Answer:
(-1,5)
Step-by-step explanation:
When a line segment is divided in the ratio m:n, we use the section formula to determine the point P which divides the line segment:
The coordinates of x and y are:
[tex](x,y)=\left(\dfrac{mx_2+nx_1}{m+n}, \dfrac{my_2+ny_1}{m+n}\right)[/tex]
Given:
[tex]A(x_1,y_1)=(-7, 4)\\B(x_2,y_2)=(8, 9)\\AP:PB=m:n=2:3[/tex]
The coordinates of P is:
[tex](x,y)=\left(\dfrac{2*8+3*-7}{2+3}, \dfrac{2*9+3*4}{2+3}\right)\\=\left(\dfrac{-5}{5}, \dfrac{25}{5}\right)\\\\=(-1,5)[/tex]
The diameter of a sphere is 4 centimeters, which represents the volume of the sphere?
Answer:
10 2/3π or 33.51
Step-by-step explanation:
the volume of a sphere is 4/3πr^3
if the sphere has a diameter of 4 the radius is half the diameter so it would be 2. 2^3 = 8 now multiply 8 by 4/3 to get 10 2/3. now multiply by pi to get 10 2/3 π or 33.5103 which rounds to 33.51
Answer:
32π/3 cubic cm
Step-by-step explanation:
Help meeeee and thank u so much god bless u haha
Answer:
[See Below]
Step-by-step explanation:
For Point Slope Form:Point slope form is: [tex]y-y_1=m(x-x_1)[/tex]
'm' is the slope
(x1, y1) is a coordinate point.
Slope:Slope is rise over run. [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
We are given the points (-1,5) and (3,-3).
[tex]\frac{-3-5}{3-(-1)}=\frac{-8}{4}= -2[/tex]
The slope of the line is -2.
I will use (-1,5) as the point:
[tex]y-y_1=m(x-x_1)\rightarrow\boxed{y-5=-2(x+1)}[/tex]
For Slope Intercept:Slope intercept is: [tex]y=mx+b[/tex]
'm' - Slope
'b' - y-intercept
We can use the point slope equation to convert it into slope intercept form:
[tex]y-5=-2(x+1)\\\\y-5=-2x-2\\\\y-5+5=-2x-2+5\\\\\boxed{y=-2x+3}[/tex]
For Standard Form:Standard form is [tex]Ax+By=C[/tex]
Using out slope intercept form equation:
[tex]y=-2x+3\\\\y+2x=-2x+2x+3\\\\1y+2x=3\\\\\boxed{2x+1y=3}[/tex]
Which expanded expressions represent the exponential expression (–4)3 · p4? Select all that apply. (–4) · (–4) · (–4) · (–4) · p · p · p p · p · p · p · (–4) · (–4) · (–4) p · (–4) · (–4) · p · (–4) · p p · p · (–4) · (–4) · p · p · (–4) (–4) · p · p · p · (–4) · (–4) · (–4) (–4) · (–4) · p · (–4) · p · p · p
The expanded form of the given exponential expression is (-4)×(-4)×(-4)×p×p×p×p.
What is the exponent?Exponent is defined as the method of expressing large numbers in terms of powers. That means, exponent refers to how many times a number multiplied by itself.
The given expression is (-4)³·p⁴.
Here, (-4)³= (-4)×(-4)×(-4)
p⁴=p×p×p×p
So, (-4)×(-4)×(-4)×p×p×p×p
= -64×p×p×p×p
Therefore, the expanded form is (-4)×(-4)×(-4)×p×p×p×p.
To learn more about an exponents visit:
https://brainly.com/question/15993626.
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Jeff's net monthly income is $2550. His monthly expense for rent is $625. What percent of his net monthly income is his rent? (Round your answer to the nearest whole percent.)
Answer:
25%
I cannot really describe how I did it but I am pretty sure it is correct.
2(3y+6)−3(−4−y) simplified
Answer:
9y+24
Step-by-step explanation:
2(3y+6)-3(-4-y)
Expand the brackets.
6y+12+12+3y
Rearrange.
6y+3y+12+12
Add like terms.
9y+24
Answer:
9y+24solution,
[tex]2(3y + 6) - 3( - 4 - y) \\ = 6y + 12 + 12 + 3y[/tex]
Collect like terms,
[tex]6y + 3y + 12 + 12[/tex]
Simplify
[tex]9y + 24[/tex]
hope this helps...
Good luck on your assignment..
Which expression is equal to -3b(6b^-8)
Answer:a^2/b
Step-by-step explanation:
(a^6b^−3)1^/3
a^6 ^ 1/3 b ^ -3 ^ 1/3
using the power of power rule we can multiply the exponents
a ^ (6*1/3) b ^ (-3* 1/3)
a^ 2 b ^ -1
the negative exponent flips it from the numerator to the denominator
a^2* 1/ b^1
a^2/b
Answer:
A. -18b^-4
second answer is B. -18/b^-4
Step-by-step explanation:
PLEASE I NEED HELP ASAP sally drives for 2 hours at an average speed of 70 m/h. she then drives for half an hour at an average speed of 40 m/h work ot the total distance that sally has travelled
Answer:
Total Distance = 160 m
Average speed = 64 m/hr
Step-by-step explanation:
For first 2 hours:
Distance = Speed × Time
D = 70 × 2
D = 140 m
For the next half hour:
Distance = Speed × Time
Distance = 40 × 0.5
Distance = 20 m
Now total Distance:
Total Distance = 140+20
Total Distance = 160 m
After that,
Average Speed = Total Distance Covered/ Total Time taken
Average Speed = 160 m / 2.5 hours
Average speed = 64 m/hr
in a church wing with 8 men and 10 women members find the probability that a 5 member committee chosen randomly will have.......
a).all men.
b).3men and 2 women
Answer:
a) Probability that a 5 member committee will have all men = 0.0065
b) probability that a 5 member committee chosen randomly will have 3 men and 2 women = 0.294
Step-by-step explanation:
Number of men = 8
Number of women = 10
Total number of members = 10 + 8 = 18
Probability = (Number of possible outcomes)/(Total number of outcomes)
Number of ways of selecting a 5 member committee from 18 people = [tex]^{18}C_5 = \frac{18!}{(18-5)!5!} = \frac{18!}{13!5!}[/tex] = 8568 ways
a) Probability that a 5 member committee will have all men
Number of ways of selecting 5 men from 8 men
= [tex]^8C_5 = \frac{8!}{(8-5)!5!} = \frac{8!}{3!5!}[/tex] = 56 ways
Probability that a 5 member committee will have all men = 56/8568
Probability that a 5 member committee will have all men = 0.0065
b)probability that a 5 member committee chosen randomly will have 3men and 2 women
Number of ways of selecting 3 men from 8 men
= [tex]^8C_3 = \frac{8!}{(8-3)!3!} = \frac{8!}{5!3!}[/tex] = 56 ways
Number of ways of selecting 2 women from 10 men
= [tex]^{10}C_2 = \frac{10!}{(10-2)!2!} = \frac{10!}{8!2!}[/tex] = 45 ways
Number of ways of selecting 3 men and 2 women = 56*45
Number of ways of selecting 3 men and 2 women = 2520
Probability of selecting 3 men and 2 women = 2520/8568 = 0.294
probability that a 5 member committee chosen randomly will have 3 men and 2 women = 0.294
The point (-7,1) when reflected across the origin maps onto
Answer:
(7,-1)
Step-by-step explanation:
common rule for reflections across the origin; im guessing you meant a reflection across the line y=x since it goes through the origin too.
for this make sure to add this transformation:
(x,y) --> (-x,-y)
According to Brad, consumers claim to prefer the brand-name products better than the generics, but they can't even tell which is which. To test his theory, Brad gives each of 199 consumers two potato chips - one generic, and one brand-name - then asks them which one is the brand-name chip. 92 of the subjects correctly identified the brand-name chip.
Required:
a. At the 0.01 level of significance, is this significantly greater than the 50% that could be expected simply by chance?
b. Find the test statistic value.
Answer:
a. There is not enough evidence to support the claim that the proportion that correctly identifies the chip is significantly smaller than 50%.
b. Test statistic z=-1.001
Step-by-step explanation:
This is a hypothesis test for a proportion.
The claim is that the proportion that correctly identifies the chip is significantly smaller than 50%.
Then, the null and alternative hypothesis are:
[tex]H_0: \pi=0.5\\\\H_a:\pi<0.5[/tex]
The significance level is 0.01.
The sample has a size n=199.
The sample proportion is p=0.462.
[tex]p=X/n=92/199=0.462[/tex]
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.5*0.5}{199}}\\\\\\ \sigma_p=\sqrt{0.001256}=0.035[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p-\pi+0.5/n}{\sigma_p}=\dfrac{0.462-0.5+0.5/199}{0.035}=\dfrac{-0.035}{0.035}=-1.001[/tex]
This test is a left-tailed test, so the P-value for this test is calculated as:
[tex]\text{P-value}=P(z<-1.001)=0.16[/tex]
As the P-value (0.16) is greater than the significance level (0.01), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that the proportion that correctly identifies the chip is significantly smaller than 50%.
The next 3 options are:
A: x=1 or x= -3
A: x= -1 or x=3
B: Since the quadratic equation has two real solutions, the graph of the quadratic equation intercepts the x axis at (-1,0) and (3,0)
please please help. Thank you so much.
Answer:
A: x= -1 or x=3
B: Since the quadratic equation has two real solutions, the graph of the quadratic equation intercepts the x axis at (-1,0) and (3,0)
Step-by-step explanation:
x^2 -2x -3 =0
Factor
(x-3 )(x+1) =0
Using the zero product property
x-3 =0 x+1 =0
x=3 x=-1
The zeros are
(3,0) (-1,0)
It intersects the x axis at (3,0) (-1,0)
The amount of money that is left in a medical savings account is expressed by the equation y = negative 24 x + 379, where x represents the number of weeks and y represents the amount of money, in dollars, that is left in the account. After how many weeks will the account have $67 left in it? 10 weeks 13 weeks 15 weeks 21 weeks
Answer: 13 weeks
Step-by-step explanation:
y = -24x + 379
67 = -24x + 379
24x = 379 - 67
x = 312 / 24
x = 13
Answer:
the answer is 13 weeks
Step-by-step explanation:
y = amount left
y = 67
67 = -24x+379
-312 = -24x
x = -312 / -24
x = 13
Math 7th grade. help please!!!
Answer:
1 .angle S is 90 degree
2. 12
3. 155 degree
1. x = 3
hope it helps .....
Which of the following are equations for the line shown below? Check all that apply.
A. Y= x-2
B. Y-1=(x-3)
C. Y=x-2
D. Y+4=(x+2)
Answer: D. [tex]y+4=(x+2)[/tex]
Step-by-step explanation: Once you subtract [tex]4[/tex] from both sides, in order to solve for y (as the equation needs to be in the slope-intercept form, otherwise known as [tex]y=mx+b[/tex]), you end up with [tex]y=x-2[/tex], which is the right answer. It is the correct answer because the y-intecept shown in the equation matches what is on the graph, in addition to the fact that the slope is just [tex]x[/tex].
A sample of 8 students was asked how often they used campus dining facilities during the past month. The responses were as follows. 4 1 6 1 2 10 2 6 The sample standard deviation is _____.
Answer:
Your answer is 3.16227766
Step-by-step explanation:
A restaurant borrows from a local bank for months. The local bank charges simple interest at an annual rate of for this loan. Assume each month is of a year. Answer each part below.Do not round any intermediate computations, and round your final answers to the nearest cent. If necessary, refer to the list of financial formulas.
(a) Find the interest that will be owed after 4 months
(b) Assuming the restaurant doesn't make any payments, find the amount owed after 4 months
Complete Question:
A restaurant borrows $16,100 from a local bank for 4 months. The local bank charges simple interest at an annual rate of 2.45% for this loan. Assume each month is 1/12 of a year.
Answer each part below.Do not round any intermediate computations, and round your final answers to the nearest cent. If necessary, refer to the list of financial formulas.
(a) Find the interest that will be owed after 4 months
(b) Assuming the restaurant doesn't make any payments, find the amount owed after 4 months
Answer:
a) Interest that will be owed after 4 months , I = $131.48
b) Amount owed by the restaurant after 4 months = $16231.48
Step-by-step explanation:
Note that the question instructs not to round any intermediate computations except the final answer.
Annual rate = 2.45%
Monthly rate, [tex]R = \frac{2.45\%}{12}[/tex]
R = 0.20416666666%
Time, T = 4 months
Interest, [tex]I = \frac{PRT}{100}[/tex]
[tex]I = \frac{16100 * 0.20416666666 * 4}{100} \\I = 161 * 0.20416666666 * 4\\I = \$131.483333333\\I = \$131.48[/tex]
b) If the restaurant doesn't make any payments, that means after four months, they will be owing both the capital and the interest ( i.e the amount)
Amount owed by the restaurant after 4 months = (Amount borrowed + Interest)
Amount owed by the restaurant after 4 months = 16100 + 131.48
Amount owed by the restaurant after 4 months = $16231.48
A lake has a large population of fish. On average, there are 2,400 fish in the lake, but this number can vary by as much as 155. What is the maximum number of fish in the lake? What is the minimum number of fish in the lake?
Answer:
Minimum population of fish in lake = 2400 - 155 = 2245
Maximum population of fish in lake = 2400 + 155 = 2555
Step-by-step explanation:
population of fish in lake = 2400
Variation of fish = 155
it means that while current population of fish is 2400, the number can increase or decrease by maximum upto 155.
For example
for increase
population of fish can 2400 + 2, 2400 + 70, 2400 + 130 etc
but it cannot be beyond 2400 + 155.
It cannot be 2400 + 156
similarly for decrease
population of fish can 2400 - 3, 2400 - 95, 2400 - 144 etc
but it cannot be less that 2400 - 155.
It cannot be 2400 - 156
Hence population can fish in lake can be between 2400 - 155 and 2400 + 155
minimum population of fish in lake = 2400 - 155 = 2245
maximum population of fish in lake = 2400 + 155 = 2555
-12.48 -(-2.99)-5.62
Answer:
[tex]-15.11[/tex]
Step-by-step explanation:
[tex]-12.48-(-2.99)-5.62=\\-12.48+2.99-5.62=\\-9.49-5.62=\\-15.11[/tex]
Answer:
-15.11
Step-by-step explanation:
-12.48+2.99-5.62=
-9.49 - 5.62= - (9.49+5.62)=-15.11
The shorter leg of a right triangle is 14 feet less than the other leg. Find the length of the two legs of the hypotenuse is 25 feet.
Answer:
9.233 ft, 23.233 ft
Step-by-step explanation:
If the shorter leg is x, then the longer leg is x+14 and the Pythagorean theorem tells you ...
x^2 + (x +14)^2 = 25^2
2x^2 +28x +196 = 625
x^2 +14x = 214.5
x^2 +14x +49 = 263.5
(x +7)^2 = 263.5
x = -7 +√263.5 ≈ 9.23268
The two leg lengths are √263.5 ± 7 feet, {9.23 ft, 23.23 ft}.
Answer: 9 ft, 23 ft
Step-by-step explanation:
We know the Pythagorean Theorem is a²+b²=c². Since one leg is 14 less than the other leg, we can use x-14 and the other leg would be x. We can plug these into the Pythagorean Theorem with the given hypotenuse.
(x-14)²+x²=25²
(x²-28x+196)+x²=625
2x²-28x+196=625
2x²-28x-429=0
When we solve for x, we get [tex]x=\frac{14+\sqrt{1054} }{2}[/tex] and [tex]x=\frac{14-\sqrt{1054} }{2}[/tex].
Note, since we rounded to 23, the hypotenuse isn't exactly 25, but it gets very close.
An engineering study indicates that 8.5% of the bridges in a large state are structurally deficient. The state's department of transportation randomly samples 100 bridges. What is the probability that exactly 6 bridges in the sample are structurally deficient
Answer:
[tex]P(X=6)=(100C6)(0.085)^6 (1-0.085)^{100-6}=0.1063[/tex]
Then the probability that exactly 6 bridges in the sample are structurally deficient is 0.1063 or 10.63%
Step-by-step explanation:
Let X the random variable of interest "number of bridges in the sample are structurally deficient", on this case we now that:
[tex]X \sim Binom(n=100, p=0.085)[/tex]
The probability mass function for the Binomial distribution is given as:
[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]
Where (nCx) means combinatory and it's given by this formula:
[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]
And we want to find this probability:
[tex] P(X=6)[/tex]
And if we use the probability mass function and we replace we got:
[tex]P(X=6)=(100C6)(0.085)^6 (1-0.085)^{100-6}=0.1063[/tex]
Then the probability that exactly 6 bridges in the sample are structurally deficient is 0.1063 or 10.63%
can some one answer this plsss
Answer:
D
Step-by-step explanation:
0.2x+5=8
0.2x=3
x=15
Therefore, the correct answer is choice D. Hope this helps!
Find the area of the largest rectangle that can be inscribed in a right triangle with legs of lengths 4 cm and 6 cm if two sides of the rectangle lie along the legs. webassign cengage
Answer:
[tex]6cm^2[/tex]
Step-by-step explanation:
Let x and y be the sides of the rectangle.
Area of the Triangle, A(x,y)=xy
From the diagram, Triangle ABC is similar to Triangle AKL
AK=4-y
Therefore:
[tex]\dfrac{x}{6} =\dfrac{4-y}{4}[/tex]
[tex]4x=6(4-y)\\x=\dfrac{6(4-y)}{4} \\x=1.5(4-y)\\x=6-1.5y[/tex]
We substitute x into A(x,y)
[tex]A=y(6-1.5y)=6y-1.5y^2[/tex]
We are required to find the maximum area. This is done by finding
the derivative of Aand solving for the critical points.
Derivative of A:
[tex]A'(y)=6-3y\\$Set $A'=0\\6-3y=0\\3y=6\\y=2$ cm[/tex]
Recall that: x=6-1.5y
x=6-1.5(2)
x=6-3
x=3cm
Therefore, the maximum rectangle area is:
Area =3 X 2 =[tex]6cm^2[/tex]
Solve the system of equations below by graphing them with a pencil and
paper. Enter your answer as an ordered pair.
y= -x+5
y=x-3
Answer:
X+5= -x-3
2x = 2
X=1
then y1 is 4
y2 is -1
Answer:
Answer is 4, 1. If you graph the lines, they intersect at 4, 1.
Step-by-step explanation:
Question from quadratic equation .
solve.
(x-3)(x+7)=0
Answer:
x = 3, -7
Step-by-step explanation:
Since you already have the factored form, all you need to do is set the equations equal to zero to find you roots:
x - 3 = 0
x + 7 = 0
x = 3, -7
Answer:
3 or -7
Step-by-step explanation:
For it to equal 0, x must be 3 or -7 because anything multiplied by 0 is 0. So you take each part, x-3 and see how you can make that a 0. x-3=0, therefore x must be 3. Other part x+7=0, x must be -7.
(b) How many different groups of children can be chosen from a class of 18 children if the class contains one set of twins who must not be separated?
Preciso de ajudaa! Resolução também! - Considere as funções f e g tais que f(x)= x³+1 e g(x)= x-2 Determine: a)(fog)(0) b)(gof)(0) c)(fof)(1) d)(gog)(1)
Answer:
(fog)(x) means that we have the function f(x) evaluated in the function g(x), or f(g(x)).
So, if f(x) = x^3 + 1 and g(x) = x - 2.
we have:
a) (fog)(0) = f(g(0)) = (0 - 2)^3 + 1 = -8 + 1 = -7
b) (gof)(0) = g(f(0)) = (0^3 + 1) - 2 = -1
c) (fof)(1) = f(f(1)) = (1^3 + 1)^3 + 1 = 2^3 + 1 = 8 + 1 = 9
d) (gog)(1) = g(g(1)) = (1 - 2) - 2 = -1 -2 = -3
What is the end behavior of the graph of the polynomial function f(x) = 2x3 – 26x – 24?
Answer:
Step-by-step explanation:
Answer:
its b on edge
Step-by-step explanation:
What is the solution for this inequality? 5x ≤ 45
A. x ≥ -9
B. x ≤ 9
C. x ≤ -9
D. x ≥ 9
Answer:
[tex]x\le \:9[/tex]
Step-by-step explanation:
[tex]5x\le 45[/tex]
[tex]\frac{5x}{5}\le \frac{45}{5}[/tex]
[tex]x\le \:9[/tex]
Answer:
B
Step-by-step explanation:
We divide the entire inequality by 5 to get rid of the coefficient of x. The ≤ stays the same so we get x ≤ 9.
Which of the following are point-slope equations of the line going through (3,
6) and (1,-2)? Check all that apply:
Answer:
y+2=4(x-1)
y-6=4(x-3)
Step-by-step explanation:
Slope between (3, 6) and (1, -2)
6-(-2)/3-1
8/2
4
y+2=4(x-1)
y-6=4(x-3)
Consider the next 1000 98% CIs for μ that a statistical consultant will obtain for various clients. Suppose the data sets on which the intervals are based are selected independently of one another. How many of these 1000 intervals do you expect to capture the corresponding value of μ?
Answer:
980 intervals.
Step-by-step explanation:
For each interval, there are only two possible outcomes. Either it captures the population mean, or it does not. One interval is independent of other intervals. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
98% confidence interval
Has a 98% probability of capturing the population mean, so [tex]p = 0.98[/tex]
1000 intervals
This means that [tex]n = 1000[/tex]
How many of these 1000 intervals do you expect to capture the corresponding value of μ?
[tex]E(X) = np = 1000*0.98 = 980[/tex]
980 intervals.