What is the greatest integer value of y for whic 5y - 20 < 0 ?
Answer:
3
Step-by-step explanation:
Step 1: Isolate y
5y < 20
y < 4
When we figure out the inequality, we see that y has to be less than 4. Therefore, the highest integer value will have to be 3.
Which equation describes a rational function with x-intercepts at –4 and 2, a vertical asymptote at x = 1 and x = –1, and a horizontal asymptote at y = –3?
Answer:
d on edge
Step-by-step explanation:
-3(x+4)(x-2)/x^2-1`
The equation of the rational function is: [tex]f(x) = \frac{-3(x + 4)(x -2)}{x^2-1}[/tex]
The x-intercepts of the rational function are given as: -4 and 2.
This means that, the zeroes of the function are (x + 4) and (x -2)
Multiply the zeroes of the function
[tex]f(x) = (x + 4)(x -2)[/tex]
The vertical asymptotes of the rational function are given as: 1 and -1.
This means that, the denominator is the product of (x + 1) and (x -1)
So, we have:
[tex]f(x) = \frac{(x + 4)(x -2)}{(x + 1)(x-1)}[/tex]
Express the denominator as the difference of two squares
[tex]f(x) = \frac{(x + 4)(x -2)}{x^2-1}[/tex]
Lastly, the horizontal asymptote is given as y = -3.
So, the actual function is:
[tex]f(x) = y \times \frac{(x + 4)(x -2)}{x^2-1}[/tex]
Substitute -3 for x
[tex]f(x) = -3 \times \frac{(x + 4)(x -2)}{x^2-1}[/tex]
This gives
[tex]f(x) = \frac{-3(x + 4)(x -2)}{x^2-1}[/tex]
Hence, the equation of the rational function is: [tex]f(x) = \frac{-3(x + 4)(x -2)}{x^2-1}[/tex]
Read more about rational functions at:
https://brainly.com/question/1851758
Triangle ABC was dilated using the rule Y, 5/4. FCA is equal to eight what is C’A’ 10 units 12 and 16 units 20 units
Answer:
C'A' = 10units (A)
Question
A complete question related to this found at brainly(question ID 2475535) is stated below.
Triangle ABC was dilated using the rule Dy, 5/4
If CA = 8, what is C'A'?
10 units
12 units
16 units
20 units
Step-by-step explanation:
Given:
Scale factor = 5/4
CA = 8units
Find attached the diagram for the question.
This is a question on dilation. In dilation, figures have the same shapes but different sizes.
Y is the center of dilation
Lengths of ∆ABC: CB, AB, CA
Lengths of ∆A'B'C': C'B', A'B', C'A'
C'B' = scale factor × CB
A'B' = scale factor × AB
C'A' = scale factor × CA
C'A' = 5/4 × 8
C'A' = 40/4
C'A' = 10units (A)
Hee lllp!!! Now 70 points
Answer:
[tex]\huge\boxed{Option \ 1}[/tex]
Step-by-step explanation:
Since, AE = CE and BE = DE , then E is the midpoint of AC and BD. Causius can use that to show that AC and BD bisect each other which means that they both are the diagonals of a parallelogram bisecting each other. Hence, It will be proved that ABCD is a || gm.
Hope this helped!
~AnonymousHelper1807Which fraction is equivalent to 20%?
Answer:
1/5
Step-by-step explanation:
20*5 = 100, so 20 is 1/5
Please answer this correctly
Answer:
101-120=4
Step-by-step explanation:
All that you need to do is count how many data points fall into this category. In this case, there are four data points that fall into the category of 101-120 pushups
111111105113Therefore, the answer to the blank is 4. If possible, please mark brainliest.
Answer:
There are 4 numbers between 101 and 120.
Step-by-step explanation:
101-120: 105, 111, 111, 113 (4 numbers)
Allie Maxudywishes to retire 25 years. She has decided that she should be able to invest $5000 per year in her retirement fund. If she makes the payments in quarterly installments at the beginning of the each year, and earn an annual percentage rate of 8% on her money how much she will have at the time of her retirement?
Answer:
$394,772.11
Step-by-step explanation:
This requires using compound interest as follows:
Principal = $5,000
Time = 25 years
Interest rate per annum = 8%
1st year: principal = 5000
Interest capitalized (5000*0.08) = 400
Amount (5000 + 400) = $5400
2nd year: principal = 5400 + 5000 = 10,400
Interest capitalized (10,400*0.08) = 832
Amount (10,400 + 832) = $11,232
3rd year: principal = 11,232+5000 = $16,232
Interest capitalized (16,232*0.08) = 1,298.56
Amount (16,232+1,298.56) = $17,530.56
4th year: principal = 17,530.56+5000 = $22,530.56
Interest capitalized (22,530.56*0.08) = 1,802.45
Amount (22,530.56+1,802.45) = $24,333.01
5th year: principal = 24,333.01+5000 = $29,333.01
Interest capitalized (29,333.01 * 0.08) = 2,346.64
Amount (29,333.01 + 2,346.64) = $31,679.65
6th year: principal = 31,679.65 + 5000 = $36,679.65
Interest capitalized (36,679.65 * 0.08) = 2,934.37
Amount (36,679.65 + 2,934.37) = $39,614.02
7th year: principal = 39,614.02 + 5000 = $44,614.02
Interest capitalized (44,614.02 * 0.08) = 3,569.12
Amount (44,614.02 + 3,569.12) = $48,183.14
8th year: principal = 48,183.14 + 5000 = $53,183.14
Interest capitalized (53,183.14 * 0.08) = 4,254.65
Amount (53,183.14 + 4,254.65) = $57,437.79
9th year: principal = 57,437.79 + 5000 = $62,437.79
Interest capitalized (62,437.79 * 0.08) = 4,995.02
Amount (62,437.79 + 4,995.02) = $67,432.81
10th year: principal = 67,432.81 + 5000 = $72,432.81
Interest capitalized (72,432.81 * 0.08) = 5,794.63
Amount (72,432.81 + 5,794.63) = $78,227.44
11th year: principal = 78,227.44 + 5000 = $83,227.44
Interest capitalized (83,227.44 * 0.08) = 6,658.20
Amount (83,227.44 + 6,658.20) = $89,885.64
12th year: principal = 89,885.64 + 5000 = $94,885.64
Interest capitalized (94,885.64 * 0.08) = 7,590.85
Amount (94,885.64 + 7,590.85) = $102,476.49
13th year: principal = 102,476.49 + 5000 = $107,476.49
Interest capitalized (107,476.49 * 0.08) = 8,598.12
Amount (107,476.49 + 8,598.12) = $116,074.61
14th year: principal = 116,074.61 + 5000 = $121,074.61
Interest capitalized (121,074.61 * 0.08) = 9,685.97
Amount (121,074.61 + 9,685.97) = $130,760.58
15th year: principal = 130,760.58 + 5000 = $135,760.58
Interest capitalized (135,760.58 * 0.08) = 10,860.85
Amount (135,760.58 + 10,860.85) = $146,621.43
16th year: principal = 146,621.43 + 5000 = $151,621.43
Interest capitalized (151,621.43 * 0.08) = 12,129.71
Amount (151,621.43 + 12,129.71) = $163,751.14
17th year: principal = 163,751.14 + 5000 = $168,751.14
Interest capitalized (168,751.14 * 0.08) = 13,500.09
Amount (168,751.14 + 13,500.09) = $182,251.23
18th year: principal = 182,251.23 + 5000 = $187,251.23
Interest capitalized (187,251.23 * 0.08) = 14,980.10
Amount (187,251.23 + 14,980.10) = $202,231.33
19th year: principal = 202,231.33 + 5000 = $207,231.33
Interest capitalized (207,231.33 * 0.08) = 16,578.51
Amount (207,231.33 + 16,578.51) = $223,809.84
20th year: principal = 223,809.84 + 5000 = $228,809.84
Interest capitalized (228,809.84 * 0.08) = 18,304.79
Amount (228,809.84 + 18,304.79) = $247,114.63
21st year: principal = 247,114.63 + 5000 = $252,114.63
Interest capitalized (252,114.63 * 0.08) = 20,169.17
Amount (252,114.63 + 20,169.17) = $272,283.8
22nd year: principal = 272,283.8 + 5000 = $277,283.8
Interest capitalized (277,283.8 * 0.08) = 22,182.70
Amount (277,283.8 + 22,182.70) = $299,466.5
23rd year: principal = 299,466.5 + 5000 = $304,466.5
Interest capitalized (304,466.5 * 0.08) = 24,357.32
Amount (304,466.5 + 24,357.32) = $328,823.82
24th year: principal = 328,823.82 + 5000 = $333,823.82
Interest capitalized (333,823.82 * 0.08) = 26,705.91
Amount (333,823.82 + 26,705.91) = $360,529.73
25th year: principal = 360,529.73 + 5000 = $365,529.73
Interest capitalized (365,529.73 * 0.08) = 29,242.38
Amount (365,529.73 + 29,242.38) = $394,772.11
John took all his money from his savings account. He spent $48 on a radio and 3/8 of what was left on presents for his friends. Of the money remaining, John put 2/3 into a checking account and the last remaining $100 was left to charity. How much money did John orginally have in his savings account?
Answer:
Step-by-step explanation:
Let a = original amt in the savings account
"He spent $48 on a radio and 3/8 of what was left on presents for his friends."
Therefore he kept 5/8 of what was left
5/8(a - 48)
5/8(a - 30) left
:
John then put 2/3 of his remaining money into a checking account and donated the $100 that was left to charity.
a = 2/3(5/8a - 30) + 100
a = 5/12a - 20 + 100
a = 5/12a + 80
a - 5/12a = 80
7/12a = 80
a = $137.17 originally in his saving acct
Find the perimeter ? Plsss
Hey there!
Answer:
25.1 units.
Step-by-step explanation:
Calculate the lengths of sides AB, BC and AC. Use the distance formula: [tex]d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}[/tex]
Solving for AB:
[tex]d = \sqrt{(4 -(-4))^2 + (5-(-1))^2}[/tex]
[tex]d = \sqrt{8^2 + 6^2}[/tex]
[tex]d = \sqrt{100}[/tex]
[tex]AB = 10[/tex]
Solving for BC:
This side is a vertical line, meaning simply find the difference of y values between each endpoint.
[tex]5-(-2) = 7[/tex]
[tex]BC = 7[/tex]
Solving for AC:
[tex]d = \sqrt{(4-(-4))^2 + (-2-(-1))^2}[/tex]
[tex]d = \sqrt{(8)^2 + (-1)^2}[/tex]
[tex]d = \sqrt{65}[/tex]
d≈ 8.06 units
Add up all of the side lengths:
10 + 7 + 8.06 = 25.06 ≈ 25.1 units.
11. cos theta = 3/4, in quadrant 1
Answer:
Step-by-step explanation:sin
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a number minus 8 is no more than -3, write as an inequality
Answer:
11
Step-by-step explanation:
HELP ME Answer it from the forst one to the last one with the rght answer please.This is Urgent so do it Faster if u now the answers
Step-by-step explanation:
2) 63
3) 7000
4) 10
These are some answers
A line has a slope of -3/2 and has a y-intercept of 3. What is the x-intercept of the line?
Answer:
x = 2
Step-by-step explanation:
the equation of the line can be found using the slope intercept form
y = mx +b
y= -3/2 x + 3
x intercept is found by setting y=0 bc that will give you the x-value at which the line crosses the x -axis so
0 = -3/2x+3 (subtract the 3 on both sides) would cancel out the + 3 and would
-3 = -3/2 x (divide by -3/2 on both sides to cancel out the -3/2)
x = 2
f(x) = 2x – 1 g(x) = 7x – 12 What is h(x) = f(x) + g(x)?
Answer:
h(x)=9x-13Solution,
[tex]h(x) = f(x) + g(x) \\ \: \: \: \: \: \: \: = 2x - 1 + 7x - 12 \\ \: \: \: \: \: \: = 2x + 7x - 1 - 12 \\ \: \: \: \: \: \: = 9x - 13[/tex]
hope this helps...
Good luck on your assignment..
Answer:
h(x)=9x-13
Step-by-step explanation:
We want to find out what h(x) is. We know what h(x) is equal to, which is
h(x)= f(x)+g(x)
We know that f(x)=2x-1 and g(x)=7x-12. Substitute the expressions in.
h(x)= (2x-1)+(7x-12)
Simplify by combining like terms. Add all the terms with a variable (x), then all the terms without a variable, or constants.
h(x)=(2x+7x)+(-1+-12)
Add 2x and 7x.
h(x)=(2+7)(x)+(-1+-12)
h(x)= 9x+(-1+-12)
Add -1 and -12.
h(x)= 9x+(-13)
h(x)=9x-13
dakota received a bonus check for $2,500 and is going to deposit the money into a bank account that receives 5.5% compounded annually. What is dakotas account balance after five years?
Answer: $3267.40
Step-by-step explanation:
A = P (1+r/n)^nt
A= 2500 (1+0.055)^nt
A= 2500 x 1.30696
A = 3267.40
How many solutions does 6-3x=4-x-3-2x have?
Answer:
no solutions
Step-by-step explanation:
6-3x=4-x-3-2x
Combine like terms
6-3x =1 -3x
Add 3x to each side
6 -3x+3x = 1-3x+3x
6 =1
This is not true so there are no solutions
Answer:
No solutions.
Step-by-step explanation:
6 - 3x = 4 - x - 3 - 2x
Add or subtract like terms if possible.
6 - 3x = -3x + 1
Add -1 and 3x on both sides.
6 - 1 = -3x + 3x
5 = 0
There are no solutions.
Janice really likes potatoes. Potatoes cost $1.00 per pound, and she has $6.00 that she could possibly spend on potatoes or other items. Suppose she feels that the first pound of potatoes is worth $1.50, the second pound is worth $1.14, the third pound is worth $1.05, and all subsequent pounds are worth $0.30. how many pounds of potatoes will she purchase?
Answer:
6 pounds
Step-by-step explanation:
The height of Maury’s room is 8.4 feet from the floor to the ceiling. Maury wants to install a ceiling fan that hangs 1.875 feet below the ceiling. If Maury is 6.6 feet tall, which explains whether Maury’s head will hit the fan? Maury’s head will hit the fan because there are 6.525 feet between the floor and the fan, and 6.525 is less than 6.6. Maury’s head will not hit the fan because there are 6.525 feet between the floor and the fan, and 6.525 is less than 6.6. Maury’s head will hit the fan because there are 6.675 feet between the floor and the fan, and 6.675 is less than 6.6. Maury’s head will not hit the fan because there are 6.675 feet between the floor and the fan, and 6.675 is less than 6.6.
Subtract the ceiling fan from the height of the room:
8.4 - 1.875 = 6.525 feet
The answer is:
Maury’s head will hit the fan because there are 6.525 feet between the floor and the fan, and 6.525 is less than 6.6.
Answer:
it is A
Step-by-step explanation:
how to simplify 2x^2 - 18 =0
Answer:
X=3 or x= -3
Step-by-step explanation:
2x^2 - 18 =0
Take a common factor
2(x^2 - 9) = 0
2(x-3)(x+3)=0
X-3=0 or x+3=0
X=3 x=-3
Hope this helps!
Step-by-step explanation:
Hope this is correct
HAVE A GOOD DAY!
Use the given function f(x)=|x| to graph g(x) =|x+2|-4
Answer:
see the attachment for a graph
Step-by-step explanation:
The vertex of f(x) is (0, 0). The transformation g(x) = f(x -h) +k moves the vertex to (h, k). That is, the graph is translated right by h units, and up by k units.
Your transformation has h = -2, and k = -4. That is, the original graph is translated left 2 units and down 4 units. The result is the blue curve in the attachment.
PLEASE HELP ME WITH THIS, HELP NEEDED ASAP
Answer:
x = 16.5
Step-by-step-explanation:
The height of the larger triangle is 11, and the height of smaller triangle is 2. Which means that the larger triangle height is 5.5 times greater than the smaller triangle's height.
If the base of the smaller triangle is 3, that means that base of the whole/larger triangle is 16.5 because 3 * 5.5 = 16.5
find the x value to make L||M
Answer:
X=7[tex]solution \\ 2x - 3 = x + 4(being \: alternate \: exterior \: angles) \\ or \: 2x - x = 4 + 3 \\ x = 7 \\ hope \: it \: helps[/tex]
A film distribution manager calculates that 4% of the films released are flops. If the manager is correct, what is the probability that the proportion of flops in a sample of 667 released films would be greater than 5%
Answer:
9.34%
Step-by-step explanation:
p = 4%, or 0.04
n = Sample size = 667
u = Expected value = n * p = 667 * 0.04 = 26.68
SD = Standard deviation = [tex]\sqrt{np(1-p)} =\sqrt{667*0.04*(1-0.04)}[/tex] = 5.06
Now, the question is if the manager is correct, what is the probability that the proportion of flops in a sample of 667 released films would be greater than 5%?
This statement implies that the p-vlaue of Z when X = 5% * 667 = 33.35
Since,
Z = (X - u) / SD
We have;
Z = (33.35 - 26.68) / 5.06
Z = 1.32
From the Z-table, the p-value of 1.32 is 0.9066
1 - 0.9066 = 0.0934, or 9.34%
Therefore, the probability that the proportion of flops in a sample of 667 released films would be greater than 5% is 9.34%.
According to a Harris Poll in 2009, 72% of those who drive and own cell phones say they use them to talk while they are driving. If you wish to conduct a survey in your city to determine what percent of the drivers with cell phones use them to talk while driving, how large a sample should be if you want your estimate to be within 0.02 with 95% confidence.
Answer:
We need a sample of at least 1937.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
For this problem, we have that:
[tex]\pi = 0.72[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
How large a sample should be if you want your estimate to be within 0.02 with 95% confidence.
We need a sample of at least n.
n is found when M = 0.02. So
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.02 = 1.96\sqrt{\frac{0.72*0.28}{n}}[/tex]
[tex]0.02\sqrt{n} = 1.96\sqrt{0.72*0.28}[/tex]
[tex]\sqrt{n} = \frac{1.96\sqrt{0.72*0.28}}{0.02}[/tex]
[tex](\sqrt{n})^{2} = (\frac{1.96\sqrt{0.72*0.28}}{0.02})^{2}[/tex]
[tex]n = 1936.16[/tex]
Rounding up to the nearest number.
We need a sample of at least 1937.
❗️❗️❗️Find the length of side x in simplest radical form with a rational denominator.❗️❗️❗️
Plzzz helppp meeee
Answer:
[tex]x=\frac{\sqrt{14} }{2}[/tex]
Step-by-step explanation:
Notice that you are given an isosceles right-angle triangle to solve, since each of its two acute angles measures [tex]45^o[/tex]. Then such means that the sides opposite to these acute angles (the so called "legs" of this right angle triangle) must also be of the same length (x).
We can then use the Pythagorean theorem that relates the square of the hypotenuse to the addition of the squares of the triangles legs:
[tex](\sqrt{7})^2=x^2+x^2\\7=2\,x^2\\x^2=\frac{7}{2} \\x=+/-\sqrt{\frac{7}{2}} \\x=+/-\frac{\sqrt{14} }{2}[/tex]
We use just the positive root, since we are looking for an actual length. then, the requested side is:
[tex]x=\frac{\sqrt{14} }{2}[/tex]
Write an expression without exponent that is equivalent to 2 to 3rd power nd 4 to the 3rd power
Answer:
2 to the 3rd power,
2*2*2
4 to the 3rd power,
4*4*4
Step-by-step explanation:
The "3rd power" means how many times the number given to it would be multiplied. Aka, 2 to the 4th power would mean 2 times 2 times 2 times 2, (2 four times).
How many different triangles can you make if you are given
these three lengths for sides?
Answer:
Step-by-step explanation:
i think its 3
Answer:
0
Step-by-step explanation:
You cannot make any triangles with this angle
Compare (−1) to the power of two and −1 to the power of 2
Answer:
(-1)² = 1
-1² = -1
Step-by-step explanation:
(-1)² means you are squaring the value of -1 to -1.
-1² means you are squaring the value of -1 to 1.
if x=2 find y 5x-y=5
Answer:
y=5
solution,
X=2
now,
[tex] \\ 5x - y = 5 \\ or \: 5 \times x - y = 5 \\ or \: 5 \times 2 - y = 5 \\ or \: 10 - y = 5 \\ or \: - y = 5 - 10 \\or \: - y = - 5 \\ y = 5[/tex]
hope this helps..
Good luck on your assignment..
A standard deck of cards contains 52 cards. One card is selected from the deck. (a) Compute the probability of randomly selecting a diamond or club. (b) Compute the probability of randomly selecting a diamond or club or heart. (c) Compute the probability of randomly selecting a three or club.
Answer:
Ok, in a deck of 52 cards we have:
13 clubs, 13 diamonds, 13 hearts, and 13 spades.
For this problem, we assume that the probability of selecting a card at random is the same for all the cards, so each card has a probability of 1/52 of being selected.
then the probability of drawing a given outcome, is equal to the number of times that the outcome appears in the deck divided the number of cards.
a) probability of randomly selecting a diamond or club.
in the 52 cards deck, we have 13 diamonds and 13 clubs, so the probability of drawing a diamond or a club is equal to:
P = (13 + 13)/52 = 26/52 = 0.5
b) Compute the probability of randomly selecting a diamond or club or heart.
Same reasoning as before, here we have 13 + 13 + 13 = 39 possible options, so the probability is:
p = 39/52 = 0.75.
c) Compute the probability of randomly selecting a three or club.
we have 13 club cards, and in the deck, each number appears 4 times, so we have 4 cards with a number 3 on them.
But one of those 3's is also a club card, so we already counted it in the 13 club cards, then the number of possible options here is:
13 + 4 - 1 = 13 +3 = 16
then the probability is:
p = 16/52 = 0.31
To solve the questions we must know the concept of Probability.
The probability of randomly selecting a diamond or club is 50%.The probability of randomly selecting a diamond or a club or heart is 75%The probability of randomly selecting a diamond or a club or heart is 30.77%.What is Probability?The probability helps us to know the chances of an event occurring.
[tex]\rm{Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
Explanations
(a) Compute the probability of randomly selecting a diamond or club.
Probability( Diamond or club)The number of diamond cards = 13
The number of club cards = 13
The total number of diamond and club cards = 26
[tex]\rm{Probability(Diamond\ or\ club)=\dfrac{Number\ of\ diamond\ or\ club\ cards}{Total\ Number\ of\ cards}[/tex]
[tex]\rm{Probability(Diamond\ or\ club)=\dfrac{26}{52}=\dfrac{1}{2} = 0.5 = 50\%[/tex]
(b) Compute the probability of randomly selecting a diamond or club or heart.
Probability( Diamond or club or heart)The number of diamond cards = 13
The number of club cards = 13
The number of heart cards = 13
The total number of diamond, heart, and club cards = 39
[tex]\rm{Probability(Diamond\ or\ club\ or\ hearts)=\dfrac{Number\ of\ diamond\ or\ club\ or\ hearts\ cards}{Total\ Number\ of\ cards}[/tex]
[tex]\rm{Probability(Diamond\ or\ club\ or\ hearts)=\dfrac{39}{52}=\dfrac{3}{4} = 0.75 = 75\%[/tex]
(c) Compute the probability of randomly selecting a three or club.
Probability( three or club)The number of three cards = 4
The number of club cards = 13
The total number of diamond and club cards = 13+4 - 1 =16
we reduced a card because card three of the club is calculated twice.
[tex]\rm{Probability(three\ or\ club)=\dfrac{Number\ of\ three\ or\ club\ cards}{Total\ Number\ of\ cards}[/tex]
[tex]\rm{Probability(three\ or\ club)=\dfrac{16}{52}=0.3077 = 30.77\%[/tex]
Learn more about Probability:
https://brainly.com/question/743546