Question 10 (2.5 points) ✓ Saved
Write the comparison below as a ratio in simplest form using a fraction, a colon (:), and the word to.
15 dollars to 27 dollars

Answer:

20 x 20 x 20 = 8000

The graph whuch best represents the solution to the system of equations is; A coordinate grid is shown from negative 10 to positive 10 on the x axis and also on the y axis. Two lines are shown intersecting on the ordered pair 3, 8.

As an alternative, solving the system of equations algebraically, we have;

-2x +14 = 2x +2

x = 3 and by substitution;

y = 8.

On this note, the point (3,8) is a solution of the graph and hence, the answer choice with two lines intersecting at (3,8) is correct.

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The complete fraction is 24/30=4/5

The expression is given as:

blank over 30=4/5

Represent the blank with x.

So, we have:

x/30=4/5

Multiply both sides by 30

x = 30 * 4/5

Evaluate

x = 24

Substitute x = 24 in x/30=4/5

24/30=4/5

Hence, the complete fraction is 24/30=4/5

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Answer:

c. [-1, infinity)

Step-by-step explanation:

the domain the interval or set of valid x values (while the range is the same for the valid y values).

what is the smallest value of x we see for the graph ?

for x values we need to look left and right.

and the more left the value, the smaller it is.

so, in other words, what is the left-most x value e can find ?

x = -1

that is the "starting point" of the function. there is no functional value for any smaller x.

and then clearly, the function goes on and on to the right without any boundary in sight. so, it keeps going to the right in all eternity, that means it goes to infinity.

therefore the answer.

keep in mind that "infinity" is not a number, only a concept. so, when writing "infinity" at an interval end, it is not included (and we use a round bracket).

If these coordinates are rotated 270° counterclockwise, the resulting coordinates will be;

X' = (3, -1)

Y' = (2, -2)

Z' = (-1, -3)

If the coordinates (x, y) is rotated 270° counterclockwise, the resulting coordinate point will be;

(x, y) - > (y, -x)

From the given triangles, the coordinate points are expressed as

X = (1, 3)

Y = (2, 2)

Z = (3, -1)

If these coordinates are rotated 270° counterclockwise, the resulting coordinates will be;

X' = (3, -1)

Y' = (2, -2)

Z' = (-1, -3)

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i. P(A) = 0. 4

ii. P(AB) = 0. 9

iii. P(A∩B) =0. 25

From the information given,

Universal set = 40% + 50% + 25% = 0.40 + 0. 50 + 0. 25

A = Mechanical defects = 40%

B = Electrical defects = 50%

A∩B =25%

i. Probability of A , P(A)

= [tex]\frac{40}{100}[/tex]

= [tex]0. 4[/tex]

ii. Probability of B, P(AB)

= [tex]\frac{40}{100} + \frac{50}{100}[/tex]

= [tex]0. 4 + 0. 5[/tex]

= [tex]0. 9[/tex]

iii. Probability of A∩B entails the common factor between A and B

P(A∩B)  = [tex]\frac{25}{100}[/tex] = [tex]0. 25[/tex]

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Answer:

there shouldnt be an answer, they are not like terms, for a proper answer it would have to be like terms, for example:

x^2+x^2=2x^2

or

w^12+w^12=2w^12

they need to have the same exponent for addition to happen

Answer:

16[tex]n^{3}[/tex]

Step-by-step explanation:

we evaluate from left side to right side

so -2*n =-2n

-2n *8 = -16n

-16n * n =-16n^2

-16 n * -n =16 n^3

hope this helps

The solution to the inequality expression is x>5 and the correct representation is a number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.

Inequality expressions are expression not separated by an equal sign

Given the following inequality expression

–3(2x – 5) < 5(2 – x)

Expand

-6x + 15 < 10 - 5x

Collect the like terms

-6x + 5x < 10 -15

-x < -5

x > 5

Hence the solution to the inequality expression is x>5 and the correct representation is a number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.

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The value of the ratio based on the angle illustrated is 1:12.

From the information given, it should be noted that the angle in a circle is 360°. Therefore, the value of theta will be:

= 360° - 330°

= 30°

The equivalent expression based on the angle will be:

= 30/360

= 1/12

= 1:12

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The correct answer is Yes. The graph represents a function. The function given is: F(x) = y(-5). Note that the value of x is zero.

A function's graph is the set of all points in the plane of the form (x, f(x)). The graph of f might similarly be defined as the graph of the equation y = f. (x).

Thus, the correct answer or function represented in the graph is f(x) = y(-5)

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Step-by-step explanation:

1) if m(∠A)∈[0;90°), then

[tex]cos(A)=\sqrt{1-sin^2A} =\frac{3}{5};[/tex]

[tex]sin2A=2sinAcosA=2*\frac{3}{5} *\frac{4}{5}=\frac{24}{25};[/tex]

[tex]cos2A=cos^2A-sin^2A=\frac{9}{25}-\frac{16}{25}=-\frac{7}{25};[/tex]

[tex]tan2A=\frac{sin2A}{cos2A}=-\frac{\frac{24}{25}}{\frac{7}{25}}=-\frac{24}{7}.[/tex]

2) if m∠A∈[90°;180°), then

cos(A)=-0.6;

sin2A=-0.96;

cos2A=-0.28;

tan2A=-24/7.

[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Let's solve ~

[tex]\qquad \sf  \dashrightarrow \: 10x + 30 = 90[/tex]

[ according to given figure ]

[tex]\qquad \sf  \dashrightarrow \: 10x = 90 - 30[/tex]

[tex]\qquad \sf  \dashrightarrow \: 10x = 60[/tex]

[tex]\qquad \sf  \dashrightarrow \: x = 60 \div 10[/tex]

[tex]\qquad \sf  \dashrightarrow \: x = 6 \degree[/tex]

Correct choice is D

Considering the given proportion, the value of [tex]\frac{a}{a - b}[/tex] is:

C) 2

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The proportion between a and b is given by:

a/b = 2.

Then:

a = 2b.

The expression is:

[tex]\frac{a}{a - b} = \frac{2b}{2b - b} = \frac{2b}{b} = 2[/tex]

Hence option C is correct.

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Answer

1 possible solution:

(5x7) in the first blank

(-3!) in the second blank

(-1) in the third blank

Step-by-step explanation:

(5x7) + -(3!) + -(1)          3! equals 3x2x1 or 6

35 + (-6) + (-1)

Using it's concept, the probability that you flip heads and roll a number greater than 5 is: [tex]\frac{1}{12}[/tex].

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, we have that:

Hence the probability of both events is:

[tex]p = \frac{1}{2} \times \frac{1}{6} = \frac{1}{12}[/tex].

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Using the normal distribution, the probability is given as follows:

[tex]P(X \geq 10) = 0.0485[/tex].

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The parameters for the binomial distribution are:

p = 0.5, n = 13.

Hence the mean and the standard deviation are:

Using continuity correction, the desired probability is P(X > 9.5), which is one subtracted by the p-value of Z when X = 9.5, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{9.5 - 6.5}{1.8028}[/tex]

Z = 1.66

Z = 1.66 has a p-value of 0.9515.

1 - 0.9515 = 0.0485, then:

[tex]P(X \geq 10) = 0.0485[/tex].

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Answer:

18.5 miles

Step-by-step explanation:

the Sun at an average speed of 67,000 mph, or 18.5 miles a second.

The cross sectional area of the conduit not part of the 7 cables is; 706.5cm²

It follows from the task content that the conduit in discuss has 7 cables all same diameter and has a circular cross section.

Since, the cross sectional area of the conduit not part of the 7 cables is required; it follows that the cross sectional area of the inside cavity can be evaluated as follows;

where radius, r = D/2 = 30/2.

Area = πr² = 3.14 × (30/2)² = 706.5cm²

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If 3 people take the day off, they will need (9 + 3/5) hours to mow the lawn. The correct option is B.

Let's say that each person works at a rate R.

8 people can mow the lawn in 6 hours, then we can write:

(8*R)*6 hours = 1 lawn.

Solving for R:

R = (1/48 lawns per hour).

If 3 people take the day off, then the lawn is mowed by 5 people in a time T, then we need to solve:

(5*R)*T = 1 lawn.

Replacing the value of R:

(5/48 lawns per hour)*T = 1 lawn.

Then we have:

T = (48/5) hours.

We can rewrite that as:

T = (45/5 + 3/5) hours

T = 9 + 3/5 hours.

Then we conclude that the correct option is B.

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The scaled copy of the polygon is added as an attachment

The complete question is added as an attachment

The coordinates of the polygon are

A = (-7, 6)

B = (-10, 8)

C = (-10, 10)

D = (-6, 10)

The scale factor is 3.

So, the rule of dilation is

(x, y) = (3x, 3y)

Using the above rule, we have:

A' = (-21, 18)

B' = (-30, 24)

C' = (-30, 30)

D' = (-18, 30)

See attachment for the scaled copy of the polygon

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Answer: B. g(x) is shifted 2 units to the right and 6 units up.

Step-by-step explanation:

See attached image.

Answer:

$73915.40

Step-by-step explanation:

→ Find the multiplier

( 3 + 100 ) ÷ 100 = 1.03

→ Multiply by principal amount and raise it to the power of years

55000 × 1.03¹⁰ = 73915.40

Answer: $630,513.36

Step-by-step explanation:

Let's make a table of values to see how much he earns every year after graduation.

1 year -> $55,000

2 years -> 55,000 * 103% = $56,650

3 years -> 56,650 * 103% = 55000 * 103% * 103% = $58,349.50

4 years ->  58349.50 * 103% = 55,000 * 103% * 103% * 103% = 55000(1.03)³

Here, we see that every year, he gets 103% of what he got the previous year, which is also 1.03 times his previous salary.

We also see that we multiply 55000 by 1.03 three times in the fourth year, and two times in the third year. This means that we multiply 55000 by 1.03 n-1 times.

Using this, let's generalize this for n.

n years -> [tex]55000(1.03)^{n-1}[/tex]

We are trying to find his total income after ten years, or the sum of his salary from year 1 to year 10. We can represent this in sigma notation like this

[tex]% Adjusted limits of summation$\displaystyle\sum_{n=1} ^{10} 55000(1.03)^{n-1}$[/tex]

This essentially translates to the sum of the first ten terms in the sequence [tex]55000(1.03)^{n-1}[/tex], starting at n=1.

Since this is a geometric sequence, or a sequence where we need to multiply by the same number to get to the next term, we can find the sum using the sum of geometric series formula. This formula is as follows:

[tex]S_n=a_1\frac{1-r^n}{1-r}[/tex]

where [tex]S_n[/tex] is the sum of the first n terms, [tex]a_1[/tex] is the first term, r is the common ratio, and n is the number of terms. In this question, [tex]S_n[/tex] is the total income after n years, [tex]a_1[/tex] is his salary after the first year, r is how much his salary increases by each year, and n is the number of years we are calculating the sum for.

[tex]a_1[/tex] -> 55000

r -> 1.03

n -> 10

Now that we have the values for each variable, let's plug them in and solve

[tex]S_{10}=55000(\frac{1-1.03^{10}}{1-1.03})\\S_{10}=630513.36[/tex]

The total income he will have received after ten years is $630,513.36.

Based on the given horizontal and vertical sides of a rectangle and its perimeter, the value of x in the expression is 6

Perimeter of rectangle = 2(length + width)

= 3x - 6

= 4x - 7 - 2x

= 2x - 7

Perimeter of rectangle = 2(length + width)

34 = 2{(3x - 6) + (2x - 7)}

34 = 2(3x - 6 + 2x - 7)

34 = 2(5x - 13)

34 = 10x - 26

34 + 26 = 10x

60 = 10x

x = 60/10

x = 6

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The decimals would be ordered as:

72.1, 72.5, 73.77, 73.943

42.1, 42.59, 43.2, 43.219

28.23, 38.4, 38.507, 38.507, 39.5

71.3, 71.3, 71.743, 72.43, 72.5

To order decimals from the least to the greatest, first state the lowest value, then progress to the highest taking account of the figures that come immediately after each decimal point.

The decimals will be ordered as shown below:

72.1, 72.5, 73.77, 73.943

42.1, 42.59, 43.2, 43.219

28.23, 38.4, 38.507, 38.507, 39.5

71.3, 71.3, 71.743, 72.43, 72.5

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Answer:

f(x) = 2 for x < -2

f(x) = -2x + 11 for x > 3

The average rate of change for this function for the interval from x = 1 to x = 3 is 3

The average rate of change is calculated as:

m = (f(b)- f(a))/(b - a)

The interval is given as:

x = 1 to x = 3

From the table of values, we have:

f(1) = 7

f(3) = 13

So, we have:

m = (13-7)/(3-1)

Evaluate

m = 3

Hence, the average rate of change for this function for the interval from x = 1 to x = 3 is 3

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The limit for the given piecewise function does not exist(DNE).

4th option is correct.

In mathematics, limits are the points at which a function approaches the output for the specified input values. Calculus and mathematical analysis depend heavily on limits, which are required to determine integrals, derivatives, and continuity. It is applied during the analysis process and always focuses on the function's behavior at a certain time.

Unique real numbers are limits in mathematics.

According to the question,

Left hand limit of the function= -5(3)+4 = -15+4 = -11

Right hand limit of the function= (3)(3)+2 = 11

As the left and right-hand limits are not equal. Thus, the limit of the function does not exist.

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The derivative of the function [tex]f(x)=5^{2x}[/tex] is [tex]\frac{df}{dx} =2ln5(5^{2x})[/tex]

The derivative of a function f(x) is the ratio of the change in f(x) to the change in x

The given function is:

[tex]f(x)=5^{2x}[/tex]

Let u = 2x

Find the derivative of u. That is, du/dx

du/dx = 2

f(x) = 5^u

[tex]\frac{df}{du} =5^ulnu[/tex]

Using the chain rule of derivative

[tex]\frac{df}{dx}=\frac{df}{du} \times\frac{du}{dx}[/tex]

[tex]\frac{df}{dx} =5^uln5 \times 2\\\\\frac{df}{dx} =2ln5(5^{2x})[/tex]

The derivative of the function [tex]f(x)=5^{2x}[/tex] is [tex]\frac{df}{dx} =2ln5(5^{2x})[/tex]

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