There is not enough evidence to conclude that the mean is less than 14 hours, as the p-value of the test is greater than 0.05, using the t-distribution.
What are the hypothesis tested?At the null hypothesis, it is tested if the mean is not less than 14 hours, hence:
[tex]H_0: \mu \geq 14[/tex]
At the alternative hypothesis, it is tested if there is enough evidence that the mean is less than 14 hours, hence:
[tex]H_1: \mu < 14[/tex]
What is the test statistic?The test statistic is given by the equation presented as follows:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
In which the parameters are defined as follows:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.s is the standard deviation of the sample.n is the sample size.In the context of this problem, the values of these parameters are:
[tex]\overline{x} = 13.5, \mu = 14, s = 3, n = 64[/tex]
Hence the test statistic is:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{13.5 - 14}{\frac{3}{\sqrt{64}}}[/tex]
t = -1.33.
P-value and conclusionUsing a z-distribution calculator, with a left-tailed test, as we are testing if the mean is less than a value, with t = -1.33 and 64 - 1 = 63 df, the p-value of the test is of 0.094.
Since the p-value of the test is greater than the significance level of 0.05, there is not enough evidence to conclude that the mean is less than 14 hours.
More can be learned about the t-distribution at https://brainly.com/question/13873630
#SPJ1
What is the equation of the line that passes through the point (8, 2) and has a slope of -3/4
The equation of the line that passes through the point (8, 2) and has a slope of -3/4 is y = -3/4(x-8)+2.
In the given question we have to find the equation of line that passes through the point (8, 2) and has a slope of -3/4.
The given points are (8, 2).
The slope(m) = -3/4
The standard equation of slope intercept form is
y-y(1) = m(x-x(1))
From the question; x(1) = 8 and y(1) = 2.
Putting the value
y-2 = -3/4(x-8)
Add 2 on the both side, we get
y = -3/4(x-8)+2
Hence, the equation of the line that passes through the point (8, 2) and has a slope of -3/4 is y = -3/4(x-8)+2.
To learn more about equation of line link is here
brainly.com/question/21298390
#SPJ1
Find two positive numbers whose difference is 20 and whose product is 429.
The cost to attend a public university in a recent year is $16,241. The circle graph to
the right shows the percentage of that cost for tuition/fees, room, board, and
computer costs. Determine the cost, in dollars, for each category.
The cost of tuition and fees is $.
(Round to the nearest cent as needed.)
The cost of room is $.
(Round to the nearest cent as needed.)
The cost of board is $.
(Round to the nearest cent as needed.)
The computer costs are $
(Round to the nearest cent as needed.)
Cost to Attend a Public University
Tuition/Fees 36.9%
Room 31.5%
Board 24.9%
Computer costs 6.7%
Answer:
Tuition and Fees = $5,992.93
Room = $5,115.92
Board = $4,044.01
Computer Costs = $1,088.15
Solve the equation for y in terms of x
8x=1-3y
enclose numerator and denominators in parentheses
The value of y in the equation in term of x is y= (1-8x)/(3)
What are algebraic equations?An algebraic equation can be defined as a mathematical statement in which two expressions are set equal to each other. The algebraic equation usually consists of a variable, coefficients and constants. For example, 8x = 1-3y is an algebraic equation with two variables x and y with coefficient 8 and 3 respectively and 1 is the constant.
The value of y can there be solved by firstly making 3y the subject of formula
3y= 1-8x
dividing both sides by 3
3y/3= (1-8x)/3
therefore y= (1-8x)/(3)
learn more about algebraic equations from
https://brainly.com/question/2164351
#SPJ1
calculate the distance between two points a(-9,-10) and b(0,-10)
Answer:
The distance between two points on a 2D coordinate plane can be found using the following distance formula. d = √ (x2 - x1)2 + (y2 - y1)2. where (x 1, y 1) and (x 2, y 2) are the coordinates
Step-by-step explanation:
HELP PLS!!
Determine if this table represents a linear function
Answer: im pretty sure the answer is c
Step-by-step explanation:
if the answer is not c im sorry but i hope this helps! Have a good day!
Considering the following statements, what is X → Z? X → Y: If the sum of the interior angles of a shape is 180°, then it's a triangle. Y → Z: If a shape is a triangle, then it has three sides. Question 4 options: A) X → Z: If the sum of the interior angles of a shape is 180°, then it has three sides. B) X → Z: If a shape has three sides, then it's a triangle. C) X → Z: If a shape has three sides, then the sum of the interior angles of the shape is 180°. D) X → Z: If the sum of the interior angles of a shape isn't 180°, then it doesn't have three sides.
The correct statement that is a combination of both conditional statements is; X → Z: If the sum of the interior angles of a shape is 180°, then it has three sides.
How to interpret conditional statements?
A triangle is defined as a three-sided polygon that consists of three edges and three vertices. The most important property of a triangle is that the sum of the internal angles of a triangle is equal to 180 degrees.
We are given the conditional statements as;
X → Y: If the sum of the interior angles of a shape is 180°, then it's a triangle.
Y → Z: If a shape is a triangle, then it has three sides.
Now, transitive property states that “if two quantities are equal to a third quantity, then we can say that all the quantities are equal to each other”.
Thus, applying transitive property to our given statements we can say that; X → Z: If the sum of the interior angles of a shape is 180°, then it has three sides.
Read more about Conditional Statements at; https://brainly.com/question/28600396
#SPJ1
Which of the following examples would be continuous data?
How many people are late boarding an airplane?
The amount of diapers a newborn uses in a day.
The number of television shows on Netflix.
The volume of liquid in a pop can.
The example that would be continuous data is A. The volume of liquid in a pop can.
What is a continuous data?Continuous data is data that has no fixed value. Continuous data includes height, weight, temperature, and length. Some continuous data, such as a baby's weight in its first year or the temperature in a room throughout the day, will change over time.
Discrete data is a type of numerical data that consists of whole, concrete numbers that have specific and fixed data values determined by counting. Continuous data consists of complex numbers and varying data values measured over a specific time period.
In this case, the volume of the liquid is s continuous data.
Learn more about data on:
https://brainly.com/question/17141874
#SPJ1
Which parabola will have one real solution with the line y=x-5?
The equation of the parabola that has one real solution with the line y = x - 5 is y = x² + 7·x + 4
What is the standard form of the equation of a parabola?The standard form of the equation of a parabola is y = a·x² + b·x + c
The equation of the line is; y = x - 5
The parabola that has one real solution with the line is given by the parabola that is equal to both (x - 5) and the equation for the parabola;
Analyzing the quadratic equations of the parabolas with the equation y = x - 5, gives;
y = x² + x - 4 = x - 5x² + x - 4 - x + 5 = 0
x² + 1 = 0
x² = -1
x = ±√(-1) (Complex solution)
y = x² + 2·x - 1 = x - 5x² + x + 4 = 0
The discriminant, b² - 4·a·c is 1² - 4 × 1 × 4 = -15 < 0 (Complex solution)
x² + 6·x + 9 = x - 5x² + 5·x + 14 = 0
The discriminant, b² - 4·a·c is 5² - 4 × 1 × 14 = -31 < 0 (Complex solution)
x² + 7·x + 4 = x - 5x² + 6·x + 9 = 0
The discriminant, b² - 4·a·c is 6² - 4 × 1 × 9 = 0 One real solution;The quadratic equation that gives one real solution with the equation y = x - 5 is therefore;
y = x² + 7·x + 4
Learn more about quadratic equations in algebra here:
https://brainly.com/question/472337
#SPJ1
Find the y intercept and slope of the linear equation
0 = 4.5 - 2y + 4.8x
There are 40 students in class. 12 like pink best, 4 like yellow and the rest blue. What fraction of the class likes blue?
The quotient of 8 and the cube of a number.
By using division, it is obtained that
The Quotient of 8 and cube of 2 is 1
What is division?
Division is the process by which value of single unit can be calculated from the value of multiple unit.
The number to be divided is known as dividend, the number by which the dividend is divided is the divisor, the result obtained is the quotient and the remaining part is the remainder.
There is a well known formula for division.
Divisor x Quotient + Remainder = Dividend.
Let the number be 2
cube of 2 = [tex]2^3 = 8[/tex]
Quotient of 8 and 8 = [tex]\frac{8}{8}[/tex] = 1
The Quotient of 8 and cube of 2 is 1
To learn more about division, refer to the link -
https://brainly.com/question/25289437
#SPJ9
6. MJ is creating a graph of the equation
2x + 4y = -8. Which of the following points will
lie on the line?
a. (2,4)
b. (-2,-1)
c. (2, 1)
d. (4,4)
a musician buys a guitar for $46 and a guitar amplifier. the guitar amplifier costs $1.54 more than$1.26 times the cost of the guitar. how much does the amplifier?
Answer:
$26.33
Step-by-step explanation:
I need answer asap thank you
The measure of ∠QTS = 58°
Given; A triangle QPR
PQ = PR
this means that ∠ Q = ∠ R
and QR = QT this means ∠ R = ∠ T
And ST ║ QR
and QT is the transversal
From the above mentioned information we can conclude that
∠QTS = ∠TQR -------------- 1
Thus since ∠ Q = ∠ R
by using angle sum property of triangle we can conclude that
∠ Q + ∠ R = 116 [ exterior angle sum property ]
2 ∠ Q = 116
∠ Q = 58°
this means ∠ TQR = 58°
And from 1 we know that this angle is equal to angle QTS
Thus ∠QTS = ∠TQR = 58°
To know more about triangle and parallel lines you may visit the link which is mentioned below:
https://brainly.com/question/16701300
#SPJ13
Help Please! Will give brainlest!
Answer:
[tex] = \frac{10}{0.2} = \frac{100}{2} = 50 \\ = \frac{10}{0.02} = \frac{1000}{2} = 500 \\ = \frac{10}{0.002} = \frac{10000}{2} = 5000 \\ \\ [/tex]
hopefully that will help u
Identify the function shown in this graph. 3 17 3 2 12 1 1 2 3 4 5 A. y=-3x +3 B. y = -3x-3 PLEASE HELP ME ANSWER THIS I WILL GIVE 30 POINTS AND A BRAINLYEST
Answer:
It's B. A good way to look at it is the last number. The last number is the y-intercept. Here the y-intercept is -3. That's how I would always figure it out.
Abigail is studying for the school spelling bee. She already knows 150 words from the vocabulary list. Each day, she learns 50 additional words from the vocabulary list.
Which equation can be used to determine the total number of words Abigail knows from the vocabulary list, y, over x days?
A. y = 50x + 150
B. y = 50(x + 150)
C. y = 50x - 150
D. y = 150x + 50
The equation that can be used to determine the total number of words Abigail knows from the vocabulary list, y, over x days is A. y = 50x + 150
What is an equation?An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
In this case, Abigail already knows 150 words from the vocabulary list and each day, she learns 50 additional words from the vocabulary list.
Let x be the number of days.
y = vocabulary list
The equation will be:
y = 150 + 50x
Therefore, the correct option is A.
Learn more about equations on:
brainly.com/question/2972832
#SPJ1
What is the x-intercept of the line with the equation 7x+4y=-28?
A ramp goes from a doorway of a building to the ground. The end of the ramp connected to the doorway is 1 foot above the ground. The distance along the ramp to the building is 5 feet. What is the angle of elevation of the ramp to the nearest degree?
A. 11°
B. 0°
C. 12°
D. 1°
please help?!
The angle of elevation of the ramp to doorway of a building to the ground is found as 11°.
What is described as the trigonometric functions?Simply put, trigonometric functions—also referred to as circular functions—are the functions of a triangle's angle. This means that these trig functions provide the relationship here between angles as well as sides of a triangle. Sine, cosine, tangent, cotangent, secant, and cosecant are the fundamental trigonometric functions.The ramp is the hypotenuse of a right angle triangle formed by the doorway, the ground, and the ramp.
The ramp's elevation angle is the angle Ф it makes with the ground.
Apply the tan function;
Tan Ф = length of doorway/ distance along ramp of building
Tan Ф = 1/5
Ф = 11°
Thus, the angle of elevation of the ramp to doorway of a building to the ground is found as 11°.
To know more about the trigonometric functions, here
https://brainly.com/question/25618616
#SPJ13
i need someone to help me with my math test 24 questions please
Answer:
Add the picturess!!!!!
Step-by-step explanation:
Question
Find the rate if a principal of $1,100 earned $1,089 interest in 12
years.
Answer:
Step-by-step explanation:
Intrest = PRT\100
$1089. =. ($1100x12xR)\100
$1089. = 132R
Divide through by 132.
R. =. 8.25%
Find m<1, m<2 and m<3 86 degree 12 and 3
The angle measures are <1 = 86 degrees, <2 = 94 degrees and <3 = 86 degrees
How to determine the measure of each angle?The possible diagram that completes the question is added as an attachment
From the attached diagram, we have the following representation
<1 + <2 = 180 degrees --- by the theorem of supplementary angles
Also, we have the following angle measure
Given that
<1 = 86 degrees
Substitute the known values in the above equation
So, we have the following equation
86 + <2 = 180
Evaluate the like terms
<2 = 94
Also, we have
<3 = <1 --- by the theorem of vertical angles
Substitute the known values in the above equation
<3 = 86
This is so because <1 = 86 degrees
Hence, the measures of the angles are <1 = 86 degrees, <2 = 94 degrees and <3 = 86 degrees
Read more about angles at
brainly.com/question/7620723
#SPJ1
The population of a city can be modeled using the formula P=100,000e^(0.05t), where t is the number of years after 2012 and P is the city's population. Which of the following equations can be used to find the number of years after 2012 that the population will triple to 300,000?
Group of answer choices
t=3/(0.05e)
t=ln3/0.05
t=(ln200,000)/0.05
t=log3/0.05
The equation that can be used to find the number of years after 2012 that the population will triple to 300,000 is option B t = ln(3) / 0.05
Given,
The population of a city can be modeled using the formula P=100,000e^(0.05t)
t is the number of years after 2012
P is the population of the city
We have to find the equation that can be used to find the number of years after 2012 that the population will triple to 300,000.
Here,
Substitute 300000 in for P and solve for t
300000=100000e^0.05t
Divide both sides by 100000:
We get,
3 = e^0.05t
Multiply both sides by the natural log (ln)
Then,
ln(3) = 0.05t
Now, divide 0.05 on both sides to get t by its self
t = ln(3) / 0.05
Therefore,
The equation that can be used to find the number of years after 2012 that the population will triple to 300,000 is option B t = ln(3) / 0.05
Learn more about population of a city here;
https://brainly.com/question/12494051
#SPJ1
A 150-pound person uses 5.6 calories per minute when walking at a speed of 4 mph. How long must a person walk at:
this speed to use at least 220 calories?
A person must walk for at least
(Round up to the nearest minute.)
minutes in order to use at least 220 calories.
The person must walk 2.61 miles to use 220 calories with speed of 4mph.
What is speed?
The pace at which an object's position changes in any direction is known as its speed. The distance traveled relative to the time it took to travel that distance is how fast something is moving. Due to its lack of magnitude and only having a direction, speed is a scalar quantity.
Here, At 4 mph 5.6 calories are used in = 1 minute
So, at 4 mph, 220 calories are used in,
=> 220/5.6
=> 39.28 minutes
Hence, a person must walk for 39.28 minutes to burn 220 calories.
To find the distance a person should walk, when the speed is 4 miles per hour.
In 60 minutes a person is walking = 4 miles
So, in 39.28 minutes a person will walk = 4/60*39.28
= 2.61 miles
Therefore The person must walk 2.61 miles to use atleast 220 calories.
To learn more about speed refer the below link
https://brainly.com/question/13943409
#SPJ1
2.1 & 2.2 Assessment: Vertex & Standard Form of Quadratic Functions
What is the equation, written in vertex form, of a parabola with a vertex of (1, -9) that
passes through the point (2, -7)?
Work to Support Your Answer (Required for Credit!)
The equation of the parabola, in vertex form is
[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\begin{cases} h=1\\ k=-9 \end{cases}\implies y=a(x-1)^2 - 9\qquad \textit{we also know that} \begin{cases} x=2\\ y=-7 \end{cases} \\\\\\ -7=a(2-1)^2-9\implies 2=a(1)^2\implies 2=a \\\\[-0.35em] ~\dotfill\\\\ ~\hfill {\Large \begin{array}{llll} y=2(x-1)^2 -9 \end{array}} ~\hfill[/tex]
Question 8 (1 point)
The selling price of a widget is $15 and the fixed cost per month is $4,800. The variable cost per widget is $9. Calculate the
contribution margin rate.
0000
b
C
d
Question 8 of 20 | Page 8 of 20
40%
60%
30%
50%
The contribution margin rate is 40%.
What is contribution margin rate?
A company's contribution margin rate is the total revenue minus variable costs divided by the revenue.
First we need to determine the contribution margin in order to calculate the contribution margin rate. There are two approaches to determine the contribution margin.
Contribution Margin = Net Sales Revenue – Variable CostContribution Margin = Fixed Costs + Net IncomeContribution Margin = $15 - $9 = $6
The contribution margin is $6.
Now we will calculate the contribution margin rate using this formula,
Contribution Margin Rate = Contribution Margin [tex]/[/tex] Sales Revenue
Contribution Margin Rate = $6 / $15
= 0.4 * 100
= 40%.
Hence the contribution margin rate is 40%.
To learn more about contribution margin rate from the given link
https://brainly.com/question/24039258
#SPJ1
Customer account "numbers" for a certain company consists of 4 letters followed by 3 single-digit numbers. How many different account numbers are possible if repetitions of letters and digits are allowed?
If the number of different account numbers are possible if repetitions of letters and digits are allowed is:45,697,600,000.
How to determine the total possibilities?Let assume you have 26 choices for each of the first 4 slots and 10 choices for each of the last 5 slots.
Hence,
Total possibilities = (26× 26× 26×26) × (10×10×10×10×10)
Total possibilities = 26^4 × 10^5
Total possibilities = 456976×100000
Total possibilities = 45,697,600,000
Therefore we can assume that the total possibilities is : 45,697,600,000.
Learn more about total possibilities here: https://brainly.com/question/2140875
#SPJ1
9x^7/3x^2=3x^9 true or false
Answer:
False
Step-by-step explanation:
using the rule of exponents
[tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{(m-n)}[/tex]
given
[tex]\frac{9x^7}{3x^2}[/tex]
= [tex]\frac{9}{3}[/tex] × [tex]\frac{x^7}{x^2}[/tex]
= 3 × [tex]x^{(7-2)}[/tex]
= 3[tex]x^{5}[/tex]
Identities and properties of logarithms
[tex](2a^7b^5\cdot 3ab^8)^2\implies \left( 2^2 a^{(7)(2)} b^{(5)(2)} \cdot 3^2 a^2 b^{(8)(2)}\right)\implies 4a^{14}b^{10}\cdot 9a^2b^{16} \\\\\\ (4)(9)a^{14}a^2b^{10} b^{16}\implies 36a^{14+2}b^{10+16}\implies 36a^{16}b^{26}[/tex]