Answer:
The commission rate is 9%
Step-by-step explanation:
We are given;
Alice's monthly salary is $315 Total sales were $9640Total earnings are $1182.60We are required to determine the commission rate;
We need to know that;
Total earnings = Monthly salary + Commission
Therefore;
Commission = Total earnings - monthly salary
= $1182.60 - $315
= $867.6
Therefore, assuming the commission rat is x %
Then;
x/100 × $9640 = $867.6
x/100 = $867.6 ÷ $9640
x/100 = 0.09
x = 9%
Therefore, the commission rate is 9%
rachel spent $3.60 for stamps to mail packages. Some were 30-cent stamps and the rest were 20-cent stamps. The number of 20-cent stamps was 2 less than the number of 30-cent stamps. How many stamps of each kind did rachel buy?
Rachel bought six 20-cent stamps and eight 30-cent stamps.
Step-by-step explanation:
Given,
Amount spent on stamps = $3.60 = 3.60*100 = 360 cents
Let,
x = 20 cent stamps
y = 30 cent stamps
According to given statement;
20x+30y=360 Eqn 1
x = y-2 Eqn 2
Putting value of x from Eqn 2 in Eqn 1
[tex]20(y-2)+30y=360\\20y-40+30y=360\\50y=360+40\\50y=400[/tex]
Dividing both sides by 50
[tex]\frac{50y}{50}=\frac{400}{50}\\y=8[/tex]
Putting y=8 in Eqn 2
[tex]x=8-2\\x=6[/tex]
Rachel bought six 20-cent stamps and eight 30-cent stamps.
Keywords: linear equation, substitution method
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Final answer:
Rachel bought 8 thirty-cent stamps and 6 twenty-cent stamps. We solved a system of equations representing the cost of the stamps and their quantity relationship to determine the numbers.
Explanation:
Rachel spent $3.60 for stamps to mail packages, buying 30-cent stamps and 20-cent stamps. The number of 20-cent stamps was 2 less than the number of 30-cent stamps. To solve this, we can use a system of equations to represent the total cost and the relationship between the number of stamps:
Let x be the number of 30-cent stamps.
Let y be the number of 20-cent stamps.
Based on the information given:
0.30x + 0.20y = 3.60 (Total cost equation)
y = x - 2 (Relationship between the stamps)
We substitute the second equation into the first equation:
0.30x + 0.20(x - 2) = 3.60
0.30x + 0.20x - 0.40 = 3.60
0.50x = 4.00
x = 8
Now we solve for y using the second equation:
y = 8 - 2
y = 6
So Rachel bought 8 thirty-cent stamps and 6 twenty-cent stamps.
What is the rate of change of the function described in the table?
the average rate of change of the function over the interval [tex]\(10 < x < 15\)[/tex] is [tex]\( -\frac{6}{5} \)[/tex].
To find the average rate of change of the function over the interval (10 < x < 15), we use the formula:
[tex]\[ \text{Average Rate of Change} = \frac{\text{Change in } f(x)}{\text{Change in } x} \][/tex]
We can calculate the change in [tex]\(f(x)\)[/tex] by subtracting the function values at the end and start of the interval, and the change in x by subtracting the end and start values of x.
Given the function values:
- [tex]\(f(10) = 30\)[/tex]
- [tex]\(f(15) = 24\)[/tex]
And the interval [tex]\(10 < x < 15\)[/tex], the change in [tex]\(f(x)\) is \(f(15) - f(10) = 24 - 30 = -6\)[/tex].
The change in x is [tex]\(15 - 10 = 5\)[/tex].
Now, we plug these values into the formula for the average rate of change:
[tex]\[ \text{Average Rate of Change} = \frac{-6}{5} \][/tex]
So, the average rate of change of the function over the interval [tex]\(10 < x < 15\)[/tex] is [tex]\( -\frac{6}{5} \)[/tex].
The complete Question is given below:
Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 10 < x < 15
x | f(0)
0 | 42
5 | 36
10 | 30
15 | 24
20 | 18
25 | 12
simplify this,(p-5)^2-49
Answer:
(p - 12)(p + 2) or
p^2 - 10p - 24.
Step-by-step explanation:
We use the Difference of 2 Squares Identity.
a^2 - b^2 = (a - b)(a + b).
So (p - 5)^2 - 49
= (p - 5 - 7)(p - 5 + 7)
= (p - 12)(p + 2)
= p^2 - 10p - 24.
Answer:
(p - 12)(p + 2)
Step-by-step explanation:
(p-5)² - 49 =
= (p - 5 - 7)(p - 5 + 7)
= (p - 12)(p + 2)
a² - b² = (a - b)(a + b)
a = p - 5
b = 49
Which of the following are necessary when proving that the diagonals of a
rectangle are congruent? Check all that apply.
o A. Opposite sides are congruent.
O
B. All obtuse angles are congruent.
O
C. Opposite sides are perpendicular.
O
D. All right angles are congruent.
Answer:look
Step-by-step explanation:
The diagonals of a rectangle exist congruent the necessary conditions are
A. Opposite sides are congruent.
C. Opposite sides are perpendicular.
How to verify that the diagonals of a rectangle are congruent?A quadrilateral exists named a rectangle if the opposite sides exist congruent and parallel to each other. All interior angles exist as right angles and are congruent.
To verify that the diagonals of a rectangle exist congruent the necessary conditions are:
1. Opposite sides of a rectangle exist congruent.
2. All right angles exist congruent.
Therefore, the correct answer is options A and C.
A. Opposite sides are congruent.
C. Opposite sides are perpendicular.
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complete the equation of the line through (-8, 8) and (1, -10)
Answer:
[tex]y=-2x-8[/tex]
Step-by-step explanation:
Let [tex]y=mx+c[/tex] be the equation of this line.
The points must satisfy this equation.
When x=-8, and y=8, we get:
[tex]8=-8m+c....(1)[/tex]
When x=1, and y=-10, we get:
[tex]-10=m+c...(2)[/tex]
Subtract equation (1) from equation (2) to get:
[tex]m--8m=-10-8[/tex]
9m=-18
m=-2
We put m=-2 in equation to get (2)
-10=-2+c
c=-10+2
c=-8
Therefore the equation is:
y=-2x-8
Is the ratio 3:4 the same as 4:5
Answer:
No the ratio 3:4 is not equal to 4:5
Step-by-step explanation:
3:4 = 3/4 and 4:5 = 4/5
3/4 is equal to 0.75 and 4/5 is equal to 0.8
0.75 [tex]\neq[/tex] 0.8
therefore, 3:4 [tex]\neq[/tex] 4:5
Hope this helps!
Justin wanted to wrap his moms birthday present shaped like a rectangular prism with pretty paper. The box is 2.1 feet long, 2.7 feet wide, And 3.2 feet high. What is the total surface area of the box?
Answer:
42.06 ft²
Step-by-step explanation:
2 sides = 2(2.7 ft × 3.2 ft) = 2 × 8.64 ft² = 17.28 ft²
Front + back = 2(2.1 ft × 3.2 ft) = 2 × 6.72 ft² = 13.44 ft²
Top + bottom = 2(2.1 ft × 2.7 ft) = 2 × 5.67 ft² = 11.34 ft²
Total area = 42.06 ft²
How do I do this????????????
Answer:
10 rows with the set of 100 blocks is what she will make
Step-by-step explanation:
Where
First row is 1
Second row is 3
Third row is 5
This shows that the blocks are set in an oddly fashion
Meaning each row has a odd number of blocks
Therefore from
1 block- row 1
3 blocks- row2
5 blocks- row 3
7 blocks - row 4
9 blocks- row 5
11 blocks - row 6
13 blocks- row 7
15 blocks - row 8
17 blocks- row 9
19 blocks - row 10
Add of the blocks it amounts to 100 blocks
Meaning the triangular will be at the 10th row when she has use 100 blocks
2/3 of a year is how many months
Answer:8
Step-by-step explanation:
There are 12 months in a year if you divide by 3 you get 4 and whatever you do to the numerator you have to do the denominator vice versa so you would multiply by four and get eight so it would be eight months
Answer:
2/3 of a year is 8 months
Step-by-step explanation:
Me Matthews purchases 22 boxes of pencils for 5 fourth grade classes. Each box contains 45 pencils. How many pencils will each class receive?
Answer: 198 pencils per class
Explanation:
22 boxes * 45 pencils = 990 pencils
990 pencils / 5 classes = 198 pencils per class
Answer: 198 pencils per class
Explanation:
22 boxes * 45 pencils = 990 pencils
990 pencils / 5 classes = 198 pencils per class
.
14 divied by 3/8 equals
Answer:
37 1/3
Step-by-step explanation:
14 divided by 3/8=
14*8/3=
37 1/3
Which statements are true? Check all that apply. StartRoot 1.8 EndRoot < 1.8 StartRoot 1.8 EndRoot greater-than 1 StartRoot 1.8 EndRoot less-than StartRoot 1.9 EndRoot 1.3 less-than StartRoot 1.8 EndRoot less-than 1.4 StartRoot 1.9 EndRoot + StartRoot 1.8 EndRoot greater-than 2 StartRoot 1.9 EndRoot minus StartRoot 1.8 EndRoot greater-than 0.1
The first, second, third, and fifth statements are true, but the fourth and sixth statements are false. The responses are based on evaluating the square root calculations.
Explanation:The statements we are analyzing are related to the square root of 1.8 (√1.8). Let's work through them:
√1.8 less than 1.8: This statement is true because the square root of a positive number less than its actual number.√1.8 greater than 1: This is true. Since √1.8 is approximately 1.34, which is greater than 1.√1.8 less than √1.9: This is true. Since the larger the number, the larger its square root will be.1.3 less than √1.8 less than 1.4: This is false. As previously stated, √1.8 is approximately 1.34, so it's not less than 1.3 nor greater than 1.4.√1.9 + √1.8 greater than 2: This is true. √1.9 is approximately 1.38 and √1.8 is 1.34. Adding these values exceeds 2.√1.9 − √1.8 greater than 0.1: This is false. The difference between √1.9 and √1.8 is less than 0.1.Learn more about Square Root Comparisons here:https://brainly.com/question/30877013
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How many solutions does the following system have?
y=2x-12
y=3x+12
The system has one solution
Step-by-step explanation:
Let us revise the type of the solutions of a system of equations
One solution if the coefficients of x or/and y are different in the simplest form of the two equationsInfinite many solutions if the coefficients of x , y and the numerical terms are equal in the simplest form of the two equationsNo solution if the coefficients of x and y are equal and the numerical terms are different in the simplest form of the two equationsThe system of equations is:
y = 2x - 12 ⇒ (1)
y = 3x + 12 ⇒ (2)
∵ The equations are in its simplest form
∵ The coefficients of x in the two equations are different
- That is the 1st case above
∴ The system has one solution
Let us prove that by solving the system
To solve the system of equations equate (1) and (2) to find x
∵ 3x + 12 = 2x - 12
- Subtract 2x from both sides
∴ x + 12 = -12
- Subtract -12 from both sides
∴ x = -24
- Substitute the value of x in equation (1) or (2) to find y
∵ y = 3(-24) + 12
∴ y = -72 + 12
∴ y = -60
∴ The solution of the system is (-24 , -60)
The system has one solution
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Tom drinks 8oz of water for every 3 miles he bikes after 21 miles how much water did he drink
Answer:
he drinks 56oz of water
Step-by-step explanation:
divide 21 by 3 that would equal seven than multiply it by 8 which is 56
Answer:
57 ounces
Step-by-step explanation:
[tex]\frac{3 miles}{8oz water}[/tex] × 7 = [tex]\frac{21miles}{56ozwater}[/tex]
Answer the questions
Answer:
I just know that for number 9.)It's C because it has a greater number, meaning it has a greater chance of containing Adam's house number.
The ratio of people to books in a classroom is 10:4 what is the unit rate of people per book
Answer:
Unit rate of people per book = 2.5
Step by step explanation:
Given:
Number of peoples = [tex]10[/tex]
Number of books = [tex]4[/tex]
Their ratios = [tex]10 : 4[/tex]
We have to find the unit rate of people per book.
To find out the unit rate of people per book we have to divide the total number of peoples by the total number of books.
Or
For this we will follow the unitary method:
For [tex]4[/tex] book there are [tex]10[/tex] persons.
For [tex]1[/tex] book there will be [tex]\frac{10}{4}[/tex] persons.
So,
The numeric value = [tex]\frac{10}{4}[/tex]
= [tex]2.5[/tex]
There are 2.5 people per book and that it also the unit rate of people per book.
If a figure was dilated using a scale factor of 2/3, the first step in mapping it back
onto itself is to dilate the new figure with a scale factor of ?
2/3
2
3
3/2
Answer:3/2
Step-by-step explanation:
What is the value of y?
Enter your answer in the box.
Answer:64
Step-by-step explanation:
Add 79 with 37 an you will get 116 you need to know the total angle for a triangle is 180 so 180 minus 116 is 64
The measure of the angle y for the triangle is 64°.
What is the angle of a triangle?The triangle is a shape having three sides and the sum of the angles of the triangle is always equal to 180°.
Here in the given triangle, the two angles are 79° and 37°. The measure of the unknown angle y° will be calculated as:-
y + 79 + 37 = 180
Now solve for the value of angle y below,
y = ( 180 - 79 - 37 )
y = 64°
Therefore, the measure of the angle y for the triangle is 64°.
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the ratio of girls to boys in a gym class is 1 to 2 if there are 30 students in the class how many girls are in the class?
Answer:
10 Girls
Step-by-step explanation:
This shows that there is twice as many boys in the gym class than girls.
Step 1: Determine what the ratio relates to the amount
1:2 -> 10:20
10 Girls
20 Boys
Answer:
The enswer is corect because is the biggest then girls to boys
Step-by-step explanation:
Can you show the work for (4x-4)(x-4)
Answer:
4x² - 20x + 16
Step-by-step explanation:
Given
(4x - 4)(x - 4)
Each term in the second factor is multiplied by each term in the first factor, that is
4x(x - 4) - 4(x - 4) ← distribute both parenthesis
= 4x² - 16x - 4x + 16 ← collect like terms
= 4x² - 20x + 16
on the last friday in may, one fourth of the 280 students in a school were away on a field trip how many students were on the field trip
What is nine - fifteenths minus two - sixths
Answer: four-fifteenths or [tex]\frac{4}{15}[/tex]
Step-by-step explanation:
What is written with words is mathematically expressed as:
[tex]\frac{9}{15}-\frac{2}{6}[/tex]
We can simplify both fractions, by dividing the numerator and denominator of the first by 3 and dividing the numerator and denominator of the second by 2:
[tex]\frac{9}{15}=\frac{3}{5}[/tex]
[tex]\frac{2}{6}=\frac{1}{3}[/tex]
Then:
[tex]\frac{3}{5}-\frac{1}{3}[/tex]
Calculating the least common multiple (l.c.m) in the denominator as [tex]15[/tex]:
[tex]\frac{9-5}{15}=\frac{4}{15}[/tex] This is the result: four-fifteenths
The 1984 movie footloose made $8,556,965 in its opening weekend. The 2011 remake of footloose made $15,556,113 in its opening weekend. What is the absolute and relative change in opening weekend earnings from the original footloose to its remake? Round your answer for relative change to the nearest hundreth of a percent. Do not round until your final answer.
Answer:
absolute change: $6,999,148relative change: 81.79%Step-by-step explanation:
The absolute change is the difference between the earnings numbers:
$15,556,113 -8,556,965 = $6,999,148
__
The relative change is the ratio of this difference to the original amount:
$6,999,148/$8,556,965 × 100% ≈ 81.794748% ≈ 81.79%
The absolute change in opening weekend earnings from the original Footloose to its remake is $6,999,148, and the relative change is approximately 81.74%.
Explanation:To calculate the absolute change in opening weekend earnings from the original Footloose movie to its 2011 remake, we subtract the earnings of the original movie from the earnings of the remake. Thus, the absolute change is $15,556,113 - $8,556,965 = $6,999,148.
To find the relative change, we divide the absolute change by the original amount and then multiply by 100 to get a percentage. This gives us ($6,999,148 / $8,556,965) * 100 ≈ 81.74%. Hence, the relative change is approximately 81.74%.
The absolute change represents the direct increase in dollar amount, while the relative change gives us the percentage increase from the original to the remake's opening weekend earnings, providing insight into the growth rate.
3. The Assistant Principal for Curriculum administered a practice SAT test with 50 questions
to students during an after-school tutoring program. She said a score of 30 or above predicts
a good SAT test score. How many students took the test and how many can expect a good
SAT test score?
O
O
A. 28 students took the test and 14 of them can expect a good SAT test score.
B.28 students took the test and 4 of them can expect a good SAT test score.
C. 28 students took the test and 21 of them can expect a good SAT test score.
D. 26 students took the test and 14 of them can expect a good SAT test score.
OO
O Mark for review (Will be highlighted on the review page)
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Answer:
A
Step-by-step explanation:
Answer:
the answer is c
Step-by-step explanation:
When 15 is subtracted from 3 times a number the result is -32. what is the number?
Answer:
15.6
Step-by-step explanation:
15+32=47
47/3=15.6
since the - is there
it will be -15.6
Answer:
Step-by-step explanation:
let x represent the number
3x - 15 = -32
3x = -32 + 15
3x = -17
x = -17/3 or - 5 2/3 <====
What Is 6 divided by 2/6?
Can you explain step by step please
Answer:
18Step-by-step explanation:
[tex]\frac{6}{\frac{2}{6} } =6*\frac{6}{2} =6*3=18[/tex]
Answer:
18
Step-by-step explanation:
6/(2/3)
Turn 6 into a fraction first.
(6/1) / (2/6)
(6/1) x (6/2)
36/2
18
The measures of the angles of triangle RST are in the ratio 2:4:9. What are the measures of the angles ?
Measures of the angles are 24°, 48° and 108°
Step-by-step explanation:
Step 1: Given ratio = 2:4:9. Sum of angles of triangle = 180°Let angles be 2x, 4x and 9x.
⇒ 2x + 4x + 9x = 180
⇒ 15x = 180
⇒ x = 180/15 = 12
Step 2: Find angles.2x = 24°, 4x = 48° and 9x = 108°
Find the value of 49/ 50 ÷ 7/ 6 using any method. Type your answer as a fraction in simplest form.
To divide fractions, multiply the first fraction by the reciprocal of the second fraction. Simplify the resulting fraction.
Explanation:To divide fractions, we need to multiply the first fraction by the reciprocal of the second fraction. So, the reciprocal of 7/6 is 6/7. Therefore, 49/50 ÷ 7/6 = 49/50 x 6/7. When we multiply the numerators (49 x 6) and the denominators (50 x 7), we get 294/350. This fraction can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 14. Therefore, 294/350 simplifies to 21/25.
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what kind of shape will be this rule on a graph
y= x^2
Answer:
a parabola, sort of like a u shape
Step-by-step explanation:
Match each function with its inverse function.
Answer:
check the photo.
Step-by-step explanation:
The inverse of the function
f(x) = ax + b is g(x) = (x/a) - (b/a)
(learn it by heart)