just to clarify some part of the notation
\(a_n=-\cfrac{3}{4}a_{n-1}\) this is simply saying that whatever "nth" term you wish to get, is -3/4 times whatever is before it, so another wording for that will be, the next term is the current term times -3/4, so in short -3/4 is the common ratio.
\(\qquad \qquad \textit{sum of a finite geometric sequence} \\\\ \displaystyle S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad \begin{cases} n=\textit{last term's}\\ \qquad position\\ a_1=\textit{first term}\\ r=\textit{common ratio}\\[-0.5em] \hrulefill\\ a_1=64\\ n=4\\ r=-\frac{3}{4} \end{cases}\)
\(S_4=64\left( \cfrac{1-\left( -\frac{3}{4} \right)^4}{1-\left( -\frac{3}{4} \right)} \right)\implies S_4=64\left( \cfrac{~~ \frac{ 175 }{ 256 } ~~}{\frac{7}{4}} \right) \\\\\\ S_4=64\left( \cfrac{25}{64} \right)\implies S_4=25\)
No need to explain. check picture.
Answer: What you chose was correct :>
Four pieces of rope of unknown (but equal) length and 10 more feet of rope are attached together. The resulting rope is 30 feet long.
How long is each of the pieces of rope that is not 10 feet?
Answer:
5 feet each
Step-by-step explanation:
So we know that 4 pieces of rope out of 5 are equal. So, we simply subtract 10 from 30 for that 10-foot piece of rope, which leaves us with 20. Divide 20 by 4 (since there is 4 pieces of rope of equal value) and it leaves us with 5 feet.
Hope I helped! :)
what annual medical costs will ronald pay using the sample medical expenses provided if he enrolls in the blue cross/blue shield plan?
Annual Medical cost = 1269.86
monthly premium cost to Ronald for the Blue Shield plan = $48.48.
For all doctor office visits, prescriptions, and major medical charges, Ronald will be responsible for 35 percent and the insurance company will cover 65 percent of covered charges.
The annual deductible cost = $630.
Ronald decided to review his medical bills from the previous year to see what costs he had incurred and to help him evaluate his choices. He visited his general physician 6 times during the year at a cost = $105 for each visit.
He also spent $71 and $95 on two prescriptions during the year.
= (Monthly premium cost × 12) + Deductible cost + (Coinsurance percent × Coinsurance expenses)
= (48.48 x 12) + 630 + (0.35 x 166)
= 1269.86
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Consider a hypothesis test of difference of means for two independent populations x1 and x2.(a) What does the null hypothesis say about the relationship between the two population means?H0 says that the population means are different.H0 says that the population standard deviations are equal. H0 says that the population means are equal.H0 says that the population standard deviations are different.
H0 says that the population means are equal.
In the context of a hypothesis test for the difference of means between two independent populations (x1 and x2), the null hypothesis (H0) states the following about the relationship between the two population means:
H0 says that the population means are equal.
In other words, the null hypothesis assumes that there is no significant difference between the means of the two populations. The alternative hypothesis would then state that the population means are different. Remember that hypothesis testing is a process to determine whether there is enough evidence to reject the null hypothesis in favor of the alternative hypothesis.
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A design for a library has a scale of 1/3in=1 foot. The height of the library in the drawing is 12 inches.What is the actual height of the library
The actual height of the library is 36 feet.
Given a scale of 1/3 inch = 1 foot
therefore, 1 inch = 3 feet
then, 12 inches = 12 × 3
36 inches.
therefore the actual height of the library is:
12 × 36
= 432 inches
= 36 feet.
It is obvious which dimension is intended when a rectangle is drawn with both horizontal and vertical sides when the term height is used; height designates how high (or how tall) the rectangle is. As a result, using the word width to describe the other dimension—the width of the rectangle from side to side—is simple. As long as there is no ambiguity, it is also appropriate to refer to the side-to-side measurement as the rectangle's length if it is bigger than its height.
hence we get the height of the library as 36 feet.
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What is the simplified expression for the expression below? –1(2x + 3) – 2(x – 1)
Answer:
-4x - 1.
Step-by-step explanation:
-1(2x + 3) - 2(x - 1)
= -2x - 3 - 2x + 2
= -4x - 1.
Answer:
-4x -1
Step-by-step explanation:
-2x -3 -2x + 2
hi can someone pls help me, it’s confusing
Answer:
options C -x^2/3z
Step-by-step explanation:
this is the correct answer after we cancelled them
Answer:
C
Step-by-step explanation:
This requires you to know the law of quotient for exponents. For this I recommend separating everything with the same variable into its own fraction to make it easier so you have (-2x^4/6x^2), (y^2/y^2), (z/z^2). Then to simplify you divide the coefficients and signs like normal but for the exponents, you subtract the exponent of the numerator from the denominator. This gives
(-x^2 / 3), (1), and ( 1/z), which you can multiple together to get c.
Hope this helps. Ask if you need me to clarify something.
Use Micpoint and Supe Romuls to complete the tables below
1 Find the micpoint of given the coordinates R(58) and P (86)
m:
Midpoint
#1
Answer:
1) Midpoint: (4,7) and slope: 1
2) Midpoint: (5,3/2) and slope: 9/2
3) Midpoint: (9/2,1) and slope: 0
Step-by-step explanation:
1) R = (5,8) and P = (3,6)
Midpoint: (5+3)/2 = 4 and (8+6)/2 = 7
= (4,7)
Slope: (8-6)(5-3) = 2/2 = 1
2) M=(6,6) and N=(4,-3)
Midpoint: (6+4)/2 and (6 + - 3)/2
= (5,3/2)
Slope: (-3-6)/(4-6)
= -9/-2 = 9/2
3) A=(5,1) and M=(4,1)
Midpoint: (5+4)/2 and (1+1)/2
= (9/2, 1)
Slope: (1-1)/(5-4)
= 0/1
the perimeter of square $abcd$ is 2. two cars start from $a$ and $b$ simultaneously and drive clockwise on the perimeter of square $abcd$ in the same speed. a drone maintains its location as the midpoint of the two cars. how far did the drone fly after both cars get back to where they started?
The drone has flown a total distance of 4 units, as it has travelled the same distance as the two cars (2 units each).
What is perimeter?Perimeter is the total length of a two-dimensional shape's boundary. It is the sum of all the sides of a shape. Perimeter is used in many areas such as geometry, architecture, landscaping, and more. Perimeter is a measure of the distance around a shape and is often used to measure the size of a space or area.
As the cars have completed a full circuit of the square $abcd$, the drone has also completed a full circuit of the square. The perimeter of the square is 2, so the drone has flown a total distance of 4 units.
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The drone has flown a total distance of 4 units, as it has travelled the same distance as the two cars (2 units each). This can be solved by applying the concept of perimeter.
What is perimeter?Perimeter is the total length of a two-dimensional shape's boundary. It is the sum of all the sides of a shape. Perimeter is used in many areas such as geometry, architecture, landscaping, and more. Perimeter is a measure of the distance around a shape and is often used to measure the size of a space or area.
As the cars have completed a full circuit of the square abcd, the drone has also completed a full circuit of the square. The perimeter of the square is 2, so the drone has flown a total distance of 4 units.
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You are a rising star in the music industry, and you have just received word that you will be rewarded a $500,000 bonus this year. As your chauffer drives you home in the company's limousine, you call your accountant, who suggests investing your bonus in a high-yield account offering 12% continuous interest. A friend, however wants you to invest your bonus in their restaurant business, and has promised 12% interest, compounded quarterly. You want to compare both accounts before making a decision, you can crunch the numbers and find out: • How long will it take to earn an extra $100,000? • When will the account have $750,000? • How long will it take to double my money? • How long will it take to triple my investment
It will take 5.78 years to earn an extra $100,000 regardless of which option you choose. if we double the amount then it will take approx 10 year.
The high-yield account with continuous compounding interest is a safer investment since it won't be at risk of losing money in a business venture.
Since High-yield account offering 12% continuous interest.
\(A = Pe^{rt}\)
Where A is the final amount, P is the principal amount, r is the annual interest rate, t is the time in years, and e is Euler's number, approximately equal to 2.71828.
we can plug in the given values to find out how long it will take to earn an extra $100,000:
\((P + $500,000)e^{0.12t} - P = $100,000\)
t = ln[(P + $500,000 + $100,000)/P] / 0.12,
where P = $500,000
Substituting the values,
t = ln[(500,000 + 500,000 + 100,000)/500,000] / 0.12t
= ln(2.2)/0.12t = 5.78 years (approx.)
Now we can plug in the given values to find out how long it will take to earn an extra $100,000:
\((P + $500,000)(1 + 0.12/4)^{4t} - P = $100,000\)
t = [ln(P + $600,000) - ln(P)] / [4 ln(1.03)]
where P = $500,000
Substituting the values, we get:
t = [ln(1,100,000) - ln(500,000)] / [4 ln(1.03)]t = 5.78 years (approx.)
After comparing both investment options, it will take approximately 5.78 years to earn an extra $100,000 regardless of which option you choose. However, the high-yield account with continuous compounding interest is a safer investment since you won't be at risk of losing money in a business venture.
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"Suppose X --> N(20,5)
(a) Find: (i) P(X> 18)
(ii) P(7 < X < 15)
(b) Find the value a such that P(20-a < X < 20+ a) = 0.99
(c) Find the value b such that P(20-b< X < 20+ b) = 0.95
a) i)P(X > 18)= 0.65542
ii)P(7 < X < 15)=0.154
b)The value of a using the standard normal table or a calculator is 12.875
c)the value of b using the standard normal table or a calculator is 9.8
a) Let X be the normal random variable with mean μ = 20 and standard deviation σ = 5. We have to find P(X > 18) and P(7 < X < 15).
(i) P(X > 18)
This can be calculated using the standard normal table or a calculator as follows:
z = (18 - μ)/σ
= (18 - 20)/5
= -0.4
P(X > 18) = P(Z > -0.4)
= 1 - P(Z ≤ -0.4).
Using the standard normal table or a calculator, P(Z ≤ -0.4) = 0.34458
Therefore, P(X > 18) = 1 - 0.34458 = 0.65542
(ii) P(7 < X < 15). This can be calculated using the standard normal table or a calculator as follows:
z₁ = (7 - μ)/σ
(7 - 20)/5 = -2.6z₂
(15 - μ)/σ = (15 - 20)/5
= -1
P(7 < X < 15) = P(-2.6 < Z < -1)
= P(Z < -1) - P(Z < -2.6)
Using the standard normal table or a calculator,
P(Z < -1) = 0.15866P(Z < -2.6) = 0.00466
Therefore, P(7 < X < 15) = 0.15866 - 0.00466 = 0.154
b) We have to find the value of a such that
P(20 - a < X < 20 + a) = 0.99.
This can be calculated as follows:
z₁ = (20 - a - μ)/σ
= (20 - a - 20)/5
= -a/5z₂ = (20 + a - μ)/σ
= (20 + a - 20)/5 = a/5
We need to find a such that
P(z₁ < Z < z₂) = 0.99
Using the standard normal table or a calculator,
P(Z < z₂) - P(Z < z₁) = 0.99P(Z < a/5) - P(Z < -a/5) = 0.99
This can be rewritten as
P(Z < a/5) - [1 - P(Z < a/5)] = 0.99P(Z < a/5) - P(Z < -a/5) = 0.995
From the standard normal table or a calculator,
P(Z < 2.575) = 0.995P(Z < -2.575) = 0.005
Therefore,
2.575 = a/5 or -2.575 = -a/5a = 12.875
Therefore, the value of a is 12.875.
c) We have to find the value of b such that P(20 - b < X < 20 + b) = 0.95.
This can be calculated as follows:
z₁ = (20 - b - μ)/σ
= (20 - b - 20)/5
= -b/5z₂
= (20 + b - μ)/σ
= (20 + b - 20)/5 = b/5
We need to find b such that
P(z₁ < Z < z₂) = 0.95
Using the standard normal table or a calculator,
P(Z < z₂) - P(Z < z₁) = 0.95P(Z < b/5) - P(Z < -b/5) = 0.95
This can be rewritten as
P(Z < b/5) - [1 - P(Z < b/5)] = 0.95P(Z < b/5) - P(Z < -b/5) = 0.975
From the standard normal table or a calculator,
P(Z < 1.96) = 0.975P(Z < -1.96) = 0.025
Therefore,1.96 = b/5 or -1.96 = -b/5b = 9.8
Therefore, the value of b is 9.8.
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Which of the type directions lie in the (110) plane? [101] [110] [o īl] (110
The type directions that lie in the (110) plane are Crystal planes are equivalent planes that represent a group of crystal planes with a common set of atomic indexes.
Crystallographers use Miller indices to identify crystallographic planes. A crystal is a three-dimensional structure with a repeating pattern of atoms or ions.In a crystal, planes of atoms, ions, or molecules are stacked in a consistent, repeating pattern. Miller indices are a mathematical way of representing these crystal planes.
Miller indices are the inverses of the fractional intercepts of a crystal plane on the three axes of a Cartesian coordinate system.Let us now determine which of the type directions lie in the (110) plane.[101] is not in the (110) plane because it has an x-intercept of 1, a y-intercept of 0, and a z-intercept of 1. So, this direction does not lie in the (110) plane.[110] is in the (110) plane since it has an x-intercept of 1, a y-intercept of 1, and a z-intercept of 0.
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What is the slope-intercept form of the line represented in the table shown?
X Y
-2 14
-1 12
0 10
1 8
2 6
3 4
Step 1: Find the y-intercept:
Step 2: Choose any two points from the table to find the slope:
Step 3: Use the newly-found slope to write the slope-intercept equation. The form
for that is y = mx + b.
Step 4: Check your work. Choose an ordered pair from the table and substitute
into the newly-found equation
Answer: The slope-intercept form is y = -2x + 10
Step-by-step explanation:
Step 1: The y-intercept is the point where x=0, so that is (0,10)
Step 2: Use the points (-2,14) and (-1,12) to find the slope
Slope (m) = ΔY/ΔX = -2/1 = -2
Step 3: The slope-intercept form is:
y = mx+b
y = (step 2 value) x + (step 1 value)
y = -2x+10
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What must be true of x/y÷3a/b=3a/b? Assume a does not equal 0, b does not equal 0 and y does not equal 0
For the linear equation (x/y) ÷ (3a/b) = 3a/b to be true, x must equal 9a² × y/b² if a does not equal 0, b does not equal 0 and y does not equal 0.
To determine what must be true of x/y ÷ 3a/b = 3a/b, we can follow the order of operations, which is to perform the division before the multiplication.
First, we can simplify the left side of the equation by dividing x/y by 3a/b, which is equivalent to multiplying x/y by b/3a.
This gives us x / (y × (3a/b)) = 3a/b.
We can simplify further by multiplying both sides of the equation by y*(3a/b), which eliminates the denominators.
This gives us x = 3a × (y/b) × (3a/b).
Simplifying further, we get x = 9a² × y/b².
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-7,5 + 4,2 =?
-0,9 * 2,7 =?
\(-7,5 + 4,2 = -3.3\)
\(-0,9 \cdot 2,7 = -2.43\)
Which expression is represented by the model?O 4X-3O 4x+30 -4X-30 -4x+3
There are four x and 3 negative signs, it implies the answer is option A, 4x - 3
______are set of repeated activitieswhich have well defined results
Answer:
statistical experiments performed on a well defined sample space
Step-by-step explanation:
experiments can be performed either by probability, or other repetitive actions on sample space for possible outcomes.
A clinical trial was conducted to test the effectiveness of the drug zopiclone for treating insomrua in older subjects. Before treatment with zopiclone, 16 subjects had a mean wake time of 102.8 min. After treatment with zopiclone, the 16 subjects had a mean wake time of 98.9 min and a standard deviation of 42.3 min (based on data from "Cognitive Behavioral Therapy vs Zopiclone for Treatment of Chronic Primary Insomrua in Older Adults," by Sivertsen et al., Journal of the American Medical Association, Vol. 295, No. 24). Assume that the 16 sample values appear to be from a normally distributed population, and test the claim that after treatment with zopiclone, subjects have a mean wake time of less than 102.8 min. Does zopiclone appear to be effective?
A 98% confidence interval estimate of the mean wake time for a population with zopiclone treatments is 74.26 to 125.54.
What is a confidence interval?
A confidence interval (CI) is a range of values that, with a particular level of certainty, is likely to encompass a population value. A population mean that sits between an upper and lower interval is frequently stated as a percentage.
Here,
From the standard normal table, the z-critical value at 98% confidence interval is 2.33 so,
98%C.I. = µ ± z * σ / n = 98.90 ± 2.33 * 42.30 / sqrt of 16 = 98.90 ± 24.64 = 74.26 to 125.54
The mean wake time of 102.80 minutes before the treatment due to the mean wake time of 102.80 minutes included in the 98% confidence interval which is between 74.26 and 125.54. Zopiclone does not appear effective.
Hence, A 98% confidence interval estimate of the mean wake time for a population with zopiclone treatments is 74.26 to 125.54.
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Given T(x, y)=(x+2, y+5), state the translation S(x, y) that would yield the identity transformation, I=S(T(x,y)).
Answer:
The translation S(x, y) for the identity transformation, I = ST(x, y) is S(x, y) = ( x - 2, y + 5)
Step-by-step explanation:
Identity transformation is the transformation that results in the copying of the source data to the destination data without change.
Given that T(x, y) = (x + 2, y + 5)
The identity transformation I = S(T(x, y)) that would allow a data (x, y) to remain the same at the destination after the transformation T(x, y) is given as follows;
Where S(x, y) = ( x - 2, y + 5), we have;
S(T(x, y)) = S(x + 2, y + 5) = (x + 2 - 2, y + 5 - 5) = (x, y)
Therefore the translation S(x, y) that would yield the identity transformation, I = ST(x, y) is S(x, y) = ( x - 2, y + 5).
4(3n-2)=show your work
Answer:
(2 n)/3-2/3 = n/6+4/3
(2 n)/3-2/3 = (2 n-2)/3:
(2 n-2)/3 = n/6+4/3
Put each term in n/6+4/3 over the common denominator 6: n/6+4/3 = n/6+8/6:
(2 n-2)/3 = n/6+8/6
n/6+8/6 = (n+8)/6:
(2 n-2)/3 = (n+8)/6
Multiply both sides by 6:
(6 (2 n-2))/3 = (6 (n+8))/6
6/3 = (3×2)/3 = 2:
2 (2 n-2) = (6 (n+8))/6
(6 (n+8))/6 = 6/6×(n+8) = n+8:
2 (2 n-2) = n+8
Expand out terms of the left hand side:
4 n-4 = n+8
Subtract n from both sides:
(4 n-n)-4 = (n-n)+8
4 n-n = 3 n:
3 n-4 = (n-n)+8
n-n = 0:
3 n-4 = 8
Add 4 to both sides:
3 n+(4-4) = 8+4
4-4 = 0:
3 n = 8+4
8+4 = 12:
3 n = 12
Divide both sides of 3 n = 12 by 3:
(3 n)/3 = 12/3
3/3 = 1:
n = 12/3
The gcd of 12 and 3 is 3, so 12/3 = (3×4)/(3×1) = 3/3×4 = 4:
Answer: | n = 4
Step-by-step explanation:
Jeff has 10 packages that he wants to mail. 9 identical packages weigh 2 7/8
pounds each. A tenth package weighs two times as much as one of the other packages. How many pounds do all ten packages weigh?
does anyone know hot to find the area?
help me please if you are good at 8th-grade math I need help!!!!!!!
Answer:
A. slope is 7 3 is y itercept B. -2 slope 1 y intercept
Jenna traveled to Mexico. Before returning home, she converted all her pesos back into dollars. How much did she receive if she exchanged 1047.5 pesos at a rate of 5 dollars = 115.21 pesos?
Answer:
Dollars= $45.46
Step-by-step explanation:
Giving the following information:
Pesos= 1,047.5
Exchange rate:
5 dollars= 115.21
First, we need to determine the exchange rate for 1 dollar:
1 dollar= 115.21/5
1 dollar= 23.042 pesos
Now, for 1,047.5 pesos:
Dollars= total pesos / exchange rate
Dollars= 1,047.5/23.042
Dollars= $45.46
Answer:
45.46 dollars
Step-by-step explanation:
when a person's test performance can be compared with that of a representative and pretested sample of people, the test is said to be group of answer choices reliable. standardized. valid. normally distributed.
When a person's test performance can be compared with that of a representative and pretested sample of people, the test is said to be standardized.
Standardization refers to the process of establishing norms or standards for a test by administering it to a representative and pretested sample of individuals. This allows for a comparison of an individual's test performance to that of the larger group. When a test is standardized, it means that it has undergone rigorous development and validation procedures to ensure that it is fair, consistent, and reliable.
Standardized tests provide a benchmark for evaluating an individual's performance by comparing their scores to those of the norm group. The norm group consists of individuals who have already taken the test and represents the population for which the test is intended. By comparing an individual's scores to the norm group, it is possible to determine how their performance ranks relative to others.
Therefore, when a person's test performance can be compared with that of a representative and pretested sample of people, it indicates that the test is standardized. Standardization is an essential characteristic of reliable and valid tests, as it ensures consistency and allows for meaningful comparisons among test-takers.
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1. Find the area of the parallelogram. (1 point)
67 ft
60 ft
52ft
A 3,302 ft 2
B 3,484 ft 2
C 3,752 ft 2
D 4,020 ft 2
Solve the inequality. And show work please
5
-- y = 12
6
Answer:
y= \(\frac{72}{5}\) or 14.4
Step-by-step explanation:
\(\frac{5}{6}y = 12\\\)
Multiply both sides by 6/5, the reciprocal of 5/6.
\(y = 12 * (\frac{6}{5} )\)
Express 12 x (6/5) as a single fraction.
\(y = \frac{12 * 6}{5}\)
Multiply 12 and 6 to get 72.
\(y = \frac{72}{5}\)
Simplify the following radical expression by rationalizing the denominator. (-6)/(\sqrt(5y))
The simplified radical expression by rationalizing the denominator is, \(\frac{-6}{\sqrt{5y}}\times\frac{\sqrt{5y}}{\sqrt{5y}}\) = \(\frac{-6\sqrt{5y}}{5y}$$\) = $\frac{-6\sqrt{5y}}{5y}$.
To simplify the radical expression by rationalizing the denominator, multiply both numerator and denominator by the conjugate of the denominator.
The given radical expression is \($\frac{-6}{\sqrt{5y}}$\).
Rationalizing the denominator
To rationalize the denominator, we multiply both the numerator and denominator by the conjugate of the denominator, \($\sqrt{5y}$\)
Note that multiplying the conjugate of the denominator is like squaring a binomial:
This simplifies to:
(-6√(5y))/(√(5y) * √(5y))
The denominator simplifies to:
√(5y) * √(5y) = √(5y)^2 = 5y
So, the expression becomes:
(-6√(5y))/(5y)
Therefore, the simplified expression, after rationalizing the denominator, is (-6√(5y))/(5y).
\($(a-b)(a+b)=a^2-b^2$\)
This is what we will do to rationalize the denominator in this problem.
We will multiply the numerator and denominator by the conjugate of the denominator, which is \($\sqrt{5y}$\).
Multiplying both the numerator and denominator by \($\sqrt{5y}$\), we get \(\frac{-6}{\sqrt{5y}}\times\frac{\sqrt{5y}}{\sqrt{5y}}\) = \(\frac{-6\sqrt{5y}}{5y}$$\)
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simplify -4 1/4 - (-9 1/2)
Answer:
the answer is 5 1/4
Answer: it’s d
Step-by-step explanation:
evaluate 0.67y + 4 when y = 2 and when y = -2
Answer:
2.66 and 4.34
Step-by-step explanation:
To evaluate, substitute the values of y and solve.
So, when y =-2
0.67y + 4 = -1.34 + 4 = 2.66
And when y = 2
0.67y + 4 = 1.34 + 4 = 4.34
Hope this helps.
Answer:
y = 2
5.34
y = -2
- 2.66
Step-by-step explanation:
0.67y + 4
y = 2
.67(2)+2
1.34+4 = 5.34
y = -2
-.67(2)+2
-1.34+4 = 2.66