The regular admission price for an amusement park is $72. For a group of 15, or more, the admission price is reduce by $25 per person. How many people need to be in a group to save $500?
=========================================
Explanation:
x = number of people
Without the discount, each person pays $72, so the total cost is 72x dollars if x people go through the gate individually.
Now applying the group discount, those x people pay 72-25 = 47 dollars each. Meaning the total cost is now 47x. Keep in mind that [tex]x \ge 15[/tex] in order for the discount to kick in.
Subtracting the two amounts leads to 72x-47x = 25x. It is not a coincidence that we get a coefficient of 25 here.
Set this equal to 500 and solve for x
25x = 500
x = 500/25
x = 20
------------
If x = 20 people attend individually, then they pay 72*x = 72*20 = 1440 dollars.
If 20 people go as one group, they pay 47x = 47*20 = 940 dollars
We have a savings of 1440-940 = 500 dollars. This confirms the answer.
All 20 people must go as one group if they want to save $500.
how many number of subsets in set D
Answer: A proper subset is a subset that is not identical to the original set—it contains fewer elements. You can see that there are 16 subsets, 15 of which are proper subsets. Listing the sets is fine if you have only a few elements.
The fraction model below shows the steps that a student performed to find a quotient. Which statement best interprets the quotient? There are fraction 6 and 1 over 4 two-thirds in fraction 4 and 1 over 6.
a. There are fraction 6 and 1 over 4 five and one-sixths in fraction 2 over 3.
b. There are fraction 8 and 1 over 6 two-thirds in fraction 5 and 1 over 6.
c. There are fraction 8 and 1 over 6 five and one-sixths in fraction 2 over 3.
Answer:
C. D. E. or 3. 4. 5.
Step-by-step explanation:
State the domain of the relation (1,2,3,3,4,5) (-3,-1,1,2,3)
1
2
3
Use the order of operations to fin
3 x 15 + 3 x 20 - 35 = n
by which smallest number can 275 be multiplied to get perfect square
At Sakaro's Sushi, you can get 18 wraps for $30.06 What is the price for 1 wrap?
Answer: $1.67
Let's make an equation for the problem. To find the price for each sushi roll, divide the price by the number of sushi rolls.
30.06 ÷ 18 = 1.67
The GCF of 14 and a number is 7. Which of the following could be the number?
A 49
B 42
C 56
Answer:
A 49
Step-by-step explanation:
Any odd number that has 7 as a factor will be a candidate. Of the choices listed, the only possibility is ...
49
__
If the number is even and has 7 as a factor, then it will be a multiple of 14. That is, the GCF will not be 7, but will be 14. Hence, the number must be an odd multiple of 7.
Rewrite the following using the GCF and Distributive properly ?
63 + 27
I would really appreciate some help. Thanks!
Seth has game and education apps on his tablet. He noticed that he has 5 game apps for every 2 education apps. Which of the following is another way to write this ratio?
A. 2:3
B. 2:5
C. 3:2
D. 5:2
Answer:
D
Step-by-step explanation:
the question says that he has 5 to 2 and if you put it in a fraction you cant reduce it so therefore the answer has to be 5:2
Answer:
D. 5:2
Step-by-step explanation:
He has 5 games so 5: for every 2 school apps so 5:2
HELP!!!! (zoom in to see it better)
Answer:
C and D
Step-by-step explanation:
The lines are parallel to eachother dont worry about what the lines is in the middle
for the second question, it is the same thing, the lines are both going straight
which means that they are parallel
Answer:
C and D
Step-by-step explanation:
This table gives a few (x, y) pairs of a line in the coordinate plane. What is the y-intercept of the line?
Answer:
The Y-intercept is the Y value when X = 0.
Find the change in X:
-56 to -42 = 14
-42 to -28 = 14
The X value changes by 14.
For every change in X the Y change:
66-58 = 8
58-50 = 8
For X to get from -28 to 0 would be 2 more changes:
-28 +14 = -14
-14 + 14 = 0
2 more changes of Y would be:
50-8 = 42
42-8 = 34
So when X = 0, Y = 34
The Y-intercept would be (0,34)
Step-by-step explanation:
like if it helps <3
The toco toucan, the largest member of the toucan family, possesses the largest beak relative to body size of all birds. This exaggerated feature has received various interpretations, such as being a refined adaptation for feeding. However, the large surface area may also be an important mechanism for radiating heat (and hence cooling the bird) as outdoor temperature increases. Here are data for beak heat loss, as a percent of total body heat loss, at various temperatures in degrees Celsius:
Temperature (degrees Celsius) 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Percent heat loss from beak 35 36 38 28 41 43 55 46 39 54 45 58 60 56 62 67
a. The equation of the least-squares regression line for predicting beak heat loss, as a percent of total body heat loss from all sources, from temperature is: _____ (Use decimal notation. Give your answer to four decimal places.)
b. Use the equation to predict (
±
0.01) beak heat loss, as a percent of total body heat loss from all sources, at a temperature of 25 degrees Celsius.
c. What percent (
±
0.01) of the variation in beak heat loss is explained by the straight-line relationship with temperature?
d. Find the correlation r (
±
0.001) between beak heat loss and temperature.
Answer:
Kindly check explanation
Step-by-step explanation:
Given the data:
Temperature (degrees Celsius) : 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Percent heat loss from beak : 35 36 38 28 41 43 55 46 39 54 45 58 60 56 62 67
Using an online regression calculator ; the regression equation obtained is :
ŷ = 2.0927X + 0.6029
X = independent variable
Y = predicted variable
2.0927 = slope
0.6029 = intercept
B.) temperature = 25
ŷ = 2.0927(25) + 0.6029
= 52.9204
C.) the explained variance is the value of the coefficient of determination (R²) which is the square of the correlation Coefficient
0.8785² = 0.7718
D.) the correlation Coefficient r is 0.8785 using the Coefficient of regression calculator
A coral reef grows 0.14 m every week. How much does it grow in 14 weeks? Write your answer in millimeters.
Answer:
0.14*14= 1.96
Step-by-step explanation:
Must multiply 0.14 times 14 for the answer.
Text a friend and write a clear set of instructions on how to find a ratios amount
Answer:
Hi ___
A ratio is created from two numbers it can also be a fraction.
To find a ratio you have to have 2 numbers
You can take these 2 numbers and divide them so they are a unit ratio
For example 3:6 can be reduced to 1:3
Step-by-step explanation:
Hope this helps please give brainliest
If a =
3
5
, b = 3, c = 1, d = 5, which equality is true?
A)
d
a
=
b
c
B)
a
b
=
c
d
C)
b
a
=
c
d
D)
a
d
=
b
c
Answer:
could you give a picture of the problem. cause I may be able to help but I cant really understand the question with what you typed
Answer:
D
Step-by-step explanation:
just took this test
please help me with this i will mark you brainliest
Answer:
(-3,7)
Step-by-step explanation:
Hope it helps
David has 574 cereal bars that he wants to fit in bags of 10 and bags of 8. The number of bags of 8 is 2 more than the number bags of 10. How many bags of 8 and 10 can david pack the cereal bar into
Answer: lol have the same question
Step-by-step explanation:
Please help I would appreciate
Answer:
the 1st 2nd and 5th since if there is even one negative in the fraction it makes the whole fraction negative
Helppp me plssss! ASAP
Answer:
140 ft.
Step-by-step explanation:
first find the area of the rectangle
16 x 8 = 128
Area: 128
then find the area of the triangle
Base: 4
Height: 6
Area: 12
Then all u need to do is add
12 + 128 = 140
Jon used 64.4 cups of flower to make 8 loaves of bread. How much flower did he use for each loaf?
Answer:
8.05 cups per loaf
Step-by-step explanation:
divide 64.4 and 8
equation
64.4÷8=8.05
*HELP*. I need help on this stuff on I-ready... *HELP*
Answer:
First one
Step-by-step explanation:
50 + 30 can be broken up into (10x5)+(10x3). You can simplify that into 10(5+3) because 10 x 5 =50 and 10x 3 = 30. :)
Answer:
10(5+3)
Step-by-step explanation:
If If you multiply 5 and 3 by 10 you'll get 50 + 30
12x + 7 < -11
OR
5.2 – 8 > 40
Answer:
x < - 3/2 or x > 48/5 (option a in your list of answers)
Step-by-step explanation:
We solve for x in each inequality:
12 x + 7 < -11
subtract 7 from both sides:
12 x < - 11 - 7
12 x < -18
divide both sides by 12 to isolate "x" on the left:
x < - 18 / 12
simplify a common factor 6 in numerator and denominator on the right:
x < - 3 / 2
Now the other inequality:
5 x - 8 > 40
add 8 to both sides:
5 x > 40 + 8
5 x > 48
divide both sides by 5:
x > 48 / 5
So the answer is:
x < - 3/2 or x > 48/5
which coincides with answer a) in your list.
Mr. Javier purchased a number of pencils for ₱180 and sold all except 6 at a profit of ₱2 per pencil. With the total amount received, he could buy 30 more items than before. Find the number of items he bought and the cost of each in pesos
Answer:
36 pencils
[tex]Cost = 0.2[/tex]
Step-by-step explanation:
Given
Cost Price = 180
Represent the number of items by x
This implies that the cost of each item is [tex]\frac{x}{180}[/tex]
[tex]Selling\ Price = Cost + Profit[/tex]
[tex]Selling\ Price = \frac{x}{180} + 2[/tex]
Since all but 6 items were sold, the total selling price is:
[tex]Total = (x - 6)(\frac{x}{180} + 2)[/tex]
This amount can be used to buy 30 more items.
So, we have:
[tex](x - 6)(\frac{x}{180} + 2) = x + 30[/tex]
Multiply both sides by 180
[tex]180 * (x - 6)(\frac{x}{180} + 2) =180(x + 30)[/tex]
[tex](x - 6)(x + 360) = 180x + 5400[/tex]
Expand brackets
[tex]x\² + 360x - 6x - 2160 = 180x + 5400[/tex]
[tex]x\² + 354x - 2160 = 180x + 5400[/tex]
Equate to 0
[tex]x\² + 354x - 180x - 2160 - 5400 = 0[/tex]
[tex]x\² + 174x - 7560 = 0[/tex]
Expand
[tex]x\² + 210x - 36x - 7560 = 0[/tex]
[tex]x(x + 210) - 36(x + 210) = 0[/tex]
[tex](x - 36)(x + 210) = 0[/tex]
[tex]x - 36 = 0[/tex] or [tex]x + 210 = 0[/tex]
[tex]x = 36[/tex] or [tex]x = -210[/tex]
Since, number of items can't be negative, we have to discard x = -210.
Hence:
[tex]x = 36[/tex]
We can then conclude that, Mr. Javier purchased 36 pencils
Recall that
[tex]Cost = \frac{x}{180}[/tex]
[tex]Cost = \frac{36}{180}[/tex]
[tex]Cost = 0.2[/tex]
if m 2 =6x+8 and m 6 = 8x-6, find the value of x so that l is parallel to m
Answer:
[tex]x = 7[/tex]
Step-by-step explanation:
Given
[tex]m_2 = 6x + 8[/tex]
[tex]m_6 = 8x - 6[/tex]
Required
Determine x when both lines are parallel
For parallel lines, slopes must be equal.
i.e.
[tex]m_1 = m_2[/tex]
In this case,
[tex]m_6 = m_2[/tex]
Substitute values for m6 and m2
[tex]8x - 6 = 6x + 8[/tex]
Collect Like Terms
[tex]8x - 6x = 8 + 6[/tex]
[tex]2x = 14[/tex]
Solve for x
[tex]x = 14/2[/tex]
[tex]x = 7[/tex]
Answer:7
Step-by-step explanation:
Find the value of
5x^2 if x = -3.
Step-by-step explanation:
5x²
If x = 3
Then,
5(3)²
= 5×9
= 45
Which transformation of a shape may result in a new shape not congruent with the original shape?
O dilation
O reflection
O rotation
O translation
Answer:
dilation
Step-by-step explanation:
dilation will make the shape larger or smaller which will change the shape.
ms.smith bought a 5 pound bag of candy for her 6th grade classroom.She gave away 2 pounds of candy to her students during the first unit of instructions and ate 6 ounces of candy during planning.How many ounces of candy does Ms.Smith still have in her bag?
Answer:
42
It was on my test I put 42 a day later i checked my test the answer was correct. Sorry that I didn't really have a explanation.
But at least its correct.
Ms. Smith still have 42 ounces of candy in her bag.
What is Subtraction?To subtract means to take away from a group or a number of things.
Given that Ms. Smith bought a 5 pound bag of candy for her 6th grade classroom. She gave away 2 pounds of candy to her students during the first unit of instructions and ate 6 ounces of candy during planning.
1 pound = 16 ounces
She gave away 2 out of 5 pounds, so she is left with 5 - 2 = 3 pounds
3 pounds = 16*3 ounces = 48 ounces
She ate 6 ounces of candy
Therefore, she now has, 48 - 6 = 42 ounces of candies left with her.
Hence, Ms. Smith still have 42 ounces of candy in her bag.
For more references on Subtraction, click;
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Which expression is a prime polynomial, x^3-1, x^2+1, x^3+1, x^2-1
Answer:
[tex]x^2+1[/tex] cannot be factored, thus it's a prime polynomial
Step-by-step explanation:
A prime number or expression cannot be factored in any factor different from 1 and the number or expression itself.
One of the following expressions is prime. The rest of them can be factored.
[tex]x^3-1[/tex] is the difference of two cubes. It can be factored as:
[tex]x^3-1=(x-1)(x^2+x+1)[/tex]
[tex]x^3+1[/tex] is the sum of two cubes. It can be factored as:
[tex]x^3+1=(x+1)(x^2-x+1)[/tex]
[tex]x^2-1[/tex] is the difference of two squares. It can be factored as:
[tex]x^2-1=(x-1)(x+1)[/tex]
[tex]\mathbf{x^2+1}[/tex] cannot be factored, thus it's a prime polynomial
the value of x in logx(9/63)=1/2 is
Answer: x = 7/2
Step-by-step explanation: u juss simplify 1/2 x 7 to 7/2 so x = 7/2
The value of x in logarithmic equation [tex]log_{10}x(\frac{9}{63} )=\frac{1}{2}[/tex] is [tex]1000\sqrt{10}[/tex].
What is a logarithmic equation?
"A logarithmic equation is an equation that involves the logarithm of an expression containing a variable."
Given logarithmic equation
[tex]log_{10}x(\frac{9}{63} )=\frac{1}{2}[/tex]
⇒ [tex]log_{10}x(\frac{1}{7} )=\frac{1}{2}[/tex]
⇒ [tex]log_{10}x=\frac{1}{2}({7} )[/tex]
⇒ [tex]log_{10}x=\frac{7}{2}[/tex]
⇒ [tex]x = 10^{\frac{7}{2} }[/tex]
⇒ [tex]x = 10^{3+\frac{1}{2} }[/tex]
⇒ [tex]x = 10^{3}[/tex] × [tex]10^{\frac{1}{2} }[/tex]
⇒ [tex]x = 1000\sqrt{10}[/tex]
The value of [tex]x = 1000\sqrt{10}[/tex]
Hence, the value of x in logarithmic equation [tex]log_{10}x(\frac{9}{63} )=\frac{1}{2}[/tex] is [tex]1000\sqrt{10}[/tex].
Learn more about logarithmic equation here
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