Answer:
see explanation
Step-by-step explanation:
(f - g)(x) = f(x) - g(x) , that is
f(x) - g(x)
= - 5x³ - 4x² + 8x - (- 4x² + 8) ← distribute parenthesis by - 1
= - 5x³ - 4x² + 8x + 4x² - 8 ← collect like terms
= - 5x³ + 8x - 8
Substitute x = - 2 into this expression, thus
(f - g)(- 2)
= - 5(- 2)³ + 8(- 2) - 8
= - 5(- 8) - 16 - 8
= 40 - 16 - 8
= 16
The graph of F(x), shown below, has the same shape as the graph of
G(x) = x, but it is shifted up 2 units. What is its equation?
Greetings from Brasil...
We know that the translations are established as follows:
→ Horizontal
F(X + k) ⇒ k units to the left
F(X - k) ⇒ k units to the right
→ Vertical
F(X) + k ⇒ k units up
F(X) - k ⇒ k units down
G(X) = X and F(X) is G(X) shifted up 2 units.
In the statement it is said that there was a translation of 2 units upwards, so
F(X) = G(X) + k where k = 2 units up
F(X) = X + 2Find the total area of all the shaded rectangles.
4
The total area of all the shaded rectangles is
(Simplify your answer. Type an expression using x as the variable
Answer:
25x^2 + 40x + 16
Step-by-step explanation:
area = 5x * 5x + 5x * 4 + 5x * 4 + 4 * 4
area = 25x^2 + 40x + 16
25x² + 40x + 16 is the required equation in variable x.
What is mensuration ?
Mensuration is a branch of mathematics where we calculate length, width, area, volume, lateral surface area, total surface area.
The sum of the areas of the shaded rectangles is the total area.
By observation we can see that the four shaded rectangles together form a square.
We all know that the area of the square is (side)²
= (5x + 4)²
= 25x² + 40x + 16 this is the required equation.
learn more about mensuration here :
https://brainly.com/question/23877107
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logx-log(x-l)^2=2log(x-1)
Answer:
x = 1.00995066776
x = 2.52925492433
Step-by-step explanation:
This sort of equation is best solved using a graphing calculator. For that purpose, I like to rewrite the equation as a function whose zeros we're seeking. Here, that becomes ...
[tex]f(x)=\log{(x)}-\log{(x-1)}^2-2\log{(x-1)}[/tex]
The attached graph shows zeros at
x = 1.00995066776 and 2.52925492433
_____
Comment on the equation
Note that we have taken the middle term to be the square of the log, rather than the log of a square. For the latter interpretation, see mberisso's answer at https://brainly.com/question/17210068
Comment on the answer refinement
We have used Newton's method iteration to refine the solutions to this equation. The solution near 1.00995 requires the initial guess be very close for that method to work properly. Fortunately, the 1.01 value shown on the graph is sufficient for the purpose.
A certain game involves tossing 3 fair coins, and it pays .14 for 3 heads, .06 for 2 heads, and .01 for 1 head. The expected winnings are?
Answer:
Total expected amount = $0.04375
Step-by-step explanation:
We need to calculate probability of getting heads on every combination of coin tosses
HHH = 1/8 = 3 heads
HHT = 1/8 = 2 heads
HTH = 1/8 = 2 heads
HTT = 1/8 = 1 head
THH = 1/8 = 2 heads
THT = 1/8 = 1 head
TTH = 1/8 = 1 head
TTT = 1/8 = 0 head
So the probability of 3 heads is 1/8 and the amount is (1/8)* 0.14 = $0.0175
Probability of 2 heads is 3/8 and the amount is (3/8) * 0.06 = $0.0225
Probability of 1 head is 3/8 and amount is (3/8) * 0.01 = $0.00375
Total expected amount = 0.00375 + 0.0225 + 0.0175
Total expected amount = $0.04375
confidence interavls for a population proportion. suppose that a random sample of 1000 mortgage loans that were defaulted within the first year reveals 410 of these loans were approved on hte basis of falsified applications. what is point estiamte of and a 95% confidence interval for p, the proportion of all first year defaults that are approved on the basis of flsified application
Answer:
The 95% confidence interval is [tex]0.3795 < p < 0.4405[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 1000[/tex]
The number of approved loan is k = 410
Generally the sample proportion is mathematically represented as
[tex]\r p = \frac{k}{n}[/tex]
substituting values
[tex]\r p = \frac{410}{1000}[/tex]
[tex]\r p = 0.41[/tex]
Given that the confidence level is 95% then the level of significance is mathematically represented as
[tex]\alpha = 100 - 95[/tex]
[tex]\alpha = 5\%[/tex]
[tex]\alpha = 0.05[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table,the value is
[tex]Z_{\frac{\alpha }{2} } =Z_{\frac{0.05 }{2} }= 1.96[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \sqrt{\frac{\r p(1- \r p)}{n} }[/tex]
substituting values
[tex]E = 1.96 * \sqrt{\frac{ 0.41(1- 0.41)}{1000} }[/tex]
[tex]E = 0.03048[/tex]
The 95% confidence interval for p is mathematically represented as
[tex]\r p - E < p < \r p + E[/tex]
substituting values
[tex]0.41 - 0.03048 < p < 0.41 + 0.03048[/tex]
[tex]0.3795 < p < 0.4405[/tex]
2. Write the equation of the circle in general form. Show your work.
Answer:
[tex] {(x + 1)}^{2} + {(y - 1)}^{2} = 9[/tex]
[tex] {x} ^{2} + {y} ^{2} + 2x - 2y - 7 = 0 [/tex]
If the sum of the daily unpaid balances is $7,812 over a 31-day billing cycle, what is the average daily balance?
Answer:
252
Step-by-step explanation:
Divide 7812 by 31 and we get the average daily answer... Hope this helps!!
Use the frequency distribution, which shows the number of American voters (in millions) according to age, to
find the probability that a voter chosen at random is in the 18 to 20 years old age range
Ages
18 to 20
21 to 24
25 to 34
35 to 44
45 to 64
65 and over
Frequency
4.2
7.8
20.8
23.7
50.1
28 2
Date
07/2
3:29
The probability that a voter chosen at random is in the 18 to 20 years old age range is 0.0311
(Round to three decimal places as needed.)
07/2
8:52
Question Viewer
07/1
8:03
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5:46
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07/1
12:2
07/1
5:39
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2:42
Question is complete. Tap on the red indicators to see incorrect answers.
07/1
12:00
Answer:
The probability that a voter chosen at random is in the 18 to 20 years old age range is = 4.2/ 134.8= 0.0311572
Step-by-step explanation:
We can find the probability by simply dividing the frequency of the ages range of 18-20 by the total frequency.
Ages Frequency
18 to 20 4.2
21 to 24 7.8
25 to 34 20.8
35 to 44 23.7
45 to 64 50.1
65 and over 28.2
∑ 134.8
The probability of an event is given by the occurrence of an event by the total occurrences .
So
Here the occurrence of ages 18-20 is given by 4.2
and the total frequency is 134.8
The probability that a voter chosen at random is in the 18 to 20 years old age range is = 4.2/ 134.8= 0.0311572
Find the measure of A.
A. 50
B. 70
C. 100
D. 90
Answer:
D
Step-by-step explanation:
I don't know how to eliminate the wrong answers.
Two line segments which have one end at a diameter and the other end meeting at a common point, make a 90 degree angle.
A is made that way, so A is 90 degrees.
Answer:
Step-by-step explanation:
I believe it is 90
Which phrase describes the algebraic expression 8f+7?
the product of 8 and 7 more than a number
the quotient of 8 and 7
8 times the sum of a number and 7
8 times a number plus 7
Answer:
8 times a number plus 7
Step-by-step explanation:
Let the number be f.
Simply, 8 f+7 is the expression.
Thank you!
The following is the number of minutes to commute from home to work for a group of 25 automobile executives. 35 36 39 43 37 35 34 30 36 34 30 39 37 40 38 33 31 28 39 35 35 36 41 24 36 How many classes would you recommend? What class interval would you suggest? (Round up your answer to the next whole number.) Organize the data and plot a frequency distribution on a piece of paper. Comment on the shape of the frequency distribution. It is not symmetric. It is fairly symmetric, with most of the values between 24 and 43. It is not very symmetric, but most of the values lie between 24 and 43.
Answer:
It is not symmetric, but skewed left. Data appears more to be on the left side.
Step-by-step explanation:
The smallest value is 24 and the largest is 43 . The difference between these two values is 19 which can be divided into into intervals of 4.
19/4= 4.75 It will be rounded to 5.
The class interval can of 5. Starting from 20 we get class intervals and frequency distribution as
Class Intervals Data Frequency
20-24 24 1
25- 29 28, 1
30-34 34,30,34,30,33,31, 6
35-39 35,36,39,37,35,36,39,37, 14
38,39,35,35,36,36
40-44 43,40,41 3
The class intervals are inclusive of both upper and lower limits. The difference between the lower limits of two consecutive classes or upper limits of two consecutive classes must be the same.
As we see the difference here is that of 5 between the two upper or lower limits of consecutive classes.
The histogram is attached which shows the class intervals along x- axis and data frequency along y- axis.
What is the 25th term in the following arithmetic sequence? -7, -2, 3, 8, ...
Answer:
108.
Step-by-step explanation:
-7, -2, 3, 8 is an arithmetic sequence with a1 (first term) = -7 and common difference (d) = 5.
The 24th term = a1 + (24 - 1)d
= -7 + 23 * 5
= -7 + 115
= 108.
Use the dot product to determine whether v and w are orthogonal.
v=-i-j, w=-i+j
Select the correct choice below and fill in the answer box to complete your choice.
O A. The vectors v and w are not orthogonal because their dot product is ___
O B. The vectors v and w are orthogonal because their dot product is ___
Answer:
B. The vectors v and w are orthogonal because their dot product is 0
Step-by-step explanation:
Given that :
v= - i - j
w= - i + j
Therefore;
vw = ( - i - j ) ( - i + j )
Taking each set of integer of the vector into consideration:
vw = ( -1 × - 1) ( -1 × 1)
vw = 1 - 1
vw = 0
Hence, we can conclude that :
The vectors v and w are orthogonal because their dot product is 0
Rational equation of 3/x+1=2/x-3
Answer:
x = 11
Step-by-step explanation:
3/x+1=2/x-3
Solve by using cross products
2 (x+1) = 3 (x-3)
Distribute
2x+2 = 3x-9
Subtract 2x
2x+2-2x = 3x-2x-9
2 = x-9
Add 9 to each side
2+9 =x-9+9
11 =c
(16 points) Find the radius of convergence and the interval of convergence of the power series. g
Answer:
The equation to be solved is missing in the question.
I will explain power series and ways to find the radius and interval of convergence of a powers series in the attached image.
Step-by-step explanation:
Understand the power seriesFind radius of convergenceDetermine interval of convergenceBilly has x marbles. Write an expression for the number of marbles the following have… a) Charlie has 5 more than Billy b) Danny has 8 fewer than Billy c) Eric has three times as many as Billy
Answer:
Charlie: 5 + xDanny: x - 8Eric: x × 3woman has 7 coworkers' man. How many different possible groups of four people could do the project, if one out of three is women? g
Answer: 24ways
Step-by-step explanation:
Given data:
No of men in the workplace = 7
No of women in the workplace = 1
How many ways can a group of 4 people carry out a project if on out of the 3 must be a woman.
Solution.
A group of 4 can carry out the project with one be a woman
This means there must be 3 males and 1 female in the group
= 4p3
= 24ways
The project can be carried out by 4 groups in 24 ways
Joey’s pizza sells large cheese pizzas for $12.00. Each additional topping costs $0.50. Basketball Boosters bought 12 large pizzas, each with 3 toppings. There are 8 slices per pizza. How much does it cost per slice? Round to the nearest cent.
Answer:
So first you do $0.50 x 3 = 1.5
then you add that to $12.00
$12.00 + 1.5 = 13.5
13.5 is the cost of one pizza.
Since they bought 12:
The total cost of the 12 pizza is $162 <== not important
13.5 divided by 8 is 1.687
round 1.56875 to the nearest cent 1.7 = $2
so each slice costs $2
Suppose that you borrow $1000.00 from a friend and promise to pay back $1390.00 in 2 years. What simple interest rate will you pay?
The simple interest rate is % (Round to the nearest tenth as needed.)
Answer:
19.5%
Step-by-step explanation:
Use the formula I = prt, where I is the interest money, p is the starting amount of money, r is the interest rate, and t is the time that the money was borrowed.
Plug in the values and solve for r:
390 = (1000)(r)(2)
390 = 2000r
0.195 = r
r = 19.5%
Answer:
19.5%
Step-by-step explanation:
Simple Interest = Principal x Time x Rate in % / 100
SI = 1000 x 2 x a / 100
=> SI = 10 x 2 x a
=> SI = 20a
Total Amount = SI + Principal
=> 1390 = 20a + 1000
=> 1390 - 1000 = 20a +1000 - 1000
=> 390 = 20a
=> 390/20 = 20a/20
=> 19.5 = a
Let's recheck
=> 1000 x 2 x 19.5 /100
=> 10 x 2 x 19.5
=> 195 x 2
=> 390
1390 = 390 + 1000
=> 1390 = 1390
So, the interest rate is 19.5 %
The sum of 8 times a number and 7 equals 9!
Answer:
0.25*8+7=9
Step-by-step explanation:
8x+7=9
2/8=x
0.25=x
Find the x-values (if any) at which f is not continuous. Which of the discontinuities are removable? (Enter your answers from smallest to largest. Enter NONE in any unused answer blanks.) f(x) = x + 3 x2 − 2x − 15
Answer:
-3 (removable), +5
Step-by-step explanation:
Maybe you have ...
[tex]f(x)=\dfrac{x+3}{x^2-2x-15}=\dfrac{x+3}{(x+3)(x-5)}=\dfrac{1}{x-5}\quad x\ne-3[/tex]
This will have discontinuities (points where the function is undefined) at ...
x = -3x = 5The discontinuity as x = -3 is removable by defining f(-3) = -1/8.
the grasshopper population in Georgia is currently 4,000. It's growing by 2.3% each year. Write an equation that models the situation.
Answer:
[tex]4000(1.023)^t\\\\[/tex]
Step-by-step explanation:
Using this exponential growth equation we can get an equation that models the situation.
A= Principal Amount
R= Rate of Growth
T= Amount of time
[tex]A=4000\\R=2.3/100=.023\\T= Non[/tex]
[tex]A(1+R)^t\\4000(1+0.23)^t\\4000(1.023)^t\\\\[/tex]
What is the volume of a rectangular prism with a length, width,
2
1
5
and height of
cm, -
cm, and
cm, respectively?
3
4
6
Step-by-step explanation:
Hey, there!!
It's so simple,
Given,
length (l)= 2/3cm
Breadth (b) = 1/4cm
and height (h)=5/6cm
now, we use the formula for volume of rectangular prism is,
v = l× b× h
or, v= (2/3 × 1/4 × 5/6)^3
By simplifying it we get,
The volume is 5/36cm^3.
Hope it helps...
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.
A quality control manager is concerned about variability of the net weight of his company’s individual yogurt cups. To check the consistency, he takes a random sample of sixteen 6-ounce yogurt cups and finds the mean of the sampled weights to be 5.85 ounces and the sample standard deviation to be 0.2 ounce.
Requried:
a. Test the hypotheses H0: µ ≥ 6 Ha: µ < 6 at the 5% level of significance. Assume the population of yogurt-cup net weights is approximately normally distributed.
b. Based on the results of the test, will the manager be satisfied that the company is not under-filling its cups?
c. State the decision rule, the test statistic, and the manager’s decision.
Answer:
a) We reject H₀
b) The manager won´t be satisfied with nominal filling its cup
c) See step-by-step explanation
Step-by-step explanation:
Normal distribution n < 30, therefore, we should use t - student table
Sample size n = 16
degree of freedom = df = n - 1 df = 15
Sample mean μ = 5,85 ou
Sample standard deviation is s = 0,2 ou
Hypothesis test
Null hypothesis H₀ μ >= μ₀
Alternative hypothesis Hₐ μ < μ₀
CI = 95 % then α = 5 % α = 0,05 α/2 = 0,025
Then in t-student table we find t(c) = 1,753
To calculate t(s)
t(s) = ( μ - μ₀ ) s/√n
t(s) = ( 5,85 - 6 ) / 0,2/√16
t(s) = - 0,15* 4 / 0,2
t(s) = - 3
To compare t(s) and t(c)
|t(s)| > |t(c)| 3 > 1,753
Then t(s) is in the rejection region. We should reject H₀. Data indicate that at 95 % of CI μ seems to be smaller than 6 ou
b) The manager won´t be satisfied with nominal filling its cup
You have found the following ages (in years) of all 666 lions at your local zoo: 13,2,1,5,2,7 What is the average age of the lions at your zoo? What is the standard deviation? Average age: _____ years old Standard deviation: ____ years
Answer:
[tex]Mean = 5[/tex]
[tex]S_x = 4.123[/tex]
Step-by-step explanation:
Given
Number of Lions, n: 6
Ages: 13, 2, 1, 5, 2, 7
Required
Determine the:
1. Mean
2. Standard Deviation
Mean is calculated as;
[tex]Mean = \frac{\sum x}{n}[/tex]
[tex]Mean = \frac{13+2+1+5+2+7}{6}[/tex]
[tex]Mean = \frac{30}{6}[/tex]
[tex]Mean = 5[/tex]
Standard Deviation is calculated as follows
[tex]S_x = \sqrt{\frac{\sum (x_i - Mx)^2}{N}}[/tex]
Where Mx represent mean
Substitute values for x, Mean and Land
[tex]S_x = \sqrt{\frac{(13 - 5)^2+(2 - 5)^2+(1 - 5)^2+(5 - 5)^2+(2 - 5)^2+(7 - 5)^2}{6}}[/tex]
[tex]S_x = \sqrt{\frac{(8)^2+(- 3)^2+(-4)^2+(0)^2+(-3)^2+(2)^2}{6}}[/tex]
[tex]S_x = \sqrt\frac{64+9+16+0+9+4}{6}}[/tex]
[tex]S_x = \sqrt\frac{102}{6}}[/tex]
[tex]S_x = \sqrt{17}[/tex]
[tex]S_x = 4.123[/tex]
The mean and standard deviation is 5 and 4.123 respectively
We want to find the mean or average and the standard deviation of the given set.
The average age is 5 years old and the standard deviation is 4.52 years old.
We know that for a general set of N elements {x₁, x₂, ..., xₙ} the average or mean is given by:
[tex]M = \frac{x_1 + x_2 + ... + x_n}{N}[/tex]
And the standard deviation is given by:
[tex]S = \sqrt{\frac{(x_1 - M)^2 + ... + (x_n - M)^2}{N - 1}[/tex]
The given set is:
{13, 2, 1, 5, 2, 7}
Now we just need to use the two given formulas for our set.
The mean is:
[tex]M = \frac{13 + 2 + 1+ 5 + 2 +7}{6} = 5[/tex]
And the standard deviation is:
[tex]S = \sqrt{\frac{(13 - 5)^2 + (2 - 5)^2 + (1 - 5)^2 + (5 - 5)^2 + (2 - 5)^2 + (7 - 5)^2}{6 - 1} } = 4.52[/tex]
So the average age is 5 years old and the standard deviation is 4.52 years old.
If you want to learn more you can read:
https://brainly.com/question/12402189
A publishing company claims that in fall 2019, the average price of college textbooks for a single semester is $385. Suppose you decide to collect data from a random sample of students to assess whether the publisher's claim is reasonable, and you find that in a random sample of 22 college students, the mean price of textbooks for the fall 2019 semester was $433.50 with a standard deviation of $86.92. At the 0.01 significance level, is there sufficient evidence to conclude that the mean price of college textbooks for a single semester is different from the value claimed by the publisher?
Answer:
We accept H₀ . We don´t have enough evidence to express the publisher claim is not true
Step by Step explanation:
We must evaluate if the mean of the price of college textbooks is different from the value claimed by the publisher
n < 30 then we must use t - distrbution
degree of freedom n - 1 df = 22 - 1 df = 21
As the question mentions " different " that means, a two-tail test
At 0,01 significance level α = 0,01 α/2 = 0,005
and t(c) = 2,831
Test Hypothesis
Null Hypothesis H₀ μ = μ₀
Alternative hypothesis Hₐ μ ≠ μ₀
To calculate t(s)
t(s) = ( μ - μ₀ ) /σ/√n
t(s) = ( 433,50 - 385 ) / 86,92 / √22
t(s) = 2,6171
Comparing t(c) and t(s)
t(s) < t(c)
Then t(s) is in the acceptance region we accept H₀. We don´t have enough evidence to claim that mean price differs from publisher claim
How long will it take $3800 to grow into $5700 if it’s invested at 6% interest compounded continuously?
Answer: 25 years
Step-by-step explanation:
t = I / Pr
t = 5700 / ( 3800 × 0.06 ) = 25
t = 25 years
If the nth term is , then the (n+1)st is: Please make sure you check the image :)
Answer:
( n+1) /2 *( 3n+2)
Step-by-step explanation:
n/2 * ( 3n-1)
We want the n+1 term
Replace n with n+1
( n+1) /2 *( 3( n+1) -1)
Distribute
( n+1) /2 *( 3n+3 -1)
( n+1) /2 *( 3n+2)
Answer:
[tex]\large \boxed{\sf C. \ \frac{n+1}{2} (3n+2)}[/tex]
Step-by-step explanation:
[tex]\displaystyle \frac{n}{2} (3n-1)[/tex]
To find the (n+1)st term, replace the n variable with n+1.
[tex]\displaystyle \frac{n+1}{2} (3(n+1)-1)[/tex]
Expand brackets.
[tex]\displaystyle \frac{n+1}{2} (3n+3-1)[/tex]
Subtract like terms in brackets.
[tex]\displaystyle \frac{n+1}{2} (3n+2)[/tex]
If the weight (in grams) of cereal in a box of Lucky Charms is N(470,5), what is the probability that the box will contain less than the advertised weight of 453 g?
Answer:
The probability that the box will contain less than the advertised weight of 453 g is 0.00034.
Step-by-step explanation:
Let X represent the weight (in grams) of cereal in a box of Lucky Charms.
It is provided that X follows a Normal distribution with parameters, μ = 470 and σ = 5.
Compute the probability that the box will contain less than the advertised weight of 453 g as follows:
[tex]P(X<453)=P(\frac{X-\mu}{\sigma}<\frac{453-470}{5})[/tex]
[tex]=P(Z<-3.4)\\=0.00034[/tex]
*Use the z-table.
Thus, the probability that the box will contain less than the advertised weight of 453 g is 0.00034.
