The numbers of large bowl sold at the fair is 20
Data;
Total bowl sold = 32Total amount made = $916Cost of small ceramic bowl = $18Cost large bowl = $35System of EquationTo solve this problem, we need to write system of equations for this.
Let x represent the numbers of small ceramic bowl
let y represent the numbers of large ceramic bowl
[tex]x+y=32...eq (i)\\18x + 35y = 916 ...eq(ii)[/tex]
From equation (i), let's make x the subject of formula
[tex]x + y = 32\\x = 32 - y...eq(iii)[/tex]
Let's substitute equation (iii) into equation (ii)
[tex]18x+35y = 916\\x = 32 - y\\18(32 -y) + 35y = 916\\576- 18y + 35y = 916\\17y = 916 - 576\\17y = 340\\\frac{17y}{17} = \frac{340}{17}\\ y = 20[/tex]
The numbers of large bowl sold at the fair is 20
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Students are making the scenery for a school play. They use a large piece of plywood to represent the front of a house, with a semicircular window cut out. Now they need to paint the plywood. Find the area that will be painted. 2. Describe your strategy for finding the area that needs to be painted. (2 points)
Considering the figures, the area that will be painted is of 38.9 square feet.
What is the area of a rectangle?
The area of a rectangle of length l and width w is given by:
[tex]A = lw[/tex]
What is the area of a triangle?The area of a triangle of base b and height h is given by:
[tex]A = \frac{bh}{2}[/tex]
What is the area of a semi-circle?The area of a semi-circle of radius r is given by:
[tex]A = 0.5\pi r^2[/tex]
In this problem:
The rectangle with l = 6 ft and w = 8 ft will be painted, along with the triangle of dimensions b = 8 ft and h = 4 ft.The semi-circle with r = 4 ft will not be painted.Hence, the area that will be painted, in square feet, is given by:
[tex]A = 6 \times 8 + \frac{8(4)}{2} - 0.5\pi 4^2 = 64 - 8\pi = 38.9[/tex]
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-PLEASE ANSWER-
Find the other endpoint given one endpoint: (-14,9) and the midpoint: (-9,-4)
A. (-2.5, -6.5)
B. (-4, -17)
C. (-2.5, 6.5)
D. (-3.5, 7)
The posted speed limit along Elm Street is 25 mph. Homeowners living on Elm Street claim that the
average speed of automobiles traveling on Elm Street is greater than the posted limit of 25 mph and plan to
investigate their claim by measuring the speed of 20 randomly selected cars. If the data support the claim,
the residents plan to ask the city council for more police patrol along Elm Street. Here are the speeds (in
mph) of the 20 cars:
26. 2 22. 9 28. 8 29. 0 24. 8
24. 7 24. 0 24. 4 25. 2 31. 1
25. 6 21. 6 27. 4 25. 6 26. 4
23. 7 28. 2 24. 1 26. 7 26. 8
(a) Is there convincing evidence at the a = 0. 05 significance level that the true mean speed of all cars
traveling on Elm Street is more than 25 mph?
(b) Referring to your conclusion, what type of error may have been made? Describe the error in the
context of this study
The sample of the speeds of 20 cars and at a 0.05 confidence level, we
have;
(a) There is not enough convincing evidence to suggest that the true mean speed of all cars travelling on Elm Street is more than 25 mph
(b) Type II error
What are the process to test the hypothesis?(a) Based on the given data, using MS Excel, we have;
The sample size, n = 20
The mean, [tex]\overline x[/tex] = 25.86
The standard deviation of the sample, s = 2.284
The null hypothesis, H₀; [tex]\overline x[/tex] = 25 mph
Alternative hypothesis, Hₐ; [tex]\overline x[/tex] > 25 mph
Given that the sample size is less than 30, the t-test is used, and the t-score is found as follows;
[tex]t= \mathbf{\dfrac{\bar{x}-\mu }{\dfrac{s}{\sqrt{n}}}}[/tex]
Which gives;
[tex]t=\dfrac{25.86-25 }{\dfrac{2.284}{\sqrt{20}}} \approx \mathbf{1.684}[/tex]
Using a graphing calculator, we have;
The probability ≈ 0.054
The critical-t ≈ 1.729
Given that the probability is larger than the significance level, we fail to
reject the null hypothesis.
There is not enough convincing statistical evidence to conclude that the
true mean of all cars travelling on Elm Street is more than 25 mph.
(b) The type of error is Type II error, given that there is a possibility that
the null hypothesis is failed to be rejected when it is actually false.
Given that the sample size is less than 30, it may be insufficient for the
Central Limit Theorem to be in effect.
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Simplify: 1/2(8 - 6y) + 1/5(10y - 25)
Hey there!
1/2(8 - 6y) + 1/5(10y - 25)
DISTRIBUTE 1/2 & 1/5 WITHIN the PARENTHESES
= 1/2(8) + 1/2(-6y) + 1/5(10y) + 1/5(-25)
= 4 - 3y + 2y - 5
COMBINE the LIKE TERMS
= (-3y + 2y) + (4 - 5)
= -3y + 2y + 4 - 5
= -1y - 1
≈ -y - 1
Therefore, your answer is: -y - 1
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
f(x) = 2x + 7 Find a solution for the function if the dependent variable has a value of -1 Identify the independent and dependent variables. In the form of a paragraph, explain the steps necessary to find the solution. Complete your work in the space provided.
Answer:
x=-4
Step-by-step explanation:
-1=2x+7
-1-7=2x
2x=-8
x=-8/2=-4
Jessica is building a cardboard box that has a length of 16 inches, width of 9 inches, and height of 4 inches. If she decided to triple the height of the box, how much more cardboard does she need?
Answer:
Step-by-step explanation:
I assume you have a prism with a length of 16 inches, a width of 9 inches and a height of 4 inches and you want to know the surface area
1st...convert these to feet
16 in = 1 + 1/3 ft = 4/3 ft
9 in = 3/4 ft
4 in = 1/3 ft
And the surface area =
2 [ 4/3 * 3/4 + 4/3 * 1/3 + 3/4* 1/3 ] =
2 [ 1 + 4/9 + 1/4 ] =
2 [ ( 36 + 16 + 9 ) / 36 ] =
(1/18) ( 61) =
(61 / 18) sq ft ≈ 3.38 sq ft.
I hope everyone is having a lovely day!! Why is 3x+1 considered an impossible equation to solve? (basically TAKE THE POINTS!) :D love y'all!
Answer: there is no x on either sides of the equation
Step-by-step explanation:
Answer:
I answered in comments but I want the points :p
Step-by-step explanation:
What is the area of a regular triangle with perimeter = 36 in??
Round your answer to the nearest whole number.
Answer:
Step-by-step explanation:
Equilateral triangle
Solve for area
A≈62.35in²
P Perimeter
36
in
a
a
a
a
a
a
a
P
A
Using the formulas
A=3
4a2
P=3a
Solving forA
A=3P2
36=3·362
36≈62.35383in²
Triangle ABC has vertices A(1,4), B(-2,4), and C(-1, -1). A dilation with a scale factor of 0.25 and center at the origin is applied to the triangle
What are the coordinates of B' in the dilated image?
Enter your answer by filling in the boxes.
B' has a coordinate pair of (__,__)
Please help! There is no picture btw
[Figured it out (see comments), putting this here so that it stops showing up as unanswered]
Janile got 4 kilograms of candy when she went trick-or-treating at Halloween. Since she didn’t want to eat it all, she decided to share it with her 4 friends. If the 5 of them share the 4 kilograms, how much will each of them have?
200 grams
1,000 grams
500 grams
800 grams
HELP NEEDED!
Answer:
Each of them will have 0.8 kg of the Halloween candy. In a fraction form that would be 4/5.
Step-by-step explanation:
F. Evelyn is running a snack sale during lunch to raise money for charity. She is selling hot Cheetos with
cheese for $1.50 each and chili-cheese fries for $2.50 each. At the end of the day she has raised $150 and
sold 80 items. How many of each item did she sell?
The number of hot Cheetos with cheese sold is 50, while the number of chilli cheese sold is 30.
What is a System of equations?A set of simultaneous equations, often known as a system of equations or an equation system, is a finite collection of equations for which common solutions are sought.
Let the number of hot Cheetos with cheese sold be represented by x, while the number of chilli cheese is represented by y.
It is given that the total number of items sold by Evelyn during the event is 80. Therefore,
x + y = 80
x = 80 - y
Given that the cost of hot Cheetos with cheese is $1.50, while the cost of chilli cheese is $2.50, also the total amount that was collected in the event is $150. Therefore, we can write,
1.50x + 2.50y = 150
1.50(80 - y) + 2.50y = 150
120 - 1.50y + 2.50y = 150
1y = 150 - 120
y = 30
Substitute the value of y in the first equation,
x + y = 80
x + 30 = 80
x = 80 - 30
x = 50
Hence, the number of hot Cheetos with cheese sold is 50, while the number of chilli cheese sold is 30.
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The number of hot Cheetos with cheese sold is 50, while the number of chili cheese sold is 30.
What is a System of equations?
"A system of equations is a collection of two or more equations with a same set of unknowns. In solving a system of equations, we try to find values for each of the unknowns that will satisfy every equation in the system. The equations in the system can be linear or non-linear."
Let the number of hot Cheetos with cheese sold be represented by P, while the number of chili cheese is represented by Q.
It is given that the total number of items sold by Evelyn during the event is 80. Therefore,
P + Q = 80
P = 80 - Q --------- (1)
Given that the cost of hot Cheetos with cheese and chili cheese
So the equation
1.50P + 2.50Q = 150 --------- (2)
Put the equation (1) in equation (2)
1.50(80 - y) + 2.50y = 150
120 - 1.50Q + 2.50Q = 150
1Q = 150 - 120
Q = 30
Substitute the value of Q in the first equation,
P+Q = 80
P + 30 = 80
P = 80 - 30
P = 50
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evaluate the answer
12 • (-5/4)
Answer:
-15
Step-by-step explanation:
12 * (-5/4)
= -60/4
= -15
Consider the following expression and determine which statements are true.
7
- 23
+ 11
Choose 2 answers:
The entire expression is a sum
В
The coefficient of sis 3.
The term is a quotient
T
The term 2 has a variable.
Answer:
The answer is -5 well that's what I think if you go in order so it would not be The entire explanation is a sum so that leaves three more The coefficient of sis 3, The term is a quotient T, and The term has a variable so And I think the answers are The term is the quotient T and the term 2 has a variable. Hopefully, this is helpful.
Step-by-step explanation:
(9.7 x 10^6) + (8.3 x 10^5)=
Hey there!
9.7(10^6)+8.3(10^5)
9.7(1,000,000) + 8.3(100,000)
9,700,000+830,000
=10,530,000
Which equation will Alex want to use to determine the total amount of
food ( f ) a dolphin will eat over 5 years if a dolphin eats x pounds of food
per year?
A. f = 5 + x
B. f = 5x
C. f = [tex]\frac{5}{x}[/tex]
D. f = [tex]\frac{x}{5}[/tex]
Answer:
f= 5x
Step-by-step explanation:
x is the amount of food you want over 5 years so you would have to times it to get the whole amount eaten after 5 years.
of the 35 students on student counsil 60% of the students are boys how many are girls
Known facts:
total number of students on the council: 3560% of the council students are boysResults:
therefore 40% of the total number of council students are girls.Calculation:
[tex]\frac{40}{100} *35=14[/tex]
Therefore there are 14 girls.
Hope that helps!
3x-5y=4
-2x+6y=18
solve for x and y
Madison is entering a bicycle race for charity. Her mother pledges $0.80 for every .5 miles she bikes. If Madison bikes 12 miles, how much will her mother donate?
Answer:
19.2
Step-by-step explanation: take 0.80 and multiply by 24 instead of 12 so you can count the half mile
find the nth term of 67,56,45,34
Answer:
an = 67 -11(n -1)
Step-by-step explanation:
The terms of your arithmetic sequence have a common difference of -11. The first term is 67.
These values can be used in the generic formula for the n-th term:
an = a1 +d(n -1) . . . . . . first term a1, common difference d
an = 67 -11(n -1) . . . . . formula for the n-th term
Brianna is going to invest in an account paying an interest rate of 5.2% compounded continuously. How much would Brianna need to invest, to the nearest dollar, for the value of the account to reach $134,000 in 6 years?
Your answer would be 98086.
The value of money Brianna need to invest is,
⇒ P = $99,259
What is Simple interest?A quick and easy method of calculating the interest charge on a loan is called a Simple interest.
Given that;
Brianna is going to invest in an account paying an interest rate of 5.2% compounded continuously.
Here, We have;
Final amount (A) = $134,000
Time (n) = 6 years
Rate (r) = 5.2%
We know that;
⇒ Amount = P (1 + r)ⁿ
Substitute the values we get;
⇒ 134,000 = P (1 + 0.052)⁶
⇒ 134,000 = P (1.052)⁶
⇒ P = 134,000 / 1.35
⇒ P = $99,259
Thus, The value of money Brianna need to invest is,
⇒ P = $99,259
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lcm of 42 and another number is 252 what is the largest possible value of this number
Answer:
252
Step-by-step explanation:
The largest possible value of the second number is the least multiple itself: 252.
Find the missing side length.
Assume that all intersecting sides meet at right angles.
Be sure to include the correct unit in your answer.
?
Answer:
9ft
Step-by-step explanation:
14 ft (top) - 5ft (bottom) = missing side (which is 9ft)
Answer:
9ft
Step-by-step explanation:
suppose that the side of 7ft was dragged to the right till it meets the side of 4ft
and the unknown side was dragged downwards till it meets the side of 5ft
Then, also considering that all angles are right angles, this structure becomes a square.
So the answer is 14ft - 5ft = 9ft
For the function y=3x−1, when the input (x)= 7, the output (y) = ?
Answer:
y=3x-1 (replace x with 7 )
Step-by-step explanation:
y=3 (7)-1
y= 21-1
y= 20
note: multiply 3 with seven and minus 1 the answer is y so y=20
A tropical storm has been moving at 15 miles per hour for the past two days Bess recorded that the storm moved 135 miles yesterday and 75 miles today for how many hours has Bess been keeping track of the storm draw a bar diagram and a write equation to help you solve
Which is the graph of the function y=3x^2?
Answer:
Top left
Step-by-step explanation:
Since the function has a degree of 2, the curve must have a parabolic (u) shape. The only option that satisfies this is the top left graph.
About how many cells are in the human body?
You can assume that a cell is a sphere with radius 10-3 cm and that the density of a cell is approximately the density of water which is 1g/cm3.
please explain
I think its 30 trillion cells
hope it helps
What is the slope of the line in the following graph?
1. 1/3
2. 1/2
3. 2
4. 3
Answer:
1. 1/3
Step-by-step explanation:
Slope = Rise/run
=> It rises by 1, then runs by 3
=> Therefore, slope = 1/3
Need help suck on this problem
Hi!
Given:
[tex]2xy*xy^2[/tex] if [tex]x=2[/tex] and [tex]y=4[/tex]
Plug in the numbers for [tex]x[/tex] and [tex]y[/tex]
[tex]2(2)(4)*(2)(4)^2[/tex]
Using PEMDAS (Order of Operations - see below), simplify exponents first:
[tex]2(2)(4)*(2)(16)[/tex]
Multiply from left to right:
[tex](4)(4)*(2)(16)[/tex]
[tex]16*32[/tex]
[tex]512[/tex]
Your answer is 512.
-------------------------------------------------------------------------------------------------------------
ORDER OF OPERATIONS:
P - Parentheses
E - Exponents
M/D - Multiplication/Division
A/S - Addition/Subtraction
-------------------------------------------------------------------------------------------------------------
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HELP PLEASE!!!!!!!!!!!! 100 bonus points!!!! NO LINKS OR GUESSES!
Answer:
The amount increased by 102 units. The amount has increased by 120%
Step-by-step explanation:
187-85=102
85x=187
(187/85)-1=1.2
1.2*100=120
Answer:
Step-by-step explanation:
187 - 85 = 102
( 102 ÷ 85 ) × 100 = 120
please help me!! I know the answer to the question but I don't know how to get it.
Answer:
S = 3770.25 in^2
Step-by-step explanation:
20/15 = 4/3
5027/ 4/3 = 3770.25