Answer:
x could be 3 or 1
Step-by-step explanation:
x²+3=4x
x²-4x+3=0
(x-3)(x-1)
x could be 3 or 1
The values could be 1 or 3.
Let the number be n.In this exercise, you're required to write a mathematical (algebraic) expression for the given word problem and determine which values could be the unknown number.
Translating the word problem into an algebraic expression, we have;
[tex]n^{2} = 4n - 3\\\\n^{2} - 4n + 3 = 0[/tex]
We would solve the quadratic equation by using the factorization method;
[tex]n^{2} - 3n -n + 3 = 0\\\\n(n - 3) - 1(n - 3) = 0\\\\(n - 1)(n - 3) = 0[/tex]
Therefore, the values could be 1 or 3.
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An initial deposit of $10000 is left in account for 5.5 years at 3.6% interest compounded continuously. What is the
final value of the account to the nearest dollar after the 5.5 years?
Answer:
11980
Step-by-step explanation:
This is simple interest.
We use the formula i=prt. Interest = price x rate x time
You just plug in your numbers, 10000 is your price, 5.5 years is the time, and 3.6% interest is rate.
Now our equation looks like this: i = 10000 x 5.5 x 0.036
(i converted the percent to a decimal)
So the interest is 1980, but the question asks for the final value, so we add the interest to the initial deposit, 1980 + 10000, and we get 11980 for our final value.
I apologize if my answer is wrong, but if it isn't I hope I helped :)
9514 1404 393
Answer:
$12,190
Step-by-step explanation:
The formula for the balance in an account where continuous compounding occurs is ...
A = Pe^(rt) . . . . where P is the principal invested at annual rate r for t years
A = $10,000e^(0.036·5.5) = $10,000e^0.198
A ≈ $12189.62 ≈ $12,190 . . . . rounded to the nearest dollar
Which expression is equivalent to: 16x - 16
4(2x - 2)
4(4x - 16)
4(4x - 4)
Answer:
4(4x-16)
Step-by-step explanation:
If you like my answer than please mark me as brainliest
Is {(4,2),(4,-2),(9,3),(9,-3)} a function
Answer:
no
Step-by-step explanation:
If any x-value is repeated, the relation is not a function. Both x=4 and x=9 are repeated values, so this relation is not a function.
HELP PLZ A circle inscribed in a triangle:
Answer:
The answer is the second photo.
Step-by-step explanation:
It's literally a circle in a triangle. So, it's the second one.
Solve this inequality: 14 <-7x
Answer:
-2 > x
Step-by-step explanation:
14 <-7x
Divide each side by -7, remembering to flip the inequality
14/ -7 > -7x/-7
-2 > x
On dividing polynomial p(x) by a linear binomial, X - a, we get a quotien
statements must be proven true for the remainder theorem to be true
Answer:
Step-by-step explanation:
Hello, we can write
(1) p(x)=(x-a)q(x)+r
[tex]\boxed{\sf v}[/tex] True
It means that p(a)=0 * q(a) + r = r
so the first one is true.
[tex]\boxed{}[/tex] False
The second one is not to be proven true from the remainder theorem.
[tex]\boxed{\sf v}[/tex] True
For x different from a we can divide the equation (1) by (x-a).
[tex]\boxed{}[/tex] False
We cannot say anything on q(a).
[tex]\boxed{\sf v}[/tex] True
If the rest is 0 then it means that p(a) = 0
[tex]\boxed{\sf v}[/tex] True
If p(a) = 0 it means that the rest r = 0 and then p(x)=q(x)(x-a)
Thank you
An equation for the depreciation of a car is given by y=A(1-r)t where y=current value of the car.A=original cost r=rate of depreciation and t=time in years. The value of a car is half what it originally cost. The rate of depreciation is 10%. Approximately how old is the car?
The more accurate value is 6.57881347896059, which you can round however you need. I picked two decimal places.
==================================================
Explanation:
Let's pick a starting value of the car. It doesn't matter what the starting value, but it might help make the problem easier. Let's say A = 1000. Half of that is 1000/2 = 500.
So we want to find out how long it takes for the car's value to go from $1000 to $500 if it depreciates 10% per year.
The value of r is r = 0.10 as its the decimal form of 10%
t is the unknown number of years we want to solve for
---------------------------
y = A(1 - r)^t
500 = 1000(1 - 0.1)^t
500 = 1000(0.9)^t
1000(0.9)^t = 500
0.9^t = 500/1000
0.9^t = 0.5
log( 0.9^t ) = log( 0.5 )
t*log( 0.9 ) = log( 0.5 )
t = log( 0.5 )/log( 0.9 )
t = 6.57881347896059
Note the use of logs to help us isolate the exponent.
The mean salary of federal government employees on the General Schedule is $59,593. The average salary of 30 state employees who do similar work is $58,800 with \sigmaσσ= $1500. At the 0.01 level of significance, can it be concluded that state employees earn on average less than federal employees? What is the critical value? Round your answer to the nearest hundredths.
Answer:
Yes it can be concluded that state employees earn on average less than federal employees
The critical value is [tex]Z_{\alpha } = - 2.33[/tex]
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = \$ 59593[/tex]
The sample size is n = 30
The sample mean is [tex]\= x = \$ 58800[/tex]
The standard deviation is [tex]\sigma = \$ 1500[/tex]
The significance level is [tex]\alpha = 0.01[/tex]
The null hypothesis is [tex]H_o : \mu = \$ 59593[/tex]
The alternative hypothesis is [tex]H_a : \mu < \$ 59593[/tex]
The critical value of [tex]\alpha[/tex] from the normal distribution table is [tex]Z_{\alpha } = - 2.33[/tex]
Generally the test statistics is mathematically evaluated as
[tex]t = \frac{\= x - \mu}{ \frac{ \sigma }{ \sqrt{n} } }[/tex]
=> [tex]t = \frac{ 58800 - 59593 }{ \frac{ 1500 }{ \sqrt{30} } }[/tex]
=> [tex]t = -2.896[/tex]
The p-value is obtained from the z-table
[tex]p-value = P(t < -2.896) = 0.0018898[/tex]
Since [tex]p-value < \alpha[/tex] , we reject the null hypothesis, hence it can be concluded that state employees earn on average less than federal employees
Help me please…………………….
Answer:
8.7
Step-by-step explanation:
If you like my answer mark me brainliest
The expression −50x+100 represents the balance, in dollars, of a bank account after x months. What is the rate of change, in dollars per month, of the bank account balance?
Answer:
-50
Step-by-step explanation:
Basically get two slopes -50(1)+100 will get you 1,50 (1 is x and 50 is y since its the answer)
-50(0)+100 (0,100) Y₂-Y₁/X₂-X₁ 50-100/1-0
Rate of change per month = -$50
Find the next term of the sequence.
16, 9, 2, -5,
Answer: The next term is -12.
Step-by-step explanation:
16,9,2,-5
Looking at these numbers to go from 16 to 9 you will add -7 or subtract 7 . The same way you subtract 7 from 9 to get 2 and subtract 7 from 2 to get -5.
So to determine the next term subtract 7 from -7 or add -7.
-5 - 7 = -12
0r -5 + -7 = -12
[tex] 👋 [/tex] Hello ! ☺️
Step-by-step explanation:
•Find the next term of the sequence.
Let us find the interval between two successive terms:
16 - 9= 7
-7 is therefore the common différence of this sequence. (d)
Find the next term :
-5 + (-7)= -12
[tex]\boxed{\color{gold}{N = -12}} [/tex]
[tex]<marquee direction="left" scrollamount="2" height="100" width="150">💘Mynea04</marquee>[/tex]
Is Statistics mathematics or science? Defend your answer.
Answer:
Statistics is a mathematical science pertaining to the collection, analysis, interpretation or explanation, and presentation of data. It is applicable to a wide variety of academic disciplines, from the physical and social sciences to the humanities.
Statistics is maths.
Why:-
Statistics is related to maths because we study, use and even consider statistic problems with reference to mathematics.
• It is mostly used to find the census, which is maths.
• It is used to find interest rates and other banking terms using statistics, which is again related to math.
• It is also used to find the average people living in a village or panchayat, which is also math.
Therefore I strongly believe that Statistics is Maths.
Thank You!
what is the area of rectangle
Answer:
Step-by-step explanation:
complete the equation describing how x and y are related.
Answer:
y=-2x+1
Step-by-step explanation:
The slope of the line is (y(2)-y(1))/(2-1)=(-3+1)/1=-2. The equation of the line is y=mx+(y intercept), y=-2x+1
The complete equation describes how x and y are related y=-2x+1.
We have given, the equation,
We have to determine the complete equation describing how x and y are related.
What is the formula for the slope?
The slope of the line is(m)=y2-y1/x2-x1
Where m is the slope,
Therefore we get,
(y(2)-y(1))/(2-1)
=(-3+1)/1
=-2.
The equation of the line is y=mx+(y-intercept), y=-2x+1.
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Is 100 a good estimate for the difference of 712 and 589? If it is, explain why it is a good estimate. If it is not, explain why it is a bad estimate.
Answer is D , others say it’s 64 but I got it wrong
Answer:
Oh no I am sorry! If you want answers to be done the real way let me know
Answer:I'm so sorry for you but congrats you did get the answer right it's just the test I guess
Step-by-step explanation:
22. f(x) is stretched horizontally by a factor of 2 and reflected across the x-axis. Which choice shows the correct representation of f(x) after these transformations?
Options:
A. –f(1/2x)
B. f(–2x)
C. –f(2x)
D. f(–1/2x)
Answer:
A. -f(1/2 x)
Step-by-step explanation:
Reflextion about the x-axis is
f(x) -> -f(x)
and horizontal dilation is
f(x) -> f(-x/b) where b is the factor of dilation.
so the proper answwer is
A. -f(1/2 x)
9x-5
14x+24
A
Determine the value of x.
1) x= -5.8
2) x= -7
3) x= 7
4) x= 32.2
Answer:
the answer to the question
is x=-5.8
If 5x + 2 =12x- 5, then x = ?
Answer:
x = 1
Step-by-step explanation:
First, move all the variables to one side by subtracting 5x on both sides:
5x + 2 = 12x - 5
2 = 7x - 5
Add 5 to both sides:
7 = 7x
1 = x
Answer:
x=1
Step-by-step explanation:
5x + 2 =12x- 5
Subtract 5x from each side
5x-5x + 2 =12x-5x- 5
2 = 7x-5
Add 5 to each side
2+5 = 7x-5+5
7 = 7x
Divide each side by 7
7/7 = 7x/7
1 =x
A 3-gallon jug of water costs $15.00. What is the price per quart?
Answer:
1.25 dollars per quart
Step-by-step explanation:
There are 4 quarts per gallon
3 gallons * 4 quarts/ gallon = 12 quarts
15 dollars/ 12 quarts
1.25 dollars per quart
Is the following relation a function? (1 point) x y −1 −2 2 3 3 1 6 −2 No Yes
Answer:
Yes because no same x-value resulted in different y-values.
Answer:
Yes
Step-by-step explanation:
While you can use the correlation coefficient as its own test statistic, what is the other appropriate test statistic often used to examine the significance of a correlation
Answer:
T-test
Step-by-step explanation:
Significance of correlation between two variables x and y measures the strength and direction of their relationship. This is used to make future forecasts of the behaviour of a variable under study.
Correlation coefficient can be used to measure significance of correlation, but we can also use the t-test.
T-test is a statistics that is inferential. It measures the significance of difference between the means of two groups.
T-test is the statistic of choice when carrying out hypothesis testing.
T distribution values and degrees of freedom are used to determine statistical significance.
For example the means of two samples can be compared to determine of the come from the same population
Factor quadratic plz 15x^2-4x-4=
Answer:
x = 2/3 or x = -2/5
Step-by-step explanation:
15x^2 - 4x - 4 = ?
factor the left side of the expression and set factors equal to zero:
(3x-2)(5x+2)=0
3x - 2 =0 or 5x + 2 =0
3x =2 or 5x = -2
x = 2/3 or x = -2/5
Helppppp thxxxxxxxxxx
Answer:
F. [tex] \frac{3}{2} [/tex]
Step-by-step explanation:
[tex] \frac{a + 2b}{b} = \frac{7}{2} [/tex]
Cross multiply:
7b= 2(a +2b)
Expand:
7b= 2a +4b
Bring all common variables to 1 side:
7b -4b= 2a
3b= 2a
divide by 2 on both sides:
[tex] \frac{3}{2} b = a[/tex]
divide by b on both sides:
[tex] \frac{3}{2} = \frac{a}{b} \\ \frac{a}{b} = \frac{3}{2} [/tex]
Combine like terms. What is a simpler form of each expression? 4c-4d+8c-3d
Answer:
12c-7d
Step-by-step explanation:
[tex]4c-4d+8c-3d=0\\4c+8c=3d+4d\\12c=7d\\12c-7d[/tex]
===============================================
Explanation:
The terms 4c and 8c are one pair of like terms that combine to 4c+8c = 12c. We add 4 and 8 to get 12, then tack a 'c' at the end
The other pair of like terms are -4d and -3d. They combine to -7d for similar reasoning.
12c and -7d are not like terms, so we can't combine them and we stop here.
-----------
One way to think of combining like terms is consider simplifying 2c+3c. You could say that 2c represents having 2 cups while 3c is having 3 cups. Writing 2c+3c means we start with 2 cups and add on 3 more getting a total of 2+3 = 5 cups. Symbolically we would then write 5c. Therefore 2c+3c = 5c.
The residents of a city voted on whether to raise property taxes. The ratio of yes votes to no votes was 6 to 5 . If there were 4545 no votes, what was the total number of votes?
Answer:
The total number of votes= 9999
Step-by-step explanation:
The ratio of vote specifically the ratio of yes to no vote in a city vote is 6 to 5.
There is a total of 4545 no votes.
Yes/no = 6/5
Yes= no(6/5)
Yes= 4545(6/5)
Yes= 5454
The total number of yes votes are 5454.
The total number of votes= yes votes+ no votes
The total number of votes= 5454+4545
The total number of votes= 9999
Find the value of x.
A. 3
B. 9
C. 0
D. 12
Answer:
x=3
Step-by-step explanation:
(segment piece) x (segment piece) = (segment piece) x (segment piece)
3x(x+1) = 4x(x)
Divide each side by x
3x(x+1)/x = 4x(x)/x
3(x+1) = 4x
Distribute
3x+3 = 4x
Subtract 3x
3x+3-3x= 4x-3x
3 =x
Answer:
x = 3
Step-by-step explanation:
0 is a rediculas answer 9 and 12 are to big.
The lines are supposed to have a simular length:
3(3) + 4 = 13
4(3) + 3 = 15
These are the best answers that fit.
A population of values has a normal distribution with μ= 106.9 and σ=14.5
You intend to draw a random sample of size n=20
What is the probability that a single randomly selected value is less than 109.8?
P(X < 109.8)
How do you the probability that a sample of size n= 20 is randomly selected with a mean less than 109.8?
P(M < 109.8)
Also, I have to round the answer to the 4th decimal place. How do I do that?
Step-by-step explanation:
Find the z-score.
z = (x − μ) / σ
z = (109.8 − 106.9) / 14.5
z = 0.2
Use a chart or calculator to find the probability.
P(Z < 0.2) = 0.5793
Find the mean and standard deviation of the sampling distribution.
μ = 106.9
σ = 14.5 / √20 = 3.242
Find the z-score.
z = (x − μ) / σ
z = (109.8 − 106.9) / 3.242
z = 0.894
Use a calculator to find the probability.
P(Z < 0.894) = 0.8145
Ugh I’m going insane trying to do this. Please help.
Answer:
y(x)=6^(x)-3
Step-by-step explanation:
Let the exponential function be y(x) = ab^(x) but since the graph is translated 3 units down, y(x) = ab^(x)-3. Now, y(0)=-2=a*b^(0)-3. a=1. The equation is nearly complete but we need b, we can find it by using the point y(1)=3. y(x)=b^(x) - 3. y(1)=3=b-3, b=6. The equation of the function is y(x)=6^(x)-3
Answer:
I agree with the first one
Laura is bowling 5 games. Her first 4 scores were 135, 144, 116, and 132.
To end up with an average score of at least 136.8, what is the lowest score Laura will need in the fifth game?
Answer:
it doesnt add up. the question doesnt make sense.
Step-by-step explanation:
Answer:
157
Step-by-step explanation:
To find the average score, add all individual scores and divide the sum by the number of individual scores.
She has 5 individual scores. Let's say her scores are A, B, C, D, and E.
average score = (A + B + C + D + E)/5
Now we plug in the average and the 4 known scores for A through D, and we solve for E.
average score = (A + B + C + D + E)/5
136.8 = (135 + 144 + 116 + 132 + E)/5
E = 157
Answer: 157