Kersha has two jobs. During the day she works as an office clerk, and in the evening she works as a cashier. Her office job pays her $12.00 per hour. Her cashier job pays her $8.25 per hour. In one week, Kersha worked 55 hours. She earned a total of $585.
How many hours did Kersha work in each job?
a.) Office clerk: 35 hours; cashier: 20 hours
b.) Office clerk: 31 hours; cashier: 24 hours
c.) Office clerk: 20 hours; cashier: 35 hours
d.) Office clerk: 28 hours; cashier: 27 hours
A trial has markers every 1/8 mile. Jody starts at the 2 1/4-mile marker, hikes to the 4 3/8-mile marker, and then hikes back to the 1 1/2 mile marker. Did Jody hike more than 4 miles? Explain.
Which expression is equivalent to ? m-4/m+4 / (m+2)
Answer:
[tex]\frac{m - 4}{m + 4} / (m + 2)[/tex] is equivalent to [tex]\frac{(m - 4)}{(m + 4)(m + 2)}[/tex]
Step-by-step explanation:
Given Parameters;
(m-4)/(m+4) and (m+2)
Required:
To divide and write out the equivalent expression.
Two or more expressions are said to equivalent if and only if they give the same result.
Solving (m-4)/(m+4) divided by (m+2)
We have
[tex]\frac{m - 4}{m + 4}[/tex] divided by [tex]m + 2[/tex]
[tex]= \frac{m - 4}{m + 4} / (m + 2)[/tex]
Convert division to multiplication
[tex]= \frac{m - 4}{m + 4} *\frac{1}{(m + 2)}[/tex]
= [tex]\frac{(m - 4) * 1}{(m + 4) * (m + 2)}[/tex]
[tex]= \frac{(m - 4)}{(m + 4)(m + 2)}[/tex]
We can't simplify any further;
Hence, [tex]\frac{m - 4}{m + 4} / (m + 2)[/tex] is equivalent to [tex]\frac{(m - 4)}{(m + 4)(m + 2)}[/tex]
To check if this is true
Let m = 1
[tex]\frac{m - 4}{m + 4} / (m + 2)[/tex] becomes
[tex]\frac{1 - 4}{1 + 4} / (1 + 2)[/tex]
[tex]\frac{-3}{5} / (3)[/tex]
[tex]\frac{-3}{5} * \frac{1}{3}[/tex]
[tex]\frac{-1}{5}[/tex]
And
[tex]\frac{(m - 4)}{(m + 4)(m + 2)}[/tex] becomes
[tex]\frac{(1 - 4)}{(1 + 4)(1 + 2)}[/tex]
[tex]\frac{(-3)}{(5)(3)}[/tex]
[tex]\frac{-1}{5}[/tex]
Hence, [tex]\frac{m - 4}{m + 4} / (m + 2)[/tex] is equivalent to [tex]\frac{(m - 4)}{(m + 4)(m + 2)}[/tex]
The equations for two lines in the coordinate plane are 2dx - y = -4 and 4x - y = -6, where d represents an unknown value. What value(s) of d would make these lines perpendicular?
The value of d that makes the lines 2dx - y = -4 and 4x - y = -6 perpendicular is -1/8, as this value makes the product of their slopes equal to -1.
Explanation:To determine which value(s) of d would make the two lines perpendicular, we have to evaluate the slopes of the two lines and set their product to be -1, since perpendicular lines have slopes that are negative reciprocals of each other. Rearranging the first equation, 2dx - y = -4, we get y = 2dx + 4, which has a slope of 2d. For the second equation, 4x - y = -6, rearranging gives y = 4x + 6, with a slope of 4.
The product of the slopes of two perpendicular lines should be -1, so:
(2d) * 4 = -1
Solving for d: d = -1/8.
Thus, when the value of d is -1/8, the two lines are perpendicular.
Find 1/4+13/20
. Write your answer as a fraction in simplest form.
A fraction is a way to describe a part of a whole. The sum of the two of the given fractions is equal to 9/10.
What is a Fraction?A fraction is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25.
The given fractions can be added as shown below.
(1/4) + (13/20)
Taking the LCM of the denominator which is equal to 20,
= (1×5 / 4×5) + (13/20)
= (5/20) + (13/20)
= (5 + 13)/20
= 18/20
Divide both the numerator and the denominator by 2,
= 9/10
Hence, the sum of the two of the given fractions is equal to 9/10.
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In professor shannon's economics class there are 12 male students. females represent 60% of the class total. how many students does professor shannon have in his economics class?
Answer:
There are total 30 students in the class.
Step-by-step explanation:
Let the total number of students in class = x
Number of males in the class = 12
Number of females in the class = 60% of Total students = 60% of x = 0.6x
So, we get that,
Number of males + Number of females = Total students
i.e. [tex]12+0.6x=x[/tex]
i.e. [tex]12=x-0.6x[/tex]
i.e. [tex]12=0.4x[/tex]
i.e. [tex]x=\frac{12}{0.4}[/tex]
i.e. x = 30
Thus, there are total 30 students in the class.
what is 31 billion in scientific notation
we know that
[tex] 1 billion=1,000,000,000 [/tex]
In scientific notation
[tex] 1,000,000,000=1*10^{9} [/tex]
To find the value of [tex] 31 billion [/tex]
Multiply the value of one billion for [tex] 31 [/tex]
so
[tex] 31*1*10^{9} =31*10^{9}\\ =3.1*10^{10} [/tex]
therefore
the answer is
[tex] 3.1*10^{10} [/tex]
The scientific notation of [tex]31 \text{billion}[/tex] is [tex]\boxed{3.1 \times \left( {{{10}^{10}}} \right)}[/tex].
Further explanation:
Scientific notation is also called as the standard form of writing a number.
The number has two parts in the scientific notation.
First part is digits or digit with decimal and the second part is 10 to the power.
If the number is greater than 10, move the decimal point to the left.
If the number is less than 10, move the decimal point to the right.
Calculation:
One billion is equal to [tex]1000000000[/tex].
In scientific notation one million can be expressed as,
[tex]\boxed{{\text{1}}\,{\text{billion}} = {10^9}}[/tex]
Thirty one billion is equal to [tex]31000000000[/tex].
Now find the scientific notation SN of 31 billion.
[tex]\begin{aligned}\text{SN} &= 31000000000 \\&= 31 \times \left( {{{10}^9}} \right) \\&= 3.1 \times \left( {{{10}^{10}}} \right) \\ \end{aligned}[/tex]
The first part of the scientific notation is [tex]\boxed{3.1}[/tex].
The second part of the scientific notation is [tex]\boxed{{10^{10}}}[/tex].
Hence, the scientific notation of [tex]31 \text{billion}[/tex] is [tex]\boxed{3.1 \times \left( {{{10}^{10}}} \right)}[/tex].
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Answer details:
Grade: Middle School
Subject: Mathematics
Chapter: Scientific notation
Keywords: scientific notation, one billion, thirty one billion, million, standard form, first part of scientific notation, second part of scientific notation, power.
Janet earns $300 per week plus a commission of 10% on all sales that she makes. Write a formula for E, Janet's weekly earnings, in term of s, her sales for the week. Then solve your firmula for s
Worth 37 points answer asap
this is a college question
a farmer is given 500 ft of fencing. He will be constructing a rectangular coral to keep pigs and sheep, however he wants to keep them separate so there will be a wall of fence in the middle of the coral as well (the dividing wall will be parallel to 2 of the sides). What are the dimensions of the coral that will maximize the area, and what is the area?
hi therrre you are an awesome person
What is the zero r(x)=3/8x-16 ?
The price of an item selling at 150% of its $63 value is
Answer:
94.50
Step-by-step explanation:
i used a calculator
Sam’s parents agreed to pay 25 percent of the cost of a new bike if Sam paid the rest.If Sam’s parents paid $65, what was the price of Sam’s new bike?
Which doubles fact would you use to find 6+7
A. 2+2=4
B. 4+4=8
C. 6+6=12
D. 8+8=16
A line passes through (2, −1) and (4, 5).
Which answer is the equation of the line?
(choices in picture)
Answer:
Yep the answer is −3x+y=−7
Step-by-step explanation:
What is the side length of a cube that has a volume of 24 cm 3?
if 5 doses of medicine weigh 29.925 grams, how much would 1 dose weigh?
2 divided by 880 = ?
The weights of steers in a herd are distributed normally. the standard deviation is 200 lbs and the mean steer weight is 1300 lbs. find the probability that the weight of a randomly selected steer is between 1000 and 1437 lbs. round your answer to four decimal places.
If 9:7 is the ratio, there are here 116 more boys than girls how many total students are there
The amount of cholesterol in a person's body produced by their liver and other cells is proposed to be normally distributed with mean 75% and standard deviation 0.5%. the probability that a person produces more than 76.7% of the cholesterol in their body is
After standardizing the given value using a Z-score, it is found that the probability of a person producing more than 76.7% of the cholesterol in their body is essentially zero.
Explanation:The question is asking for the probability that a person produces more than 76.7% of the cholesterol in their body, given this production is normally distributed with a mean of 75% and a standard deviation of 0.5%. To calculate this, we can utilize Z-score which standardizes the deviation of a value from the mean, considering the standard deviation.
The Z-score for the value 76.7% is calculated as follows: (76.7 - 75) / 0.5 = 3.4.
Using the standard normal distribution, the probability of a Z-score being above 3.4 is extremely low, it's practically zero. Therefore, the probability that a person produces more than 76.7% of the cholesterol in their body is essentially zero.
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Jason draws a line in the sand at the beach the line is 7/8 feet long he wants to divide the line into sections that are 1 8 feet long how many sections with a line be divided into?
When certain kinds of chemicals are combined, the rate at which the new compound is formed is modeled by the autonomous differential equation dX/dt = k(a-X)(B-X) where k > 0 is a constant of proportionality and B > a > 0. Here X(t) denotes the number of grams of the new compound formed in time t. (a) Use a phase portrait of the differential equation to predict the behavior of X(t) as t -> infinity. (b) Consider the case when a = B. Use a phase portrait of the differential equation to predict the behavior of X(t) as t -> infinity when X(0) < a. When X(0) > a. (c) Verify that an explicit solution of the DE in the case when k=1 and a=B is X(t)=a-1/(t+c). Find a solution that satisfies X(0) = a/2. Then find a solution that satisfies X(0)=2a. Graph these two solutions. Does the behavior of the solutions as t->infinity agree with your answers to part (b)?
To predict the behavior of the autonomous differential equation as t -> infinity, analyze the phase portrait of the system. The behavior of X(t) as t approaches infinity depends on the initial conditions. Verify the explicit solution of the DE when k=1 and a=B. Graph the solutions and observe their behavior as t-> infinity.
Explanation:To predict the behavior of the autonomous differential equation dX/dt = k(a-X)(B-X) as t -> infinity, we can analyze the phase portrait of the system. The phase portrait will show the equilibrium points and the direction of the solutions as time increases. In this case, there will be two equilibrium points, one at X = a and one at X = B, assuming a < B. The behavior of X(t) as t approaches infinity depends on the initial conditions. If X(0) < a, the solution will approach X = a, and if X(0) > a, the solution will approach X = B.
To verify the explicit solution of the differential equation when k=1 and a=B, we substitute these values into the equation: X(t) = a - 1/(t+c). For the solution that satisfies X(0) = a/2, we substitute t=0 and X(0) = a/2 into the equation and solve for c. Similarly, for the solution that satisfies X(0) = 2a, we substitute t=0 and X(0) = 2a into the equation and solve for c. We can then graph these two solutions and observe that as t approaches infinity, X(t) approaches a for both solutions, which confirms our analysis from part (b).
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Find the equation of a cosine curve that is obtained by shifting the graph of y=cos(x) to the left 5 units and upward 9 units and vertically compressed by a factor of 4 and vertically flipped
We want to find the equation of a cosine function after we apply some given transformations to it.
The equation of the resulting cosine curve is:
g(x) = -(1/4)*cos(x + 5) - 9/4.
Let's see how we got that equation:
First, we need to define all the transformations that we will be using:
Vertical shift:
For a given function f(x) a vertical shift of N units is written as:
g(x) = f(x) + N.
If N is positive the shift is upwards.IF N is negative the shift is downwards.Horizontal shift:
For a given function f(x) a horizontal shift is written as:
g(x) = f(x + N).
If N is positive the shift is towards the left.If N is negative the shift is towards the right.Vertical compression.
For a function f(x) a vertical compression by a factor k is written as:
g(x) = (1/k)*f(x).
Vertical flip (or vertical reflection).
For a general function f(x) a vertical reflection is written as:
g(x) = -f(x).
So we start with:
f(x) = cos(x).
First we shift it to the left 5 units, so we get:
g(x) = f(x + 5)
Then we shift it up 9 units, then we get:
g(x) = f(x + 5) + 9
Then we compress it vertically by a factor of 4:
g(x) = (1/4)*(f(x + 5) + 9)
Then we flip it vertically:
g(x) = -(1/4)*(f(x + 5) + 9)
Replacing f by the cosine function we get:
g(x) = -(1/4)*( cos(x + 5) + 9)
g(x) = -(1/4)*cos(x + 5) - 9/4.
This is the equation of the resulting cosine curve.
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Ingrid collected 6 cans of food and 18 boxes of food for the food bank. Which describes the relationship between cans of food and boxes of food?
The relationship between the cans of food and boxes of food that Ingrid collected can be determined by the mathematical equations involving addition/subtraction and multiplication/division.
For addition/subtraction:
D = x – y
Where D is difference, x is the number of cans of food, and y is the boxes. Substituting the known values,
D = 6 – 8 = -2
For multiplication/division:
R = x/y
Where R is the ratio. Substituting the known
values,
R = 6/8 = ¾ = 0.75
The relationship between the number of cans of food and boxes of food collected by Ingrid is a ratio of 1 can to 3 boxes after simplification. This means there is 1 can for every 3 boxes.
Ingrid collected 6 cans of food and 18 boxes of food for the food bank. To describe the relationship between cans of food and boxes of food, we can use a mathematical ratio.
The ratio of cans to boxes is calculated by dividing the number of cans by the number of boxes. This gives us:
6 cans : 18 boxes
To simplify this ratio, we divide both numbers by their greatest common divisor, which is 6:
6 ÷ 6 = 1
18 ÷ 6 = 3
Therefore, the simplified ratio is:
1 can : 3 boxes
This means there is 1 can of food for every 3 boxes of food. This ratio helps us understand the proportional relationship between the two quantities.
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A parallelogram is transformed according to the rule (x, y) → (x, y). Which is another way to state the transformation?
R0, 90°
R0, 180°
R0, 270°
R0, 360°
Answer:- R(0, 360°) is the right answer.
Given: A parallelogram is transformed according to the rule (x, y) → (x, y).
⇒The points of the image is same as the points of the original figure.
⇒ The given mapping create an image onto itself.
We know that the mapping of all points of a figure in a plane is done by basic rigid transformations such as translation, reflection or rotation.
In rotation to create a image that is onto itself , then the rotation must be about 360°, so that the rotation will take a complete turn to get back the original figure with the same points.
Thus in rotation the another way to state the transformation is R(0, 360°).
To get to a dog show, Mr. Luna first drives 7 miles west from his home and then 3 miles north. Next, he turns east and drives 11 miles. Finally, he turns north and drives 4 miles to the dog show. How far north of Mr. Luna's home is the dog show?
Answer:
Step-by-step explanation:
1/2 (4-k)=2/5
Distribute and find LCM
Answer:
20 -5k = 4the LCM of the denominators is 10Step-by-step explanation:
I find it convenient to do the problem in the reverse order: find the LCM, then distribute. That way, I'm not distributing a fraction.
The LCM of 2 and 5 is their product: 2·5 = 10. Multiplying the equation by 10 gives ...
5(4 -k) = 4
Now, distributing, we get ...
20 -5k = 4
the ratio of the sides of two squares is 3:1. what is the ratio of their perimeters?
The ratio of the perimeters of two squares with a side ratio of 3:1 is 3:1.
Explanation:The ratio of the sides of two squares is 3:1. To find the ratio of their perimeters, we need to compare the lengths of their sides. Let's assume the length of the larger square is 3x and the length of the smaller square is x. The perimeter of the larger square is 4 times the length of its side, so it is 4 × 3x = 12x. The perimeter of the smaller square is 4 times the length of its side, so it is 4 × x = 4x. Therefore, the ratio of their perimeters is 12x:4x. Simplifying this ratio gives us 3:1.
A box of crayons costs $1.75, including tax. Mr. Valentino wants to purchase boxes of crayons for his class and has a $25 budget. Write an inequality to solve for the number of boxes of crayons Mr. Valentino can purchase with his budget
a.$1.75x ≤ $25
b.$1.75x ≥ $25
c.$25x ≤ $1.75
d.$25x ≥ $1.75
it is multiple choice
The correct inequality to solve for the number of boxes of crayons Mr. Valentino can purchase with his budget is $1.75x ≥ $25.
Explanation:The correct inequality to solve for the number of boxes of crayons Mr. Valentino can purchase with his budget of $25 is b. $1.75x ≥ $25.
This inequality states that the product of the cost per box, $1.75, and the number of boxes, x, must be greater than or equal to $25 to remain within his budget.
You can solve this inequality by dividing both sides by $1.75 to find the minimum number of boxes he can buy and still stay within his budget.
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17.50 with a 7% sales tax?
To find the total cost of an item with sales tax, convert the tax rate to a decimal, multiply by the item's price, add the result to the original price, and round to the nearest cent. A $17.50 item with a 7% sales tax would cost a total of $18.73 after tax.
To calculate the total cost of an item with sales tax, you first need to determine the amount of sales tax by converting the percentage to a decimal and then multiplying by the item's cost. For an item priced at $17.50 with a 7% sales tax, you would convert 7% to a decimal (0.07) and then multiply this by $17.50. Therefore, the calculation would be:
Sales Tax = $17.50 x 0.07 = $1.225
Once you have the sales tax amount, you add it to the original price to find the total cost:
Total Cost = Original Price + Sales Tax
$17.50 + $1.225 = $18.725. After rounding to the nearest cent, the total cost would be $18.73.