Answer:
Due to the higher z-score, Norma should be offered the job
Step-by-step explanation:
Z-score:
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
In this question:
Whoever has the higher z-score should get the job.
Norma:
Norma got a score of 84.2; this version has a mean of 67.4 and a standard deviation of 14.
This means that [tex]X = 84.2 \mu = 67.4, \sigma = 14[/tex]
So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{84.2 - 67.4}{14}[/tex]
[tex]Z = 1.2[/tex]
Pierce:
Pierce got a score of 276.8; this version has a mean of 264 and a standard deviation of 16.
This means that [tex]X = 276.8, \mu = 264, \sigma = 16[/tex]
So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{276.8 - 264}{16}[/tex]
[tex]Z = 0.8[/tex]
Reyna:
Reyna got a score of 7.62; this version has a mean of 7.3 and a standard deviation of 0.8.
This means that [tex]X = 7.62, \mu = 7.3, \sigma = 0.8[/tex]
So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{7.62 - 7.3}{0.8}[/tex]
[tex]Z = 0.4[/tex]
Due to the higher z-score, Norma should be offered the job
PLEASE HELP
In two or more complete sentences, compare the number of x-intercepts in the graph of f(x) = x2 to the number of x-intercepts in the graph of g(x) = (x-2)2 -3. Be sure to include the transformations that occurred between the parent function f(x) and its image g(x).
Answer:
Ok, for f(x) = x^2 we have only one x-intercept (actually, two equal x-intercepts) at x = 0.
Now, for g(x) = (x - 2)^2 - 3
First, let's analyze the transformations.
When we have g(x) = f(x - a) this means that we moved "a" units to the right (if a is positive)
When we have g(x) = f(x) + a, this means that (if a > 0) we move the graph "a" units up.
In this case we have both those transformations:
g(x) = f(x - 2) - 3
this means that we move 2 units to the right, and 3 units down (because the number is negative)
now we can find the roots of g(x) as:
g(x) = (x - 2)^2 - 3 = x^2 - 4x + 4 - 3 = x^2 - 4x + 1 = 0
using the Bhaskara's equation:
[tex]x = \frac{4 +-\sqrt{4^2 - 4*1*1} }{2*1} = \frac{4 +- 3.5}{2}[/tex]
then the roots are:
x = (4 + 3.5)/2 = 3.75
x = (4 - 3.5)/2 = 0.25
Here we have two different x-intercepts
If P(-2, 1) is rotated 90°, its image is
Salinas Corporation has net income of $15 million per year on net sales of $90 million per year. It currently has no long-term debt but is considering a debt issue of $20 million. The interest rate on the debt would be 7%. Salinas Corp. currently faces an effective tax rate of 40%. What would be the annual interest tax shield to Salinas Corp. if it goes through with the debt issuance?
Answer:
The annual interest tax shield to Salinas Corp would be of $560,000
Step-by-step explanation:
In order to calculate the annual interest tax shield to Salinas Corp if it goes through with the debt issuance we would have to calculate the following formula:
Annual Interest tax shield = Interest * tax
Interest = debt *rate of interest
Interest=$20 million * 0.07
Interest= $ 1.40 million
tax= 40%
Therefore, Annual Interest tax shield =$1.40 million * 0.40
Annual Interest tax shield = $560,000
The annual interest tax shield to Salinas Corp would be of $560,000
Problem PageQuestion The mass of a radioactive substance follows a continuous exponential decay model, with a decay rate parameter of per day. Find the half-life of this substance (that is, the time it takes for one-half the original amount in a given sample of this substance to decay).
Answer:
8.55 days for a decay rate parameter of 8.1% per day
Step-by-step explanation:
Assuming a decay rate parameter of 8.1% per day
the general equation for radioactive decay is;
N = N₀e^(-λt)
x - decay constant (λ) - rate of decay
t- time
N - amount remaining after t days , since we are calculating the half life, amount of time it takes for the substance to to be half its original value, its N₀/2
N₀ - amount initially present
substituting the values
N₀/2 = N₀e^(-0.081t)
0.5 = e^(-0.081t)
ln (0.5) = -0.081t
-0.693 = -0.081t
t = 0.693 / 0.081 = 8.55
half life of substance is 8.55 days
how do you add 9 in 1 6 + 2 1/12
Step-by-step explanation:
9 + 1/6 + 2 1/12
9 + 2.25
11.25
The mean height of women in a country (ages 20-29) is 64.3 inches. A random sample of 75 women in this age group is selected. What is the probability that the mean height for the sample is greater than 65 inches? Assume sigma=2.81.
Answer:
z(65) = (65-64.2)/[2.81/sqrt(60)] = 0.8/(0.3279)
Step-by-step explanation:
Using the normal probability distribution and the central limit theorem, it is found that there is a 0.0154 = 1.54% probability that the mean height for the sample is greater than 65 inches.
In a normal distribution 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]
It 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, which is the percentile of X. By the Central Limit Theorem, for samples of size n, the standard deviation is [tex]s = \frac{\sigma}{\sqrt{n}}[/tex]In this problem:
Mean of 64.3 inches, thus [tex]\mu = 64.3[/tex]Standard deviation of 2.81 inches, thus [tex]\sigma = 2.81[/tex]Sample of 75, thus [tex]n = 75[/tex].The probability that the mean height for the sample is greater than 65 inches is 1 subtracted by the p-value of Z when X = 65, thus:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]Z = \frac{65 - 64.3}{\frac{2.81}{\sqrt{75}}}[/tex]
[tex]Z = 2.16[/tex]
[tex]Z = 2.16[/tex] has a p-value of 0.9846.
1 - 0.9846 = 0.0154
0.0154 = 1.54% probability that the mean height for the sample is greater than 65 inches.
A similar problem is given at https://brainly.com/question/24663213
WILL GIVE BRAINLIEST! HURRY
Answer:
[tex]x = - 8[/tex]
Second answer is correct
Step-by-step explanation:
[tex] - 4(2x + 3) = 2x + 6 - (8x + 2) \\ - 8x - 12 = 2x + 6 - 8x - 2 \\ - 8x - 12 = - 6x + 4 \\ - 8x + 6x = 12 + 4 \\ - 2x = 16 \\ \frac{ - 2x}{ - 2} = \frac{16}{ - 2} \\ x = - 8[/tex]
hope this helps
What is the value of X?
Answer:
x = 41 ft
Step-by-step explanation:
35(35+23) = 29(29+x)
2030 = 29(29+x)
70 = 29 + x
x = 41 ft
Choose the inequality that could be used to solve the following problem.
Three times a number is at most negative six.
Answer:
3x ≤ -6
Step-by-step explanation:
"At most" means "less than or equal to." If x represents the number, then you have ...
(three) times (a number) (is at most) negative 6 . . . . . English
3 · x ≤ -6 . . . . . . . . . . . . . . . . Math
__
3x ≤ -6
Answer:
3x ≤ -6
Step-by-step explanation:
Solve Systems of Algebraic Equations in Two Variables
Hello I need some help on setting up 2 equations of this problem. The answers are cheeseburger costs $1.55 and the milkshake $0.85
Four cheeseburgers and two chocolate milkshakes cost a total of $ 7.90. Two
Shakes cost 15 cents more than a hamburger with
cheese so What is the price of a cheeseburger?
And the price of a shake?
Answer:
4c+ 2m = 7.90
2m -.15 = c
Step-by-step explanation:
Let c = cheese burger
m = milkshake
4c+ 2m = 7.90
2m -.15 = c
Substitute into the first equation
4( 2m -.15) +2m = 7.90
Distribute
8m -.6 +2m = 7.90
Combine like terms
10m - .6 = 7.90
Add .6 to each side
10m = 7.90+.6
10m = 8.50
Divide by m
10m = 8.50/10
m = .85
Now find c
2m -.15 = c
2(.85) - .15=c
1.70-.15 = c
1.55 =c
My son and I are stuck on this one. Can anyone give some insight to this problem? Thank you.
Answer:
I made is clear for you, now you may match each one
Step-by-step explanation:
f(1)= 11, f(n)= 3*f(n-1)
11*3= 33, 33*3= 99, 99*3= 297, ...11, 33, 99, 297...⊕ middle
f(1)= -18, f(n)= f(n-1)+21
-18+21= 3, 3+21= 24, 24+21= 45, ...-18, 3, 24, 45, ...f(1)= -18, f(n)= f(n-1) + 22
-18+22= 4, 4+22= 26, 26+22= 48, ...-18, 4, 26, 48, ...f(1)= -18, f(n)= 2*f(n-1)
-18*2= -36, -36*2= -72, -72*2= -144, ...- 18, -36, -72, -144...⊕ bottom
f(1)= -18, f(n)= 6*f(n-1)
-18*6= -108, -108*6= -648, -648*6= -3888, ...- 18, - 108, - 648, -3888, ...⊕ top
f(1)= 11, f(n)= f(n-1) + 22
11+22= 33, 33+22= 55, 55+22= 77, ...11, 33, 55, 77, ...Solve the following inequality. |-2x + 1| < 13
Please help!!!!
Answer:
x>−6 and x<7
Step-by-step explanation:
Let's solve your inequality step-by-step.
|−2x+1|<13
Solve Absolute Value.
|−2x+1|<13
We know−2x+1<13and−2x+1>−13
−2x+1<13(Condition 1)
−2x+1−1<13−1(Subtract 1 from both sides)
−2x<12
−2x
−2
<
12
−2
(Divide both sides by -2)
x>−6
−2x+1>−13(Condition 2)
−2x+1−1>−13−1(Subtract 1 from both sides)
−2x>−14
−2x
−2
>
−14
−2
(Divide both sides by -2)
x<7
Answer:
x>−6 and x<7
Factorizar e indicar cuántos factores primos tiene -3+3x^2+y-x^2*y-y^2+x^2*y
How did governments pursue mercantilist policies?
Answer:
Most of the mercantilist policies were the outgrowth of the relationship between the governments of the nation-states and their mercantile classes
Step-by-step explanation:
In the British empire Mercantilism, an economic policy designed to increase a nation's wealth through ... Mercantilism did, however, lead to the adoption of enormous trade
Hope this helps. :)
Given cot ø = 4/3. Find the other two reciprocal trigonometic ratios. 1) scs 2) sec
Answer:
csc ø = 5/3 ; sec ø = 5/4
Step-by-step explanation:
cot ø = adj/opp
adj = 4
opp = 3
after that, we must find the hypotenuse by using phytagoras theorem
hpy² = adj² + opp²
hpy² = 4² + 3²
hpy² = 25
hpy = 5
now let's find the other
csc ø (not scs) = hyp/opp = 5/3
sec ø = hyp/adj = 5/4
The probability of teenager owning a game system is .72 and the probability of teenager owning a cell phone is .93.
the probability of a teenager owning both gaming system and cell phone is .68
what is the probability of a teenager owning a gaming system or a cell phone? round to the nearest thousandth
Answer: 0.97
Step-by-step explanation:
Formula : For events A and B
P(A or B) = P(A) + P(B) - P(A and B)
Given : The probability of teenager owning a game system is .72.
i.e. P(game system) =0.72
The probability of teenager owning a cell phone is .93.
i.e. P(cell phone) = 0.93
The probability of a teenager owning both gaming system and cell phone is .68
i.e. P( game system and cell phone) = 0.68
Now , the probability of a teenager owning a gaming system or a cell phone is given by :_
P(game system or cell phone) = P(game system) +P(cell phone)- P( game system and cell phone)
= 0.72+0.93-0.68
= 0.97
Hence, the probability of a teenager owning a gaming system or a cell phone is 0.97.
(-1/4 - 1/2) ÷ (-4/7)
Answer:
1 5/16
Step-by-step explanation:
(-1/4 - 1/2) ÷ (-4/7)
PEMDAS says parentheses first
Get a common denominator
(-1/4 - 2/4) ÷ (-4/7)
(-3/4) ÷ (-4/7)
Copy dot flip
-3/4 * -7/4
21/16
Change to a mixed number, 16 goes into 21 1 time with 5 left over
1 5/16
Which steps can be used to solve for the value of y?
(2013
(y +57) = 178
Answer: [tex]y = 121[/tex]
[tex](y+57) = 178[/tex]
[tex]y+57= 178[/tex]
[tex]y = 178 -57[/tex]
[tex]y = 121[/tex]
The perimeter of a rectangular parking lot is 320 m.
If the length of the parking lot is 97 m, what is its width?
Answer:
63 metres
Step-by-step explanation:
A rectangle has 4 sides
2 of these sides are the lengths
The other 2 sides are the width
If the length of one side is 97 metres, the other side length must also be 97 metres
The two lengths then add together (97 + 97) to become 194 metres
Now we can use this information to calculate the width
320 (the total perimeter) subtract 194 (The total length) = 126 metres
This means that 126 metres is the total width
Because there are two sides which add up to the total width we divide 126 by 2
This allows us to get the measurement of the width
126 divided by 2 = 63 metres
What is the missing number in the pattern? Please Help. Been stuck on this for hours.
Answer:
8
Step-by-step explanation:
The other patterns go with the two factors on top (2 x 3 = 6 and 3 x 3 = 9).
So, 2 x 4 = 8
What is the y coordinate of the point that divides the directed line segment from j to k into a ratio of 2 to 3
Answer:
y = [tex]y_{1}[/tex] + rise * 2/5
Step-by-step explanation:
Jeanie wrote the correct first step to divide 8z2 + 4z – 5 by 2z.
Which shows the next step?
A.4z + 2 –
B.4z2 + 2 –
C.4z2 + 2 –
D.4z + 2 –
Answer:
4z + 2 - 5/2z
Step-by-step explanation:
8z^2 + 4z -5
divided by 2z
8z^2 /2z = 4z
4z/2z =2
5/2z = 5/2z
Putting them back together
4z + 2 - 5/2z
Answer:
A 4z + 2 - 5/2z
Step-by-step explanation:
express 0.8342 as a fraction A: 8342/10 B: 8342/1000 C: 8342/10000
Answer:
[tex]\frac{8342}{10000} \\ [/tex]
Answer C is correct
Step-by-step explanation:
[tex]0.8342 = \frac{8342}{10000} [/tex]
To check whether this correct or wrong.
[tex]0.8342 \times 10000 = 8342[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
The decimal 0.8342 expressed as a fraction is (c) 8342/10000
How to express the decimal 0.8342 as a fraction.From the question, we have the following parameters that can be used in our computation
The decimal 0.8342
Express the decimal 0.8342 as a fraction
So, we have the following representation
Fraction = 8342/10000
When the fraction is simplified, we have
Fraction = 8342/10000
Hence, the decimal 0.8342 as a fraction is (c) 8342/10000
Read more about fraction at
brainly.com/question/78672
#SPJ6
Among 25- to 30-year-olds, 29% say they have used a computer while under the influence of alcohol. Suppose five 25- to 30-year-olds are selected at random. Complete parts (a) through (d) below. (a) What is the probability that all five have used a computer while under the influence of alcohol? (Round to four decimal places as needed.) (b) What is the probability that at least one has not used a computer while under the influence of alcohol? (Round to four decimal places as needed.) (c) What is the probability that none of the five have used a computer while under the influence of alcohol? (Round to four decimal places as needed.) (d) What is the probability that at least one has used a computer while under the influence of alcohol? (Round to four decimal places as needed.)
Answer:
(a) The probability that all five have used a computer while under the influence of alcohol is 0.0021.
(b) The probability that at least one has not used a computer while under the influence of alcohol is 0.9979.
(c) The probability that none of the five have used a computer while under the influence of alcohol is 0.1804.
(d) The probability that at least one has used a computer while under the influence of alcohol is 0.8196.
Step-by-step explanation:
We are given that among 25- to 30-year-olds, 29% say they have used a computer while under the influence of alcohol.
Suppose five 25- to 30-year-olds are selected at random.
The above situation can be represented through the binomial distribution;
[tex]P(X = x) = \binom{n}{r}\times p^{r} \times (1-p)^{n-r} ; x = 0,1,2,3,.........[/tex]
where, n = number of trials (samples) taken = Five 25- to 30-year-olds
r = number of success
p = probability of success which in our question is probability that
people used a computer while under the influence of alcohol,
i.e. p = 29%.
Let X = Number of people who used computer while under the influence of alcohol.
So, X ~ Binom(n = 5, p = 0.29)
(a) The probability that all five have used a computer while under the influence of alcohol is given by = P(X = 5)
P(X = 5) = [tex]\binom{5}{5}\times 0.29^{5} \times (1-0.29)^{5-5}[/tex]
= [tex]1 \times 0.29^{5} \times 0.71^{0}[/tex]
= 0.0021
(b) The probability that at least one has not used a computer while under the influence of alcohol is given by = P(X [tex]\geq[/tex] 1)
Here, the probability of success (p) will change because now the success for us is that people have not used a computer while under the influence of alcohol = 1 - 0.29 = 0.71
SO, now X ~ Binom(n = 5, p = 0.71)
P(X [tex]\geq[/tex] 1) = 1 - P(X = 0)
= [tex]1-\binom{5}{0}\times 0.71^{0} \times (1-0.71)^{5-0}[/tex]
= [tex]1 -(1 \times 1 \times 0.29^{5})[/tex]
= 1 - 0.0021 = 0.9979.
(c) The probability that none of the five have used a computer while under the influence of alcohol is given by = P(X = 0)
P(X = 0) = [tex]\binom{5}{0}\times 0.29^{0} \times (1-0.29)^{5-0}[/tex]
= [tex]1 \times 1 \times 0.71^{5}[/tex]
= 0.1804
(d) The probability that at least one has used a computer while under the influence of alcohol is given by = P(X [tex]\geq[/tex] 1)
P(X [tex]\geq[/tex] 1) = 1 - P(X = 0)
= [tex]1-\binom{5}{0}\times 0.29^{0} \times (1-0.29)^{5-0}[/tex]
= [tex]1 -(1 \times 1 \times 0.71^{5})[/tex]
= 1 - 0.1804 = 0.8196
Please answer this correctly
Answer:
1.2 km
Step-by-step explanation:
The first thing that we should go over is the formula for the area of a trapezoid.
Recall that it is [tex]A= \frac{b_1 +b_2}{2} *h[/tex]
From this image, we have the following information
[tex]b_1=2.5\\\\b_2=1.5\\\\A=2.4[/tex]
Now, we can plug this information into our formula and then solve for h.
[tex]2.4=\frac{2.5+1.5}{2} *h\\\\2.4=\frac{4}{2} *h\\\\2.4=2h\\\\h=1.2[/tex]
Another method that can be employed is to use the pythagorean theorem.
A trapezoid can be be broken into a rectangle and two triangles.
If we look at the difference in the sizes of the bases, the bottom base is 1 km larger. This means that the base of each triangle would be 0.5 km long.
As we have two side lengths of the triangle, we can now use the Pythagorean theorem to find the third side, which is h.
[tex](1.3)^2=h^2+(0.5)^2\\\\h^2=1.69-0.25\\\\h=\sqrt{1.44} \\\\h=1.2[/tex]
Answer:
h=1.2 km
Step-by-step explanation:
This is the formula of a Trapezium
A=[tex]\frac{h(a+b)}{2}[/tex]
[tex]2.4=\frac{(2.5+1.5)h}{2}\\ 2.4=\frac{4h}{2}\\ 2.4*2=4h\\4.8=4h\\h=1.2[/tex]
The following question involves a standard deck of 52 playing cards. In such a deck of cards there are four suits of 13 cards each. The four suits are: hearts, diamonds, clubs, and spades. The 26 cards included in hearts and diamonds are red. The 26 cards included in clubs and spades are black. The 13 cards in each suit are: 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King, and Ace. This means there are four Aces, four Kings, four Queens, four 10s, etc., down to four 2s in each deck.
You draw two cards from a standard deck of 52 cards without replacing the first one before drawing the second. (a) Are the outcomes on the two cards independent? Why?
1. No. The events cannot occur together. 2. Yes. The events can occur together. 3. No. The probability of drawing a specific second card depends on the identity of the first card. 4. Yes. The probability of drawing a specific second card is the same regardless of the identity of the first drawn card.
(b) Find P(ace on 1st card and jack on 2nd). (Enter your answer as a fraction.)
(c) Find P(jack on 1st card and ace on 2nd). (Enter your answer as a fraction.)
(d) Find the probability of drawing an ace and a jack in either order. (Enter your answer as a fraction.)
Answer:
(a)No. The probability of drawing a specific second card depends on the identity of the first card.
(b)4/663
(c) 4/663
(d) 8/663
Step-by-step explanation:
(a)The events are not independent because we are drawing cards without replacement and the probability of drawing a specific second card depends on the identity of the first card.
(b) P(ace on 1st card and jack on 2nd).
[tex]P$(Ace on 1st card) =\dfrac{4}{52}\\ P$(Jack on 2nd card)=\dfrac{4}{51}\\\\$Therefore:\\P(ace on 1st card and jack on 2nd) =\dfrac{4}{52}\times \dfrac{4}{51}\\=\dfrac{4}{663}[/tex]
(c)P(jack on 1st card and ace on 2nd)
[tex]P$(Jack on 1st card) =\dfrac{4}{52}\\ P$(Ace on 2nd card)=\dfrac{4}{51}\\\\$Therefore:\\P(jack on 1st card and ace on 2nd) =\dfrac{4}{52}\times \dfrac{4}{51}\\=\dfrac{4}{663}[/tex]
(d)Probability of drawing an ace and a jack in either order.
We can either draw an ace first, jack second or jack first, ace second.
Therefore:
P(drawing an ace and a jack in either order) =P(AJ)+(JA)
From parts (b) and (c) above:
[tex]P$(jack on 1st card and ace on 2nd) =\dfrac{4}{663}\\P$(ace on 1st card and jack on 2nd) =\dfrac{4}{663}\\$Therefore:\\P(drawing an ace and a jack in either order)=\dfrac{4}{663}+\dfrac{4}{663}\\=\dfrac{8}{663}[/tex]
The aspect ratio of a rectangular shape is it's length divided by it's width (L/W). If the aspect ratio of a chalkboard is 4:3 and the width is 5 in, what is the length of the chalkboard? A. 6.67 in B. 9.33 in C. 12 in D. 14 in
Answer:
A. 6.67 in
Step-by-step explanation:
length/width = 4/3 = x/5
Multiply by 5:
5(4/3) = x = 20/3 = 6 2/3
The length of the chalkboard is 6.67 inches.
It’s a math riddle please help Id appreciate it I need this quickly I’ll give additional points... I’d do need an explanation because the question requires it.
The puzzle are: 21, 30, 15, 333.
PuzzleClock:
Clock time=9 o'clock+9 o'clock+3 o'clock
Clock time=21
Calculator:
Calculator 1=1+2+3+4=10
Calculator 2=1+2+3+4=10
Calculator 3=1+2+3+4=10
Calculator=10+10+10
Calculator=30
Bulb:
The 3 bulb has 5 light each which represent the brightness of the 3 bulb.
Bulb=15+(15-15)
Bulb =15+0
Bulb=15
Fourth puzzle
Clock+Calculator×Bulb
9 o'clock+(1+2+2+4)× [3 bulb(3 bulb×4 light)]
9+9×(3×12)
Apply BODMAS
9+9×36
9+324
=333
Inconclusion the puzzle are: 21, 30, 15, 333.
Learn more about puzzle here:https://brainly.com/question/16999211
Solve the inequality and graph the solution set. Write the answer in interval notation. Write your answer in exact simplified form
0> 20x+2>-32
what is the solution?
Answer:
The solution is [tex]\:\left(-\frac{17}{10},\:-\frac{1}{10}\right)[/tex].
Step-by-step explanation:
An inequality is a mathematical relationship between two expressions and is represented using one of the following:
≤, "less than or equal to"<, "less than">, "greater than" ≥, "greater than or equal to"To find the solution of the inequality [tex]0>\:20x+2>\:-32[/tex] you must:
[tex]\mathrm{If}\:a>u>b\:\mathrm{then}\:a>u\quad \mathrm{and}\quad \:u>b\\\\0>20x+2\quad \mathrm{and}\quad \:20x+2>-32[/tex]
First, solve [tex]0>20x+2[/tex]
[tex]\mathrm{Switch\:sides}\\\\20x+2<0\\\\\mathrm{Subtract\:}2\mathrm{\:from\:both\:sides}\\\\20x+2-2<0-2\\\\\mathrm{Simplify}\\\\20x<-2\\\\\mathrm{Divide\:both\:sides\:by\:}20\\\\\frac{20x}{20}<\frac{-2}{20}\\\\\mathrm{Simplify}\\\\x<-\frac{1}{10}[/tex]
Next, solve [tex]20x+2>-32[/tex]
[tex]20x+2-2>-32-2\\\\20x>-34\\\\\frac{20x}{20}>\frac{-34}{20}\\\\x>-\frac{17}{10}[/tex]
Finally, combine the intervals
[tex]x<-\frac{1}{10}\quad \mathrm{and}\quad \:x>-\frac{17}{10}\\\\-\frac{17}{10}<x<-\frac{1}{10}[/tex]
The interval notation is [tex]\:\left(-\frac{17}{10},\:-\frac{1}{10}\right)[/tex] and the graph is:
Can anybody please help me with this one??
Answer:
[tex]the \: answer \: is \: d.(x + 4) {}^{2} = 8(y + 4)[/tex]
