Answer:
C
Step-by-step explanation:
Firstly, we set up the null and alternative hypothesis as follows;
The null hypothesis is;
H0: μ ≥ 12
The alternative hypothesis is;
Ha : μ < 12
Next step is to calculate the test statistic z
Mathematically;
z = (x - μ )/ σ /√n
= (11.58 - 12) /1.93/√(80
Test statistic z = -1.92
Now we proceed to find the probability value that is equal to the value of the test statistic. We can find this by using the standard normal table or NORMSTD function on excel
P(z < -1.92) = 0.0274
P-value = 0.0274
alpha = 0.05
From the above, we can see that
P-value < alpha
And because of this, we are going to reject the null hypothesis and therefore accept the alternative.
We then conclude that there is sufficient evidence to conclude that "The average battery life (between charges) of this model of tablet is at least 12 hours."
Which equation satisfies all three pairs of a and b values listed in the table ?
A) a-3b=10
B) 3a+ b=10
C) 3a-b=10
D) a+ 3b=10
Answer:
The answer is option C.
3a - b = 10
Hope this helps you
40.) Decompose 7/8 into the sum of unit fractions.
Answer:
7/8 = 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8
7/8 = 1/8 + 6/8
7/8 = 4/8 + 3/8
7/8 = 5/8 + 2/8
Step-by-step explanation:
Hope it helps!
The fraction 7/8 can be written as the sum of unit fraction i.e;
1/8+1/8+1/8+1/8+1/8+1/8+1/8+1/8.
What is unit fraction?A unit fraction can be defined as a fraction whose numerator is 1.
Given fraction 7/8
can be written as the sum of the unit fraction i.e;
7/8=1/8+1/8+1/8+1/8+1/8+1/8+1/8+1/8
Hence,7/8 can be decomposed into sum of unit fraction as
1/8+1/8+1/8+1/8+1/8+1/8+1/8+1/8.
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What is the value of 3/4 increased by 2 1/6?
Answer:
2 11/12
Step-by-step explanation:
3/4 + 2 1/6
Add the fractions.
35/12
= 2 11/12
Answer:
[tex]2\frac{11}{12}[/tex]
Step-by-step explanation:
[tex]\frac{3}{4}+2\frac{1}{6}=\\\\\frac{18}{24}+2\frac{4}{24}=\\\\2\frac{22}{24}=\\\\2\frac{11}{12}[/tex]
I NEED HELP ASAP!!!!!!! Find 2 numbers that multiply to make -24 and add to make -10
Answer:
Step-by-step explanation:
-8*3= -24+14=-10
Answer:
-12 and 2.
Step-by-step explanation:
-12*2= -24,
-12+2=-10
Find the next two !!!
It's adding 3 and subtracting 2 every time.
This means the next two terms would be +3 and -2 since the last one was -2.
The next term = 4+3=7
The next next term = 7-2=5
Answer:
Answer : 7 , 5Please see the attached picture.
Hope it helps...
Best regards!!
A triangle has side lengths of 13, 9, and 5. Is the triangle a right triangle? Explain.
Use complete sentences in your explanation.
Hint: Pythagorean Theorem: a^2+ b^2 = c^2
Answer:
see below
Step-by-step explanation:
Using the Pythagorean Theorem:
a^2+ b^2 = c^2
5^2+ 9^2 = 13^2
25+81 = 169
106 = 169
This is not true so it is not a right triangle
Answer:
[tex]\boxed{\sf Not \ a \ right \ triangle}[/tex]
Step-by-step explanation:
Apply Pythagorean theorem to check if the triangle is a right triangle.
[tex]a^2+ b^2 = c^2[/tex]
[tex]5^2+ 9^2 = 13^2[/tex]
[tex]25+81=169[/tex]
[tex]106=109[/tex]
False statement.
The triangle is not a right triangle.
find the coordinates of the vertices of the triangle after a reflection across the line y = -1 and then across the line x = -2
Answer: A) N'=(-2, 2) M'=(-1, 0) L'=(-5, -2)
Step-by-step explanation:
N = (-2, -4) M = (-3, -2) L = (1, 0)
Reflection over y = -1
N' = (-2, 2) M' = (-3, 0) L' = (1, -2)
Reflection over x = -2
N'' = (-2, 2) M'' = (-1, 0) L'' = (-5, -2)
Solve the equation: 1/3(y - 2) - 5/6(y + 1) = 3/4(y - 3) - 2
Answer:
y=2.2
Step-by-step explanation:
1: Distribute all numbers to get rid of all parenthesis
2: Solve
Hope this helped :) LET ME KNOW IF YOU NEED THE ANSWER IN A DIFFERENT FORM I CAN GET IT FOR YOU
PLEASE HELP!!! QUICKLY
Practice
Question 1: Choose the number that will complete this Pythagorean triple.
15, 17
Question 2: Choose the number that will complete this Pythagorean triple.
9,
41
Question 3: Choose the number that will complete this Pythagorean triple.
12, 35,
Reset
Submit
Answer:
1. = 8
2. =40
3. =37
Step-by-step explanation:
1. x = √(17² - 15²) = 8
2. x =√(9² +41²) = 40
3. x =√(12² + 35²) = 37
please mark brainliest
i will give brainliest and 50 points pls help ASP
pls can u show how to work this out thx !!! : )
its a simultaneous equation
Answer:
x = 3
y = -2
Step-by-step explanation:
Given:
8x - 3y = 30 ..................(1)
3x + y = 7 .......................(2)
Eliminate y by adding (1)+3*(2)
8x-3y + 3*( 3x+y) = 30 + 3*7
8x + 9x -3y + 3y = 51
17x = 51
x = 3 .....................(3)
substitute (3) in (2)
3(3) + y = 7
y = 7-9 = -2
y = -2 ....................(4)
Answer:
Step-by-step explanation:
[tex]8x-3y=30\\y=7-3x\\\\8x-3(7-3x)=30\\8x-21+9x=30\\17x=51\\x=3\\\\y=7-3(3)\\y=7-9\\y=-2[/tex]
What is x when: 2/x = 5/9
Answer: 3.6
Step-by-step explanation:
2/x=5/9
Multiply(x)
2=5/9x
Divide by 5/9
x=3.6
Hope it helps <3
use the substitution method to solve the system of equations. Choose the correct ordered pair y=3x 2x+3y=55
Answer:
(x,y) = (5,15)
Step-by-step explanation:
y = 3x
2x + 3y = 55
2x + 3(3x) = 55
2x + 9x = 55
11x = 55
x = 5
y = 3(5)
y = 15
Which is steeper: a road with a 12% grade or a road with a pitch of 1 in 8?
Answer:
A road with a pitch of 1 in 8 is steeper.
Step-by-step explanation:
Let us convert these to the same units so that we can better compare them.
[tex]\frac{1}{8} = 0.125[/tex]
0.125=12.5 %
As 12.5% is greater than 12%, the road with a pitch of 1 in 8 will be steeper.
Mariam went to a shop and bought 8 snickers, 3 galaxy and 3 kitkat. She payed 8 BD
totally. Her friend Zainab bought 4 snicker, 9 galaxy and 4 kitkat. She payed 10.9BD.
Is it possible to know the cost of each chocolate mathematically?
If yes how. If not why?
Answer:
Yes
Step-by-step explanation:
Let s be the price of snickers, g the price of galaxy and k the price of kitkat.
●For Mariam the equation will be:
8 s + 3 g + 3k = 8
●For Zainab the equation will be:
4 s + 9 g + 4 k = 10.9
Take the first equation and divide both sides by 4 to make it easier.
You get:
● 2s + 0.75 g + 0.75k = 2
Take the second equation and divide both sides by 2 to make easier.
You get:
● 2s + 4.5g + 2k = 5.45
The new system of equation is:
● 2s +0.75g + 0.75k = 2
● 2s + 4.5g + 2k = 5.45
Express s in the first equation using the other variables.
● 2s +0.75g +0.75k = 2
● 2s + 0.75(g+k) = 2
● 2s = 2-0.75(g+k)
● s = 1- 0.325 (g+k)
Replace s by the new expression in the second equation:
●2 [1-0.325(g+k)] +4.5 g +2k = 5.45
●2-0.75(g+k) +4.5g + 2k = 5.45
●2- 0.75g -0.75k +4.5 g +2k = 5.45
●2+ 3.75g + 1.25k = 5.45
● 3.75g +1.25k = 3.45
We have eliminated one variable (s)
We will keep (3.75g+1.25k=3.45) and use it.
Now that we eliminated in the second equation do it again in the first one.
You will get a system of equations with two variables.
Solve it and replace g and k with the solutions.
Finally solve the equation and find s.
2. Salvador has 10 cards, each with one number on
it. The numbers are 2, 3, 4,5,5,7,7,7,7,7.
Salvador is going to make a row containing all 10
cards. How many ways can he order the row?
Answer:
15,120 number of ways.Step-by-step explanation:
This is a permutation problem. Given the 10 cards with numbers 2, 3, 4,5,5,7,7,7,7,7 on it, if Salvador is going to make a row call, the number of ways he can order a row is as shown below;
Total number of cards = 10!
number of times the digit 5 was repeated = 2times
number of times the digit 7 was repeated = 5times
The number of ways he can make a row call = 10!/2!5!
= 10*9*8*7*6*5!/2*5!
= 10*9*8*7*6/2
= 10*9*8*7*3
= 15,120 different ways
Hence, the number of ways he can order the row is 15,120 number of ways.
Please answer this correctly without making mistakes
What is the correct answer
How far apart are the locksmith and the hotel?
The correct answer is 45.5 km
Explanation:
The total distance from the locksmith to the hotel, located in the east of the graph is not directly given; however, this distance can be calculated by considering the partial distances given. This includes the distance from the locksmith to the furniture store (18.3 km), and the distance between the furniture and the hotel (27.2) as the total distance = distance from the locksmith to the furniture store + distance from the furniture store to the hotel. Thus, the total distance is 18.3 km + 27.2 km which is equal to 45.5 km.
Find the probability of each event. A class has five boys and nine girls. If the teacher randomly picks six students, what is the probability that he will pick exactly four girls?
Answer: [tex]\dfrac{60}{143}[/tex]
Step-by-step explanation:
Given, A class has five boys and nine girls.
Total students = 5+9=14
Number of ways to choose 6 students out of 14= [tex]^{14}C_6[/tex] [Using combinations]
Number of ways to choose 4 girls out of 6 (4 girls + 2 boys = 6 ) = [tex]^{9}C_4\times\ ^{5}C_2[/tex]
If the teacher randomly picks six students, then the probability that he will pick exactly four girls:-
[tex]\dfrac{^{9}C_4\times \ ^{5}C_2}{^{14}C_6}[/tex]
[tex]=\dfrac{\dfrac{9!}{4!5!}\times\dfrac{5!}{2!3!}}{\dfrac{14!}{6!8!}}\\\\=\dfrac{1260}{3003}\\\\=\dfrac{60}{143}[/tex]
hence, the required probability = [tex]\dfrac{60}{143}[/tex] .
The graph shows how the length of time a boat is rented is related to the
rental cost. What is the rate of change shown in the graph?
Boat Rental
AY
440
400
380
320
Cost (dollars)
240
200
100
120
80
40
0
Time (hours)
A. $40/hour
B. $80/hour
C. 80 hours/dollar
D. 40 hours/dollar
A slope is also known as the gradient of a line is a number. The correct option is B.
What is Slope?A slope is also known as the gradient of a line is a number that helps to know both the direction and the steepness of the line.
slope = (y₂-y₁)/(x₂-x₁)
The rate of change shown in the graph is the slope of the given line.
Now, to know the slope of the line consider any two points on the line, such as (0,0) and (5,400).
Therefore, the slope of the line can be written as,
Slope, m = ($400 - $0)/(5-0) hour
= $400/5 hour
= $80/hour
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4, 12, 36,what is 3 other remaining sequence
Answer:
108, 324, 972
Step-by-step explanation:
This sequence is multiplying by ✖️3.
4✖️3=12✖️3=36✖️3=108✖️3=324✖️3=972
Hope this helps!
Find the four terms of the sequence given by the following expression
Answer:
47, 40, 33, 26 are the first four terms of the sequence.
Step-by-step explanation:
Expression representing the sequence is,
[tex]a_n=46-7(n-1)[/tex]
where n = number of term in the sequence
For n = 1,
[tex]a_1=47-7(1-1)[/tex]
= 47
For n = 2,
[tex]a_2=47-7(2-1)[/tex]
= 47 - 7
= 40
For n = 3,
[tex]a_3[/tex] = 47 - 7(3 -1)
= 47 - 14
= 33
For n = 4,
[tex]a_4=47-7(4-1)[/tex]
= 47 - 21
= 26
Therefore, first four terms of the sequence are 47, 40, 33 and 26.
What is the height of the cone?
Answer:
it is the inches milimeters meters
Answer:
9 cmStep-by-step explanation:
Given,
Volume of cone ( v ) = 27 π
Radius ( r ) = 3 cm
Height of cone ( h ) = ?
Now, let's find the height of cone:
Volume of cone = [tex] \frac{\pi {r}^{2}h }{3} [/tex]
plug the values
[tex]27\pi = \frac{\pi \: {3}^{2} \: h \: }{3} [/tex]
Evaluate the power
[tex]27\pi = \frac{\pi \times 9 \times h}{3} [/tex]
Divide 9 by 3
[tex]27\pi = 3\pi \: h[/tex]
Divide both sides of the equation by 3π
[tex] \frac{27\pi}{3\pi} = \frac{3\pi \: h}{3\pi} [/tex]
Calculate
[tex]9 = h[/tex]
Swipe the sides of the equation
[tex]h = 9[/tex] cm
Hope this helps..
Best regards!!
find the area under (sin x) bounded by x= 0 and x = 2π and x-axis
You probably want the unsigned area, which means you don't compute the integral
[tex]\displaystyle\int_0^{2\pi}\sin x\,\mathrm dx[/tex]
but rather, the integral of the absolute value,
[tex]\displaystyle\int_0^{2\pi}|\sin x|\,\mathrm dx[/tex]
[tex]\sin x[/tex] is positive when [tex]0<x<\pi[/tex] and negative when [tex]\pi<x<2\pi[/tex], so
[tex]\displaystyle\int_0^{2\pi}|\sin x|\,\mathrm dx=\int_0^\pi\sin x\,\mathrm dx-\int_\pi^{2\pi}\sin x\,\mathrm dx[/tex]
[tex]\displaystyle\int_0^{2\pi}|\sin x|\,\mathrm dx=(-\cos x)\bigg|_0^\pi-(-\cos x)\bigg|_\pi^{2\pi}[/tex]
[tex]\displaystyle\int_0^{2\pi}|\sin x|\,\mathrm dx=\boxed{4}[/tex]
Solve of the following equations for x: 3x = 5
Answer: 1.7
Step-by-step explanation:
5 divided by 3=1.666666667
1.6 and next 6 in line is over 5 so the 6 turns to a 7
3*1.7= 5.1 but when rounded 1 tells 5 to stay down so it = 5
A population consists of 8 items. The number of different simple random samples of size 3 that can be selected from this population is
Answer:
The correct answer will be "56".
Step-by-step explanation:
Use a combination of 8 things taken 3 at a time :
⇒ [tex]8_{C_{3}}[/tex]
⇒ [tex]\frac{8!}{(3!(8 - 3)!)}[/tex]
⇒ [tex]\frac{8!}{(3!5!)}[/tex]
⇒ [tex]\frac{8\times 7\times 6\times 5\times 4\times 3\times 2\times 1}{3\times 2\times 1}[/tex]
⇒ [tex]8\times 7[/tex]
⇒ [tex]56[/tex]
Using the principle of combination, the number of different random samples of size 3 that can be selected is 56.
Using the principle of combination :
nCr = [n! ÷ (n-r)! r!]Hence, we have ;
8C3 = [8! ÷ (8 - 3)! 3!]
8C3 = [8! ÷ 5!3!]
8C3 = (8 × 7 × 6) ÷ (3 × 2 × 1)
8C3 = 8 × 7
8C3 = 56
Hence, there are 56 different possible samples.
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In 2009 the number of vehicle sales in the United States was 10,002 thousand and in 2013 it was 17,884 thousand.a. [3 pts] Determine the average rate of change (slope) from 2009 to 2013.b.
Answer:
1970.5 thousand
Step-by-step explanation:
Given
Vehicle sales in 2009 = 10,002 thousand
Vehicle sales in 2013 = 17,884 thousand
Required
Determine the average rate of change;
From the given parameters, it can be seen that the number of vehicles is a function of year
Let x represent the years and y represent the number of vehicles;
Such that;
[tex]x_1 = 2009;\ y_1 = 10,002[/tex]
[tex]x_2 = 2013;\ y_2 = 17,884[/tex]
The rate of change is calculate as follows;
[tex]m = \frac{y_1 - y_2}{x_1 - x_2}[/tex]
[tex]m = \frac{10002 - 17884}{2009 - 2013}[/tex]
[tex]m = \frac{-7882}{-4}[/tex]
[tex]m = \frac{-7882}{-4}[/tex]
[tex]m = 1970.5[/tex]
Hence, the average rate of change is 1970.5 thousand
Which inequality is equivalent to this one y-8_<-2
Answer:
[tex]\boxed{y\leq 6}[/tex]
Step-by-step explanation:
[tex]y-8 \leq -2[/tex]
Adding 2 to both sides
[tex]y \leq -2+8[/tex]
[tex]y \leq 6[/tex]
What property do rectangles and parallelograms always share?
1
?
x + 5and
Which line is parallel to the line y =
passes through the point (-2, 1)?
x+
O y=x+3
1
y =
+2
1
y =
4
*-
oy-
1
-X
y=-2
Answer:
second option
Step-by-step explanation:
Parallel lines have the same slope, and since the slope of the given line is 1/2, we know the slope of the answer will be 1/2, which eliminates the first and last options. We know the slope and a point that belongs to the line, (-2, 1), so we can use point-slope formula to derive the equation of the line.
y - 1 = 1/2(x + 2)
y - 1 = 1/2x + 1
y = 1/2x + 2
Find the 10th term of the following geometric sequence.
2, 10, 50, 250, ...
Answer:
3906250
Step-by-step explanation:
We can notice that the ratio is 5. 10/2 = 5
Each term gets multiplied by 5 to get the next term.
250 × 5 = 1250 (5th term)
1250 × 5 = 6250 (6th term)
6250 × 5 = 31250 (7th term)
31250 × 5 = 156250 (8th term)
156250 × 5 = 781250 (9th term)
781250 × 5 = 3906250 (10th term)
The 10th term of the geometric sequence is 3906250.
Currently Shawn pays $550 per month to rent his apartment. Next year his rent will increase by 13.5% from what he currently pays . a) find the amount that shawn's rent will increase . b) what will be shawn's new monthly rent?. c) If you divide your answer from (b) by shawn's original rent of $550, what is the decimal result? do you see any connection to part (a)?
a) Simply do 0.135(13.5%)*550 to get that his rent increases by $74.25.
b) Simply do 550+74.25 to get that his new rent is $624.25.
c) 624.25/550 = 1.135, or 100%+13.5%, the amount his rent increased.
Hope it helps <3
Answer:
A. $74.25
B. $624.25
C. 1.135, and this is a connection to part a because it's what we multiplied 550 by to get our new rent.
Step-by-step explanation:
If Shawn pays $550 per month for rent, and he has a 13.5% increase, we can multiply 550 by [tex]1+\frac{13.5}{100}[/tex] to get our new number.
[tex]1+0.135=1.135[/tex]
[tex]550\cdot1.135=624.25[/tex]
This is the new monthly rent, part B. To find Part A, let's subtract 550 from thi number.
[tex]624.25-550=74.25[/tex]
Now, for part C, let's divide 624.25 by 550.
[tex]624.25\div550 = 1.135[/tex]
If you notice, 1.135 is the same number we multiplied 550 by to get our new cost, and as a percent, 1.135 is 113.5%.
Hope this helped!