Answer: 220
Step-by-step explanation:
Create ratios using fractions, one for the students, and one for the percent
students: [tex]\frac{11}{x}[/tex] percents: [tex]\frac{5}{100}[/tex]
Then cross multiply 1. [tex]11 *100 = 1100[/tex], 2. [tex]1100 / 5 = 220[/tex]
So [tex]x = 220[/tex], this means there are a total of 220 students in 7th grade
A side of a regular polygon is 10cm. If each interior angle is 156. Calculate its perimeter.
Answer:
150 cm
Step-by-step explanation:
The total of exterior angles is 360°. We can use this fact to find the number of sides. The perimeter is the total length of all of the congruent sides.
Exterior anglesThe measure of an exterior angle of the regular polygon is the supplement of the adjacent interior angle:
exterior angle = 180° -156° = 24°
The total of n of these angles is 360°, so n is ...
24°×n = 360°
n = 360°/24° = 15
The polygon has 15 exterior angles, hence 15 sides
PerimeterThe perimeter is the total length of the 15 congruent sides:
P = 15×(10 cm) = 150 cm
The perimeter of the regular polygon is 150 cm.
An investor has an account with stock from two different companies. Last year, his stock in Company A was worth $5660 and his stock in Company B was worth $2500. The stock in Company A has increased 5% since last year and the stock in Company B has increased 9%. What was the total percentage increase in the investor's stock account? Round your answer to the nearest tenth (if necessary)
Using proportions, it is found that the total percentage increase in the investor's stock account was of 6.2%.
What is a proportion?
A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
The values of the stocks of Company A and Company B, after the increase are given, respectively, by:
Company A: 5660 x 1.05 = $5,943.Company B: 2500 x 1.09 = $2,725.The total values are given as follows:
Before the increase: 5660 + 2500 = 8160.After the increase: 5943 + 2725 = 8668.The percent increase is given by the increase divided by the initial value and multiplied by 100%, hence:
P = (8668 - 8160)/8160 x 100% = 6.2%.
The total percentage increase in the investor's stock account was of 6.2%.
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What is the equation of the line that is perpendicular to the line defined by the equation 2x = 4y – 8 and goes through the point (1, 2)?
The equation of the perpendicular line is y = -2x + 4
How to determine the line equation?The line equation is given as:
2x = 4y - 8
Make y the subject
4y = 2x +8
Divide by 4
y = 0.5x + 2
The slope of the above equation is
m = 0.5
The slopes of perpendicular lines are opposite reciprocals.
This means that, the slope of the perpendicular line is:
n = -1/m
This gives
n = -1/0.5
n = -2
The equation is then calculated as:
y = n(x - x1) + y1
This gives
y = -2(x - 1) + 2
Expand
y = -2x + 2 + 2
Evaluate
y = -2x + 4
Hence, the equation of the perpendicular line is y = -2x + 4
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The length of a rectangle is 1 yd more than double the width, and the area of the rectangle is 66 yd^2 . Find the dimensions of the rectangle.
The dimensions of the rectangle as described in the task is; 12.4 by 5.7 yd.
What is the dimension of the rectangle?Since the area, length and breadth of the rectangle are as described, it follows that;
66 = x(2x+1)
66 = 2x² + 1
x² = 32.5
x = 5.7
Therefore, the dimensions are 5.7 and 12.4.
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express using positive exponent
[tex] {3c}^{ - 2} [/tex]
Answer: [tex]\frac{3}{c^2}[/tex]
Step-by-step explanation:
This uses the exponent rule [tex]a^{-b}=\frac{1}{a^b}[/tex].
please help me! i’m really confused on this because i keep getting -5 outside the thing
Answer: D.
Step-by-step explanation: First you find the common factor, which is 5x³y. Then you write in parenthesis what's left over from each term. So the answer should look like: 5x³y(-3x⁵-4z+9).
15) Allie Young has to get a new car because someone hit and destroyed her old one. She feels she can afford to
pay $90 each month, and the best loan terms she has found offer her an 8.33 percent interest rate on a 4-year
loan. What is the maximum value of the car Allie should be looking for? Give answer to nearest hundred dollars.
a.) $3900
b.) $3800
c.) $3600
d.) $3700
Answer:I beleive the answer is c-3600
Step-by-step explanation:
90$ a month for 48 months=4320
Plus the interest rate of 8.33 so 4320x0.833=3598.56
Then you have to round up from 3598.56 to the nearest 100 dollars, so it would be 3600.
Please help me quick
The product of the ages 2 years from today is 924
System of equationLet the ages of the three cousins be x, y and z. If the product of their ages is 1716, hence;
xyz = 1716
If the product of their ages last year is 1320, then;
(x-1)(y-1)(z-1) = 1320
Two years ago, the product of their ages will be;
(x-2)(y-2)(z-2) = 1320- (1716-1320)
(x-2)(y-2)(z-2) = 1320-396
(x-2)(y-2)(z-2) =924
Hence the product of the ages 2 years from today is 924
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A dairy needs 336 gallons of milk containing 6% butterfat. How many gallons each of milk containing 7% butterfat and milk containing 3% butterfat must be used to obtain the desired 336 gallons?
We need 84 gallons of 3% butterfat milk and (84 * 3) = 252 gallons of 7% butterfat milk to obtain 336 gallons of 6% butterfat milk.
How to work with percentages?Let x = number of gallons of 3% milk
Thus;
336 - x = number of gallons of 7% milk
Therefore;
0.03x + 0.07(336 - x) = 0.06(336)
0.03x + 23.52 - 0.07x = 20.16
-0.04x = -3.36
x = 84 gallons
We need 84 gallons of 3% butterfat milk and (84 * 3) = 252 gallons of 7% butterfat milk to obtain 336 gallons of 6% butterfat milk.
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Use the drawing tool(s) to form the correct answer on the provided graph.
Graph the solution to this system of inequalities in the coordinate plane.
3y 2x+122x + y ≤5
The solution of the inequalities is (0.375, 4.25)
How to graph the inequalities?The system of inequalities is given as:
3y > 2x + 12
2x + y ≤ 5
Next, we plot the inequalities on a graph (see attachment)
From the graph, both inequalities intersect at
(x, y) = (0.375, 4.25)
This represents the solution of the inequalities
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Rebecca is playing a video game that involves planting and cutting down trees. She moves up an energy level for each tree she plants, and she moves down a level for each tree she cuts. If Rebecca reaches energy level 10, she will earn bonus points.
Rebecca is currently at energy level 4. The results of her next 3 turns are:
Turn 1: 6 trees cut
Turn 2: 8 trees planted
Turn 3: 1 tree cut
Answer the questions to find out whether Rebecca earned bonus points in the next 3 turns. Use the number line to help you add.
Answer:
She does not get bonus points and she ends up at level 5.
Equation: 4 - 6 + 8 -1 = 5
Equation using only addition: 4 + -6 + 8 + -1 = 5
I hope this helps!
Hector wants to laminate the tabletop in his study room. The tabletop is the shape of an isosceles trapezoid shown here. If laminating costs $4 per square foot, what is the total cost to laminate the tabletop?
A trapezoid with a height of 4 feet and bases of 6 feet and 10 feet is shown.
$136
$128
$112
$32
The total cost to laminate the table top is $128.
What is the total cost to laminate the table top?A trapezoid is a convex quadrilateral. A trapezoid has at least on pair of parallel sides.
The first step is to determine the area of the table top.
Area of a trapezoid = 0.5 x (sum of the lengths of the parallel sides) x height
0.5 x (6 + 10) x 4 = 32 square foot
Now, multiply the area by the cost per square foot
32 x 4 = $128
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On Friday a local hamburger shop sold a combined total of 460 hamburgers and cheeseburgers The number of cheeseburgers sold was three times the number of hamburgers sold how many hamburgers were sold Friday
The local hamburger shop sold 115 hamburgers and 345 cheeseburgers on Friday.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Let x represent the number of hamburger sold and y represent the number of cheeseburgers sold, hence:
x + y = 460 (1)
Also:
y = 3x (2)
From both equations:
x = 115, y = 345
The local hamburger shop sold 115 hamburgers and 345 cheeseburgers on Friday.
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How do i plot 3 points on a graph when all I am given is "x=4" ? and I need to find "x and y" for 3 points.
Answer:
(4,-1) (4,0) (4,1)
Step-by-step explanation:
If you graph this, it will be a straight vertical line. No matter what y is, x will always be 4.
Find the value of all trigonometric functions of 135°
Answer:
sin (- 135°)= – sin 135°= – sin (1 × 90°+ 45°) = – cos 45° = – 1√2
cos (- 135°)= cos 135°= cos (1 × 90°+ 45°) = – sin 45°= – 1√2
tan (- 135°) = – tan 135° = – tan ( 1 × 90° + 45°) = – (- cot 45°) = 1
csc (- 135°)= – csc 135°= – csc (1 × 90°+ 45°)= – sec 45° = – √2
sec (- 135°)= sec 135°= sec (1 × 90°+ 45°)= – csc 45°= – √2
cot (- 135°) = – cot 135° = – cot ( 1 × 90° + 45°) = – (-tan 45°) = 1
Step-by-step explanation:
hope this helps
WILL GIVE BRAINLIEST
1. Write an expression for each of the following:
a. the sum of 6 and z
b. the difference between 20 and x
c. 8 less than the quotient of x divided by 6
d. x increased by 5 divided by 4
The expressions for each of the given statements are
a. 6 + z
b. 20 - x
c. x/6 - 8
d. x + 5/4
Writing an expressionFrom the question, we are to write an expression for each of the given statement
a. the sum of 6 and z
That is,
6 + z
b. the difference between 20 and x
That is,
20 - x
c. 8 less than the quotient of x divided by 6
That is,
x/6 - 8
d. x increased by 5 divided by 4
That is,
x + 5/4
Hence, the expressions for each of the given statements are
a. 6 + z
b. 20 - x
c. x/6 - 8
d. x + 5/4
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A bag contains 2 yellow balls, 3 green balls, 5 red balls and 6 black balls.
What is the probability of either a yellow ball or a red ball being drawn if
only one ball is drawn?
Answer:
7/16
Step-by-step explanation:
(2+5)/(2+3+5+6) = 7/16
The probability of either a yellow or a red ball being drawn if only one is drawn is 7/16.
What is probability?The probability is the measure of the likelihood of an event to happen. It measures the certainty of the event. The formula for probability is given by; P(E) = Number of Favourable Outcomes/Number of total outcomes.
According to the given question.
Numnber of yellow balls = 2
Number of green balls = 3
Number of red balls = 5
Number of black balls = 6
So,
The total number of balls in a bag = 2+ 3+ 5 + 6 = 16
And,
The sum of yellow and red ball = 2 + 5 = 7
Therefore,
The probability of either a yellow or a red ball being drawn if only one ball is drawn
= [tex]\frac{total\ number\ of \ red \ and \ yellow\ balls }{Total\ number\ of \ balls}[/tex]
[tex]= \frac{7}{16}[/tex]
Hence, the probability of either a yellow or a red ball being drawn if only one is drawn is 7/16.
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The total age of Sana, Rabia and Saleem is 47 years. What was the total of their ages three years ago?
Answer:
38
Step-by-step explanation:
I'll say that Sana's age is A, Rabia's age is B, and Saleem's age is C.
A + B + C = 47
Three years ago, everyone was three years younger, so we can write the expression as:
(A-3) + (B-3) + (C-3) = x
x is the total age three years ago.
The above equation is the same thing as:
A + B + C - 9 = x
Since we know that A + B + C is 47, we use that number instead.
47 - 9 = x
38 = x
So three years ago, their total age was 38 years old.
The area of a rectangle is 44 ft², and the
Length of the rectangle is 3 ft less than twice
The width. Find the dimensions of the rectangle.
Answer:
Width = 5.5ft, Length = 8ft.
Step-by-step explanation:
Area of Rectangle = Length x Width
Let w be the Width of the rectangle.
From the information given from the question,
Length = 2w - 3 (3ft less than twice the width)
Area of Rectangle = [tex](2w-3)w\\=2w^{2} -3w[/tex] = 44
Now we can solve for w to find the dimensions.
[tex]2w^{2} -3w-44=0[/tex] (Quadratic Equations)
We can use the Quadratic formula to find w.
[tex]w=\frac{-b+/-\sqrt{b^{2}-4ac } }{2a}[/tex]
Since a = 2, b = -3 and c = -44,
[tex]w=\frac{-(-3)+/-\sqrt{(-3)^{2}-4(2)(-44) } }{2(2)} \\= 5.5 or -4 (reject)[/tex]
We reject negative values here.
Therefore, the width of the Rectangle = 5.5ft
While the length of the rectangle = 2(5.5) - 3 = 11 - 3 = 8ft
Will give 80 points!
Method of Travel to School
Walk/Bike Bus Car Row totals
Under age 15 60 165
Age 15 and above 65 195
Column totals 152 110 98 360
What percentage of students under age 15 travel to school by car? Round to the nearest whole percent.
11%
18%
41%
Answer:
There are about 80 students age 15 and above take a car to school.
Step-by-step explanation:
1. For all the columns the total has been given.
2. Bus is taken as 60 as walk/bike has been given 65 under age 15.
3. 195 row total Age 15 and above has been provided and updated.
4. Walk/Bike 152, 65 is already given Age 15 and above difference is 87.
5. Bus 60 under age 15 is already given total 110 difference is 50.
6. Age 15 and above 65,50,195 (Total) is already given row difference is 80.
7. Car is Age 15 and above is 80 and Total column is 98 difference is 18.
8. Age 15 and above take car is 80.
Answer:
its 41%
Step-by-step explanation:
i took the test
Y=x2+1 ordered pairs
The ordered pairs of the function are (0,1), (1,2), (2,5), (3,10) and (4,17)
How to determine the ordered pairs?The function is given as:
y = x^2 + 1
the ordered pairs are the x and y values of the function
So, we stet x = 0, 1, 2, 3 and 4
y = 0^2 + 1 = 1
y = 1^2 + 1 = 2
y = 2^2 + 1 = 5
y = 3^2 + 1 = 10
y = 4^2 + 1 = 17
Hence, the ordered pairs of the function are (0,1), (1,2), (2,5), (3,10) and (4,17)
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evaluate f(x)=4|x|+3 for x=-5
Write an equation for this word
sentence: one fifth of a number
equals 16.
Answer: x / 5 = 16
x = 80
A lawn can be mowed by 8 people in 6 hours. If 3 people take the day off and do not help mow the grass, how many hours will it take to mow the lawn? Please show me how you figured this out.
A. 6 2/5
B. 9 3/5
C. 2 1/4
D. 5 1/2
If 3 people take the day off, they will need (9 + 3/5) hours to mow the lawn. The correct option is B.
How many hours will it take to mow the lawn?Let's say that each person works at a rate R.
8 people can mow the lawn in 6 hours, then we can write:
(8*R)*6 hours = 1 lawn.
Solving for R:
R = (1/48 lawns per hour).
If 3 people take the day off, then the lawn is mowed by 5 people in a time T, then we need to solve:
(5*R)*T = 1 lawn.
Replacing the value of R:
(5/48 lawns per hour)*T = 1 lawn.
Then we have:
T = (48/5) hours.
We can rewrite that as:
T = (45/5 + 3/5) hours
T = 9 + 3/5 hours.
Then we conclude that the correct option is B.
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How do i convert the follwing Powers Of Ten into standard numbers?
[tex]10^{7}[/tex]
[tex]10^{5}[/tex]
[tex]10^{8}[/tex]
[tex]10^{12}[/tex]
[tex]10^{6}[/tex]
The standard numbers are obtained from the given numbers as follows;
10⁷ → 1000000010⁵ → 10000010⁸ → 10000000010¹² → 100000000000010⁶ → 1000000Which method can be used to express the numbers in standard form?The standard form of numbers is obtained by expressing the number completely and not using powers of 10
The given numbers in powers of 10 can be expressed in standard form by writing the specified number of zeros next to 1 given by the power of 10 as follows;
Number → Standard form
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Find DE
3x - 28
3x - 30
D
G
E
F
33
Answer:
11 units
Step-by-step explanation:
We first need to solve for x
3x -28 +3x -30 + x = 33 Combine the x's
7x - 28 -30 = 33 Combine -28 and -30
7x - 58 = 33 Add 58 to both sides
7x = 91 Divide both sides by 7
x = 13 Now plug 13 into the expression for DE
3x - 28
3(13) - 28
39 -28
11
Find the sum of the series: 4+8+12+........to 20 term. In (n
Answer:
16
Step-by-step explanation:
4 , 8 , 12 , 16 , 20 , ....................... ans goes on
A man ordered 4 times as many boxes of ballpoint pens as boxes of felt-tip pens. Ballpoint pens cost $4.41 per box, and felt-tip pens cost $3.44. If the man's order of pens totaled $63.24, how many boxes of each type of pen did he buy?
How many boxes of felt-tip pens did he buy?
Answer:
3
Step-by-step explanation:
Let x = # of boxes of felt-tip pens.
(x)(3.44)+(4x)(4.41) = 63.24
21.08x = 63.24
x = 3
Because x = 3, the man bought 3 boxes of felt-tip pens and 12 boxes of ballpoint pens.
3 On Saturday Keisha ran 35
she ran 41 kilometers. How much farther did she run on
Saturday than on Sunday?
By subtracting decimals, how much farther she ran on Saturday than on Sunday is determined as: 1.078 kilometers.
How to Subtract Decimals?When subtracting decimals, the number value is taken into consideration.
Distance ran by Keisha on Saturday = 3.218 kilometers.
Distance ran by Keisha on Sunday = 2.41 kilometers.
Subtract both decimals to determine how much farther she run on Saturday than on Sunday.
3.218 - 2.14 = 1.078 kilometers.
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Sometimes, terminology such as "the odds are 1 in 10" of an event is used. This is interpreted to mean "the probability of the event is 1/10" or "the odds in favor of the event are 1 to 9"
The odds that a member of a certain country's Senate (selected randomly) has a law degree is 1 in 1.4. What is the probability that a member of the Senate (selected randomly) has a law degree?
The probability is
Answer:
71.4% ( i think)
Step-by-step explanation:
If we translate 1 in 1.4 using what is described, it turns into (1/1.4)
Putting this into a calculator, we get 0.714286. Translated into a percent, that becomes 71.4286%
The probability that a member of the Senate (selected randomly) has a law degree is approximately 0.4167 or 41.67%.
When the odds are given as "1 in 1.4," it means that there is 1 chance of success (having a law degree) for every 1.4 chances of failure (not having a law degree).
To find the probability that a member of the Senate (selected randomly) has a law degree, you can use the formula:
Probability = 1 / (1 + Odds)
In this case, the odds are 1 in 1.4, so the probability is:
Probability = 1 / (1 + 1.4) ≈ 1 / 2.4 ≈ 0.4167
So, the probability that a member of the Senate (selected randomly) has a law degree is approximately 0.4167 or 41.67%.
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