List all the pairs of integers with a product of 30
Javier is evaluating the expression (-8)[10 + (-5) + (-8)]
Multiplying the numbers 10, -5, and -8 by a certain number and then adding the three products together will give Javier the fully simplified evaluated expression. What is that number?
The number that will give Javier the fully simplified evaluated expression is 24.
Explanation:To evaluate the expression (-8)[10 + (-5) + (-8)], we need to multiply the numbers inside the parentheses by a certain number and then add the three products together. Let's solve it step by step:
Multiplying -8 by 10: (-8) * 10 = -80Multiplying -8 by -5: (-8) * (-5) = 40Multiplying -8 by -8: (-8) * (-8) = 64Add the three products: -80 + 40 + 64 = 24Therefore, the number that will give Javier the fully simplified evaluated expression is 24.
simplify 5p2 5p3?
whats the answer
A city had a parade for a winning basketball team. Since it was put together in five days, only 25% of the groups asked to be in the parade were able to participate. If the parade committee asked 128 groups to participate, how many were able to be in the parade?
A. 27
B. 103
C. 11
D. 32
Information about the age of participants in a robotics competition is below: A box plot titled "Age of Participants" and labeled "Age" uses a number line from 10 to 35 with primary markings and labels at 10, 15, 20, 25, 30, and 35. The box extends from 13 to 31 on the number line. A line in the box is at 16. The whiskers end at 11 and 33. The middle 50% of the data is between what two numbers?
The middle 50% of the age of participants in the robotics competition falls between 13 and 31.
Explanation:The box plot represents the age distribution of participants in a robotics competition. The box extends from the lower quartile (Q1) to the upper quartile (Q3), which in this case are 13 and 31, respectively. The line within the box represents the median, which is 16. The whiskers represent the range of the data, ending at 11 and 33.
To find the middle 50% of the data, we need to determine the values that lie between Q1 and Q3. Therefore, the middle 50% of the age of participants in the robotics competition falls between 13 and 31.
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There are approximately 2.6 million deaths per year in country A. Express this quantity as deaths per minute.
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Let f be a function of two variables that has continuous partial derivatives and consider the points a(7, 3), b(12, 3), c(7, 7), and d(15, 9). the directional derivative of f at a in the direction of the vector ab is 5 and the directional derivative at a in the direction of ac is 4. find the directional derivative of f at a in the direction of the vector ad. (round your answer to two decimal places.)
To answer this question, it is necessary to make use of the concepts of directional derivative and gradient of a function.
The solution is:
grad F( x, y ) ×ad(u) =64/10
The gradient of a function f (x,y) is a vector defined by:
grad f(x,y) = δf(x,y)/δx × i + δf(x,y)/δy × j
and directional derivative, in the direction of ab is defined by :
grad f( x,y) × Uᵃᵇ(u) (1) where Uᵃᵇ is a unitary vector in the direction of ab
according to that Uᵃᵇ (u) = Uᵃᵇ/|ab|
Then if the directional derivative of f (x,y) in the direction of the vector ab is 5.
A ( 7 , 3 ) B ( 12 , 3 ) then vector ab is:
ab = [ 12 - 7 , 3 - 3 ] ⇒ ab = [ 5 , 0 ] and |ab| = √ (5)² (0)² |ab| = 5
a unitary vector in the direction of ab is:
ab(u) = 5×i/ 5 and according to equation (1)
δf(x,y) / δx × i × 5 × i / |5| = 5
δf(x,y) / δx × i × 5 × i = 25
δf(x,y) / δx = 5 then f( x,y ) = 5 × x + ????
We go on to calculate the component on j of f(x,y)
Following the same procedure
ac = ( 7 , 7 ) - ( 7 , 3 ) ⇒ ac = [ 0 , 4 ] |ac| = √(4)² + (0)²
|ac| = 4
Unitary vector in the direction of ac(u) is:
ac/|ac| = 4 × j / 4
Then :
δf(x,y) / δy × j × + 4 × j / 4 = 4
δf(x,y) / δy × j × + 4 × j = 16
δf(x,y) / δy = - 4 and f(x,y) = -4×y
f(x,y) = 5 × i + 4 × j
Finally:
vector ad = [ ( 15 - 7 , 9 - 3 ) ] ⇒ ad = ( 8 , 6 )
Unitary vector in direction ad is
ad(u) = ( 8 ×i + 6 ×j ) / √ (8)² + (6)² ⇒ ad(u) = ( 8 ×i + 6 ×j ) /√ (8)² + (6)²
ad(u) = ( 8 ×i + 6 ×j ) /10
Now we have f (x,y ) = 5 × i + 4 × j and ad(u) = ( 8 ×i + 6 ×j ) /10
We can calculate the directional derivative of f(x,y) in the direction of ad with the use of equation (1)
grad F( x, y ) ×ad(u) = ( 5 × i + 4 × j ) × ( 8 ×i + 6 ×j ) /10
grad F( x, y ) ×ad(u) = 4 + ( 24/10)
grad F( x, y ) ×ad(u) =64/10
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the original value of an investment is $1,800. if the value has increased by 7% each year, write an exponential to model the situation. then, find the value of the investment after 15 years
The value of the investment after 15 years is approximately [tex]$4,410.67.[/tex]
To model the situation where an investment of [tex]$1,800[/tex] increases by 7% each year, we can use the exponential growth formula:
[tex]\[ A = P(1 + r)^t \][/tex]
where:
-[tex]\( A \)[/tex]is the amount of money accumulated after n years, including interest.
- [tex]\( P \)[/tex]is the principal amount (the initial amount of money).
- [tex]\( r \)[/tex]is the annual interest rate (in decimal form).
-[tex]\( t \)[/tex] is the time the money is invested for, in years.
Given:
[tex]- \( P = \$1,800 \)[/tex]
[tex]- \( r = 7\% = 0.07 \)[/tex](as a decimal)
-[tex]\( t = 15 \)[/tex] years
We substitute these values into the formula to get:
[tex]\[ A = 1800(1 + 0.07)^{15} \][/tex]
Now, we calculate the value of[tex]\( A \):[/tex]
[tex]\[ A = 1800(1.07)^{15} \][/tex]
Using a calculator, we find:
[tex]\[ A \approx 1800 \times (1.07)^{15} \approx 1800 \times 2.45037 \][/tex]
[tex]\[ A \approx \$4,410.67 \][/tex]
Therefore, the value of the investment after 15 years is approximately [tex]$4,410.67.[/tex]
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Which expression is equivalent to [log9+1/2logx+log(x^3+4)]-log6
Answer:
A.) log 3 sqrt x(x^3+4)/2
PLZ HELP ASAP TANGENTS OF CIRCLES
Heather and Joel bought a house for $157,200 and know that the house appreciates every year. They keep track of their house value for 5 years and model their data with the exponential equation y = 150000(1.004)12t How much will their house be worth in 8 years?
We have to find value of the house in 8 years so we will plug t=8 years in given equation.
[tex] y=150000(1.004)^{\left(12t\right)} [/tex]
[tex] y=150000(1.004)^{\left(12*8\right)} [/tex]
[tex] y=150000(1.004)^{96} [/tex]
[tex] y=150000(1.46702133432) [/tex]
[tex] y=220053.200148 [/tex]
Hence house will worth approx $220053.20 in 8 years.
Heather and Joel bought a house for $157,200 and know that the house appreciates every year. They keep track of their house value for 5 years and model their data with the exponential equation y = 150000(1.004)12t How much will their house be worth in 8 years?
Solution:
Equation of the appreciation of the value of house is given by:-
[tex]y=150000(1.004)^{12t}[/tex]
We need to find the worth of the house after 8 years
So, that means time, t=8
Let us plug t=8 in the equation [tex]y=150000(1.004)^{12t}[/tex]
So, we get,
[tex]y=150000(1.004)^{12*(8)}[/tex]
[tex]y=150000(1.004)^{96}[/tex]
[tex]y=150000(1.467021)[/tex]
y=150000*1.467021
y=220053.20
In 8 years the value appreciates to $220053.20, that s, worth of house after 8 years=$22005320
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Which logarithmic graph can be used to approximate the value of y in the equation 3y = 7?
six friends are going to buy a pizza. Their chices are to biu 2 medium 10-inch diameter pizzas for 7:00 each, or 1 large 14 inch diameter pizza for 15.00. Both prices include tax and tip. The friends agree that their best choice is the one that gives them the most pizza for their money. which is the best choice?
Divide the following polynomials. Then place the answer in the proper location on the grid. Write your answer in order of descending powers of x. Write the quotient and remainder as a sum in this format: . Do not include parentheses in your answer. ( x^3 + y^3) ÷( x- y )
The quotient is [tex]\(x^2 + xy + y^2\)[/tex]s [tex]\(0\)[/tex]
Explanation:To divide the polynomial [tex]\(x^3 + y^3\) by \(x - y\),[/tex]division. The process yields a quotient of [tex]\(x^2 + xy + y^2\)[/tex]f [tex]\(0\)[/tex]s result indicates that the given polynomial is divisible by \(x - y\) without any remainder. The quotient represents the solution, showcasing the expression obtained when [tex]\(x^3 + y^3\)[/tex]y [tex]\(x - y\).[/tex] in the quotient is arranged in descending powers of [tex]\(x\)[/tex] ering to the instructions.
The remainder being [tex]\(0\)[/tex] irms the complete divisibility of the original polynomial by \(x - y\). This concise and ordered format aligns with the specified requirements for presenting the solution on the grid. In summary, the division of [tex]\(x^3 + y^3\) by \(x - y\)[/tex] [tex]\(x^2 + xy + y^2\)[/tex] f [tex]\(0\)[/tex]
Sherrod deposits $500 each year in a savings account earning 3% interest compounded annually. He makes no withdrawals. How much interest will the account earn after 3 years?
The formula for annual compound interest, including principal sum, is:
A = P (1 + r/n) (nt)
Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (500)
r = the annual interest rate (.03)
n = the number of times that interest is compounded per year (1)
t = the number of years the money is invested (3)
A=5000(1+.03/1)^1(3)
A=546.36
Interest (I) gained is A-P
I=546.36-500
I=46.36
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A car dealer buys a new car for $24,500. The dealer then marks the car's price up 27%
What is the selling price of the car?
What is 84%, percent of 300?
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Lisa has a scholarship that pays 75% of her tuition for all four years she attends college. What is the total amount the scholarship is worth if Lisa's classes cost 12,000 per year
To choose a mascot for a new middle school, 8th-grade students were polled, and their top choice was selected as the mascot. Was the sample a biased sample?
Answer:
Yes, the sample was biased.
Step-by-step explanation:
We are told that to choose a mascot for a new middle school, 8th-grade students were polled, and their top choice was selected as the mascot.
We know that an unbiased sample is an accurate representation of the entire population and it can help us draw conclusions about the population.
For an unbiased sample each member of a population should equally likely to be chosen and the sample should be representative of the population as a whole.
For an unbiased sampling for mascot students should be chosen randomly from each grade of the middle school.
Since all the students were polled from the same grade, so their choice can not represent the choices of all the students of the school, therefore, the sample was a biased sample.
For a popular Broadway musical, theater box office all $356 apiece 275, tickets and $60 apiece, and 369 tickets and $45 apiece. How much money did the box office ticket Take in?
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Write the sum using summation notation, assuming the suggested pattern continues. 16 + 25 + 36 + 49 + ... + n2 + ...
Answer:
Hence, the sum using summation notation, assuming the suggested pattern continues [tex]16+25+36+49+......+n^2+.....[/tex] is:
[tex]\sum_{n=4}^{\infty}n^2[/tex]
Step-by-step explanation:
We have to write the sum using summation notation, assuming the suggested pattern continues:
[tex]16+25+36+49+......+n^2+.....[/tex]
Clearly we may also write this pattern as:
[tex]4^2+5^2+6^2+.....+n^2+......[/tex]
So, in terms of the summand it is written as:
[tex]\sum_{n=4}^{\infty}n^2[/tex]
( We have started our summation from 4 since the term in the summation starts with 16 which is 4^2 and goes to infinity )
Write the quotient as a mixed number. 33 ÷ 5 = 6 R2
Miles had a piece of paper 1/4 of a large circle cut in three equal parts from the center point of the circle. What angle is the measure of each part?
The measure of the each part of the large circle is 90 degrees.
What is the measue of each part?
A circle is a bounded figure which points from its center to its circumference is equidistant. The sum of angles in a circle is 360 degrees.
Measure of the angle of each part = 1/4 x 360 = 90 degrees
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