The value v of an investment is given by the function, the equation indicating that the investment had a value of 8000 in 2000 is v(t) = 8000, where t represents the number of years since 1990.
The given information states that the investment had a value of 8000 in 2000. Since t represents the number of years since 1990, we can assume that in the year 2000, t is equal to 10 (2000 - 1990 = 10).
To represent this information in equation form, we can use the function v(t), where v is the value of the investment and t is the number of years since 1990. Since the investment value in 2000 is 8000, we can write the equation as v(t) = 8000.
This equation indicates that the value of the investment, represented by v(t), is equal to 8000 when t is equal to 10, which corresponds to the year 2000.
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the line on the graph passes through points (0,6) and (3,0).a - what is the gradient of the line?b - what the gradient of the line perpendicular to this line?c - what is the equation for the line that passes through a and is perpendicular to ab?
a) The gradient of the line passing through the points (0,6) and (3,0) is -2. b) The gradient of the line perpendicular to this line is 1/2. c) The equation for the line passing through point a and perpendicular to the line ab can be determined using the point-slope form of a linear equation.
a) To find the gradient (slope) of the line passing through (0,6) and (3,0), we use the formula: gradient = (change in y) / (change in x). Substituting the coordinates, we get (-6) / (3-0) = -2.
b) The gradient of a line perpendicular to another line is the negative reciprocal of the original gradient. Therefore, the gradient of the line perpendicular to the given line is 1/2.
c) To find the equation of the line passing through point a and perpendicular to line ab, we can use the point-slope form of a linear equation: y - y1 = m(x - x1), where (x1, y1) is point a and m is the gradient of the perpendicular line. Substituting the values, we get y - 6 = (1/2)(x - 0), which simplifies to y = (1/2)x + 6.
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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 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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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
The air in a 3 L balloon at 0. 945 atm and 39. 0°C. What will be its pressure if it is brought to a higher altitude where it now occupies 1. 5 L and is at 14. 0 °C? Group of answer choices
The new pressure of the balloon at the higher altitude, when it occupies 1.5 L and is at 14.0 °C, is approximately 25.46 atm/°C.
To find the new pressure of the balloon when it is brought to a higher altitude, we can use the combined gas law equation:
P1V1/T1 = P2V2/T2
Given:
P1 = 0.945 atm (initial pressure)
V1 = 3 L (initial volume)
T1 = 39.0 °C (initial temperature)
V2 = 1.5 L (final volume)
T2 = 14.0 °C (final temperature)
Substituting the given values into the equation, we have:
(0.945 atm)(3 L)/(39.0 °C) = P2(1.5 L)/(14.0 °C)
Simplifying the equation:
2.727 atm/°C = 0.1071P2
To isolate P2, we divide both sides by 0.1071:
P2 = 2.727 atm/°C / 0.1071
P2 ≈ 25.46 atm/°C
Therefore, the new pressure of the balloon at the higher altitude, when it occupies 1.5 L and is at 14.0 °C, is approximately 25.46 atm/°C.
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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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Ms. Seema’s annual salary is Rs 288000. Her annual savings is Rs 72000. The ratio of her annual spending to her annual saving is ____________ *
1 : 3
2 : 3
3 : 1
None of these
We have to find the ratio of Ms Seema's annual spending to her annual savings given that Ms. Seema's annual salary is Rs 288000 and her annual savings is Rs 72000.
The first step is to determine the annual spending of Ms. Seema.Subtracting the annual savings of Ms. Seema from her annual salary, we can determine her annual spending. Annual spending = Rs 288000 - Rs 72000 = Rs 216000We now know that Ms. Seema's annual spending is Rs 216000 per year and her annual savings is Rs 72000 per year.
We can now compute the ratio of her annual spending to her annual savings. Annual spending : Annual savings= 216000 : 72000= 3 : 1Therefore, the ratio of Ms. Seema's annual spending to her annual savings is 3 : 1. It implies that her annual spending is three times the annual savings.In conclusion, the ratio of Ms. Seema's annual spending to her annual savings is 3 : 1.
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42 + x(interior angle) + 120(exterior) = 180
Please help-
To solve the equation 42 + x (interior angle) + 120 (exterior angle) = 180, we can use the fact that the sum of an interior angle and its corresponding exterior angle is always 180 degrees.
In the given equation, 42 represents an interior angle, x represents an unknown interior angle, and 120 represents the corresponding exterior angle. The sum of an interior angle and its corresponding exterior angle is always 180 degrees. Therefore, we can set up the equation:
42 + x + 120 = 180
To solve for x, we can simplify the equation:
x + 162 = 180
Next, we can isolate x by subtracting 162 from both sides of the equation:
x = 180 - 162
x = 18
Therefore, the value of the unknown interior angle, x, is 18 degrees.
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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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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.
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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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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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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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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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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Find the perimeter and the area of a rectangle with the sides4 7/20 m and 6 2/3m.
The perimeter of the rectangle is 22 7/15 meters, and the area is 29 1/10 square meters.
To find the perimeter of a rectangle, we add the lengths of all four sides. In this case, the length of one side is 4 7/20 meters and the length of the adjacent side is 6 2/3 meters. To add these mixed numbers, we convert them to improper fractions. The first side becomes 87/20 meters and the second side becomes 20/3 meters. Adding the two lengths gives us a total of (87/20 + 20/3) meters. To add fractions with different denominators, we need to find a common denominator. The least common multiple of 20 and 3 is 60. Converting both fractions to have a denominator of 60, we get (261/60 + 400/60) meters, which simplifies to 661/60 meters. Finally, we can convert this improper fraction back to a mixed number, which is 11 1/60 meters. Since the perimeter of a rectangle is the sum of all four sides, the perimeter of this rectangle is 2 times 11 1/60 meters, which equals 22 2/60 meters or 22 7/15 meters.
To find the area of a rectangle, we multiply the length by the width. In this case, the length is 4 7/20 meters and the width is 6 2/3 meters. Converting both mixed numbers to improper fractions, we get a length of 87/20 meters and a width of 20/3 meters. Multiplying these two fractions gives us (87/20 * 20/3) square meters. Simplifying the fractions, we get (1740/60) square meters, which further simplifies to 29 square meters. Therefore, the area of this rectangle is 29 square meters.
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Santos takes the train into the city five days a week for work. For one work week he kept track of how many minutes the train ride was : 48,51,48,48,50
Calculate the mean median range in the range of the train ride times for the week
The mean train ride time for the week was 49.4 minutes, with a median of 48 minutes. The range of the train ride times was 3 minutes.
The mean, median, and range of Santos' train ride times for the week were as follows:
Mean: 49.4 minutes
The mean is calculated by adding up all the values and dividing the sum by the total number of values. In this case, the sum of the train ride times (48 + 51 + 48 + 48 + 50) is 245 minutes. Dividing this sum by the total number of days (5), we get the mean of 49.4 minutes.
Median: 48 minutes
The median is the middle value in a sorted list of numbers. To find the median, we arrange the train ride times in ascending order: 48, 48, 48, 50, 51. Since there is an odd number of values, the middle value is the median. In this case, the median is 48 minutes.
Range: 3 minutes
The range is the difference between the largest and smallest values in a set. To calculate the range, we subtract the smallest value (48 minutes) from the largest value (51 minutes). In this case, the range of the train ride times for the week is 3 minutes.
In summary, the mean train ride time for the week was 49.4 minutes, with a median of 48 minutes. The range of the train ride times was 3 minutes. These metrics provide insights into the average, central tendency, and variability of Santos' train rides throughout the week.
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A mark of humility is a willingness to resolve differences. How does the Apostle Paul show humility in Acts 15:36-39 and 2 Timothy 4:11?
The Apostle Paul demonstrates humility in Acts 15:36-39 and 2 Timothy 4:11 through his willingness to resolve differences. In these passages, Paul's actions and attitudes reflect his humility and his desire for reconciliation and unity among believers.
In Acts 15:36-39, Paul and Barnabas had a disagreement regarding taking John Mark on a missionary journey. Barnabas wanted to bring John Mark along, but Paul did not because John Mark had previously left them on a previous journey. Despite the disagreement, Paul shows humility by accepting Barnabas' decision and allowing him to take John Mark as his companion, while Paul chooses Silas as his own companion. This act demonstrates Paul's willingness to prioritize unity and reconciliation over personal preferences.
In 2 Timothy 4:11, Paul shows humility by reconciling with John Mark. He requests Timothy to bring Mark with him because Paul considers Mark to be helpful in his ministry. This shows a change in Paul's attitude towards Mark, indicating that he was willing to put aside any past differences and extend forgiveness and acceptance. Paul's willingness to reconcile and work alongside Mark reveals his humility and his understanding of the importance of resolving differences for the sake of the Gospel and the unity of believers.
Overall, both passages highlight Paul's humility through his willingness to resolve differences and prioritize unity, showcasing his desire for reconciliation and harmony among fellow believers.
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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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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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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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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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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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How much wire will be needed to put a double fence around a square plot with 50m?
To find out how much wire will be needed to put a double fence around a square plot with 50m, we first need to calculate the perimeter of the square plot.
Perimeter of a square = 4 x SideWhere Side = 50mPerimeter = 4 x 50m = 200mNow, since we need to put a double fence around the square plot, we will multiply the perimeter by 2. Therefore, the total length of wire needed for double fencing = 200m x 2 = 400m. Therefore, 400m of wire will be needed to put a double fence around a square plot with 50m.Long Answer:The given plot is a square with the side of the square being 50m. To find out the amount of wire needed to put a double fence around the square plot, we first need to calculate the perimeter of the square plot.A square is a 4 sided figure with all sides of equal length.
Therefore, the perimeter of a square can be calculated by multiplying the length of one side of the square with 4, as shown below.Perimeter of a square = 4 x SideWhere Side is the length of one side of the square plot.In this case, the side of the square plot is given as 50m. Therefore, the perimeter of the square plot can be calculated as shown below:Perimeter of a square = 4 x 50m = 200mTherefore, the perimeter of the square plot is 200m.Now, since we need to put a double fence around the square plot, we will multiply the perimeter by 2. This is because a double fence means that we will be putting two fences back to back around the perimeter of the square plot. Therefore, the total length of wire needed for double fencing can be calculated as shown below:Total length of wire needed for double fencing = 2 x Perimeter of the square plotTotal length of wire needed for double fencing = 2 x 200mTotal length of wire needed for double fencing = 400mTherefore, 400m of wire will be needed to put a double fence around a square plot with 50m.
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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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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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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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Part C
Rewrite the expression you developed in Part B as a single term with a fractional coefficient.
In Part B, the expression developed was 10 + 6b. To rewrite it as a single term with a fractional coefficient, we need to combine 10 and 6b into a single term.
Let's begin by multiplying 6 by b, then adding the result to 10.6b can be expressed as 6/1 multiplied by b. Then, we add it to 10:10 + 6/1 × bCommon denominator is 1, so we can add 10 to 6b as follows:10 + 6/1 × b/1 = 10/1 + 6b/1 = (10 + 6b)/1Therefore, the expression 10 + 6b is the same as (10 + 6b)/1. Its single term with a fractional coefficient is (10 + 6b)/1 = 10/1 + 6b/1 = (10 + 6b)/1.
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Kentucky Kingdom is a popular field trip destination. This year the senior class at NAHS and the senior class at FCHS both planned trips there. The senior class at NAHS rented and filled 6 vans and 12 buses with 504 students. FCHS rented and filled 2 vans and 5 buses with 204 students. Each van and each bus carried the same number of students. How many students can a van carry? How many students can a bus carry?
A van can carry 12 students, and a bus can carry 36 students. The senior class at NAHS rented and filled 6 vans and 12 buses with 504 students.
To determine how many students a van can carry and how many students a bus can carry, we can use a system of equations based on the given information.
Let's assume that the number of students a van can carry is "v" and the number of students a bus can carry is "b".
According to the information provided:
The senior class at NAHS rented and filled 6 vans and 12 buses with a total of 504 students.
The senior class at FCHS rented and filled 2 vans and 5 buses with a total of 204 students.
Based on these conditions, we can form the following equations:
Equation 1: 6v + 12b = 504
Equation 2: 2v + 5b = 204
We now have a system of two equations with two unknowns (v and b). We can solve this system to find the values of v and b.
Let's solve the system using any preferred method, such as substitution or elimination.
Multiplying Equation 2 by 6, we get:
12v + 30b = 1224
Subtracting this equation from Equation 1, we can eliminate v:
6v + 12b - (12v + 30b) = 504 - 1224
-6v - 18b = -720
Simplifying this equation, we get:
-6v - 18b = -720
Dividing this equation by -6, we obtain:
v + 3b = 120
Now we have a new equation:
v + 3b = 120 -------------- Equation 3
We can now solve Equations 2 and 3 as a new system of equations.
Multiplying Equation 3 by 2, we get:
2v + 6b = 240
Subtracting this equation from Equation 2, we can eliminate v:
2v + 5b - (2v + 6b) = 204 - 240
b = -36
Dividing both sides of the equation by -1, we find:
b = 36
Now, substituting the value of b back into Equation 3:
v + 3(36) = 120
v + 108 = 120
v = 12
Therefore, a van can carry 12 students, and a bus can carry 36 students.
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A bobsled team is practicing runs on a track. Their first run takes 4.85 minutes. On each of the next two run the team theme changes by -5 1/2% compared the previous time
The team's time on their final run, given the decrease in speed, would be 4. 33 minutes
How to find the minutes ?On the next run, the time that the bobsled team would take is :
= 4. 85 - ( 4. 85 x 5. 5 % )
= 4. 85 - 0.26675
= 4. 58325 minutes
The run after that would see a time of :
= 4. 58325 - ( 4. 58325 x 5. 5 %)
= 4. 58325 - 0.25207875
= 4. 33 minutes
In conclusion, the team's time on their final run, would be 4. 33 minutes.
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.
The question is:
What was the team's time on their final run?
