Answer:
[tex]y-7=-\frac{4}{3}(x+7)[/tex]
Step-by-step explanation:
The slope of the line is [tex]\frac{-9-7}{5-(-7)}=-\frac{4}{3}[/tex].
The equation of the line passing through the point [tex](x_1, y_1)[/tex] and slope [tex]m[/tex] is [tex]y-y_1=m(x-x_1)[/tex], so the equation is [tex]y-7=-\frac{4}{3}(x+7)[/tex].
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
Learn more about binomial theorem
brainly.com/question/27813780
#SPJ13
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.
Learn more about equations on:
brainly.com/question/2972832
#SPJ1
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%
Learn more about percentages on:
brainly.com/question/24304697
#SPJ1
Which of the terms below correctly describe(s) the number 40?
A-irrational
B-real
C-inter
D-imaginary
E-rational
F-natural
David and his children went into a grocery store and he bought $7.50 worth of apples and bananas. Each apple costs $0.75 and each banana costs $0.50. He bought 5 more bananas than apples. By following the steps below, determine the number of apples, x, and the number of bananas, y, that David bought.
DETERMINE THREE WAYS TO HAVE 5 MORE BANANAS THAN APPLES
Answer:
Let the number of apples and bananas bought be x and y respectively.
x + 5 = y ------ equation (1)
0.75x + 0.50y = 7.50 ------ equation (2)
Substitute equation (1) into equation (2):
0.75x + 0.50(x+5) = 7.50
0.75x + 0.50x + 2.50 = 7.50
1.25x = 5
∴x = 4
Substitute x = 4 into equation (1):
∴y = 4+5
= 9
∴David bought a total of 4 apples and 9 bananas.
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!
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]
-3x+16+5x+8 x=??????????
The simplified expression of the expression given as -3x+16+5x+8 is 2(x + 12)
How to evaluate the equation?From the question, the equation is given as
-3x+16+5x+8
To start with, we need to rewrite the expression
So, we have the following representation
-3x + 16 + 5x + 8
The above expression is not an equation
Instead, it is an expression
This is so because there is no equality symbol i.e. = in the expression
So, we collect the like terms
-3x + 5x + 8 + 16
Solving further, we need to evaluate the like terms
So, we have the following equation
-3x + 5x + 24
Evaluate the like terms again
So, the equation becomes
2x + 24
The above expression cannot be further simplified, however, it can still be factored
Factor out 2 from the expression
This gives
2(x + 12)
Hence, the solution is 2(x + 12)
Read more about equations at
https://brainly.com/question/2476251
#SPJ1
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
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
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.
To know more about arithmetic operations:
https://brainly.com/question/13585407
#SPJ1
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.
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.
More can be learned about the test of an hypothesis at https://brainly.com/question/13873630
#SPJ1
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.
Learn more about the greatest common factor at https://brainly.com/question/219464
#SPJ1
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
Learn more about Area
brainly.com/question/26181567
#SPJ13
←
Suppose a bunny farm initally has 20 bunnies. After 2 years the population grew to 80 bunnies.
A) Find f(T)=mT+b, where f(T) is the bunny population after every 2 months. Answers must be in Exact Form, Round 3 decimals, and Change of Base
B) What is the bunny population after 16 weeks?
C) How many months will it take for the bunny population to reach 300 bunnies? Answers must be in Exact Form, Round 3 decimals, and Change of Base
A) The bunny population after every 2 months is f(T)=5T+20
B) The bunny population after 16 weeks is x=29.205
C) The number of months that the bunny population to reach 300 bunnies is 112 months.
What is meant by population?All nationals present in, or temporarily absent from, a country, as well as aliens permanently settled in a country, are characterized as population. This indicator depicts the average number of people who live in a given location. The annual changes in population caused by births, deaths, and net migration during the year are referred to as growth rates.
Given,
0 months -------- 20 bunnies
2 years ------- 80 bunnies
In two years, bunnies are increased by,
=80-20
=60
2 years ------>60
1 year ------>30
A) f(T)=mT + b
1 year -----> 12 months -----> 30 bunnies
12/6 months ------>30/6 bunnies
2 months -----> 5 bunnies
f(T)= initial population+ increased population in two months
f(T)=20+5
f(T)==25
f(T)= 2.5T+20
f(T)=5T+20
Where T =time in months
B) For 10 years ------> 10 bunnies
52 weeks -------->30 bunnies
16 weeks ------?
x=(16*30)/52
x=29.205
C) 1 month -------> 2.5 bunnies
? ---------------->280 bunnies
x=280/2.5
x=112 months
To know more about population, visit:
https://brainly.com/question/27991860
#SPJ1
Answer:
A) The bunny population after every 2 months is f(T)=5T+20
B) The bunny population after 16 weeks is x=29.205
C) The number of months that the bunny population to reach 300 bunnies is 112 months.
What is meant by population?
All nationals present in, or temporarily absent from, a country, as well as aliens permanently settled in a country, are characterized as population. This indicator depicts the average number of people who live in a given location. The annual changes in population caused by births, deaths, and net migration during the year are referred to as growth rates.
Given,
0 months -------- 20 bunnies
2 years ------- 80 bunnies
In two years, bunnies are increased by,
=80-20
=60
2 years ------>60
1 year ------>30
A) f(T)=mT + b
1 year -----> 12 months -----> 30 bunnies
12/6 months ------>30/6 bunnies
2 months -----> 5 bunnies
f(T)= initial population+ increased population in two months
f(T)=20+5
f(T)==25
f(T)= 2.5T+20
f(T)=5T+20
Where T =time in months
B) For 10 years ------> 10 bunnies
52 weeks -------->30 bunnies
16 weeks ------?
x=(16*30)/52
x=29.205
C) 1 month -------> 2.5 bunnies
? ---------------->280 bunnies
x=280/2.5
x=112 months
I rode my bike to my
grandparents' house in 1
hours and 15 minutes. My
grandparents live 33 blocks
from me, and each block is
560 feet. What was my
average speed in miles per
hour?
(Hint: 5,280 feet per mile)
By using the formula of average speed, it can be inferred that
My average speed is 14 miles per hour
What is average speed?
Speed of an object is the distance covered by the object per unit time
Average speed is calculated by dividing the total distance covered by the total time taken
Length of one block = 560 feet = [tex]\frac{560}{5280}[/tex] miles
Number of blocks = 33
Total distance = [tex]\frac{560}{5280} \times 33\\[/tex]
= [tex]\frac{7}{2}[/tex] miles
Total time = 15 minutes = [tex]\frac{15}{60}[/tex] hours = [tex]\frac{1}{4}[/tex] hours
Average speed = [tex]\frac{\frac{7}{2}}{\frac{1}{4}}[/tex] = [tex]\frac{7}{2} \times 4[/tex] = 14 miles per hour
To learn more about average speed, refer to the link-
brainly.com/question/553636
#SPJ1
(2,y) and (x,−3).
4x+2y=14
Solve for the Value of R
Answer:
whats the question
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.
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
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.
Learn more about Proportion here:
https://brainly.com/question/26974513
#SPJ1
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.
Learn more about z-statistic here:
https://brainly.com/question/1640298
#SPJ1
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
Learn more about compound interest here:
https://brainly.com/question/24924853
#SPJ1
Find the side length of x. Round your answer to nearest hundredth
Answer:
9
Step-by-step explanation:
I hope this helps!
3. what is the probability of drawing four red cards in a row without replacement.
out of a standard deck with 52 playing cards
Answer: There are 52 cards in a standard deck and half of them, 26 in all, are red.
Suppose that you are drawing 4 cards without replacement from a thoroughly shuffled deck. You have 26 cards choose 4 over 52 choose 4.
∴ P(pulling 4 cards from deck) = (264)(524)
Which ordered pairs in the form (x,y) are solutions to equation 3x -4y =21? SELECT MORE THAN ONE ANSWER. a- (11,30) b-(7,0) c-(-1,-6) D- (-3,3) please help
In linear equation, option A,B,C are equal expect D .
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.The given equation is 3x -4y =21.
A. (11, 3)
3(11) - 4(3) = 21
21 = 21 > equal
B. (7, 0)
3(7) - 4(0) = 21
21 = 21 > equal
C. (−1, −6)
3(-1) - 4(-6) = 21
21 = 21 > Equal
D. (−3, 3)
3x – 4y = 21
3(-3) - 4(3) = 21
-21 = 21 > not equal
Learn more about linear equation
brainly.com/question/11897796
#SPJ13
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.
Learn more about combinations on;
brainly.com/question/4658834
#SPJ1
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.
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.
To know more about Average here.
https://brainly.com/question/16956746
#SPJ1
The dimensions of the old stage at the concert hall were 30 feet wide and 15 feet deep. The new stage has a total area of 1000 square feet. The
dimensions of the new stage were created by adding the same distance x to the width and the length of the old stage. What deepth of the new stage?
The 30 feet by 15 feet dimension of the old stage and the 1,000 square feet of the new stage generates equations that gives the depth of the new stage;
The depth of the new stage is 25 feetWhat is an equation?An equation states the relationships between two expressions as being of the same value.
The width and depth of the concert hall for the old stage are 30 feet and 15 feet respectively
Area of the new stage = 1000 ft.²
The dimensions of the new stage are;
Width = 30 + x
Depth = 15 + x
Which gives;
(30 + x) × (15 + x) = 1,000
(30 + x) × (15 + x) - 1,000 = 0
x² + 45·x - 550 = 0
(x + 55)·(x - 10) = 0
The distance added to the width and length of the old stage, x = 10
The width of the new stage = 30 feet + 10 feet = 40 feet
The depth of the new stage = 15 feet + 10 feet = 25 feet
Learn more about writing algebraic equations here:
https://brainly.com/question/10892115
#SPJ1
