Answer:
The north campus had [tex]800[/tex] while the south campus had [tex]200[/tex].
Step-by-step explanation:
The question stated that there are [tex]1000[/tex] students in the merged campus. That's the sum of the number of students in the north and the south campus before the merger.
Let [tex]x[/tex] denote the number of students in the north campus before the merger. The other [tex](1000 -x)[/tex] students would all belong to the south campus before the merger.
Before the merger, [tex]20\%[/tex] of the students of the north campus are of music majors. In terms of [tex]x[/tex], that's [tex](20\%)\cdot x = 0.20\,x[/tex] students.
On the other hand, [tex]70\%[/tex] of the students of the south campus are of music majors. That corresponds to [tex](70\%)\cdot (1000 - x) = 0.70\cdot (1000 - x) = 700 - 0.70\, x[/tex] students.
With a similar logic, the number of music students in the merged east campus will be [tex]30\% \times 1000 = 300[/tex].
The question implies that the sum of students in the two campuses should be equal to the number of music students in the east campus. That is:
[tex]0.20\, x+ (700 - 0.70\, x) = 300[/tex].
Solve for [tex]x[/tex]:
[tex]x = 800[/tex].
In other words, there are [tex]800[/tex] students in the north campus and [tex](1000 - 800) = 200[/tex] students in the south campus before the merger.
An integer between 7.2 and 8.8.
Answer:
1
Step-by-step explanation:
Answer: 8
Step-by-step explanation:
integer has no decimal point.
The 2 integer seemingly that is present is 7 and 8.
HOWEVER, 7 is less than 7.2, so it is not the answer
7.2<8<8.8
So it fits in the range
ANSWER IS 8Hope this helps!! :)
Please let me know if you have any question
Ms. Sanders invested in a stock. During the first year, the value of the stock tripled. The next year, the value of the stock decreased by $600. Write an expression that can be used to represent the value of her stock at the end of the second year. Be sure to indicate what the variable in your expression represents. (please help I am lost)
Answer:
Value in $= 3x -600
Step-by-step explanation:
Let the value of the stock before investment= x
At the first year , the value tripled
Value after first year=3x
The second year , the stock reduces by $600.
So
The value of the stock after the second year
Value in $= 3x -600
Suppose your car averages 38 miles per gallon on the high-
way if your average speed is 55 miles per hour, and it aver-
ages 32 miles per gallon on the highway if your average speed
is 70 miles per hour.
a. What is the driving time for a 2000-mile trip if you drive
at an average speed of 55 miles per hour? What is the driving
time at 70 miles per hour?
b. Assume a gasoline price of $2.55 per gallon. What is the
gasoline cost for a 2000-mile trip if you drive at an average
speed of 55 miles per hour? What is the gasoline cost at
70 miles per hour?
Some one please help me on these questions! They’re getting a little harder now!!
Answer:
a. around 36.36 hours; around 28.57 hours
b. $134.21; $159.38
Step-by-step explanation:
a. The driving time at 70 miles per hour is 28.57 hours
b The gasoline cost for this trip would be $159.38.
How to calculate the costa. At an average speed of 55 miles per hour:
Time = 2000 miles / 55 miles per hour = 36.36 hours
At an average speed of 70 miles per hour:
Time = 2000 miles / 70 miles per hour = 28.57 hours
b. At an average speed of 55 miles per hour:
The car averages 38 miles per gallon on the highway.
Therefore, the gasoline required for a 2000-mile trip would be: 2000 miles / 38 miles per gallon = 52.63 gallons
The gasoline cost for this trip would be: 52.63 gallons * $2.55 per gallon = $134.13.
At an average speed of 70 miles per hour:
The car averages 32 miles per gallon on the highway.
Therefore, the gasoline required for a 2000-mile trip would be: 2000 miles / 32 miles per gallon = 62.50 gallons.
The gasoline cost for this trip would be: 62.50 gallons * $2.55 per gallon
= $159.38.
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You are at a family reunion and the cooler contains ten bottles of soda; four Sprite, three Dr. Pepper, and three Cherry Coke. Three times, you randomly pick up a drink for your grandmother. The first time, you get a Dr. Pepper. The second and third times, you get Cherry Coke. What is the probability of getting Dr. Pepper the fourth time and then an Dr. Pepper the fifth time without replacement?
Answer:
[tex]Probability = \frac{18}{1860480}[/tex]
Step-by-step explanation:
Given
Soda = 10
Sprite = 4
Dr. Pepper = 3
Cherry Coke = 3
Required
Determine the probability of picking Dr. pepper the fourth and fifth
First, we need to sum up the number of drinks
[tex]Total = 10 + 4 + 3 + 3[/tex]
[tex]Total = 20[/tex]
First Selection: Dr. Pepper
[tex]P_1= \frac{3}{20}[/tex]
Since its probability without replacement;
At this stage: Dr. Pepper = 2 and Total = 19
Second Selection: Cherry Coke
[tex]P_2= \frac{3}{19}[/tex]
At this stage: Dr. Pepper = 2; Cherry Coke = 2 and Total = 18
Third Selection: Cherry Coke
[tex]P_3= \frac{2}{18}[/tex]
[tex]P_3= \frac{1}{9}[/tex]
At this stage: Dr. Pepper = 2; Cherry Coke = 1 and Total = 17
Fourth Selection: Dr. Pepper
[tex]P_4= \frac{2}{17}[/tex]
At this stage: Dr. Pepper = 1; Cherry Coke = 1 and Total = 16
Fifth Selection: Dr. Pepper
[tex]P_5= \frac{1}{16}[/tex]
Multiply the calculated probabilities, to give the required probability
[tex]Probability = P_1 * P_2 * P_3 * P_4 * P_5[/tex]
[tex]Probability = \frac{3}{20} * \frac{3}{19} * \frac{1}{9} * \frac{2}{17} * \frac{1}{16}[/tex]
[tex]Probability = \frac{3 * 3 * 1 * 2 * 1}{20 * 19 * 18 * 17 * 16}[/tex]
[tex]Probability = \frac{18}{1860480}[/tex]
Find the value of x. Round you answer to the nearest tenth.
20
18
X
Answer:
21.9
Step-by-step explanation:
The altitude of an isosceles triangle bisects the base. So, x represents the hypotenuse of a right triangle with legs of 9 and 20. It can be found using the Pythagorean theorem:
x^2 = 9^2 +20^2 = 81 +400
x = √481 ≈ 21.932
The length x is about 21.9 units.
slope m=-1/2 passing through (2,-8)
I hope this helps you
The ratio of yes votes to no votes was 4 to 7. If there were 4746 no votes, what was the total number of votes?
Answer:
7458
Step-by-step explanation:
I hope this helps you
Please Help! I'm stuck!
Answer:
C. [tex]5 (\frac{x}{z}) ^1^0[/tex]
Step-by-step explanation:
Hey there!
Given
[tex]\frac{15 x^-^3 z^5}{3 x^7 z ^-^5}[/tex]
Well to solve this we first need to do 15 ÷ 3
= 5
When dividing exponents we actually subtract.
-3 - 7 = -10
5 - -5 = 10
[tex]5 x^-^1^0 z^1^0[/tex]
Hope this helps :)
Answer:
D. 5 (z/x)^10.
Step-by-step explanation:
15/3 = 5
x^-3 / x^7 = x^-10 = 1/x^10
z^5 / z^-5 = z ^10
So the answer is 5 * z^10 * 1/x^10
= 5 z^10 / x^10
= 5 (z/x)^10.
What are all the terms in the expression 4mn + m + 5 and which is a constant
Answer:
m and n are variables whereas 4 and 5 are constant terms or coefficient.
Step-by-step explanation:
hope it will help ^_^
Answer:
Below
Step-by-step explanation:
● 4 and 5 are constants since their values don't change.
● m and n are variables since they can take any value.
A maritime flag is shown. What is the area of the shaded part of the flag? Explain
or show your reasoning.
8 in
6 in
6 in
4 in
Answer:
[tex]Area = 72in^2[/tex]
Step-by-step explanation:
Your question is incomplete without an attachment (See attachment)
Required
Determine the area of the shaded part
From the attachment;
Assume that the shaded portion is closed to the right;
Calculate the Area:
[tex]Area_1 = Length * Width[/tex]
[tex]Area_2 = 8in * (6in + 6in)[/tex]
[tex]Area_2 = 8in * 12in[/tex]
[tex]Area_1 = 96in^2[/tex]
Next;
Calculate the Area of the imaginary triangle (on the right)
[tex]Area_2 = \frac{1}{2} * base * height[/tex]
[tex]Area_2 = \frac{1}{2} * (6in + 6in) * 4in[/tex]
[tex]Area_2 = \frac{1}{2} * 12in * 4in[/tex]
[tex]Area_2 = \frac{1}{2} * 48in^2[/tex]
[tex]Area_2 = 24in^2[/tex]
Lastly, calculate the Area of the Shaded Part
[tex]Area = Area_1 - Area_2[/tex]
[tex]Area = 96in^2 - 24in^2[/tex]
[tex]Area = 72in^2[/tex]
Hence,
The area of the shaded part is 72in²
Solve 2x + 2 > 10
A. x < 6
B. x > 4
C. x > 6
D. x < 4
Answer:
2x + 2 > 10
2x > 10 - 2
2x > 8
x > 8
B. x > 4.
Answer:
B. x>4
Step-by-step explanation:
2x + 2 > 10
In order to solve this inequality, we must isolate the variable, x , on one side of the inequality.
2 is being added to 2x. The inverse of addition is subtraction. Subtract 2 from both sides of the inequality.
2x+ (2-2) > 10-2
2x > 10-2
2x > 8
x is being multiplied by 2. The invers of multiplication is division. Divide both sides of the inequality by 2.
2x/2 > 8/2
x > 8/2
x > 4
The solution to the inequality 2x+2 > 10 is x > 4 and the correct answer is B.
write a real world problem for the following experssions. m+9
Answer:
A number increased by 9.
Step-by-step explanation:
A number= can be denoted by any letter.
increased= +
by 9= 9
Hope this helps ;) ❤❤❤
7m+11=-4(2m+3) answer
Answer:
See below.
Step-by-step explanation:
So we have the equation:
[tex]7m+11=-4(2m+3)[/tex]
Distribute the right:
[tex]7m+11=-8m-12[/tex]
Add 12 to both sides:
[tex]7m+23=-8m[/tex]
Subtract 7m from both sides:
[tex]23=-15m[/tex]
Divide by -15:
[tex]m=-23/15\approx-1.5333[/tex]
21. Name 8 different rays.
22. Name 2 pairs of opposite rays.
23. Name 2 lines that intersect at point Z.
W
24. Draw three noncollinear points A, B, and C. Sketch. AB Then add a point D and
sketch CD so that CD intersects AB at point B.
Focus
00
8
Answer:
See below
Step-by-step explanation:
21. Name 8 different rays.
ZX, ZY, ZV, ZW, XY, YX, VW, WV22. Name 2 pairs of opposite rays.
ZX and ZY, ZV and ZW23. Name 2 lines that intersect at point Z.
XY and VW24. Draw three noncollinear points A, B, and C. Sketch. AB Then add a point D and sketch CD so that CD intersects AB at point B.
See attachedFind the volume of a sphere with a diameter of 3 cm.
Answer:
9/2π
=14.13716694
Step-by-step explanation:
The equation of the volume of the sphere:
V=4/3πr^3
If the diameter is 3cm, the radius is divided by 2, so 1.5cm.
Plug that in, 4/3π1.5^3
Use a calculator:
9/2π
=14.13716694
[tex]14,14~cm^{3}[/tex]
Step-by-step explanation:d = 3cm = 2r => r = d/2 = 3cm/2 = 1,5 cm
[tex]V=\frac{4}{3}\pi*r^{3}\\\\=\frac{4}{3}*\frac{22}{7}*3.375cm^{3}\\ \\=\frac{4*22*3.375}{21}cm^{3}\\ \\=\frac{297}{21}cm^{3}\\ \\[/tex]
≈ [tex]14,14~cm^{3}[/tex]
m+q+ p; use m = 2, p = 1, and q = 3
Why does 9,324 have a different value than 9,234?
One way to determine this is to take the difference of numbers.
If the difference results in 0 then we can assume numbers that we subtracted are the same, mathematically:
[tex]a-a=0\implies a = a[/tex]
So,
[tex]9324-9234=90\implies 9324\neq9234[/tex].
Hope this helps.
Step-by-step explanation:
9,324 have a different value than 9,234 because 9,324 is greater than 9,234.
9,324-9,234=90
9,324 is 90 more than 9,234.
Tavon has a gift card for $165 that loses $4 for each 30-day period it is not used. He has another gift card for $145 that loses $3.50 for each 30-day period it is not used. Write an equation for the number of 30-day periods until the value of the gift cards will be equal. Let x represent the number of 30-day periods.
Answer:
Equation 1 = Equation 2
165 - 4x = 145 - 3.50x
Step-by-step explanation:
Let x represent the number of 30-day periods.
Tavon has a gift card for $165 that loses $4 for each 30-day period it is not used.
Therefore the equation =
$165 -$4 × x
= 165 - 4x.......... Equation 1
He has another gift card for $145 that loses $3.50 for each 30-day period it is not used.
$145 -$3.50 × x
= 145 - 3.50x........... Equation 2
Hence, an equation for the number of 30-day periods until the value of the gift cards will be equal is obtained by equating Equation 1 and Equation 2 together
So, we have
Equation 1 = Equation 2
165 - 4x = 145 - 3.50x
We simplify further:
165 - 145 = -3.50 + 4.0x
20 = 0.5x
x = 20/0.5
x = 40
Therefore, number of each 30-day periods until the value of the gift cards will be equal is 40
Factor 9x2 - 4y2 Group of answer choices
(3x - 2y) (3x + 2y )
(3x - 2y) (3x - 2y )
(x - 2y) (x + 2y )
(3x - y) (3x + y )
Answer:
(3x-2y)(3x+2y)
Step-by-step explanation:
Proof:
(3x-2y)(3x+2y)-use FOIL method (First, Outer, Inner, Last)
3x*3x+2y3x-2y3x-2y*2y
9x^2+0-4y^2
9x^2-4y^2
The answer is (3x-2y)(3x+2y).
1. Calculate your total revenue for the summer at each price. w a. $25.00 per lawn x 35 lawns per weekx 12 weeks = b. $30.00 per lawn x 20 lawns per weekx 12 weeks = c. $35.00 per lawn x 5 lawns per weekx 12 weeks =
Step-by-step explanation:
Average Cost to Mow a Lawn Per Square Foot
Most mowing pros do not charge by the square foot. For smaller properties, expect to pay between $0.01 and $0.04 per square foot.
National Average: $132
Typical Range: $49 - $219
Low End - High End: $30 - $520
royal paid 48 dollars for 12 cartons of orange juice. wha is the unit rate per carton of orange juice that royal paid
Answer:
$4
Step-by-step explanation:
If 1 carton is $4 than 12 cartons would be 48 dollars because 12*4 is 48. So each carton is $4. Please give brainliest Thanks
What’s the awnser to this please
Answer:
BC=6
Step-by-step explanation:
The perimeter is the sum of all the side lengths.
Thus, add up all the sides.
And we already know the perimeter is 64. Thus:
[tex](3z)+(10)+(z-1)+(2z+3)+(10)=64[/tex]
Combine like terms and add the numbers:
[tex]6z+22=64[/tex]
Subtract 22 from both sides:
[tex]6z=42[/tex]
Divide by 6:
[tex]z=7[/tex]
So, z is 7.
BC is z-1. Therefore:
[tex]BC=z-1\\BC=7-1=6[/tex]
So, BC is 6.
In a report prepared by the Economic Research Department of a major bank the Department manager maintains that the average annual family income on Metropolis is $48,432. What do you conclude about the validity of the report if a random sample of 400 families shows and average income of $48,574 with a standard deviation of 2000?
Answer:
This report is valid
Step-by-step explanation:
We use this z score formula to solve for a question where a random number of samples is given:
z-score is z = (x-μ)/σ/√n
where x is the raw score
μ is the population mean
σ is the population standard deviation
n = number of samples
When σ/√n = Standard error
From the above question,
x = $48,574
μ = $48,432
σ = 2000
n = 400 families
z = $48, 574 -$48,432/(2000/√400)
= $48, 574 -$48,432/(2000/20)
= $48, 574 -$48,432/100
= 1.42
The z score is 1.42
H0 = μ = $48,432
At 0.05, we reject H0 if z < - 1.96 or > 1.96
z = 1.42
Therefore, H0 cannot be rejected.
The central limit theorem also holds because a sufficiently large amount of random samples (400) where taken from the population and replaced and this causes the mean to be randomly distributed.
Therefore, from the above z score, what we can conclude about the validity of the report is that the REPORT IS VALID because H0 cannot be rejected and the central limit theorem holds.
Use the graph below to determine the number of solutions the system has.
Answer:
The system has 4 solutions
Step-by-step explanation:
When the two lines meet at a point it means that the point is a solution, in this case the lines meet 4 times.
a pack of cinnamon-scented pencils sells for 5.00 dollars what is the sales tax rate if the total cost of the pencils is 5.15
calculate the percentage increase,work out the difference (increase) between the two numbers you are comparing. Then divide the increase by the original number and multiply the answer by 100.
520-500 = 20
20÷500 =.04
.04 ×100= 4%
Find the conjugate of 9 - (-4i).
Answer:
9 + (-4i) = 9 - 4i
Which number below is not a rational number? *
325
-45
0
Square root of 3
—7times(—8) help plz
Answer:
[tex]56[/tex]
Step-by-step explanation:
[tex]-7*(-8)[/tex]
The only one thing we have to do on this question is simplify.
[tex](-7)(-8)[/tex]
And this equals
[tex]56[/tex]
Now you got your answer!
Hope this helps!
The solution to the expression -7 times (-8) is 56
How to evaluate the expressionFrom the question, we have the following parameters that can be used in our computation:
-7 times (-8)
Express using product expression
So, we have
-7 times (-8) = -7 * -8
Evaluate all the products in the expression
so, we have the following representation
-7 times (-8) = 56/1
Evaluate all the quotients in the expression
so, we have the following representation
-7 times (-8) = 56
Lastly, we have
-7 times (-8) = 56
Hence, the solution is 56
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Prove that \P(A) \cup \P(B) \subseteq \P(A \cup B) and find a counter-example to show that we don't always have equality
Answer:
P(A) ∪ P(B) ⊆ P(A ∪ B) can be proved when [tex]X[/tex] ∈ P ( A U B )
Step-by-step explanation:
To Prove that P(A) ∪ P(B) ⊆ P(A ∪ B) is attached below and also a counter example to prove that we do not always get an equality is attached below as well
Pablo drew a square that had a side of length of 6 inches. What is the perimeter of pablos square
Answer:
24 inches
Step-by-step explanation:
Because we know that Pablo drew a square, we can correctly assume that all sides have equal lengths. There are four sides to a square, so taking the number 6, 4 times (6*4) gives us 24!