Sam and Larry’s Ice Cream Shoppe sells the following sizes of ice cream cones: single at $0.89, double at $1.19; triple at $1.39. One day, Danielle sold 52 ice cream cones. She sold two more than twice as many doubles as triples. If she sold $58.98 in cones, how many of each size did she sell?
9514 1404 393
Answer:
17 singles24 doubles11 triplesStep-by-step explanation:
Let s, d, t represent the numbers of singe, double, and triple cones sold. The problem statement tells us three relationships.
s + d + t = 52 . . . . . . Danielle sold 52 cones one day
d -2t = 2 . . . . . . . doubles is 2 more than twice the number of triples
0.89s +1.19d +1.39t = 58.98 . . . . total amount of sales
__
There are many ways to solve this set of equations. A graphing calculator can quickly tell you the solution is ...
(s, d, t) = (17, 24, 11)
__
If you want to solve this by hand, it may work well to use substitution.
The second equation gives an expression for d:
d = 2t +2
The first equation gives an expression for s that can be written in terms of t.
s = 52 -d -t
s = 52 -(2t +2) -t = 50 -3t
Using these in the last equation, we have ...
0.89(50 -3t) +1.19(2t +2) +1.39t = 58.98
1.10t = 12.10 . . . . . . . . collect terms, subtract 46.88
t = 11 . . . . . . . . . . . . . . divide by 1.10
d = 2(11) +2 = 24
s = 50 -3(11) = 17
Danielle sold 17 singles, 24 doubles, and 11 triple cones.
Basic Computation: Testing M1 2 M2 A random sample of 49 measurements from a population with population standard deviation 3 had a sample mean of 10. An independent random sample of 64 measurements from a second population with population standard deviation 4 had a sample mean of 12. Test the claim that the population means are different. Use level of significance 0.01. (a) Check Requirements What distribution does the sample test statistic follow
Answer:
The sample statistics follows a standard normal distribution since the sample size are large enough.
Step-by-step explanation:
Given that:
First population:
Sample size [tex]n_1[/tex] = 49
Population standard deviation [tex]\sigma_1[/tex] = 3
Sample mean [tex]\overline x _1[/tex]= 10
Second population:
Sample size [tex]n_2[/tex] = 64
Population standard deviation [tex]\sigma_2[/tex]= 4
Sample mean [tex]\overline x_2[/tex]= 12
The sample statistics follows a standard normal distribution since the sample size are large enough.
The null and alternative hypotheses can be computed as:
[tex]\mathbf{H_o:\mu_1=\mu_2}[/tex]
[tex]\mathbf{H_1:\mu_1\ne\mu_2}[/tex]
Level of significance = 0.01
Using the Z-test statistics;
[tex]Z = \dfrac{\overline x_1 - \overline x_2}{\sqrt{\dfrac{\sigma_1^2}{n_1} + \dfrac{\sigma_2^2}{n_2}}}[/tex]
[tex]Z = \dfrac{10- 12}{\sqrt{\dfrac{3^2}{49} + \dfrac{4^2}{64}}}[/tex]
[tex]Z = \dfrac{-2}{\sqrt{\dfrac{9}{49} + \dfrac{16}{64}}}[/tex]
[tex]Z = \dfrac{-2}{\sqrt{0.18367 +0.25}}[/tex]
[tex]Z = \dfrac{-2}{\sqrt{0.43367}}[/tex]
[tex]Z = \dfrac{-2}{0.658536}[/tex]
Z = - 3.037
Z [tex]\simeq[/tex] - 3.04
The P-value = 2P (z < -3.04)
From the z tables
= 2 × (0.00118)
= 0.00236
Thus, since P-value is less than the level of significance, we fail to reject the null hypotheses [tex]H_o[/tex]
please answer, what is the solution of the system below? how do you know?
Answer:
(1,3)
Step-by-step explanation:
The solution is where the two lines intersect.
In this graph, it's (1,3)
Given the quadratic equation: 1/2x^2+3x−10=0
Answer:
x=2.3851648071345037,−8.385164807134505
Step-by-step explanation:
answer this!! will mark brainliest! 20 points
Answer:
Step-by-step explanation:
is the first choice, no other terms have anything in common with the number
399 or variable w
Sharon runs a screen-printing business. To print T-shirts each day, it costs her $200 in labor plus $5 per T-shirt for materials. Her income is $15 for each T-shirt she sells. How many T-shirts does Sharon need to sell each day in order for her costs to equal her income for that day?
(i mainly need the equation for this problem)
Answer:
Equation: 15n = 200 + 5n
Number of T-shirts: 20
Step-by-step explanation:
We need to find an expression for the costs for 1 day for making n number of T-shirts and an expression for the income for 1 day for selling n number of T-shirts. Then we set the expressions equal and solve for n, the number of T-shirts.
Expenses in 1 day:
The expenses are a fixed cost of $200 plus the cost per T-shirt.
$200 plus $5 per T-shirt
We need an expression for the cost per T-shirt in terms of n, the number of T-shirts.
If she makes 1 T-shirt, she spends $5 * 1.
If she makes 2 T-shirts, she spends $5 * 2.
If she makes n T-shirts, she spends $5 * n, or simply 5n.
Her total costs for a day are:
200 + 5n
Income in 1 day:
All the income comes from selling T-shirts.
She sells 1 T-shirt for $15 * 1.
She sells 2 T-shirts for $15 * 2.
She sells n T-shirts for $15 * n, or simply 15n
Her total income for 1 day is:
15n
Now we set the costs equal to the income and solve for n.
15n = 200 + 5n <--------- here is the equation you need
Subtract 5n from both sides.
10n = 200
Divide both sides by 10.
n = 20
Answer: She needs to sell 20 T-shirts.
259 students enrolled in a freshman level chemistry class by the end of semester 6 times the number of students passed as failed find the number of students who passed and the number of students who failed
Answer:picture?
Step-by-step explanation:
how many millilmeters are in 3 gallons
Answer:
11,356 ml.....................
Are the following equations parallel, perpendicular, or neither? y= 3x - 1 and y =
-1/3x + 10 *
Parallel
Perpendicular
Neither
Answer:
Perpendicular
Step-by-step explanation:
B=14 what is 3b-5
Please help me someone
Answer:
37
Step-by-step explanation:
14×1
24×2
42×3
42-5 = 37
What is the decimal multiplier to decrease by 2.7%?
Multiplying by 1 keeps it the same. A number greater than 1 would be an increase and a number below 1 would be a decrease.
The decrease is 2.7% which is written as 0.027 as a decimal.
Subtract that from 1:
1 - 0.027 = 0.973
The multiplier would be 0.973
Determine the total surface area of each right triangle-based prism
Answer:
small prism: 630 m²large prism: 2520 m²Step-by-step explanation:
The total surface area of the prism is the sum of the base area and the lateral area. The base area is made up of two right triangles, so will be the product of the triangle leg dimensions. The lateral area is made up of three rectangles whose width is that of the prism and whose equivalent length is the perimeter of the triangle base.
For the smaller prism, the area is ...
(20 m)(21 m) +(3 m)(20 m + 21 m + 29 m) = 420 m² +210 m² = 630 m²
The larger prism is similar, with a scale factor of 2, so its area will be 2² = 4 times that of the smaller prism:
4×630 m² = 2520 m²
__
In summary, the total surface area of each prism is ...
small prism: 630 m²large prism: 2520 m²A local insurance agent visits the high school and tells the students that his insurance company will give students a 7% discount on liability insurance, PIP. comprehensive insurance, and collision insurance for three years if they take a defensive driving course. Maria spends $1,437.00 on her auto insurance annually.
The question is vague, but I'll try and help.
Answer:
She saves $100.59 a year.
Step-by-step explanation:
Saving 7% of $1,437.00 each year.
7% of $1,437.00 (0.07 x $1,437.00) = $100.59
If it asks how much she saves over a certain number of years, just multiply 100.59 times how many years it asks for. Hope this helps.
The required, if Maria takes the defensive driving course and receives the 7% discount on her auto insurance, she will save a total of $301.77 over three years.
What is the investment?Investment is defined as when an individual spends money on something that returns him or her higher money than the money they invested.
Here,
If Maria spends $1,437.00 on her auto insurance annually and she takes the defensive driving course, she will get a 7% discount on her liability insurance, PIP, comprehensive insurance, and collision insurance for three years.
To calculate the amount of the discount, we first need to find 7% of $1,437.00:
Discount = 0.07 × $1,437.00 = $100.59
So, the amount of the discount that Maria will receive annually is $100.59.
To find the total savings over three years, we multiply the annual discount by three:
Total savings = $100.59 × 3 = $301.77
Therefore, if Maria takes the defensive driving course and receives the 7% discount on her auto insurance, she will save a total of $301.77 over three years.
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Evaluate the function at the given value. f(a) = a^3 + 5a^2 + 10a + 12 at a = -2
Answer:
4
Step-by-step explanation:
Please help me with both the questions ty.
Answer:
4) 26+4/842-/×375-^×
5)/^9+37+×+454+12
Step-by-step explanation:
Brian borrows $7,400 from Ed, who charges him 12% simple interest each year. How much will Brian pay Ed, if he repays after 5 years?
Answer:
$11,840
Step-by-step explanation:
Answer:
$11,840
Step-by-step explanation:
TRUST ME
Find the value of x.
Group of answer choices
77
34
69
146
Answer:
69
Step-by-step explanation:
Use the 3x-2 and take it out
Solve for the complimentary angle b
Answer:
b = 38
Step-by-step explanation:
The two angles form a 90 degree angle so they add to 90
b+52 = 90
Subtract 52 from each side
b+52-52 =90-52
b = 38
Answer:
38
Step-by-step explanation:
90-52=38
and the little box indicates it's a right angle which is 90 degrees
Please help I will mark brainliest
Answer:
a)(2x+1)² - 3
4x² + 4x + 1 - 3
4x² + 4x - 2
4(-2)² + 4(-2) - 2
16 - 8 - 2
6 (final answer)
b) 4(3)² + 4(3) - 2
36 + 12 - 2
46 ( final answer)
c) 2(x²-3) + 1
2x² - 6 + 1
2(3)² - 5
18 - 5
13(final answer)
Merry Christmas please help
Answer:
All Of The Number At The Top
Step-by-step explanation:
Like Said, The Tables Functions f
So, Basically It's A Challenge,
All Of The Numbers In Row X From Above Table
I Hope You Found This Answer Helpful
Good Day
You'll Get 100% Don't Stress It✨
By: LocalLesMara
how many cookies will Julie make in 7 days?
Answer:
700 cookies
Step-by-step explanation:
that's easy but there you go
Answer:
700 cookies in 7 days
Step-by-step explanation:
Which investment would be worth the MOST after 20 years?
A) An initial investment of $3000 compounded annually at a rate of 12%
B) An initial investment of $3000 compounded quarterly at a rate of 11.9%
C) An initial investment of $3000 compounded weekly at a rate of 11.85%
D) An initial investment of $3000 compounded continuously at a rate of 11.8%
Answer:
D) An initial investment of $3000 compounded continuously at a rate of 11.8%
Step-by-step explanation:
Item 12
The graph represents the height y, in feet, above the ground of a water balloon x seconds after it is dropped from a window.
Which statement is true?
Select each correct answer.
The maximum height of the water balloon occurs at x = 0.
The water balloon is in the air for 2 s.
The water balloon hits the ground in 64 s.
The water balloon rises above 64 ft before falling toward the ground.
The maximum height of the water balloon is 64 ft.
Answer:
O The maximum height of the water balloon occurs at x = 0.
O The water balloon is in the air for 2 s.
O The maximum height of the water balloon is 64 ft.
Step-by-step explanation:
Firstly, by simply looking at the x axis on the graph (time), you will see that it starts at 0 and the 64 ft maximum height is aligned with the starting point of 0 seconds.
The graph also shows (x axis) the 'time' represented, and as the height rapidly decreases the graph eventually reaches the 2 second mark, going no further and no lower.
Finally, the graph shows (y axis) the peak of the water balloon's height is 64 ft, as it is the highest number reached while the water balloon was airborne.
The following statement is True.
The maximum height of the water balloon occurs at x = 0.The water balloon is in the air for 2 s.The maximum height of the water balloon is 64 ft.A true statement to be chosen from the following.
What is a graph?The graph is a demonstration of curves that gives the relationship between the x and y-axis.
From the graph, the following points are to be noted.
The water balloon is at 64 ft at x = 0.
The water balloon takes 2 sec to reach y = 0.
The water balloon has a maximum height of x = 0.
Thus, points 1,2, and 5 are true.
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In preparation for the school play, the number of adult tickets sold by the ticket office was 5 less than twice the number of children's tickets. They sold 95 adult tickets. Write an equation you can use to find how many children's tickets were sold.
Answer:
3
Step-by-step explanation:
i think 5-2
This my homework and I'm bad at math if you can take the time please help me out f(x)= (x-5)to the power of 2 +12
I need the vertex
Axis of symmetry
Domain
Range
Answer:
Vertex: (5,12)
Axis of Symmetry: x=5
Domain: (-infinity, +infinity)
Range: [12, +infinity)
Step-by-step explanation:
What is the perimeter of the triangle?
a
84 in
b
94 in
c
74 in
d
64 in
Answer:
The answer is C
Step-by-step explanation:
We alsreadyknow that 37 and 12 is the 2 given lines. and The last line is not 37 but pretty close making C the answer.
Answer:
D) 64 In
Step-by-step explanation:
P=12+37+64
Plzzz answer it :( :
All fraction or mixed number answers are in simplest form or reduced form .
True or false
Answer:
false it is not always reduced form
In 1992, Jason bought a gallon of gas for $1.15. Yesterday, he bought a gallon of gas for $2.12. What is the percentage increase of the price of a gallon of gas from 1992 to yesterday? If necessary, round to the nearest tenth of a percent.
A.
84.3%
B.
45.8%
C.
54.2%
D.
15.7%
god please help me i’ve been stuck on this problem for hours and i’m so hungry:(
Answer:
B
Step-by-step explanation:
u should go eat
Answer:
A)
because it passes the line twice instead of once
(fuctions only cross once)
hope that helped you:)
please make my answer brainiest as im trying get 3 brainiest answers
pleassssssssse hellpp
Answer:
c
Step-by-step explanation: