Answer:
Slope passes through (-6, 5) and (-2, 7)
[tex]m_1=\frac{y_2-y_1}{x_2-x_1} =m_1=\frac{7-5}{-2+6}[/tex]
[tex]m_1=\frac{2}{4} =\frac{1}{2}[/tex]
Slope passes through (4, 2) and (6, 6)
[tex]m_2=\frac{6-2}{6-4}[/tex]
[tex]\frac{4}{2} =2[/tex]
[tex]m_1\times m_2 \neq -1[/tex] [tex]m_1\neq m_2[/tex]
Answer:- A) neither perpendicular nor parallel.
OAmalOHopeO
Consider the function z(x,y) describing the paraboloid \[z = (2x - y)^2 - 2y^2 - 3y.\]Archimedes and Brahmagupta are playing a game. Archimedes first chooses $x.$ Afterwards, Brahmagupta chooses $y.$ Archimedes wishes to minimize $z$ while Brahmagupta wishes to maximize $z.$ Assuming that Brahmagupta will play optimally, what value of $x$ should Archimedes choose?
Answer: -3/8
Step-by-step explanation:
Expanding z we get
z = 4x^2 - 4xy + y^2 - 2y^2 - 3y
= -y^2 - (4x + 3) y + 4x^2.
After Archimedes chooses x, Brahmagupta will choose
y=-(4x+3/2) in order to maximize z
Then
z=-((-4x+3)/2)^2 -(4x+3)(-4x+3)/2)^2)+4x^2
z=8x^2+6x+9/4
To minimize this expression, Archimedes should choose x=-3/8
In Riverview Middle school, 20 percent of the students participate in an after school club for every 100 students how many are in an afterschool club
Answer:
What is the diferentes between and red bolos celos ?
Step-by-step explanation:
Translate To An Algebraic Expression:
S% of 1/r
Answer:
S/100r
Step-by-step explanation:
S% of 1/r = (1/r x S) : 100
(1/r x S) : 100
S/r : 100
S/100r
Find the volume of the solid whose base is the region in the first quadrant bounded by y=x^4, y=1 and the y-axis and whose cross-sections perpendicular to the x axis are semicircles.
The base of the solid - call it B - is the set of points
B = {(x, y) : 0 ≤ x ≤ 1 and x ⁴ ≤ y ≤ 1}
Recall the area of a circle with radius r is πr ²; in terms of the diameter d = 2r, the area is π (d/2)² = π/4 d ². Then the area of a semicircle with the same diamater is half of this, π/8 d ².
Cross sections of the solid in question are semicircles arranged perpendicular to the x-axis, which means the diameters of each cross section corresponds to the vertical distance between y = x ⁴ and y = 1 for any given values of x between 0 and 1. So d = 1 - x ⁴, which makes the area of each cross section come out to π/8 (1 - x ⁴)².
Split up the solid into very thin cross sections with "base" area π/8 (1 - x ⁴)² and thickness ∆x. Take the sum of these half-cylinders' volumes, then let ∆x converge to 0. In short, we get the total volume by integrating,
[tex]\displaystyle \int_0^1\frac\pi8(1-x^4)^2\,\mathrm dx = \frac\pi8\int_0^1(1-2x^4+x^8)\,\mathrm dx = \boxed{\frac{4\pi}{45}}[/tex]
The ages of a group of 142 randomly selected adult females have a standard deviation of 18.1 years. Assume that the ages of female statistics students have less variation than ages of females in the general population, so let σ=18.1 years for the sample size calculation. How many female statistics student ages must be obtained in order to estimate the mean age of all female statistics students? Assume that we want 99% confidence that the sample mean is within one-half year of the population mean. Does it seem reasonable to assume that the ages of female statistics students have less variation than ages of females in the general population? The required sample size is
Answer:
Start with the formula for Z:
Z = (x-µ)/(σ/√n)
We want the sample mean to be within one-half year of the population mean, so we set x-µ=0.5. We are looking for a 99% confidence interval, so we set Z=2.7578. We are told to use σ=18.1. Plugging those values into the formula, we get:
2.5758 = 0.5(18.1/√n)
We can rearrange to solve for n:
((2.5758-18.1)/0.5)2 = n
Plugging that into our calculator, we get n = 964.003. Since we can't have a fraction of a person in our sample, it would be safest to round up to n=965. (But since .003 is so small, I'd also accept 964 as an answer.)Step-by-step explanation:
The required sample size for the given population distribution is; n = 8696 female ages
We are given;
Standard deviation; σ = 18.1
Confidence level; CL = 99%
Now, formula to find the margin of error is;
E = z(σ/√n)
Where;
E is margin of error
z is critical value at confidence level
σ is standard deviation
n is required sample size
Now we are told that the sample mean is within one-half year of the population mean.
Thus;
E = 0.5
z value at 99% Confidence level is;
z = 2.576
Thus, Making n the subject of the formula is;
n = (zσ/E)²
n = (2.576 × 18.1/0.5)²
n = 8695.78
Approximating to a whole number gives;
n = 8696 female ages
Read more about margin of error at; https://brainly.com/question/6650225
Please helpppp me I really confused
Answer:
The answer would be D
Step-by-step explanation:
This is a piecewise function, meaning that it is split into two parts. The right side is an exponential and that part is greater than one, the left side is a line less than or equal to one. The only equation that matches the criteria for that is D.
porfavor se los agradeceria mucho y de corazon :D
Answer:
1=2p+3
2=
Step-by-step explanation:
a test has 20 multiple-choice questions with 5 choices each, followed by 35 true/false questions. if a student guesses on each question, how many ways can he answer the questions on the test
Answer
There are 170 ways the student can answer the test.
Explanation
If there are 20 multiple-choice questions with 5 choices each, the student has 100 choices. The first question has 5 choices to pick from. The second has 5 as well. So does the third. Hopefully now you realize that you have to multiply the number of choices by the number of questions.
The same thing goes with the true/false questions. There are 2 choices for each true/false question, and there are 35 of those. 35×2 is 70. There are 70 ways to answer on the true/false questions.
Now combine the number of choices on the first part and the second part; 100+70 is 170.
The coordinates of three points are A(- 1, - 3) , B(2, 3) and C(6, k) . If AB is perpendicular to BC find (i) the value of k, (ii) the gradient of AC (iii) the acute angle that AC makes with the x-axis.
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Answer:
(i) k = 1
(ii) 4/7
(iii) arctan(4/7) ≈ 29.7°
Step-by-step explanation:
(i) A graph of the given points is helpful. It shows us the slope of AB is ...
mAB = rise/run = 2/1 = 2
so the slope of BC must be the opposite reciprocal, -1/2.
Point C is 6-2 = 4 units to the right of point B, so will be (-1/2)(4) = -2 units from point B in the vertical direction. That is, ...
k = 3 -2
k = 1
__
(ii) The gradient of AC is found from the slope formula:
m = (y2 -y1)/(x2 -x1)
m = (1 -(-3))/(6 -(-1))
mAC = 4/7
__
(iii) The angle that line AC makes with the +x axis is the arctangent of the slope:
arctan(4/7) ≈ 29.7° . . . angle between AC and +x axis
Write the equation of a line in the slope-intercept form that has a slope of 4
and contains the point (4, 12).
Answer:
The equation of the point (4, 12) is y=4x+12
Random samples of size 81 are taken from a population whose mean is 45 and standard deviation is 9. Calculate the probability that a sample mean is less than 42. (round to 4 decimal places)
HINT: When you randomly select a group (n > 1) then you need to re-calculate the standard deviation using the formula:
σ n
Answer:
Using z table
= 0.0013
The probability = 0.0013
Step-by-step explanation:
Given that,
mean = μ = 45
standard deviation = σ = 9
n=81
μT = μ =45
[tex]\sigma T = \sigma / \sqrt n = 9 / \sqrt81 =1[/tex]
[tex]P(T <42 )\\= P[(T - \mu T ) / \sigma T < (42-45) /1 ]\\\\= P(z <-3 )[/tex]
Using z table
= 0.0013
probability= 0.0013
Find the number of distinguishable arrangements of the letters of the word SEPTILLION
Answer:
10!
Step-by-step explanation:
Septillion-10 letters
1-s-10 places to be in
2-e-9
3-p-8
4-t-7
5-i-6
6-l-5
7-l-4
8-i-3
9-o-2
10-n-1
So, then
10×9×8×7×6×5×4×3×2×1=10!
or 3628800
The arrangement of the number will be equal to 3628800.
What are permutation and combination?A permutation is an orderly arrangement of things or numbers. Combinations are a way to choose items or numbers from a collection or group of items without worrying about the items' chronological order.
A combination in mathematics is a choice made from a group of separate elements where the order of the selection is irrelevant.
The given word is SEPTILLION. The word has 10 characters. The different ways of the arrangement will be calculated as,
Arrangement = 10!
Arrangement = 10×9×8×7×6×5×4×3×2×1
Arrangement = 3628800
Therefore, the arrangement of the number will be equal to 3628800.
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If f(x) = 2(x - 5), find f(8).
04
06
O 8
16
Answer:
6
Step-by-step explanation:
f(x) = 2(x - 5)
f(8) = 2(8 - 5)
f(8) = 16 - 10
f(8) = 6
The answer is 6, hope this helps.
[tex]\boxed{ \sf{Answer}} [/tex]
[tex]\sf \: f(x) = 2(x - 5) \\ \\\sf x = 8 \\ \\\sf f(8) = 2(8 - 5) \\\sf \: f(8) = 2(3) \\ \sf \: f(8) = 2 \times 3 \\\sf f(8) =\underline 6[/tex]
Option B - 06 is the correct answer.
ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ
꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐
The cost of an apple has decreased from $0.50 to $0.40. Work out the decrease cost of an apple as a percentage.
Answer:
Decreased by 20%
Step-by-step explanation:
0.5 x ? = 0.4
? = 0.4/0.5
? = 0.8
1 - 0.8 = 0.2
0.2 = 20%
To check, 20% of 0.5 is 0.1. 0.5 - 0.1 is 0.4. So the answer is correct.
Two accountants for the firm of Elwes and Wright are arguing about the merits of presenting an income statement in a multiple-step versus a single-step format. The discussion involves the following 2020 information related to Bramble Company ($000 omitted).
Administrative expense
Officers' salaries
$5,006
Depreciation of office furniture and equipment
4,066
Cost of goods sold
60,676
Rent revenue
17,336
Selling expense
Delivery expense
2,796
Sales commissions
8,086
Depreciation of sales equipment
6,586
Sales revenue
96,606
Income tax
9,176
Interest expense
1,966
Common shares outstanding for 2020 total 38,960 (000 omitted).
(a) Prepare an income statement for the year 2020 using the multiple-step form. (Round earnings per share to 2 decimal places, e.g. 1.48.)
(b) The parts of this question must be completed in order. This part will be available when you complete the part above.
Answer:
73,188
Step-by-step explanation:
fees plus costs minus expenses
What is the range of the data set shown below?
A. 36
B. 34
C. 32
D. 30
Answer:
b 34 the higest is 40 an the lowest 6 the diferens is 34
Step-by-step explanation:
Mark me brainlest pliz
Answer:
i would but this not my question this is theres he right A.
Step-by-step explanation:
Tony invested $9538 in an account at 8% compounded daily. Identify the compound
interest C after 1 years.
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Answer:
$794.30
Step-by-step explanation:
The account balance for principal P invested at rate r compounded daily for t years is ...
A = P(1 +r/365)^(365t)
We have P=$9538, r=0.08, t=1, and we want the value of P-A, the interest earned.
P-A = P(1 +0.08/365)^365 -1) = $9538(1.08327757 -1) ≈ $794.30
The interest earned in one year is $794.30.
Solve the following system of equations by using the inverse of a matrix.
Give your answer as an ordered triple (x , y , z)
Answer:
(x, y, z) = (-8,4,-2)
Step-by-step explanation:
.......................................
For f(x) = x2 - x + 3, find
a, f(2)
b. f(3a)
Answer:
a.5
b.3a+3
Step-by-step explanation:
in a,u need to replace 2 with x,so it will be 4-2+3
in b,replace 3a with x and so it will be6a-3a+3
Which statement is true about the parts of this expression?
StartFraction 5 over 6 EndFraction + one-fourth x minus y
The constant is StartFraction 5 over 6 EndFraction.
The only coefficient is One-fourth.
The only variable is y.
The terms StartFraction 5 over 6 EndFraction and One-fourth x are like terms.
Answer:
The constant is StartFraction 5 over 6 EndFraction
Step-by-step explanation:
StartFraction 5 over 6 EndFraction + one-fourth x minus y
5/6 + 1/4x - y
A. The constant is StartFraction 5 over 6 EndFraction.
True
B. The only coefficient is One-fourth.
False
There are two coefficients: the coefficient of x which is 1/4 and the coefficient of y which is 1
C. The only variable is y
False
There are 2 variables: variable x and variable y
D. The terms StartFraction 5 over 6 EndFraction and One-fourth x are like terms.
False
5/6 and 1/4x are not like terms
The only true statement is: The constant is StartFraction 5 over 6 EndFraction
Answer:
It's A if you don't want to read. A). The constant is 5/6
Step-by-step explanation:
Find the area of a triangle with a height of 38 and one side of 44
In triangle it is given that,
→ Height (h) = 38 cm
→ Base (b) = 44 cm
The formula we use,
→ Area of triangle = ½ × b × h
Now we have to,
find the area of the triangle,
→ ½ × b × h
→ ½ × 44 × 38
→ (44 × 38)/2
→ 1672/2 = 836 cm²
So, 836 cm² is area of triangle.
a) A box contains 6 red balls, 4 white balls, and 10 black balls. Two balls are drawn at random from the box (with replacement of the first before the second is drawn). What is the probability of getting a red ball on the first draw and a white ball on the second
Answer:
Red ball=3/10
White ball=1/5
Step-by-step explanation:
Red balls=6. And all the balls are equal to 20. So probability of red ball=6/20=3/10.
White balls=4. So probability of white ball=4/20=1/5.
NB: Since the first ball was replaced, there's no need to deduct a ball from the original 20 balls.
(4-21)(1 + 71) help plz
the answer would be -1,224 because the parentheses is your multiplication and the it is a negative
Simplify: x^d • x ^18
Answer:
x^(d+18)
Step-by-step explanation:
using the law of indices
you must add the powers
Answer:
[tex] {x}^{d + 18} [/tex]
Step-by-step explanation:
[tex]\sf{x^d.x^{18} }[/tex] [tex]\sf{ x^{d+18} }[/tex]Based on a poll, among adults who regret getting tattoos, 24% say that they were too young when they got their tattoos. Assume that six adults who regret getting tattoos are randomly selected, and find the indicated probability.
a. Find the probability that none of the selected adults say that they were too young to get tattoos.
b. Find the probability that exactly one of the selected adults says that he or she was too young to get tattoos.
c. Find the probability that the number of selected adults saying they were too young is 0 or 1.
Answer:
a) 0.1927 = 19.27% probability that none of the selected adults say that they were too young to get tattoos.
b) 0.3651 = 36.51% probability that exactly one of the selected adults says that he or she was too young to get tattoos.
c) 0.5578 = 55.78% probability that the number of selected adults saying they were too young is 0 or 1.
Step-by-step explanation:
For each person, there are only two possible outcomes. Either they say they were too young to get tattoos, or they do not say this. The probability of a person saying this is independent of any other person, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
24% say that they were too young when they got their tattoos.
This means that [tex]p = 0.24[/tex]
Six adults
This means that [tex]n = 6[/tex]
a. Find the probability that none of the selected adults say that they were too young to get tattoos.
This is P(X = 0). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{6,0}.(0.24)^{0}.(0.76)^{6} = 0.1927[/tex]
0.1927 = 19.27% probability that none of the selected adults say that they were too young to get tattoos.
b. Find the probability that exactly one of the selected adults says that he or she was too young to get tattoos.
This is P(X = 1). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 1) = C_{6,1}.(0.24)^{1}.(0.76)^{5} = 0.3651[/tex]
0.3651 = 36.51% probability that exactly one of the selected adults says that he or she was too young to get tattoos.
c. Find the probability that the number of selected adults saying they were too young is 0 or 1.
This is:
[tex]p = P(X = 0) + P(X = 1) = 0.1927 + 0.3651 = 0.5578[/tex]
0.5578 = 55.78% probability that the number of selected adults saying they were too young is 0 or 1.
Jean and Marie decided to buy new living room furniture worth $6000. They make a down payment of $600. They decide to pay off what they owe in 30 monthly payments. Find the amount of the payments at 9% add-on interest.
Answer:
5886$ is the ans
Step-by-step explanation:
Paid amount= 6000-600
Total Amount or Interest applicable amount = 5400$
Then
Interest Rate= 9%
by using formula
=. Total amount + Interest rate × Total
=. 5400+0.09×5400
=. 5886$
How many gallons each of 15% alcohol and 10% alcohol should be mixed to obtain 5 gal of 13% alcohol?
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Answer:
3 gallons 15%2 gallons 10%Step-by-step explanation:
Let x represent the quantity of 15% alcohol required. Then (5-x) is the amount of 10% alcohol needed. The amount of alcohol in the mix is ...
0.15x +0.10(5-x) = 0.13(5)
0.05x +0.5 = 0.65 . . . . . . . simplify
0.05x = 0.15 . . . . . . . . . subtract 0.5
x = 3 . . . . . . . . . . . . . divide by 0.05
3 gallons of 15% alcohol and 2 gallons of 10% alcohol should be mixed.
Evaluate 210three x 12three
Answer:
2520
Step-by-step explanation:
210×12=2520
2520three
Scores on the SAT are approximately normally distributed. One year, the average score on the Math SAT was 500 and the standard deviation was 120. What was the score of a person who did better than 85% of all the test-takers
Answer:
The score of a person who did better than 85% of all the test-takers was of 624.44.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
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. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
One year, the average score on the Math SAT was 500 and the standard deviation was 120.
This means that [tex]\mu = 500, \sigma = 120[/tex]
What was the score of a person who did better than 85% of all the test-takers?
The 85th percentile, which is X when Z has a p-value of 0.85, so X when Z = 1.037.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.037 = \frac{X - 500}{120}[/tex]
[tex]X - 500 = 1.037*120[/tex]
[tex]X = 624.44[/tex]
The score of a person who did better than 85% of all the test-takers was of 624.44.
HELP PLEASE!!!!
I need the answer ASAP!!!!
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Answer:
c. y = (x +2)² -5
Step-by-step explanation:
If you replace the squared term with zero, you are choosing the minimum of the remaining values. (A squared term cannot have a negative value.)
a) 3
b) 4
c) -5 . . . . the graph with the least possible y-value
d) 0
