Solve 15.9 = 11.3 + b for b

The equation for the height exists h = 31 sin((8π)t + π/2) + 35.

The model for the height can be emanated from the general formula of the sine function, then

y = A sin(Bt - C) + D

Maximum point = 70 - 4 = 66 at t = 0

Minimum point = 4

Amplitude, A = (66 - 4) ÷ 2 = 31

D = 4 + 31 = 35

At t = 0, we have;

66 = 31 × sin(B × 0 - C) + 35

31 = 31 × sin(- C)

sin(- C) = 1

C = -π/2

1 minute = 60 seconds

1 second = 1 minute/60

15 seconds = (15/60) minutes

Period = 15 seconds = 15/60 minutes

Period = 2π/B

Therefore, 15/60 = 2π/B

1/4 = 2π/B

B = 2π/(1/4) = 8π

y = Height of the function

Let h denote the height of the wristband.

The equation for the height exists h = 31 sin((8π)t + π/2) + 35.

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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 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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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

Multiplication of 3495 by 30595 is: 106,929,525.

Multiplication can be defined as the way of multiplying a number by another name.

Using  a calculator to multiply  3495 by 30595.

Hence:

Multiplication= 3495×30595

Multiplication= 106,929,525

Therefore Multiplication of 3495 by 30595 is: 106,929,525.

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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 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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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:

f(x) = 2 for x < -2

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

The equation of the line in standard form is 6x - 7y = - 11

The standard form for linear equations in two variables is Ax + By = C.

Therefore, using (-3, -1)(1 / 2, 2)

y = mx + b

where

Hence,

m = 2 + 1 / 1  /2 + 3 = 6 / 7

Hence,

-1 = 6 / 7(-3) + b

- 1 = - 18 / 7 + b

-1 + 18 / 7 = b

b =  -7 + 18/ 7

b = 11 / 7

Therefore,

y = 6 / 7 x + 11 / 7

Using the standard form,

6 / 7 x - y = - 11 / 7

6x - 7y = - 11

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The linear equation in standard form is:

6x - 7y = -11

Which is the last option.

The line in slope-intercept form is written as:

y = a*x + b

We can see that the line passes through the points (-3, -1) and (1/2, 2), then the slope is:

[tex]a = \frac{2 - (-1)}{1/2 - (-3)} = \frac{3}{3.5} = \frac{6}{7}[/tex]

Then we can write:

y = (6/7)*x + b

To find the value of b, we use the first point. It means that when x = -3, the value of y is -1, then we get:

-1 = (6/7)*-3 + b

-1 + 18/7 = b

-7/7 + 18/7 = b

11/7 = b

Then the equation is:

y = (6/7)*x + 11/7

If we multiply both sides by 7 we get:

7y = 6x + 11

Now we move the term with "x" to the left:

7y - 6x = 11

That is the line in standard form.

If we multiply both sides by -1, we get the last option:

6x - 7y = -11

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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 time taken for 3 machines to pack 5000 articles is 8 hours.

It is given that,

A machine can pack 5000 articles in 24 hours. I.e,

1 machine → 5000 articles → 24 hours

3 machines → 5000 articles → 24/3 hours

Thus, 3 of such machines can pack the same number of articles in

24 ÷ 3 = 8 hours.

Therefore, 3 of such machines take 8 hours to pack 5000 articles.

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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:24

Step-by-step explanation:

Answer:

Step-by-step explanation:

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

Step-by-step explanation:

See attached image.

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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Step-by-step explanation:

solution:

given,

or, 2:5 = 8:x

or, 2/5 = 8/x [ changing into fraction form ]

or, 2x = 40 [ doing cross-multiplication ]

or, x = 20 [ dividing both sides with 2]

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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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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The point that is on the graph of the function [tex]F(x) = 5^x[/tex] is given by:

D. (1,5).

The function is defined by:

[tex]F(x) = 5^x[/tex]

When x = 0, [tex]F(x) = 5^0 = 1[/tex], hence point (0,1) is on the graph of the function.

When x = 1, [tex]F(x) = 5^1 = 5[/tex], hence point (1,5) is on the graph of the function, which means that option D is correct.

When x = 5, [tex]F(x) = 5^5 = 3125[/tex], hence point (5,3125) is on the graph of the function.

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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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Answer:

1/2

Step-by-step explanation:

[tex]f( - 3) = 4 {(2)}^{ - 3} = \frac{1}{2} [/tex]

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 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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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).

The expression for a in terms of c is [tex]a^{2}= \sqrt{c^{2} -9}[/tex]. The correct option is the third option [tex]a^{2}= \sqrt{c^{2} -9}[/tex]

From the question, we are to determine the expression for a in terms of c

In the given right triangle, we can write that

[tex]c^{2} = a^{2} +3^{2}[/tex] (Pythagorean theorem)

Thus,

[tex]c^{2} = a^{2} +9[/tex]

[tex]a^{2}= c^{2} -9[/tex]

[tex]a^{2}= \sqrt{c^{2} -9}[/tex]

Hence, the expression for a in terms of c is [tex]a^{2}= \sqrt{c^{2} -9}[/tex]. The correct option is the third option [tex]a^{2}= \sqrt{c^{2} -9}[/tex]

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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.

Answer:

The correct awnser is A : )

Step-by-step explanation: