100 Points! Algebra question, only looking for an answer to B. Photo attached. Please show as much work as possible. Thank you!

Answer:

$638641.33

Step-by-step explanation:

Adam earns $45,000 in his first year.

His salary increases by 3% each successive year. Therefore, his salary the next year is 103% of his previous year.

This is a geometric sequence where the:

(a)

Sum of  geometric series\(=\dfrac{a(r^n-1)}{r-1}\)

Substituting the given values, Adam's total earnings over n years

\(=\dfrac{45000(1.03^n-1)}{1.03-1}\\\\$Adam's Total Earnings=\dfrac{45000(1.03^n-1)}{0,03}\)

(b)When n=12 years

\(\text{Adam's Total Earnings for the first 12 years=}\dfrac{45000(1.03^{12}-1)}{0.03}\\=\$638641.33$ (correct to the nearest cent)\)

The chi-square value = 4.5

Before we can determine the chi-square value, we must first determine the anticipated number of hand and other injuries:

Expected hand injuries = (Total injuries / Total number of injuries) * Expected number of hand injuries

= (14/14) * 4

= 4

Expected other injuries = (Total injuries / Total number of injuries) * Expected number of other injuries

= (14/14) * 12

= 12

Now we can calculate the chi-square value:

χ² = Σ ((O - E)² / E)

Where O = Observed frequency and E = Expected frequency

For hand injuries, the calculation would be:

χ² = ((7-4)²/4) + ((7-8)²/8) = 1.25

For other injuries, the calculation would be:

χ² = ((7-12)²/12) + ((7-5)²/5) + ((14-12)²/12) = 3.25

Total chi-square value = 1.25 + 3.25 = 4.5

The degrees of freedom for this calculation would be (number of categories - 1) = (2-1) = 1.

The critical value is 3.84 when a chi-square distribution table with one degree of freedom and a significance level of 0.05 is used.

We are able to reject the null hypothesis, which states that the observed data are not significantly different from the expected data, because the calculated chi-square value of 4.5 is greater than the critical value of 3.84.

TA framework for making decisions based on data can be provided to the safety professional by the hypothesis testing procedure. By setting up an invalid speculation and an elective theory, the security expert can test whether noticed information contrasts fundamentally from anticipated information.

This can assist in determining where safety enhancements are required and assessing the efficacy of safety interventions. Additionally, hypothesis testing may offer a means of communicating outcomes and making decisions based on data to enhance workplace safety.

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Answer:

Step-by-step explanation:

\( {x}^{2} + 6x - 14 = 0\)

Roots :- 6 and -14

Sum of the roots :

[6 + (-14)]

= (-8)//

Product of the roots :

[(6)(-14)]

= (-84)//

The length of the base of the triangle is 8 yards whose height is half of 28 yards.

A triangle is a two-dimensional geometric shape that is formed by three straight lines that connect three non-collinear points. These three lines are called the sides of the triangle, and the points where the sides meet are called the vertices of the triangle.

The following formula provides the area of a triangle:

Area = (1/2) x base x height

We are given that the height of the triangle is half of 28 yards, which is:

height = 1/2 x 28 = 14 yards

We are also given that the area of the triangle is 56 square yards. Substituting these values into the formula for the area, we get:

56 = (1/2) x base x 14

Simplifying this equation, we get:

56 = 7 x base

Dividing both sides by 7, we get:

base = 8

Therefore, the length of the base of the triangle is 8 yards.

The vertices are typically denoted by letters, such as A, B, and C. The three angles formed by the sides are also part of the triangle.

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Answer:

2/3

Step-by-step explanation:

Answer:

15 square meters.

Hope this helped!

Based on the price he purchased the stock and the amount he sold them for, Jeff's annualized HPR on the investment is 2,395%.

First find the net profit:

= (1,000 x 9.26) - (1,000 x 1.89) - 10

= $7,360

The HPR is:

= 7,360 / (1,000 x 1.89)

= 389.4%

The annualized HPR is:

= (1 + 389.4%)² - 1

= 2,395%

Note: Taken to the power of 2 because there are two six-month periods in a year.

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Based on law of sine, the value of angle C is equal to 94.5 degree.

For any triangle ABC, with side measures |BC| = a. |AC| = b. |AB| = c,

we have, by law of sines,

\(\dfrac{sin\angle A}{a} = \dfrac{sin\angle B}{b} = \dfrac{sin\angle C}{c}\)

\(\dfrac{\sin(angle)}{\text{length of the side opposite to that angle}}\)

we have, by law of sines,

We will use the law of sines to find c as;

sin c                sin 97.5

--------------- = -------------

14.5                      13.7

(13.7)sin c= 14.5 sin 97.5

sin c =  14.5 sin 97.5 / (13.7)

sin c = - 0.1168

Angle c = 94.5

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Answer:  if with 3.14 v= 37512.5333

if with pi v= 37531.56

Step-by-step explanation:

the formula is 1/3hπr^2

r= 2d so radius is 32

plus numbers in (square it multiple times pi or 3.14 then multiply times height and divide by 3)

Step-by-step explanation:

the area of a triangle is

baseline × height / 2

so, we only have to sum all 6 triangles and the base area :

6 × 6×8/2 + 93.5 = 36×4 + 93.5 = 144 + 93.5 =

= 237.5 in²

Answer:

2 * 1 ==> 1st option

Step-by-step explanation:

Matrix dimensions are:

number of rows by number of columns

The number of rows is 2   :   ( 2 and 12 are the rows)

The number of columns is 1   :  ( 2      

                                                    12 )    

Hence, the dimensions is 2 * 1.

Answer:

i think it is

8km

i THINK .

Step-by-step explanation:

sorry if its wrong .

Answer:

Rhoda, whose ACT has a z-score of 1, scored in the 84th percentile in the ACT, compared to Bill, whose SAT has a z-score of -2, who scored in the 2nd percentile on the SAT. Due to the higher percentile(higher z-score)  on her test, Rhoda did better on her respective test than Bill, and thus, his logic is wrong.

Step-by-step explanation:

Z-score:

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Bill:

Scored 300, so \(X = 300\)

SAT has a μ of 500 and a σ of 100.

His z-score is:

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{300 - 500}{100}\)

\(Z = -2\)

\(Z = -2\) has a p-value of 0.02.

This means that Bill, whose SAT score has Z = -2, scored in the 2nd percentile.

Rhoda

Scored 25, so \(X = 25\).

ACT has a μ of 20 and a σ of 5

Her z-score:

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{25 - 20}{5}\)

\(Z = 1\)

\(Z = 1\) has a p-value of 0.84

This means that Rhoda, whose ACT score has Z = 1, scored in the 84th percentile.

What is wrong with Bill’s logic ?

Rhoda, whose ACT has a z-score of 1, scored in the 84th percentile in the ACT, compared to Bill, whose SAT has a z-score of -2, who scored in the 2nd percentile on the SAT. Due to the higher percentile(higher z-score)  on her test, Rhoda did better on her respective test than Bill, and thus, his logic is wrong.

the answer is C 61 because 10x is 40 plus 21 is 61

Answer:

Option C

The answer is 61

Step-by-step explanation:

10x + 21 when x = 4

10(4) + 21

40 + 21 = 61

Thus, The answer is 61

-TheUnknownScientist 72

Answer:

what you need help with? ill help if i can

Step-by-step explanation:

Answer:

Step-by-step explanation:

We are supposed to find the least likely, which means we are looking for the smallest number.

.9 is the largest

.5 is next

.35 is second to smallest

A is the answer 0.01

Still stuck? Get 1-on-1 help from an expert tutor now.

Answer:

*  The mean (a measure of central tendency) weight value is the average of the weights of all pennies in the study.

* The standard deviation (a measure of variability or dispersion) describes the lowest and highest any individual penny weight can be. Subtracting 0.02g from the mean, you get the lowest penny weight in the group.

Step-by-step explanation:

Recall that a penny is a money unit. It is created/produced, just like any other commodity. As a matter of fact, almost all types of money or currency are manufactured; with different materials ranging from paper to solid metals.

A group of pennies made in a certain year are weighed. The variable of interest here is weight of a penny.

The mean weight of all selected pennies is approximately 2.5grams.

The standard deviation of this mean value is 0.02grams.

In this context,

*  The mean (a measure of central tendency) weight value is the average of the weights of all pennies in the study.

* The standard deviation (a measure of variability or dispersion) describes the lowest and highest any individual penny weight can be. Subtracting 0.02g from the mean, you get the lowest penny weight in the group.

Likewise, adding 0.02g to the mean, you get the highest penny weight in the group.

Hence, the weight of each penny in this study, falls within

[2.48grams - 2.52grams]

The explicit equation for the table is,

f(n) = n² + 4

Given, the values of an explicit function,

Let the function be,

f(n) = an² + bn + c

f(1) = a(1)² + b(1) + c

5 = a + b + c

f(2) = a(2)² + b(2) + c

8 = 4a + 2b + c

f(3) = a(3)² + b(3) + c

13 = 9a + 3b + c

On subtracting the equations, we get

5 = 5a + b

3 = 3a + b

Again, on subtracting we get

2 = 2a

a = 1

On putting the values we get,

b = 0.

a + b + c = 5

1 + 0 + c = 5

c = 4

Hence, the explicit equation for the table is,

f(n) = n² + 4

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Answer:

$23,465

$4,693

Step-by-step explanation:

To find a percent of a number, multiply the percent by the number.

6.5% of $361,000 = 0.065 × $361,000 = $23,465

20% of $23,465 = 0.2 × $23,425 = $4,693

In this case, the amount of the paint that she used to paint her room is 4 1/2 of the paint

Here are the general steps to follow when forming an equation from a word problem:

Read the problem carefully and identify the quantities and variables involved. Look for keywords that indicate the mathematical operation to be performed, such as "sum", "difference", "product", "quotient", "is", "was", "will be", "more than", "less than", "equal to", etc.

Translate the words into mathematical expressions and equations. Use the quantities and variables identified in step 1 to form equations. Assign variables to unknown quantities, and use algebraic symbols and operations to represent the relationships between the quantities.

Solve the equations to find the answer to the problem. Simplify the equations and solve for the unknown variable. Check your answer to make sure it makes sense in the context of the problem.

1) 5 * 19/4

= 95/4

23 3/4

2) Total weight = 3(14/3) + 5(15/2)

14 + 75/2

28 + 75/2

= 51  1/2 pounds

3) x = 45/8 *  4/5

= 9/2

= 4 1/2

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Answer:

10

Step-by-step explanation:

Solving $4x=3y$ for $x$ gives $x = \frac{3}{4}y$. Substituting this into the desired expression gives\begin{align*}\frac{2x+y}{3x-2y} &= \frac{2\left(\frac34\right)y + y}{3\left(\frac34y\right) - 2y}\\

&=

\frac{\frac32y + y}{\frac94y - 2y} = \frac{\frac52y}{\frac{y}{4}} \\

&=\frac{5}{2}\cdot 4 = \boxed{10}.\end{align*}

Answer:

10

Step-by-step explanation:

Substitution and simplification

Given

To find

Let the purchase value be P,

ATQ,

P -3 x 0.1P = Rs 43,740

P-0.3P = Rs 43,740

0.7P = Rs 43,740

P = Rs 43,740/0.7

P = Rs 62,486 (approx)

Hence, the purchase value of the machine would be Rs 62,486

A total of 7 Cyclists traveled more than 45 miles. 4 cyclists traveled 50 miles or more, and 3 cyclists traveled more than 54 1/4 miles.

A line plot is drawn with the cyclists' names plotted on the x-axis and their corresponding distances covered plotted on the y-axis.

The dots are then joined to form a line, revealing the relationship between the cyclist's names and their corresponding distance traveled. The cyclist names and their corresponding distances are given in the table below.

Name Distance (in miles) Gina 40 1/2 Rey 50 Faye 35 3/4 Mark 60 John 45 1/2 James 40 1/2 Albert 40 1/4 William 54 1/4 Nathan 40 Kate 40 1/4 Mary 60 Risa 40 Abi 35 3/4 Joan 50 1/2 1. The number of cyclists is 14. 2. The longest distance covered by a cyclist is 60 miles.

Mary and Mark both covered this distance.3. A total of 7 cyclists traveled less than 50 miles. 4. The most common distance traveled by cyclists is 40 1/2 miles. Gina, James, and Albert covered this distance. 5. 2 more cyclists traveled 45 miles than 55 1/4 miles. Only William traveled 55 1/4 miles, while John and James both traveled 45 1/2 miles.6.

A total of 7 cyclists traveled more than 45 miles. 4 cyclists traveled 50 miles or more, and 3 cyclists traveled more than 54 1/4 miles.

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Answer:

the number of protons in the nuclues of an atom

1. The x - intercepts of the parabola are

2. The meaning of the x-intercepts are the plane takes of at x = 2.5 s and lands at x = 7.5 s

3. The vertex of the parabola is at (5, 80).

A parabola is a curved shape

1. Given the parabola above, to find the x - intercepts, we proceed as follows.

The x-intercepts are the points at which the graph cuts the x-axis.

They are

2. The meaning of the x-intercepts in this problem are the points where the plane takes off and lands on the ground.

The plane takes of at x = 2.5 s and lands at x = 7.5 s

3. The vertex is the maximum point on the graph.

So, we see that the vertex is at x = 5 s and y = 80 ft

So, the vertex is at (5, 80).

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The solution to the system of equations is x = -3 and y = -4.

To solve the system of equations:

Equation 1: 2x - y = -10

Equation 2: 3x + 2y = -1

We can use the method of substitution or elimination to find the values of x and y.

Let's use the method of elimination:

Multiply Equation 1 by 2 to make the coefficients of y in both equations equal:

2(2x - y) = 2(-10)

4x - 2y = -20

Now, we can eliminate y by adding Equation 2 and the modified Equation 1:

(3x + 2y) + (4x - 2y) = -1 + (-20)

7x = -21

x = -3

Substitute the value of x into Equation 1 to solve for y:

2(-3) - y = -10

-6 - y = -10

y = -10 + 6

y = -4

Therefore, the solution to the system of equations is x = -3 and y = -4.

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The conclusion that they would arrive at based on the rejection region would be to reject the null hypothesis.

This is the region that tells us that we are not to accept the null. The conclusion would be to reject the null.

This happens when the rejection region is found to be around the area that is in the critical value.

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It will take 15 days for the hair to grow from 12mm to 16.5mm

By "average rate" in this context, we mean the typical or usual amount of hair growth per unit of time, which is often measured in millimeters per day. This rate can vary slightly depending on factors such as age, gender, genetics, diet, and overall health.

Let's first find out how much the hair needs to grow by subtracting its initial length (12mm) from its target length (16.5mm):

16.5mm - 12mm = 4.5mm

Now we can divide this growth by the average rate of hair growth to find the number of days it will take to grow this much:

4.5mm ÷ 0.3mm/day = 15 days

Therefore, it will take 15 days for the hair to grow from 12mm to 16.5mm.

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The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

Consider the next 1000 98% CIs for μ that a statistical consultant will obtain for various clients. Suppose the data sets on which the intervals are based are selected independently of one another. How many of these 1000 intervals do you expect to capture the corresponding value of μ?

What is the probability that between 970 and 990 of these intervals contain the corresponding value of μ? [Hint: Let Y = the number among the 1000 intervals that contain μ. What kind of random variable is Y?]

(Round your answer to four decimal places.)

Answer:

The expected value is

\(E(Y) = n \times p \\\\E(Y) = 1000 \times 0.98 \\\\E(Y) = 980\)

\(P(970 < Y < 990) = 0.9753 \\\\P(970 < Y < 990) = 97.53 \%\)

There is a 97.53% probability that between 970 and 990 of these intervals contain the corresponding value of μ.

Step-by-step explanation:

Consider the next 1000 98% CIs for μ that a statistical consultant will obtain for various clients.

From the above information, we know that,

n = 1000

p = 0.98

How many of these 1000 intervals do you expect to capture the corresponding value of μ?

The expected value is given by

\(E(Y) = n \times p \\\\E(Y) = 1000 \times 0.98 \\\\E(Y) = 980\)

What is the probability that between 970 and 990 of these intervals contain the corresponding value of μ?

We can use the Normal distribution as an approximation to the Binomial distribution since n is quite large and p is also greater than 0.50.

n×p ≥ 10

1000×0.98 ≥ 10

980 ≥ 10  (satisfied)

n×(1 - p) ≥ 10

1000×(1 - 0.98) ≥ 10

20 ≥ 10 (satisfied)

Let Y be the random number among the 1000 intervals that contain μ

\(P(970 < Y < 990) = P(Y < 990) - P(Y < 970) \\\\P(970 < Y < 990) = P( Z < \frac{Y - \mu}{\sigma}) - P( Z < \frac{Y - \mu}{\sigma} )\\\\\)

Where the mean is

\(\mu = 980\)

and the standard deviation is

\(\sigma = \sqrt{n \times p(1-p)} \\\\\sigma = \sqrt{1000 \times 0.98(1-0.98)} \\\\\sigma = 4.4272\)

Finally, the required probability is

\(P(970 < Y < 990) = P( Z < \frac{990 - 980}{4.4272}) - P( Z < \frac{970 - 980}{4.4272} )\\\\\)

We need to consider the continuity correction factor whenever we use continuous probability distribution (Normal distribution)  to approximate discrete probability distribution (Binomial distribution).

\(P(970 < Y < 990) = P( Z < \frac{989.5 - 980}{4.4272}) - P( Z < \frac{969.5 - 980}{4.4272} )\\\\P(970 < Y < 990) = P( Z < \frac{9.5}{4.4272}) - P( Z < \frac{-10.5}{4.4272} )\\\\P(970 < Y < 990) = P( Z < 2.15) - P( Z < -2.37 )\\\\\)

From the z-table, the z-score corresponding to 2.15 is 0.9842

From the z-table, the z-score corresponding to -2.37 is 0.0089

\(P(970 < Y < 990) = 0.9842 - 0.0089\\\\P(970 < Y < 990) = 0.9753 \\\\P(970 < Y < 990) = 97.53 \%\)

Therefore, there is a 97.53% probability that between 970 and 990 of these intervals contain the corresponding value of μ.

Step-by-step explanation:

there is a nice formula for the height in a right-angled triangle :

h = sqrt(p×q)

h being the height to the 90° angle, p and q being the segments (left and right of the height) of the Hypotenuse.

so, in our case

x = sqrt(25×144) = 5×12 = 60