. How much you have to deposit in an account earning 8 percent compound monthly to pay a retired officer $1000 monthly for 12 years.

The value of the variables 'x' and 'y' will be 8√2 cm and 9√2 cm, respectively.

Given that:

Area of a small triangle, A = 72 square cm

The ratio of the matching sides will remain constant if two triangles are comparable to one another.

The equation is given as,

x² / (32)² = y² / (36)² = 72 / (1/2 x 32 x 36)

The value of 'x' is calculated as,

x² / (32)² = 72 / (1/2 x 32 x 36)

x = 8√2 cm

The value of 'y' is calculated as,

y² / (36)² = 72 / (1/2 x 32 x 36)

y = 9√2 cm

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Answer: should be 24?

Step-by-step explanation:

im not sure

The value of the line AC is  100. 07 inches

Trigonometric identities are equations that involve trigonometric functions such as sine, cosine, and tangent, which hold true for all values of the variables in the equation.

Note that there are six trigonometric identities. They are;

From the information given, we have;

Using the sine identity, we have;

sin 58 = Line AC/118

cross multiply the values

Line AC = 100. 07 inches

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Step-by-step explanation:

yes .. when you put x=2 y will be 3 .. you get it?

If 31.2 out of every 100 pregnant women in India deliver their babies by C-section.

First, we need to find the fraction of pregnant women who deliver by C-section

31.2 out of 100 = 31.2/100 = 0.312

Then, we can use this fraction to find the number of pregnant women out of 85,733 who would be expected to deliver by C-section.

0.312 x 85,733 = 26,723.896

Rounding to the nearest whole number, we get

26,724 pregnant women.

26,724 pregnant women out of 85,733 would be expected to deliver by C-section.

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As a result, a = 7 + (n - 1) * 15 is the formula for the nth term of the series with first term 7 and common difference.

An ordered set of number with a pattern or rule regulating their values is referred to as a sequence in mathematics. A word is used to characterize each number in a sequence. There are many various kinds of sequences, but a few of the most popular ones are as follows: A common differential, or constant number, is added to the respective period to produce an arithmetic series, each term of which is obtained. One arithmetic series with a following differences of three is 1, 4, 7, 10, 13, etc.

given

Given an arithmetic series with a first term (a1) and a common difference (d), the formula for the nth term (an) is as follows:

[tex]a = a1 + (n - 1) * d[/tex]

In this instance, the common difference (d) is 15, and the first term (a1) is 7. When these values are added to the formula, we obtain:

[tex]a = 7 + (n - 1) * 15[/tex]

As a result, a = 7 + (n - 1) * 15 is the formula for the nth term of the series with first term 7 and common difference.

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Domain and range of function is (D)=D={x|x≥2}, R={y|y≥0}.

In mathematics, the domain of a function is the set of all possible input values for which the function is defined. The range of a function is the set of all possible output values that the function can produce, based on its input values. In other words, the domain is the set of all x-values that the function can take, while the range is the set of all corresponding y-values that the function can take.

The given graph is oriented toward x direction

Domain of function =x≥2

For every value of x the y is always positive

So, range =y≥0

Hence, domain and range of function is (D)=D={x|x≥2}, R={y|y≥0}

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(c)  [tex]q \le \pi[/tex]

(d)  [tex]2 \ge d \ge 1[/tex]

Explanation:

The "less than or equal to" sign is ≤ which has a "less than sign" placed on top of a single horizontal bar. It can be thought of something like this [tex]\stackrel{ < }{=}[/tex] except there isn't a second horizontal bar.

The "d is between 2 and 1" seems to have a strange order to it. I have a feeling your teacher is wanting 2 ≥ d ≥ 1 because of that order. Normally we would list things from smallest to largest. We involve "or equal to" if we want to include the endpoints.

Part a: q is less than or equal to π: q ≤ π.

Part b: d is between 2 and 1: 1 < d < 2.

Less than (<), more than (>), less than or equal (≤), greater than or equal (≥), and not equal (≠) are the inequality symbols.

Numbers are compared using inequalities to identify the range (or ranges) of values which satisfy the requirements of a certain variable.

Part a: q is less than or  equal to π.

In this case:

q < π and q = π

Combining both:

q ≤ π

Part b: d is between 2 and 1

Here values 1 and 2 will not be taken for d.

d < 2 and d > 1

Thus,

1 < d < 2

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A box contains 5 orange pencils, 8 yellow pencils, and 8 green pencils. Two pencils are selected, one at a time, with replacement.

There are a total of 21 pencils in the box.

The probability of selecting a green pencil on the first draw is 8/21, since there are 8 green pencils out of 21 total.

After replacing the first pencil, there are still 21 pencils in the box, including 8 yellow pencils.

The probability of selecting a yellow pencil on the second draw, given that a green pencil was selected first, is 8/21.

By the Multiplication Rule of Probability, we can multiply these probabilities together to find the probability of both events occurring

P(green and yellow) = P(green) × P(yellow|green)

P(green and yellow) = (8/21) × (8/21)

P(green and yellow) = 64/441

Therefore, the probability of selecting a green pencil first and a yellow pencil second is 64/441 or approximately 0.145.

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Answer:

Step-byeat -step explanation:

The value of P for A and B to be independent is 3/8.

Probability is a mathematical concept used to determine the likelihood or chance of an event occurring. It's a measure of how likely it is that a specific outcome will happen in a given situation. Probability values are expressed as numbers between 0 and 1, where 0 means the event is impossible, and 1 means it is certain to occur.

The probability of an event is calculated by dividing the number of outcomes that favor the event by the total number of possible outcomes. The total number of outcomes is the number of ways the event could happen, while the number of favorable outcomes is the number of outcomes that satisfy the event's conditions.

Probability theory has many applications in various fields, including finance, economics, science, engineering, and statistics. It is an essential tool for analyzing data, predicting outcomes, and making decisions.

Two events A and B are independent if and only if P(A and B) = P(A) * P(B).

Using the formula for the probability of the union of two events, we have:

P(A or B) = P(A) + P(B) - P(A and B)

Substituting the given values, we get:

1/2 = 1/5 + P - P(A and B)

Simplifying, we get:

3/10 = P - P(A and B)

We also know that P(A) = 1/5. Using the formula for the probability of the intersection of two events, we have:

P(A and B) = P(A) * P(B | A)

Substituting the given values, we get:

P(A and B) = (1/5) * P

Since we want to find the values of P for which A and B are independent, we can substitute this expression for P(A and B) in the earlier equation:

3/10 = P - (1/5) * P

Simplifying and solving for P, we get:

P = 3/8

Therefore, A and B are independent if and only if P = 3/8.

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A simplification of the fractions (-5/8) ÷ (-3/4) is equal to: B. -20/24.

The step in which Johnetta made her error include the following: A. step 1.

In Mathematics and Geometry, a fraction simply refers to a numerical quantity (numeral) which is not expressed as a whole number. This ultimately implies that, a fraction is simply a part of a whole number.

Based on the information provided above, the division can be calculated as follows;

Fraction = (-5/8) ÷ (-3/4)

Fraction = -5/8 × (-4/3)

Fraction = -20/24

For Johnetta, we have:

Fraction = 7/9 ÷ 3/8

Fraction = 7/9 × 8/3

Fraction = 56/27

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The value of angle B and C are 63° and 61° respectively.

The sine rule states that if a, b and c are the lengths of the sides of a triangle, and A, B and C are the angles in the triangle; with A opposite a, etc., then a/sinA=b/sinB=c/sinC.

Therefore;

32/sin56 = 34/sinC

32sinC = 34sin56

32sinC = 28.187

divide both sides by 32

sinC = 28.187/32

sinC = 0.88

C = sin^-1(0.88)

C = 61°( nearest degree)

The sum of angle in a triangle is 180°

therefore, B = 180-(61+56)

B = 180-(117)

B = 63°

therefore the value of angle B and C are 63° and 61°.

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The amounts needed to make 6 servings are given as follows:

The needed amounts to make 6 servings of the recipe are obtained applying the proportions in the context of the problem.

From the first line of the table, we get the amounts of sauce and oregano per serving are follows:

Hence the amounts for six servings are given as follows:

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hi

4/7  =   8

7/7 =  ?  

so ?  =  7/7 * 8  /4/7 =   8/4/7 =  8 *7/4 = 4*2*7 /4 =   2*7 = 14

so whole thing  is  14

let's check :    14 * 4/7 =   56/7 = 8

Match initial data. answer is correct.

Answer:

Let's call the unknown number "x". According to the problem, we know that:

x * (x - 6) = 27

Expanding the left side of the equation, we get:

x^2 - 6x = 27

Subtracting 27 from both sides, we get:

x^2 - 6x - 27 = 0

Now we can use the quadratic formula to solve for x:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

In this case, a = 1, b = -6, and c = -27, so:

x = (-(-6) ± sqrt((-6)^2 - 4(1)(-27))) / 2(1)

x = (6 ± sqrt(180)) / 2

x = (6 ± 6sqrt(5)) / 2

x = 3 ± 3sqrt(5)

So the two possible solutions are:

x = 3 + 3sqrt(5) ≈ 8.746

x = 3 - 3sqrt(5) ≈ -2.746

Since the problem statement doesn't specify whether the number should be positive or not, both solutions are valid.

Answer: The answer could be 9 or -3.

Step-by-step explanation: The product(multiply) of a number(x) and 6 less than a number(x-6) is 27.

x(x-6)=27

x^2-6x-27=0

(x-9) (x+3)=0

x=9 or x=-3

The number is 9 or -3.

The sequences that show that the two figures are similar, but not congruent, are:

This sequence includes a dilation with a different scale factor for each figure and reflections, which preserve the shape of the figures but not their size or orientation.

In conclusion, the correct options are A and C

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Considering the binomial random variable, the probabilities are:

a. 0.1611

b. 0.8915

c. 0.7588

d. 0.1085

e. 0.0576

The binomial distribution formula is:

P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)

where:

P(X = k) is the probability of getting k successes

n is the number of trials

p is the probability of success on one trial

(n choose k) is the binomial coefficient, which is equal to n! / (k! * (n - k)!)

k is the number of successes we want to find the probability for

Using this formula, we can find the probabilities for the given scenarios:

a. P(X = 4) = (10 choose 4) * 0.15^4 * (1 - 0.15)^(10 - 4) = 0.1611

b. P(X <= 1)

= P(X = 0) + P(X = 1)

= (10 choose 0) * 0.15^0 * (1 - 0.15)^(10 - 0) + (10 choose 1) * 0.15^1 * (1 - 0.15)^(10 - 1)

= 0.8915

c. P(X >= 1)

= 1 - P(X = 0)

= 1 - (10 choose 0) * 0.15^0 * (1 - 0.15)^(10 - 0)

= 0.7588

d. P(X > 1)

= 1 - P(X <= 1)

= 1 - (P(X = 0) + P(X = 1))

= 1 - ((10 choose 0) * 0.15^0 * (1 - 0.15)^(10 - 0) + (10 choose 1) * 0.15^1 * (1 - 0.15)^(10 - 1))

= 0.1085

e. P(X < 1)

= P(X = 0)

= (10 choose 0) * 0.15^0 * (1 - 0.15)^(10 - 0)

= 0.0576

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Answer:

C.

Step-by-step explanation:

C. is an impossible equation.

The surface area of the cylinder is approximately 3015.93square inches when rounded to the nearest hundredth.

To find the surface area of a cylinder, we need to add the areas of the top and bottom circles, and the area of the lateral surface, which is the curved part of the cylinder.

The formula for the surface area of a cylinder is:

S.A. = 2πr² + 2πrh

where r is the radius of the cylinder, h is the height, and π is approximately equal to 3.14.

Given that the diameter is 32 inches, we can find the radius by dividing by 2:

r = d/2 = 32/2 = 16 inches

Now we can substitute the values into the formula and simplify:

S.A. = 2πr² + 2πrh

S.A. = 2π(16)² + 2π(16)(14)

S.A. = 2π(256) + 2π(224)

S.A. = 512π + 448π

S.A. = 960π

To approximate the answer to the nearest hundredth, we can use the value of π rounded to two decimal places (3.14):

S.A. ≈ 960(3.14)

S.A. ≈ 3015.93 square inches

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The surface area of the cylinder figure is derived to be equal to 3014.40 square inches rounded to the nearest hundredth.

The surface area of a cylinder can be calculated using the formula:

Surface Area = 2πr² + 2πrh

Where r is the radius of the base of the cylinder, h is the height of the cylinder, and π (pi) is a mathematical constant approximately equal to 3.14159.

From the figure we have that:

r = 16 in

h = 14 in

surface area = 2 × 3.14 × 16 in × 16 in + 2 × 3.14 × 16 in × 14 in

surface area = 1607.68 in² + 1406.72 in²

surface area = 3014.40 in²

Therefore, the surface area of the cylinder figure is derived to be equal to 3014.40 square inches rounded to the nearest hundredth.

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Answer:

dependent

Step-by-step explanation:

its dependent because the names getting pulled depends on the names pulled first

Therefore, the value of f(m-2) is 5/(m-2) + 2, and the value of function g(1/2) is 2.

In mathematics, a function is a rule or correspondence between two sets, where each input value from the first set (called the domain) corresponds to exactly one output value in the second set (called the range). A function is often represented by a formula, equation, or graph.

Here,

1. To find f(m-2), we substitute (m-2) for x in the expression for f(x):

f(m-2) = 5/(m-2) + 2

So the value of f(m-2) is 5/(m-2) + 2.

2. To find g(1/2), we substitute 1/2 for x in the expression for g(x):

g(1/2) = -2(1/2) + 3

So the value of g(1/2) is -1 + 3, which simplifies to 2.

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Step-by-step explanation:

AREA = pi r^2

144 = pi r^2     shows      r = 6.77  m       ( or sqrt ( 144/pi)  ) 

        then          diameter = 2 * r = 13.54 m    (or   2 sqrt (144/pi)  )

Answer:

7.64

Step-by-step explanation

This is what I did so I take the root of 144 = 12 and 12/3.14 = roughly 3.82 thats the radius and that times 2 = 7.64 have a great day success to homework yay! Have a great day!!! :D

Answer:

I'm sorry, but I'm not sure what you are trying to convey with the string of characters "C 17 39 511 -U D 28 4 10 6". It doesn't appear to be a meaningful sentence or question. Could you please provide me with more information or context so I can better understand what you are trying to communicate?

Step-by-step explanation:

A histogram would be the most effective graphic depiction to compare the distribution of the hours spent online among teenagers, young adults, and the elderly.

What is a histogram ?

A histogram is a graph that displays the distribution of a continuous variable. It divides the data into a set of intervals (called bins) and counts the number of data points that fall into each bin.

This creates a bar-like representation of the data, with the height of each bar indicating the frequency of data points in that bin. By using a histogram, we can see the shape of the distribution, as well as any patterns or trends that may exist. We can compare the distribution of the hours spent online by teenagers, young adults, and the elderly by placing the histograms of their data side by side. This will allow us to visually compare the shape, spread, and central tendency of the distributions for each group. Additionally, we can use different colors for each group to make the comparisons even clearer. This will enable us to quickly see if there are any significant differences in the hours spent online among the three groups.

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A circumscribed angle is an angle that has its vertex on the circumference of a circle and whose sides are chords of the circle. The measure of a circumscribed angle is equal to half the measure of the intercepted arc. Circumscribed angles are important in geometry because they are used to prove theorems about angles, chords, and arcs in circles. The opposite angles of a cyclic quadrilateral are always supplementary, and the sum of the angles in a cyclic polygon is always equal to (n-2)180 degrees, where n is the number of sides of the polygon.

Answer:

$9.10 per person

Step-by-step explanation:

34 / 4 is 8.50

15% is 2.40, then divided 2.40 by 4 and get 0.60.

0.60 + 8.50 = 9.10 per person

Answer:

To find -5u, we simply need to multiply each component of u by -5:

-5u = -5<-9, 2> = <(-5)(-9), (-5)(2)> = <45, -10>

Therefore, -5u is equal to the vector <45, -10>.