Aubrey has a new art box in the shape of a rectangular prism. The box is 5 inches, by 8 inches, by 2 inches. How much volume is not take-up by the eraser if the dimension of the eraser is 5.5 inches^3
volume of the rectangular prism = base area * height
base area = length * breadth
volume of the rectangular prism = length * breadth * height
volume of the rectangular prism = 5*8*2 = 80 inches ^3
volume of taken up by the eraser = 5.5 inches^3
volume that is not take-up by the eraser = 80-5.5 = 74.5 inches^3
What is the GCF of the terms in 4a^4+6a^2?
The GCF (Greatest Common Factor) of the terms in the algebraic expression 4a^4+6a^2 is found by observing the numerical coefficients (4 and 6) and the variables (a^4 and a^2). The GCF of 4 and 6 is 2, and the GCF of a^4 and a^2 is a^2, so the GCF of the terms in the expression is 2a^2.
Explanation:The GCF (Greatest Common Factor) of two or more terms is the greatest number that divides each of the terms without any remainder. The GCF of the terms in the algebraic expression 4a^4+6a^2 can be found by observing the numerical coefficients and the variables.
1. The numerical coefficients of the terms are 4 and 6. The GCF of 4 and 6 is 2.
2. The variables in the terms are a^4 and a^2. The GCF of a^4 and a^2 is a^2, because a^2 is the factor that appears in both terms to the smallest power.
By combining the GCF of the numerical coefficients with the GCF of the variables, we find that the GCF of the terms in the algebraic expression 4a^4+6a^2 is 2a^2.
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Write the expression in complete factored form 5(y-7)+b(y-7)
The window is 60 inches wide. What is the width of the window in feet.
How do you work with bidmas?
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maria's school is selling tickets to a choral performance. on the first day of ticket sales the school sold 4 adult tickets and 1 child ticket for a total of $47. the school took in $58 on the second day by selling 5 adult tickets and 1 child ticket. what is the price each of one adult ticket and one child ticket?
Which phrase describes the algebraic expression x/15?
the quotient of a number and 15
the product of a number and 15
the sum of a number and 15
15 divided by a number
The school yearbook committee surveyed the student body for an article about colleges in which they are pursuing enrollment. the table below shows the number of students in each grade level; who are pursuing one or more colleges. If there are 170 students in 12th grade, what percentage of the twelfth grade students have more than one college in mind? round your answer to the nearest percent
12th grade----- 1 college= 75 2 colleges= 27 3 colleges or more= 23
Identify the values that create ordered pairs that are solutions to the equation 3x - 5y = 20.
(5,y) (x,2)
The number of students enrolled at a community college increase by 12% from last year to this. The enrollment last year to this year was 15,500 how many students are enrolled this year
The number of students enrolled this year are 17,360.
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Given that, the number of students enrolled at a community college increase by 12% from last year to this.
The enrollment last year to this year was 15,500.
Increased number of students are
12% of 15500
= 12/100 ×15500
= 12×155
= 1860
Number of students enrolled this year are 15,500+1860
= 17360
Therefore, the number of students enrolled this year are 17,360.
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Larry bought a trampoline measuring 10 feet by 12 feet. what is the length of the diagonal of the trampoline?
Kyle was playing a new video game.He scored 128 points on his first game.He scored 305 points on his second game,and 490 on his third game.how many points did Kyle score?
Kyle scored a total of 923 points after playing all the three games.
What is addition ?Addition is defined as combining two or more number together.
Given is Kyle who is playing a new video game. He scored 128 points on his first game, 305 points on his second and 490 points on his third game
The total points scored by Kyle will be the sum of the individual points in each game. Therefore, adding each set of points, we get -
P[T] = 128 + 305 + 490 = 923 points.
Therefore, Kyle scored a total of 923 points after playing all the three games.
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A car leaves a town at 70 kilometers per hour. how long will it take a second car, travelling at 125 kilometers per hour, to catch the first car if it leaves 1 hour later?
Which of the following represents the zeros of f(x) = 6x3 − 35x2 + 26x − 5?
-5,1/3,1/2
5,-1/3,1/2
5,1/3,-1/2
5,1/2,1/3
we have
[tex]f(x)=6x^{3}-35 x^{2} +26x-5[/tex]
we know that
The zeros of the function are the values of x when the value of the function is equal to zero. The zeros of the function are the x-intercepts of the function
Using a graphing tool
see the attached figure
the answer is the option
[tex](5,\frac{1}{2}, \frac{1}{3})[/tex]
Find the value of z /2 that corresponds to a confidence level of 89.48%.
Answer: [tex]1.6202[/tex]
Step-by-step explanation:
The given confidence level : c= 89.48%.
⇒ c= 0.8948 [ in decimal]
Then, the significance level = [tex]\alpha= 1-c[/tex]
[tex]=\alpha= 1-0.8948=0.1052[/tex]
Now, to find the value of [tex]z_{\alpha/2}[/tex] , we need to find the two -tailed z-value using z-table for [tex]\alpha=0.1052[/tex] or we can also find the one-tailed z-value for for [tex]\alpha/2=0.1052/2=0.0526[/tex]
Using z-value table , the value is [tex]1.6202[/tex]
Hence , [tex]z_{\alpha/2}=1.6202[/tex] that corresponds to a confidence level of 89.48%.
Using confidence interval concepts, it is found that the critical value is [tex]z_{\frac{\alpha}{2}} = 1.62[/tex]
For a confidence level of [tex]\alpha[/tex], the critical value of z is z with a p-value of:
[tex]\frac{1 + \alpha}{2}[/tex]
The p-value is found looking at the z-table.In this problem, confidence level of 89.48%, thus [tex]\alpha = 0.8948[/tex] the p-value of the z-score is:
[tex]\frac{1 + 0.8948}{2} = 0.9474[/tex]
Looking at the z-table, this value is [tex]z_{\frac{\alpha}{2}} = 1.62[/tex].
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Linda has completed 24 deliveries so far this week. she needs to make 40 deliveries for the week. what percentage of her deliveries has linda completed?
Final answer:
Linda has completed 60% of her deliveries for the week.
Explanation:
Linda has completed 24 deliveries out of a total of 40 deliveries for the week. To find the percentage of deliveries Linda has completed, we can divide the number of completed deliveries by the total number of deliveries and multiply by 100.
Percent of deliveries completed = (Number of completed deliveries / Total number of deliveries) * 100
Percent of deliveries completed = (24/40) * 100 = 60%
The ratio of the height of a wall to the length of the wall is 2:3. the area of the wall is 384 sq. ft. what are the height and length of the wall?
The dimensions of the wall are found by defining variables based on the given ratio and area, resulting in a height of 16 ft and a length of 24 ft.
The question involves finding the dimensions of a wall given the ratio of its height to length and its total area. To solve this, let's denote the height of the wall as 2x and the length of the wall as 3x, based on the ratio 2:3. The area of the wall is the product of its height and length, which means (2x) ×(3x) = 384 sq. ft.
Now, by simplifying the equation, we get [tex]6x^2[/tex] = 384. Dividing both sides by 6 gives us [tex]x^2[/tex] = 64. Taking the square root of both sides, we find x = 8. Therefore, the height of the wall is 2x = 16 ft and the length of the wall is 3x = 24 ft.
What constant term should be used to complete the square? x 2 - 5x + _____ = 7
The was designed to make it easier for people to own a home.
A. community reinvestment act of 1977
B. federal home loan mortgage corporation
C. comprehensive mortgage reform act
D. federal national mortgage association
Which statement is true about the circumference of a circle?
The circumference is the measurement around the circle.
The circumference is the measurement of the radius.
The circumference is the measurement of the diameter.
The circumference is double the radius.
[tex]\boxed{\large{\bold{\textbf{\textsf{{\color{blue}{Answer}}}}}}:)}[/tex]
circumference of a circle:-The circumference is the measurement around the circle.
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In a large population, 61 % of the people have been vaccinated. if 4 people are randomly selected, what is the probability that at least one of them has been vaccinated?
Final Answer:
The probability that at least one of the four randomly selected people has been vaccinated is approximately 0.9606.
Explanation:
To find the probability that at least one of the four randomly selected people has been vaccinated, we can use the complement rule. The complement of "at least one person vaccinated" is "none of the people vaccinated." Then, we subtract the probability of none of them being vaccinated from 1.
Given that 61% of the population has been vaccinated, the probability that a randomly selected person has been vaccinated is [tex](P(\text{vaccinated}) = 0.61\)[/tex].
So, the probability that a randomly selected person has not been vaccinated is [tex]\(P(\text{not vaccinated}) = 1 - P(\text{vaccinated}) = 1 - 0.61 = 0.39\).[/tex]
Now, we can find the probability that none of the four randomly selected people has been vaccinated:
[tex]\[P(\text{none vaccinated}) = (0.39)^4\][/tex]
And the probability that at least one of them has been vaccinated is the complement of this:
[tex]\[P(\text{at least one vaccinated}) = 1 - P(\text{none vaccinated}) = 1 - (0.39)^4\][/tex]
Let's calculate it:
[tex]\[P(\text{at least one vaccinated}) = 1 - (0.39)^4\][/tex]
[tex]\[P(\text{at least one vaccinated}) \approx 1 - 0.0394179 \][/tex]
[tex]\[P(\text{at least one vaccinated}) \approx 0.9605821\][/tex]
So, the probability that at least one of the four randomly selected people has been vaccinated is approximately 0.9606.
The probability that at least one of the 4 randomly selected people has been vaccinated is calculated using the complement rule and is found to be 0.9769.
To determine the probability that at least one of the 4 randomly selected people has been vaccinated, we can use the complement rule. The probability of an individual not being vaccinated is 1 - 0.61 = 0.39.
We need to calculate the probability that none of the 4 selected people are vaccinated and subtract this from 1:
Probability that a single person is not vaccinated: 0.39Probability that all 4 people are not vaccinated: 0.39⁴0.39⁴ = 0.0231Thus, the probability that at least one of them is vaccinated is:
1 - 0.0231 = 0.9769
Therefore, the probability that at least one of the 4 randomly selected people has been vaccinated is 0.9769.
A ball is kicked into the air and follows the path described by h(t)= -4.9t^2+6t+0.6. where t is the time in seconds and h is the height in meters above the ground. Find the maximum height of the ball. What value would you have to change in the equation if the maximum height of the ball is more than 2.4 meters?
FIND THE VETEX!!!!
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Suppose your friend’s parents invest $20,000 in an account paying 5% interest compounded annually. What will the balance be after 10yr?
To find the balance after 10 years when $20,000 is invested at 5% interest compounded annually, we can use the formula for compound interest:
A = P(1+r)ⁿ
Where:
*A is the complete volume of money obtained after
*n years, including interest.
*P embodies the initial investment, or the principle amount.
*The yearly interest rate, calculated by decimal, is r.
*n is the number of periods the money has been put into investments for.
Given:
*P = $20,000
*r = 5% = 0.05
*n = 10 years
Taking appropriate values to carry out the calculation:
A = 20000(1 + 0.05)¹⁰
A = 20000(1.05)¹⁰
Now, let's calculate:
A ≈ 20000 × (1.05)¹⁰
A ≈ 20000 × 1.62889462677744
A ≈ 32577.89
So, the balance after 10 years will be approximately $32,577.89.
After 10 years, the balance of the investment can be calculated using the formula for compound interest: A = P(1+r)ⁿ
Where:
*A is the amount of money accumulated after
*n years, including interest.
*P is the principal amount (the initial investment).
*r is the annual interest rate (in decimal).
*n is the number of times the interest is compounded per year.
In this case, the principal (P) is $20,000, the annual interest rate (r) is 5%, and the investment is compounded annually. Substituting these values into the formula:
A = 20000(1.05)¹⁰
A ≈ 20000 × (1.05)¹⁰
After computation, the balance after 10 years is approximately $32,577.89. This represents the accumulated amount including the initial investment and the interest earned over the 10-year period.
Complete Question:
Suppose your friend’s parents invest $20,000 in an account paying 5% interest compounded annually. What will the balance be after 10yr?
Angles 4 and 5 form what type of angles?
Angles 4 and 5 form a pair of vertical angles. Vertical angles are two angles that are opposite each other when two lines intersect. They have the same measure and are congruent.
Vertical angles are a pair of angles formed when two lines intersect. In this case, angles 4 and 5 are considered vertical angles because they are opposite each other at the point where the lines intersect. These angles have a special property: they are congruent, which means they have the same measure. This is a fundamental principle in geometry.
Imagine drawing two straight lines that intersect, creating four angles. Angles 4 and 5 are positioned opposite each other, and they share the same measurement. This relationship is true regardless of the lengths of the lines or the specific angles involved. It's a geometric rule that holds true in all cases where vertical angles are formed.
Understanding vertical angles is important in various mathematical and geometric applications, as it allows us to make deductions about the relationships between angles and lines in different configurations.
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The perimeter of a rectangle is 26 inches and its area is 40 square inches. what are its dimensions?
Answer:
The shorter side is 5 inches and the longer side is 8 inches.
Explanation:
We start by listing formulas for solving for the area and perimeter of a rectangle, which will then determine how we find the dimensions we are looking for.
The area of a rectangle is length (l) times width (w), often represented as:
A = l(w), or A = lw
The perimeter of a rectangle is the sum of twice the length and twice the width, often represented as:
P = 2l + 2w
If product of length and width is 40 inches per the rectangle's given area, then a factor pair of 40 must be the dimensions of the rectangle. These values can then be checked to see if they also satisfy the perimeter of the rectangle.
So first, list factors of 40:
1, 40; 2, 20; 4, 10; 5, 8
Now, we plug these pairs into the perimeter equation.
2(1) + 2(40) = 2 + 80 = 82
82 > 26
2(2) + 2(20) = 4 + 40 = 44
44 > 26
2(4) + 2(10) = 8 + 20 = 28
28 > 26
2(5) + 2(8) = 10 + 16 = 26
26 = 26
Therefore, the factors 5 and 8 are what we use. 5 inches by 8 inches are the dimensions.
If 8a−4b=20 and 4a−8b=4, then what is the value of a−b?
What is the place value of the digit 4 in 6,296.04
The digit 4 in 6,296.04 is in the hundredths place, representing four hundredths or 4/100. This can also be expressed in scientific notation as 4 x 10⁻².
The place value of the digit 4 in 6,296.04 is in the hundredths position. This is because the digit 4 is two places to the right of the decimal point. In a decimal number, the first place to the right of the decimal point is the tenths place, the second is the hundredths place, and it continues with thousandths, ten-thousandths, and so on. Therefore, in the number 6,296.04, the 4 represents four hundredths, or 4/100, which can also be written in scientific notation as 4 × 10⁻².