Answer: There are 168 adult tickets that were sold.
Step-by-step explanation:
Let the number of adult tickets were sold be 'a'.
Let the number of student tickets were sold be 'b'.
Since we have given that
The ticket sales for opening night totaled as
[tex]10.50a+3.75b=2071.50[/tex]
And the number of students attended = 82
so, b = 82
So, we will put the value of b in the above equation:
[tex]10.50a+3.75\times 82=2071.50\\\\10.50a+307.5=2071.50\\\\0.50a=2071.50-307.5\\\\10.50a=1764\\\\a=\dfrac{1764}{10.50}\\\\a=168[/tex]
Hence, there are 168 adult tickets that were sold.
what does the y-intercept mean in terms of the graph? Select all that apply.
a. the x-value at a y-value of 0.
b. the y-value at an x-value of 0.
c. where the function crosses the y-axis
d. where the function the x-axis
△R′S′T′ is the image of △RST under a dilation through point C. RS=5 and R′S′=8 . What scale factor was used in the dilation?
Answer:
1.6
Step-by-step explanation:
To find the scale factor, we compare the image size to the pre-image size.
R'S' = 8 and RS = 5; this makes the scale factor 8/5, which is 1.6.
Dilation is a transformation that allows you to resize an object. Dilation is a technique for making items bigger or smaller. The scale factor that was used in the dilation is 1.6.
What is dilation?Dilation is a transformation that allows you to resize an object. Dilation is a technique for making items bigger or smaller. This transformation yields a picture that is identical to the original shape. However, there is a size discrepancy in the form.
Scale factor = Dimension of the new shape/Dimension of the original shape
Given that △R′S′T′ is the image of △RST under a dilation through point C. Also, given that RS=5 and R′S′=8. Therefore, the scale factor that was used in the dilation is,
Scale factor = Dimension of the new shape/Dimension of the original shape
Scale factor = R′S′ / RS = 8/5
= 1.6
Hence, the scale factor that was used in the dilation is 1.6.
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What is 3a-2b if a=-1 and b=-2
Algebra expression ; Nine more than the product of 51 and the number T
Last year shantell bought a car for $24,000 the current value of the car is $21,000 find the percent decrease in the value of the car
Please help me with this!!!
caryssa makes bracelets to sell at craft fairs. The supplies she needed to start her business cost $45. In addition, the supplies for each bracelet cost her $3. She sells her bracelets for $5. What is the minimum number of braclets she must sell to make a profit?
For a certain model of car the distance d required to stop the vehicle if it is traveling at v mi/h is given by the formula d = v + v2 20 where d is measured in feet. kerry wants her stopping distance not to exceed 75 ft. at what range of speeds (in mi/h) can she travel? (enter your answer using interval notation.) c
The range of speeds in miles per hour Kerry can travel is [tex]-50\ge v\le30[/tex] .
Given that, a certain model of car the distance d required to stop the vehicle if it is traveling at v mi/h is given by the formula [tex]d = v + \frac{v^2}{20}[/tex].
Here,
[tex]75=v+\frac{v^2}{20}[/tex]
[tex]75=\frac{(20v+v^2)}{20}[/tex]
[tex]v^2+20v=20\times75[/tex]
[tex]v^2+20v=1500[/tex]
[tex]v^2+20v-1500=0[/tex]
[tex](v+50)(v-30)=0[/tex]
[tex]v-30=0[/tex]
[tex]v=30[/tex]
First thing is to realize what 'not to exceed' means. More than 75 feet exceeds 75 feet, but exactly 75 feet or anything less does not. So you want to determine v such that [tex]d\le75[/tex].
[tex]d=v+\frac{v^2}{20}[/tex]
is the given model. This is a reasonably good model presuming you have a better than average reaction time, dry pavement, new tires, etc. Be that as it may, you need to determine v such that:
[tex]v+\frac{v^2}{20} \le75[/tex]
Multiply by 20, we get
[tex]20v+v^2\le1500[/tex]
Add -1500 to both sides
[tex]v^2+20v-1500\le0[/tex]
[tex](v+50)(v-30)\le0[/tex]
So, [tex]v\le-50[/tex] or [tex]v\le30[/tex]
Thus, the range is [tex]-50\ge v\le30[/tex]
Therefore, the range of speeds in miles per hour Kerry can travel is [tex]-50\ge v\le30[/tex] .
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Kerry can travel at speeds in the range [tex]{(-\infty, 30]} mi/h[/tex].
To find the range of speeds Kerry can travel while ensuring her stopping distance doesn't exceed 75 feet, we need to solve the inequality [tex]v + \frac{v^2}{20} \leq 75[/tex], where v represents her speed in miles per hour.
First, we rearrange the inequality:
[tex]v^2 + 20v - 1500 \leq 0[/tex]
Next, we factor the quadratic equation:
[tex](v - 30)(v + 50) \leq 0[/tex]
This gives us two critical points: v = 30 and v = -50.
Since speed cannot be negative, we discard v = -50.
Now we test the intervals created by the critical point:
- For v < 30, the inequality holds.
- For v > 30, the inequality does not hold.
You are considering leasing one of two store sites of equal size. The first site features a percentage lease of 4% of sales per month. The second site features a triple net lease with these monthly terms: rent is 3% of sales, insurance is $175, maintenance is $50, utilities total $345, and property tax is $165. Your business plan estimates your monthly sales to average $85,000. Which lease is better for you financially?
The amount due for the first term of payment is the product of the total sales and the percentage.
(1) Amount due = ($85,000)(0.04) = $3,400
The total amount due for the second term of payment is the product of the total sales and the percentages together with all the fees specified in the item (insurance, maintenance, and utilities).
(2) Amount due = ($85,000)(0.03) + $175 + $50 + $345 = $3,120
If we are to compare the two amounts, using the second term of payment, lesser amount will be paid. Thus, the answer to this item is the second choice.
Answer: Second site
Step-by-step explanation:
just did the quiz
The quotient of y and 3 is 25
Help please !! It’s geometry credit recovery
The iq scores of the five members of the duluth family are 100, 82, 104, 96, and 118. for this distribution of scores, the range is:
Final answer:
The range of the IQ scores (100, 82, 104, 96, and 118) for the Duluth family is calculated by subtracting the lowest score from the highest (118 - 82), resulting in a range of 36 points.
Explanation:
The IQ scores of the five members of the Duluth family are 100, 82, 104, 96, and 118. To find the range of this distribution of scores, you first identify the highest and lowest scores in the set. The highest IQ score is 118, and the lowest is 82. The range is the difference between the highest and lowest scores, so:
Range = Highest score - Lowest score
Range = 118 - 82
Range = 36
Therefore, the range of the distribution of IQ scores for the Duluth family is 36 points.
A washer and a dryer cost $942 combined. The washer costs $42 more than the dryer. What is the cost of the dryer?
what is the answer to this problem?
Barbie is thinking of s number. Twenty less than one third of the number is 72. Find barbies number
One number is 5 more than another number. their sum is −15 . what are the numbers?
Show that (2-√x)^2 divided by √x can be written as 4x^(-1/2)-4+x^1/2
m=(x+n)/(p)
An answer would be sweet!! God bless
Which figures are polygons? Figure A has 6 sides all made of line segments. figure b is a regular hexagon. it has 6 sides made all of segments. Figure c is shaped iike a long semicircle. the bottom is a segment. The top part is curved. Figure D has 7 sides which are all segments.
Answer:
A,B,D
Step-by-step explanation:
i go to k-12 and the answer is correct
mixed number change into a improper fraction 3 9/12 + 6 1/2 show ur work
Ramona is ordering carpet for a room that is 19.5 feet by 41.6 feet. the carpet is $9.50 per square foot. about how many square feet of carpet will ramona need to order to cover the entire room
Can someone Please help me? How did I get this question wrong? I chose the last option, but that's incorrect. Please answer asap. Most helpful answer gets brianliest!
The triangle JKL shown on the coordinate grid below is reflected once to map onto triangle J'K'L':
If vertex L' is at (−3, 4), what are the coordinates of vertex J'?
(1, −8)
(−8, 1)
(−1, 8)
(8, −1)
Indicate the equation of the given line in standard form.
The line through (2, -1) and parallel to a line with slope of 3/4
Find the circumference of a circle with a radius of 6. Leave your answer in terms of
Look at the diagram. Which of the following is another name for < 1
A. < CBA
B. < ACB
C. < CAB
D. < BAC
Answer: A. ∠CBA
Step-by-step explanation:
We need three points to write a name of an angle. One point on each ray with the vertex lies in the middle.
There are total three ways to write a name of an angle.
For example :- M and N are points on each ray of an angle with vertex O.
Then, the name of angle can be ∠O, ∠MON or ∠NOM.
From the given picture , it can be observe that A and C are points on each ray of ∠1 with vertex B.
Then, the possible name of ∠1 will be ∠B , ∠ABC or ∠CBA.
Since, ∠CBA in given in option A.
Thus OPTION A is the correct option.
An airplane descends at a rate of 300 feet for every 5000 horizontal feet that the plane travels. What is the slope of the path of descent?
Answer:
slope=-3/50
Step-by-step explanation:
slope= y/x
y=-300
x=5000
substituting into the equation:
slope=-300/5000
What is the equation of a horizontal line passing through the point (-7,5)
The simplified version of what you’re asking, and by simolified i mean solved, is Y= 5
Manda uses the recipe shown to make punch for a family party. amanda’s punch recipe 7 parts mixed fruit juice 2 parts lemonade how much lemonade will she need to make 180 fluid ounces of punch
Answer:
40 fluid ounces of lemonade.
Step-by-step explanation:
Amanda uses the recipe shown to make punch for a family party.
Amanda's punch recipe 7 parts mixed fruit juice 2 parts lemonade.
7 + 2 = 9 parts
She will need to make 180 fluid ounces of punch.
she will need lemonade = (180/9) × 2
= 20 × 2
= 40 fluid ounces lemonade
She will need fruit juice = (180/9) × 7
= 20 × 7
= 140 fluid ounces fruit juice.
Amanda will need 40 fluid ounces lemonade to make 180 fluid ounces of punch.
Why does the limit as x approaches zero for the function f(x)=sin(π/x) not exist?
limx→0 sin(π/x)
Don't worry about the pics at the bottom plz help