What is the exact measure of an angle whose measure is 18° in radians?

pi over 18
18π
pi over 10
pi over 5

The volume of the cylinder will be 666 cubic centimeters. Then the correct option is D.

Volume is a measurement of three-dimensional space that is utilized. It is frequently mathematically quantified using SI-derived units or different imperial or US traditional units. The concept of length is linked to the notion of capacity.

The radius and height of the cone and the cylinder are the same. Then the ratio of the volume of the cylinder to the volume of the cone is 3. Then we have

(Volume of the cylinder) / (Volume of the Cone) = 3

Volume of the cylinder  / 222 = 3

Volume of the cylinder = 666 cubic cm

The volume of the cylinder will be 666 cubic centimeters. Then the correct option is D.

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The function g(x) = 8(2)^x is also a shift left by 3 units of f(x) = 2^x, as 8 = 2³, hence 8(2)^x = 2^(x + 3).

A translation happens when either a figure or a function are moved horizontally or vertically.

The four translation rules for functions are given as follows:

The functions for this problem are given as follows:

8 is the third power of 2, hence:

8 = 2³.

When two terms with the same base and different exponents are multiplied, we keep the base and add the exponents, hence:

8(2)^x = 2³ x 2^x = 2^(3 + x) = 2^(x + 3).

As x -> x + 3, a translation left 3 units happened.

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Answer:

=17 + 6n.

Step-by-step explanation:

[tex]4 \times 5 + 6n - 3 \\ = 20 + 6n - 3 \\ = 20 - 3 + 6n \\ = 17 + 6n[/tex]

The length of side DF is 5 units.

If two figures possess the same shape but not necessarily the same size, they are considered to be similar. We may remark that all circles are similar as an example. Equilateral triangles and squares are similar to one another. Although similar figures need not be congruent, all congruent figures are similar.

Property 1:

Two triangles are similar if their respective sides have the same ratio and their corresponding angles are equal.

Property 2:

The corresponding angles of two similar triangles will have equal values . Equiangular triangles are what they are called.

Now by property 1,

The pairs of  corresponding sides of similar traingles are proportional .

Therefore, in the given triangles,

[tex]\frac{BA}{ED} =\frac{AC}{DF}[/tex]

[tex]\frac{6}{3} =\frac{10}{x} \\\\x=5[/tex]

Hence, the value of x = 5 units.

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The value of k is given as follows:

k = 2x.

The exponential function that models the growth of the first virus is given as follows:

y = P(3)^x.

The exponential function that models the growth of the second virus is given as follows:

y = P(9)^x = P(3)^k.

We have that 9 is the second power of 3, hence we have that:

y = P(3²)^x = P(3)^k.

Applying the power of power rule, we have that:

y = P(3)^(2x) = P(3)^k.

Hence the value of k is given as follows:

k = 2x.

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The required trigonometric ratios are as follows: sin t = 1/2 and cos t = √3/2.

Trigonometric functions are defined as the functions which show the relationship between the angle and sides of a right-angled triangle.

According to the given figure, we have a right triangle ΔABC which has:

AB = 1/2

BC = √3/2

CA = AB² + BC²

CA = √(1/2)² + (√3/2)²

CA = √1/4 + 3/4

CA = √4/4 = 1

As we know that the trigonometric ratios are as follows:

sin (180°- t) = AB/CA

sin t = (1/2)/1

sin t = 1/2

cos (180°- t) = BC/CA

cos t = (√3/2)/1

cos t = √3/2

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The formula to calculate the nth term of the sequence is an = -3n+18.

The difference between any two consecutive integers in an arithmetic progression (AP) sequence of numbers is always the same amount. It also goes by the name Arithmetic Sequence.

Given that the arithmetic series is 15,12,9,6.....

The nth term of the arithmetic sequence will be calculated as:-

an = a₁ + (n-1)d

The first term is 15 and the common difference for the series is 12-15 = -3.

The nth term will be calculated as:-

an = a₁ + (n-1)d

an = 15 + (n-1)-3

an = 15 -3n +3

an = -3n + 18

Therefore, an = -3n+18 is the formula to find the nth term in the sequence.

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Step-by-step explanation:

A=4πr²

A = 4× 22/7 ×8²

A = 4 ×22\7×64

A=804.6m²

Answer:

please review the attachment

Answer:

He can eat 6 pies in 198 seconds.

Step-by-step explanation:

Divide

132÷4=33

Divide

198÷33=6 pies in 198 seconds

Answer:

Step-by-step explanation:

we have two rectangles side by side, the larger one measures 8m by 6m, the smaller one 5m by 4m, the 4 meters is the difference between the base  (10m) and the 6m side, so we find the areas and add them using the formula A = L x W, the result is not in the choices but it is right.

6 * 8 + 4 * 5 =                     remember PEMDAS

48 + 20 =

68 m²

The final price of Thomas Peters' new SUV  is $30,309 , can be calculated by subtracting the rebates from the initial cost.

The initial cost of the SUV was $32,984, and he received a $2,175 rebate from the car dealer and a $500 rebate from the manufacturer. So, the final price would be calculated as follows:

Final Price = $32,984 - $2,175 - $500

Final Price = $30,309

Therefore, the final price of Thomas Peters' new SUV is $30,309.

It is important to note that rebates can play a significant role in reducing the cost of a car purchase. In this case, Thomas Peters was able to receive a total of $2,675 in rebates, which reduced the cost of his new SUV by over 8%. This shows that it is often worth the time and effort to research available rebates and incentives when making a car purchase. Additionally, it is also a good idea to negotiate the price with the car dealer, as there may be room for further discounts.

By taking these steps, you may be able to save a significant amount of money on your car purchase and get a better value for your money. Ultimately, it is important to weigh the cost and benefits of each car option to determine the best choice for your needs and budget.

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Answer: Width = 73 m

Step-by-step explanation:

Perimeter = Length(2) + Width(2)

330 - (92 x 2)

330 - 184 = 146

146 = Width of 2 sides

146/2 = 73 m

Answer:

Step-by-step explanation:

Here's a step by step explanation of how to calculate the number of cakes baked if the bakery baked 96 loaves of bread:

First, determine the number of sets of 12 loaves of bread that were baked:

96 loaves of bread ÷ 12 loaves per set = 8 sets of 12 loaves

Next, determine the number of cakes baked for each set of 12 loaves of bread:

For every set of 12 loaves, 5 cakes are baked.

Finally, multiply the number of sets by the number of cakes baked per set to find the total number of cakes baked:

8 sets × 5 cakes per set = 40 cakes

So, if the bakery baked 96 loaves of bread, they would have baked 40 cakes.

Answer:

40

Step-by-step explanation:

12 times 8 equals 96 and 5 times 8 equals 40, there for 40 cakes will be backed

Answer:32

Step-by-step explanation: 24 divided by .75=32

Answer: x=10

Step-by-step explanation:

Answer:

To find the coefficient of variation (CV) of a sample, we divide the standard deviation by the mean and multiply by 100 to get the percentage.

1. For the systolic sample:

•Find the mean:

mean = (116 + 130 + 157 + 94 + 155 + 122 + 115 + 138 + 124 + 122) / 10 = 130

•Find the standard deviation:

sum = (116 - 130)^2 + (130 - 130)^2 + (157 - 130)^2 + (94 - 130)^2 + (155 - 130)^2 + (122 - 130)^2 + (115 - 130)^2 + (138 - 130)^2 + (124 - 130)^2 + (122 - 130)^2

sum = 165.4

std = sqrt(sum/9) = 7.3

•Calculate the coefficient of variation:

CV = (std / mean) × 100 = (7.3 / 130) × 100 = 5.62%

2. For the diastolic sample:

•Find the mean:

mean = (82 + 78 + 74 + 51 + 89 + 88 + 56 + 63 + 72 + 83) / 10 = 72.5

•Find the standard deviation:

sum = (82 - 72.5)^2 + (78 - 72.5)^2 + (74 - 72.5)^2 + (51 - 72.5)^2 + (89 - 72.5)^2 + (88 - 72.5)^2 + (56 - 72.5)^2 + (63 - 72.5)^2 + (72 - 72.5)^2 + (83 - 72.5)^2

sum = 624.75

std = sqrt(sum/9) = 12.24

•Calculate the coefficient of variation:

CV = (std / mean) × 100 = (12.24 / 72.5) × 100 = 16.82%

So the CV for systolic is 5.62% and the CV for diastolic is 16.82%. We can see that the diastolic measurement has higher variation than the systolic measurement.

Answer:

this is not belongs to mathematics

Step-by-step explanation:

Answer:

a.18%

b.68%

Step-by-step explanation:

for a you need to multiply 2 to get 18 out of 100 to get 18% and for b you need to multiply 4 to get 68 out of 100 to get 68%

The given expression simplifies to sin 2x.

Option (D) is correct.

What are trigonometric ratios?

Trigonometric ratios are ratios of the sides of a right triangle that are used to define the relationships between the angles and the sides of the triangle. The three basic trigonometric ratios are sine, cosine, and tangent, which are commonly abbreviated as sin, cos, and tan, respectively.

The expression (sin 3x)(cos x) − (cos 3x)(sin x) is an example of a trigonometric identity known as the "sin of a difference" formula:

sin(A - B) = sin A cos B - cos A sin B

By comparing this formula to the given expression, we can see that:

A = 3x

B = x

Substituting these values into the formula, we get:

sin(3x - x) = sin 2x = (sin 3x)(cos x) − (cos 3x)(sin x)

Hence, the given expression simplifies to sin 2x.

Option (D) is correct.

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The area of the triangle with side lengths 28 and 21 and an angle of 118 degrees is 260 squared unit.

A triangle is simply a two-dimensional polygon with 3 sides and 3 interior angles.

The area of a triangle can be determine using the formula;

A = ( a × b × sin( C ) ) / 2

From the diagram;

Plug the given values into the above formula.

A = ( a × b × sin( C ) ) / 2

A = ( a × m × sin( R ) ) / 2

A = ( 28 × 21 × sin( 118° ) ) / 2

A = ( 588 × sin( 118° ) ) / 2

A = ( 588 × 0.8829 ) / 2

A = 519.17 / 2

A = 260 square unit.

Therefore, the area of the triangle is 260 square unit.

Option D) 260 is the correct answer.

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The area of the figure  to the nearest whole number is 260

The area of a triangle is the region contained by the triangle's sides. The length of the sides and internal angles affect a triangle's area differently from one triangle to the other.

From the given triangle:

The required area of a triangle is:

[tex]A = a*b * \dfrac{sin \gamma}{2}[/tex]

where;

[tex]A = 28*21 * \dfrac{sin \ 118}{2}[/tex]

A = 14 × 21 × sin 118

A = 14 × 21 × 0.8830

A = 259.602

A = 260

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The equation of the line with slope 3 that goes through the point (2, 5) is y = 3x - 1.

What is the slope-point form of the line?

The point-slope form of the equation of a line is given by:

y - y1 = m(x - x1)

where m is the slope of the line, and (x1, y1) is a point on the line.

Using the given slope of 3 and the point (2, 5), we can substitute into the point-slope form to get:

y - 5 = 3(x - 2)

Expanding the right-hand side:

y - 5 = 3x - 6

Adding 5 to both sides:

y = 3x - 1

Hence, the equation of the line with slope 3 that goes through the point (2, 5) is y = 3x - 1.

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Answer:

36.

Step-by-step explanation:

o find F'(4), we need to use the chain rule of differentiation. The chain rule states that if F(x) = f(g(x)), then F'(x) = f'(g(x)) * g'(x).

Given that f(-2) = 5, f'(-2) = 9, f'(4) = 3, g(4) = -2, and g'(4) = 4, we can calculate F'(4) as follows:

F'(4) = f'(g(4)) * g'(4) = f'(-2) * g'(4) = 9 * 4 = 36

Therefore, F'(4) = 36.

The average rate of change of the function over the interval (-1, 2) is 3.

Average rate of change of a function is defined as the rate at which the value of the function is changing with respect to the change in the input values.

Difference quotient of a function over an interval is also the same concept as the average rate of change of a function.

Average rate of change of a function f(x) over an interval (a, b) is [tex]\frac{f(b) - f(a)}{b-a}[/tex].

Given interval is (-1, 2).

From the graph, f(-1) = -4 and f(2) = 5

Average rate = [tex]\frac{f(2) - f(-1)}{2--1}[/tex] = (5 - -4) / (3) = 9/3 = 3

Hence the given function has an average rate of change over the interval (-1, 2) at 3.

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Answer:

a = 5, b = 5√3

Step-by-step explanation:

Use sin law

sin A/a = sin C/c

sin 30/a = sin 90/10

sin 30/(sin90/10) = a

a = 5

sin B/b = sin C/c

sin 60/b = sin 90/10

sin 60/(sin90/10) = b

b = 5√3

The value of the composite functions of h(g(x)) is h(g(x)) = -20x + 6.

In mathematics, a function is composed when two functions, f and g, are used to create a new function, h, such that h(x) = g(f(x)). The function of g is being applied to the function of x, in this case. Therefore, a function is essentially applied to the output of another function.

Given that, h(x) = 4x + 6 and g(x) = -5x.

The value of h(g(x)) is calculated by substituting x = -5x in the equation of h(x).

h(g(x)) = 4(-5x) + 6

h(g(x)) = -20x + 6

Hence, the value of the composite functions of h(g(x)) is h(g(x)) = -20x + 6.

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Reason:

The standard deviation is the square root of the variance.

[tex]\text{Standard deviation} = \sqrt{\text{variance}}\\\\\text{Standard deviation} = \sqrt{1.56}\\\\\text{Standard deviation} \approx 1.24899959967968\\\\\text{Standard deviation} \approx 1.25\\\\[/tex]

Round the answer however you need to, or however your teacher instructs. I rounded to two decimal places since 1.56 is to two decimal places.

The standard deviation of the discrete random variable if the variance is 1.56 is 1.25

Given that, a discrete random variable has a variance of 1.56, we need to find its standard deviation

We know that,

The standard deviation is the square root of the variance.

Standard deviation = √ variance

Standard deviation = √1.56

Standard deviation = 1.24899959967968

Standard deviation = 1.25

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Answer:x intercept (2,0)

Yintercept (0,-10)

Step-by-step explanation:

y=mx+b b= y intercept

To find x you just solve

Y=5x-10

10=5x

2=x

The only correct option for the given quadratic function, is the graph of the function is a parabola. (there is only one correct option)

A quadratic function is a polynomial function with one or more variables in which the highest exponent of the variable is two.

Given is a quadratic function f(x) = x² - 5x + 12, there are some options given, we need to select the option which are correct according to the given quadratic function,

So, firstly we will plot the graph of the given function,

From the graph, we get,

The function is a parabola which opens up, the points (20, -8) and (0, 0) do not lie in the graph,

Now, finding the value of f(-10), put x = -10

(-10)² - 5(-10) + 12 = 100+52+12 = 164

Hence, in the conclusion the only correct option for the given quadratic function, is the graph of the function is a parabola. (there is only one correct option)

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