Answer:
5
Step-by-step explanation:
:)
Answer:5
Step-by-step explanation:|-10|-|-5|
10-5
5
What is the coefficient of the 6th term of (2x - 7)9 ?
Answer: the coefficient of the 6th term of (2x - 7)⁹ is -33882912
Step-by-step explanation:
[tex](2x-7)^9[/tex]
In this problem we use the following formula:
[tex](a+b)^n=\sum\limits _{k=0}^nC_n^ka^{n-k}b^k[/tex]
a=2x b=-7 n=9
The 1th term of (2x-7)^9 is k=0
The 2th term of (2x-7)^9 is k=1
The 3th term of (2x-7)^9 is k=2
..........................................................
The 6th term of (2x-7)^9 is k=5
Hence,
[tex]\displaystyle\\C_9^5(2x)^{9-5}(-7)^5=\\\\\frac{9!}{(9-5)!*5!}(2x)^4(-7)^5 =\\\\\frac{9!}{4!*5!} 2^4x^4(-7)^5=\\\\126(16)(-16807)(x^4)=\\\\=-33889212x^4[/tex]
- 33889212x⁴ is the coefficient of the 6th term in binomial theorem .
What is binomial theorem?
The formula for the binomial theorem is (a+b)n= nr=0nCr an-rbr, where r is a real number, a, and b are real numbers, and n is a positive integer. This equation aids in the expansion of binomial formulae like (x + a)10, (2x + 5)3, (x - (1/x)), and so forth.( 2x - 7 )⁹
compare with formula
a = 2x b = - 7 n = 9
The 1th term of (2x-7)^9 is k=0
The 2th term of (2x-7)^9 is k=1
The 3th term of (2x-7)^9 is k=2
...................................................
The 6th term of (2x-7)^9 is k=5
hence
⁵C₉( 2x )⁹⁻⁵ ( - 7)⁵ = 9!/( 9-5)!* 5! (2x)⁴( -7)⁵
= 9!/4! * 5! 2⁴x⁴( -7)⁵
= 126(16) ( - 16807 )(x)⁴
= - 33889212x⁴
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The amount of Jerry's pay every week before taxes, J, is given below as a function of the number of overtime hours that he works (the number of hours over 40), h.
J = $493.60 + $18.51h
Assuming that Jerry is only paid for each whole hour that he works, how many total hours would Jerry have to work during a week to make at least $700.00?
A. 51
B. 52
C. 62
D. 11
The total number of hours that Jerry would work during a week to make at least $700.00 is 11 hours
How to determine number of hours that Jerry would workinformation given in the query
The amount of Jerry's pay every week before taxes, J,
a function of the number of overtime hours that he works (the number of hours over 40), h
J = $493.60 + $18.51h
The given equation is an equation of linear function
considering the equation J = $493.60 + $18.51h, the number of hours that Jerry would work is gotten by substituting the value of $700.00 and solving for number of hours
J = $493.60 + $18.51h
700 = 493.60 + 18.5h
18.5h = 700 - 493.60
18.5h = 206.4
h = 11.16
h = 11 hours
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In triangle GHJ, K(8,6) is the midpoint of GH, L(2,2) is the midpoint of HJ, and
M(10,4) is the midpoint of GJ. Find the coordinates of G, H, and J.
The coordinates of G(4, 4) , H (0, 2), J(8, 0)
In order to construct the three sets of relationships between the coordinates of each triangle's three sides' ends and the shared midpoint, we must first set up the three sets of relationships.
G(x(G), y(G))
K(2, 3) (2, 3)
M(6, 2) (6, 2)
H(x(H) and y(H))L (4, 1)
J(x(J), y(J))
K(2, 3) at the midway of side GH
According to the x-component:
x(H) = x(G - x(H))/2
x(G)-[x(H)-x(G)] = 2*x(H)
x(H) + x(G) = 4
x(H) = 4 - x(G) (G)
According to the y-component:
y(H) plus [y(G) - y(H)]/2 = 3.
2*y(H) plus [y(G-y(H)] = 6
y(H) + y(G) = 6
y(H) = 6 - y(G) (G)
Midpoint L(4) and side JH(1):
According to the x-component:
(x(H) + [x(J) - x(H)]/2) equals four.
2*x(H) plus [x(J)-x(H)] = 8
x(H) + x(J) = 8
x(H) = 8 - x(J) (J)
According to the y-component:
y(H) = y(J - y(H)]/2 + y(J) = 1
y(J) - y(H) = 2*y(H)
y(H) + y(J) = 2
y(H) = 2
Side GJ with M(6, 2) as the midpoint:
For the x - component, the formula is: x(J) = [x(G) - x(J)]/2 = 6 2*x(J) = [x(G)- x(J)] = 12 x(J) = 12 - x (G)
y(J) + [y(G) - y(J)]/2 = 2 2*y(J) + [y(G)- y(J)] for the y-component. = 4 y(J) = 4 - y + y(G) = 4 y(J) (G)
The x and y coordinates may now be easily separated, and we can use algebra to isolate each one and determine its location.
x(H) = 4 - x(G), 8 - x(J), and 12 - x(J) (G)
Because x(H) = x (H)
4 - x(G) = 8 - x(J) (J)
8 - x(J) - 8 - x(G) - 4 = -x(J) x(J) x(J) = 4 + x (G)
Using 1.c above and this relationship now x(J) = x(J), so:
-2 * x(G) = -8 x(G) =, 4 12 - x(G) = 4 + x(G) 12 - x(G) - x(G) - 12 = 4 + x(G) - x(G) - 12
Given that x(J) = 4 + x(G) above, x(J) = 4 + 4 = 8 and x(H) = 4 - x(G) = 4 - 4 = 0 respectively.
Let's now perform the identical procedure using the y-coordinates.
y(H) = 6 - y(G), y(H) = 2 - y(J), y(J) = 4 - y(G),
and since y(H) = y(H), 6 - y(G) = 2 - y(J), -y(G) = 2 - y(J) - 6 = -y(J) - 4 y(G) = y(J) + 4 Now that y(J) = 4 - y,
we may substitute (G).
y(H) = y(G) - 2 and y(H) + 4 - y(G) = 2
and y(H) + 4 - y(G) = 2 - 4 and y(G)
Since y(H) = 6 - y(G)
according to 1. above, y(H) = y(G) - 2 + 6 - y(G) 2 * y(H) = 4 y(H) = 2 y(H) = 2 - y(J) 2 = 2 - y(J) y(J) = 4 - y(G) 0 = 4 - y(G) y(G)
H(x(H), y(H)), G(x(G), y(G)), and J(x(J), y(J)) are the results.
To determine the coordinates of the angles or triangle's tips, we used the midpoints of each side.
The coordinates are: H (0, 2) G(4, 4) J(8, 0)
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Find the side length of x. Round your answer to nearest hundredth
Answer:
9
Step-by-step explanation:
I hope this helps!
Ray's favorite activity is taking a leisurely bike ride through the park after work. Suppose his bike has a flat tire, so he decides to go for a jog instead. Jogging burns 745 calories an hour. How long does he need to jog in order to burn off that same extra doughnut and large frozen latte that he ate that afternoon? The doughnut had approximately 320 calories, and the latte had 820 calories.
Ray have to jog 1.53 hours to burn the calories he had taken by eating doughnut and latte.
Given,
The amount of calorie burns while jogging = 745 calories
The amount of calorie in Doughnut = 320 calories
The amount of calorie in latte = 820 calories
Here,
Total calorie intake by Ray = 320 + 820 = 1140
The calorie burnt while jogging = 745
Number of hours Ray needs to jog for burning 1140 calories;
1140/745 = 1.53 hours.
That is,
Ray have to jog 1.53 hours to burn the calories he had taken by eating doughnut and latte.
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A 2 1/2 foot by 8-foot concrete wall is to be built using concrete blocks. Find the area of the wall.
20 foot² is the area of the wall.
What does a math area mean?
The amount of space occupied by a flat (2-D) surface or an object's shape is known as its area. On a sheet of paper, use a pencil to create a square. It has two dimensions. Its Area refers to the area that the shape occupies on the paper. Consider your square as being composed of smaller unit squares.Length of concrete wall = [tex]2\frac{1}{2}[/tex] foot
Breadth of concrete wall = 8 foot
Since, area means product of dimensions so we use the formula mentioned below:
Area of the concrete wall = length× breadth
= [tex]2\frac{1}{2}[/tex] * 8
= 5/2 * 8
= 5 * 4 = 20 foot²
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Which of the terms below correctly describe(s) the number 40?
A-irrational
B-real
C-inter
D-imaginary
E-rational
F-natural
Solve for (A) current ratio, (B) acid test (quick), (C) average day's collection (D) asset turnover, and (E) profit margin on sales. Round to nearest hundredth or hundredth percent as needed. Current Assets $ 21,000 Accounts Receivable 4,200 Current Liabilities 16,000 Inventory 3,500 Net Sales 41,000 Total Assets 32,000 Net Income 6,000
a. The current ratio is 1.3125
b. The acid test is 1.09375.
c. The average day collection is 37 days.
d. The asset turnover is 1.28.
e. The profit margin on sales is 14.63%.
How to calculate the current ratio?a. The current ratio will be:
= Current asset / Current liability
= 21000 / 16000
= 1.3125
b. Acid test quick ratio will be:
= (Current asset - Inventory) / Current liability
= (21000 - 3500) / 16000
= 1.09375
c. Average day collection will be:
= Account receivable / (Net sales / 360)
= 4200 / (41000 / 36)
= 4200 / 114
= 37 days.
d. Asset turnover will be:
= Net sales / Total asset
= 41000 / 28000
= 1.28
e. Profit margin will be:
= Net income / Net sales
= 6000 / 41000
= 14.63%
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Which option shows an expression meaning 4 less than 5 times
a number?
You can earn 5 coins
4n-5
5n+ 4
5n-4
4n+5
Submit
Answer: 5n - 4
Step-by-step explanation:
n is the number, 5 times the number is 5n. 4 less means subtract 4. So the correct expression is 5n - 4
a.) find the test statistic
b.) what is the p-value
c.)what is the conclusion about the null hypothesis
d.) what is the final conclusion?
a) The test statistic is: t = -7.44.
b) The p-value is: < 0.0001.
c) The conclusion is that the null hypothesis is rejected.
d) The final conclusion is that there is sufficient evidence to conclude that the mean prediction error is different of zero.
What are the features of the test and how does it relates to the hypothesis?From the pop-up shown at the complete problem given by the image at the end of the answer, the test statistic and the p-value are given as follows:
Test statistic: t = -7.44.P-value: < 0.0001.The conclusion regarding the null hypothesis is to reject the null hypothesis, as the test statistic has an absolute value less than the critical value, as we are using a two-tailed test, comparing if the mean is different of zero.
Considering that the null hypothesis is rejected, and also that the p-value is less than the significance level of 0.05, there is sufficient evidence to conclude that the mean prediction error is different of zero.
Missing InformationThe pop-ups with the information of the test are given by the image at the end of the answer.
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It is estimated that only around 200,000 Americans have central heterochromia (two different eye colors in the same eye). If the population of the United States
was 327,750,000 people at the time of this report, what percent of Americans had central heterochromia?
0.0061%
0.00061%
0.61%
0.061%
The percent of Americans that had central heterochromia is A. 0061%.
What is percentage?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.
In this case, it's estimated that only around 200,000 Americans have central heterochromia and the population of the United States
was 327,750,000 people.
The percent of Americans that had central heterochromia will be:
= Those with the disease / Total population × 100
= 200,000 / 327,750,000 × 100
= 0.0061%
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A frozen yogurt stand charges per ounce of frozen yogurt purchased. There is an extra charge for a waffle bowl. The total cost (c), in dollars, for f ounces of frozen yogurt in a waffle bowl, is described by the function c = 0.45f + 1.
Which statement is true?
A.
The cost of 0.45 ounce of frozen yogurt in a waffle bowl is $1.
B.
Each ounce of frozen yogurt costs $1 and a waffle bowl is $0.45 extra.
C.
Each ounce of frozen yogurt costs $0.45 and a waffle bowl is $1 extra.
D.
The cost of 0.45 ounce of frozen yogurt in a waffle bowl is $1.45.
Answer:
$0.45 and a waffle bowl is $1 extra.
Step-by-step explanation:
PLEASE HELP BY 8/11/2022
Answer:
9 m
Step-by-step explanation:
given,
area of floor of play pen = 5 m²
we know, area of a square = (side)² sq units
now according to the question,
5 = (side)²
⇒√(side)² = √5 [taking square root on both sides]
⇒ side = √5 m
now, we know,
perimeter of a square = 4 × side = 4 × √5 = 8.94 m (app.) ≈ 9 m
Abe digs a hole at a steady rate of (meaning negative) 1.2 feet every hour.
Consider ground level to be 0.
What value represents the elevation of the hole relative to ground level after digging for 2.5 hours?
Enter your answer in the box.
Use the compound interest formula to compute the total amount accumulated and the interest earned.
$3500 for 2 years at %3 compounded quarterly.
The total amount accumlated after 2 years is ____.
(Round to the nearest cent as needed.)
The total amount accumulated after 2 years is $3704. 0
How to determine the compound interestThe formula for calculating compound interest is expressed as;
A = P ( 1 + r/ n) ^nt
Where;
A is the final amountP is the principal amountr is the ratet is the timen is the number of times interest applied per periodNow, let's substitute the values into the formula, we have;
A = $3500 ( 1 + 0. 03 / 0. 25) ^(0.25× 2)
Find the exponent
A = $3500 ( 1 + 0. 03 / 0. 25) ^0.5
A = $3500( 1+ 0. 12)^0. 5
Expand the bracket
A = $3500 (1. 12)^0. 5
A = $3500(1. 05)
multiply the values
A = $3704. 0
Hence, the value is $3704. 0
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Abigail is studying for the school spelling bee. She already knows 150 words from the vocabulary list. Each day, she learns 50 additional words from the vocabulary list.
Which equation can be used to determine the total number of words Abigail knows from the vocabulary list, y, over x days?
A. y = 50x + 150
B. y = 50(x + 150)
C. y = 50x - 150
D. y = 150x + 50
The equation that can be used to determine the total number of words Abigail knows from the vocabulary list, y, over x days is A. y = 50x + 150
What is an equation?An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
In this case, Abigail already knows 150 words from the vocabulary list and each day, she learns 50 additional words from the vocabulary list.
Let x be the number of days.
y = vocabulary list
The equation will be:
y = 150 + 50x
Therefore, the correct option is A.
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the product of a number and 12 increased by two
After solving the formed equation from the question, the result will be equal to 4.
What is an arithmetic operation?The four fundamental operations of arithmetic are addition, subtract, multiply, and division of two or more numbers. Included in them is the study of integers, especially the order of operations, which is important for all other aspects of mathematics, notably algebra, information management, and geometry.
The given statement of the question in the equation form will be,
5x + 12 = 32
5x = 20
x = 4
Therefore, the value of x will be equal to 4.
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Your complete question must be like this:
The product of a number and 5 is increased by 12 the result is 32 to find the number.
Elijah has red and yellow napkins. He must set out napkins for 4 people. What are different ways to make groups of 4?
The different ways to make groups of 4 based on the napkins given is 6 ways.
What is combination?Combinations are also referred to as selections. Combinations implies the selection of things from a given set of things. In this case, we intend to select the objects. Thus can be illustrated by nCr
Combination formula
nCr = n! / ((n – r)! r!)
n = the number of items.
r = how many items are taken at a time
In this case, Elijah has red and yellow napkins. He must set out napkins for 4 people. This will be:
= n! / ((n – r)! r!)
= 4! / (4 - 2)! 2!
= 4! / 2!2!
= 4 × 3/2
= 6
Therefore, there are 6 ways.
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Mexico City had an estimated population of 18,066,000 people while Tokyo had an estimated population of 34,450,000 people. What was their combined population?
Answer:
Scientific notation: 5.2516 x [tex]10^{7}[/tex]
Standard notation 52,516,000
Step-by-step explanation:
Are you asking for the answer to be in scientific notation?
5.2516 x [tex]10^{7}[/tex] or 52,516,000
(1.8066 x [tex]10^{7}[/tex]) + (3.445 x [tex]10^{7}[/tex])
(1.8066 + 3.445) x [tex]10^{7}[/tex]
5.2516 x [tex]10^{7}[/tex]
if a volume of an object varies directly with its width and if the volume is 16, while the with is 4 what is k?
The value of k is 4.
What is Proportion ?In general, the term "proportion" refers to a part, share, or amount that is compared to a total.
According to the concept of proportion, two ratios are in proportion when they are equal. Two ratios or fractions are equal when an equation or a declaration to that effect is utilised.
A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.
Given:
Volume= 16
Width = 4
So, we can write the relation as
Volume= k (width)
k = Volume/ width
k= 16/4
k = 4
Hence, the value of k is 4.
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Brainly your my last hope :( please if its the last thing you do
Answer:
3/20
Step-by-step explanation:
3/5 : 4
3/5 x 1/4
3/20
(7x2) x 3
Drag numbers to the boxes to show how to find the product.
(7x2) x3 = 7x (
(7x2) x3 = 7x
(7×2)×3={______
x3
2 3 6 7 13 21 42 49
how many integers are between square root of 7 and 220
Step-by-step explanation:
sqrt(7) is larger than 2 (2² = 4) but smaller than 3 (as 3² is 9).
sqrt(220) is larger than 14 (14² = 196) but smaller than 15 (15² = 225).
so, the integers between them are
3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14
these are 12 integer values.
(2,y) and (x,−3).
4x+2y=14
X/-9 = 3
X equals what?
Answer:
X=-27
Step-by-step explanation:
X/-9 = 3
(-9) * X/-9 =(-9) * 3
X=(-9) * 3
X=-27
Answer:
x=-27
Step-by-step explanation:
x/-9=3
Multiply each side by -9
x=-27
That's it!
shopping at savers mart, Lisa buys her children four shirts and three pairs of pants for $85.50. she comes back the next day and buys three shirts and five pairs of pants for $115. What is the price of each shirt and each pair of pants.
LoWatts Ltd makes light bulbs that are identical in size
They have regular orders from company A for 120 light bulbs and from Company B for 168 light bulbs.
LoWatts Ltd uses one size of box to supply both company A and company B. Each box used contains the same number of light bulbs and is full.
The number of boxes used is as few as possible
How many light bulbs does each box hold?
Using the greatest common factor, the number of light bulbs in each box is 24.
What is the greatest common factor?The greatest common factor (GCF) is the number that can divide two or more numbers without a remainder.
The GCF is a divisor that divides dividends evenly, leaving only quotients without remainders.
For instance, the greatest common factor of 120, 168, and even 288 is 24.
Using this GCF implies that 24 can divide 120, 168, and 288 without leaving any remainders.
Company A Company B Total
Total orders for light bulbs 120 168 288
Greatest common factor of 24 24 24
Number of boxes delivered 5 7 12
Thus, with the greatest common factor as 24 light bulbs in each box, Company A will be supplied 5 boxes, while Company B will be supplied with 7 boxes.
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The time required for an automotive center to complete an oil change service on an automobile approximately follows a normal distribution, with a mean of 15 minutes and a standard deviation of 4 minutes. (a) The automotive center guarantees customers that the service will take no longer than 20 minutes. If it does take longer, the customer will receive the service for half-price. What percent of customers receive the service for half-price? (b) If the automotive center does not want to give the discount to more than 7% of its customers, how long should it make the guaranteed time limit?
a) 25 % of customers receive the service for half-price.
b) The guaranteed time limit should be of 16 minutes.
What is Z-score?The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score.
When the distribution is normal, we use the z-score formula.
The p-value is the probability that the value of the measure is smaller than X, which is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
we have that mean of 15 minutes and a standard deviation of 4 minutes.
(a) Longer than 20 minutes is 1 subtracted by the p value of Z when X = 20. So
[tex]Z = \dfrac{{x} - \mu}{\sigma}[/tex]
Z = (20 - 15)/4
Z = 5/4
Z = 1.25
1.25 has a pvalue of 0.25
1 - 1.25= 0.25
25 % of customers receive the service for half-price.
(b) The time limit should be the 100 - 7 = 93th percentile, which is X when Z has a pvalue of 0.93. So X when Z = 0.25.
[tex]Z = \dfrac{{x} - \mu}{\sigma}[/tex]
0.25= (x- 15)/4
x = 16
The guaranteed time limit should be of 16 minutes.
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Consider the equation and the following ordered pairs: (6,y) and (x,1).
y=−2x+5
The values of y and x are -7 and 2 respectively, completing the ordered pairs: (6,-7) and (2,1).
What are the values of y and x?Given the equation in the question;
y = −2x + 5Ordered pairs: (6,y) and (x,1)To find the y-value that completes the ordered pair ( 6,y ), replace all occurrence of x with 6 in the equation and solve for y.
y = −2x + 5
y = −2( 6 ) + 5
Multiply -2 and 6
y = -12 + 5
y = -7
Hence, the output value is -7, this forms an ordered pair of (6,-7).
To find the x-value that completes the ordered pair ( x,1 ), replace all occurrence of y with 1 in the equation and solve for x.
y = −2x + 5
1 = −2x + 5
Add 2x to both sides
1 + 2x = −2x + 2x + 5
1 + 2x = 5
2x = 5 - 1
2x = 4
x = 4/2
x = 2
Hence, the input value is 2, this forms an ordered pair of (2,1).
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On average, Jaya drinks of a 6-ounce glass of water in 13 hours. How many glasses of water does she drink in one hour?
On average, Jaya drinks 0.46 ounces glasses of water does she drink in one hour.
Average:
Average refers the mean value which is equal to the ratio of the sum of the number of a given set of values to the total number of values present in the set.
Given,
On average, Jaya drinks of a 6-ounce glass of water in 13 hours.
Here we need to find the number of glasses of water does she drink in one hour.
Let x be the number of glasses of water does she drink in one hour.
We know that, Jaya drinks of a 6-ounce glass of water in 13 hours.
So, in order to find the average we have to divide the number of glasses by the time taken.
So, it can be written as,
=> 6/13
=> 0.46
Therefore, for one hour Jaya drinks 0.46 ounces of water.
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