 1:

To find the area (A) of a trapezoid, we can use the formula:

A = (1/2) x (a + b) x h

where 'a' and 'b' are the lengths of the parallel bases and 'h' is the height or the perpendicular distance between the bases.

Given:

Length of the parallel bases:

a = 11 km

b = 19 km

Length of the other two sides:

c = 17 km

d = 15 km

To find the height (h), we can use the Pythagorean theorem since the trapezoid is not necessarily a right trapezoid.

Let's consider the right triangle formed by the height (h), one of the other sides (c = 17 km), and the difference in lengths between the parallel bases (b - a = 19 km - 11 km = 8 km).

Using the Pythagorean theorem:

h² = c² - (b - a)²

h² = 17² - 8²

h² = 289 - 64

h² = 225

h = √225

h = 15 km

Now we have all the values to calculate the area (A):

A = (1/2) x (11 km + 19 km) x 15 km

A = (1/2) x 30 km x 15 km

A = 225 km²

Therefore, the area (A) of the trapezoid is 225 square kilometers.

Question 2:

The area of Figure #12 can be described as.

A  = (6 x 18) + (3 x 12)

A = 108 + 36 square centimeters

A = 144 square centimeters.

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The variance of the data set can be found to be 169. 17.

The standard deviation would also be 13 .

The exam scores for the ten students are:

94 99 67 60 78 89 80 82 77 99

First, find the mean :

= ( 94 + 99 + 67 + 60 + 78 + 89 + 80 + 82 + 77 + 99) / 10

= 82. 5

Then the Sum of the squared deviations from the mean :

= ( 132.25 + 272.25 + 240.25 + 506.25 + 20.25 + 42.25 + 6.25 + 0.25 + 30.25 + 272.25 )

= 1, 522. 5

Variance is:

= Sum of squared deviations / n

= 1, 153. 50 / 10

= 169. 17

The standard deviation is :

= √Variance

= √ 151.35

=  13

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Answer:

Step-by-step explanation:

What are the other colors?

if there are two colors ( red and another color ) then the probability of the pointer landing on red will be 1/2

similarly if there are 3 colors ( red and two other colors) then the probability of the pointer landing on red will be 1/3 ....

depends on how many colors are there

Area of rectangle is,

A = 45 units²

And, Perimeter of rectangle is,

⇒ P = 28 units

We have to given that;

Vertices of rectangle are,

⇒ (- 4, - 5)  

⇒ (-4, 0)

⇒ (5, 0)

⇒ (5, - 5)

Since, The distance between two points (x₁ , y₁) and (x₂, y₂) is,

⇒ d = √ (x₂ - x₁)² + (y₂ - y₁)²

Hence, Length of rectangle is distance between (- 4, - 5) and (- 4, 0).

Which is,

⇒ d = √ (x₂ - x₁)² + (y₂ - y₁)²

⇒ d = √ (- 4 + 4)² + (0 + 5)²

⇒ d = √ 25

⇒ d = 5

And,  Width of rectangle is distance between (- 4, 0) and (5, 0).

Which is,

⇒ d = √ (x₂ - x₁)² + (y₂ - y₁)²

⇒ d = √ (- 4 - 5)² + (0 - 0)²

⇒ d = √ 81

⇒ d = 9

Thus, Area of rectangle is,

A = L x W

A = 5 x 9

A = 45 units²

And, Perimeter of rectangle is,

⇒ P = 2 (L + W)

⇒ P = 2 (5 + 9)

⇒ P = 2 × 14

⇒ P = 28 units

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Answer:

equations and stuff

Step-by-step explanation:

To calculate the number of 18-inch by 24-inch cake pans needed, we need to determine how many 3-inch by 3-inch portions can be cut from each pan.

First, we need to find the area of the cake pan:

Area of one cake pan = Length × Width = 18 inches × 24 inches = 432 square inches.

Next, we need to find the area of one portion of cake:

Area of one portion = Length × Width = 3 inches × 3 inches = 9 square inches.

Now we can calculate how many portions of cake can be cut from one cake pan:

Number of portions per pan = Area of one cake pan / Area of one portion = 432 square inches / 9 square inches = 48 portions.

Since each pan can yield 48 portions of cake, we can divide the total number of attendees by the number of portions per pan to find the number of pans needed:

Number of pans needed = Total number of attendees / Number of portions per pan = 210 people / 48 portions = 4.375.

Since we cannot have a fraction of a cake pan, we need to round up to the nearest whole number. Therefore, the club will need 5 (or more precisely, 5 pans and some extra portions) of the 18-inch by 24-inch cake pans to serve each person one portion of cake.

Answer:

-4 * 3^(n-1)

Step-by-step explanation:

The rule for a geometric sequence is given by the formula an = a1 * r^(n-1), where a1 is the first term, r is the common ratio, and n is the term number. To find the common ratio, we can use the formula r = a2/a1 = a3/a2, since any two consecutive terms in a geometric sequence have the same ratio.

Given that a3 = -12 and r = 3, we can solve for a1 as follows:

a3 = a1 * r^(3-1)

-12 = a1 * 3^2

a1 = -4

Therefore, the rule for this geometric sequence is an = -4 * 3^(n-1).

Answer:for 14 C and for 15 1/34

Step-by-step explanation:

The correct option is C, this can be modeled with a linear function.

We know that the attendance increases by 15 units each time that the team wins a game.

So, if the initial attendance was A, then the attendance after the team wins x games is modeled by the linear function:

f(x) = A + 15x

Then the correct statement for this case is C, the best option is a linear function because the attendance increases by a constant rate, which is 15.

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There is a 95% confident that the true population mean annual earnings of college students lies within the interval ($2657, $3583).

To construct a 95% confidence interval for the population mean, μ, use the following formula:

CI = x ± t × s / √n

where:

x = sample mean

t = t-statistic for the desired confidence level and degrees of freedom

s = sample standard deviation

n = sample size

In this case:

x = $3120

s = $677

n = 20

The t-statistic for a 95% confidence level and 19° of freedom is 1.96.

Therefore, the 95% confidence interval for the population mean is:

CI = $3120 ± 1.96 × $677 / √20

CI = ($2657, $3583)

This means that there is a 95% confident that the true population mean annual earnings of college students lies within the interval ($2657, $3583).

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The necessary condition for ordered pairs (a,b) is that the following characterizing property of them can be proved; (a,b)=(c,d)

And if and only if a=c and b=d

Since we can prove that

{{a},{a,b}}={{c},{c,d}} if and only if a=c and b=d

Thus defining (a,b)  as an abbreviation for {{a},{a,b}} suffices for ordered pairs.

We can also consider that

U = {ordered pairs on a coordinate plane}

A = {ordered pair solutions,y = x}

B = {ordered pair solutions to y = 2x}

if  (x,y) belongs to AnB then y = x and y = 2x

x = 0

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Total amount John has to pay = [tex]\$3 + (\$5.25 * X[/tex])

To determine the equation that represents the total amount John has to pay for tax, we need to consider the cost of the watermelon and the cost of the grapes he purchased.

The cost of the watermelon is $3, which remains constant regardless of the weight of the grapes.

The cost of the grapes is given as $5.25 per pound. Multiplying the price per pound by the number of pounds (X), we get the cost of the grapes:

Cost of grapes = $5.25 * X

To find the total amount John has to pay, including tax, we need to add the cost of the watermelon and the cost of the grapes:

Total amount John has to pay = Cost of watermelon + Cost of grapes

Total amount John has to pay =[tex]\$3 + (\$5.25 * X)[/tex]

Therefore, the equation that represents the total amount John has to pay for tax is:

Total amount John has to pay = [tex]\$3 + (\$5.25 * X)[/tex]

The simplified equation shows that the total amount John has to pay for the grapes depends on the cost per pound ($5.25), the tax rate (t), and the weight of the grapes (x).

Note that the specific value of the tax rate (t) is not provided in the question. To calculate the total amount accurately, the value of the tax rate needs to be known or specified.

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Based on the expression, Mr. Mbhalati's prediction is correct. His water bill will decrease in Polokwane.

Let's calculate Mr. Mbhalati's water bill in Polokwane and Tzaneen.

Polokwane

Monthly use: 50 kl

Rate: R15.10/kl

Total bill: 50 kl * R15.10/kl

= R755

Tzaneen

Monthly use: 50 kl

Rate: R23.70/kl

Total bill: 50 kl * R23.70/kl

= R1185

As you can see, Mr. Mbhalati's water bill will decrease in Polokwane. His bill in Tzaneen is R430 more than his bill in Polokwane.

Therefore, Mr. Mbhalati's prediction is correct. His water bill will decrease in Polokwane.

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The value of n in the expression [tex]\sqrt[6]{2}[/tex] as 2ⁿ is 1/6.

The correct option is A.

Given information:

The expression is [tex]\sqrt[6]{2}[/tex] .

To write as 2ⁿ, simplify the expression.

Step 1: Simplify the expression inside the root:

[tex]\sqrt[6]{2}[/tex] = 2^(1/6)

Step 2: Rewrite sqrt(2) as a power of 2:

To find the value of n in the expression 2ⁿ that is equivalent to sqrt(2), we need to express sqrt(2) as 2 raised to some power.

The given expression can be simplified as,

[tex]\sqrt[6]{2}[/tex] = (2)¹/⁶.

Now compare the simplified expression with the expression 2ⁿ.

We get,

n = 1/6.

Now, it can not be simplified further, so the value of n is 1/6.

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Answer:

B

D

D

Step-by-step explanation:

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