Answer:
4^6
Step-by-step explanation:
Because they have the same base (4) and are being multiplied together, the powers simply add together so:
4^2 * 4^4 = 4^(2+4) =4^6
Hope this helped!
A standardized exam consists of three parts: math, writing, and critical reading. Sample data showing the math and writing scores for a sample of 12 students who took the exam follow.
Student Math Writing
1 540 474
2 432 380
3 528 463
4 574 612
5 448 414
6 502 526
7 480 430
8 499 453
9 610 615
10 572 541
11 390 335
12 593 613
(a) Use a 0.05 level of significance and test for a difference between the population mean for the math scores and the population mean for the writing scores. (Use math score − writing score.)
(b) Calculate the test statistic.
Answer:
Calculated t= 0.011659
t ≥ t ( 0.025,11) = 2.201
So the null hypothesis is accepted.
Step-by-step explanation:
Student Math Writing Difference d²
math score − writing score
1 540 474 66 4356
2 432 380 52 2704
3 528 463 65 4225
4 574 612 -38 1444
5 448 414 34 1156
6 502 526 -24 576
7 480 430 50 2500
8 499 453 46 2116
9 610 615 -5 25
10 572 541 31 961
11 390 335 55 3025
12 593 613 -20 400
∑ 6168 5856 312 23488
1) We state our null and alternative hypothesis as
H0: ud= 0 Ha: ud≠0
2) The significance level alpha is set at α= 0.05
3) The test statistic under H0 is
t= d`/ sd/√n
which has t distribution with n-1 degrees of freedom.
4) The critical region is t ≥ t ( 0.025,11) = 2.201
5) Computations
d`= ∑di/n= 312/12= 31.2
Variance = ∑(di- d`)²/n-1= 1/n-1 [ ∑di²-( ∑di)²/n]
= 1/11[ 23488- (312)²/12]
= 1/11[ 23488- 8112] = 1/11[15376]= 5976.7272
Standard Deviation= √ 5976.7272= 77.2510= 77.25
Now t= 3.12/77.25/√12= 0.011659
The calculated t value= 0.011659 falls in the acceptance region . So we accept our null hypothesis and reject the alternative hypothesis.
6. aA box in a certain supply room contains four 40-watt light bulbs, five 60-watt bulbs, and six 75-watt bulbs. Suppose that three bulbs are randomly selected. a. What is the probability that exactly one of the selected bulbs are rated 75-watt? b. What is the probability that all three of the elected bulbs have the same rating? c. What is the probability that one bulb of each type is selected? d. What is the probability that at least two of the selected bulbs are rated 75-watt?
Answer:
A) 0.2967
B) 0.0747
C) 0.2637
D)0.6933
Step-by-step explanation:
We are told the box contains four 40-watt light bulbs, five 60-watt bulbs, and six 75-watt bulbs.
Thus, total number of bulbs = 4 + 5 + 6 = 15 bulbs
This is a combination problem.
Thus;
A) probability that exactly one of the selected bulbs are rated 75-watt will be = ((6C2) × (9C1))/(15C3)
= (15 × 9)/455
= 0.2967
B) probability that all three of the elected bulbs have the same rating;
Number of ways to select three 40 watt bulbs out of the 4 in the box = 4C1 = 4!/(3! × 1!) = 4
Number of ways to select three 60 watt bulbs out of the 5 in the box = 5C1 =
5!/(3! × 2!) = 10
Number of ways to select 75 watt bulbs out of the 6 in the box = 6C1 = 6!/(3! × 3!) = 20
Total number of ways = 4 + 10 + 20 = 34.
Thus, probability that all three of the elected bulbs have the same rating = 34/15C3 = 34/455
= 0.0747
C) probability that one bulb of each type is selected =
[(4C1) × (5C1) × (6C1)]/(15C3)
= (4 × 5 × 6)/455
= 0.2637
D) probability that at least two of the selected bulbs are rated 75-watt =
[(4C1 × 5C1 × 6C2)/15C3] + 6C3/15C3
= (4 × 5 × 15/455) + 20/455
= 0.6493 + 0.044
= 0.6933
Give the most appropriate reason for using three significant figures in reporting results of typical engineering calculations.a. Three significant figures gives better than one-percent accuracy. b. Most of the original data used in engineering calculations do not have accuracy better than one percent. c. Historically slide rules could not handle more than three significant figures. d. Telephone systems designed by engineers have area codes consisting of three figures
Answer:
The answer is "Option b".
Step-by-step explanation:
In the calculation of engineering or modeling, it is used to assess its necessary system, that performance, and also used to evaluate the distribution network adjustments, which is used to accommodate the slew of other distribution network adjustments, that's why except "choice b" all were incorrect.
zane bought a pair of jeans that originally cost $56. he used a coupon for 25% off and paid$8 in sales tax
Answer:
$38.64
Step-by-step explanation:
so the equation needed to solve is $56*0.25 and that number is 14. Since it is a coupon you subtract 14 from 56 and end up with 42. Now multiply 0.08*42 and you got your sales tax, $3.36. now subtract that from 42 and you have your answer
Answer:
He paid 50 dollars
Step-by-step explanation:
25% off = 75/100 x 56 = 42
42 + 8 = 50
if this question is about what percentage the tax is, then the answer would be 19.05%
x/100 x 42 = 50
42x/100 = 50
42x = 5000
x = 5000/42
x = 119.05
119.05 - 100 = 19.05%
6. Joe runs 3/4 mile in 1/2 hour. Find his average speed in miles per hour.
Answer:
1.5 MPH
Step-by-step explanation:
3/4 = 0.75
3/4 x 2 = 0.75 x 2 = 1.5
The expression (q16)(q−5)2 is equivalent to qn. What is the value of n? 42 22 -160 13
Answer:
22
Step-by-step explanation:
In order to get one of the answer choices, it appears we need to interpret your input as ...
[tex](q^{16}q^{-5})^2 = (q^{16-5})^2=q^{11\cdot 2}=q^{22}[/tex]
The value of n is 22.
__
The applicable rules of exponents are ...
(a^b)(a^c) = a^(b+c)
(a^b)^c = a^(bc)
Answer:
6
Step-by-step explanation:
A particular computer takes 14 minutes to download a 42-minute TV show. How long will it take the computer to download a 2.5-hour movie?
Answer
about 15 min to 1 hour
Peter bought 45 greeting cards at 3 for $2.00. he sold them for 5 for $4.00. how much money did he make
Step 1) Set up a proportion to find how much Peter spent
45 cards / x dollars = 3 cards / 2 dollars
Step 2) Cross-multiply to solve the proportion
3x = 90
x = $30
Step 3) Set up a proportion to find how much Peter made
45 cards / x dollars = 5 cards / 4 dollars
5x = 180
x = $36
Step 4) Subtract the amount Peter made by the amount he spent
36 - 30 = $6
Answer: Peter made $6
($2/3) * 45 = $30
($4/5) * 45 = $36
$36 - $30 = $6
what is the solution of the equation? 3(y-5)+2=5
Answer:
Y=- 6
3(y-5)+2=5
multiply
3y-15+2=5
add
3y-13=5
add pos 13 to the neg 13 to
cancel it out and add +13 to 5
3y=18
divide -3 to pos 3 and 18 to cancel it out
y= -6
what value does the 2 represent in the number 168,526
Answer:it is the tens place
Step-by-step explanation:
Answer:
2 represents the the tenths place
Step-by-step explanation:
You have 168,526 remember your tenth hundred and thousands 2 is in the tenth place that is what represents
Hope that answers ur question
Solve for x. 95=35 Express the answer to the hundredths place (i.e., two digits after the decimal point).
Answer:
[tex]x = 1.28[/tex]
Step-by-step explanation:
Given
[tex]95 = 35^x[/tex]
Required
Solve for x
[tex]95 = 35^x[/tex]
Take Log of both sides
[tex]Log95 = Log35^x[/tex]
Apply law of logarithm
[tex]Log95 = xLog35[/tex]
Divide both sides by Log35
[tex]x = \frac{Log95}{Log35}[/tex]
[tex]x = \frac{1.97772360529}{1.54406804435}[/tex]
[tex]x = 1.28085262338[/tex]
Approximate
[tex]x = 1.28[/tex]
Name the rays on line c.
Answer:
BC, BD, BQ, CB, CD, CQ, DB, DC, DQ, QB, QC, QD
Step-by-step explanation:
"BC, BD, BQ, CB, CD, CQ, DB, DC, DQ, QB, QC, QD" Are all the possible rays on line c.
Jaquarius has a pair of limited edition Jordan tennis shoes that are 12 inches long each. What is the total length of both of his shoes in feet?
Answer:
Total length of shoes in feet = 2 feet
Length of each shoe = 1 feet
Step-by-step explanation:
Given:
Length of each shoe = 12 inches
Find:
Total length of shoes in feet
Computation:
Total length of shoes = [12 + 12] inches
Total length of shoes = 24 inches
12 inches = 1 feet
Total length of shoes in feet = 24 / 12
Total length of shoes in feet = 2 feet
Length of each shoe = 1 feet
P (x) is a polynomial. Here are a few values of P (x): P(-5)=-2 and P (5)=-1 What is the remainder when P(x) is divided by (x+5)? (Answer choices in the picture)
Answer:
– 2
Step-by-step explanation:
From the question given above, the following data were obtained:
P(x) = polynomial
P(–5) = – 2
P(5) = –1
Remainder when P(x) is divided by
(x + 5) =?
To obtain the remainder when P(x) is divided by (x + 5), we shall apply the reminder theorem as follow:
Let (x + 5) be equal to 0
(x + 5) = 0
x + 5 = 0
Subtract 5 from both side
x + 5 – 5 = 0 – 5
x = –5
Replace x in P(x) with –5 as shown below:
P(x) = polynomial
x = – 5
P(–5)
From the question given above,
P(–5) = – 2
Therefore, when P(x) is divided by
(x + 5), the remainder is – 2.
which number represents a whole number
Answer: The answer is D
Step-by-step explanation:
I divided 24 by 3 and it gave me 8 which is a whole number.
Which point would represent the value of v—72 Include the letter of the answer and then justify your response using complete sentences.??
Answer:
Verbal expression x more than 7 can be represented ... If a team scores 27 points in a game, then 6T + p ... Algebraic expressions include variables, numbers, ... the sides of a cube all have the same length, V = x • x • x, or x ... Write a sentence describing what the length of ... REASONING Explain how to evaluate a[(b − c)
Step-by-step explanation:
What is 8.6 increased by 75%
Answer:
15.05
Step-by-step explanation:
8.6 is 100% of 8.6.
To increase it by 75%, you'll end up with 175% of 8.6
175% of 8.6 =
= 1.75 * 8.6
= 15.05
h(x)=x^2+1 k(x)=x-2
(h+k)(2)=
(h-k)(3)=
Evaluate 3h(2)+2k(3)=
(h + k)(2) = 5
(h - k)(3) = 9
evaluate 3h(2) + 2k(3) = 17
The composition of functions is solved
a) ( h + k ) ( 2 ) = 5
b) ( h - k ) ( 3 ) = 9
c) 3h ( 2 ) + 2k ( 3 ) = 17
What is Composition of functions?Evaluation of a function at the value of another function is known as Composition of function. A function composition is a process in which two functions, f and g, form a new function, h, in such a way that h(x) = g(f(x)). This signifies that function g is being applied to the function x. So, in essence, a function is applied to the output of another function.
Given data ,
Let the first function be represented as f ( x )
Now , the value of f ( x ) is
h ( x ) = x² + 1
Let the second function be represented as g ( x )
Now , the value of g ( x ) is
k ( x ) = x - 2
Now , the composition of function is
To calculate (h+k)(2), we substitute x = 2 in both h(x) and k(x), add them together and simplify:
h(2) = 2² + 1 = 5
k(2) = 2 - 2 = 0
(h+k)(2) = h(2) + k(2) = 5 + 0 = 5
To calculate (h-k)(3), we substitute x = 3 in both h(x) and k(x), subtract k(x) from h(x), and simplify:
h(3) = 3² + 1 = 10
k(3) = 3 - 2 = 1
(h-k)(3) = h(3) - k(3) = 10 - 1 = 9
To evaluate 3h(2)+2k(3), we substitute x = 2 and x = 3 in h(x) and k(x), respectively, and simplify:
3h(2) + 2k(3) = 3(5) + 2(3-2) = 15 + 2 = 17
Therefore , ( h + k ) ( 2 ) = 5 , ( h - k ) ( 3 ) = 9, and 3h( 2 ) + 2k( 3 ) = 17
Hence , the composition of functions is solved
To learn more about composition of functions click :
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What number is greater than 271,680 but less than 276,108
Answer:
276,108 < x < 271,680
Step-by-step explanation:
*Hope this helped*
At the beginning of a snowstorm, Sydney had 11 inches of snow on her lawn. The
snow then began to fall at a constant rate of 0.5 inches per hour. Assuming no snow
was melting, how much snow would Sydney have on her lawn 3 hours after the snow
began to fall? How much snow would Sydney have on her lawn after t hours of snow
Answer:
12.5in.
x=.5t+11
Step-by-step explanation:
First of all, create the equation so you can solve both questions at once. We know that Sydney had eleven inches of snow on her lawn, and it doesn't dissapear, so it starts with x=11. Then every hour she gets .5 inches per hour, and the amount of hours is t, so that will translate to .5t. that makes the equation x=.5t+11. To find out how much she would have in three hours, substitute 3 for t, which which goes like this: x=.5(3)+11
x=1.5+11
x=12.5
Answer:
Snow after 3 hours: 12.5
Snow after t hours: 11+0.5t
While riding on a carousel, Angela travels a distance of 65 meters every 15 seconds. What is her speed in kilometers per hour? A. 3.9 km/hr B. 14.4 km/hr C. 15.6 km/hr D. 156.0 km/hr
Write 2^-3 in word form
Answer:
two raised to the power of -3
Two to the power of negative 3
Step-by-step explanation:
[tex]2^-^3 = \frac{1}{2^3}[/tex]
1 divided by 2 to the power of 3
Which statement about this system of equations is true?
A. The system has a unique solution at (0,6)
B. The system has a unique solution at (0,-4)
C. The system has no solution
D. The system has infinitely many solutions
Answer:
The system has NO solution
Answer C in your list
Step-by-step explanation:
Notice that the lines are parallel, they will not intercept, and therefore there is no answer to the system
What does point A represent on the graph? Jordan needs 3 cups of diced chicken for 2 salads. Jordan needs 2 cups of diced chicken for 3 salads. Jordan needs 3 cups of diced chicken for 1 and one-half salads. Jordan needs 1 and one-half cups of diced chicken for 3 salads.
Answer:
The answer is 3
Step-by-step explanation:
The following table presents the time taken to review articles that were submitted for publication to a particular journal during a recent year. A few articles took longer than 6 months to review; these are omitted from the table. Consider the data to be a population. (image) (a) Approximate the variance of the times. Round the answer to at least two decimal places. The variance is (b) Approximate the standard deviation of the times. Round the answer to at least two decimal places. The standard deviation is
Answer:
Variance = 0.1645
Standard deviation = 0.4056
Step-by-step explanation:
Kindly check attached picture for detailed explanation
you must be at least 18 years old to vote
Answer:
To vote you need to be a US citizen and be at least 18 years old by election day
Answer:
18 years old to vote
Step-by-step explanation:
You must be 18 years old to vote and you have to be a citizen. Also to vote, you have to be a resident of Florida. So therefore, yes you have to be 18 years old to vote.
Hope this Helps!
what does this sideways E stands for in alg 2 ?
Answer:
The sideways E is used for indcating that a point, object, or number belongs to a certian set.
Step-by-step explanation:
If M2BAC = (3x – 1)º, m_chD = (6x + 10)°, m2DAE (2x + 6)°, and m_BAE = 103°, then find the mZCAD
Answer:
mZCAD=310°
Step-by-step explanation:
M2BAC=1,m2DAE=3 and m-BAE=0 therefore solution will be 310°
What is your average speed in miles per hour and in feet per second if you travel a mile in 16 minutes?
Step-by-step explanation:
Mile Per Hour to Foot Per Second Conversion Table
Miles Per Hour Feet Per Second
16 mph 23.47 ft/s
17 mph 24.93 ft/s
18 mph 26.4 ft/s
19 mph 27.87 ft/s
There are two different music download companies that offer a monthly plan for downloading songs. S-Jams charges $1.29 per song plus $10 monthly fee. C-tunes charges $0.99 per song plus $16 monthly fee. When will the company’s plans cost the same? Write an expression for the cost of S-Jams.
Answer:
Thus, when both S-jams and C-tunes have 20 songs downloaded in a month , the cost will be same.
an expression for the cost of S-Jams $0.99n + $16
Step-by-step explanation:
For
S-Jams
cost of 1 song = $1.29
let there be n songs downloaded in a month
then
cost of n songs = n*cost of 1 song = $1.29n
monthly fee = $10
Total cost of S-Jams = $1.29n+$10
________________________________________
For
C-Tunes
cost of 1 song = $0.99
let there be n songs downloaded in a month
then
cost of n songs = n*cost of 1 song = $0.99n
monthly fee = $16
Total cost for C-Tunes= $0.99n + $16
we have to find When will the company’s plans cost the same.
Total cost of S-Jams = Total cost of C- Tunes
1.29n+10 = 0.99n + 16
=> 1.29n - 0.99n = 16-10
=> 0.30n = 6
=> n = 6/0.3 = 20
Thus, when both S-jams and C-tunes have 20 songs downloaded in a month , the cost will be same.
an expression for the cost of S-Jams $0.99n + $16