In a rectangular prism, given a base area of 64 cm2 and a
height of 7.2 cm, what would be the volume of the
figure?
Answer:
46.8 cm^3
Step-by-step explanation:
The following chart shows a store’s records of sales of stuffed toys for two months. 2 circle graphs. A circle graph titled September. Teddy bears is 346, rabbits is 297, cats is 199, horses is 245, other is 225. A circle graph titled October. Teddy bears is 308, rabbits is 260, cats is 285, horses is 186, 275 is other. Which of the following are accurate assessments of trends displayed in this graph? I. The market share held by cats increased by about 6.5 percentage points. II. Roughly 22.2% more stuffed toys in the “other” category were sold in October than in September. III. The total number of stuffed toys sold increased by about 2%. a. I and II b. II only c. I and III d. I, II, and III
Statement III is not accurate, as the increase in the total number of stuffed toys sold is approximately 0.15%, which is significantly lower than about 2%.
a. I and II
To assess the trends displayed in the given circle graphs for September and October, let's analyze each statement:
I. The market share held by cats increased by about 6.5 percentage points.
In September, the percentage for cats is 199 / 1312 ≈ 15.2%. In October, the percentage for cats is 285 / 1314 ≈ 21.7%.
The difference between these two percentages is approximately 21.7% - 15.2% ≈ 6.5 percentage points.
Therefore, Statement I is accurate, as the market share held by cats increased by about 6.5 percentage points.
II. Roughly 22.2% more stuffed toys in the "other" category were sold in October than in September.
In September, the number of toys in the "other" category is 225. In October, it is 275.
The difference between these two quantities is 275 - 225 = 50.
To assess whether this represents roughly 22.2% more, we calculate 50 / 225 ≈ 0.222, which is approximately 0.222 * 100% ≈ 22.2%.
Therefore, Statement II is accurate, as roughly 22.2% more stuffed toys in the "other" category were sold in October than in September.
III. The total number of stuffed toys sold increased by about 2%.
To calculate the total number of toys sold, we sum the quantities for each category in September (1312) and October (1314).
The difference between these two totals is 1314 - 1312 = 2.
To assess whether this represents an increase of about 2%, we calculate 2 / 1312 ≈ 0.0015, which is approximately 0.0015 * 100% ≈ 0.15%.
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Answer:
Answer is A.) I and II
36/48 simplify plsssss
Fill in the table of values so that this is a proportional relationship with k=3/2 X. Y. *blank*. 0 2. *blank*. *blank*. 6. -2. *blank*
Answer:
x => y
0 => 0
2 => 3
4 => 6
-2 => -3
Step-by-step explanation:
The equation of a proportional relationship is represented as y = kx,
where, k = y/x
We are given that k = ³/2
This means that, equation of the relationship therefore would be:
y = ³/2x
Use this equation to solve for each missing value on the table given:
✔️Where, y = 0, substitute y = 0 into y = ³/2x to find x:
0 = ³/2x
0 * 2 = 3x
0 = 3x
0/3 = x
x = 0
✔️Where, x = 2, substitute x = 2 into y = ³/2x to find y:
y = ³/2(2)
y = 3
✔️Where, y = 6, substitute y = 6 into y = ³/2x to find x:
6 = ³/2x
6 * 2 = 3x
12 = 3x
12/3 = x
x = 4
✔️Where, x = -2, substitute x = -2 into y = ³/2x to find y:
y = ³/2(-2)
y = -3
The cost of a newspaper subscription
includes a discounted initial week. Beatriz
pays $55 for 7 weeks of the newspaper
subscription and $100 for 12 weeks.
As a result, the original discounted price is $1 while the weekly normal price is $9.
How does arithmetic work with discounts?The fundamental formula for calculating a reduction is to increase the initial price by the provided percentage rate in decimal form. We must deduct the reduction from the initial price to determine the item's sale price.
From the given information, we have:
d + 6x = 55 (discounted price for 7 weeks)
d + 11x = 100 (discounted price for 12 weeks)
We can solve this system of equations by eliminating d. Subtracting the first equation from the second, we get:
5x = 45
Dividing both sides by 5, we get:
x = 9
Substituting x = 9 into one of the equations, we can solve for d. Using the first equation, we get:
d + 6(9) = 55
d + 54 = 55
d = 1
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Find the value of (f o g)' at the given value.
To find the value of (f o g)' at a given value, you first need to understand the concept of composite functions and the chain rule of differentiation. Let's break it down step by step.
To find the value of (f o g)' at a given value, you need to evaluate g(x) and f(x), find their derivatives, and use the chain rule to find the derivative of (f o g) at the given value. It is important to understand the concepts of composite functions and the chain rule to be able to solve problems involving these concepts.
What are composite functions? Composite functions are functions that are formed by composing two or more functions. The notation used to denote composite functions is (f o g)(x), which means that the output of function g is used as the input for function f. In other words, we first evaluate g(x), and then use the result as the input for f(x).
What is the chain rule of differentiation? The chain rule of differentiation is a method used to find the derivative of composite functions. It states that if a function is composed of two or more functions, then its derivative can be found by taking the derivative of the outer function and multiplying it by the derivative of the inner function.
To find the value of (f o g)' at a given value, we need to follow these steps:1. Find g(x) and f(x)2. Find g'(x) and f'(x)3. Evaluate g(x) at the given value4. Use the chain rule to find (f o g)' at the given value
step 1: Find g(x) and f(x)Let's say that we have two functions: g(x) = x^2 + 3x + 1 and f(x) = sqrt(x). To find (f o g)(x), we first need to evaluate g(x) and then use the result as the input for f(x). Therefore, (f o g)(x) = f(g(x)) = sqrt(x^2 + 3x + 1)
Step 2: Find g'(x) and f'(x)To find g'(x), we need to take the derivative of g(x) using the power rule and the sum rule. Therefore, g'(x) = 2x + 3To find f'(x), we need to take the derivative of f(x) using the power rule and the chain rule. Therefore, f'(x) = 1/2(x)^(-1/2)
Step 3: Evaluate g(x) at the given valueSuppose we want to find (f o g)' at x = 2. To do this, we need to first evaluate g(x) at x = 2. Therefore, g(2) = 2^2 + 3(2) + 1 = 11
Step 4: Use the chain rule to find (f o g)' at the given value now we can use the chain rule to find (f o g)' at x = 2. Therefore, (f o g)'(2) = f'(g(2)) * g'(2) = 1/2(11)^(-1/2) * (2)(3) = 3/sqrt(11)
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Ver en español
Pam, the CEO of Zettabyte Tek, set up a $750,000 education fund. She wants to give each employee who takes a computer security class a $350 reimbursement toward the cost of the class. You can use a function to describe the amount of money left in the fund after x employees receive the reimbursement.
Write an equation for the function. If it is linear, write it in the form f(x)=mx+b. If it is exponential, write it in the form f(x)=a(b)x.
The formula for this linear function is f(x) = mx + b, where m is the slope (in this example, -350), and b is indeed the y-intercept (750,000 in this case).
What does a simple equation represent?An equation expressing the connection between the expressions on either side of a sign. Normally, it has an equal sign and just one variable. such as: 2x - 4 is equal to 2. The variable x is present in the example above.
Workers who complete the computer security course will each receive a reimbursement of $350.
We deduct $350x from of the initial $750,000 to determine how much money will remain inside the education fund once x employee gets the reimbursement.
Thus, f(x) = 750,000 - 350x is the equation again for function that describes that amount of money still in the fund when x employees receive the refund.
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(showing work would be appreciated)You are planning to rent a condo. Your monthly rent will be $750, and your renter's insurance will be $1,800 per year. What is the adjusted monthly cost for renting this condo?
Using proportions, it is found that the adjusted monthly cost for renting this condo is of $900.
What is a proportion?A proportion is a fraction of a total amount.
The rent also involves the insurance of $1,800 a year. The monthly amount corresponding to the insurance is given by:
$1,800/12 = 150.
Hence, the adjusted monthly cost for renting this condo is given by:
$750 + $150 = $900.
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Find the value of X
40°
(12x-8)
please help I have 10 mins left on my test
Answer:
B.4 12x-8 would be 12x_-8=40 this is because 12x-8 is congruent to the 40 degree angle. so what -8 is 40? 48 12x_=48 x=4 12x4=48 48-8 is 40
plz let me know if i am wrong mark brainliest if right
Step-by-step explanation:
the top of an electric pole is s supported by a wire of 26 ft long on the ground level. how far is tightened spot from the foot of the pole if its height is 24 ft?
Answer:
The tightened spot is 10 feet away from the foot of the pole.
Step-by-step explanation:
1. Draw the diagram. Notice that the shape of the electric pole and its supporting wire creates a right triangle.
2. We know 2 side lengths already (26ft, 24ft), and we need to find 1 more side length. Therefore, to find the 3rd side length of a right-triangle, utilize Pythagoras' Theorem.
⭐What is the Pythagoras' Theorem?
\((C)^2 = (A)^2 + (B)^2\)An equation to find a 3rd side lengthC = hypotenuseA = one legB = another leg3. Substitute the values of the side lengths into the equation, and solve for the unknown side length.
Let B= the distance from the tightened spot to the foot of the pole.
\((C)^2 = (A)^2 + (B)^2\)
\(26^2 = 24^2 + B^2\)
\(676 = 576 + B^2\)
\(100 = B^2\)
\(\sqrt{100} = \sqrt{(B)^2}\)
\(10 = B\)
∴ The tightened spot is 10 feet away from the foot of the pole.
Diagram:
17/2 is bigger than what?
Answer:
7/2= 8.5 so it can be bigger then 1/2 or anything under 8.5
Step-by-step explanation:
A right triangle has sides of lengths 18 , 24 , and 30 units. What is the area of the triangle? Draw the shape on a grid to help find the area.
Answer:216
Step-by-step explanation:The formula to find the area of a triangle is Length times Base divided by 2. The length of the triangle could be 18 or 24, but that doesn’t matter. The base could also be 18 or 24, but that also doesn’t matter, because the hypotenuse (the longest part of a right triangle, in this case being 30), is not a part of the formula. 18 times 24 is 432, and 432 divided by 2 is 216. So the area is 216
The following information was obtained from the accounting records of Letty Stores for the financial year ended 30 June 2021:
R
Inventory (1 July 2020)
100 000
Sales
600 000
Purchases
400 000
Sales returns
2 000
Purchases returns
3 000
Drawings: Bank
1 000
Inventory (30 June 2021)
120 000
Additional information:
1. On 29 June 2021, the owner took inventory with a cost price of R20 000 for own use. This transaction has not yet been recorded.
The entity uses the periodic inventory control system.
Required:
Use the information provided above to calculate the cost of sales for the year ended 30 June 2021.
Answer:
333234
Step-by-step explanation:
333234$ for the next 4 years and the ecvation is 69$+-2$
A car drove 249.48 miles on 12.6 gallons of gas. How far could the car drive on a full tank of 14.8 gallons of gas? Drag and drop a number to correctly complete the statement. Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. The car could drive Response area miles on a full tank of gas. I REAALY NEED HEEEEELP PLEASE HELP ME I WILL GIVE FIVE STARS AND HEART TO WHOEVER ANSWERS IT!!!!!!!!!!!!!!!!!!!!!!!!!
The car could drive approximately 293.04 miles on a full tank of gas. Drag and drop the number "293.04" into the response area to complete the statement.
What is Algebraic expression ?
An algebraic expression is a mathematical phrase that contains variables, numbers, and mathematical operations such as addition, subtraction, multiplication, and division. Algebraic expressions are used to represent mathematical relationships and can be used to solve equations and perform calculations.
We can use the given information to find the car's fuel efficiency in miles per gallon (mpg) as follows:
mpg = miles driven / gallons of gas used
mpg = 249.48 miles / 12.6 gallons
mpg ≈ 19.8
This means that the car can travel approximately 19.8 miles on one gallon of gas. To find out how far the car could drive on a full tank of 14.8 gallons of gas, we can multiply the tank capacity by the car's fuel efficiency:
miles on full tank = mpg * gallons in full tank
miles on full tank = 19.8 mpg * 14.8 gallons
miles on full tank ≈ 293.04 miles
Therefore, the car could drive approximately 293.04 miles on a full tank of gas. Drag and drop the number "293.04" into the response area to complete the statement.
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Convert 21.9 liters to quarts. Round your answer to the nearest tenth. (Hint: There are approximately 1.06 quarts in 1 liter).
Using proportions the volume of the substance is converted from liters to quarts which is 23.214 quarts
Converting Liter to QuartsIn this problem, we need to convert the volume of a substance from liters to quarts. In doing so, we can use a conversion factor which is given as;
1.06 quarts = 1 liter
However, we are given 21.9 liters
Let's equate this proportion and solve
1.06 quarts = 1 liter
x quarts = 21.9 liter
cross multiply both sides
x = (21.9 * 1.06) / 1
x = 23.214
The volume of the substance is 23.214 quarts
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the level of temperature of liquid in a thermometer is 26.52'c lower than the boiling poin. of water. what is the thermometer reading
The thermometer reading would be 73.48°C.
The boiling point of water is generally considered to be 100°C. According to the given information, the temperature of the liquid in the thermometer is 26.52°C lower than the boiling point of water. Therefore, to find the thermometer reading, we subtract 26.52 from 100.
100 - 26.52 = 73.48
Hence, the thermometer reading would be 73.48°C.
In this scenario, we are assuming that the thermometer is calibrated to measure temperature in Celsius. The boiling point of water at standard atmospheric pressure is 100°C, and the given information states that the liquid in the thermometer is 26.52°C lower than the boiling point.
By subtracting 26.52 from 100, we obtain a reading of 73.48°C.
Thermometers work by utilizing the principle that certain substances, such as mercury or alcohol, expand or contract with changes in temperature. The expansion or contraction is measured using a scale, which is marked with various temperature values.
In this case, the thermometer is calibrated in Celsius, so we refer to the Celsius scale. By subtracting 26.52 from 100, we find the temperature at which the liquid in the thermometer is settled, which is 73.48°C.
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In a pre algebra class containing 43 students, there are 4 freshman, 35 sophomores, and 4 juniors. what fraction of the class are sophomores
The fraction of the class that is sophomores is \(35/43\).
The fraction of the class that is sophomores, divide the number of sophomores by the total number of students in the class.
Number of sophomores = 35
Total number of students = 43
Fraction of sophomores = (Number of sophomores)/(Total number of students Fraction of sophomores)
Fraction of sophomores \(= 35 / 43\)
Therefore, the fraction of the class that are sophomores is = \(35/43\).
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Clarksville Middle School spends $14 for every workbook it buys. At most how many workbooks can Clarksville Middle School buy if it has $28 to spend? workbooks
Answer
coochie man
Step-by-step explanation:
Is it possible to find the prime factorization of 29 explain why or why not
Answer:
NoStep-by-step explanation:
29 is a prime number and therefore you can't factorize it.Answer:
No
Step-by-step explanation:
29 is a primeIt has only two factors.i.e 1 and the number itself 29.PLEASE HELPPP THANKS
Answer: The last option. X is greater than or equal to -3
Step-by-step explanation:
If you are searching for all of the values highlighted in red, then it must be every single value greater than x=-3 including the value itself (the dot located on the value is shaded, therefore you must include it within the domain).
A rectangular prism measures 3 ft by 6 ft by 5 ft. If the dimensions of the box were all quadrupled, how would the surface area of the box change?
1.The new surface area would be 16 times the original surface area.
2.The new surface area would be quadruple the original surface area.
3.The surface area would not change.
4.The new surface area would be 12 times the original surface area.
To determine how the surface area of a rectangular prism changes when all dimensions are quadrupled, we need to compare the original surface area to the new surface area.
The original surface area of the rectangular prism is given by:
SA_original = 2lw + 2lh + 2wh
where l, w, and h represent the length, width, and height of the prism, respectively.
In this case, the dimensions of the original box are:
Length (l) = 3 ft
Width (w) = 6 ft
Height (h) = 5 ft
Substituting these values into the formula, we have:
SA_original = 2(3)(6) + 2(3)(5) + 2(6)(5)
= 36 + 30 + 60
= 126 square feet
Now, if we quadruple all the dimensions of the box, the new dimensions would be:
Length (l_new) = 4(3) = 12 ft
Width (w_new) = 4(6) = 24 ft
Height (h_new) = 4(5) = 20 ft
The new surface area of the enlarged box is given by:
SA_new = 2(l_new)(w_new) + 2(l_new)(h_new) + 2(w_new)(h_new)
= 2(12)(24) + 2(12)(20) + 2(24)(20)
= 576 + 480 + 960
= 2016 square feet
Comparing the original surface area (SA_original = 126 sq ft) to the new surface area (SA_new = 2016 sq ft), we can see that SA_new is 16 times greater than SA_original.
Therefore, the correct answer is:
1. The new surface area would be 16 times the original surface area.
To eliminate the x terms and solve for y in the fewest steps, by which constants should the equations be multiplied by before adding the equations together? First equation: 6x -5y = 17 Second equation: 7x + 3y = 11 The first equation should be multiplied by 3 and the second equation by -5. The first equation should be multiplied by 3 and the second equation by 5. The first equation should be multiplied by 7 and the second equation by -6. The first equation should be multiplied by 7 and the second equation by 6.
Answer:
its c
Step-by-step explanation:
i did the test
The first equation should be multiplied by 7 and the second equation by -6. The correct option is C.
What is an expression?In mathematics, an expression is a group of symbols (variables, constants, and mathematical operations) used to represent a quantity or a relationship between two numbers.
In order to eliminate the x terms and find y in the fewest steps feasible, the equations should be multiplied by constants such that the coefficient of x in one equation is equal to the negative coefficient of x in the other.
The coefficients of x in the first and second equations in this situation are 6 and 7, respectively. To make these coefficients opposite in sign, we can multiply the first equation by 7 and the second equation by -6.
The correct solution is obtained by multiplying the first equation by 7 and the second equation by -6.
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convert 44 oz. to a mixed measure
The number of cups in 44 oz is \(5\frac{1}{2}\) as a mixed measure.
We have,
There are different types of mixed measures, but one common one is the mixed number and fraction form.
To convert 44 oz. to a mixed number and fraction, you need to divide the total amount by the size of each unit in the mixed measure and express the result as a whole number and a fraction.
For example,
If the units are cups and there are 8 oz. in a cup, then:
= 44 oz ÷ 8 oz / cup
= 5.5 cups
So
44 oz. is equivalent to 5 cups and 12 oz.
or
44 oz. = \(5\frac{4}{8}\) cups = 5 1/2 cups
Thus,
The number of cups in 44 oz is \(5\frac{1}{2}\) as a mixed measure.
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Two cylinders, a and b, each started with different amounts of water. The graph shows how the height of the water changed as the volume of water increased in each cylinder. Match the graphs of a and b to Cylinders P and Q. Explain your reasoning. height in centimeters b volume in milliliters P
To match the graphs of cylinders a and b to cylinders P and Q, we need to analyze the relationship between the height of the water and the volume of water in each cylinder.
Cylinder P would correspond to graph b, while Cylinder Q would correspond to graph a.
The reasoning behind this is as follows:
Cylinder P, corresponding to graph b, shows a steeper increase in height with increasing volume. This indicates that the water level rises quickly as more volume is added, suggesting that the cylinder has a smaller cross-sectional area. Since height is directly proportional to volume for a cylinder, a smaller cross-sectional area would result in a higher rise in height for the same volume of water.
Cylinder Q, corresponding to graph a, shows a slower increase in height with increasing volume. This implies that the water level rises more gradually as more volume is added, indicating a larger cross-sectional area. A larger cross-sectional area would result in a smaller increase in height for the same volume of water.
In summary, the steeper graph b matches Cylinder P with a smaller cross-sectional area, while the gentler graph a matches Cylinder Q with a larger cross-sectional area.
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Leah and Chris have 3 sushi rolls to share equally for lunch. Leah wants to know how many sushi rolls she will get.
Answer:
She will get 1.5.
Step-by-step explanation:
Because 3/2 is 1.5 so they are equal
y = 1/2x + 1 and 2y - x = 6 How many solutions does this system have?(: -none, one, or ifinite?
Answer:
none
Step-by-step explanation:
___________________
what is question 4????
Answer:
2.2
Step-by-step explanation:
(1.85 x 2) - 1.50
...............
Question 46 of 50
Congruent figures are:
figures that are exactly the same size and shape.
figures that are the same shape.
figures that are the same size.
Congruent figures are figures that are exactly the same size and shape, option A.
What make a figure congruent?A figure is considered congruent when it is exactly the same size and shape as another figure. In other words, two figures are congruent if they can be superimposed on each other perfectly, without any stretching or distortion.
Congruence can also be defined as: if one of the figures can be obtained after a series of rigid motions of the other, the figures are said to be congruent. They both have congruent sides and angles.
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Select all of the expressions that are equal to 6.
l6l
-l-6l
-l6l
l-21 × l3l
l-6l
10-6l
Expressions would be, l-21 × l3l = 6 and l-6l = 6
What is Expressions?
In maths, an expression is a combination of numbers, variables, functions (such as addition, subtraction, multiplication or division etc.)
Equations and expressions are often used in higher levels of mathematics and can require special calculations to solve graphical problems and geometric figures. Sometimes they are used in explanations of lines, cartoons, and diagrams. They also have their place in computer software and used for developing animations.
Expressions can be thought of as similar to phrases. In language, a phrase on its own may include an action, but it doesn't make a complete sentence.
The expressions that are equal to 6 are:
l-21 × l3l = 6
l-6l = 6
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calculate the area of a circle whose circumference is 44cm
Answer:
153.94 square centimeters.
Step-by-step explanation:
To calculate the area of a circle when the circumference is given, you can use the formula:
Circumference = 2 * pi * r, where pi is approximately equal to 3.14 and r is the radius of the circle.
We can rearrange this formula to solve for the radius:
r = Circumference / (2 * pi)
Substituting the given value of circumference:
r = 44 cm / (2 * 3.14) = 7.006 cm (rounded to three decimal places)
Now that we have the radius, we can calculate the area of the circle using the formula:
Area = pi * r^2
Substituting the value of r:
Area = 3.14 * 7.006^2 = 153.94 cm^2 (rounded to two decimal places)
Therefore, the area of the circle is approximately 153.94 square centimeters.