FOR 20 points
Show your work neatly for each problem.
1. Michelle and Cameron are selling popcorn for a school fundraiser. Michelle sold 10 tins of cheese
popcorn and 8 tins of caramel popcorn for a total of $446. Cameron sold 22 tins of cheese popcorn and
11 tins of caramel popcorn for a total of $803. Write a system of equations to determine the cost one tin
of cheese popcorn and one tin of caramel popcorn. Show all your work.
Answer:
one tin of cheese $23
one tin of caramel $27
Step-by-step explanation:
let 'x' = cost of cheese tin
let 'y' = cost of caramel tin
10x + 8y = 446
22x + 11y = 803
i multiplied the first equation by -11 and the second by 8 to eliminate the 'y' terms
-110x - 88y = -4906
+ 176x + 88y = 6424
66x = 1518
x = 1518 / 66
x = 23
find 'y': 10(23) + 8y = 446
230 + 8y = 446
8y = 216
y = 27
1. Evaluate the expression for the given value of the variable. 4(z+ 4) + 5 for z = 2
A 4(2z + 4) +5
B -3
C 17
D 29
Answer:
D
Step-by-step explanation:
4(z+ 4) + 5 z = 2
4(2+4)+5
4(6)+5
24+5
=29
Answer:
theres a bunch of online calculators for equations of any type I reccomend saving your points for other subject questions
Step-by-step explanation:
calculate the unit rate of change for each linear function using the formula. (4,9) (8,12) (16,18) (32,30)
Answer:
The unit rate of change is of [tex]\frac{3}{4}[/tex]
Step-by-step explanation:
We are given a set of points (x,y).
To find the unit rate of change, we take two points, and divide the change in y by the change in x.
Points (4,9) and (8,12)
Change in y: 12 - 9 = 3
Change in x: 8 - 4 = 4
Unit rate of change: [tex]\frac{3}{4}[/tex]
A grid has lines at 90-degreree angles. There are 12 lines in one direction and 9 lines in the other direction. Lines that are parallel are 11 inches apart. What is the least number of 12in by 12in floor tiles needed to cover all of the line intersections of the grid? The tiles do not have too touch each other.
Answer:
70
Step-by-step explanation:
Given that:
There are twelve (12) lines in a direction and another nine 9 lines in another direction.
If we draw the above illustration out, we will realize that we will have 11 squares by 8 squares.
i.e these 11 squares are 11 inches apart.
Hence, the length of their grid = 11 inches × 11 inches = 121 inches²
Thus, for 12 in by 12 in tiles; we will have:
= [tex]\dfrac {121}{12}[/tex]
= [tex]10 \dfrac{1}{12}[/tex]
This implies that there are 10 files with just [tex]\dfrac{1}{2}[/tex] inch gap in length.
Similarly, for 8 squares and 11 inches apart;
The width = 8 inches × 11 inches = 88 inches²
Thus; the 12 in tiles needed = [tex]\dfrac{88}{12}[/tex]
= [tex]7 \dfrac{1}{3}[/tex]
It signifies that there are 7 tiles with [tex]\dfrac{1}{3}[/tex] inch gap in width.
Thus, the least number of tiles required = 10 × 7 = 70
The next number in the arithmetic sequence 10, 23, 36, __is:
49.
46.
43.
50.
Answer:
49
Step-by-step explanation:
Answer:
49
Step-by-step explanation:
From the sequence it is obvious that the next number was simply the addition of 13, so by adding 13 to 36 we get 49
I NEED HELP ( WILL GET BRAINLYIST FOR CORRECT ANSWER)
Answer:
36 units.
Step-by-step explanation:
Will mark brainliest!!
Solve for x
Answer:
The x=22
Step-by-step explanation:
What is the distance between point (8,4) and point (3,2) rounded to the nearest tenth?
Step-by-step explanation:
the answer of this question is 5.39
Simplify
(45x6y%) = (5x4y2
Answer:
0 would be your anwswer
Step-by-step explanation:
does anyone know when the next season of cobra kai is coming out?
Answer:
Early 2022
Step-by-step explanation:
Lila decided to make more baked goods for the bake sale. She used 1/8 less flour to make bread to make cookies. She used 1/4 more flour to make cookies than to make brownies. If she used 1/2 of flour to make the bread, how much flour did she use to make the brownies. Explain your answer.
Answer:
3/7 cup
Step-by-step explanation:
Ignore the units for the time being. Just to give it units, you could call it cups. This question is really about ratios.
Let the cookies = x
Then the bread = x - 1/8 x = 7/8x
The brownies = cookies - 1/4 cookies
The brownies = 3/4 cookies = 3/4 x
==============
Now start again.
The bread uses 1/2 cup.
That translates into 1/2 = 7/8 x
x = 1/2 // 7/8 = 4/7 cup for the cookies (4/7 is larger than 1/2)
Whatever the cookies are, the brownies take 3/4 as much
4/7 * 3/4 = 12/28 = 3/7
The answer should be 3/7 of a cup.
9514 1404 393
Answer:
3/8 lb
Step-by-step explanation:
If all units are pounds, then we have ...
bread = cookies - 1/8 lb
cookies = brownies + 1/4 lb
bread = 1/2 lb
Using the last value in the first equation, we find ...
1/2 lb = cookies - 1/8 lb
cookies = 5/8 lb . . . . . . . add 1/8 lb to both sides
Using this in the second equation gives ...
5/8 lb = brownies + 1/4 lb
3/8 lb = brownies . . . . . subtract 1/4 lb from both sides
__
Lila used 3/8 lb of flour to make the brownies.
PLZ HELP MY TEACHER IS GIVING ME SO MUCH WORK
If you walking on the sidewalk and your pencil falls how many toddlers did you eat last night with Tom Holland???
Solve for k:
8 36
K 1.8
Step-by-step explanation:
I there a picture for the problem ?
help plss , thanksss !!
Answer:
a or c
Step-by-step explanation:
What is the area, in square feet, of the rectangle shown below?
Answer:
D
Step-by-step explanation:
= 34/5 × 19/4
= 646/20
= [tex]32 \frac{6}{20} [/tex]
The area of the given rectangle is [tex]32\frac{6}{20}[/tex] square feet
For better understanding check the calcualtion here .
Calcualtion :
Area of the rectangle is the space inside the given triangle .
Formula : Formula to find the area of the triangle is length times width
Length and width are given as mixed fractions
Lets convert mixed fractions into improper fractions
[tex]Length =6\frac{4}{5}=\frac{6 \cdot 5+4}{5}=\frac{34}{5} \\Width=4\frac{3}{4}=\frac{4 \cdot 4+3}{4}=\frac{19}{4}[/tex]
Now we find out the area
[tex]Area= length \cdot width \\Area=\frac{34}{5} \cdot \frac{19}{4} \\Area= \frac{646}{20}[/tex]
Now we divide the number and find out the quotient and remainder
[tex]Area= \frac{646}{4} \\Quotient = 32 \\remainder =6\\Area= 32\frac{6}{20}[/tex]
The area of the given rectangle is [tex]32\frac{6}{20}[/tex] square feet
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find the value of x in the equation below.
x+1=6
A beachfront hotel is planning for its summer busy season. It wishes to estimate with 95% confidence the average number of nights each guest will stay in a single visit. Using a sample of guests who stayed last year, the average number of nights per guest is calculated at 5 nights. The standard deviation of the sample is 1.5 nights. The size of the sample used is 120 guests and the beachfront hotel desires a precision of plus or minus 0.5 nights.
Required:
a. What is the standard error of the mean in the lakefront resort example?
b. Within what range below can the resort expect with 95% confidence for the true population mean to fall?
Answer:
0.1369
(4.732, 5.268)
Step-by-step explanation:
Given that:
Mean, m = 5
Standard deviation, s = 1.5
Error margin, E = 0.5
Sample size, n = 120
Zcritical at 95% = 1.96
Standard Error of the mean (S. E) :
S. E = s /sqrt(n)
S. E = 1.5 / sqrt(120
S.E = 1.5 / 10.954451
S. E = 0.1369306
S. E = 0.1369
Confidence interval (C. I)
Mean ± (Zcritical * S.E)
5 ± (1.96 * 0.1369)
Lower boundary = 5 - 0.268324 = 4.731676
Upper boundary = 5 + 0.268324 = 5.268324
(4.732, 5.268)
Find two integers whose sum is -9 and product is 14
for the figure below, give the following
Answer:
(a) <1 & <6 (b) <5 & <6 (c) 7 & <3
Step-by-step explanation:
Vertical angles are angle that make an X
Linear pair angles are next to each other
Supplementary angles are angles that form a straight line
Answer:
a) 1 and 6 , 3 and 8, 7 and 4, or 2 and 5
b) 5 and 6
c) 1 and 5
Step-by-step explanation:
I need help... plssss :))
Answer:
(1, -1), (1, -2), (2, -3), (2, -4)
NO
Step-by-step explanation:
✔️Each ordered pair is written as (input, output).
Thus, we would have the following:
(1, -1), (1, -2), (2, -3), (2, -4)
✔️This cannot be a function because every input value do not have exactly one output value related to it. A function should not have an input value related to more than one output value.
So, the answer is NO. It is not a function.
John has 4.5 x 10^6 dollars in his bank account. Jacob has 1.3 x 10^7 dollars in his bank account. who has more money and by how much
Answer:
Jacob has more. $8,500,000 more.
Step-by-step explanation:
4.5 x 10^6 can be expressed as 4500000. and 1.3 x 10^7 can be expressed as 13000000. subtract, and you get %8,500,000
A rectangular room measures 21 feet by 28 feet with a 10-foot-high ceiling. The flooring is being replaced with carpeting that sells for $10.45 per square foot and entails a $149 installation fee. What is the total pricing for the carpeting with an 8.0% sales tax
9514 1404 393
Answer:
$6,797.09
Step-by-step explanation:
The area of the floor is ...
(21 ft)(28 ft) = 588 ft²
Then the cost of the carpet material is ...
(588 ft²)($10.45/ft²) = $6,144.60
The subtotal with installation fee is ...
$6,144.60 +149.00 = $6,293.60
Adding the sales tax multiplies this amount by 1 +8% = 1.08, so the final price is ...
1.08 × $6,293.60 = $6,797.09 . . . total price
Find the slope of the line that passes through the points (2,8) and (6,8).
Answer:
8-8/6-2
0/4
answer is 0
y=0x+c
8=0(2)+c
8=0+c
8=c
y=0x+8 i thinkkk
Step-by-step explanation:
Answer:
8-8/6-2
0/4
answer is 0
y=0x+c
8=0(2)+c
8=0+c
8=c
y=0x+8
Step-by-step explanation:
3 Times Square root of 200 simplified
Answer:
C. [tex]30\sqrt{2}[/tex]
I hope this helps!
The simplified form of expression 3 times the square root of 200 is 30√2 ( thirty times square root 2 ) .
To simplify the expression 3 times the square root of 200, we can break it down into smaller components .
First, let's simplify the square root of 200 :
√ 200 = √ ( 100 × 2 ) = √ 100 × √ 2 = 10√2
Now, we substitute this simplified value back into the original expression :
3 × √ 200 = 3 × ( 10√ 2 ) = 30√ 2
Therefore, the simplified form of 3 times the square root of 200 is 30√2 .
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A biologist studied the frequency of croaks for frogs from two different regions. From a random sample of 32 frogs located in the northern region, the mean number of croaks per hour was 21.3, and from a random sample of 38 frogs located in the southern region, the mean number of croaks per hour was 28.9. To estimate the difference in the mean number of croaks (southern minus northern), a 95 percent confidence interval was constructed from the samples. The interval was reported as (7.1, 8.1). Which of the following claims is supported by the interval?
A. All southern frogs croak more times per hour than do all northern frogs.
B. The northern frogs are likely to have a greater mean number of croaks per hour than the southern frogs.
C. The southern frogs are likely to have a greater mean number of croaks per hour than the northern frogs.
D. All frogs in the study have about the same number of croaks per hour.
E. The northern and southern frogs have the same mean number of croaks per hour.
Answer:
C
Step-by-step explanation:
Since at the 95% confidence, the difference between the number of croaks per hour between southern and northern region frog is lying in the rage 7.1 to 8.1, this shows that the southern region's frogs' croak frequency is highly likely to be greater than that of northern region's frogs' croaks' frequency.
The claim supported by the interval is
Option C. The southern frogs are likely to have a greater mean number of croaks per hour than the northern frogs.
What does the interval tell obtained in the hypothesis testing?The interval we obtain at certain confidence tells that the value of the test statistics will lie in that interval with that confidence.
How to identify what is the obtained interval indicating?Since the test statistics was measuring the croak frequency difference
with southern - northern, and since at 95% confidence, the difference will lie in interval (7.1, 8.1), which is positive, thus the frequency of crocks for southern frogs is greater than the frequency of crocks for northern frogs.
Thus,
The claim supported by the interval is
Option C. The southern frogs are likely to have a greater mean number of croaks per hour than the northern frogs.
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Kimmie sells custom T-shirts for $12 each at the flea market every Saturday She usually sells 36 T-shirts Kimmie surveys her customers about whether they would buy her T-shirts at a different price. She determines that for every $1 increase in price she would sell two fewer T-shirts and for even $1 decrease in price, she would sell two more T-shirts, Which quadratic function can Kimmie use to model price increments vs. total income so that she can find the price at which her income is maximized?
Answer:
y = -2*x² + 60*x
Step-by-step explanation:
The general form of a quadratic function is:
y = a*x² + b*x + c
We need to determine a ; b ; and c. For that we have three conditions therefore
Condition 1 at x = 12 $ each T-shirts kimmie sells 36 units, then she gets
12* 36 = 432 $ or y = 432 and
432 = a(12)² + 12*b + c or 432 = 144*a + 12*b + c
Second condition selling at 13 $ each T-shirt she sells 34 , then
13*34 = 442
442 = a(13)² + 13*b + c or 442 = 169*a + 13*b + c
And the third condition
11*38 = 418
418 = a* ( 121) + 11*b + c 418 = 121*a + 11*b + c
We have a three equation system
432 = 144*a + 12*b + c (1)
442 = 169*a + 13*b + c (2)
418 = 121*a + 11*b + c (3)
We need to solve it for a, b and c
Subtracting (2) - (1) 10 = 25*a + b and subtracting (2) - (3)
24 = 48*a + 2*b
Then b = 10 - 25*a and 24 = 48*a + 2*( 10 - 25*a )
24 = 48*a + 20 - 50*a
24 - 20 = -2*a
4 = - 2*a
a = - 2 and b = 10 - 25*( -2) b = 60
Finally c is: 432 = 144*a + 12*b + c
432 = 144* ( -2) + 12*60 + c
432 = - 288 + 720 + c
432 = 432 + c
c = 0
The quadratic function is:
y = -2*x² + 60*x
Need help in math!!!!!!!!
Answer:
1.9x+2(1.5)>30
Step-by-step explanation:
1.9(15)+2(1.5)
28.5+3
31.5 dollars
therefore the equation is grater than 30 dollars
Write the standard form of the equation of the circle below.
Center (0,-1) passes through the point (-1,-2)
Answer:
[tex]x^2+(y+1)^2=2[/tex]
Step-by-step explanation:
We use the formula for a circle with center at (0, -1), that goes through the (x, y) point (-1, -2):
[tex](x-0)^2 + (y-(-1))^2 = R^2\\Using \,\,\,point\,\,\,(-1, -2)\\(-1-0)^2+ (-2+1)^2 = 1 + 1 = 2 = R^2[/tex]
Therefore, the equation of this circle can be written as:
[tex]x^2+(y+1)^2=2[/tex]
6 more than 7 times 3 ?
Answer:
27
Step-by-step explanation:
A bass guitarist worked on 15 music projects last year. He wrote and produced 5 projects. He wrote a total of 9 projects. Use a Venn diagram to determine:
a. How many projects he wrote but did not produce
b. How many projects he produced but did not write.
Let W be the set of projects the bass guitarist wrote and P be the set of projects he produced
Step-by-step explanation:
W = Set of projects the guitarist wrote
P = Set of products he produced
A bass guitarist worked on 15 music projects last year.
Universal set = 15
He wrote and produced 5 projects.
W ∩ P = 5
He wrote a total of 9 projects.
W = 9
The Venn Diagram is given in the attached image.
a. How many projects he wrote but did not produce (W - P)?
W - P = W - W ∩ P
W - P = 9 - 5 = 4
He wrote 4 projects but did not produce them.
b. How many projects he produced but did not write (P - W)?
Universal set = (W - P) + (P - W) + W ∩ P
15 = 4 + (P - W) + 5
(P - W) = 15 - 9 = 6
He produced 6 projects but did not write them