Using the z-distribution, it is found that since the test statistic is less than the critical value, there is not enough evidence that the manufacturer needs to recalibrate the machines.
What are the hypothesis tested?At the null hypothesis, it is tested if the machine is calibrated correctly, that is, the mean is of 4 cm, hence:
[tex]H_0: \mu = 4[/tex]
At the alternative hypothesis, it is tested if the machine is not calibrated correctly, that is, the mean is different of 4 cm, hence:
[tex]H_1: \mu \neq 4[/tex]
What is the test statistic?The test statistic is:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.[tex]\sigma[/tex] is the standard deviation of the population.n is the sample size.For this problem, the parameters are given as follows:
[tex]\overline{x} = 3.97, \mu = 4, \sigma = 0.14, n = 81[/tex]
Hence the test statistic is given by:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{3.97 - 4}{\frac{0.14}{\sqrt{81}}}[/tex]
z = -1.93.
What is the critical value and what is the conclusion?We have a two-tailed test, as we are testing if the mean is different of a value, with a significance value of 0.01, hence, using a z-distribution calculator, the critical value is given by:
|z| = 2.575 -> z < -2.575 or z > 2.575.
Hence:
Since the test statistic is less than the critical value, there is not enough evidence that the manufacturer needs to recalibrate the machines.
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A rectangular field is 294 yards in length and 340 yards in width. Find the area of the field in ACRES (1 acre = 43,560 square feet). Round to the nearest tenth of an acre
Answer:
20.7 acres
Step-by-step explanation:
A=wl=340·294=99960
convert 99960 yards to acres
Formula
divide the area value by 4840
= 20.7 acres
Calculate the size of angle ABC in each of these triangles. X B b A a 570 A 95⁰ 55⁰ 60% 5 Calculate the size of angle BCD in each of these diagrams. B b A C 110⁰ C 49⁰ 63° C 9⁰ D A B B 125% 30° 40° 62⁰ 289 b C 6 Three angles of a quadrilateral are 60°, 80° and 110°. How big is the fourth angle? 7 Calculate the sizes of the lettered angles in these quadrilaterals. 35° D 25 C Q 35° 71% D B 172 38° B 132 100⁰ A
Answer:
4.
∠ABC + ∠BCA + ∠CAB = 180
therefore, ∠ABC = 180 - ∠BCA - ∠CAB
using this formula to solve 4a, 4b and 4c:
4a. ∠ABC = 180 - ∠BCA - ∠CAB = 180 - 49 -57 = 26
∠ABC = 26
4b. ∠ABC = 180 - ∠BCA - ∠CAB = 180 - 28 -90 = 62
∠ABC = 62
4c. ∠ABC = 180 - ∠BCA - ∠CAB = 180 - 38 - 25 = 117
∠ABC = 117
5a. In the Triangle ABC, ∠BCA + ∠CAB + ∠ABC = 180
∠BCA = 180 - ∠CAB - ∠ABC = 180 - 55 - 60 = 65
∠BCA = 65
∠BCD + ∠BCA = 180
therefore substituting for ∠BCA in, ∠BCD = 180 - ∠BCA = 180 - 65 = 115
∠BCD =115
5b. In the Triangle ABC, ∠BCA + ∠CAB + ∠ABC = 180
∠BCA = 180 - ∠CAB - ∠ABC = 180 - 125 - 30 = 25
∠BCA = 25
∠BCD + ∠BCA = 180
therefore substituting for ∠BCA in, ∠BCD = 180 - ∠BCA = 180 - 25 = 155
∠BCD = 155
5c. ∠ABD + ∠CBD = 180
therefore ∠CBD = 180 - ∠ABD = 180 - 132 = 48
∠CBD = 48
In the Triangle BCD, ∠CBD + ∠BDC + ∠BCD = 180
therefore ∠BCD = 180 - ∠CBD - ∠BDC = 180 - 48 - 71 = 61
∠BCD =61
6. 4 angles of a quadrilateral = 360
∠a+110+60+80=360
∠a=360-110-60-80=110
∠a = 110
7. four angles of a quadrilateral = 360
using his formula to solve for ∠a, ∠b and ∠c.
for angle a: ∠a+110+95+63=360
∠a=360-110-95-63=92
∠a = 92
for angle b: ∠b+40+62+35=360
∠b=360-40-62-35=223
∠b=223
for angle c: ∠c+100+172+35=360
∠c=360-100-172-35=53
∠c=53
1 a) A restaurant is open 24 hours a day. The manager wants to divide the day into work shifts of equal length. The shifts w=should not overlap. All shifts durations should be a whole number of hours. Describe the different ways this can be done.
b) The manager turns on the restaurant's two neon signs at the same time. Both signs blink as they are turned o. One blinks every 9 seconds. The other sign blinks every 15 seconds. In how many seconds will they blink together again?
The possible answers for the restaurants are Three 8-hour shifts; four 6-hour shifts; six 4-hour shifts.
2. The seconds that they will blink together again is 45 seconds.
How to illustrate the information?Here we have to determine the factors of 24 for the shifts i.e. 1, 2, 3, 4, 6, 8, 12, 24 .
A 1-hour shift does not make much sense; most employers will also not use a 2-hour or 3-hour shift.
Restaurants typically do not use 12-hour shifts either, and employers do not use 24-hour shifts either.
Since both signs blink as they are turned on and one blinks every 9 seconds. The other sign blinks every 15 seconds. The least common multiple is 45.
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The diameter of Jupiter at its equator is approximately 1.43 x 10 to the 5th power kilometers. Write this number in standard notation. An astronomer's infrared telescope is able to detect radiation with a wavelength of 0.000439 meters. Write this number in scientific notation.
The number in standard notation is 143,000.
The number in scientific notation is 4.39 x 10^-4
What is scientific and standard notation?
Scientific notation is used to compress large numbers into smaller numbers. In order to write a number in scientific notation, the number is written as a decimal number, between 1 and 10 and multiplied by a power of 10.
For example:
• The number : 1 x 10² is equivalent to 100
• The number 5 x 10³ is equivalent to 500
When changing a number that is less than 1 to scientific notation, there would be a negative sign before the power.
0.000439 = 4.39 x 10^-4
In order to convert a number from scientific notation to standard notation, multiply the number by its power.
1.43 x 10^5
= 1.43 x 100,000 = 143,000
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50 points help show your work and I’m giving brainliest
The values of the expressions in the table following their evaluation are;
1. 73
2. 97
3. x = 108
4. -13/6
5. 1 and 97
6. 1 and 41
7. The graph of the number line
8. She needs to add 5/36 cup of sugar
The length of the actual is 6 miles
How can the expressions be evaluated?1. The given expression is 5•x + 14 - 6
The value of x at which the expression is evaluated is x = 13
Which gives;
5×13 + 14 - 6 = 73
2. Twelve times six plus 25 can be expressed as 12 × 6 + 25
12 × 6 + 25 = 97
3. x/9 = 12
Multiplying across gives;
x × 1 = 9 × 12 = 108
x = 108
4. The expression is 3/16 - 3/8
= (3 - 2× 3)/16
3/16 - 3/8 = (3 - 2× 3)/16 = -3/16
(3 - 2× 3)/16 = -3/16
5. The prime factors of 97 are; 1 and 97
6. 41 is a prime number.
The factors of 41 are; 1 and 41
7. The graph of x = -1/3
8. Quantity of sugar required = 3¼
Quantity added = 3⅑
Quantity needed = 3¼ - 3⅑ = 5/36
9. 4 inches is equivalent to 2 miles
Therefore;
12 inches = 3 × 4 inches is equivalent to 3 × 2 mi = 6 mi
The length of the actual trail is 6 miles
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Write the property that justifies each mathematical statement. Look carefully!!
1. a(cd) = ac - ad
2. 2x + y = y + 2x
3. — 3(4c) = (- 3 * 4)c
4. 3(4ab) = (4ab)3
5. - 9(3 + 2x) = -9(3) - 9(2x)
6. 3+ (2 + n) = (3 + 2) + n
The properties of algebra used here are
For first point the algebraic properties used is Distributive Properties of Addition Over Multiplication.
For Second point the algebraic properties used is Associative Property of Addition
For third point the algebraic properties used is Associative Property of Multiplication.
For fourth point the algebraic properties used is Commutative Property of Multiplication
For fifth point the algebraic properties used is Distributive Properties of Addition Over Multiplication.
For sixth point the algebraic properties used is Associative Property of Addition
The correct question is Write the property that justifies each mathematical statement. Look carefully!!
1. a(c-d) = ac - ad
2. 2x + y = y + 2x
3. — 3(4c) = (- 3 * 4)c
4. 3(4ab) = (4ab)3
5. - 9(3 + 2x) = -9(3) - 9(2x)
6. 3+ (2 + n) = (3 + 2) + n
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What is ratio in mathematics?
Answer:
Ratio is a comparison between 2 numbers.
Hope this helps :)
The price of one ounce of gold is approximately $1750 US dollars. If the exchange rate is $1 US dollar = $0.85 Euro, how much will gold cost in Euro per gram?
Step-by-step explanation:
mm/kyc-kbiy-rvk come.
Answer:
Step-by-step explanation: Gold will cost €2.06 per gram.
Use the graph of the function to find its domain and range. Write the domain and range in interval notation.
Can someone pls help me with this question
Domain: (-infinity, 5)
Range: [-3, infinity)
Sasha has 520cm of rope she uses 2m 72mm of the rope how many millimeters of rope does Sasha have left?
Accoding to the given statements;
Sasha have left 2480 mm of rope.
According to the given values;
Sasha has 520 cm of rope
She used 2m 72 mm of rope
So, 1 cm = 10mm
And 1m = 1000mm
So, 520 × 10 = 5200mm
2.72× 1000 = 2720mm
5200 - 2720 = 2480mm
Sasha have left 2480 mm of rope.
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What is the vertex for the graph below?
A. (0, 2)
OB. (-2,0)
C. (2,0)
D. (0, -2)
[tex] \bf \implies \:(x,y) = (2,0)[/tex]
Additional information:There are four quadrants in graph:
I quadrant shows (x,y)II quadrant shows (-x,y)III quadrant shows (-x,-y)IV quadrant shows (x,-y)Note that : x axis is also known as abscissa and y axis is also known as ordinate
What is the scale for 3 cm on the map correspond to 120 km in the actual distance?
how do i express the answer in the box. see attachment.
The scale of the map is 1:4000000
Scale of a mapFrom the question, we are to determine the scale of the map
From the given information,
3cm on the map correspond to 120 km
First, we will convert 120 km to cm
120 km = 120000 m
120000 m = 12000000 cm
Thus,
3cm on the map correspond to 12000000 cm
Then,
The scale of the map is
3:12000000
Reducing to the lowest term
1:4000000
Hence, the scale of the map is 1:4000000
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3422 divided by 12. What would the decimal turned into a fraction?
When 3,422 is divided by 12, the decimal that remains when converted to fraction form is 1 / 6
What is the decimal remaining?First, divide 3,422 by 12 to find the result.
Dividing 3,422 by 12 gives:
= 3,422 / 12
= 285.16667
You need to convert 0.16667 to a fraction. When done, this is:
= 16,667 / 100,000
= 2 / 12
= 1 / 6
In conclusion, the decimal when turned to a fraction is 1/6.
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The total arm and blade of a windshield wiper is 15 in. long and rotates back and forth through an angle of 98°. The shaded region in the figure is the portion of the windshield cleaned by the 10-in. wiper blade. What is the area of the region cleaned?
The area of the portion of the windshield cleaned by the 10-in wiper blade is 106.85in² .
We have been provided that the Length of blade is 15 inches and the Angle of rotation = 98°
We are required to calculate the area of the portion of the windshield cleaned by the 10-in wiper blade.
We have to solve this by using area of a sector.
Area of a sector = ½r²θ
where θ is in radians.
So, angle of rotation (98°) must first be converted to radians
Converting 98º to radians, we get
98×π/180 = 49π/90
The area of the region swept out by the wiper blade
= (area of the sector where r = 15 and θ = 49π/90) - (area of the sector where r = (15-10) and θ = 49π/90).
So, Area = ½×15²×49π/0 - ½×5²×49π/90
= ½×49π/90(15²-10²)
= 49π/180× (225 - 100)
= 49π/180 × 125
= 1225π/36
Area = 106.8472in²
=106.85 in²
Hence, the area of the portion of the windshield cleaned by the 10-in wiper blade is 106.85in²
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A frequency table of grades has five classes A B C D F with frequencies of 4,11,14,5 and 3 using percentages what are the relative frequencies
Answer:
A frequency table of grades has five classes A B C D F
Step-by-step explanation:
A frequency table of grades has five classes A B C D F
The top numbers for 8 and 20
Answer:
Step-by-step explanation:
2/4 is equal to 0.5
4/8 is equal to 0.5
10/20 is equal to 0.5
A plane travels 600 mph for the first three hours of the trip. Then, the plane travels at a constant speed of 300 mph for two hours. Calculate the plane's average speed.
A piece of wood is 7 1/4 feet long. How many 2-foot long pieces can Sue cut from the wood?
A. 1
B. 2
C. 3
D. 4
Answer:
7.25 feet/2 feet = 3.625 pieces so you can have 3 pieces of 2 feet each and 1 piece left over that is less than 2 feet.
AB=20
A and B are integers; they may or may not be distinct.
Which of the following could be equal to A-B?
A. 9
B.7
C.6
D.8
Please show me how you figured this out.
Each graph shows a relation. The first and second numbers of each ordered pair in the relation are members of the set of real numbers. In each case, find the domain and the range of the relation and determine whether the relation is a function.
Answer:
Domain: [-2, 2]Range: [-2, 2]Not a functionStep-by-step explanation:
The domain is the set of x values and the range is the set of y values.
For the relation to the function, each value of x must map onto no more than one value of y.
Answer:
Domain: -2≥x≥2
Range: -2≥x≥2
Not a function
Step-by-step explanation:
Margo borrows $1100, agreeing to pay it back with 3% annual interest after 11 months. How much interest
will she pay?
Round your answer to the nearest cent, if necessary.
Answer:
$30.25
Step-by-step explanation:
1100 (.03) [tex](\frac{11}{12})[/tex]
The table shows the total distance of four trails. You want to complete a trail in 1 1/2 hours with an absolute deviation of at most 15 minutes. you hike at a rate of 3 miles per hour. CREATE AN ABSOLUTE VALUE INEQUALITY
Answer:
The answer would be: A = 5 1/4
At the beginning of every soccer practice, Coach Alex has the players warm up and stretch. They do 3 minutes of warm-up exercises for every 2 minutes of stretching.
Answer:
See attached table and graph!
Step-by-step explanation:
Brainly says there was "inappropriate language" in my explanation ( I assure you, there isn't!) So I attached it as an an image below! Hope this helps!
larry has 4 pounds of dirt He gives Curly 1 1/3 pounds of dirt and Moe 2 3/5 of dirt. how much dirt does larry have left.
Larry is carrying 4 pounds of dirt. Moe receives 2 3/5 pounds of dirt, and Curly receives 1 1/3 pounds. Larry has 0.07 pounds of dirt.
Given that,
Larry is carrying 4 pounds of dirt. Moe receives 2 3/5 pounds of dirt, and Curly receives 1 1/3 pounds.
We have to find how much dirt does Larry have
Larry =4 pounds of dirt
Larry=4 pound of dirt-Moe receives 2 3/5 pounds of dirt- curly receives 1 1/3 pounds of dirt.
Larry=4-2 3/5-1 1/3
Larry=4-13/5-4/3
Larry=4-2.6-1.33
Larry=4-3.93
Larry=0.07
Therefore, Larry has 0.07 pounds of dirt.
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Jaspar deposits £2,500 into a savings account at 7% per annum compound interest.
How much does he have in his account after 2 years?
Jasper had 362.25 in his account after two years, per the given statement.
What exactly is compound interest?The interest you earn upon interest is known as compound interest. This may be demonstrated with simple math: if you have $100 and that it earns 5% interest every year, you will have $105 at the end of the first year. You'll have $110.25 by the end of the second year.
According to the given data:Given:
Jaspar deposits £2,500
interest rate = 7
Time = 2 year
Compound interest is interest calculated on the aggregate amount rather than the principle amount alone.
Amount = P(1+r/100)^n
=2500(1+7/100)²
=2500(100+7/100)²
= 2500(107/100)²
= 2862.25
C.I.= Amount - Principal
= 2862.25-2500
= 362.25
According to the given statement jasper have 362.25 in his account after 2 years.
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JK = 5x-8, KL = 7x-12, JL = 52. Find x.
The value of x is 6
What is a line segment?A line segment can be defined as the partition formed by end points of a line.
From the information given, we have that line JL is the line with segments JK, KL and JL and K and the midpoint between J and L
This can be represented as;
JK + KL = JL
Where;
JK = 5x-8KL = 7x-12JL = 52Substitute the values into the formula, we have;
5x -8 + 7x - 12 = 52
Now, collect like terms
12x = 52 + 20
Add like terms
12x = 72
Make 'x' the subject of formula
x = 72/12
x = 6
Thus, the value of x is 6
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Triangle PQR has vertices P (3,8), Q (-5, 7), and R (0, 2). What are the coordinates of the vertices of the image after a reflection in the y-axis?
A) P' (3,-8)
B) P (-3,8)
□C) Q' (5,7)
□D) Q' (5-7)
□E) R¹ (-2,0)
OF) R¹ (0,2)
Triangle PQR has vertices P (3,8), Q (-5, 7), and R (0, 2) then the coordinates of the vertices of the image after a reflection in the y-axis will be:
P'' (-3,-8)
P' (3,8)
Q'' (-5,7)
Q'' (-5,-7)
R'' (2,0)
R'' (0,2).
A reflection around the axis and is given by the following rule:
(x, y) ----> (-x, y)
Applying the rule to each vertices of the reflection y - axis we have:
A) P' (3,-8) ----> P'' (-3,-8)
B) P (-3,8) ----> P' (3,8)
C) Q' (5,7) ----> Q'' (-5,7)
D) Q' (5,-7) ----> Q'' (-5,-7)
E) R¹ (-2,0) ----> R'' (2,0)
F) R¹ (0,2) ----> R'' (0,2)
Therefore,
Triangle PQR has vertices P (3,8), Q (-5, 7), and R (0, 2) then the coordinates of the vertices of the image after a reflection in the y-axis will be:
P'' (-3,-8)
P' (3,8)
Q'' (-5,7)
Q'' (-5,-7)
R'' (2,0)
R'' (0,2).
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Evaluate −y when y=6.
Answer:
-6
Step-by-step explanation:
y=6
-y=-6
What is the range of possible sizes for side x? (Khan)
The range of possible sizes for side x is 2.3 < x < 8.7.
What are the possible sizes for the missing side of a triangle?
Herein we have a triangle, of which two of its sides are known and we can now the set of all possible values by using the law of the cosine:
x² = 3.2² + 5.5² - 2 · 3.2 · 5.5 · cos θ
x = √(40.49 - 35.2 · cos θ)
The cosine is bounded between - 1 and 1, then the possible sizes for the side x are:
2.3 < x < 8.7
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Which rational number equals 0.5?
A. 1/50
B. 1/5
C. 5/10
D. 5/9
Answer:
C. 5/10
Step-by-step explanation:
Using a calculator:
Divide each numerator by each denominator. The answer must be 0.5
A. 1/50 = 0.02
B. 1/5 = 0.2
C. 5/10 = 0.5
D. 5/9 = 0.555...
Answer: C. 5/10
Without a calculator.
0.5 as a fraction is 1/2. Notice the denominator, 2, is twice the numerator, 1.
The answer also must have a denominator that is twice the numerator.
A. 1/50 2 × 1 = 2, not 50
B. 1/5 2 × 1 = 2, not 5
C. 5/10 2 × 5 = 10; this is it.
D. 5/9 2 × 5 = 10, not 9
Answer: C. 5/10
