The null and alternative hypotheses are H0: µ ≥ 1000 and Ha: µ < 1000 respectively.
The evidence to reject the manufacturer's claim is in the rejection region for the test statistic which is z < -1.54.
What is the null and alternative hypothesis?The null hypothesis consist of the inequality sign “equal” sign (“=” or “≥” or “≤”).
Alternative hypothesis is the complement to the null hypothesis.
The claim: The mean life of a certain type of light bulb is at least 1000 hours”. At least in inequality is represented by “≥” sign, it is null hypothesis.
H0: µ ≥ 1000
Alternative hypothesis:
The alternative hypothesis is the complement, that is, the mean life of a certain type of light bulb is less than 1000 hours.
Ha: µ < 1000
As the alternative hypothesis contains “<” sign, the test is left-tailed.
Using α = 0.02, we have critical value from standard table of normal distribution:
z0 = -1.54
Therefore, the rejection region for the test statistic is z < -1.54.
Complete question:
A light bulb manufacturer claims that a certain type of bulb they make has a mean lifetime of 1000 hours and a standard deviation of 20 hours. Each package sold contains 4 of these bulbs. Suppose that each package represents an SRS of bulbs, and we calculate the sample mean lifetime \bar x x ˉ x, with, \bar, on top of the bulbs in each package. 1. What is the null and alternative hypotheses? 2. At a = .02, do you have enough evidence to reject the manufacturer's claim?
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if I have 10 pancakes and I give 5 to jimmy how many pancakes do I have
Answer: 5 is the ancer
Step-by-step explanation:!
Write the equvalent fractions using 35 as a common denominater
The equvalent fractions of 5/7 using 35 as a common denominator is 25/35.
What is a fraction?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.
In this case, it should be noted that the fraction given is 5/7.
The equivalent fraction will be:
= 5/7 × 5/5
= 25/35
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Complete question
Write the equvalent fraction of 2/5 using 35 as a common denominater
The principal P is borrowed at a simple interest rate r for a period of time t. Find the simple interest owed for the use of the money. Assume days in a year.
P = 7000$, r = 7.5%,15 t = months
The simple interest owned for the use of the money is $2625.
What is Simple Interest?
Simple interest is a quick and simple way to figure out how much money has accrued interest. Interest is always applied to the original principal amount and is calculated at the same rate for each period of time. Any bank where we deposit money will pay us interest on that amount. Simple interest is one of many forms of interest that banks charge. Now, let's first clarify what a loan is before delving further into the idea of simple interest. A loan is a sum of money that someone borrows from a bank or other financial institution to cover expenses. Home loans, auto loans, student loans, and personal loans are a few instances of loans.
In the given question we have:
Principal amount = 7000$,
Rate of interest r = 7.5%,
Time t = 15 months;
So, applying the formula to calculate simple Interest:
S.I = [tex]\frac{PRT}{100}[/tex]
S.I = [tex]\frac{7000 \times 7.5 \times 15}{ 12 \times 100}[/tex]
S. I = $2625;
Hence, The Simple Interest owed for the use of the money. is $ 2625.
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What is the intermediate step in the form (x+a)^2=b as a result of completing the square for the following equation?
x^2+32+116=12x
Answer:
Below
Step-by-step explanation:
x^2 + 32 + 116 = 12x 1st intermediate step: put everything on one side
x^2 -12x + 148 = 0 2nd intermediate step : re-arrange with constant on R
x^2 -12x = -148 3 rd intermediate step : take 1/2 of the 'x' coefficient
square it and add to both sides
x^2 -12x + 36 = -148 + 36 4th intermediate step : simplify
(x-6)^2 = -112
Question 8
Angel Garcia deposited his $750 federal income tax refund check into his savings account.
The account pays 5% and he made no other deposits or withdrawals. How much is in the
account after 3 months?
O $937.50
$787.50
O $759.38
1 pt
O $752.12
The amount his account will have after 3 months be $ 759.38.
Given, Angel Garcia deposited his $750 federal income tax refund check into his savings account. The account pays 5% and he made no other deposits or withdrawals.
we have to find the amount in the account after 3 months,
So, the amount he made is,
Amount = 750(1 + 5/100)^0.25
Amount = 759.38
So, the amount his account will have after 3 months be $ 759.38.
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megan left her house and walked 5 blocks north and 4 blocks east to a friends house. From there,she walked 5 blocks north and 6 blocks west to school for volleyball pratice. Describe where the school is in the relation to Megan's house in words and using notations
Answer: School is 10 blocks north and 2 blocks west of Megan's house. A straight line from Megan's house to school is 10.2 blocks long, Northwest
Step-by-step explanation:
5 blocks north, then 4 east, then 5 north is a total of 10 blocks north. The last turn is 6 blocks west. So she walks 4 blocks west to get her back to due north of her house then an additional 2 more blocks west.
Use the pythagorean theorem to calculate the straight line if Megan were able to take a straight path there:
find the slope of (-4,4) (0,0)
The slope for the following question is = 4.
What is slope?Slope is used to describe the steepness of a line. The definition of slope is the rise of a line over the run of a line, or the change in the vertical direction (y) over the change in the horizontal direction (x). When one thinks of skiing down a hill or climbing up a mountain, the angle at which they are descending or ascending is the slope. Sometimes the slope can be fairly flat or very steep depending on what it is.The slope of an object indicates how steep it is. Slope knowledge is crucial for daily decision-making. For instance, understanding a roof's slope enables builders to determine whether specific construction materials are required for shingling projects. Since there must be sufficient grade for water to pass through the tile, slope is crucial in agriculture when tiling a field. Slope can also be calculated using elevation points on a GIS, a type of digital map that can highlight areas with sharp elevation changes in the ground.acc to our question-
the two y's are 0 and 4 so its 0-4then the two x's are0 and one so its 0-10-4/0-1 is -4/-1 which when simplified the negatives cancel out leaving you with a positive 4hence the value of slope=4
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How many cubic inches are in an aluminum can with a 2 3/5 diameter and 5 1/4 in height?
According to the volume of cylinder formula, an aluminum can with a 2 3/5 diameter and 5 1/4 in height are in 27.86 cubic inches.
Volume of Cylinder
The formula to calculate the volume of the cylinder is
Volume of a cylinder = πr²h cubic units.
where
r refers the radius
h refers the height.
Given,
Here we have an aluminum can with a 2 3/5 diameter and 5 1/4 in height and now we have to find the volume in cubic inches.
While we looking into the given question, we know the following values,
Diameter = 2 3/5
When we simplify it, then we get the value of diameter as
d = 13/5 or 2.6
Similarly, the value of height is rewritten as,
h = 5.25
So, based on the formula of volume of cylinder,
We get the value as,
=> V = π x (2.6/2)² x 5.25
Apply the value of π as 3.14, then we get,
=> V = 3.14 x (1.3)² x 5.25
=> V = 16.485 x 1.69
Therefore, the volume in cubic inches is 27.86 cubic inches.
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Solve for x. Round to the nearest tenth, if necessary.
Answer:
46.9
Step-by-step explanation:
sin54=x/58
58sin54=46.922
Brainliest if correct 5 points
Answer:
NOT CONGRUENT
Step-by-step explanation:
There are several types of congruence:
ASA - Angle Side Angle
AAS - Angle Angle Side
HL - Hypotenuse Leg
This image shows two triangles which have 2 congruent sides and one congruent angle.
Is it ASA?
There is only one congruent angle, so this cannot be congruent by ASA
Is it AAS?
By the same reasoning, it cannot be congruent by AAS.
Is it HL?
Although there are 2 congruent sides, neither one is the hypotenuse. Is is not congruent by HL.
There is no such thing as SSA congruence, because it is actually possible to have 2 non-congruent triangles who have 2 congruent sides and 1 congruent angle. Therefore, these are NOT CONGRUENT
Find the equation for a polynomial f(x) that satisfies
▪ Degree 5
▪ Root of multiplicity 2 at x =
= -4
▪ Root of multiplicity 1 at x = -1
■ Root of multiplicity 2 at x = -2
▪y-intercept of (0, 128)
The polynomial function that has the degree of 5 is written as f(x) = 2x⁵ + 26x⁴ + 128x³ + 296x² + 320x + 128
Polynomial function:
The equations formed with variables, exponents and coefficients are known as the polynomial equations. And it can have different exponents, where the higher one is called the degree of the equation.
Given,
Here we have the following things,
Degree = 5
Root of multiplicity 2 is x = -4
Root of multiplicity 1 at x = -1
Root of multiplicity 2 at x = -2
y-intercept of (0, 128)
Here we need to find the polynomial equation of the function.
According to the given roots of multiplicity, we have the factors of the polynomials are,
=> (x + 4)² (x + 1) (x + 2)²
So, the general form of the polynomial function can be written as,
=> f(x) = A (x + 4)² (x + 1) (x + 2)²
In order to find the 5 degree polynomial function, we have to calculate the value of A.
To Find the value of A, we have to apply the y - intercept point on the equation then we get,
=> 128 = A (0 + 4)² (0 + 1) (0 + 2)²
=> 128 = A (4)² (1) (2)²
=> 128 = A (16 x 1 x 4)
=> 128 = 64A
=> A = 2
Now, the polynomial function is written as,
=> f(x) = 2 (x + 4)² (x + 1) (x + 2)²
When we expand this one then we get,
=> f(x) =2 [x⁵ + 13x⁴ + 64x³ + 148x² + 160x + 64]
Therefore, the resulting polynomial function is,
=> f(x) = 2x⁵ + 26x⁴ + 128x³ + 296x² + 320x + 128
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sorry i put the wrong pic in here my question i do need help so im putting in more point
Answer:
A. (10x^2) / (5x + 4y)
B. (8xy) / (4y + 5x)
Step-by-step explanation:
A. Factor the numerator and denominator, then cancel out like terms
(10x^2(2a + 3b)) / (2a(5x + 4y) + 3b(5x + 4y))
(10x^2(2a + 3b)) / ((2a + 3b)(5x + 4y))
(10x^2) / (5x + 4y)
B. Factor the numerator and denominator, then cancel out like terms.
(8xy(3p - 4q)) / (3p(5x + 4y) - 4q(4y + 5x))
(8xy(3p - 4q)) / ((3p - 4q)(4y + 5x))
(8xy) / (4y + 5x)
Please I need help I don’t understand
For give expression Ben's work is correct.
In this question, Ben and Jerry both simplified the expression √24x⁵y³
where x > 0, y > 0
We need to determine which student is correct.
First we simplify given expression.
√24x⁵y³
= √(2)(2)(2)(3)(x)(x)(x)(x)(x)(y)(y)(y)
= √(2²)(2)(3)(x²)(x²)(x)(y²)(y)
= √(2²) * √(2) * √(3) * √(x²) * √(x²) * √(x) * √(y²) * √(y) ...(seperate the radical symbol)
= 2 * √(2) * √(3) * x * x * √(x) * y * √(y) ...........exponent rule
= 2x²y√(2)(3)(x)(y) ........(combine terms with same powers)
= 2x²y √6xy
So, Ben's work is correct.
We observe that by rule of exponents, the fourth step in Jerry's work is incorrect.
Therefore, Ben's work is correct.
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if ally worked 20.56 hours , and makes $10 an hour . how much is pay check? show work.
Answer:
$205.6
Step-by-step explanation:
20.56hours × $10/hour = $205.6
Please help I was sick and missed out on class.Thank you
Answer:
slope = (1/3)
Step-by-step explanation:
(-8, 2), (-11, 3)
(x₁, y₁) (x₂, y₂)
m = slope
y₂ - y₁ 3 - 2 1 1
m = ------------ = -------------- = ----------- = -------
x₂ - x₁ -11 - (-8) -11 + 8 3
I hope this helps!
There are 7 highway routes from City A to City B, 8 highway routes from City B to City C, and 10 highway routes from City
C to City D. How many different highway routes are there if you want to travel to City A, B, C, and D in that order?
highway routes from City A to City D.
There are how many highway routes from city a to city d
The number of highway routes from A to D is 560
Number of highway routes from A to B = 7 highways
Number of highways routes from B to C = 8 highways
Number of highways routes from C to D = 10 highways
Number of routes from A to D = Number of highway routes from A to B × Number of highways routes from B to C × Number of highways routes from C to D
Here we have to use multiplication
Substitute the values in the equation
Number of routes from A to D = 7 × 8 × 10
= 560 highways
Hence, the number of highway routes from A to D is 560
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Simplify: (x^5) ^5?
Answer:
x^25
Step-by-step explanation:
The simplified expression is x²⁵.
Given is an expression (x⁵)⁵, we need to simplify the expression.
To simplify the expression (x⁵)⁵, we need to apply the exponentiation rules.
The exponent outside the parentheses should be distributed to each term inside the parentheses.
In this case, the exponent outside is 5, and the term inside the parentheses is x⁵.
To distribute the exponent, we multiply the exponents together.
Applying the rule, we get:
(x⁵)⁵ = x⁵⁽⁵⁾ = x²⁵
Therefore, the simplified expression is x²⁵.
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What’s the answer by chance
The sales tax rate of the cocktail table is 0.055
What is sales tax ?A sales tax is a consumption tax imposed by the government on the sale of goods and services
The cocktail table sold for $250 and the sales tax amount was $13.75. The sales tax rate can be calculated as follows:
Sales tax = list price * sales tax rate
Therefore,
sale tax rate = sales tax / list price
sales tax = $13.75
list price = $250
sale tax rate = 13.75 / 250
sales tax rate = 0.055
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Find the equation (in slope-intercept form) of the line with the given slope that passes through the point with the given coordinates.
slope: −43, ordered pair: (0,−25)
Answer:
[tex] \huge{ \bold{y = - 43x - 25}}[/tex]
Step-by-step explanation:
Equation of a line in slope-intercept form is given by
[tex]y = mx + c[/tex]
where
m is the slope
c is the y intercept
From the question
m = - 43
In order to find c we substitute the point (0,−25) into the equation y = mx + c
That's
[tex] - 25 = - 43(0) + c \\ - 25 = 0 + c \\ c = - 25[/tex]
We now substitute m and c into the equation
We have the final answer as
[tex] \bold{y = - 43x - 25}[/tex]
Hope this helps you
The amount of money that Ryan earns is directly proportional to the number hours that he works. How much does Ryan earn per hour?
The earnings of Rayan per hour is $5 per hour
The first point = (1, 5)
The second point = (2, 10)
The slope of the line is the change in y coordinates with respect to the change in x coordinates of the function
The slope of the line m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Where m is the slope of the line
[tex](x_1,y_1)[/tex] is the coordinates of the first point
[tex](x_2,y_2)[/tex] is the coordinates of the second point
Substitute the values in the equation
The slope of the line m = (10-5) / (2-1)
Subtract the terms
= 5 / 1
= $5 per hour
Hence, the earnings of Rayan per hour is $5 per hour
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Which pair of lines are perpendicular?
A. y = -8 and y = 2
B. x = 4 and y = -1
C. x-y = 7 and y = x + 3
D. y = -4x + 1 and 8x + 2y = -10
Applying the slope-intercept form for perpendicular lines, we find out that no given pair of lines are perpendicular.
There are 4 different pairs of lines given to us.
We have to find out the pair of lines that are perpendicular to each other.
We know that the general equation of a line in slope-intercept form is represented as -
y = mx + c --- (1)
where
(x, y) = coordinates of the lines
m = slope of the line
c = y-intercept
It is also known to us that for two lines to be perpendicular the product of their slope must be equal to -1.
A. y = -8 and y = 2
Comparing these two lines to the general equation of a line in equation (1), we see that the slope of both these lines is equal to 0.
So, these two pair of lines are not perpendicular.
B. x = 4 and y = -1
Comparing these two lines to the general equation of a line in equation (1), we see that the slope of both these lines is equal to 0.
So, these two pair of lines are not perpendicular.
C. x - y = 7 and y = x + 3
Now, x - y = 7
=> -y = 7 - x
=> y = x - 7
Comparing this to the equation (1), we have slope of the line, m = 1.
Also, y = x + 3
Comparing this to the equation (1), we have slope of the line, m = 1.
We see that the product of the slope of these pair of lines is not equal to -1.
So, these two pair of lines are not perpendicular.
D. y = -4x + 1 and 8x + 2y = -10
Now, y = -4x +1
Comparing this to the equation (1), we have slope of the line, m = -4.
Also, 8x + 2y = -10
=> 2y = -8x - 10
=> y = -4x - 10
Comparing this to the equation (1), we have slope of the line, m = -4.
We see that the product of the slope of these pair of lines is not equal to -1.
So, these two pair of lines are not perpendicular.
Thus, according to the slope-intercept form for perpendicular lines, we find out that no given pair of lines are perpendicular.
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For the function f(x) = x + 7, construct and simplify the difference quotient
f(x+h)-f(x) Over h
H
The value of f(x+h)-f(x) = h.
Given function:
f(x) = x + 7
difference quotient = f(x+h) - f(x)
= (x+h) - 7 - (x - 7)
= x + h - 7 - x + 7
= x - x + 7 - 7 + h
= 0 + 0 + h
= h
Therefore the value of f(x+h)-f(x) = h.
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Lisa wants to buy a hat that costs 114 Argentine Pesos.She has $25.Does she have enough money to buy the hat?
Answer:
150
Step-by-step explanation:
I had this on one of my quizzes, hope this helps :D
can someone help with this
Answer:
z=38
Step-by-step explanation:
Using the fact that angles on a straight line add to 180°, the interior angles of the triangle are 86°, (180-3z)°, and (180-4z)°.
Angles in a triangle add to 180°, so:
[tex]86+180-3z+180-4z=180 \\ \\ 86-3z+180-4z=0 \\ \\ 266-7z=0 \\ \\ 7z=266 \\ \\ z=38[/tex]
X-y=3 determine the x and y intercepts of linear equations
Answer:
y-intercept (0,-3)
x-intercept (3,0)
Step-by-step explanation:
Let x = 0
-y =3
y = -3
(0,-3)
Let y = 0
x = 3
(3,0)
write an equation in point slope form of the line through point J(4,1) with slope -4
Answer:
y - 1 = - 4(x - 4)Step-by-step explanation:
Point- slope form:
y - y₁ = m(x - x₁), where m- the slope, (x₁, y₁) - the point on the lineGiven:
m = - 4,Point J(4, 1)Substitute into equation to get the line:
y - 1 = - 4(x - 4)Help find intercept and the slope of the line?
slope= -3/2, y-intercept=8
y=mx+b m is the slope while b is the y-inteecept
The median monthly rent in 2005 was $694 and $810 in 2010. What was the percent increase in the median monthly rent prices from 2005 to 2010? Round to the nearest tenth of a percent.
The percent increase in the median monthly rent prices is 14.3%
How to calculate the percentage?From the information, the median monthly rent in 2005 was $694 and $810 in 2010.
The increase in the amount will be:
= $810 - $694.
= $116
The percent increase in the median monthly rent prices from 2005 to 2010 will be:
= Increase in amount / Old rent × 100
= 116/810 × 100
= 14.3%
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cannot decide which of two washing machines to buy. The selling price of each is $550. The first is marked down by 40%. The second is marked down by 30% with an additional 10% off. Find the sale price of each washing machine. Use pencil and paper. Explain why should buy the first washing machine rather than the second if the machines are the same except for the selling price.
The selling price of the two washing machies are
first washing machine is $330second washing machine is $346.5I will buy the first because it has a lower selling price
How to determine the best washing machine to buyThe question is a percentage problem
The first washing machine has a mark down by 40%
= 40 percent
= 40 / 100
= 0.4
marked down factor = 1 - 0.4 = 0.6
selling price of the first machine = 550 * 0.6 = 330
the second washing machine has mark down of 30%
30% = 0.3
marked down factor = 1 - 0.3 = 0.7
selling price of the second washing machine at first mark down
= 550 * 0.7 = 385
marked down again
10% = 0.1
the factor here is = 1 - 0.1 = 0.9
selling price of the second washing machine at second mark down
= 385 * 0.9 = 346.5
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77 is 0.7% of what number? Use pencil and paper. Would you expect the answer to be a lot less than 77, slightly less
77, slightly greater than 77, or a lot greater than 77? Explain.
77 is 0.7% of 11000
this number is a lot greater than 77.
Let 77 is 0.7% of m
0.7 percent of m = 77
(0.7/100) * m = 77
m = 77 * (100/0.7)
m = 11000
Therefore, 77 is 0.7% of 11000
this number is a lot greater than 77.
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