Solution :
The amount invested by Yvonne = $ 4,000
Time of investment = 3 years
The simple interest earned by Yvonne in 3 years = $ 960
a). Therefore, the amount Yvonne earned by the end of three years is
= principal + interest earned
= 4,000 + 960
= $ 4,960
b). The formula for simple interest(S.I.) is given by :
[tex]$S.I. =\frac{P.T.R}{100}$[/tex]
or [tex]$R = \frac{SI \times 100}{P.T}$[/tex]
[tex]$ = \frac{960 \times 100}{4000 \times 3}$[/tex]
= 8%
c). Now if the interest rate is 1% greater, i.e. R = (8+1) = 9%
∴ [tex]$SI =\frac{P.T.R}{100}$[/tex]
[tex]$SI =\frac{4000 \times 3 \times 9}{100}$[/tex]
SI = $1,080
Therefore, the amount at the end of 3 years with 9% rate of interest will be
= 4000 + 1080
= $ 5080
Thus, Yvonne will have 5080 - 4960 = $ 120 money more in her account if the rate of interest was 1% greater.
A box of jerseys for a pick-up game of basketball contains 8 extra-large jerseys, 6 large jerseys, and 4 medium jerseys. If you are first to the box and grab 2 jerseys, what is the probability that you randomly grab 2 extra-large jerseys
The probability that a randomly grab 2 extra large jerseys is 18.3%.
Given that a box of jerseys for a pick-up game of basketball contains 8 extra-large jerseys, 6 large jerseys, and 4 medium jerseys.
The number of jerseys in the box is 8+6+4=18
To find the probability of picking 2-extra large jerseys by finding the probability of 1 extra large and probability of 2 extra large.
The probability of picking 1 extra large jersey is
P₁=8/18
P₁=4/9
The probability of picking 2 extra large jerseys is remaining jerseys
P₂=7/17
The total probability of getting 2 extra large jerseys is
P=P₁×P₂
P=(4/9)×(7/17)
P=28/153
P=0.183
P=18.3%
Hence, the probability that randomly grab 2 extra-large jerseys when basketball contains 8 extra-large jerseys, 6 large jerseys, and 4 medium jerseys is 18.3%.
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In a binomial experiment, the probability of success is. 6. What is the probability of two successes in seven trials?.
The probability of two successes in seven trials is 0.0774144.
We can find the probability as shown below:The probability can be found using the binomial formula.
The probability of success is given as 0.6.
Therefore, the probability of failure is 0.4.
We have to find the probability of two successes in seven trials.
It is given by:
[tex]P = nC_x p^{n} q^{n-x}\\=7C_{2} (0.6)^{2} (0.4)^{7-2} \\=7C_{2} (0.6)^{2} (0.4)^{5} \\=\frac{(7)(6)}{(1)(2)} (0.36)(0.01024)\\=0.0774144[/tex]
The probability of two successes in seven trials is found to be 0.0774144.
Therefore, we have found that the probability of two successes in seven trials is 0.0774144.
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slope:
y-intercept:
HELP
Answer:
Slope: 1
Y-intercept: -1
Step-by-step explanation:
The line touches the y-axis at -1, and using rise over run for the slope, it would be 1, since you go up 1 unit and move to the right 1 unit. 1/1 which is our rise/run would be 1 and that would make the slope 1.
I hope it helps! Have a great day!
bren~
Simplify: x^3-1/x^2-1
Answer:(x-1)(x^2+x+1) / (x+1)(x-1)
Step-by-step explanation:
For x^3-「1」→ 1=1^3
For x^2-「1」→ 1=1^2. this way of thinking might help you understand better:)
You can just use a formula of factorizationヾ ^_^♪
Charlotte is solving the following equation for X (x+3)^2-10=2 her first steps are given below (x+3)^2=12 x+3= + square root 12
The values of the x in the given equation are x = 6.46 and x = -0.46
Solving an equationFrom the question, we are to solve the equation for x
The given equation is
(x+3)² -10 = 2
First, add 10 to both sides of the equation
(x+3)² -10 +10 = 2 +10
(x+3)² = 12
Now, take the square root of both sides to get
x + 3 = ±√12
∴ x = 3 ± √12
x = 3+√12 OR 3-√12
x = 3 + 3.46 OR 3 - 3.46
x = 6.46 OR -0.46
Hence, the values of the x in the given equation are x = 6.46 and x = -0.46
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Please help em fast I really need help
lf ƒ(x) = 2(x + 1)² and g(x) = 3x- 2 determine f[g(2)]
Answer:
f(g(2)) = 50
Step-by-step explanation:
evaluate g(2) then substitute the result obtained into f(x)
g(2) = 3(2) - 2 = 6 - 2 = 4 , then
f(4) = 2(4 + 1)² = 2(5)² = 2(25) = 50
Answer:
f[g(2)] = 50
Step-by-step explanation:
Given functions:
[tex]f(x)=2(x+1)^2[/tex]
[tex]g(x)=3x-2[/tex]
We are asked to determine f[g(2)], which is known as a composite function. When solving composite functions, you always work inside out.
Step 1: Find the value of g(2) by substituting 2 for x in function g(x).
[tex]\implies g(2)=3(2)-2[/tex]
[tex]\\\implies g(2)=6-2\Rightarrow g(2)=\boxed{4}[/tex]
Step 2: Substitute the found value into the composite function.
[tex]\\\implies f[g(2)]= 2(4+1)^2[/tex]
[tex]\implies f[g(2)] = 2(5)^2 \Rightarrow 2(25) \Rightarrow \boxed{50}[/tex]
Hence, the value of the composite function f[g(2)] is 50.
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8. A company has 350 workers. The
president of the company wants to know
what percent increase in employment
would be necessary for the number of
workers to be greater than 375.
Help!
The percent increase in employment would be necessary for the number of workers to be greater than 375 is 25%
How to determine the rates?The given parameters are:
Initial = 350
Final = 375
The rate is calculated as:
Rate = Final/Initial - 1
So, we have:
Rate = 375/300 - 1
Evaluate
Rate = 1.25 - 1
This gives
Rate = 0.25
Express as percentage
Rate = 25%
Hence, the percent increase in employment would be necessary for the number of workers to be greater than 375 is 25%
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If the range for a set of number is 8 and the maximum number is 2 what is the answer/
The range is -6.
What is a range?The range of a collection of data in statistics is the difference between the largest and lowest values. The difference here is that the range of a collection of data is determined by subtracting the sample maximum and minimum. In descriptive statistics, however, the concept of the range has a more nuanced meaning.To find the answer, calculate as follows:
Range = Maximum - Minimum
Range = 8 and Maximum = 2
Let, the minimum be x.
Now, substitute values in the formula.
8 = 2 - x
x = 2 - 8
x = -6
Therefore, the answer is -6.
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Write as an equation: The sum of -7 and a is equal to 37.
A. −7+a=37
B. −7+a=−37
C. −7−a=−37
D. −7−a=37
forty-seven marbles are shared between some children. each child receives six marbles and there are five marbles left over. how many children share the marbles?
The total number of children can be calculated using linear equation in one variable. The marbles are shared among 7children.
Solution
Total number of marbles = 47
The number of marbles received by each child = 6
Let the number of children be x
Then according to the question'
Total number of marbles received by all children + 5 = Total number of marbles
6x + 5 = 47
6x = 47- 5
6x = 42
x = 7
now, the number of children is 7.
What is linear equation in one variable?An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation.A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, while B is a constant. A linear equation with two variables has the conventional form Ax + By = C.Here, the variables x and y, the coefficients A and B, and the constant C are all present.A linear equation's graph will always be a straight line.One-variable linear equations are fairly simple to solve. To determine the value of the unknown variable, the variables are divided and placed on one side of the equation, and the constants are combined and placed on the other side.Know more about linear equation https://brainly.com/question/12974594
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Tommy has created a new tomato soup recipe. Before he cans and sells his soup, he must gather information about how much soup cans of different sizes will hold.
The better way to calculate the amount of substance is Volume.
According to the statement
we have to find the all information about the soup cans.
So we know that if we put a liquid in the container then in that case surface area is not important but a volume is more important for this purpose.
So, That's why The weight in the case of soup is not important when evaluating a package to be able to sell the product. A container is usually specified according to its volume, especially those containing liquids. Because the weight can vary concerning the concentration of the product, the best way to calculate the amount of substance to be packaged is the volume.
So, The better way to calculate the amount of substance is Volume.
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Scarlett made a profit of $250.00 with her mobile car wash company. she charged $75.00 per car wash and received $35.00 in tips, but also had to pay $5.00 in cleaning supplies per car. write an equation to represent this situation
The equation representing the given situation is, 250 = 70x + 35, where x is the number of cars washed by the company.
In the question, we are given that Scarlett made a profit of $250.00 with her mobile car wash company. She charged $75.00 per car wash and received $35.00 in tips, but also had to pay $5.00 in cleaning supplies per car.
We are asked to represent the situation with an equation.
We assume the number of cars washed by the company to be x.
Charge for washing 1 car = $75.00.
Cost for cleaning supplies for 1 car = $5.00.
Thus the profit on the wash of 1 car = $75.00 - $5.00 = $70.00.
The total profit received by the company, on washing x number of cars = $70x.
The tips received = $35.00.
Thus, the total profit of the company = $(70x + 35).
But, the total profit is given to be $250.00.
Thus, we get an equation, 250 = 70x + 35.
Thus, the equation representing the given situation is, 250 = 70x + 35, where x is the number of cars washed by the company.
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What are the x-intercepts of the function y = 22 -x - 120? Check all that apply. O (-120. 0) O (-11.466, 0) O (-10.466, 0) O (0, -120) (10.466, 0) O (11.466, 0)
The x-intercepts of the function y = 2x^2 -x - 120 are (-7.5, 0) and (8, 0)
How to determine the x-intercept?The function is given as:
y = 2x^2 - x - 120
Set the function to 0
2x^2 - x - 120 = 0
Factor out 2
2(x^2 - 0.5x - 60) = 0
Divide by 2
x^2 - 0.5x - 60 = 0
Expand the function
x^2 + 7.5x - 8x - 60 = 0
Factorize the function
(x + 7.5)(x - 8) = 0
Split
x + 7.5 = 0 and x - 8 = 0
Solve for x
x = -7.5 and x = 8
Hence, the x-intercepts of the function y = 2x^2 -x - 120 are (-7.5, 0) and (8, 0)
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What is 3x^3+5x^2-11x+3/x+3
The solution to the expression (3x³ + 5x² - 11x + 3)/(x + 3) is (x - 1/3)(x - 1)
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given the expression:
(3x³ + 5x² - 11x + 3)/(x + 3)
= (x + 3)(x - 1/3)(x - 1) / (x + 3)
= (x - 1/3)(x - 1)
The solution to the expression (3x³ + 5x² - 11x + 3)/(x + 3) is (x - 1/3)(x - 1)
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Mr.Nguyen saves $120 of his income of 800.00 what percent of his income does Mr.Nguyen save?
Nguyen saves 15% of his income
How to determine the percentage?The given parameters are:
Savings = $120
Income = $800
The percentage saved is calculated as:
Percentage = Savings/Income * 100%
This gives
Percentage = 120/800 * 100%
Evaluate
Percentage = 15%
Hence, Nguyen saves 15% of his income
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[tex]x^{8}+x^{4}+1[/tex]
You did not provide directions. What do you want us to do with your 8th degree polynomial?
True or false: f(x) is a function.
A. True
Step by step explanation:
1. if we where given a graph and told to determine whether it's a function or not, we would have used a VERTICAL LINE TEST.
2. In this case we have points, and for every x value we have one corresponding y value which makes it a function that is a ONE-TO- ONE FUNCTION
CAN ANYONE HELP ME WITH QUESTION 7
Answer:
x = 4.
Step-by-step explanation:
Each angle in an equilateral triangle is 60 degrees, so we have:
10x + 20 = 60
10x = 40
x = 4.
Answer:
X = 4
Step-by-step explanation:
The angles of a triangle add up to 180 degrees and this is an equilateral triangle which means that all the angles are the same. which means you set up the equation:
10x + 20 + 10x + 20 + 10x + 20 = 180
Simplify: 30x + 60 = 180
- 60 - 60
You have : 30x = 120
(Divide by 30)
You end up with: X = 4
Explain how you could use the dimensions of a reduced rectangle and one given measurement of an original rectangle to find a missing measure?
Using the dimensions of a reduced rectangle and one given measurement of an original rectangle:
Set up a proportion using the corresponding partsSolve the proportion to find the missing measureWhat is Reduction?Reduction is a type of dilation that reduces the size of an original figure to form a new figure that is similar to the original. The corresponding lengths of both figures are therefore proportional.
Assuming the dimensions of the reduced rectangle are 10 cm by 4 cm, and the length of the original rectangle is given as 8 cm, to find the missing measure (x), do the following:
Set up a proportion using the corresponding parts
10/8 = 4/x
Solve the proportion using cross products to find x:
10x = (8)(4)
10x = 32
x = 32/10
x = 3.2 cm
The missing length is 3.2 cm.
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Answer:
Using the given measurements of both figures, set up a proportion that has the corresponding parts in the same position. Then solve the proportion using cross products to find the value for the unknown.
Step-by-step explanation:
Set up a proportionCorresponding sides are in the same place in the proportion.Use cross products in the proportion to solve for the unknown.The graph of Y= sin x--
= sin(x-3);
3%
O
units to the left
○ 3 units to the right
3x
2 units up
Зл
2
2 is the graph of the y = sin(x) shifted in which direction?
units down
The graph of y=sin(x-3π/2) is the graph of the y =sinx shifted right by 3π/2 units.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
If we have a parent function y = Sin(x), the function
y = Sin(x-b) would be the parent shifted b units right
y = Sin (x+b) would be the parent shifted b units left
The function given is y=sin(x-3π/2)
So from the rules, we can clearly say that it is parent function shifted right by 3π/2 units.
Hence, the graph of y=sin(x-3π/2) is the graph of the y =sinx shifted right by 3π/2 units.
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There are 15 players on a volleyball team. Only 6 players can be on the court for a game. How many different groups of players of 6 players can the coach make, if the position does not matter?
There are 5005 different groups
How to determine the number of groups?The given parameters are:
Players, n = 15
Selected, r = 6
The number of groups is then calculated as:
[tex]Group = ^{n}C_r[/tex]
This gives
[tex]Group = ^{15}C_6[/tex]
Apply the combination formula
[tex]Group = \frac{15!}{9!6!}[/tex]
Evaluate the expression
Group = 5005
Hence, there are 5005 different groups
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A soccer team played 25 games last season. they won 16 games, lost 5 games, and tied the rest.
[tex]\frac{25}{4}[/tex] of the games was a tie.
What is a fraction?A fraction is a portion of a whole or, more broadly, any number of equal parts. In everyday English, a fraction represents the number of pieces of a specific size, such as one-half, eight-fifths, or three-quarters.To find what fraction of the games was a tie:
Total game played = 25
Win 16 lose 5 total = 21
So, tie matches = 4
The fraction will be 25/4.
Therefore, [tex]\frac{25}{4}[/tex] of the game was a tie.
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Complete question:
A soccer team played 25 games last season they won 16 games, lost 5 games, and tied the rest what fraction of the games was a tie?
Harriet earned $4,334 for the month. state and local taxes are 6.3% in her state and locality. how much state and local taxes were withheld from her check?
Total tax from state and local taxes were withheld from her check:
= $273.04
What is Percentage ?
A % is a number or ratio that, in mathematics, can be expressed as a fraction of 100. If we need to determine a percentage of a number, multiply it by 100 and divide it by the total. So, a part per hundred is what the percentage refers to. Percent signifies for every 100. The sign "percent" is used to denote it.
Solution:
Harriet earned for the month = $4334
state and local taxes are = 6.3%
= [tex]\frac{4334}{100} *6.3%[/tex]
=$273.04
Total tax from state and local taxes were withheld from her check:
= $273.04
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Surface area=
Help me please thanks
The surface area of the sphere is 324π square units
Calculating the surface areaFrom the question, we are to calculate the surface area of the sphere
The surface area of a sphere can be calculated by using the formula
[tex]Surface \ area = 4 \pi r^{2}[/tex]
Where r is the radius of the sphere
In the given diagram,
r = 9
Thus,
Surface area = 4π × 9²
Surface area = 4π × 81
Surface area = 324π square units
Hence, the surface area of the sphere is 324π square units
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The typical pole for pole vaulting is 17 feet long. How fast would a pole vaulter have to run (in the direction of the pole) in order for a spectator sitting in the stands to see it 15 feet long
A pole vaulter have to run at 18m/s speed.
According to the statement
The typical pole for pole vaulting is 17 feet long
we use the formula
1/2 m(v)^2 = mgh
Now rearrange the terms
(v)^2 = 2gh
here g = 10 and h = 15 then
substitute the values
(v)^2 = 2*10*15
v = 17.32
So, A pole vaulter have to run at 18m/s speed.
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If 111 is divided into pieces that are each \dfrac19
9
1
start fraction, 1, divided by, 9, end fraction of a whole, how many pieces are there?
1\div\dfrac19=1÷
9
1
=1, divided by, start fraction, 1, divided by, 9, end fraction, equals
The results of dividing 1 into pieces that are each 1/9 of a whole is 9
Division of fraction1 ÷ 1/9
multiply by the reciprocal of 1/9 which is 9/11 ÷ 1/9
= 1 × 9/1
= (1 × 9) / (1 × 1)
= 9/1
= 9
Complete question:
If 1 is divided into pieces that are each 1/9 of a whole, how many pieces are there
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500 +126 200 + 129 129+100 123+34 123+123 1000+12 2013+1200 123+120 100+304 123+103 104+1200
3,471,738 this is the answer
What is the solution set to the following equation?
x4+2x−48=0
Select one:
a. { ±2i2–√,±6–√ }
b. { ±i6–√,±2–√ }
c. { ±2i2–√,±3 }
d. { ±i3–√,±22–√ }
The solution set of the equation x^2 + 2x - 48 = 0 is x = -1 ± 7
How to determine the solution set of the equation?The equation is given as:
x^2 + 2x - 48 = 0
A quadratic equation is represented as:
ax^2 + bx + c = 0
By comparing both equations, we have
a = 1, b = 2 and c = -48
The solution of the quadratic equation is then calculated using
x = (-b ± √(b^2 - 4ac))/2a
Substitute values for a, b and c in the above equation
x = (-2 ± √(2^2 - 4 * 1 * -48))/2 * 1
This gives
x = (-2 ± √196)/2
Evaluate the square root of 196
x = (-2 ± 14)/2
Divide through by 2
x = -1 ± 7
Hence, the solution set of the equation x^2 + 2x - 48 = 0 is x = -1 ± 7
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The director of research and development is testing a new drug. She wants to know if there is evidence at the 0.01 level that the drug stays in the system for more than 377 minutes. After performing a hypothesis test, she decides to reject the null hypothesis. What is the conclusion
Here null hypothesis is rejected in this problem.
According to the statement
We have a given that the evidence at alpha level is 0.02, ANd the sample size n is 67. And mean time equal to 330 minutes and the variance that is the sigma square is equal to 529 point.
And We have to make the decision to reject or feel fail to reject the null hypothesis to solve this problem.
Firstly we solve alternative and null hypothesis
So, the null hypothesis h naught will be that mu is less than equal to 327 point and alternative hypothesis ha will be.
That mu is greater than 327 point now. This alternative hypothesis is claimed.
Next we will find the value of s which is given by sigma divided by under root n.
So, s = 67/ (529)^1/2
s = 2.8099.
Now we find the value of Z
So, Z = 327 - 330 / 2.8099
Z = 1.0677
Now the critical value of z is 2.05
Critical, we can say fail to reject the null hypothesis, and this is the result from the null hypothesis test.
With this test, we can conclude that the the data do not support that. There is evidence at 0.02 level that the drug stays in the system for more than 327 minutes. So this is the conclusion for the test for the hypothesis test and the answer to the problem.
So, Here null hypothesis is rejected in this problem.
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what is the result of 6 divided by 15
Answer:
If you have 6 chocolate and you have to divide that into 15 people than the answer will be 2 upon 5 or 0.4 for each.