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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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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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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What is the value of x?
Use the triangle to answer the question.
Enter your answer in the box.
x =
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?
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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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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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 someone show me way of solving this
Step-by-step explanation:
[tex]f(x) = ln( \frac{1}{x} ) [/tex]
To find the derivative, notice we have a function 1/x inside of another function, ln(x)
We use what we call the chain rule,
It states that
derivative of a '
[tex] \frac{d}{dx} f(g(x)) = f '(g(x)) \times \: g '(x)[/tex]
Here f is ln(x)
f is 1/x
So first, we know that
[tex] \frac{d}{dx} ( ln(x) = \frac{1}{x} [/tex]
so
[tex]f'(g(x)) = \frac{1}{ \frac{1}{x} } [/tex]
We know that
[tex]g'(x) = - \frac{1}{ {x}^{2} } [/tex]
So we have
[tex]x \times - \frac{1}{ {x}^{2} } = \frac{ - 1}{x} [/tex]
Solve this please!!!
Answers:
i) [tex]\sf (x + 2)(x+ 3)[/tex]
ii) [tex]\sf \left(3x+1\right)\left(3x+2\right)\left(9x^2+9x-16\right)[/tex]
Factorize expression's:
i.
[tex]\sf (x + 1)^2 + 3(x + 1) + 2[/tex]
apply perfect square and distributive method
[tex]\sf (x^2 + 2(x)(1) + 1^2) + 3x + 3 + 2[/tex]
expand
[tex]\sf x^2 + 2x + 1 + 3x + 3 + 2[/tex]
collect like terms
[tex]\sf x^2 + 2x + 3x + 3 + 2 + 1[/tex]
add/subtract like terms
[tex]\sf x^2 + 5x + 6[/tex]
breakdown
[tex]\sf x^2 + 3x + 2x+ 6[/tex]
factor common term
[tex]\sf x(x + 3) + 2(x+ 3)[/tex]
collect into groups
[tex]\sf (x + 2)(x+ 3)[/tex]
ii.
[tex]\sf (9x^2 + 9x - 4)(9x^2 + 9x - 10) - 72[/tex]
breakdown
[tex]\sf (9x^2 + 12x - 3x - 4)(9x^2 + 15x - 6x - 10) - 72[/tex]
factor common term
[tex]\sf (3x(3x + 4) -1( 3x + 4)) ( (3x(3x + 5)- 2(3x +5) )- 72[/tex]
collect like terms
[tex]\sf (3x -1)( 3x + 4) (3x- 2)(3x +5) - 72[/tex]
expand
[tex]\sf 81x^4+162x^3-45x^2-126x-32[/tex]
factor
[tex]\sf \left(3x+1\right)\left(3x+2\right)\left(9x^2+9x-16\right)[/tex]
Answer:
[tex]\textsf{1.} \quad (x+3)(x+2)[/tex]
[tex]\textsf{2.} \quad (3x+1)(3x+2)(9x^2+9x-16)[/tex]
Step-by-step explanation:
Question 1
[tex]\textsf{Given expression}: \quad(x+1)^2+3(x+1)+2[/tex]
[tex]\textsf{Let }u=(x+1) \implies u^2+3u+2[/tex]
[tex]\textsf{To factor }\:\:u^2+3u+2:[/tex]
Rewrite the middle term as u + 2u:
[tex]\implies u^2+u+2u+2[/tex]
Factorize the first two terms and the last two terms separately:
[tex]\implies u(u+1)+2(u+1)[/tex]
Factor out the common term (u+1):
[tex]\implies (u+2)(u+1)[/tex]
Replace [tex]u[/tex] with [tex](x+1)[/tex] :
[tex]\implies (x+1+2)(x+1+1)[/tex]
Simplify:
[tex]\implies (x+3)(x+2)[/tex]
Question 2
[tex]\textsf{Given expression}: \quad (9x^2+9x-4)(9x^2+9x-10)-72[/tex]
Expand:
[tex]\implies 9x^2(9x^2+9x-10)+9x(9x^2+9x-10)-4(9x^2+9x-10)-72[/tex]
[tex]\implies 81x^4+81x^3-90x^2+81x^3+81x^2-90x-36x^2-36x+40-72[/tex]
Collect like terms:
[tex]\implies 81x^4+81x^3+81x^3-90x^2+81x^2-36x^2-90x-36x+40-72[/tex]
Combine like terms:
[tex]\implies 81x^4+162x^3-45x^2-126x-32[/tex]
Use the Factor Theorem:
If f(x) is a polynomial, and f(a) = 0, then (x – a) is a factor of f(x).
[tex]\begin{aligned}\implies f \left(-\dfrac{1}{3}\right) & =81\left(-\dfrac{1}{3}\right)^4+162\left(-\dfrac{1}{3}\right)^3-45\left(-\dfrac{1}{3}\right)^2-126\left(-\dfrac{1}{3}\right)-32\\ & = 1-6-5+42-32\\ & = 0\end{alilgned}[/tex]
Therefore (3x + 1) is a factor.
[tex]\begin{aligned}\implies f \left(-\dfrac{2}{3}\right) & =81\left(-\dfrac{2}{3}\right)^4+162\left(-\dfrac{2}{3}\right)^3-45\left(-\dfrac{2}{3}\right)^2-126\left(-\dfrac{2}{3}\right)-32\\ & = 16-48-20+84-32\\ & = 0\end{alilgned}[/tex]
Therefore (3x + 2) is a factor.
Therefore:
[tex]\implies f(x)=(3x+1)(3x+2)(ax^2+bx+c)[/tex]
Compare the coefficient of x⁴ and the constant to find a and c:
[tex]\implies 3 \cdot 3 \cdot a=81 \implies a=9[/tex]
[tex]\implies 2c=-32 \implies c=-16[/tex]
Therefore:
[tex]\implies f(x)=(3x+1)(3x+2)(9x^2+bx-16)[/tex]
Expand:
[tex]\implies f(x)=81x^4+(81+9b)x^3-(126-9b)x^2-(144-2b)x-32[/tex]
Compare the coefficient of x³ to find b:
[tex]\implies 81+9b=162 \implies b=9[/tex]
Therefore, the fully factorized expression is:
[tex]\implies (3x+1)(3x+2)(9x^2+9x-16)[/tex]
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The circumference of a circular field is 222.94 yards. What is the radius of the field? Use 3.14 for π and do not round your answer.
Answer:
35.5
Step-by-step explanation:
→ Write down the formula
2 × π × r = 222.94
→ Simplify
6.28 × r = 222.94
→ Divide both sides by 6.28
r = 35.5
Answer:
35.5 = r
Step-by-step explanation:
The circumference of a circle is given by
C = 2 * pi *r where r is the radius
222.94 = 2 * 3.14 * r
222.94 = 6.28 r
Divide each side by 6.28
222.94/6.28 = r
35.5 = r
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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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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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 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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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
Meredith is 160 cm tall. Jane’s height is 90% of Meredith’s height. How tall is jane?
Express in standard form :
42634.7
Answer:
ans is 42635 when expressed in standard form
Step-by-step explanation:
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~
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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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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Pick the correct answer.
Help me please thanks so much
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
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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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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Angle G is a circumscribed angle of circle E. Major arc FD measures 280°.
Circle E is shown. Line segments F E and D E are radii. A line is drawn to connect points F and D. Tangents F G and D G intersect at point G outside of the circle. Major arc F D measures 280 degrees.
What is the measure of angle GFD?
40°
50°
80°
90
The measure of angle GFD of the circumscribed circle is; A: 40°
How to find the measure of angle of a circumscribed circle?From the figure, we can apply the arc angles summation formula to get;
Major angle ∠FED + Minor angle ∠FED = 360°
We are given that Major arc FD measures 280°. Thus;
280° + Minor angle ∠FED = 360°
Minor angle ∠FED = 360° - 280°
Minor angle ∠FED = 80°
Also, we know that;
∠FED + ∠FGD = 180°
Thus, putting ∠FED = 80° gives us;
80° + ∠FGD = 180°
Subtract 80° from both sides using subtraction property of equality to get;
∠FGD = 180° - 80°
∠FGD = 100°
Now, GF and GD are the tangents to the circle from the same point G. Thus, we can say that;
GD = GF
Therefore,
∠FDG = ∠GFD = x
(This is because ∠FDG and ∠GFD are the angles opposite to equal sides.
In triangle FGD, we have sum of interior angles = 180°
Therefore, we have the expression;
∠FDG + ∠FGD + ∠GFD = 180° (due to the fact that sum of angles in a triangle is equal to 180°)
x + 100° + x = 180°
2x = 180° - 100°
2x = 80°
x = 40°
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Answer:
40
Step-by-step explanation:
I did a thing and it worked
convert this hight 5,2 into cm
Answer:
5.2 Inch to cm = 13.208 cm
5.2 feet to cm = 158.496 cm
Step-by-step explanation:
Inch: 1 inch = 2.54 cm, so multiply 2.54 * 5.2. We get the answer: 13.208 cm
Feet: 1 foot = 30.48 cm, so multiply 30.48 * 5.2. We get the answer: 158.496 cm
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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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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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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