Answer:
a=10.1
k=3
Step-by-step explanation:
Lets solve the first equation first.
94=10a-7
Lets add 7 to both sides.
101=10a
Divide both sides by 10 to isolate a
101/10=a
a=10.1
Lets do the second equation.
7k+10=31
Subtract 10 from both sides
7k=21
Divide 7 by both sides to isolate k
k=3
A school had decided to hire a new vice principal. A recent issue 4 of the NEA magazine stated that the average vice principal salary s for a school of similar size is $60,000. At the request of the Board of Education, the principal conducts his own survey of vice principal's salaries. His survey of 25 schools revealed an average salary or $72,000 and a standard deviation of $9,000. Perform a hypothesis test at a 5% significance level to test the magazine's claim.
Required:
a. What is the appropriate sampling distribution to use?
b. State the null and alternative hypotheses.
c. State the decision rule at a significance level of 5% show all calculations
d. Illustrate all key numbers and areas on a graph.
e. What decision should the school principal make?
f. What type of error can possibly be made with the decision in part (e)?
g. What is the value of the Maximum Tolerable Error for this problem?
Answer:
1.) t - distribution
2.) H0 : μ = 60000 ; H1 : μ > 60000
3.) P < α (Reject Null) ; P > α (fail to reject Null)
4.) Reject H0
Type 1 error
Step-by-step explanation:
Null hypothesis, H0 : μ = 60000
Alternative hypothesis, H1 : μ > 60000
Decison rule at 5% significance ;
P < α (Reject Null)
P > α (fail to reject Null)
Xbar = 72000 ; std = 9000
Test statistic :
(Xbar - μ) ÷ (std / sqrt(n))
(72000 - 60000) ÷ (9000 / sqrt(25))
12000 ÷ 1800
Test statistic = 6.667
Using the Pvalue calculator from test statistic :
Test statistic = 6.667 ; df = 24 - 1 = 24
Pvalue = 0.00001
Pvalue < α ; Hence, we reject the Null
Type 2 error : This means accepting a Null hypothesis that should be rejected.
Find the midpoint of the line segment with end coordinates of:
(-2,-4) and (-1,-5)
Give coordinates as decimals where appropriate.
Answer:
The midpoint of this line segment is (-1.5, -4.5).
Step-by-step explanation:
In finding the midpoint of a line segment we are actually averaging the x- and y-coordinates of the endpoints:
-2 -1
x-coordinate of midpoint = --------- = -3/2 = -1.5
2
-4 -5
y-coordinate of midpoint = ---------- = -4.5
2
The midpoint of this line segment is (-1.5, -4.5).
Cos Y=?
5/13
5/12
12/13
Answer:
Cos Y = 12/13
Step-by-step explanation:
Recall, SOHCAHTOA.
Cos Y = Adjacent/Hypotenuse
Reference angle = Y
Adjacent = 12
Hypotenuse = 13
Therefore:
Cos Y = 12/13
The circumference of a circle is 119.32 in what is the diameter of the circle?
Answer:
38
Step-by-step explanation:
119.32/3.14 since 3.14 is pi and c=pi*d
Answer:
d≈37.98
Step-by-step explanation:
C=2πr
d=2r
Solving for d
d=C
π=119.32
π≈37.98074
NO LINKS PLEASE
Which algebraic rule represents the pattern in the table?
multiplying each number by 8
Answer: n=m divided by 8
Step-by-step explanation:
15
12
П
[Not drawn to scale)
What is the area of the reduced rectangle?
1. Of the 100 fourth-grade students at Patterson Elementary, 57 are girls. What portion of the fourth-grade class at Patterson elementary is female? Express your answer as a decimal.
Answer:
girls 57/100 57% 0.57
Step-by-step explanation:
boys 43/100 43% 0.43
all the ways
The portion of girls in the fourth grade class will be 57/ 100 and in the decimal form it will be 0.057.
It is given that there are total 100 students at a school in fourth grade out of which 57 are girls.
We have to find out the portion of girls in the fourth grade class and express it to decimal.
What is the decimal fractions ?
Decimal fractions are the fractions in which the denominator must be 10 or a multiple of 10 i.e., 100, 1000, 10000, and so on.
As per the question ;
57 are girls out of total 100 students in a class at a school.
The number of boys will be ;
= 100 - 57 = 43
The no. of girls in fraction form will be ;
= 57 / 100
and in the decimal form it will be ;
= 0.057
The no. of boys in decimal form will be ;
= 47 / 100
= 0.047
Thus , the portion of girls in the fourth grade class will be 57/ 100 and in the decimal form it will be 0.057.
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50 POINTS!! WILL MARK BRAINLIEST!!! Is ΔP'Q'R' a 180° rotation about the origin of ΔPQR? Use the drop-down menus to explain your answer.
Answer:
No that would be a 90 degree
Step-by-step explanation:
solve the equation -3(w+12)=-16
Point Q was rotated about the origin (0,0) by -165
Answer:D
Did it on khan academy
64th term of arithmetic sequence 29,38,47
Answer:
596
Step-by-step explanation:
Each term of the arithmetic sequence is 9 greater than the previous term.
Since the first term is 29, then 29+9 = 38, the second term in the sequence. Likewise, the third term, 47, is 9 greater than the previous term, 38. 47 is also 2(9) greater than the first term, 29.
Therefore, finding the 64th term in the sequence would be the same thing as adding 9 to the first term (29) a total of n-1, or 64-1 times. Instead of adding, one can simply multiply 29 by 63, since 64-1 = 63.
29 + 63(9)
= 29 + 567
= 596
So, the 64th term of the arithmetic sequence is 596.
sin 0
4. Find tan0 .
A.
B.
C.
D.
Answer:
A
Step-by-step explanation:
Answer:
D. 9/40 would be the answer.
Step-by-step explanation:
formula
sinQ= opp/hyp (9/41)
TanQ= opp/adj (which mean 9 /40)
help me dont put links while answering question
Answer:
It's A, 3.82
Step-by-step explanation:
the decimal table goes up to left
Find the value of x.
Answer:
x = 63
Step-by-step explanation:
All triangle angles add up to 180 so:
x + 62 + 55 = 180
x + 117 = 180
x = 180 - 117
x = 63
(2, 4) after a reflection over the x-axis?
Find the degree of the monomial (question in image)
Answer:
The answer to this question is 13
Find the conjugate and product of the following surds
1) i3 + i5
2) i3 + 9
3) - i2 + 1
4) - 3 + iy
Answer:
(1) Conjugate = -i8
(2) Conjugate = -i3+9
(3) Conjugate = i2+1
(4) Conjugate = -3-iy
Step-by-step explanation:
From the question,
Conjugate of a surd is formed by changing the sign between a rational number and a surd in an expression.
The conjugate of a surd is obtained by changing the sign of the surd in the expression.
Given
(1) i3+i5 = i8
Conjugate is -i8
(2) i3+9
Conjugate is -i3+9
(3) -i2+1
Conjugate is i2+1
(4) -3+iy
Conjugate is -3-iy
A restaurant bill is $21. You leave a 15% tip. Which of the following represents the amount a customer pays including the tip of 15% if the bill was dollars?
a. 0.15b
b. 15b
c. b + 0.15b
d. 1.15b
e. 1.015b
f. b + 15/100b
g. b + 0.15
to make 20 pancakes you must use 7 eggs. How many eggs are needed to make 54 pancakes?
Answer:
18.9 eggs
Step-by-step explanation:
54÷20= 2.7
2.7 ×7=18.9
4x-3=9 what does x equal show work
Answer:
x = 3
Step-by-step explanation:
4x - 3 = 9
4x = 9 + 3
4x = 12
x = 12/4
x = 3
Divide. Round your answer to the nearest hundredth.
Answer:
775.64
Step-by-step explanation:
What is the solution of the equation 3/4x + 5 = -9 ?
Answer:
x = -56/3
And that will be ur answer
A plumber charges a customer a one-time service fee of $79, $62 per hour for labor, and a surcharge of $15 per hour due to the call being an emergency.
Write an expression to represent the total charges for the plumber in two different ways. Let h represent the number of hours the job takes.
Enter the correct answers in the boxes.
One Way:
Second Way:
Answer:
One Way: 79 + 62H + 15H = X
Second Way: 79 + ((62 + 15) x H) = X
Step-by-step explanation:
Given that a plumber charges a customer a one-time service fee of $ 79, $ 62 per hour for labor, and a surcharge of $ 15 per hour due to the call being an emergency, to write an expression to represent the total charges for the plumber in two different ways, with H representing the number of hours the job takes, the following equations should be formulated:
79 + 62H + 15H = X
So, for example, if the job had lasted 2 hours, the equation would apply as follows:
79 + 62x2 + 15x2 = X
79 + 124 + 30 = X
233 = X
79 + ((62 + 15) x H) = X
In the case, if the work had lasted 1 hour, the equation would apply as follows:
79 + (62 + 15) x 1) = X
79 + 77 x 1 = X
79 + 77 = X
156 = X
The total charge when there is an emergency is $79 + $77h. The total charge when there is no emergency is $79 + $62h.
There are two ways of representing the total charges of the plumber,one when there is an emergency call and two when there is no emergency call. The total charge a function of the one-time service fee, labor charge and the surcharge.
Total charge when there is an emergency = one-time service fee + labor charge per hour + surcharge per hour
$79 + $62h + $15h
= $79 + $77h
Total charge when there is no emergency = one-time service fee + labor charge per hour
$79 + $62h
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A traveler is trying to determine the fastest way to travel from city A to city Z. The possible travel routes, with the time required for each segment, is shown below.
What is the shortest path and what is the shortest possible time to travel from A to Z? (Round your answer to the nearest whole number.)
Shortest Path Choices: A-B, B-E, E-Z ; A-C, C-Z ; A-B, B-D, D-Z
Answer:
Shortest Path : A-C, C-Z
Shortest possible time = 143
Step-by-step explanation:
P.S - The exact question is -
Given -
T1 = 38
T2 = 52
T3 = 63
T4 = 67
T5 = 91
T6 = 62
T7 = 64
To find - What is the shortest path and what is the shortest possible time to travel from A to Z ?
Proof -
Choices for shortest path is -
Choice 1 : A-B, B-E, E-Z ;
Choice 2 : A-C, C-Z ;
Choice 3 : A-B, B-D, D-Z
Now,
For Choice 1 : A-B, B-E, E-Z
Distance between A-B = T1 = 38
Distance between B-E = T4 = 67
Distance between E-Z = T7 = 64
So,
The distance = 38 + 67 + 64 = 169
Now,
For Choice 2 : A-C, C-Z
Distance between A-C = T2 = 52
Distance between C-Z = T5 = 91
So,
The distance = 52 + 91 = 143
Now,
For Choice 3 : A-B, B-D, D-Z
Distance between A-B = T1 = 38
Distance between B-D = T3 = 63
Distance between D-Z = T6 = 62
So,
The distance = 38 + 63 + 62 = 163
∴ By comparing we get
Shortest Path = A-C, C-Z
Shortest possible time = 143
The shortest path is A→C→Z and the shortest possible time is 143 units option second is correct.
It is given that the traveler is trying to determine the fastest way to travel from city A to city Z.
It is required to find the shortest path and the shortest possible time to travel from A to Z.
What is the shortest path?It is defined as the path in which all the sum of the path will be shortest in a weighted diagram known as the shortest path.
We have the time required to travel from A to B is T1 = 38 units
Similarly, for the path A to C is T2= 52 units
For the path B to D is T3= 63 units
For the path B to E is T4 = 67 units
For the path C to Z is T5 = 91 units
For the path D to Z is T6 = 62 units
For the path E to Z is T7 = 64 units
For the path A→B→E→Z
The total time required = T1+T4+T7
= 38+67+64 ⇒169 units.
For the path A→C→Z
The total time required = T2+T5
= 52+91 ⇒143 units.
For the path A→B→D→Z
The total time required = T1+T3+T6
= 38+63+62 ⇒ 163 units.
Thus, the shortest path is A→C→Z and the shortest possible time is 143 units option seconds is correct.
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In a bag are 3 red, 9 blue, 2 yellow and 3 green marbles. If you draw out a marble at random, what the probability that you will draw a blue marble? P(blue)
Question 2 options:
3/17
9/17
2/17
14/17
Answer:
9/17
Step-by-step explanation:
there are 17 marbles in total 9 of them are blue therefore, 9/17 is the correct answer
2 1/3 x 4 4/5as a fraction
Answer:
11 1/5
Step-by-step explanation:
2 1/3 × 4 4/5
=7/3 × 24/5
=56/5
=11 1/5
A 30°- 60°- 90° triangle is shown below. Find the length of a and b. * leave the answer in simplified radical form*
Step-by-step explanation:
a = 12√3
b = 24
hope this helps
paul wanted .6 of a candy bar. He cut it into 10 equal piees. how many pieces did he take to get .6 of the candy bar
Answer:
6 pieces.
Step-by-step explanation:
A candy bar is a value of 1.
1/10 = 0.1
0.6/0.1 = 6
HELP PLEASEE no links hellpp
Select all the shapes that do not have perpendicular sides.
A. Square
B. Equilateral triangle
C. Rectangle
D. Right triangle
E. Acute triangle
Answer:
B and E
Step-by-step explanation:
perpendicular sides mean they will equal 90 degrees... so all rectangles and squares are perpendicular- a 90 degree triangle also is perpendicular. The Equatorial and the Acute triangle do not have 90 degree angles
The circumference of the base of a
5
-foot-high cylinder is
46
inches. What is the volume of the cylinder?
Answer:
V≈33238.05
Step-by-step explanation:
The circumference of the cylinder base is
= ( 2 )*(pi)*( r ) cm where r = radius of the circular base.
That is ( 2 )(pi)( r ) = ( 44 )cm or
( radius ) = [ (44/((2)(pi)) ] = ( 7.0064 )cm.
I have approximated ( pi ) as ( 3.14 ) for this calculation.
The area of the cylindrical base is ( pi )*( radius )^2
Therefore area of the base
= ( 3.14 )*( 7.0064 )^2 =( 154.1415 )cm squared.
Volume of Cylinder
Volume = Atea of the base multiplied by cylinder height or
= ( 154.1415 ) * ( 7 )
= ( 1079.0 ) cubic centimeters approximately with some slight loss inaccuracy due to rounding of pi.
Lateral Surface Area
The lateral surface area = circumference of the cylindrical base multiplied by the height of the cylinder.
= ( 44 )*( 7 ) = ( 308 ) cm squared
Inherent Assumption
It is assumed that the thickness of the cylinder material is small and the cylinder doesn't overlap the area of the base. If it did, the lateral surface area calculated here might be understated slightly.