The correct option is B) 67.4%
What is the z- score table?A standard normal table (also called the unit normal table or z-score table) is a mathematical table for the values of ϕ, indicating the values of the cumulative distribution function of the normal distribution. Z-Score, also known as the standard score, indicates how many standard deviations an entity is, from the mean.
Given here, P(probability that a worker is a college graduate) = 32%
= 0.32
q (probability that a worker is not a college graduate) is 1-0.32 = 0.68
now μ(mean) = n×p
= 50×0.32
= 16
Again standard deviation σ = [tex]\sqrt{npq\\}[/tex]
σ = [tex]\sqrt{50\cdot 0.32\cdot 0.68}[/tex]
σ = 3.2985
now P(x<17.5) = P((x-μ)/σ <(17.5-16)/3.2985)
= P(z<0.45)
= 0.674 [using z table]
= 67.4%
Hence option 2 is the correct answer
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(SAT prep) If the lengths of two sides of a triangle are 3 and 5 then the lenght of the third side cannot be:
Answer:
A)
Step-by-step explanation:
3+3=6 6>5
3+5=8 3<8
A)
The area of the entire figure below is 111 square unit.
A rectangle that has been split into 24 parts, set in 4 rows of 6 parts each. The parts in the top 3 rows have been shaded blue. The parts in the left 5 columns have been shaded purple. The first 5 parts in the top 3 rows are striped to show they are shaded both blue and purple. Along the top of the rectangle, the columns are labeled one-sixth. Along the left side of the rectangle, the rows are labeled one-fourth.
A rectangle that has been split into 24 parts, set in 4 rows of 6 parts each. The parts in the top 3 rows have been shaded blue. The parts in the left 5 columns have been shaded purple. The first 5 parts in the top 3 rows are striped to show they are shaded both blue and purple. Along the top of the rectangle, the columns are labeled one-sixth. Along the left side of the rectangle, the rows are labeled one-fourth.
What is the area of the striped rectangle?
The striped rectangle has a total area of 69,375 cm².
How to calculate the area of the striped rectangle?To find the area of the striped rectangle we must carry out the following procedures.
Find the area of each segment of the rectangle, that is, what is the area of each of the 24 squares that make up the rectangle, for that we divide the 111cm² of the total area into 24.
111cm² ÷ 24 = 4.625cm²According to the above, we infer that each square has an area of 4.625cm².
On the other hand, to find the area of the striped rectangle we must take into account that it is 5 squares long by 3 squares high, that is, its area is 15 squares.
3 × 5 = 15Finally, each square has an area of 4.625cm², so to find the total area of the striped area we must multiply the area of each square by the number of squares.
15 × 4.625cm² = 69.375cm²
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what is the equation of the parabola passing through the points
(0,6). (3, 15.6), and (10,-4)?
Answer:
y = -0.6x^2 + 5x + 6
Step-by-step explanation:
First, find the equation of a linear line that passes through the points (0,6) and (3, 15.6) in the slope intercept form, y = mx + b. We know that the line has a y-intercept of 6, so b = 6. Substitute 3 for x, 15.6 for y, and 6 for b to find m.
y = mx + b
15.6 = 3m + 6
9.6 = 3m
m = 3.2
y = 3.2x + 6
y = a(x - 0)(x - 3) + 3.2x + 6
y = a(x)(x - 3) + 3.2x + 6
Finally, substitute 10 for x and -4 for y in the equation above to find a.
-4 = a(10)(10 - 3) + 3.2*10 + 6
-4 = a(10)(7) + 32 + 6
-4 = 70a + 38
-42 = 70a
a = -0.6
Simplify to write in standard form.
y = -0.6(x)(x - 3) + 3.2x + 6
y = -0.6x^2 + 5x + 6
A strain of bacterial cells doubles inpopulation every 2 days. A single cell is placed in a dish with sufficient nutrients to sustain a colony. Which equation will
calculate d, the number of days after which there will be 256 bacterial cells in
the dish?
The equation that will calculate the number of days after which there will be 256 bacterial cells in the dish is 2^(d/2) = 256
How to determine the equation of the number of days?The given parameters are:
Rate, r = doubles every two days
Initial number of strain, a = 1
This means that the function is an exponential function.
An exponential function is represented as:
A(d) = a * r^d
Since the strain doubles every two days, we have:
A(d) = a * r^(d/2)
Substitute the known values in the above equation
A(d) = 1 * 2^(d/2)
Evaluate the product
A(d) = 2^(d/2)
When there are 256 bacterial cells, the equation becomes
2^(d/2) = 256
Hence, the equation that will calculate the number of days after which there will be 256 bacterial cells in the dish is 2^(d/2) = 256
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PLEASE HELP YOU WILL GET ALOT OF POINTS The triangle on the left is rotated to create the triangle on the right as its
image. Which set of congruence statements below is true?
Answer:
The third one
Step-by-step explanation:
It cannot be the first 2 as the corners wouldn't line up. It cannot be the last one as B and R are not the same angles
On a coordinate plane, a circle has center (0, 0) and radius 4. A parabola opens down and goes through (3, 0), has vertex (0, 2) and goes through (negative 3, 0). Everything above the parabola and inside of the circle is shaded. Which system has the solution set shown? x squared + y squared greater-than-or-equal-to 16 and y greater-than-or-equal-to negative one-fourth x squared + 2 x squared + y squared greater-than-or-equal-to 16 and y less-than-or-equal-to negative one-fourth x squared + 2 x squared + y squared less-than-or-equal-to 16 and y greater-than-or-equal-to negative one-fourth x squared + 2 x squared + y squared less-than-or-equal-to 16 and y less-than-or-equal-to negative one-fourth x squared + 2
The inequality system that has the solution set shown will be C. x squared + y squared less-than-or-equal-to 16 and y greater-than-or-equal-to negative one-fourth x squared + 2.
How to illustrate the information?It should be noted that inequalities are simply used to compare two expressions that are unequal.
It can be seen that the solution set that's illustrated is:
x² + y² <= 16
-1/4x² + 2 <= y
Therefore, the inequality system that has the solution set shown will be option C.
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The state lottery board is examining the machine that randomly picks the lottery numbers. On each trial, the machine outputs a ball with one of the digits 0 through 9 on it. (The ball is then replaced in the machine.) The lottery board tested the machine for 20 trials and got the following results.
Using the probability concept, we have that:
a) The experimental probability is of 0.75 = 75%.
b) The theoretical probability is of 0.5 = 50%.
c) As the number of trials increases, the probabilities are expected to get closer, though they might not be equal.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes. For an experimental probability, these number of outcomes are taken from previous trials. A theoretical probability is calculated before any trial, and as the number of trials increase, the experimental and theoretical probabilities get closer.
From the table, there were 20 trials, and 2 + 3 + 4 + 4 + 2 = 15 resulted in even numbers, hence the experimental probability is:
p = 15/20 = 0.75 = 75%.
For a fair machine, even and odd numbers should be equally as likely, hence the theoretical probability is of 0.5 = 50%.
For item c, we have that as the number of trials increases, the probabilities are expected to get closer, though they might not be equal.
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Cannington, Inc., designs, manufactures, and markets personal computers and related software. The following information was taken from a recent annual report of Cannington industries: Property, Plant, and Equipment (in millions): Current Year Preceding Year Land and buildings $707,150 $410,147 Machinery, equipment, and internal-use software 671,793 530,363 Office furniture and equipment 106,073 91,930 Other fixed assets related to leases 855,652 643,507 Accumulated depreciation and amortization (898,081) (749,579) a. Compute the book value of the fixed assets for the current year and the preceding year. Current year book value $fill in the blank 1 Preceding year book value $fill in the blank 2
The book value of the fixed assets for the current year and the preceding year is: $1,442,587; $926,368.
Book valueCurrent year book value
Land and buildings $707,150
Machinery, equipment, and internal-use software $671,793
Office furniture and equipment $106,073
Other fixed assets related to leases $855,652
Less Accumulated depreciation and amortization ($898,081)
Book value $1,442,587
Preceding year book value
Land and buildings $410,147
Machinery, equipment, and internal-use software $530,363
Office furniture and equipment $91,930
Other fixed assets related to leases $643,507
Less Accumulated depreciation and amortization ($749,579)
Book value $926,368
Therefore the book value of the fixed assets for the current year and the preceding year is: $1,442,587; $926,368.
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graphs of exponential functions
An example of an exponential graph function has been attached and its' properties are as below.
How to draw the graph of an exponential function?The general formula for exponential functions is: f(x) = aˣ, a > 0, a ≠ 1.
The reasons for the restrictions are because;
If a ≤ 0, then when you raise it to a rational power, you may not get a real number.
The graph of an exponential function y = 2ˣ is shown in the attached file. Here are some properties of the exponential function when the base is greater than 1.
The graph passes through the point (0,1)The domain is all real numbersThe range is y>0.The graph is increasingThe graph is asymptotic to the x-axis as x approaches negative infinityThe graph increases without bound as x approaches positive infinityThe graph is continuousThe graph is smoothRead more about Exponential Function Graphs at; https://brainly.com/question/2456547
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Elliot borrows $3,000 from a bank that is charging three percent simple interest per year. If he pays the loan back in six months, how much interest will he pay? $30.00
$45.00
$90.00
$300.00
Answer:
The answer to that question depends
beacuse where ever you are it changes like uk you can pay 100€
or japan it can be around 1000¥
Adisa borrows $5,000 at 14% interest, compounded twice a year. How much does she owe at the end of 8 years?
The borrower owes $14,760.82 at the end of 8 years
What is compounding interest?
Compounding interest means that earlier interest would earn more interest in the future alongside the loan principal.
Note that in this case the loan continues to accumulate interest because there no repayments, in other words, the loan balance after 8 years, which comprises of the principal and interest for 8 years can be computed using the future value formula of a single cash flow(the single cash flow is the principal) as shown thus:
FV=PV*(1+r/n)^(n*t)
FV=loan balance after 8 years=unknown
PV=loan amount=$5,000
r=annual interest=14%
n=number of times in a year that interest is compounded=2(twice a year)
t=loan period=8 years
FV=$5000*(1+14%/2)^(2*8)
FV=$5000*(1.07)^16
FV=$5000*2.95216374856541
FV=loan balance after 8 years=$14,760.82
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The volume of a packing box is 5 - x cubic feet. The width of the box is x feet and the length is x - 2 feet
Answer:
Step-by-step explanation:
When a disease is rare in the general population, doctors are not likely to test everyone. Instead, they only test people that have specific risk factors or show symptoms of the disease. Even if resources are available, why do you think doctors would avoid giving a test for a rare disease to everyone in the general population? Explain using ideas from probability that were explored in this project
f(t) = 0.25t2 − 0.5t + 3.5
The resulting value of the function when the values of t is 2 and 6 are 3.5 and 6.5 respectively
Function and valuesFunctions are expressions in form of variables. Given the following quadratic equation expressed as:
f(t) = 0.25t^2 − 0.5t + 3.5
We can find the equivalent value of the function when the value of t a re 2 and 6.
If the value of t is 2. hence;
f(2) = 0.25(2)^2 − 0.5(2) + 3.5
f(2) = 1 - 1 + 3.5
f(2) = 3.5
If the value of t is 6, hence;
f(6) = 0.25(6)^2 − 0.5(6) + 3.5
f(6) = 9 - 3 + 3.5
f(6) = 6.5
Hence the resulting value of the function when the values of t is 2 and 6 are 3.5 and 6.5 respectively
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a number line shows the whole numbers from 0 to 10 describe where you would plot square root 30
ASAP Please help me with this questions ASAP
46) True
47) False
These are true by definition.
Scenario 2
You are at a restaurant with three friends (party of 4) and need to estimate the amount of tip for your portion of the bill without using a calculator. Assume a 20% tip rate. For full credit, you will need the cost of your meal, an explanation of how you would calculate your 20% tip, and the total amount.
The best approach to calculating the stipulated 20% tip by means of fractions is to note that the tip is one-fifth of the total amount charged on the bill.
What is the equivalent of the 20% tip as indicated in the task content?The percentage represented as; 20% can be expressed as a fraction.
This follows from the fact that the percentage, % symbol translates to divided by 100.
Consequently, we must note that the 20% translates to; 20/100 = 1/5.
Hence, the 20% tip is one-fifth of the total amount.
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what base could be written in the blank to make the exponential function model 15% decay ? y= (___) ^t\12
The base of the exponential function model in order to get 15% decay should be 0.85
In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation.
The first step would be figuring out the function's base.
The function's form should be, [tex]y=a*b^{t}[/tex]
Here,
'a' denotes the starting value.
'b' denotes the decrease rate.
't' denotes time.
According to the question, the exponential function model is,
[tex]y=b^{\frac{t}{12} }[/tex]
In order to get a 15% decay,
The base of the function should be (100-15)/100 = 0.85
Thus, Base of function(b) = 0.85
The exponential function model is written as:
[tex]y=0.85^{t/12}[/tex]
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Which of the following is equivalent to (5)7/3
Answer:
11 and 2/3
Step-by-step explanation:
The given expression be [tex]$(5)^{7/3[/tex] then the value exists ³√5⁷.
What is exponential form?The base number exists raised to a power of the exponent numerator and estimated to the root of the exponent denominator.
Given: [tex]$(5)^{7/3[/tex]
The given expression contains an exponent of (7/3)
When we exist transforming from exponential form to radical form you always place the numerator as our constant's exponent in the radical ( [tex]$5^{\frac{7}{3} }$[/tex] exists named the radicand because it exists found in the radical) and the denominator in front of the radical, where it would be named the index.
The formula would be: [tex]$(\sqrt[n]{x})^{q}=x^{\frac{p}{q}}$[/tex]
Therefore, the correct answer is ³√5⁷.
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you are considering an investment into Company XYZ and need to determine the company's value and the appropriate investment amount. You have been provided with historical financial statements for the past three years in order to build a forecast model. Key assumptions to use include:
Future sales revenue is assumed to increase at 2.5% annually.
Gross margin for 2021E is assumed to be equal to the average gross margin % for 2019 and 2020, but will decrease by 2.5% (i.e. 250 bps) each year thereafter
SG&A expense is assumed to be a percentage of revenue for the forecast period. That percentage is equal to the 2018-2020 average
Depreciation expense is assumed to be a percentage of revenue for the forecast period. That percentage is equal to the 2018-2020 average
The tax rate for the forecast period is assumed to be equal to the effective tax rate for 2018
Capital expenditures for any given year in the forecast period is assumed to be 3x the prior year's depreciation expense. For example, 2021 capital expenditures is equal to 3x 2020 depreciation expense.
No new debt or equity is assumed to be issued
Download CFI_-_FMVA_Practice_Exam_Case_Study_A.xlsx and answer the following 12 questions.
1
What is Gross Profit in 2028E using the assumptions listed above and on the Control Panel?
$17,545
$30,704
$27,780
$40,938
Option A is correct. The gross profit that has been calculated for this year is given as 17545
How to solve for the gross profit22050 × 97.5%(100-2.5%) = 21498.75
= 21498.75 × 0.975 = 20961.28
= 20961.28 x 0.975 = 20437.24
= 20437.24 x 0.975 = 19926.31
= 19926.31 × 0.975 = 19428.15
= 19428.15 x 0.975 = 18942.45
= 18942.45 x 0.975 = 18468.80
= 18468.89 × 0.975 = 18017
= 18007 × 0.975 = $17545
Hence we can see at the end of the solution that the value of the gross profit in 2028 = $17545
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What is the ordered pair of X' after point X (3, 4) is rotated 180°?
OX' (3,-4)
OX' (-3,-4)
OX' (-4, 3)
OX' (-4,-3)
Please help!!!!! Two copies of the same Rational Function are shown below.
On the graph below draw the Horizontal Asymptote and write the equation for the horizontal asymptote underneath.
The equation for the horizontal asymptote will be y = -2.
How to illustrate the information?Since the degree of the numerator and denominator of f(x) is the same both being 1, therefore horizontal asymptote exists and is given by:
y = Leading coefficient of numerator of f(x) / Leading coefficient of denominator of f(x)
= y = -2/1
= y = -2
The vertical asymptote will be f(x) = -2x / (x + 3). To find the vertical asymptote we will equate the denominator of f(x) = 0
= x + 3 = 0
= x = -3
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Show Work Please Thank You
Answer:
[tex]\displaystyle{x = \dfrac{\pi}{12}, \dfrac{\pi}{6}}[/tex]
Step-by-step explanation:
We are given the trigonometric equation of:
[tex]\displaystyle{\sin 4x = \dfrac{\sqrt{3}}{2}}[/tex]
Let u = 4x then:
[tex]\displaystyle{\sin u = \dfrac{\sqrt{3}}{2}}\\\\\displaystyle{\arcsin (\sin u) = \arcsin \left(\dfrac{\sqrt{3}}{2}\right)}\\\\\displaystyle{u= \arcsin \left(\dfrac{\sqrt{3}}{2}\right)}[/tex]
Find a measurement that makes sin(u) = √3/2 true within [0, π) which are u = 60° (π/3) and u = 120° (2π/3).
[tex]\displaystyle{u = \dfrac{\pi}{3}, \dfrac{2\pi}{3}}[/tex]
Convert u-term back to 4x:
[tex]\displaystyle{4x = \dfrac{\pi}{3}, \dfrac{2\pi}{3}}[/tex]
Divide both sides by 4:
[tex]\displaystyle{x = \dfrac{\pi}{12}, \dfrac{\pi}{6}}[/tex]
The interval is given to be 0 ≤ 4x < π therefore the new interval is 0 ≤ x < π/4 and these solutions are valid since they are still in the interval.
Therefore:
[tex]\displaystyle{x = \dfrac{\pi}{12}, \dfrac{\pi}{6}}[/tex]
The manger of a company planned to distribute a $50 bouns to each employee from the company fund, but the fund contained $5 less than what was needed. Instead, the manger gave each employee a $45 bouns and kept the remaing $95 in the company fund. How much money was in the company fund before any bonuses were paid?
The total company fund before any bonuses were paid is $995 and there were 20 staffs.
What is an equation?An equation is an expression that shows the relationship between two numbers and variables.
An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.
Let y represent the total company fund and x represent the number of staffs.
From the first statement:
y - 50x = -5 (1)
Also:
y - 45x = 95 (2)
From equation 1 and 2:
x = 20, y = 995
The total company fund before any bonuses were paid is $995 and there were 20 staffs.
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a studio has 1600 square feet of floor space. the studio then buys the neighboring building and expands by 75%
Answer:
the total new area is 2800 ft²
Step-by-step explanation:
original area: 1600 ft²
new expanded area: 1600 ft² + 75% of 1600 ft²
new expanded area = 1600 ft² + 0.75 × 1600 ft²
new expanded area = 1600 ft² + 1200 ft²
total new area = 2800 ft²
I really need help I work a 12 hr shift in less then 3 hrs and if I don't answer this correct I don't graduate and have to redo over 100 questions so please if you answer please make it the right answer please someone show mercy and help me
Answer:
72 Degrees
Step-by-step explanation:
10 / 50 = 0.2
A circle has 360 degrees.
0.2 X 360 = 72
Select the correct answer.
What is the equation of the line that has a slope of 3 and goes through the point (-3,-5)?
OA.
y=3x+4
OB. y=3x-14
OC. y=3x-4
OD. y=3x + 12
Answer: [tex]\Large\boxed{A.~y=3x+4}[/tex]
Step-by-step explanation:
Given information
Slope = 3
Point = (-3, -5)
Given the format of the equation
Slope-intercept form: y = mx + b
m = Slopeb = y-interceptSubstitute values into the equation
y = (3)x + b
y = 3x + b
Substitute the given point into the equation to get the value of [ b ]
(-5) = 3(-3) + b
-5 = -9 + b
b = -5 + 9
b = 4
Therefore, the equation of the line is [tex]\Large\boxed{y=3x+4}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
A sundae requires 3 ice-cream scoops and 4 strawberries, and a milkshake requires 2 ice-cream scoops and 6 strawberries. Ramses wants to make sundaes and milkshakes with at most 25 ice-cream scoops and 37 strawberries. Let S denote the number of sundaes he makes and M the number of milkshakes he makes. Write an inequality that represents the condition based on the number of ice-cream scoops. Write an inequality that represents the condition based on the number of strawberries.
The system of inequalities be
3x+2y ≤ 25, 4x+6y ≤ 37
1) Maximum number of sundaes possible exists 9.
2) Maximum number of milkshakes possible exists 6.
3) Combination that uses the most of both Ice-cream and Strawberries = 7 scoops of ice cream and 1 scoop of strawberries.
What is system of inequalities?A system of inequalities exists the system where the set of more than one inequalities in more than or equivalent to one variable.
Given: A sundae needs 3 ice-cream scoops and 4 strawberries, and a milkshake requires 2 ice-cream scoops and 6 strawberries.
Ramses have to create sundaes and milkshakes with at most 25 ice-cream scoops and 37 strawberries.
Let x represent the number of sundaes he creates and y the number of milkshakes he creates.
We represent in tabular form,
Sundae(x) Milkshake(y) Total
Ice-cream 3 2 3x+2y
Strawberries 4 6 4x+6y
System of inequalities:
Sundaes and milkshakes with at most 25 ice-cream scoops exist
33x+2y ≤ 25.
Sundaes and milkshakes with at most 37 strawberries exist 4x+6y ≤ 37.
1) Maximum number of sundaes possible:
Maximum number of sundaes possible when y = 0
From the graph y = 0 at x = 9.25
Therefore, the maximum number of sundaes possible exists at 9.
2) Maximum number of milkshakes possible:
Maximum number of milkshakes possible when x = 0
From the graph x = 0 at y = 6.167
Therefore, the maximum number of milkshakes possible exists at 6.
3) Combination that utilizes the most of both Ice-cream and Strawberries:
A combination of both is possible there exists an intersection of both the equation.
From the graph, the intersection point exists x = 7.6 and y = 1.1.
Therefore, the Combination that utilizes the most of both Ice-cream and Strawberries = 7 scoops of ice cream and 1 scoop of strawberries.
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HOW MANY 7 DIGIT TELEPHONE NUMBERS ARE POSSIBLE IF THE FIRST DIGIT CANNOT BE ZERO AND:
A) THE TELEPHONE NUMBER MUST BE A MULTIPLE OF 100?
B) ONLY ODD DIGITS CAN BE USED?
C) THE FIRST 3 DIGITS ARE 277?
Using the Fundamental Counting Theorem, the number of possible telephone numbers is given by:
a) 900,000.
b) 78,125.
c) 10,000.
What is the Fundamental Counting Theorem?It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
For item a, a multiple of 100 means that the last two digits are 00, hence the parameters are:
[tex]n_1 = 9, n_2 = n_3 = n_4 = n_5 = 10, n_6 = n_7 = 1[/tex]
Hence the number is:
N = 9 x 10^5 = 900,000.
For item b, odd digits are 1, 3, 5, 7 and 9, hence the parameters are:
[tex]n_1 = n_2 = n_3 = n_4 = n_5 = n_6 = n_7 = 5[/tex]
Hence the number is:
N = 5^7 = 78,125.
For item c, if the first 3 digits are 277, the parameters are:
[tex]n_1 = n_2 = n_3 = 1, n_4 = n_5 = n_6 = n_7 = 10[/tex]
Hence the number is:
N = 10^4 = 10,000.
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The volume of a rectangular box is 3x(3x + 4)(3x - 1). (Drawing is not to
scale.)
Length 3x + 4
Width 3x
Height 3x - 1
Which statement about the volume of the box is tru?
The volume of the rectangular box is the product of the base area and the height 3x - 1
How to determine the true statement?The given parameters are:
Length = 3x + 4
Width = 3x
Height = 3x - 1
The base area of the rectangular box is calculated as
Base area = Length * Width
Substitute the known values in the above equation
Base area = 3x(3x + 4)
This means that the volume of the rectangular box is the product of the base area and the height 3x - 1
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