1. The table of values for Dianely's salary can be represented for 4 years as follows:
Year Salary
1 $40,000
2 $42,500
3 $45,000
4 $47,500
2. The equation that models Dianely's salary after n years is S = 40,000 + 2,500n.
What is an equation?An equation is a mathematical statement stating that two mathematical expressions are equivalent or equal.
For instance, given the number of years, one can claim that Dianely's salary will be a given amount based on the above equation.
Equations involve variables, numbers, and the use of the equation sign (=) with some mathematical operands.
Initial salary = $40,000
Salary raise per year = $2,500
Disney's salary after n years in equation form, S = 40,000 + 2,500n.
Table of Values for Dianely's Salary:
Year Salary
1 $40,000
2 $42,500 (40,000 + 2,500)
3 $45,000 (42,500 + 2,500)
4 $47,500 (45,000 + 2,500)
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kieran tried to shade all the multiples of 3 on the hundred chart, but he made a mistake. what mistake did kieran make?
Answer:
Kieran shaded the multiples of 9 instead of the multiples of 3
Step-by-step explanation:
How many numbers are there from 10 to 99 in which the difference between the largest digit and the smallest digit equals 4?
For example 15 and 51, where 5 – 1 = 4.
There are 9 numbers from 10 to 99 in which the difference between the largest digit and the smallest digit equals 4
How to determine the count of the numbers?The difference can be represented as
Largest - Smallest = 4
Also, we have two instances to be
15 and 51
And the range is given as
Range = 10 to 99
In a range of 10, there is only one number whose difference between the digits is 4
There are 9 ranges of 10 from 10 to 99
So, the count of the range is
Count = 9 range * one number
Rewrite as
Count = 9 * 1
Evaluate
Count = 9
Hence, there are 9 of such numbers from 10 to 99
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Two times the sum of a number and 3 is 8.
Use the variable c for the unknown number.
My answer is : 2(c+3)=8
The " is" throwing my brain off, thanks so much
Two times or Twice the sum of a number and 3 is 8. The value of the number will be 1.
Let the value of the unknown number or variable be c.
Given,
"Two times the sum of a number and 3 is equal to 8", which means when you add the unknown number with 3 and then multiply it by 2, then the final answer will come as 8.
If we form the statement into an equation, then finding the value of the unknown variable will be a lot easier.
The equation will be:
2(c + 3) = 8
=> 2c + 6 = 8
=> 2c = 8- 6
=> 2c = 2
=> c = 2/2
=> c = 1.
Hence, the value of the unknown number c will be 1.
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Version 1 for Game Design Determine the center and radius of the circle with equation x² + y² + 4x − 6y + 12 = 0
Answer:
Step-by-step explanation:
Equation of circle is, (x-h)^2+ (y-k)^2=r .......(eqn1)
where, (h,k) is the center and r is the radius.
therefore, from the question by rearranging the equation,
x² + y² + 4x − 6y + 12=0
viz, (x² +4x+4) + (y²-6y+9)-1=0
(x+2)^2 + (y-3)^2=1
therefore from eqn1, (-2,3) is the center and radius is 1
The following set of four ordered pairs below defines the vertices, in counterclockwise order, of a quadrilateral (four-sided figure). {(0,−2),(6,0),(4,5),(−2,3)} Step 1 of 3 : Find the slopes of the indicated sides of the quadrilateral. Simplify your answer.
The slope of the side connecting (0,−2) and (-2, 3) is: -5/2.
The slope of the side connecting (6, 0) and (4, 5) is: -5/2.
How to Find the Slope Between Two Points?The slope (m) of a side connecting two points with given coordinates can be calculated using the slope formula shown below:
Slope (m) = change in y / change in x = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex].
Slope of the side connecting (0,−2) and (-2, 3):
Slope (m) = change in y / change in x = (3 - (-2)) / (-2 - 0)
m = 5/-2
Slope (m) = -5/2.
Slope of the side connecting (6, 0) and (4, 5):
Slope (m) = change in y / change in x = (5 - 0) / (4 - 6)
m = 5/-2
Slope (m) = -5/2.
Therefore, the slope of both sides are the same, which is: -5/2.
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carolina and her friends are training for a kayaking competition. the average distance and time traveled by each is shown in the table below. if the distance kayaked in the competition is 3 miles, predict who will win based on the rates shown. predict how long it will take the winner to complete the race if their rate remains constant
Carolina, 7/8 mi in 1/2 hr
Leslie, 1 mi in 1/3 hr
Bryan 3/4 mi in 3/4 hr
Javier 1 mi in 2/3 hr
The winner of the race among the friends would be Leslie.
Who would win the race?The person who has the highest average speed will win the race. Average speed is the total distance travelled per time.
Average speed = total distance / total time
Carolina's average speed = 7/8 ÷ 1/2
7/8 x 2 = 7/4 = 1 3/4 miles per hour
Leslie's average speed = 1 ÷ 1/3
1 x 3 = 3 miles per hour
Bryan's average speed = 3/4 ÷ 3/4
3/4 x 4/3 = 1 mile per hour
Javier's average speed = 1 ÷ 2/3
1 x 3/2 = 1 1/2 miles per hour
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A Norman window is a window with a semicircle on top of a regular rectangular window as shown in the diagram. What should the dimensions of the rectangular part of a Norman window be to allow in as much light as possible if there is only 12 ft of the framing material available?
The dimensions of the rectangular window that gives a maximum area are as follows;
Width = [tex]\dfrac{12}{2+\pi }[/tex] feet and length = 3 feet
What is the maximum value of a function?The maximum value of a function is given by the point at which the graph of the function has the highest value.
The parameters of the window are;
Length of the framing material available = 12 ft.
The shape of the window = A semicircle on top of a regular rectangular window
Required; The dimension of the rectangular part of the Norman window that allows the most light
Solution;
Diameter of the semicircular part of the window = The width of the rectangular part
Let x represent the width of the window, we have;
Perimeter of the semicircle = π·x/2
Side length of the rectangular window = (12 - π·x/2 - x)/2
Area of the rectangular part of the window, A = x × (12 - π·x/2 - x)/2
Area of the semicircle = π·x²÷4
Area of the window, is therefore;
[tex]A =\dfrac{ x \times (12 - \dfrac{\pi \cdot x}{2} - x)}{2} +\dfrac{ \pi \cdot x^2}{4}[/tex]
At the maximum area, of the rectangular part, we have;
[tex]A_r' =\dfrac{d}{dx}\left( A =\dfrac{ x \times (12 - \dfrac{\pi \cdot x}{2} - x)}{2} \right) = -\dfrac{x\cdot \pi +2\cdot x-12}{2} = 0[/tex]
x·π + 2·x - 12 = 0
The width, x = [tex]\dfrac{12}{2+\pi }[/tex] feet
The length of the rectangle is therefore;
[tex](12 - \pi \cdot \dfrac{6}{2+\pi } - \dfrac{12}{2+\pi })/2 = 6 - \pi \cdot \dfrac{3}{2+\pi } - \dfrac{6}{2+\pi } = 3[/tex]
The length of the rectangular window = 3 feet
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A group of 16 people is choosing a chairperson and vice-chairperson. They put all 16 people's names into a hat. The first name drawn becomes chair. The second name drawn becomes vice-chair. How many possible combinations of chair and vice-chair are there?
Based on the number of people present, the total number of combinations of Chairperson and Vice Chairperson is 240 combinations.
How to carry out Probability combinations?In order for us to find out the total possible combinations, we will use the formula as:
Total possible combinations = Number of possible chairpersons * Number of possible vice chairpersons
We are given that;
Number of possible chairpersons = 16
Number of possible vice chairpersons = 15 (This is because a chairperson is chosen first and leaves 15 people.)
Thus, we can say that;
Total possible combinations = 16 * 15
Total possible combinations = 240 combinations
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what fraction of the numbers from 1 to 20 contain the digit 7
Answer:
2/20
Step-by-step explanation:
Only 7 and 17 contain the number 7
solve the equation 619m + 313m = 2813for m.
Answer:
2813
m = ----------
932
Step-by-step explanation:
619m + 313m = 2813
932m = 2813
÷932 ÷932
2813
m = ----------
932
I hope this helps!
Answer:
[tex]m=\frac{2813}{932}[/tex]
Step-by-step explanation:
Combine like terms:
[tex]{619m}+{313m}=2813{932m}=2813[/tex]
Divide both sides by the same factor:
932m=2813
[tex]\frac{932m}{932}}=\frac{2813}{932}}\\[/tex]
Simplify
Cancel terms that are in both the numerator and denominator
[tex]m=\frac{2813}{932}[/tex]
The price of a technology stock was $9.69 yesterday. Today, the price fell to $9.56. Find the percentage decrease. Round your answer to the nearest tenth of a percent.
Answer:
1.3% decrease
Step-by-step explanation:
% change = (9.69 - 9.56) / 9.69) x 100 = 1.3% decrease
9.69-9.56 = 0.13
0.13/0.69= 0.0134158972
Multiply by 100 and you get 1.34158927
Round to nearest tenth and you get = 1.3%
Therefore, the percentage decrease is 1.3
2/5 divided by 8/15 please
The value of 2/5 divided by 8/15 is 3/4
What is a fraction?A fraction can be defined as the he or portion of a whole set or element
There are different types of fractions, which includes;
Proper fractionsImproper fractionsMixed fractionsComplex fractionsSimple fractionsSome examples include;
Simple fractions; 1/ 2, 1/3
Proper fractions; 1/ 4, 2/ 3
Improper fractions; 3/ 2, 5/3
Mixed fractions; 2 1/ 6
We have that;
2/ 5 ÷ 8/15
Take inverse of divisor and multiply
2/ 5 × 15/ 8
Divide through
3/4
Hence, the value is 3/4
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A human disease known as cystic fibrosis is inherited as a recessive trait. For example, the possible outcomes of a child inheriting cystic fibrosis genes are CC Cc cC cc if the child’s parents had one copy of each version of the gene so the probability of having a disease is ¼. Find the probability that 3 out of 6 children of these parents will have a cystic fibrosis.
The probability that 3 of the 6 children of this parents has the genes would be 0.1318
How to solve for the probabilityThe possibility of the result of any random event is known as probability. This phrase refers to determining the likelihood that any given occurrence will occur.
The total number of children from the family is n = 6
and the probability of those with the cystic fibrosis is x = 3,
Probability of the disease = 0.25
We have the formula as
[tex]^{6} C_{x} *P^{x} *(1-p)^{n-x}[/tex]
The probability is 1/4 = 0.25
This is then written as
6C3 x 0.25³ x (1 - 0.25)⁶⁻³
= 20 x 0.015625 0.421875
= 0.1318
The probability that 3 out of the 6 children would have this gene is 13.18%
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1. A sign in front of a roller coaster says "You must be 40 inches tall to ride." What percentage of this
height is:
a) 34 inches?
b) 54 inches?
The required percentage of height of 34 and 54 inches are 85% and 135%.
Given that,
The percentage of the height of 34 inches and 54 inches against the height of 40 inches is to be determined.
The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
Here,
a,
percentage = 34/40 × 100%
Percentage = 85%
b,
percentage = 54/40 × 100%
Percentage = 135%
Thus, the required percentages of height of 34 and 54 inches are 85% and 135%.
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find the sum of the first 50 terms of the sequence
[tex]a(n)=3n+2[/tex]
The sum of first 50 terms of the sequence a(n) = 3n + 2 is 3925
In this question, we have been given a sequence a(n) = 3n + 2
We need to find the sum of the first 50 terms of the sequence
a(1) = 3 + 2
= 5
a(2) = 6 + 2
= 8
a(3) = 9 + 2
= 11
a(4) = 12 + 2
= 14
...
Given sequence is arithmetic sequence with common difference d = 3 and the first term a = 5
Using the formula for the sum of first n terms of AP
Sum of n terms of A.P. = n/2[2a + (n - 1)d]
For n = 50
S(50) = (50/2) * [2(5) + (50 - 1)3]
S(50) = 25 * [10 + (49 * 3)]
S(50) = 25 * 157
S(50) = 3925
Therefore, the sum of first 50 terms of the sequence a(n) = 3n + 2 is 3925
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You can afford a $1100 per month mortgage payment. You've found a 30 year loan at 8% interest.
a) How big of a loan can you afford?
b) How much total money will you pay the loan company?
c) How much of that money is interest?
a) $149911.84 can be afforded
b) $39600 is the total money you will pay the loan company
c) $246088.16 is the interested amount
What is interest ?The cost of borrowing money is called interest, and it is typically stated as a percentage, such as an annual percentage rate (APR).Lenders may charge interest to borrowers for using their funds, or borrowers may charge interest to lenders for using their funds.Interest is frequently regarded as simple interest (based on the principal amount) or compound interest (based on principal and previously-earned interest).Credit cards, mortgages, auto loans, personal loans, savings accounts, and penalty assessments are all frequently linked with interest.The macroeconomic policy set by the Federal Reserve's federal funds rate has a significant impact on interest rates.Calculation
Given,
d=$1100
N= 30 years
r = 8% or 0.08
a) Loan amount that can be afforded
[tex]=\frac{d[1- (1+\frac{r}{k})^{-Nk} }{\frac{0.08}{12} }[/tex]
[tex]=\frac{1100[1- (1+\frac{0.08}{12})^{-30*12} }{\frac{0.08}{12} }[/tex]
= $149911.84
b) Total money you pay = d×N×k
=1100×30×12
=$39600
c) Interest paid = Total money paid – loan amount
⇒39600–14911.84 = $246088.16
Hence,
a) $149911.84 can be afforded
b) $39600 is the total money you will pay the loan company
c) $246088.16 is the interested amount
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Encuentra el área de la región coloreada.
4. Solve the equation m² = 14.
Answer:
m=3.7
Step-by-step explanation:
m²=14
m=√14
m=3.7416573868
m=3.7(2 d.p)
The third grade teachers had a pizza party. They ordered 11 large pizzas and each pizza had 8 slices. There were 4 classrooms in the grade. Estimate how many slices of pizza each classroom can have if the pizzas are shared equally.
Choose 1 answer: 20 slices 50 slices 300 slices 320 slices
Answer:
20 slices
Step-by-step explanation:
If there were 11 large pizzas with 8 slices per pizza, that would mean that there are a total of 88 slices of pizza.
If there are four classrooms, that means that if each classroom had 20 slices, there would be enough for everyone with 8 pieces leftover.
20 x 4 = 80
what is:
s . s + 0.5s . s
if s=8.2
Answer:
100.86
Step-by-step explanation:
8.2*8.2+0.5(8.2)*8.2
A line is perpendicular to y = 6x +3
and intersects the point (6, 1).
Find the equation for this line.
y-1=-(x-[?])
Answer:
1
Step-by-step explanation:
Perpendicuar lines have slopes that are opposite reciprocals: 6 ==> -1/6
y=mx+b
y=-x/6 + b ==> plug in slope -1/6 into slope equation
1 = -6/6 + b ==> plug in x and y values into slope equation
1 = -1 + b
1 + 1 = -1 + 1 + b
b = 2 ==> solve for b
y = -x/6 + 2 ==> plug in the value of b into the equation
y - 1 = -x/6 + 2 - 1
y - 1 = -x/6 + 1
y - 1 = -(x/6-1) ==> answer: 1
Anika earns $5 a week for doing all of her chores around the house. Which graph below represents this relationship between x, the number of weeks she has been doing chores, and y, the amount of money she has earned?
The graph of the linear equation can be seen in the image at the end.
Which graph represents the amount of money Anika has?We start by defining the variables we will use:
x = number of weeks.
y = money that Anika has.
We assume that Anika starts with $0, and then she wins $5 each week, so after x weeks she has:
y = $5*x
To graph this linear equation we need to find two points on the line, if x = 0 we get:
y = $5*0 = $0
So we have the point (0, 0)
if x = 1
y = $5*1 = $5
So we have the point (1, 5)
Now we can graph these two points and connect them with a line, the graph can be seen below.
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The probability that a 50-year-old male in the U.S. will die within one year is about 0.00142. An insurance company is preparing to sell a 50-year-old male a one-year, $60,000 life insurance policy. How much should it charge for its premium in order to have an expectation of $0 for the policy (i.e., make no profit and make no loss)? (Round your answer to the nearest dollar.)
They should charge for its premium in order to have an expectation of $0 for the policy is $85.
Given that, the probability that a 50-year-old male in the U.S. will die within one year is about 0.00142.
What is the probability?Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
Here, probability of alive 100-0.00142
= 0.99858
P(A)=0.99858A+0.00142(A+60000)
Put A=0, in the obtained function, we get
P(0)=0.99858(0)+0.00142(0+60000)
=0.00142×(60000)
=$85.2
= $85
Therefore, they should charge for its premium in order to have an expectation of $0 for the policy is $85.
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A courier service company wishes to estimate the proportion of people in various states that will use its services. Suppose the true proportion is 0.05.
If 202 are sampled, what is the probability that the sample proportion will differ from the population proportion by greater than 0.03? Round your answer to four decimal places.
The probability that the sample proportion of the number of people using the courier will differ from the population proportion by greater than 0.03 is 0.0504
How to get the required probabilityThe probability is calculated using z score, this is used to determine the amount of standard deviations a sample, X is from the mean
The z score is given by the formula
z = (X - μ) / σ
Definition of variables
mean, μ = p = 0.05
sample size, n = 202
standard deviation, σ
= √{(p(1 - p)) / n}
= √{(0.05(1 - 0.05)) / 202}
= √{(0.05 * 0.95) / 202}
= 0.01533
The probability
differ from the population proportion by less than 3%
|X - 0.05| > 0.03
X < 0.02 OR X > 0.08
P(z < 0.02) + P(z > 0.08 )
z score for z < 0.02
z = (0.02 - 0.05) / 0.01533
= -1.9569
p value for z < -1.9569 = 0.02518
z score for z > 0.08
z = (0.08 - 0.05) / 0.02196
= 1.9569
p value for z > 1.9569 = 1 - 0.9748 = 0.02518
The probability required = 0.02518 + 0.02518 = 0.0504 = 5.04%
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Select all the terms which are equivalent to the slope in a proportional relationship.
The terms which are equivalent to the slope in a proportional relationship include:
Constant of proportionalityOriginRise over runWhat is a proportional relationship?Proportional relationships are those in which the ratios of two variables are equal. Another way to think about them is that one variable in a proportional relationship is always a constant value multiplied by the other. This is known as the "constant of proportionality."
The proportionality constant is the ratio that connects two given values in a proportional relationship. The constant of proportionality is also known as the constant ratio, constant rate, unit rate, constant of variation, or even the rate of change.
The slope of a line indicates its steepness. Slope is calculated mathematically as "rise over run" (change in y divided by change in x). The slope formula is the rise over run formula, where the fraction consists of a rise, whether the line is going up or down, divided by the run.
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Complete question
Select all the terms which are equivalent to the slope in a proportional relationship.
Constant of proportionality
Origin
Inverse
Rise over run
Unit rate
Of the 600 loads of clothes washed at a cleaners in one week.450 of those loads are washed in an extra large- washer what percent of loads of clothes are washed in an extra large washer
The percent of loads of clothes are washed in an extra large washer is 75%.
What is the percentage?It was stated that out of the 600 loads of clothes washed at a cleaners in one week.450 of those loads are washed in an extra large- washer
Therefore, the percentage that are washed in extra large washer will be:
= Number washed in extra large washer / Total number of clothes × 100
= 450/600 × 100
= 3/4 × 100
= 75%
The percentage is 75%.
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Jake and Llana make and sell wooden birdhouses. Jake spent $150 buying supplies. He sells each birdhouse for $15. The equation P = 12x - 120
represents the profit, P, Liana earns for selling x birdhouses. Jake and Llana each made 50 birdhouses.
Which statements are true? Choose all that apply.
A. Jake spent $30 more on supplies than Liana.
B. Jake's birdhouses cost $3 more than Liana's.
C. Llana will have a greater profit than Jake if they each sell all 50 birdhouses.
D.
Llana and Jake will have the same profit if they each sell exactly 20 birdhouses.
E. Llana and Jake each need to sell a minimum of 11 birdhouses in order to make a profit.
(A) and (E) are the true statement.
Given,
In the question:
Jake and Liana make and sell wooden birdhouses. Jake spent $150 buying supplies. He sells each birdhouse for $15. The equation P = 12x - 120 represents the profit, P, Liana earns for selling x birdhouses. Jake and Llana each made 50 birdhouses.
To find the which statement is true?
Now, According to the question:
Jake's Profit: J = 15x - 150
Liana's Profit : P = 12x - 120
(A) when x = 0, P = -120, J = -150
then, 150 - 120 = $30
So, Jake spent $30 more than Liana
So, A is true, B is wrong.
(C) when x = 50 , J = 15 x 50 - 150 = $600
P = 12 x 50 - 120 =$480
Since, 600> 480
(D) when J = P
then, 15x - 150 = 12x = 120
3x = 30
x = 10
x = 10 not equal to 20
So, D is wrong
(E) when P> -0 , and J > 0
then, 12x -120 > 0 and 15x - 150 > 0
=> x > 10
So, the minimum is 11, E is true .
Hence, Above the solution (A) and (E) are the true statement.
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6. Solve the following equation: 28 ÷ 7 + 2 × 3 = ?
O A. 12
OB. 10
OC. 24
O D. 18
Answer:
B. 10
Step-by-step explanation:
According to BODMAS rule, the brackets have to be solved first followed by powers or roots, then Division, Multiplication, Addition, and at the end Subtraction.[tex]\rm \implies 28 \div 7 + 2 \times 3 \\ \\ \rm \implies 4 + 2 \times 3 \\ \\ \rm \implies 4 + 6 \\ \\ \rm \implies 10[/tex]
The expression on the left side of an equation is shown below.
3(x+1)+9-
k
If the equation has no solution, which expression can be written in the box on the other side of the equation?
Q3(x+4)
O 2(x+6)+x
O 4(x-3)-x
O 3(x+1)+9x
Answer:
3x + 12
Step-by-step explanation:
3(x+1)+9
= 3x + 3 + 9
= 3x + 12
Use the graph of the following function (x) to find the value.
f(1)
From the graph of the given function , the value of f(1) = -1.
As given in the question,
From the graph of the given function,
Two coordinates from the graph are as follow:
( x₁ , y₁) = (1, -1)
( x₂ , y₂ ) = ( 0, -3 )
Equation of the line representing the function is given by:
(y - y₁) /(x-x₁) = ( y₂ -y₁)/ (x₂ -x₁)
⇒(y +1)/ (x-1) = (-3 +1)/ (0-1)
⇒ (y +1)/ (x-1) = 2
⇒y +1 = 2x -2
⇒ y = 2x -3
To get the value of x we have,
y = f(x)
⇒f(x) = 2x -3
⇒f(1) = 2(1) -3
⇒f(1) = -1
Therefore, from the graph of the given function , the value of f(1) = -1.
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