Given that, parallelogram ABCD is a rectangle. And
AC = 6y − 1 and
BD = 4y + 13.To find AC. To find the value of AC, we can use the properties of a rectangle. In a rectangle, opposite sides are equal and parallel.
So, in parallelogram ABCD, AC is one of the diagonals, and since it is a rectangle, the opposite side is parallel, and they have the same length. So, BD = AC.
Substituting BD = 4y + 13, we get;
AC = 4y + 13 Now, the value of
AC is 4y + 13. Therefore, the answer is 4y + 13. So, in parallelogram ABCD, AC is one of the diagonals, and since it is a rectangle, the opposite side is parallel, and they have the same length. So, BD = AC.
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Factor completely 10x2 2x − 8. 2(5x − 1)(x 4) 2(5x − 4)(x 1) 2(5x 2)(x − 2) 2(5x − 2)(x 2).
This means that the expression 10x² + 2x - 8 completely factored as 2(5x - 2)(x + 2).
The correct factored form of the expression 10x² + 2x - 8 is:
2(5x - 2)(x + 2).
To factor the quadratic expression completely for common factors first that the coefficient 2 is a common factor in all three terms. After factoring out 2, left with (5x² + x - 4).
An factor the trinomial (5x² + x - 4). However, this trinomial cannot be factored further using integer coefficients.
So, the factored form of the expression is 2(5x - 2)(x + 2).
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John flipped a coin 9 times and recorded 5 heads. What is the ratio of heads to tails John recorded?
John recorded 5 heads and flipped a coin 9 times. The ratio of heads to tails recorded by John is 5:4.
John flipped a coin 9 times and recorded 5 heads. To determine the ratio of heads to tails, we need to compare the number of heads to the number of tails. Since John recorded 5 heads, the remaining flips would be tails.
Therefore, the number of tails recorded would be 9 - 5 = 4. The ratio of heads to tails recorded by John is thus 5:4, which means for every 5 heads, there were 4 tails. This ratio represents the relative frequency of heads and tails in John's coin flips.
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A hiker whose eye level is 2m above the ground wants to find the heigh of a tree. He places a mirror horizontally on the ground 20m from the base of the tree, and find that if he stands at a point c, which is 4m from the mirror b, he can see the reflection of the top of the tree. How tall is the tree
The height of the tree is 12 meters.
To solve this problem, we can use similar triangles.
Let's denote the height of the tree as 'h'.
We have a right triangle formed by the hiker's line of sight, the mirror, and the reflected image of the top of the tree.
The vertical leg of this triangle is 'h', and the horizontal leg is the sum of the distance between the mirror and the base of the tree (20m) and the distance between the mirror and the hiker (4m).
So the horizontal leg is 20m + 4m = 24m.
Now, we can set up the proportion between the similar triangles:
(hiker's eye level)/(horizontal leg) = (reflected image height)/(vertical leg)
Plugging in the given values:
2 / 24 = 1 / h
Cross-multiplying:
2h = 24
Dividing both sides by 2:
h = 24 / 2
h = 12
Therefore, the height of the tree is 12 meters.
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Rita has two lengths of rope that are 9 feet and 1 foot long. Jeremy says there is only one possible additional rope length Rita can get to form a
triangle, Rita disagrees.
Who do you agree with? Explain your reasoning.
I agree with Rita. Jeremy is incorrect in claiming that there is only one possible additional rope length for Rita to form a triangle.
To form a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. In this case, Rita has two rope lengths of 9 feet and 1 foot. For a triangle to be formed, the sum of the two shorter sides must be greater than the longest side. However, in this case, 1 foot + 9 feet is greater than 9 feet, which satisfies the triangle inequality. Therefore, Rita can form a triangle with these two rope lengths.
Rita's disagreement is valid as there are multiple possible additional rope lengths she can obtain to form a triangle, not just one.
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Sammy has $43.75 for her visit to the zoo she must pay $9.25 for admission and wants to feed as many animals as she can food for the animals cost $2.75 each what is an inequality that right what inequality represents the largest number of food that say we can buy
The inequality that represents the largest number of food Sammy can buy, given her budget, is 2.75x ≤ 43.75 - 9.25, where x represents the number of food items she can purchase.
To find the inequality representing the largest number of food items Sammy can buy, we need to consider her budget and the cost of admission and food. Let x be the number of food items she can purchase.
The cost of admission is $9.25, which needs to be subtracted from her total budget. The remaining amount can be used to purchase food. Each food item costs $2.75.
Therefore, the inequality can be written as 2.75x ≤ 43.75 - 9.25, where the left side represents the cost of the food (2.75x), and the right side represents the remaining budget after deducting the admission fee (43.75 - 9.25).
By solving this inequality, Sammy can determine the largest number of food items (represented by x) that she can afford to buy within her budget.
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Calvin wants to sell a basic badminton kit to his friends. In that kit, he puts two rackets worth ₹140₹140₹, 140 each and a shuttlecock worth ₹80₹80₹, 80. He wants to have a profit of 25\%25%25, percent?
The selling price for Calvin's badminton kit, with a desired profit of 25%, is ₹450.
To determine the selling price for Calvin's badminton kit, including a desired profit of 25%, we need to calculate the cost price and add the profit margin.
The cost price of the badminton kit consists of two rackets worth ₹140 each and a shuttlecock worth ₹80. Let's calculate the total cost price:
Cost Price = (2 * ₹140) + ₹80 = ₹280 + ₹80 = ₹360
To find the selling price with a 25% profit margin, we need to add 25% of the cost price to the cost price:
Profit = 25% of ₹360 = (25/100) * ₹360 = ₹90
Selling Price = Cost Price + Profit = ₹360 + ₹90 = ₹450
Therefore, the selling price for Calvin's badminton kit, with a desired profit of 25%, is ₹450.
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What are the new diminsions of a 4x6 photo enlarged 2:3
Answer:
Step-by-step explanation:
To enlarge a 4x6 photo with a ratio of 2:3, we can multiply the dimensions of the photo by the enlargement ratio to find the new dimensions.
Original photo dimensions: 4 inches x 6 inches
Enlargement ratio: 2:3
To find the new dimensions, we can multiply the original dimensions by the enlargement ratio:
New width = 4 inches x 2 = 8 inches
New height = 6 inches x 3 = 18 inches
Therefore, the new dimensions of the enlarged photo would be 8 inches x 18 inches.
There are 640 acres in a square mile, and 5280 feet in 1. 00 mile. What is the length in feet (to the nearest foot) of the side of a square having an area of 1. 00 acre?
The side lengt of the square is approximately 1839 feet.
How to find the side length?To find the length in feet of the side of a square with an area of 1.00 acre, we need to convert the acreage to square feet.
Given:
1 acre = 640 acres/mile² (640 acres in a square mile)
1 mile = 5280 feet (conversion factor from miles to feet)
To convert acres to square feet, we can multiply by the conversion factor:
1 acre = 640 acres/mile² * 1 mile² * 5280 feet
Simplifying the units:
1 acre = 640 * 5280 square feet
Now, to find the length of the side of the square, we can take the square root of the area:
Side length = √(1 acre * 640 * 5280 square feet)
Calculating:
Side length ≈ √(1 * 640 * 5280) ≈ √3379200 ≈ 1839.29 feet
Rounding to the nearest foot, the length of the side of the square with an area of 1.00 acre is approximately 1839 feet.
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2 cyclists leave town 86 kilometers apart at the same time and travel toward each other. one cyclist travel 7 km/h faster than the other.
Two cyclists leave a town 86 kilometers apart at the same time and travel towards each other. One cyclist is traveling 7 km/h faster than the other. The task is to find their speeds.
Let's assume the speed of the slower cyclist is x km/h. Since the other cyclist is traveling 7 km/h faster, their speed would be x + 7 km/h.
The total distance between the two cyclists is 86 kilometers, and they are traveling towards each other. This means that the sum of the distances covered by both cyclists will equal the total distance of 86 kilometers.
Using the formula Distance = Speed × Time, we can set up the equation:
Distance covered by the slower cyclist + Distance covered by the faster cyclist = 86
The time taken by both cyclists will be the same since they start at the same time. So, we can rewrite the equation as:
(x km/h) × (t hours) + (x + 7 km/h) × (t hours) = 86
Simplifying the equation, we get:
xt + (x + 7)t = 86
xt + xt + 7t = 86
2xt + 7t = 86
Since we have two variables (x and t), we need another equation to solve the system. Without additional information, it is not possible to determine the exact values of x and t.
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Four transformations of the function f(x)=2x−4 are given below. For each transformation, drag the expression that shows the result of that transformation into the box under it.
1. Vertical stretch: f(x) = 2(2x-4)
2. Horizontal stretch: f(x) = 2(x/2-4)
3. Vertical shift up: f(x) = 2x-4+3
4. Vertical shift down: f(x) = 2x-4-3
1. Vertical stretch: To vertically stretch the function, we multiply the function by a constant outside the parentheses. In this case, multiplying f(x) by 2 results in f(x) = 2(2x-4).
2. Horizontal stretch: To horizontally stretch the function, we divide the input variable (x) by a constant inside the parentheses. In this case, dividing x by 2 gives us f(x) = 2(x/2-4).
3. Vertical shift up: To vertically shift the function upward, we add a constant to the function. Adding 3 to f(x) results in f(x) = 2x-4+3.
4. Vertical shift down: To vertically shift the function downward, we subtract a constant from the function. Subtracting 3 from f(x) gives us f(x) = 2x-4-3.
These transformations modify the original function f(x)=2x-4 in different ways, stretching it vertically, horizontally, and shifting it vertically up or down.
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Which fractions are equivalent?
26 and 12
14 and 36
26 and 14
12 and 24
To find which fractions are equivalent, we need to simplify each fraction. the fractions that are equivalent are 12/24 and 1/2.
The fractions 26/12 and 14/36 cannot be simplified since both already are in their simplest form. Hence 26/12 and 14/36 are not equivalent.14 and 36The fractions 26/12 and 14/36 cannot be simplified since both already are in their simplest form. Hence 26/12 and 14/36 are not equivalent.26 and 14The fractions 26/12 and 14/36 cannot be simplified since both already are in their simplest form.
Two fractions are equivalent if they represent the same part of a whole. To find which fractions are equivalent, we can simplify each fraction by dividing the numerator and denominator by their greatest common factor. The simplified fractions will represent the same part of a whole as the original fraction and will be equivalent fractions.
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Quadrilateral ABCD is congruent to quadrilateral
AMCG. Determine mZDAB.
12 cm
M
28
620
C
А
B
13 су
10 cm
16 cm
810
D
To determine the measure of angle DAB, we need to use the congruence of quadrilaterals ABCD and AMCG.
Quadrilateral ABCD is congruent to quadrilateral AMCG.
Since the two quadrilaterals are congruent, their corresponding angles are equal. Therefore, we can write:
m∠DAB = m∠MAC
However, the measure of angle MAC is not given in the given information. Therefore, without additional information, we cannot determine the exact measure of angle DAB.
The options provided in the question do not correspond to the measure of angle DAB. Therefore, the correct answer cannot be determined based on the given information.
It is important to have additional information about the measures of angles or the side lengths in order to determine the measure of angle DAB accurately.
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What INVERSE OPERATION is used to solve the equationx/7=5?
The inverse operation used to solve the equation x/7 = 5 is multiplication
Inverse operations are mathematical operations that reverse or undo each other. To isolate the variable, inverse operations are used. For example, addition and subtraction are inverse operations, as are multiplication and division.
In an equation, inverse operations can be used to solve for a variable. In order to solve the equation x/7 = 5, we will use inverse operations.The inverse operation of division is multiplication. So, we can isolate x by multiplying both sides of the equation by 7.x/7 = 5Multiplying both sides by 7 gives:x = 7 × 5x = 35Therefore, x = 35 is the solution to the equation.
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Cindy has scores of 72, 82, 83 and 89 on her Biology tests. The Final Exam counts as two tests and she will receive a C in the course if her average is from 77-84. What score must she receive on her Final Exam to earn a C in Biology?
Cindy has scores of 72, 82, 83 and 89 on her Biology tests. Cindy must score between 68 and 89 on her final exam to earn a C in Biology.
Cindy's current average score in Biology is:
(72 + 82 + 83 + 89) / 4 = 81.5
Since the final exam counts as two tests, we can calculate the total number of points Cindy can earn in the course as follows:
Total points = 4 tests + 2 tests = 6 tests
To earn a C in the course, her average score must be between 77 and 84. Let's assume she needs to score x on her final exam to achieve a C. Then her total points would be:
Total points = 72 + 82 + 83 + 89 + x + x
Simplifying this equation, we get:
Total points = 326 + 2x
To earn a C, Cindy's average score must be between 77 and 84. Therefore, we can set up an inequality:
77 <= (326 + 2x) / 6 <= 84
Multiplying both sides by 6, we get:
462 <= 326 + 2x <= 504
Subtracting 326 from all sides, we get:
136 <= 2x <= 178
Dividing by 2, we get:
68 <= x <= 89
Therefore, Cindy must score between 68 and 89 on her final exam to earn a C in Biology.
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Brandon is running errands for his mother. It is 1 4 mile from his house to the library and 2 3 mile from the library to the grocery store. Brandon claims that he walks a total of 11 12 mile if he goes from his house to the library to the grocery store. Which of the following shows whether Brandon is correct and why? A. Yes; the correct distance is 11 12 mile, because 1 4 2 3 = 3 12 8 12 = 11 12. B. No; the correct distance is 10 12 mile, because 1 4 2 3 = 4 12 6 12 = 10 12. C. No; the correct distance is 1 mile, because 1 4 2 3 = 4 12 8 12 = 12 12 = 1. D. No; the correct distance is 1 1 12 miles, because 1 4 2 3 = 4 12 9 12 = 13 12 = 1 1 12.
The correct answer is D. No; the correct distance is 1 1/12 miles, because 1/4 + 2/3 = 4/12 + 8/12 = 12/12 = 1 1/12.
To solve this problem, we first need to convert the mixed numbers to fractions. 1 4 = 4 12 and 2 3 = 8 12. Then, we can add the fractions together. 4 12 + 8 12 = 12 12 = 1 1 12.
Therefore, Brandon is incorrect. He walks a total of 1 1/12 miles, not 11 1/2 miles.
Type in a full solution to this problem. Use "^" to show me exponents.
Marjorie and Harold Rabbit escape their separate prison cages and elope to Las Vegas.
When they return from their honeymoon, they decide to settle in the neighbours yard
due to the large crop of carrots at there disposal. A month later little Holly and Jack
Rabbit are born. The size of their family doubles one month later and continues to
double every month thereafter. How many rabbits will be living in the neighbours yard
after 12 months. Do you think they'll notice??? *
There will be 22544 rabbits living in the neighbour's yard after 12 months.
The given problem states that the size of Marjorie and Harold Rabbit's family doubles one month later and continues to double every month thereafter.
It is required to find the number of rabbits that will be living in the neighbours yard after 12 months.
The given data can be organized in a tabular form as follows:
Time (in months)
Number of rabbits at the end of the month
01 (at birth)
2 (after one month)
24(after two months)
28(after three months)
216(after four months)
232(after five months)
264 (after six months)
2128(after seven months)
2256(after eight months)
24192(after nine months)
28384 (after ten months)
267,68 (after eleven months)
225,44 (after twelve months)
Yes, it is quite possible that they will notice this huge number of rabbits in their yard.
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Suppose in Problem 3 that we wished to design a test so that if the pH were really equal to 8. 20 this conclusion will be reached with probability equal to 0. 95. On the other hand, if the pH differs from 8. 20 by 0. 03 (in either direction), we want the probability of picking up such a difference to exceed 0. 95. What is the test procedure that should be used and what is the required sample size
The test procedure that should be used would be hypothesis testing and power analysis. The sample size would be 6.
How to find the test procedure and sample size ?The null hypothesis (H₀) is that the pH is equal to 8.20, and the alternative hypothesis (H₁) is that the pH differs from 8.20 by more than 0.03, i.e., pH < 8.17 or pH > 8.23.
To ensure a type I error probability (rejecting H₀ when it is true) of 0.05 (1-0.95), we set our significance level α = 0.05. Therefore, if we calculate a sample mean pH that falls into the critical regions (mean pH < 8.17 or mean pH > 8.23), we would reject the null hypothesis.
Given the standard deviation (σ) is 0.02, we can use the formula for calculating the sample size:
n = [(Z_α/2 + Z_β)σ/Δ]²
Let's substitute the values:
n = [(1.96 + 1.645) * 0.02 / 0.03]²
n = [3.605 * 0.02 / 0.03]²
n = [0.0721]²
n = 5.2
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1) What is the formula used to
find the volume of a cylinder?
2)What is the difference
between the volumes of the
Chunky Chicken Noodle Soup
can and the Condensed
Chicken Noodle Soup can?
"Use 3. 14 for pi in all calculations
"You must show what you multiplied to find
the volumes of both cans AND the difference
between the two volumes.
"Remember to label your answers
cm
Answer:
for 1.
Step-by-step explanation:
the formula is pir2h
Jessie tried to solve an equation step by step. 1. 5b+9=111. 5b=3Step 1b=2Step 2\qquad\begin{aligned} 1. 5b+9&=11\\\\ \\ 1. 5b&=3&\green{\text{Step } 1}\\\\ \\ b&=2&\blue{\text{Step } 2}\\\\ \end{aligned}1. 5b+91. 5bb=11=3=2Step 1Step 2Find Jessie's mistake. Choose 1 answer:Choose 1 answer:(Choice A)AStep 1\green{\text{Step }1}Step 1start color #28ae7b, start text, S, t, e, p, space, end text, 1, end color #28ae7b(Choice B)BStep 2\blue{\text{Step }2}Step 2start color #6495ed, start text, S, t, e, p, space, end text, 2, end color #6495ed(Choice C)CJessie did not make a mistake
Jessie made a mistake in Step 1 of solving the equation. The correct equation should be 5b + 9 = 111 instead of 5b + 9 = 11.
In Step 1, Jessie mistakenly wrote the right-hand side of the equation as 11 instead of 111. The correct equation should be 5b + 9 = 111, not 5b + 9 = 11. This error occurred in the process of trying to isolate the variable b by subtracting 9 from both sides of the equation.
Step 2, where Jessie obtained 5b = 3, is correct. However, the mistake in Step 1 led to an incorrect starting point, which affected the subsequent steps.
Therefore, the correct answer is Choice A: Jessie made a mistake in Step 1.
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In preparation for the homecoming football game, members of the student body are painting the school rock. If Angela works alone, it will take
her 5 and one-half hours. If Brandon works alone it will take him 7 hours. If they work together, approximately how long will it take?
4
3
6. 25
125
When working together, it will take Angela and Brandon about 3 hours and 12 minutes to paint the school rock.
The answer is 3
Let's first assume that Angela can paint the school rock in x hours, then Brandon would be able to paint the school rock in y hours.Angela’s work rate: \frac{1}{x} of the rock per hour .
So, Angela’s work rate = [tex]$\frac{1}{5.5}$[/tex]and Brandon’s work rate = \frac{1}{7} Working together, Angela and Brandon’s work rate will be: \frac{1}{5.5} + \frac{1}{7} of the rock per hour [tex]$\frac{1}{5.5} + \frac{1}{7}$ = $\frac{0.1818 + 0.1429}{1}$ = $\frac{0.3247}{1}$[/tex] Working together, they will paint the rock in \frac{1}{0.3247} hours = 3.08 hours. Rounding off to the nearest minute, it will take them about 3 hours and 12 minutes .
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Suppose a chemist combines a 25% acid solution and a 50% acid solution to make 40 L of 45% acid solution. How many liters of each solution did she use? Use the blanks below to fill in your numerical answers.
__________ L of 50% solution; __________ L of 25% solution
To create a 40 L solution with a 45% acid concentration, a chemist combines a 25% acid solution and a 50% acid solution. Therefore, the chemist used 32 L of the 50% acid solution and (40 - 32) = 8 L of the 25% acid solution to create the 40 L solution with a 45% acid concentration.
Let's assume the chemist uses "x" liters of the 50% acid solution. Since the total volume of the mixture is 40 L, the remaining volume will be (40 - x) liters of the 25% acid solution.
The acid content in the 50% solution is 0.5x, while the acid content in the 25% solution is 0.25(40 - x).
To find the acid content in the final 45% solution, we multiply the acid concentration (0.45) by the total volume (40):
0.45 * 40 = 0.5x + 0.25(40 - x)
Simplifying the equation:
18 = 0.5x + 10 - 0.25x
Combining like terms:
0.25x = 8
Dividing both sides by 0.25:
x = 32
Therefore, the chemist used 32 L of the 50% acid solution and (40 - 32) = 8 L of the 25% acid solution to create the 40 L solution with a 45% acid concentration.
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4) Emily can walk 3/4 of a mile in 1/4 of an hour. At
this same rate, how long does it take Emily to walk 1
mile?
A.1/2 of an hour
B. 2/5 of an hour
C. 1/3 of an hour
D. 2/3 of an hour
Emily can walk 3/4 of a mile in 1/4 of an hour. At the same rate, time taken to walk 1 mile =1/3 of an hour.
Mathematical representation
We know that, Emily can walk 3/4 of a mile in 1/4 of an hour.
Meaning,
Time taken to walk 3/4 of a mile = 1/4 of an hour
Distance covered = 3/4 mile
We need to find the time taken by Emily to walk 1 mile.
The rate is defined as the distance covered in unit time. So,
Rate = Distance / Time
We know that Rate of Emily = 3/4 ÷ 1/4
= 3/4 × 4/1
= 3 miles/hour
The rate of walking is 3 miles/hour.
Now we can find the time taken to walk 1 mile using rate formula.
Distance = Rate × Time
We have to walk 1 mile and the rate of walking is 3 miles/hour.
Time = Distance / Rate
Time taken to walk 1 mile = 1 / 3 = 1/3 hour.
So, the answer is option C.
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Mrs. rodriguez is selling popcorn at the snack stand. Each bag holds 2.3 ounces of popcorn. in one hour, she sold 56 bags of popcorn. How may ounces of pop corn are in 56?
Mrs. Rodriguez sold 128.8 ounces of popcorn.We know that each bag of popcorn weighs 2.3 ounces. Therefore, to find out the total amount of popcorn Mrs. Rodriguez sold in 56 bags, we need to multiply 2.3 by 56. That is;2.3 × 56 = 128.8Therefore, there are 128.8 ounces of popcorn in 56 bags
We are given that Mrs. Rodriguez is selling popcorn at the snack stand. Each bag holds 2.3 ounces of popcorn. In one hour, she sold 56 bags of popcorn. Our task is to find out how many ounces of popcorn are in 56 bags.In order to find out how many ounces of popcorn are in 56 bags, we need to first find out the weight of one bag of popcorn. We are told that each bag holds 2.3 ounces of popcorn. So, we have:
Weight of one bag of popcorn = 2.3 ounces Now, we can use this information to calculate the total weight of popcorn Mrs. Rodriguez sold in 56 bags. To do this, we need to multiply the weight of one bag of popcorn (2.3 ounces) by the number of bags she sold (56). That is;Weight of 56 bags of popcorn = 2.3 × 56= 128.8Therefore, Mrs. Rodriguez sold 128.8 ounces of popcorn in one hour.
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A manufacturing company has determined that the daily revenue R(n) in thousands of dollars is given by the formula R(n) =12n - 0.6n where n represents the number of palettes of product sold (0
sold in a day if the revenue was 45 thousand dollars.
To make $45.000 they would have to sell either __________palettes or
_______palettes. (Put the smaller of the two numbers in the first box!)
A manufacturing company has determined that the daily revenue R(n) in thousands of dollars is given by the formula R(n) = 12n - 0.6n where n represents the number of palettes of product sold (0 < n < 500).
If the company wishes to make a revenue of 45 thousand dollars, we are supposed to find the number of palettes of product sold .Solution :Let us substitute the value of R(n) = 45 in the given equation and solve for n45 = 12n - 0.6n45 = 11.4n, n = 3.9474Hence, the manufacturing company has to sell either 3 or 4 palettes of product to make $45.000.
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the scale on a map is stated as 1 : 250000to villages are 9 cm apart on the maphow far from each other are the two villages in kilometres
The two villages are approximately 225 kilometers apart.
The scale on the map is given as 1:250000, which means that 1 unit on the map represents 250,000 units in reality.
If the distance between the villages on the map is 9 cm, we can set up the following proportion:
1 cm / 250,000 km = 9 cm / x km
Cross-multiplying, we have:
1 * x km = 9 cm * 250,000 km
x km = 2,250,000 km / 1 cm
Simplifying the expression, we find:
x km = 225 km
Therefore, the two villages are approximately 225 kilometers apart.
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PLEASE SOMEONE HELP I NEED IT URGENTLY
The missing side lengths are x = 4 and y = 4.The correct answer choice is D) x = 4, y = 4.
To find the missing side lengths in a triangle, we can use trigonometric ratios. In this case, we are given the length of one side (8) and the measure of one angle (30 degrees), and we need to find the lengths of the other two sides (x and y).
In a right triangle, the trigonometric ratios can be used to relate the angles and side lengths. In this case, we are not given that the triangle is a right triangle, so we will assume it is not.
The sine ratio relates the ratio of the length of the side opposite an angle to the length of the hypotenuse. In this case, the side opposite the 30-degree angle is y, and the hypotenuse is 8. So we can write:
sin(30 degrees) = y/8
Using the known value of sin(30 degrees) = 1/2, we can solve for y:
1/2 = y/8
Cross-multiplying, we get:
y = 4
So we have found the length of side y to be 4.
To find the length of side x, we can use the law of sines. The law of sines states that the ratio of the length of a side to the sine of its opposite angle is constant for all sides and angles in a triangle.
Using the law of sines, we can write:
sin(30 degrees)/x = sin(angle opposite x)/8
Since we know the sine of 30 degrees is 1/2, we can rewrite the equation as:
(1/2)/x = sin(angle opposite x)/8
Since the angle opposite x is 180 degrees - 30 degrees = 150 degrees, we have:
(1/2)/x = sin(150 degrees)/8
Using the known value of sin(150 degrees) = 1/2, we can solve for x:
(1/2)/x = 1/2/8
Cross-multiplying, we get:
x = 4
So we have found the length of side x to be 4.
Therefore, the missing side lengths are x = 4 and y = 4.
The correct answer choice is D) x = 4, y = 4.
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If a manufacturing company uses a single, weight-losing raw material to manufacture its finished product, then most likely the company will:_________.
i. Choose to outsource its labor component.
ii. Locate its manufacturing plant at the raw material site.
iii. Locate several manufacturing plants close to consumers.
iv. Use a ubiquitous raw material.
v. Agglomerate close to similar factories
Option B : Locate its manufacturing plant at the raw material site.
Given,
Weight losing raw material to manufacture its finished products .
Here,
Weight loss raw materials are those which loses their weight while production sugar, iron and steel, and aluminum that lose weight during production.
For example we can take the industries that require minerals for their production works .
Another example is of sugar industry which require weight losing raw material .
Thus the correct option will be B .
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Maija is building a square sandbox with sides 2 feet long. She wants to put sand 1.55 feet deep in the box. How much sand should Maija order?
To calculate the amount of sand Maija should order, we need to find the volume of the sandbox. The sandbox is in the shape of a cube, so its volume is determined by multiplying the length, width, and height.
Given that the sides of the square sandbox are 2 feet long and the desired depth of the sand is 1.55 feet, we can calculate the volume as follows:
[tex]\[ \text{Volume} = \text{Length} \times \text{Width} \times \text{Height} \][/tex]
Since all sides of the sandbox are equal in length (2 feet), the formula simplifies to:
[tex]\[ \text{Volume} = \text{Side}^3 \][/tex]
Substituting the values:
[tex]\[ \text{Volume} = 2 \, \text{ft} \times 2 \, \text{ft} \times 1.55 \, \text{ft} \][/tex]
[tex]\[ \text{Volume} = 6.2 \, \text{cubic feet} \][/tex]
Therefore, Maija should order 6.2 cubic feet of sand for her sandbox.
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Convert. If necessary, round to the nearest tenth.
(Recall: 1 gal. = 3.79 L.)
Igal. x 20 L.
a. 10.5
b. 5.8
C.
10.1
d.
5.3
Therefore, the answer rounding to the nearest tenth is d. 5.3.
To convert 1 gallon to liters, we multiply by the conversion factor of 3.79 L/gal.
1 gal. * 3.79 L/gal = 3.79 L
Now, to find the equivalent of 20 liters, we can set up a proportion:
1 gal / 3.79 L = x gal / 20 L
Cross-multiplying and solving for x, we get:
x = (1 gal / 3.79 L) * 20 L = 20 / 3.79 gal
Rounding to the nearest tenth, we have:
x ≈ 5.3
Therefore, the answer is d. 5.3.
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A.
Write a recursive formula for the sequence 8, 10, 12, 14, 16,. Then find the next term.
a = a,-1 + 2, where a, 8; 18
b.
a.
+ 2, where a
18; 8
c.
a, = a -1 -2, where a, 8; 18
d. A, = a. -1
2, where a, = = 2; -2
= a. - 1
The recursive formula for the sequence is a(n) = a(n - 1) + 2 and the next term is 18
Writing a recursive formula for the sequenceFrom the question, we have the following parameters that can be used in our computation:
8, 10, 12, 14, 16,.
In the above sequence, we have
First term, a(1) = 8
And we have the common difference to be
d = 2
So, we have
a(n) = a(n - 1) + 2
The next term of the sequence is
Next = 16 + 2
Evaluate
Next = 18
Hence, the recursive formula for the sequence is a(n) = a(n - 1) + 2
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