By answering the presented question, we may conclude that As a result, the vertex's x-coordinate is h = 15/2, or 7.5.
what is slope intercept?In mathematics, the slope-intercept form of a linear equation is an equation of the form y = mx + b, where m is the slope of the line и b is the y-intercept, corresponding to the point on the line where it intersects the y-axis. Since it allows you to easily view the line and identify its slope and y-intercept, the slope-intercept form is a useful way to describe a line's equation. The slope of the line denotes its steepness, while the y-intercept indicates where the line crosses the y-axis.
[tex]f(x) = a(x-h)2/k\\f(x) = a(x-3) (x-3)\\(x-12)\\f(x) = a(x^2 - 15x + 36)\\f(x) = ax2 -15ax + 36a\\f(3) = a(3-3)(3-12) = 0\\f(12) = a(12-3)(12-12) = 0\\a(0)(-9) = 0\\a(9)(0) = 0\\f(x) = a(x2 - 15x + (225/4a2) - (225/4a2) - (225/4a2)) + 36a\\f(x) = a(x - (15/2a) - (225a/4) + 36a\\[/tex]
Using the quadratic function in standard form, we can read off the vertex coordinates, which are provided by (h,k) = (15/2a, -225a/4 + 36a). Given that the x-intercepts are at (3,0) and (12,0), we may suppose that the quadratic function has the following form:
f(x) = a(x-3)(x-12) (x-12)
When we plug this into the formula for the vertex's x-coordinate, we get:
h = 15/2a
h = 15/2(1) (1)
h = 15/2
As a result, the vertex's x-coordinate is h = 15/2, or 7.5.
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A tabletop in the shape of a trapezoid has an area of 6,350 square centimeters. Its longer base measures 115 centimeters, and the shorter base is 85 centimeters. What is the height?
The height of the trapezoid can be found by dividing the area (6,350 cm2) by the average of the two bases (100 cm). The height is 63.5 cm.
The formula used to find the area of a trapezoid is A = (1/2)(b1 + b2)h, where b1 and b2 are the lengths of the two bases and h is the height. We are given the area (A) and the lengths of both bases (b1 and b2). All we need to do is solve for h.
To do this, we first need to find the average of the two bases. The average of the two bases is the sum of the two bases divided by two. In this case, the longer base (b1) is 115 cm and the shorter base (b2) is 85 cm, so we can calculate the average as (115 + 85) ÷ 2 = 100 cm.
We can now substitute this value into the area formula and solve for h. A = (1/2)(100)h, so h = A ÷ (1/2)(100). Plugging in the area given (6,350 cm2), we get h = 6,350 ÷ (1/2)(100) = 63.5 cm. The height of the trapezoid is 63.5 cm.
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Jeremiah's ice cream was 23.9 ounces when he checked out at the store. He ate 11.38 ounces before leaving, how many ounces did he take home as leftovers?
Answer:
12.52 ounces
Step-by-step explanation:
Leftovers= 23.9-11.38
=12.52 ounces
line segment wx is the radius of circle x, and line segment zy is the radius of circle y. points w, x, c, y, and z are all on line segment wz. what is the area of circle c, which passes though points w and z? 81 164 324 1296
The area of circle C, which passes though points W and Z is 324π square meters.
The center of the outer circle, Point D, is where we want to calculate the area of the circle has a WZ diameter and WC and CZ radii.
That YZ = YD = 10 cm is known.
Let DC = x and CY = 10 - x
The outer circle's radius can be expressed as 8 + 8 + x or 10 + 10 - x, which we can equate to determine its value of x
8 + 8 + x = 10 + 10 - x
Simplify
16 + x = 20 - x
Subtract 16 on both side, we get
x = 4 - x
Add x on both side, we get
2x = 4
Divide by 2 on both side, we get
x = 2
As a result, the circle's radius is
= 8 + 8 + x
= 16 + x
= 16 + 2
= 18 cm
The area of circle = πr²
The area of circle = π(18)²
The area of circle = 324π
Thus, the circle's area is 324π square meters.
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The complete question is:
Line segment WX is the radius of circle X, and line segment ZY is the radius of circle Y. Points W, X, C, Y, and Z are all on line segment WZ.
What is the area of circle C, which passes though points W and Z?
A. 81
B. 164
C. 324
D. 1296
Please answer this :(
Answer:
a = 4, b = 5
Step-by-step explanation:
we need to complete the square to get it in that form.
x^2 - 8x + 21
= x^2 - 8x + 16 + 5
= (x-4)^2 + 5
a = 4, b = 5
In the 2021 football season, the Riverside Red Dragon's manager gathered the points scored by the team during the regular season games. The following data set shows the values collected by the manager.
{15, 0, 26, 15, 20, 15, 34, 11, 20, 39, 31, 20, 23, 20, 39, 5}
Which of the following stem-and-leaf plots correctly graphs the data set?
2021 Riverside Red Dragon Football Season Points
0 0 5
1 1 5
2 0 3 6
3 1 4 9
Key 1|1 = 11
2021 Riverside Red Dragon Football Season Points
1 1 5
2 0 3 6
3 1 4 9
Key 1|1 = 11
2021 Riverside Red Dragon Football Season Points
1 1 5 5 5
2 0 0 0 0 3 6
3 0 1 4 9 9
Key 1|1 = 11
2021 Riverside Red Dragon Football Season Points
0 0 5
1 1 5 5 5
2 0 0 0 0 3 6
3 1 4 9 9
Key 1|1 = 11
Not answer but helpful:
The required stem-and-leaf plot shown below that the majority of the scores fall in the 20s and 30s, with some scores in the teens and low 20s.
What is stem-and-leaf plots?
A stem-and-leaf plot is a type of data display that helps to show the distribution of a set of numerical data.
here,
For the given data set:
Stem Leaf
0 4
1 1, 3, 3
2 0, 0, 0, 6, 7
3 0, 0, 0, 7
The stem-and-leaf plot shows that the majority of the scores fall in the 20s and 30s, with some scores in the teens and low 20s. The plot makes it easier to see the distribution of the data, rather than just looking at the raw values.
the equation
-8x-y=3
8x+y=-3
have the same/different what slopes and the same/different what y-intercepts?
Answer:
same for both ; slope = -8 and y-intercept is (0, -3)
Step-by-step explanation:
First, lets write both of these in slope-intercept form!
-8x-y=3 is the same as -y = 8x+3, which is the same as y = -8x-3.
8x+y=-3 is the same as y = -8x-3.
As you can see, these equations are the same, which means that they have the same slopes and y-intercepts.
Since the equation for slope intercept form is y= mx + b where m is the slope and b is the y-intercept, this means that the slope is -8 and the y-intercept is (0, -3).
The trampoline park charges $50 to reseve the place and then $9 per person
The expression to represent the cost for any number of people is $50 + ($9 × x)
The trampoline park charges a fee of $50 to reserve the place. This means that, no matter how many people are going to visit the park, you will have to pay this flat fee of $50 to reserve the place. This fee is fixed and doesn't change with the number of people who will be visiting the park.
In addition to the reservation fee, the park charges $9 per person. So, if there is only one person visiting the park, you will have to pay $50 + $9 = $59. If there are two people visiting the park, you will have to pay $50 + ($9 × 2) = $68. If there are three people visiting the park, you will have to pay $50 + ($9 × 3) = $77, and so on.
To represent the total cost for any number of people, we can use the variable "x" to represent the number of people visiting the park. Then, we can express the total cost as:
Total Cost = Reservation Fee + (Cost per person × Number of people)
Total Cost = $50 + ($9 × x)
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The given question is incomplete, the complete question is:
The trampoline park charges for $50 to reserve the place and then $9 per person. Write an expression to represent the cost for any number of people.
cual es la respuesta
Answer:
48
Step-by-step explanation:
a² - 16
a = 8
8² - 16 = 64 - 16 = 48
So, the answer is 48
[tex]306^{2} +270^2[/tex]
#9: If the mean value test score in a math class was an 82%
and there were 25 students in the class, how much would the
mean score increase if another student scored a 100%?
After answering the provided question, we can conclude that As a result, equation if another student achieved 100%, the mean score would rise by 0.35%.
What is equation?An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x + 3" equals the number "9". The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. In the equation "x2 + 2x - 3 = 0," for example, the variable x is raised to the second power. Lines are utilized in many different areas of mathematics, such as algebra, calculus, and geometry.
You can use the following formula to compute the new mean score:
(Old Sum of Scores + New Score) / (Old Number of Scores + 1) = New Mean
Where:
Old Score Sum = Mean x Number of Scores
Number of old scores = 25 (the original number of students)
The new score is 100.
Then, compute the previous score sum:
Old Score Sum = Mean x Number of Scores = 0.82 x 25 = 20.5
New Total Scores = Old Total Scores + New Score = 20.5 + 100 = 120.5
Finally, compute the new mean score as follows:
New Mean = New Score Sum / (Old Score Sum + 1) = 120.5 / 26 = 4.6346 or 46.35% (rounded to two decimal places)
As a result, if another student achieved 100%, the mean score would rise by 0.35%.
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Please help me I really stuck
Answer:
We can find the value of Y when k = 5/4 by substituting k = 5/4 in the given expression for Y:
Y = 16 × 10^8 × k
Y = 16 × 10^8 × (5/4)
Y = 20 × 10^8
To express this in standard form, we can convert it to scientific notation:
Y = 2.0 × 10^9
Step-by-step explanation:
y^(5/4) = (16×10^(8k))^(5/4)
remember all the rules of exponents :
an exponent of an exponent : we multiply both exponents.
x^(a/b) =
[tex] \sqrt[b]{ {x}^{a} } = ({ \sqrt[b]{x} })^{a} [/tex]
and
(a×b)^c = a^c × b^c
so, with that we can do the trick here :
y^(5/4) = (16×10^(8k))^(5/4) =
= 16^(5/4) × 10^(8k × 5/4)
16^(5/4) =
[tex] \sqrt[4]{ {16}^{5} } = ( \sqrt[4]{16} )^{5} = ( \sqrt[4]{ {2}^{4} })^{5} = {2}^{5} = 32[/tex]
10^(8k × 5/4) = 10^(40k/4) = 10^(10k)
so, the result is
32 × 10^(10k)
[tex]32 \times {10}^{10k} [/tex]
The width of a rectangle measures ( 9.5 c + 6.2 d ) (9.5c+6.2d) centimeters, and its length measures ( 5.1 c − 3.4 d ) (5.1c−3.4d) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?
The expression that represents the perimeter, in centimeters, of the rectangle is 29.2c + 5.6d.
The perimeter of a rectangle is the sum of the lengths of all its sides. In this case, the rectangle has two sides with a length (9.5c+6.2d) and two sides with a length (5.1c−3.4d).
Therefore, the perimeter can be calculated by adding the lengths of all four sides:
Perimeter = (9.5c+6.2d) + (9.5c+6.2d) + (5.1c−3.4d) + (5.1c−3.4d)
Simplifying and combining like terms, we get:
Perimeter = 2(9.5c+6.2d) + 2(5.1c−3.4d)
Perimeter = 19c + 12.4d + 10.2c − 6.8d
Perimeter = 29.2c + 5.6d
Therefore, the expression that represents the perimeter, in centimeters, of the rectangle is 29.2c + 5.6d.
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13. A savings account earns 10% simple
interest. How much interest does an $800
deposit earn in four years?
14. a. Greg deposits $800 into a savings
account that earns 10% interest
compounded
annually. What is Greg's
balance after four years?
b. How much interest did Greg's
account earn?
Answer:
Greg's account earned 80$ because 0.10×800=80 80+800=880 total
The teacher has 1 apple she gives 1 apple to tommy how many apples does she have now
Number of apples that teacher has now is zero
Subtraction is a mathematical operation that involves taking away one quantity from another. It is one of the four basic arithmetic operations, along with addition, multiplication, and division. Subtraction is usually represented using the "-" symbol.
If the teacher had 1 apple and gave 1 apple to Tommy, then the total number of apples the teacher has now can be calculated using subtraction
Teacher's apples after giving one to Tommy = Teacher's apples before - Apples given to Tommy
Teacher's apples after giving one to Tommy = 1 - 1
Teacher's apples after giving one to Tommy = 0
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What is the solution to this equation?
x/5 = 25
A. x=20
B. x=30
C. x=20
D. x=125
Answer:D. x=125
Step-by-step explanation:
Answer:D
Step-by-step explanation:
125/5= 25
Draw the line of reflection that reflects Triangle ABC on Triangle A'B'C'.
Answer:
Step-by-step explanation:
The corresponding points of each triangle are equal distance from the line y = -2
the local diner offers a meal combination consisting of an appetizer, a soup, a main course, and a dessert. there are three appetizers, four soups, three main courses, and three desserts. your diet restricts you to choosing between a dessert and an appetizer. (you cannot have both.) given this restriction, how many three-course meals are possible? choices
The possible combination for three-course meals to be chosen from given the restriction is equal to 16.
The restriction that can only choose either a dessert or an appetizer,
Have two choices for the first course.
For the second course,
Have 4 choices for the soup.
For the third course,
Have 3 choices for the main course,
And since can only choose one of the remaining two categories (dessert or appetizer),
Have 2 choices for the third course.
Using the multiplication principle of counting,
The total combinations of number of three-course meals possible under these conditions by multiplying the number of choices for each course,
= Number of choices for the first course × Number of choices for the second course × Number of choices for the third course
= 2 × 4 × 2
= 16
Therefore, there are 16 possible combination for three-course meals that can be chosen.
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Work out the value of u in the equation below. Give your answer to 1 d.p.
tan 34° = 9/u
Answer:
u ≈ 13.3
Step-by-step explanation:
tan34° = [tex]\frac{9}{u}[/tex] ( multiply both sides by u )
u × tan34° = 9 ( divide both sides by tan34° )
u = [tex]\frac{9}{tan34}[/tex] ≈ 13.3 ( to 1 decimal place )
|||
Calculator
3.05 Quiz: Volumes of Cones
What is the approximate volume of a cone with a height of 12 in. and radius of 9 in.?
Use 3.14 to approximate pi, and express your final answer to the nearest hundredth.
Enter your answer as a decimal in the box.
in³
Rounding to the nearest hundredth, the approximate volume of the cone is 1017.36 cubic inches.
How do we find volume of cone ?To find the volume of a cone, we use the following formula:
V = 1/3 * π * r² * h
where V is the volume of the cone, π (pi) is a mathematical constant approximately equal to 3.14, r is the radius of the circular base of the cone, and h is the height of the cone.
To use the formula, we simply substitute the given values for r and h into the formula and simplify. Make sure that the radius and height are measured in the same units. The resulting volume will be in cubic units.
The formula for the volume of a cone is:
V = 1/3 * π * r² * h
where π is pi (approximately 3.14), r is the radius of the base of the cone, and h is the height of the cone.
Substituting the given values, we get:
V = 1/3 * 3.14 * 9² * 12
= 1/3 * 3.14 * 81 * 12
= 3.14 * 324
= 1017.36
Rounding to the nearest hundredth, the approximate volume of the cone is 1017.36 cubic inches.
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What is the height of the trapezoid? 3 units 5 units 10 units 12 units
In a trapezoid, the height is the perpendicular distance between the two parallel bases. It is usually denoted as "h".
In order to determine the height of a trapezoid, we need to know the lengths of the two parallel bases or have additional information about the trapezoid's dimensions.
The lengths of the bases of a trapezoid are crucial for calculating the height using various formulas. Without the lengths of the bases or any other relevant information, we cannot determine the height of the trapezoid.
To determine the height of a trapezoid, we need more information. The height of a trapezoid is typically defined as the perpendicular distance between the two parallel bases. In this case, we would need to know the lengths of the two parallel bases or have additional information about the trapezoid's dimensions. Without that information, we cannot determine the height of the trapezoid.
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Answer: 5 units
Step-by-step explanation:
for her phone service, jenny pays a monthly fee of $24, and she pays an additional $0.06 per minute of use. the least she has been charged in a month is .what are the possible numbers of minutes she has used her phone in a month?use for the number of minutes, and solve your inequality for $96.36.
Jenny must have used at least 1600 minutes of her phone service to incur a minimum monthly fee of $96.36. This can be calculated by solving the inequality $24 + 0.06x ≥ $96.36 where x is the number of minutes.
Rearranging this equation to 0.06x ≥ $72.36 and solving for x gives us the result x ≥ 1600.
Given that, For her phone service, Jenny pays a monthly fee of $24, and she pays an additional $0.06 per minute of use. The least she has been charged in a month is $96.36.To find the possible numbers of minutes she has used her phone in a month.
Inequality for $96.36 is(0.06m + 24) ≥ 96.36where m is the number of minutes used. In order to solve the above inequality, we will simplify it first(0.06m + 24) ≥ 96.360.06m + 24 - 24 ≥ 96.36 - 24.060.06m ≥ 72.36m ≥ 72.36/0.06m ≥ 1206So, the possible numbers of minutes she has used her phone in a month is greater than or equal to 1206 minutes. Answer: $\boxed{m≥1206}$
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What is the answer to this problem -2-(-9)-(-2)
the value of the expression -2-(-9)-(-2) is 9.
To solve the expression -2-(-9)-(-2), we can simplify it using the rules of arithmetic:
A double negative becomes a positive. So, -(-9) becomes +9.
Subtracting a negative is the same as adding the positive. So, -(-2) becomes +2.
Using these rules, we can simplify the expression as follows:
-2 - (-9) - (-2) = -2 + 9 + 2
= 9
Therefore, the value of the expression -2-(-9)-(-2) is 9.
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Determine whether the function is a polynomial function. Check by setting in standard from, identifying leading coefficient, constant, Highest degree, and type of function
The given function f(x) = 43 + 5x² - x + 7x³ is a polynomial function.
Standard form: f(x) = 7x³ + 5x² - x + 43; Leading coefficient = 7; constant = 43; degree = 3; type - cubic polynomial.
Explain about the polynomial function?In mathematics, there are many different kinds of functions. When studying functions as well as their applications, it's critical to be consistent with the names we use for various kinds of functions. A form of function is frequently described by more than one phrase.
A quadratic, cubic, quartic, and other functions involving purely non-negative integer powers of x are examples of polynomial functions. We can define a polynomial's degree and provide a generic definition for it.
Given polynomial:
f(x) = 43 + 5x² - x + 7x³
Arrange in standard form: ax³ + bx² + cx + d
Thus,
Standard form: f(x) = 7x³ + 5x² - x + 43;
Leading coefficient = 7;
constant = 43;
degree = 3;
type - cubic polynomial.
Thus, the given function f(x) = 43 + 5x² - x + 7x³ is a polynomial function.
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Sam is a school leader. She wants to decide whether makeup should be allowed in school or not? She collected random samples of 100 females regarding make up preference. Make at least two inferences based on the results. How many prefer lipstick out of 375 people?
The two inference we can make from this data is the proportion of females who prefer makeup and the significant difference in makeup preference between different groups of female.
What are the inference from the data?Based on the sample of 100 females regarding makeup preference, Sam could make the following inferences:
1. The proportion of females who prefer makeup can be estimated. Sam can calculate the proportion of females in her sample who preferred makeup and use that as an estimate of the proportion in the population. For example, if 70 out of the 100 females in the sample preferred makeup, then Sam could estimate that 70% of females in the population prefer makeup.
2. Sam could also determine if there is a significant difference in makeup preference between different groups of females. For example, she could compare the proportion of females who prefer makeup in different age groups or different ethnic groups.
To find out how many out of 375 people prefer lipstick, we need to know the proportion of people in the sample who prefer lipstick. If this information is not available, we cannot accurately determine the number of people who prefer lipstick out of 375.
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Can someone please help me!!
Answer: 240°
Step-by-step explanation:
The sum of the angles in a circle adds up to 360°, and the central angles are congruent to its arcs, so what we have is arcGFE + arcGHE = 360°, but we know arcGHE adds up to 120°. This makes our equation arcGFE + 120° = 360°, which means arcGHE = 240°
Is positive numbers closest to 0 than negative numbers that is like -3,-1,-2?
if there are 10 students and sum of their age is 150 then find the mean age of students
[tex]10[/tex] pupils mean in age from sum [tex]150[/tex] to [tex]15[/tex] years.
What does the math mean?The sum of all numbers divided by the entire number of values determines the mean (also known as the arithmetic mean, which differs from the scaling factor) of a dataset. This indicator of central tendency is usually referred to as the "average".
How is the mean determined?Just dividing the total number of values inside a data collection by the sum of all of the values yields it. Both raw data and data that have been compiled into a frequency distribution table may be utilized in the computation. Often, average is referred to as mean or mathematical mean. Mean is only a way of summarizing the sample's average.
Mean age [tex]=[/tex] (sum of ages) / (number of students)
Mean age [tex]= 150 / 10[/tex]
Mean age [tex]= 15[/tex]
Therefore, the mean age of the [tex]10[/tex] students is [tex]15[/tex] years.
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a sports magazine prints 12 issues per year, and a technology magazine prints 10 issues per year. the total number of pages in all the issues of the sports magazine for one year is 32 more than the total number of pages in all the issues of the technology magazine for one year. each issue of the sports magazine has 18 fewer pages than each issue of the technology magazine. which system of equations can be used to find s, the number of pages in each issue of the sports magazine, and t, the number of pages in each issue of the technology magazine?
The number of pages in each issue of the technology magazine is 74 pages.
The number of pages in each issue of the sports magazine is s and the number of pages in each issue of the technology magazine is t.
To solve this problem, we have to write a system of equations using the given information. We have to find s and t.
System of equations can be used to find s and t; 12s = 10t + 32 and t = s + 18
The given sports magazine prints 12 issues per year and the technology magazine prints 10 issues per year.
The total number of pages in all the issues of the sports magazine for one year is 32 more than the total number of pages in all the issues of the technology magazine for one year. That means we can write an equation based on the information given for the number of pages in all the issues of the sports magazine and the technology magazine.
12s = 10t + 32
We also know that each issue of the sports magazine has 18 fewer pages than each issue of the technology magazine. That means we can write another equation based on the information given for the number of pages in each issue of the sports magazine and the technology magazine.
t = s + 18
Now, we can solve for s and t by substituting t = s + 18 in the first equation: 12s = 10(s + 18) + 32
12s = 10s + 180 + 32
12s - 10s = 180 + 32s = 56
So, the number of pages in each issue of the sports magazine is 56 pages. And, the number of pages in each issue of the technology magazine is: t = s + 18t = 56 + 18t = 74 pages.
So, each issue of the technology magazine contains 74 pages.
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The table below shows Nicole's earnings on the job.
Time (hours)
Time (hours)
Earnings (dollars)
Earnings (dollars)
10
10
$
296
$296
22
22
$
651.20
$651.20
24
24
$
710.40
$710.40
What is Nicole’s rate of pay, in dollars per hour?
What is Nicole’s rate of pay, in dollars per hour?
Thus, pay of Nicole per hour for his job in dollars per hour is $29.6.
Explain about the unit value?The appraisal of a single item or constituent within a group is known as unit value. The concept of unit value is applicable in a variety of contexts, including building, inventory control, sales, and stock trading.
The unit value is typically the result of dividing the price or worth of a set of things by the total number of items. Doing unit value calculations is crucial since it enables experts to comprehend the price associated with producing each unit.
For the given question: Nicole's earnings
Time (hours) 10 22 24
Earnings (dollars) $296 $651.20 $710.40
10 hours ----> $296
1 hour ------> $296 / 10
1 hour ------> $29.6
Thus, pay of Nicole per hour for his job in dollars per hour is $29.6.
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Complete questions:
The table below shows Nicole's earnings on the job.
Time (hours) 10 22 24
Earnings (dollars) $296 $651.20 $710.40
What is Nicole’s rate of pay, in dollars per hour?
x = 30° is a zero for y = tan 3(x +30°). True or False with justification
Answer: true
Step-by-step explanation:
true