Answer:
1500
Step-by-step explanation:
75 ballons in one package, mulitiply 75 by 20 to get 1500 total balloons
Answer:1500
Step-by-step explanation:
The mean of a set of 5 numbers is 12. One of the numbers in the set is 16. If 16 is removed from the list, what is the new mean?
The new mean is 11
Step-by-step explanation:
The mean = sum of the numbers ÷ numbers
The mean of a set of 5 numbers is 12One of the number is 16We need to find the new mean if 16 is removed from the set of numbers∵ The set has 5 numbers
∵ The mean of the 5 numbers is 12
- Substitute these values in the rule of the mean above
∴ 12 = sum of the numbers ÷ 5
- Multiply both sides by 5
∴ 60 = sum of the numbers
∵ One of the number is 16
∵ 16 is removed from the set of the number
- Subtract 16 from the sum and the numbers will be four numbers
∵ The new sum = 60 - 16
∴ The new sum = 44
∵ The set has 4 numbers
∴ The new mean = 44 ÷ 4 = 11
The new mean is 11
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A $50.00 pair of shoes is discounted 20%. If sales tax is 8%, what is the amount of tax paid?
A) $0.32
B) $0.40
C) $3.20
D) $4.00
Answer:
The amount of tax paid is C. $3.20
Step-by-step explanation:
If we take $50.00 and give a 20% discount, we're taking 20% of 50 and then subtracting it from the origional price (50) which brings us down to 40, because 20% of 50 is 10 and we subtract.
Now that we have $40.00, sales tax comes in at a whopping 8%. To calculate the solution of a price with sales tax, we need to find what 8% of $40 is, which after calculations will be 3.20.
Since this question is asking on tax only, our answer is $3.200, C.
Rajeev buys good worth Rs 6650.He gets a rebate of 6% on it.After getting the rebate, he pays sales tax @10%. Find the amount he will have to pay for the goods.
Rajeev will pay Rs 6876.10 for the goods.
Step-by-step explanation:
Given,
Worth of goods = Rs 6650
Rebate = 6%
Amount of rebate = 6% of worth of goods
Amount of rebate = [tex]\frac{6}{100}*6650=0.06*6650[/tex]
Amount of rebate = Rs 399
Amount after rebate = 6650 - 399 = Rs 6251
Sales tax = 10%
Amount of sales tax = 10% of amount after rebate
Amount of sales tax = [tex]\frac{10}{100}*6251=0.1*6251[/tex]
Amount of sales tax = Rs 625.10
Total amount of goods paid = Amount after rebate + sales tax
Total amount of goods paid = 6251+625.10 = Rs 6876.10
Rajeev will pay Rs 6876.10 for the goods.
Keywords: addition, percentage
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given the following formula solve for a
s = a+b+c/2
Answer:
[tex]a=2s-b-c[/tex]
Step-by-step explanation:
Given formula:
[tex]s=\frac{a+b+c}{2}[/tex]
To solve for [tex]a[/tex]
In order to solve for [tex]a[/tex] we will try to isolate [tex]a[/tex] on one side of the equation.
Steps to isolate [tex]a[/tex].
1) Multiplying both sides by [tex]2[/tex] to remove fractions.
[tex]2\times s=2\times \frac{a+b+c}{2}[/tex]
[tex]2s=a+b+c[/tex]
2) Subtracting both sides by [tex]b[/tex]
[tex]2s-b=a+b-b+c[/tex]
[tex]2s-b=a+c[/tex]
3) Subtracting both sides by [tex]c[/tex]
[tex]2s-b-c=a+c-c[/tex]
[tex]2s-b-c=a[/tex]
Thus, we successfully isolated [tex]a[/tex] on one side. The formula for [tex]a[/tex] can be given as:
∴ [tex]a=2s-b-c[/tex]
Solve this system of linear equations. Separate
the x- and y-values with a comma.
- 19x = 26 - 9
9x = 54 - 9y
HELP!!
Answer:
x=-17/19, y=131/19. (-17/19, 131/19).
Step-by-step explanation:
-19x=26-9
-19x=17
x=-17/19
9(-17/19)=54-9y
-153/19=54-9y
9y=54-(-153/19)
9y=54+153/19
9y=1026/19+153/19
9y=1179/19
y=(1179/19)/9
y=(1179/19)(1/9)
y=1179/171
y=131/19
What is the equation of the line in the slope-interception form that passes through (3,-1) and (-1,5)
Answer:
y+1=-3/2(x-3)
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(5-(-1))/(-1-3)
m=(5+1)/-4
m=6/-4
simplify
m=-3/2
y-y1=m(x-x1)
y-(-1)=-3/2(x-3)
y+1=-3/2(x-3)
Liza is driving to her sister's house 360 miles away. After 4 hours, Liza is 2 3 of the way there.
How many more hours
does Liza have to drive?
A. 3
B. 2
C.11
_
2
Liza is driving to her sister's house 360 miles away. After 4 hours, Liza is 2/3 of the way there. How many more hours does Liza have to drive?
Answer:
Liza need to drive 2 more hours to reach her sister house
Solution:
Given that Liza is driving to her sister's house 360 miles away
So total distance = 360 miles
After 4 hours, Liza is 2/3 of the way there.
[tex]\frac{2}{3} r d \text { of total distance }=\frac{2}{3} \times 360=240[/tex]
So Liza has covered 240 miles in 4 hours
Let us find the speed
The relation between distance and speed is given as:
[tex]speed = \frac{distance}{time}[/tex]
[tex]speed = \frac{240}{4} = 60[/tex]
Thus speed = 60 miles per hour
Assuming speed is same throughout the journey, let us calculate the time taken to complete remaining distance
Remaining distance = 360 - 240 = 120 miles
Now distance = 120 miles and speed = 60 miles per hour
[tex]time taken = \frac{distance}{speed}\\\\time taken = \frac{120}{60} = 2[/tex]
Thus Liza need to drive 2 more hours to reach her sister house
Describe the transformations of the graph of y=x that will produce the graph of
y = -(x + 2)2 +3.
The graph of y = x is transformed by a reflection about the x-axis, a horizontal translation to the left by 2 units, and a vertical translation upward by 3 units to produce the graph of y = -(x + 2)^2 + 3.
Explanation:The given equation is y = -(x + 2)^2 + 3, and we need to describe the transformations of the graph of y = x that will produce this graph.
The first transformation is the reflection about the x-axis, which is indicated by the negative sign in front of the original equation. This flips the graph upside down.
The second transformation is the horizontal translation to the left by 2 units, which is indicated by the addition of 2 inside the parentheses. This shifts the graph 2 units to the left.
The third transformation is the vertical translation upward by 3 units, which is indicated by the addition of 3 to the entire equation. This moves the graph 3 units up.
How do you solve 15.00 - 6.24
Answer:
8.76
Step-by-step explanation:
Simplifying
15.00 + -6.24 = b
Combine like terms: 15.00 + -6.24 = 8.76
8.76 = b
Solving
8.76 = b
Solving for variable 'b'.
Move all terms containing b to the left, all other terms to the right.
Add '-1b' to each side of the equation.
8.76 + -1b = b + -1b
Combine like terms: b + -1b = 0
8.76 + -1b = 0
Add '-8.76' to each side of the equation.
8.76 + -8.76 + -1b = 0 + -8.76
Combine like terms: 8.76 + -8.76 = 0.00
0.00 + -1b = 0 + -8.76
-1b = 0 + -8.76
Combine like terms: 0 + -8.76 = -8.76
-1b = -8.76
Divide each side by '-1'.
b = 8.76
Simplifying
b = 8.76
Inequalities and variables
Answer:
[tex]a - 6 \leqslant 15 + 8a[/tex]
[tex] - 7a \leqslant 21[/tex]
[tex]a \geqslant - 3[/tex]
Which statement is true regarding the graphed functions?
NON
-6-5-4-3-2-1
2 3
4 5
6
TO
f(0) = g(0)
f(-2) = 9(-2)
f(0) = g(-2)
There is no graph, so it is impossible to answer this question. I apologise.
Given the function f(x) = 4(x − 11) − 9, determine the value of x such that f(x) = -13.
Answer:
For x = 10, the value of the given function f(x)= 4(x − 11) − 9 is -13.
Step-by-step explanation:
Here, the given expression is:
f(x) = 4(x − 11) − 9
Now, given: f(x) = -13
⇒ -13 = 4(x − 11) − 9
Now, solving for the value of x, we get:
-13 = 4(x-11) -9
⇒ -13 = 4 x - 44 - 9
or, -13 + 44 + 9 = 4x
or, 4 x = 40
or, x = 40/4 = 10
or, x = 10
Hence, for x = 10, the value of the given function f(x)= 4(x − 11) − 9 is -13.
The height of a wooden pole, h, is equal to 15 feet. Ataut wire is stretched from a point on the ground to the top of the pole. The
distance from the base of the pole to this point on the ground, b. is equal to 8 feet.
The question is incomplete. Here is the complete question:
The height of a wooden pole, h, is equal to 15 feet. A taut wire is stretched from a point on the ground to the top of the pole. The distance from the base of the pole to this point on the ground, b. is equal to 8 feet. What is the length of the wire?
Answer:
Length of wire = 17 feet
Step-by-step explanation:
Given:
The height of the wooden pole is, [tex]h=15\ ft[/tex]
The distance from the base of the pole to this point on the ground is, [tex]b=8\ ft[/tex]
Let the length of the wire be 'l'.
Now, consider the triangle formed by the pole, the base, and the wire. The length of the wire is the slant length and hence the hypotenuse of the triangle.
Using Pythagorean theorem, we can find the hypotenuse.
[tex](Hypotenuse)^2=(height)^2+(base)^2\\l^2=h^2+b^2[/tex]
Plug in the given values and solve for 'l'. This gives,
[tex]l^2=15^2+8^2\\\\l^2=225+64\\\\l^2=289\\\\l=\sqrt{289}\\\\l=\pm17[/tex]
As length can never be negative, we ignore the negative result.
Therefore, the length of the wire is 17 feet.
Solve 13 - 2x > 21
x>-4
x > -17
x< -17
x<-4
Answer:
x>-4
Step-by-step explanation:
13-2x > 21
-13 -13
-2x >8
(-2x)/(-2) >(8)/(-2)
x>-4
A company makes and sells headphones. The
function R= - 5x² +65x + 700 gives the amount
of money the company expects to make when the
price of the headphones is x dollars. When this
function is graphed, the vertex is 6.5, 911.25).
What does the x-value 6.5 represent?
Final answer:
The x-value 6.5 in the quadratic function's vertex represents the price of the headphones in dollars at which the company's expected revenue is maximized, according to the revenue function [tex]R= - 5x^2 +65x + 700[/tex].
Explanation:
The question involves understanding the meaning of the x-value in the vertex form of a quadratic function, which in this context represents the price of the headphones for which the company expects to make the maximum revenue. The given function is [tex]R= - 5x^2 +65x + 700[/tex], and the vertex of the graph of this function is given as (6.5, 911.25). The x-value, 6.5, therefore represents the price in dollars at which the revenue of the company is maximized. This is because, in the context of a quadratic revenue model, the vertex represents the maximum point when the parabola opens downwards (which it does, since the coefficient of x² is negative), meaning that increasing or decreasing the price from this point will lead to a decrease in the total revenue.
A clothing factory makes 7,200 t shirts in one week on average there are 45 employees at the factory if each employee makes the same number of t shirts how many t shirts does each employee make in one week
Answer:
160Step-by-step explanation:
Divide 7,200 by 45
The number of t-shirts each employee make in one week is 160 if the clothing factory makes 7,200 t-shirts in one week.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
It is given that:
A clothing factory makes 7,200 t-shirts in one week on average there are 45 employees at the factory.
Let x be the number of t-shirts each employee make in one week
The value of x can be calculated as follows:
x = 7,200/45
x = 160
Thus, the number of t-shirts each employee make in one week is 160 if the clothing factory makes 7,200 t-shirts in one week.
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four times the area of the curved surface of a cylinder is equal to 6 times the sum of the areas of its bases. if its height is 12 cm find its curved surface area
Answer:
Step-by-step explanation:
Curved surface Area = 2πrh
Area of its bases = 2πr²
6* Area of its bases = 4 * Curved surface Area
6 * 2πr² = 4 *2πrh
r² / r = 4 * 2* π*12 / 6 * 2 * π { substituting h =12 cm}
r = 4*2
r = 8 cm
Curved surface Area = 2πrh
= 2 * 3.14 * 12 * 8
= 602.88 Sq. cm
Answer:
603.42
Step-by-step explanation:
Curved Surface Area = 2πrh sq.cm
Area of the base = πr² sq. cm
Sum area of the base = πr² + πr² = 2πr² sq.cm
A.T.Q
4(2πrh) = 6x2πr²
8πrh = 12πr²
2h = 3r
r = 8 cm
Curved Surface Area = 2πrh
2x22/7x8x12
4224/7
603.42
If a certain cannon is fired from a height of 8.8 meters above the ground, at a certain angle, the height of the cannonball above the ground, h, in meters, at time, t, in seconds, is found by the function h left parenthesis t right parenthesis equals negative 4.9 t squared plus 30.5 t plus 8.8. Find the time it takes for the cannonball to strike the ground.
Answer:
It would take approximately 6.50 second for the cannonball to strike the ground.
Step-by-step explanation:
Consider the provided function.
[tex]h(t)=-4.9t^2+30.5t+8.8[/tex]
We need to find the time takes for the cannonball to strike the ground.
Substitute h(t) = 0 in above function.
[tex]-4.9t^2+30.5t+8.8=0[/tex]
Multiply both sides by 10.
[tex]-49t^2+305t+88=0[/tex]
For a quadratic equation of the form [tex]ax^2+bx+c=0[/tex] the solutions are: [tex]x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
Substitute a = -49, b = 305 and c=88
[tex]t=\frac{-305+\sqrt{305^2-4\left(-49\right)88}}{2\left(-49\right)}=-\frac{-305+\sqrt{110273}}{98}\\t = \frac{-305-\sqrt{305^2-4\left(-49\right)88}}{2\left(-49\right)}= \frac{305+\sqrt{110273}}{98}[/tex]
Ignore the negative value of t as time can't be a negative number.
Thus,
[tex]t=\frac{305+\sqrt{110273}}{98}\approx6.50[/tex]
Hence, it would take approximately 6.50 second for the cannonball to strike the ground.
If someone has 16 dollars left bus used 3/7 of it how much money did they have
Answer:
$37.33 dollars
Step-by-step explanation:
16 x 7/3= 112/3
d=37.33
How do you rewrite an equation in slope-intercept form
Answer:
y = mx + b
Step-by-step explanation:
m is slope
b is y-intercept
What does y equal? Help Plz
Answer:
y = 90°
Step-by-step explanation:
You do 110° + 80° which is 180 divides by two because there is a straight line in the middle of it. I don't know how to explain it.
Answer:
90 degrees
Step-by-step explanation:
you have angles of 110 and 70 on the sides. The triangle altogether equals 180 but that doesn't matter in this equation. Since y is directly between the two angles that are given, it is 90.
110-70=40/2=20 so add 20 to 70 and subtract 20 from 110 so you get 90.
A square pyramid is 6 feet on each side. The height of the pyramid is 6 feet. What is the total area of the pyramid?
Answer:
It is B. (36√5 + 36) ft^2.
Step-by-step explanation:
Total area = area of the base + 4 * area of the triangular side.
The slant height of a triangular side = √(6^2 + 3^2)
= √45
= 3√5
The area of this side = 3 * 3 √5
= 9√5.
Therefore the total area of the pyramid
= 6^2 + 4*9√5
= (36 + 36√5) ft^2.
Write a two column proof.
can someone please help me with these questions?
I have been struggling and have lots of other work.
Happy New Years everyone! Enjoy with your family and friends
Answer:
this should be correct.
solve this inequality 6(x-5)>3(x-1)
Answer:
x>9
Step-by-step explanation:
Open parenthesis:
6x-30>3x-3
Move all like terms to one side:
6x-3x>30-3
3x>27
x>9
Find
HCF of
(726, 255).
Good evening ,
Answer:
3Step-by-step explanation:
255 = 3×5×17
726 = 2×3×11^2
Then HCF(255,726) = 3.
:)
Grant is trying to make money to help pay for college by taking a job with Brian’s bike taxis if Baltimore. He has an agreement with Brian to rent the bike for $35.00 a night. He charges customers $3.75 for every mile he transports them. If grant needs to make at least $15.00 a day, how many miles would he need to ride?
Grant needs to ride at least 13.33 miles to male at least $ 15.00 a day
Solution:
Given that Grant has an agreement with Brian to rent the bike for $35.00 a night
He charges customers $3.75 for every mile he transports them
Grant needs to make at least $15.00 a day
To find: miles needed to ride
From given question, He charges customers $3.75 for every mile he transports them
So if he transports for "x" miles he would get,
[tex]\$ 3.75 \times x = \$ 3.75x[/tex]
So the profit he gets is $ 3.75 and initial cost invested to rent bike is $ 35. Also, Grant needs to make at least $15.00 a day
So we can frame a inequality as:
[tex]3.75x - 35 \geq 15\\\\3.75x\geq 35 + 15\\\\3.75x\geq 50\\\\x \geq 13.33[/tex]
So he needs to ride atleast 13.33 miles to male atleast $ 15.00 a day
width of a rectangle is 7 meters greater than its length
Answer:
[tex]x^{2} +7x-170=0[/tex]
Step-by-step explanation:
Here is the complete question: The width of a rectangle is 7 meters greater than its length . If the area of the rectangle is 170 m², write the quadratic equation in standard form for the equation that would represent the area of the rectangle. Let x equal to the length of the rectangle.
Given: Width of rectangle is 7 meter greater than length
Length of rectangle is x.
Area of rectangle= 170 m²
Now as given, length is x meter and width is (x+7) meter
we know that, area of rectangle= [tex]length\times width[/tex]
∴ substitute the values to get correction equation.
⇒170= [tex]x\times (x+7)[/tex]
now distributing x into (x+7).
⇒ [tex]170= x^{2} +7x[/tex]
subtracting 170 both side.
[tex]x^{2} +7x-170=0[/tex]
∴ [tex]x^{2} +7x-170=0[/tex] is the quadratic equation in standard form for the equation that would represent the area of the rectangle.
A certain region currently has wind farms capable of generating a total of 2200 megawatts (2.2 gigawatts) of power. Assuming wind farms can generate 25% of their capacity, how much energy, in kilowatt-hours, can the region's wind farm generate in one year?
Given that the average household in the region uses about 10,000 kilowatt-hours of energy each year, how many households can be powered by these wind farms?
Answer:
The correct answer is A. 4,818'000,000 kilowatt-hours per year and B. 481,800 households.
Step-by-step explanation:
1. Let's review the information provided to us for solving the questions:
Power capacity of the wind farms = 2,200 Megawatts or 2.2 Gigawatts
2. Let's resolve the questions A and B:
Part A
Assuming wind farms typically generate 25% of their capacity, how much energy, in kilowatt-hours, can the region's wind farms generate in one year?
2,200 * 0.25 = 550 Megawatts
550 Megawatts = 550 * 1,000 Kilowatts = 550,000 Kilowatts
Now we calculate the amount of Kilowatts per hour, per day and per year:
550,000 Kw generated by the farms means that are capable of produce 550,000 kw per hour of energy
550,000 * 24 = 13'200,000 kilowatt-hours per day
13'200,000 * 365 = 4,818'000,000 kilowatt-hours per year
Part B
Given that the average household in the region uses about 10,000 kilowatt-hours of energy each year, how many households can be powered by these wind farms?
For calculating the amount of households we divide the total amount of energy the wind farms can generate (4,818'000,000 kilowatt-hours) and we divide it by the average household consumption (10,000 kilowatt-hours)
Amount of households = 4,818'000,000/10,000 = 481,800
If Charlie has a total of 103 marbles how many of each size does he have
find x and y
2x+3y=80
Answer:
x = 40 + -1.5y
Step-by-step explanation:
Simplifying
2x + 3y = 80
Solving
2x + 3y = 80
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-3y' to each side of the equation.
2x + 3y + -3y = 80 + -3y
Combine like terms: 3y + -3y = 0
2x + 0 = 80 + -3y
2x = 80 + -3y
Divide each side by '2'.
x = 40 + -1.5y
Simplifying
x = 40 + -1.5y