Answer:
The number of faculty member is 45.
Step-by-step explanation:
Ratio of faculty members to students = 1 : 15
Number of students = 675
Total = Number students + faculty members
Let the total be t
Let the faculty member be f
Representing the ratio, we have:
[tex]\frac{15}{16} * t = 675\\\frac{15t}{16} = 675\\15t = 16 * 675\\15t = 10800\\\frac{15t}{15} =\frac{10800}{15} \\t = 720[/tex]
Therefore, the total number of both the students and faculty member is 720. To get the number of faculty member:
Total = Number students + faculty members
[tex]720 = 675 + f\\f = 720 - 675\\f = 45[/tex]
The number of faculty member is 45.
5 (2 x + 1 )= 50 please help me
Answer:
x = 4.5.
Step-by-step explanation:
5(2x + 1) = 50
10x + 5 = 50
10x = 50 - 5
10x = 45
x = 4.5.
Your credit score is 580. Your current credit card limit is $2,000. Your current credit card balance is $1,950. If you shrink your debt balance by 13% each month for 12 months what will your balance be?
Answer:
$366.66
Step-by-step explanation:
You start with a credit card balance of $1950. If you reduce this balance by 13% each month for 12 months, using the formula for geometric series (a(r^n)), your final balance at the end of 12 months will be approximately $452.98.
Explanation:The student's question is asking about reducing a credit card debt balance by a fixed percent each month. In this case, the student is reducing their debt by 13% every month for 12 months. To get a clear picture, let's go through this step by step.
Initially, the credit card balance is $1950. In the first month, the student reduces the debt by 13% which is $253.5. So, the remaining balance at the end of first month would be $1950 - $253.5 = $1696.5
This process is repeated each month. For example, in the second month, the student reduces the new amount of $1696.5 by 13%. The debt will continue to decrease in this manner each month.
To calculate the balance at the end of 12 months, we would use the formula for geometric series: a(r^n), where 'a' is the initial amount of debt($1950), 'r' is the percentage (1 - 13% or 0.87) and 'n' is the number of months (12).
Your final balance at the end of 12 months would be $1950*(0.87^12) which approximately equals $452.98. Hence, by reducing your debt by 13% each month for 12 months, your balance will be approximately $452.98. But remember, maintaining steady payments and not adding to the balance by new purchases is also important in managing credit card debt.
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how do you get b? show me how if you can, please.
Answer:
<ABC = 98.
Step-by-step explanation:
We know that the triangle is lying on a flat line, which is 180 degrees. We know that angle ABC and angle CBD are supplementary as they both use line ABD as their transversal.
Set up the equation (3 + 5x) + 82 = 180.
Solve for x, and you get 19.
Plug it back in to (3 + 5x), we get <ABC = 98.
What are the dimensions of the rectangle shown on the coordinate plane? On a coordinate plane, a rectangle has points (1, -1), (10, -1), (10, -5), (1, -5). The base is 3 units and the height is 9 units. The base is 9 units and the height is 4 units. The base is 10 units and the height is 4 units. The base is 11 units and the height is 6 units.
The dimensions of the rectangle shown on the coordinate plane is The base is 9 units and the height is 4 units.
Option: B.
Step-by-step explanation:
We are given with the coordinate points of a rectangle.
The points are (1, -1), (10, -1), (10, -5), (1, -5).
From the given graph, the bigger side is the base and the height is the smaller side.
The points (1, -1), (10, -1) and (1, -5), (10, -5) can be used to find the base of the rectangle.
The points (10, -1), (10, -5) and (1, -1), (1, -5) can be used to find the height of the rectangle.
Let us find the base using coordinate point (1, -5), (10, -5) .
Since the base runs horizontally on the x-axis, we have to find the run.
run = [tex]x_2-x_1[/tex].
run = 10-1.
run (base)= 9 units.
Let us find the base using coordinate point (10, -1), (10, -5) .
Since the height runs vertically on the y-axis, we have to find the rise.
rise = [tex]y_2-y_1[/tex].
rise = -5-(-1).
rise=-5+1.
rise (height)= 4 units. ( Units are always measured in positive.)
∴ The base is 9 units and the height is 4 units.
Which equation best describes the graph of the line that has slope-1/3 and passes through point
(3.-9)?
Answer:
y=-1/3x-8
Step-by-step explanation:
y-y1=m(x-x1)
y-(-9)=-1/3(x-3)
y+9=-1/3x+3/3
y+9=-1/3x+1
y=-1/3x+1-9
y=-1/3x-8
Ami is having a pizza party on Saturday night. She ordered 8 pizzas. If the average person eats 1/3 of a pizza, how many persons will 8 pizzas serve
Answer:
The answer is 24
Step-by-step explanation:
If each person eats 1/3 of the pizza then that means it takes 3 people to eat a whole pizza so you multiply three times 8 and you get twenty four.
Find the value of y. y-62=-86
Show how you got the answer
Answer:y=-24
Step-by-step explanation:
Move all terms not containing
y
to the right side of the equation.
The product of 6.3 and g increased by 14
Answer:
Step-by-step explanation:
6.3g + 14
Answer:
6.3g + 14
Step-by-step explanation:
Two angles are supplementary. The larger angle is 15 more than 10 times the smaller angle. Find the measure of each angle
15° and 165°
Step-by-step explanation:
Step 1 :
Let x and y denote the angles with x as the smaller angle and y as the larger angle
When 2 angles are supplementary, the sum of both the angles is 180 degrees.
Hence x + y = 180
Step 2:
Given that the larger angle is 15 more than 10 times the smaller angle
Hence y = 15 + 10 x
Step 3 :
Solving for the 2 equations we have
11x = 165 => x = 15
=> y = 180-15 = 165
Hence the 2 angles are 15 and 165 degrees.
find the domain and range (0,1), (3,1), (3,9)
Answer:
domain={0,3}
range={1,9}
Step-by-step explanation:
PLZZZ HELP ASAP!!!!! Part A: Explain how to write an equivalent expression for 3(4x + 2) using the distributive property. Part B: Prove the 2 expressions are equivalent by substituting x = 2 into both expressions. *
3(4x + 2)
= 3 . 2(2x + 1)
= 6(2x + 1)
proof
• 3(4x + 2)
= 3(4(2) + 2)
= 30
• 6(2x + 1)
= 6(2(2) + 1)
= 30
In country A, about three times as many cars are manufactured per day than in country B. If the total number of these cars manufactured per day is 26 comma 416, find the number manufactured in country B and the number manufactured in country A.
Answer:
country a = 19,812 cars
country b = 6,604 cars
Step-by-step explanation:
a = country a
b = country b
the 2 eqations are:
a + b = 26,416
a = 3b
now substitute 3b for a in the first equation:
3b + b = 26,416
add the variables:
4b = 26,416
now divide 26,416 by 4 (26,416/4)
b = 6,604
so country b has 6,604 cars
to find country b, substitute the number of cars in country b (which is 6,604) in the second equation:
a = 3b
a = 3 × 6,604
a = 19,812
so country a has 19,812 cars
2/5 with an exponent of 3
Answer:
2/5 with an exponent of 3 is 8/125 or 0.064
Step-by-step explanation:
Given:
A fraction = 2/5
Exponent = 3
To find the value of the fraction using the exponent.
We know that :
⇒ [tex](a)^3=a\times a\times a[/tex]
The exponents is the number of times a number is multiplied.
So,
⇒ [tex](\frac{2}{5})^3[/tex]
⇒ [tex]\frac{2\times 2\times 2}{5\times 5\times 5}[/tex]
⇒ [tex]\frac{8}{125}[/tex]
On further division the number can be written as 0.064
10. Calculate 18% of 75 to one decimal place.
First write 18% as a decimal by moving the decimal point two places to the left to get .18.
The word "of" means multiply, so we have (.18)(75) which is 13.5.
Answer:
13.5
Step-by-step explanation:
18% of 75
18% /100% x 75
0.18 x 75
13.5
how to solve 3(x+4)-2(x+4)
Answer:
1.Distribute values
(3x+12)-(2x+8)
2.Add common terms
x+4
simplify the expression -2-17+12-(-4)
Answer:
- 3
Step-by-step explanation:
hello:
-2-17+12-(-4)=(-2-17)+(12+4)= -19+16= -3
Answer:
-3
Step-by-step explanation:
-2-17+12-(-4)
From BODMAS, we begin witht the bracket
=-2-17+12+4
= -2-17+16
= -19+16
= -3
Help please!!! Show how you go the answer too
Answer:
Step-by-step explanation:
If QPS is a right angle we know a right angle equals 90 degrees. so you can find your answer by doing 90-35.
Therefore getting 56.
Hope this helps :)
Find the final price on a $1049 television that is on sale for 12% off if the sales tax is 4.5%
The final price of a $1049 television on a 12% sale, with a 4.5% sales tax, is $964.66.
Explanation:The final price on a $1049 television that is on sale for 12% off can be found by deducting the discount from the original price, and then adding the sales tax on the discounted price.
First, let's find the discount: 12% of $1049 is (12/100)*1049 = $125.88. So, the price after discount would be 1049 - 125.88 = $923.12.
Next, we need to add the 4.5% sales tax. Sales tax is calculated on the discounted price, so 4.5% of $923.12 is (4.5/100)*923.12 = $41.54.
Finally, we add the tax to the discounted price to get the final price: $923.12 + $41.54 = $964.66. So, the final price of the television is $964.66.
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What is The midpoint of AB=(1,
The midpoint of AB is point G
Explanation:The complete question has been attached below. As you can see, we have a line segment which is defined as a part of a line that is bounded by two different points that are at the end of the segment. So here we know that:
A is located at point -6.B is located at point 8Therefore, the midpoint can be calculated as:
[tex]M:midpoint \\ \\ \\ M=\frac{A+B}{2} \\ \\ M=\frac{-6+8}{2} \\ \\ M=1[/tex]
So the midpoint is [tex]M=1[/tex] that matches point G. Finally:
Conclusion: The midpoint of AB is point G
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Midpoint: https://brainly.com/question/13773601
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Please give me the answer and explain how you got it.
The measure of m∠KPN is 68°.
Step-by-step explanation:
From the given diagram, we are given with lines passing through a point P creating different angles.
Data given,
m∠KPN = 4x°.
m∠NPO = (x+5)°.
And m∠KPO= 90°.
The m∠KPO is spitted into m∠KPN and m∠NPO.
Thus the sum of m∠KPN and m∠NPO will be m∠KPO.
⇒m∠KPN + m∠NPO =m∠KPO.
Substitute the values to find x value.
4x°+(x+5)°= 90°.
(°5x+5)=90°.
5x°=90°-5°.
5x°=85°.
x=[tex](\frac{85}{5} )[/tex].
x= 17.
⇒m∠KPN = 4x°.
=4(17)°.
m∠KPN =68°.
Thus the measure of m∠KPN is 68°.
The geometric sequence bn is defined below. Find b3.
B1 = 54
R= -1/3
Answer:
6
Step-by-step explanation:
hello :
the nth term is : Bn= B1×R^n-1
calculate B3 (when n=3) R= -1/3 B1 = 54
B3 =54×(-1/3)^(3-1)
B3 =54×(1/9)=6
Knowing about geometric sequences we have that its third term will be given by 6
What is the geometric sequences formula?Geometric Progression (PG) is a numerical continuity in which the division of a term with its previous one, except the first, will result in a single value, the so-called ratio (q), that is: PG: (a1, a2, a3, a4, ..., an), where q = (a2/a1 = a3/a2 = a4/a3,.
Given that:
B1 = 54R= -1/3The formula of the term will be:
[tex]Bn= B1*R^n-1[/tex]
Calculated the B3 we have:
[tex]B3 =54*(-1/3)^{(3-1)}\\B3 =54*(1/9)=6[/tex]
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A rectangular bathroom floor is covered with square tiles that are 1 1/2 feet by 1 1/2 feet. The length of the bathroom floor is 10 1/2 feet and the width is 6 1/2 feet
Answer:
The number of square tiles required to cover the bathroom floor is approximately 31.
Step-by-step explanation:
The dimensions of the rectangular floor of the bathroom are:
Length = 10.5 ft.
Breadth = 6.5 ft.
The dimensions of the square tiles are:
Side = 1.5 ft.
The area of the rectangular floor of the bathroom is:
[tex]Area\ of Bathroom\ floor=Length\times Breadth\\=10.5\times6.5\\=68.25[/tex]
The area of 1 square tile:
[tex]Area\ of\ 1\ square\ tile=(SIde)^{2}\\=(1.5)^{2}\\=2.25[/tex]
The number of tiles required to cover the bathroom floor is:
[tex]Number\ of\ tiles=\frac{Area\ of\ bathroom\ floor}{Area\ of\ 1\ square\ tile} \\=\frac{68.25}{2.25}\\ =30.3333\\\approx31[/tex]
Thus, the number of square tiles required to cover the bathroom floor is approximately 31.
Increase 750 g by 20%.
Answer:
900 g
Step-by-step explanation:
Increase by 20% means 120% of the value
120/100 × 750
900g
If the nth term of an A.P. is 3n+2, find the sum of first 'n terms of that AP.
Answer:
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] (3n + 7)
Step-by-step explanation:
We require to find the first term a₁ and the common difference d
The n th term is given by 3n + 2, thus
a₁ = 3(1) + 2 = 3 + 2 = 5
a₂ = 3(2) + 2 = 6 + 2 = 8
d = 8 - 5 = 3
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ], substitute values
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ (2 × 5) + 3(n - 1) ] = [tex]\frac{n}{2}[/tex] (10 + 3n - 3) = [tex]\frac{n}{2}[/tex] (3n + 7)
Answer:
Sn = (3/2)n² + (7/2)n
Step-by-step explanation:
Sn = (n/2)[2a + (n-1)d]
a = 3(1)+2 = 5
d = second term - 5 = 3(2)+2 - 5 = 3
Sn = (n/2)[2(5) + (n-1)(3)]
= (n/2)[10 + 3n - 3]
= (n/2)(7 + 3n)
Sn = (3/2)n² + (7/2)n
To add 547+ 327, would you need to regroup ?
Answer:
yes
Step-by-step explanation:
when addi g the ones place it would result in 14 so u would need to regroup the 1 into the tens place
Juanita has 102 beads to make n necklaces. Each necklace will have 17 beads.
Answer:
There will be 6 necklaces
Step-by-step explanation:
102/17 is 6
Answer:Juanita can make 6 bracelets.
Step-by-step explanation:
Divide 102 and 17 then you should get 6.
PLS ANSWER AND LOOK UNDER THE QUESTION TOO :)))
What is the solution to the following system of linear equation?
y= 2x+3
y= -1/2x -2
A. (2,1)
B. (-1,-2)
C. (1,2)
D. (-2,-1)
if anyone's parents dont accept them for the way they are or they dont feel accepted then i just wanted to say them im ur new fam now and i luv ya <333333333333333
D. (-2,-1)
Hope it helps you.
Answer:
D
Step-by-step explanation:
Given the 2 equations
y = 2x + 3 → (1)
y = - [tex]\frac{1}{2}[/tex] x - 2 → (2)
Since both equations express y in terms of x, equate the right sides
2x + 3 = - [tex]\frac{1}{2}[/tex] x- 2
Multiply through by 2 to clear the fraction
4x + 6 = - x - 4 ( add x to both sides )
5x + 6 = - 4 ( subtract 6 from both sides )
5x = - 10 ( divide both sides by 5 )
x = - 2
Substitute x = - 2 into (1) for corresponding value of y
y = 2(- 2) + 3 = - 4 + 3 = - 1
Solution is (- 2, - 1 ) → D
(12 – 8)3 – 24 x 2
Evaluate the expression
I WILL MARK BRAINLIEST TO WHOEVER GETS IT FIRST.
Convert 2000 ft per minute to miles per hour. Round to the nearest tenth.
Answer:
22.7
Step-by-step explanation:
please help i will mark brainliest 50 points
Mr. Wilson is giving his students a vocabulary test tomorrow over all the terms they have learned from this semester. Today, he wants to determine how prepared the students are for the test. So, he writes each term on a note card and puts all the note cards in a paper bag. Then, he asks each student to come to his desk, select five note cards out of the bag, define those five terms, and then put the note cards back in the bag. He records the number of terms each student is correctly able to define.
What is the population in this situation? What is the sample? Use complete sentences in your answer.
Do you think the data from the sample Mr. Wilson is collecting is representative of the population? Explain your reasoning using complete sentences.
The population in this situation is all the terms that the teacher taught this semester and that are represented in the note cards and put in the paper bag.
Explanation:
The population in this situation of Mr Wilson is all the terms that the teacher taught this semester and that are represented in the note cards and put in the paper bag. The sample is every set of 5 note cards that is selected by the students.
The data is representative of the population because they are selected randomly without bias. Every of term has the same probability of being selected. Also it given that the cards are replaced every time, so all the students will face the same population when they are going to select a sample.