Answer:
65 quarts of water and 39 quarts of juice are required to make 104 quarts of banana berry smoothies
Step-by-step explanation:
Given:
Ratio of water and juice in banana berry smoothies = [tex]5:3[/tex]
To find:
Amount of water and juice required to make 104 quarts of banana berry smoothies
Solution:
Amount of water required to make 104 quarts of banana berry smoothies = [tex]\frac{5}{8}[/tex]×104 = 5×13 = 65 quarts
Amount of juice required to make 104 quarts of banana berry smoothies = [tex]\frac{3}{8}[/tex]×104 = 3×13 = 39 quarts
So,
65 quarts of water and 39 quarts of juice are required to make 104 quarts of banana berry smoothies.
To make 104 quarts of banana berry smoothies with a water to juice ratio of 5:3, Just Juice should mix 65 quarts of water with 39 quarts of juice.
Explanation:To make banana berry smoothies with a mix of water and juice in a ratio of 5 to 3, and to create a total of 104 quarts, we need to find the amount of water and juice separately. Since the total parts of the ratio is 5 parts water plus 3 parts juice, which equals 8 parts, we can calculate the amount of each as follows:
Divide the total amount of smoothie by the total number of parts: 104 quarts / 8 parts = 13 quarts per part.Multiply the quarts per part by the number of parts for water: 13 quarts x 5 parts = 65 quarts of water.Multiply the quarts per part by the number of parts for juice: 13 quarts x 3 parts = 39 quarts of juice.Therefore, Just Juice should mix 65 quarts of water with 39 quarts of juice to make 104 quarts of banana berry smoothies.
Question 3 (1 point)
.
2x - 3(x + 6) = -3(x - 2)
x =
Answer:
x=12
Step-by-step explanation:
2x - 3(x + 6) = -3(x - 2)
Distribute
2x -3x -18 = -3x +6
Combine like terms
-x -18 = -3x+6
Add 3x from each side
-x+3x -18 = -3x+3x +6
2x -18 = 6
Add 18 to each side
2x-18+18 = 6+18
2x = 24
Divide each side by 2
2x/2 = 24/2
x = 12
Answer:
[tex]x = 12[/tex]
Step-by-step explanation:
[tex]2x - 3(x + 6) = - 3(x - 2) \\ 2x - 3x - 18 = - 3x + 6 \\ 2x - 3x + 3x = 18 + 6 \\ 2x = 24 \\ \\ x = \frac{24}{2} \\ \\ x = 12[/tex]
Find the missing values in each ratio table. Then write the equivalent ratio
Answer:
Dolls: 4,8,12
Balls: 6,12,18
Step-by-step explanation:
The completed ratio table is:
Dolls 4 4 12
Balls 6 12 6
Equivalent ratios: Dolls 1:3, Balls 1:2.
To find the missing values in the ratio table, we can set up proportions using the given ratios:
For Dolls:
4 dolls correspond to 12 dolls, so the missing value can be found using the proportion:
[tex]\(\frac{4}{12} = \frac{x}{12}\)[/tex]
[tex]\(x = \frac{4 \times 12}{12}\)[/tex]
x = 4
For Balls:
6 balls correspond to 12 balls, so the missing value can be found using the proportion:
[tex]\(\frac{6}{12} = \frac{y}{12}\)[/tex]
[tex]\(y = \frac{6 \times 12}{12}\)[/tex]
y = 6
The completed ratio table is:
Dolls 4 4 12
Balls 6 12 6
Equivalent ratio for Dolls:
[tex]\(\frac{4}{12} = \frac{1}{3}\)[/tex]
Equivalent ratio for Balls:
[tex]\(\frac{6}{12} = \frac{1}{2}\)[/tex]
A box contains 3 black pens, 7 blue pens, and 5 red pens. She pulls a red pen, puts it back, pulls a blue pen, puts it back, and then pulls a black pen and uses it. P(red, then blue, then black)
Answer:
7/25
Step-by-step explanation:
Probability is the likelihood or chance that an event will occur.
Probability = expected outcome/total outcome
If the box contains 3 black pens, 7 blue pens, and 5 red pens, the total number of pens in the box is 3+7+5 = 15pens
Probability of pulling a red pen and replacing = 5/15 = 1/3
Probability of pulling a blue pen and replacing = 7/15
Probability of pulling a black pen and not replacing(using it) = 3/15
{Note that the total number of outcome used will still be 15 since the black pen was pulled out last even though it wasn't replaced.}
P(red, then blue, then black) = 1/3×7/15×3/15
= 63/225
= 7/25
- A right triangle has a hypotenuse of 5 feet. One leg measures one foot
less than the hypotenuse. What are both legs' measures?
For which value of 0 is sin 0= -1
Answer:
3/2 π
Step-by-step explanation:
If you realize that the sin is actually the y coordinate of a (unit) circle when you travel around it, you will know that it is -1 when you are 3 quarters round, assuming you started at (1,0).
The circumference is measured in radians, where one round is 2π.
So 3/4 of 2π is 3/2 π.
In degrees, the answer is 3/4 of 360°, which is 270°.
Hope that was helpful.Thank you!!!
Answer:
Step-by-step explanation:
callie has $24.65 to spend on groceries.after buying 6 potaos ,she had $18.95 left. if each potato coast the same amount,what is the price of one potato
Answer:
$5.75
Step-by-step explanation:
What is the 4th term of the geometric sequence when the first term is 6 and the common ratio is 7?
(Multiple Choice Question)
100,842
294
1176
2,058
Answer:
2,058
Step-by-step explanation:
first term : a_1 = 6
common ratio r = 7
a_n = (a_1) * r ^(n-1)
a_4 = 6 * 7^(4-1)
a_4 = 6 *7^3
a_4 = 6 * 343 = 2,058
Which rectangular prism has a surface area of 56 square units? [Note: Art is not drawn to scale.]
A rectangular prism with a length of 5, width of 3, and height of 1.
A rectangular prism with a length of 2, width of 2, and height of 6.
A rectangular prism with a length of 5, width of 3, and height of 2.
A rectangular prism with a length of 6, width of 2, and height of 4.
Answer:
2
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
trust
4. Find the value of x in the right triangle below.
60°
Answer:
12
Step-by-step explanation:
It is worthwhile memorizing the ratios of legs in a 30°–60°–90° triangle. Shortest to longest, the ratios are ...
1 : √3 : 2
Then the sides marked will have the ratio ...
6 : x = 1 : 2 = 6 : 12
x = 12
_____
You can also get there using trigonometry.
cos(60°) = 6/x
x = 60/cos(60° = 60/0.5
x = 12
what is the radius of a circle that has a circumference of 50.24 units
Answer:
r≈8
Step-by-step explanation:
Answer: 8 units
Step-by-step explanation:
C= 2*pi*r
50.24 = 2*3.14*r
50.24=6.28
50.24/6.28
8=r
please help asap ! What is the area of a circle with a radius of 6 inches?
9.7 in. ?
12 x in 2
36 in 2
81 in 2
Answer:
A = 36 pi in^2
Step-by-step explanation:
The area of a circle is given by
A = pi r^2
A = pi (6)^2
A = 36 pi in^2
Answer:
36pi in²
Step-by-step explanation:
Area = pi × r²
= pi × 6²
= 36pi
Write The decimal as a percent .065
Answer:
6.5
Step-by-step explanation:
a(1) = 20
a(n) = a(n - 1) x 3/2
What is the 3rd term in the sequence?
Answer:
45
Step-by-step explanation:
a(1) = 20
a(n) = a(n - 1) x 3/2
---
start with a(2) = a(1) * (3/2) = 20* (3/2) = 30
a(3) = a(2) * (3/2) = 30 * (3/2) = 90/2 = 45
Answer:
45
Step-by-step explanation:
how do u find the mean of a question
Answer:
you add all the number up and divide by how many numbers there are.
Answer:
The mean (average) of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set.
Step-by-step explanation:
I hope this helps you out with your question! Can you plz consider marking me brainliest and thanks! Plz tell me how the answer was! It feel nice to be appreciated! Comment /free for a giveaway entry of 20 thanks and 2 brainliest. Have an awesome day! Let me know if you have any questions! -KaraYeaton18
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Answer:
The selling price of the remote control car is $36.3
Step-by-step explanation:
In this question, we are tasked with calculating the selling price of the remote control car.
From the first part of the question, we were made to know that he applies a markup of 21% and luckily for us, we are told that the expression for the retail price given the markup is 1.21 c
This means 1.21 × the cost price of the remote car
Hence, to calculate the selling price, we simply substitute $30.00 for the value of c.
The selling price is thus 1.21(30) = $36.3
Choose a true statement
Answer:
A true statement
Step-by-step explanation:
WHAT R THE STATEMENTS
A plumber needs to transport a 12 foot pipe to a jobsite. The interior of his van is 90 inches in length, 40 inches in width and 40 inches in height. Will the pipe fit inside his van?
Answer:
No
Step-by-step explanation:
First, convert all dimensions to be uniform.
1ft=0.08333 ft
90ft=90*0.0833=7.5ft
40 ft=40*0.0833=3.33 ft
The diagonal of the vehicle will be
[tex]\sqrt 7.5^{2}+3.33^{2}=8.20738150149675\ approx 8.2 ft[/tex]
Since the diagonal of vehicle is smaller than 12 ft, the pipe can't fit unless divided into two equal parts.
Final answer:
The 12-foot pipe can fit inside the van due to its dimensions.
Explanation:
The pipe is 12 feet long, which is equivalent to 144 inches. The interior dimensions of the van are 90 inches in length, which is shorter than the length of the pipe,
40 inches in width, and 40 inches in height, providing enough width and height for the pipe to fit. Therefore, the pipe will fit inside the plumber's van comfortably.
Volunteers at Sam's school use some of the student council's savings for a special project. They buy 8 backpacks for $4 each and fill each backpack with paper and pens that cost $3. By how much did the student council's savings change because of this project?
Answer:
Student council's savings reduced by [tex]\$56[/tex]
Step-by-step explanation:
Given:
Volunteers buy 8 backpacks for $4 each and fill each backpack with paper and pens that cost $3
To find:
Change in student council's savings
Solution:
Cost of paper and pens in each backpack = [tex]\$3[/tex]
Total cost of paper and pens in 8 backpacks = [tex]\$8[/tex]× [tex]\$3[/tex] =[tex]\$24[/tex]
Cost of each backpack = [tex]\$4[/tex]
Total cost of 8 backpacks = [tex]8[/tex]×[tex]\$4[/tex] = [tex]\$32[/tex]
So, student council's savings reduced by [tex]\$32+\$24=\$56[/tex]
David bought a 5-gallon container of paint to paint his house. After he finished painting, he had 2 quarts of paint left over. How many quarts of paint did David use?
Answer:3 1/2
Step-by-step explanation:
Your nephew is standing on his deck, which is 4 feet off the ground. He tosses his toy up into the air at an initial velocity of 7 feet per second. The equation h = -2t^(2) + 7t + 4 models the toy's height h in feet from the ground at t seconds after he threw it. a) How high is the toy after 0-4 seconds?
The toy's height after 0-4 seconds can be found by substituting different values of t into the given equation.
Explanation:The equation given to model the toy's height is h = -2t^2 + 7t + 4, where h is the height in feet and t is the time in seconds. To find the height of the toy after 0-4 seconds, we substitute different values of t into the equation.
For t = 0, h = -2(0)^2 + 7(0) + 4 = 4 feet.
For t = 1, h = -2(1)^2 + 7(1) + 4 = 9 feet.
For t = 2, h = -2(2)^2 + 7(2) + 4 = 12 feet.
For t = 3, h = -2(3)^2 + 7(3) + 4 = 11 feet.
For t = 4, h = -2(4)^2 + 7(4) + 4 = 4 feet.
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Which method listed below could not be used to prove that two triangles are congruent? a. Prove all three sets of corresponding sides congruent b. Prove all three sets of corresponding angles congruent c. Prove that two sides and an included angle of one triangle are congruent to two sides and an included angle of the other triangle d. Prove that two angles and an included side of one triangle are congruent to two angles\e of the other triangle.
Answer:
All corresponding sides and angles will be congruent
Step-by-step explanation:
To prove two triangles are congruent, we can use SSS, SAS, ASA, and AAS method.
Prove all three sets of corresponding angles congruent is not method of to prove two triangles are congruent.
The SSS rule states that , If three sides of one triangle are equal to three sides of another triangle, then the triangles are congruent.The SAS rule states that If two sides and the included angle of one triangle are equal to two sides and included angle of another triangle, then the triangles are congruentThe ASA rule states that If two angles and the included side of one triangle are equal to two angles and included side of another triangle, then the triangles are congruent.The AAS rule states that , If two angles and a non-included side of one triangle are equal to two angles and a non-included side of another triangle, then the triangles are congruent.Learn more:
https://brainly.com/question/14285697
Complete the equivalent equation for -7x-60 =x^2 +10x
Answer:
(x+12)(x+5)
Step-by-step explanation:
Formula use: a²+bx+c
Make one side equal to zero:Original:
-7x-60 =x² +10x
New:
x² + 17x + 60
Multiply A with CNew:
(1)x x 60 = 60
Find factors of 60 that when added, equal to 17.New:
10 × 6, 60 × 1, 20 × 3, 5 × 12, 4 × 15
5 times 12 equal 60, but when added equal to 17.
Replace the 17 with 5 and 12New:
x² + 5x + 12x + 60
Break them off into two equationsNew:
x² + 5x l 12x + 60
Divide each equation into it's simpilest form. Make sure the numbers in the ( ) are the same.New:
x(x + 5) l +12(x+5)
Answer: (x+12)(x+5).1111111111111111111111... as a fraction
Answer:
11/100
Step-by-step explanation:
If Tyler’s height is 57 inches. what could be his height in centimeters
1 inch = 2.54 centimeters
Multiply.
57 * 2.54 = 144.78
Therefore, Tylers height is 144.78 centimeters.
Best of Luck!
the perimeters of the square and the equilateral triangle are equal. Which equation represents this scenario? What is the value of x? What is the perimeter of the polygons?
Answer:
The perimeters of the square and the equilateral triangle are equal.
Which equation represents this scenario? ✔ 4(3x + 3) = 3(5x + 0.5)
What is the value of x? ✔ 3.5
What is the perimeter of the polygons?✔ 54 units
Step-by-step explanation:
Answer:
C,D, and C
Step-by-step explanation:
You open up a new case of note cards packs for your office. Each pack contains 50 note cards and each case contains 20 packs. If you were to evenly divide up the note cards between you and your 9 co-workers, how many note cards will each person receive?
1 case of note cards = 20 packs
1 pack = 50 note cards
50 x 20 = 1000 note cards in one case.
1000 / 10 = 100
Each person will receive 100 note cards.
Hope this helps!! :)
Find a number which decreased by 24 equals 3 times it’s opposite
x - 24 = 3 (-1) x
x - 24 = -3x
-24 = -4x
x = 6
Step-by-step explanation:
The number which decreased by 24 equals 3 times its opposite is 6
Finding the number which decreased by 24 equals 3 timesLet x represent the number to calculate
The opposite of the number is -x.
According to the problem, we have the following equation:
x - 24 = 3(-x)
Simplifying the equation:
x - 24 = -3x
Adding 3x to both sides:
4x - 24 = 0
Adding 24 to both sides:
4x = 24
Dividing both sides by 4:
x = 6
Hence, the number is 6.
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Is 5 m, 7 m, 11 m a right triangle
Answer:
no
Step-by-step explanation:
The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
5 m, 7 m, and 11 m do not form a right triangle.
What is right-angle triangle?A triangle is said to be right-angled if one of its angles is exactly 90 degrees. The total of the other two angles is 90 degrees. Perpendicular and the triangle's base are the sides that make up the right angle. The longest of the three sides, the third side is known as the hypotenuse.
To determine whether 5 m, 7 m, and 11 m form a right triangle, we need to use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. That is:
c² = a² + b²
Where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.
So, let's check if the Pythagorean theorem holds true for the lengths of 5 m, 7 m, and 11 m:
11² = 5² + 7²
121 = 25 + 49
121 = 74
This is not true, so 5 m, 7 m, and 11 m do not form a right triangle.
Learn more about right-angle triangle here:
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Just before a referendum on a school budget, a local newspaper polls 354 voters to predict whether the budget will pass. Suppose the budget has the support of 55% of the voters. What is the probability that the newspaper's sample will lead it to predict defeat?
Answer:
3.07% probability that the newspaper's sample will lead it to predict defeat
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
For a proportion p with n voters, we use [tex]\mu = p, \sigma = \sqrt{\frac{p(1-p)}{n}}}[/tex]
In this problem, we have that:
[tex]p = 0.55, n = 354[/tex]
So
[tex]\mu = 0.55, \sigma = \sqrt{\frac{0.55*0.45}{345}}} = 0.0268[/tex]
What is the probability that the newspaper's sample will lead it to predict defeat?
That is, a percentage of 50% or less, which is the pvalue of Z when X = 0.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{0.5 - 0.55}{0.0268}[/tex]
[tex]Z = -1.87[/tex]
[tex]Z = -1.87[/tex] has a pvalue of 0.0307.
3.07% probability that the newspaper's sample will lead it to predict defeat
Answer choices are:
CPCTC
If alternate interior angles are congruent, then lines are parallel
Congruent by SAS
Vertical lines are congruent
Answer:ABCD
Step-by-step explanation:
Alternate interior angles are congruent if two lines are parallel, leading to the similarity of triangles through the Angle Angle Angle theorem.
Alternate interior angles are congruent only if the two other lines are parallel. If the two other lines are not parallel, the angles will still be alternate interior angles but they will not have the same measure, that is, they will not be congruent. Two triangles are similar if all three corresponding angles are congruent, established by the Angle Angle Angle (AAA) theorem.