Using the t-distribution, it is found that we do not reject the null hypothesis, which is convincing evidence that the machine is working properly.
What are the hypothesis tested?At the null hypothesis, it is tested if the mean is of 1.5 inches, that is:
[tex]H_0: \mu = 1.5[/tex].
At the alternative hypothesis, it is tested if it is different, hence:
[tex]H_1: \mu \neq 1.5[/tex].
What is the test statistic?The test statistic is given by:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
The parameters are:
[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 this problem, their values are:
[tex]\overline{x} = 1.476, \mu = 1.5, s = 0.203, n = 200[/tex].
Hence, the test statistic is given by:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{1.476 - 1.5}{\frac{0.203}{\sqrt{200}}}[/tex]
[tex]t = -1.672[/tex]
What is the decision?Considering a two-tailed test, as we are testing if the mean is diffrent of a value, with 200 - 1 = 199 df and a standard significance level of 0.05, the critical value is of [tex]|t^{\ast} = 1.972[/tex].
Since the absolute value of the test statistic is less than the critical value, we do not reject the null hypothesis, which is convincing evidence that the machine is working properly.
More can be learned about the t-distribution at https://brainly.com/question/16313918
hellllpppppppp plssssssssss
Answer:
69
Step-by-step explanation:
Find the area of the rectangle. 15 x 3 = 75.
Find the area of the cut-out triangle.
1/2bh
1/2(3(4))
1/2(12)
6
75 - 6 = 69.
Why at is 4x^2 -24x+7=3
Answer:
can you clear more I don't understand
Enter the missing numbers in the boxes to complete the table of equivalent ratios of lengths to widths.
Answer:
for number 6 the width is 24 and the blank after the length of 9 is 12 and after 48 width it is 60. your welcome.
What is the polygon being Rotated to create the blue quilt block pattern
As shown, to obtain the blue quilt block pattern, we have to rotate the parallelogram.
What is parallelogram?A parallelogram is a quadrilateral consisting of pairs of parallel sides.
To obtain the blue quilt block pattern, we have to rotate the parallelogram. This rotation allows the parallelogram to take on a new orientation, and when it is positioned correctly, it creates the blue quilt block pattern. The process of rotating the parallelogram may seem simple, but it is a critical step in achieving the desired quilt design. It requires attention to detail and precision to ensure that the parallelogram is correctly rotated, and the resulting blue quilt block pattern is aligned correctly.
Moreover, the correct rotation of the parallelogram can significantly impact the overall appearance of the quilt, and even a slight misalignment can make a noticeable difference. Therefore, it is important to carefully follow the instructions to rotate the parallelogram to achieve the intended blue quilt block pattern.
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I need help with this so it said 36 is 9 times more than this number
Answer:
36 is 9 times more than 4
Step-by-step explanation:
9 * ?? = 36
to find the unknown number we solve:
36/9 = 4
so 9 times 4 equals 36
means that 36 is 9 times more than 4
HOPE THIS HELPS :)
Answer:
4
Step-by-step explanation:
9x4=36. I corrected both the guys before me who messed up
2. Which of these lines meet at a point and produce square corner or right angle? * A. connecting lines B. parallel lines C. intersecting lines D. perpendicular lines
What is the largest whole number I could be if 9 + I is larger than 28?
Answer:
20 and greater than 20
If you add 9 and 20, you get 29, which is one greater than 28.__________________________________________________________
Questions?Ask me in the comments box.
HELP!!!!!!!!!!!!!!!!!!!!!!
What is the mean and MAD of this data set? (image below)
Answer:
Mean = 8 gerbils
MAD = 4.29 gerbils
Step-by-step explanation:
Find the mean:
Mean= 0+3+6+9+11+13+14 ÷ 7
Mean = 56 ÷ 7
Mean = 8 gerbils
you have to find the distance of each value of gerbil from the mean
8,5,2,1,3,5,6
MAD = 9+6+3+0+2+4+5 ÷ 7
MAD = 30 ÷ 7
MAD = 4.29 gerbils
9. At a high school, 40% of the students play an instrument. Of those students, 20% are freshmen. Of the students who do not play an instrument, 30% are freshmen. What is the probability that a student selected at random is a freshman who plays an instrument?
Answer:
0.6%
Step-by-step explanation:
40% is the percentange of how many students play an instrument. (the whole) 20% is how many freshmen play. (part)
30% are the freshmen. 30% is over 100%.
20 x 100= 2000 and 40 x 30= 1200.
With the answers we got (2000 and 1200) we divide!!
2000÷1200=0.6
Which means the probabillity that the student is a random freshmen is 0.6% :)
Can someone help me?
Answer:
What are you trying to do you have not Explained to us
Step-by-step explanation:
Which statements are true about triangle PRS? Select THREE options.
Which expressions are equivalent to 3(6+b)-(2b + 1)?
Select two answers.
Step 1 - Use the distributive property and pick your first answer
Step 2 - Combine like terms and pick your second answer.
Answer:
18+3b-2b-1
b+17
Step-by-step explanation:
[tex]\mathrm{Using\:the\:distributive\:law}:\quad \:-\left(a+b\right)=-a-b[/tex]
[tex]-\left(2b+1\right)=-2b-1[/tex]
[tex]=3\left(6+b\right)-2b-1[/tex]
[tex]=18+3b-2b-1[/tex]
[tex]\mathrm{Group\:like\:terms}[/tex]
[tex]=3b-2b+18-1[/tex]
[tex]\mathrm{Subtract\:the\:numbers:}\:18-1=17[/tex]
[tex]=3b-2b+17[/tex]
[tex]\mathrm{Add\:similar\:terms:}\:3b-2b=b[/tex]
[tex]=b+17[/tex]
[RevyBreeze]
Please help! I dont know how to do these :(
Answer:
t = 4 s
Step-by-step explanation:
Given function:
[tex]h(t)=-16t^2+48t+64[/tex]
where:
h = height of the ball (in feet)t = time (in seconds)When the ball hits the ground, its height will be 0 ft.
Therefore, set the function to zero and solve for t:
[tex]\begin{aligned}h(t) &=0\\ \implies -16t^2+48t+64 & =0\\ -16(t^2-3t-4)& =0\\ t^2-3t-4 &=0\\ t^2+t-4t-4&=0\\ t(t+1)-4(t+1)&=0\\(t-4)(t+1)&=0\\ \implies t&=4, -1\end{aligned}[/tex]
As time is positive, t = 4 s (only).
Given
[tex]h = - 16 {t}^{2} + 48t + 64[/tex]
Where:- h= Height of ball (given in feet[ft]) and,
t= time (in seconds [s])
To find:-Time = (t)
SolutionWe know,
[tex] \text{When the ball hits the ground its height will be 0}[/tex]
[tex] \therefore h(t) = 0[/tex]
[tex] \implies - 16 t^{2} + 48t + 64 = 0 \\ \\ \fbox{taking - 16 as common multiple} \\ \\ \implies - 16(t {}^{2} - 3t - 4) = 0 \\ \\ \implies t {}^{2} - 3t - 4 = 0 \\ \\ \fbox {factorising the \: equation} \\ \\ \implies t {}^{2} - t - 4t - 4 = 0 \\ \\ \implies t(t + 1) - 4(t + 1) = 0 \\ \\ \implies(t - 4)(t + 1) = 0[/tex]
[tex] \tt{Either} \\ t - 4 = 0 \\ t = \red{ 4 } \\ \\ \tt{Or} \\ t + 1 = 0 \\ t = \red{ - 1}[/tex]
We know, Time cannot be negative.
So, Time (t) = 4 seconds
on a linear graph, the rate of change is called the ____ of a line
Answer:
On a linear graph, the rate of change is called the slope of a line
Step-by-step explanation:
Hope this helps
The complete statement is, on a linear graph, the rate of change is called the slope of a line.
What are lines and their slopes?We know lines have various types of equations, the general type is
Ax + By + c = 0, and the equation of a line in slope-intercept form is
y = mx + b.
Where slope = m and b = y-intercept.
the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.
From the above concepts we now know that, on a linear graph, the rate of change is called the slope of a line.
It can also be defined as, (y₂ - y₁)/(x₂ - x₁).
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Identify any intervals of increase y = -4(x –3) ^2
Answer:
-4
Step-by-step explanation:
<symbol means squared or increase and so does ( )
A street trader spent 550 on x article, each costing (2x -28) find x
Answer:
the x is 538
Step-by-step explanation:
sorry if im not right
Please, I Really Need Help!
Steve bought a used banjo for $395.00 at a music store. He was charged $425.89 for the purchase. Find the sales tax and the sales tax rate.
Sales tax rate is_____%(Round to the nearest tenth of a percent.)
Answer:
3090%
Step-by-step explanation:
425.89 - 395.00 = 30.89
Round to the nearest tenth = 30.9
Convert to a percentage = 3090%
Which statement best describes the "cult of domesticity" that emerged in the late 19th century?
A. A movement to allow women into medical schools.
B. Groups of women who gathered to discuss matters of the home and family.
C A widespread set of values relating to women, their behavior, and their place in the home.
D. The movement to attain voting rights for women citizens.
Answer:
a movement one single movement cultivating one group
Answer: C
Step-by-step explanation:
The triangle on the right is a scaled copy of the triangle on the left. Identify the scale factor. Express your answer as a whole number or fraction in simplest form.
8 8 8/3 8/3
Answer:
Step-by-step explanation:
The sum of two positive integers is 31. If the sum of the squares of these numbers is 625,find the smaller of the numbers.
Step-by-step explanation:
It is given that, the sum of two positive integers is 31 and the sum of the squares of these numbers is 625 and we are to find the smaller of the numbers.
So, let the two positive integers be x and y.
Therefore,
[tex] \\ {\longrightarrow \pmb{\sf {\qquad x + y = 31 \: \: ........ \: (i) }}} \\ \\[/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad x {}^{2} + y {}^{2} = 625 \: ...... \: (ii)}}} \\ \\[/tex]
Now, From the first equation we have,
[tex]\\ {\longrightarrow \pmb{\sf {\qquad x + y = 31 }}} \\ \\ [/tex]
[tex] {\longrightarrow \pmb{\sf {\qquad y = 31 - x \: ...... \: (iii)}}} \\ \\ [/tex]
Now, substituting the value of y in equation (ii) we get :
[tex] \\ {\longrightarrow \pmb{\sf {\qquad x {}^{2} + (31 - x) {}^{2} = 625}}} \\ \\ [/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad x {}^{2} + (31 {}^{2} - 2.x.31 + x{}^{2} ) = 625}}} \\ \\ [/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad x {}^{2} + (961 - 62x + x{}^{2} ) = 625}}} \\ \\ [/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad x {}^{2} + 961 - 62x + x{}^{2} - 625 = 0}}} \\ \\ [/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad 2 x {}^{2} + 336 - 62x = 0}}} \\ \\ [/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad 2 x {}^{2} - 62x + 336 = 0}}} \\ \\ [/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad 2( x {}^{2} - 31 + 168) = 0}}} \\ \\[/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad \frac{2}{2} ( x {}^{2} - 31 + 168) = \frac{0}{2} }}} \\ \\[/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad x {}^{2} - 31 + 168 = 0}}} \\ \\[/tex]
Now using the quadratic formula :
[tex]{\longrightarrow \pmb{\sf {\qquad x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac} }{2a} }}} \\ \\[/tex]
Where,
a = 1b = -31c = 168[tex] \\ [/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad x = \frac{ - (- 31) \pm \sqrt{ {31}^{2} - 4(1)(168)} }{2(1)} }}} \\ \\[/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad x = \frac{ 31 \pm \sqrt{ 961 -672} }{2(1)} }}} \\ \\[/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad x = \frac{ 31 \pm \sqrt{ 289} }{2(1)} }}} \\ \\[/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad x = \frac{ 31 \pm 17 }{2(1)} }}} \\ \\[/tex]
Now, we have two equations,
[tex]{\longrightarrow \pmb{\sf {\qquad x = \frac{ 31 + 17 }{2} \: ... .....\: (iv)}}} \\ \\[/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad x = \frac{ 31 - 17 }{2} ... .....\: (v)}}} \\ \\[/tex]
So, Equation (iv) :
[tex] \\ {\longrightarrow \pmb{\sf {\qquad x = \frac{ 31 + 17 }{2} }}} \\ \\ [/tex]
[tex]\\ {\longrightarrow \pmb{\sf {\qquad x = \frac{ 48 }{2} }}} \\ \\ [/tex]
[tex]\\ {\longrightarrow \pmb{\sf {\qquad x = 24 }}} \\ \\ [/tex]
Now, Equation (v) :
[tex] \\ {\longrightarrow \pmb{\sf {\qquad x = \frac{ 31 - 17 }{2}}}} \\ \\ [/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad x = \frac{ 14 }{2}}}} \\ \\ [/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad x = \: 7}}}\\ \\ [/tex]
So, the value of x is 7 or 24Now, we are to find the value of y.
Substituting the value of x (24) in equation (iii) :
[tex] \\ {\longrightarrow \pmb{\sf {\qquad y = 31 - x \:}}} \\ \\ [/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad y = 31 - 24 \:}}} \\ \\ [/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad y = 7 \:}}} \\ \\ [/tex]
Again, Substituting the value of x (7) in equation (iii) :
[tex]\\ {\longrightarrow \pmb{\sf {\qquad y = 31 - x \:}}} \\ \\ [/tex]
[tex] {\longrightarrow \pmb{\sf {\qquad y = 31 - 7 \:}}} \\ \\ [/tex]
[tex]\\ {\longrightarrow \pmb{\sf {\qquad y = 24 \:}}} \\ \\ [/tex]
Therefore,
The value of y is also 7 or 24.[tex] \\ [/tex]
So, The smaller of the numbers is 7 .
The sum of two positive integers is 31. If the sum of the squares of these numbers is 625, find the smaller of the numbers.
Given : -Sum of two positive numbers = 31Sum of squares of these numbers = 625To Find : - We have to find the smaller of the numbers .Concept : -This question belongs to quadratic equations so we have to find the answer by making equation and solving it .
To Assume : -Let the first no. be x Let the second no. be ySo let's get started with Solution :According to question , sum of two positive integers is 31 . So ,
x + y = 31 --------- ( Equation 1 )According to question , sum of square
of these numbers is 625 . So ,
x² + y² = 625 --------- ( Equation 2 )From equation 1 ( x + y = 31 ) , Value
of x :
x = 31 - yNow , putting value of x in eq. 2 :
x² + ( 31 - x )² = 625 x² + ( 31 )² - ( 2 × 31 × x ) + x² = 6252x² + 961 - 62x = 6252x² - 62x = 625 - 9612x² - 62x = -3362x² - 62x + 336 = 0 2(x² - 31x + 168 ) = 0x² - 31x + 168 = 0Solving it by using middle term
splitting :
x² -24x -7x + 168 = 0x ( x - 24 ) -7 ( x - 24 ) = 0( x - 7 ) ( x - 24 )So ,First number ,
x - 7 = 0x = 7 { Smaller Number }Second Number ,
x - 24 = 0x = 24Verification :According to question ,
Sum of numbers is equal to 31 :
x + y = 317 + 24 = 31L.H.S = R.H.SSum of squares of these numbers is equal to 625 :
x² + y² = 6257² + 24² = 62549 + 576 = 625625 = 625L.H.S = R.H.STherefore , our value for x and y are true. Thus our answer is valid.#[tex] \rm{Keep \: Learning}[/tex]i need help, this is my last question
Answer:
a
Step-by-step explanation:
a maxicool consists of a cone full of ice cream with a hemisphere of ice cream on top. the radius of a hemisphere is 3cm. The height of the cone is 10cm. calculate the total volume of the ice cream round your answer to the nearest tenth
According to the information, it can be inferred that the volume of the ice cream is close to 207.33 cm³
How to calculate the volume of the maxicool?To calculate the volume of the maxicool, we must calculate the volume of the sphere of ice cream, and the volume of the cone that is filled with ice cream.
Volumen of the sphereV = [tex]\frac{4}{3}[/tex] × π × R³
V = [tex]\frac{4}{3}[/tex] × π × 3³
V = 113.09 cm³
Cone volume
V = [tex]\frac{1}{3}[/tex] × π × R² × h
V = [tex]\frac{1}{3}[/tex] × π × 3² × 10
V= 94.24 cm³
Finally we must add both values to know the total volume of the maxicool.
113.09 + 94.24 = 207.33 cm³
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Which of the following points is a solution to the system of inequalities?
6x-2y<10
6x+3y>/=15(greater than or equal to)
A. (1,2)
B. (3,3)
C. (0,5)
D. (2,1)
Answer: C (0,5)
Step-by-step explanation:
So firstly you're going to try to solve the inequality, so what I did first is used the second equation because if I divide both sides by 3, I'm able to get the y by itself:
6x+3y>/=15, 6/3=2, 3/3=1, 15/3= 5
So now its: 2x+y>/=5
now I should get the y by itself by subtracting 2x from both sides to get
y>/=15-2x, now if we wanted to plug it in to the top equation, we could make it as, y=15-2x because the it is GREATER THAN OR EQUAL TO.
so to plug it in to the first equation we get:
6x-2(15-2x)<10,
x<4, to find y we just plug it in to any equation now we have x, so I did
6(3)-2y<10
18-2y<10
-18 -18
-2y<10
divide both sides by -2 (flips the equation sign)
y>4,
So take consider both X and Y values, C would be correct because X is less than four and 0 is less than four, and 5 is greater than four.
Given the function f(x)=2x+1/x and f′(1/x)=f(−x).
Find the value of x∈R correct to 3 significant figures.
x=−2.83
x=0.382
x=−1
x=2.83
I NEED A QUICK ANSWER PLSSS
Naomi wants to take yoga classes. she can take classes at the high school for a one-time fee of $20 plus $10 per class. she can join the local gym for $50 and take classes for $5 per class. which statement is true about the average cost for the two options? the high school option costs less per class for six classes. the gym option costs less per class for six classes. the high school option costs less per class for seven classes. the gym option costs less per class for seven classes.
The gym option costs less per class for six classes(Option B), and the gym option costs less per class for seven (Option D).
How to form mathematical expression from the given description?You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.
Here we're specified that:
For high school classes:
one-time fee of $20 plus $10 per class.For local gym:
she can join for $50 and take classes for $5 per class.For 6 classes:
High school : $20 + $(10 + 10 + 10 + 10 + 10 + 10) = $20 + $10 × 6 = $(20+60) = $80
(since $20 dollar is one time cost, and $10 was price for each class)
Similarly, joining local gym's $50 cost is one time, and rest of $5 is price for each class.
Local gym : $50 + $(5+5+5+5+5+5) = $20 + $5 × 6 = $(20+30) = $50
For 7 classes:
High school : $20 + $(10 + 10 + 10 + 10 + 10 + 10 + 10) = $20 + $10 × 7 = $(20+70) = $90
Local gym : $50 + $(5+5+5+5+5+5+5) = $20 + $5 × 7 = $(20+35) = $55
Thus, the statements which are true about the average cost for the two options is given by: Option B: The gym option costs less per class for six classes., Option D: The gym option costs less per class for seven classes.
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How did Morgan solved the equation x2 - 10x + 2 = 0
Answer
Force a perfect square trinomial on the left side. Take the square root of both sides and solve for
3√ 3, − 5 − 3 √ 3
Step-by-step explanation:
How do you use exponents in a test
Answer:
An exponent is a number that is to a certain value, like 5^2.
The ^2 means multiply by itself by itself ONCE,
so it would be 5x5.
5^3 means multiply it by itself TWO TIMES,
and going on and on.
Let's say you have a test and the question it's asking is to simplify 5^4.
It's 5x5x5x5, multiplying it by itself FIVE TIMES.
Hope this helped!
 Find the length of the third side. If necessary, write in simplest radical form.
IMAGE DOWN BELOW!
SOMEONE PLEASE HELP ME!! ILL GIVE YOU BRAINLIST ANSWER
Answer:
2√6
using pythagoras theorem:
a² + b² = c²
5² + b² = 7²25 + b² = 49b² = 49 - 25b² = 24b = √24b = 2√6Answer:
2√6 unitsStep-by-step explanation:
The length of the third side can be determined using pythogoras theorem. Keep in mind that pythogoras theorem can only be used when finding the missing side length of a right triangle.
[tex]\text{Pythagoras theorem: (Longest side})^{2} = (\text{Leg of right triangle}_{1} ) ^{2} + (\text{Leg of right triangle}_{2} )^{2}[/tex]
In this triangle, we are given that:
The longest side of the triangle is measuring 7 units. A leg of the triangle is measuring 5 unitsSubstitute the measures into the pythogoras theorem:
[tex](7})^{2} = (5 ) ^{2} + (\text{Leg of right triangle}_{2} )^{2}[/tex]
Simplify both sides of the equation:
[tex]\rightarrowtail (7 \times 7}) = (5 \times 5) + (\text{Leg of right triangle}_{2} )^{2}[/tex]
[tex]\rightarrowtail49 = 25 + (\text{Leg of right triangle}_{2} )^{2}[/tex]
Subtract 25 both sides:
[tex]\rightarrowtail49 - 25 = 25 - 25 +(\text{Leg of right triangle}_{2} )^{2}[/tex]
[tex]\rightarrowtail24 = (\text{Leg of right triangle}_{2} )^{2}[/tex]
Square root both sides and simplify:
[tex]\rightarrowtail\sqrt{24} = \sqrt{(\text{Leg of right triangle}_{2} )^{2}}[/tex]
[tex]\rightarrowtail\sqrt{3 \times 2\times 2 \times 2} = \sqrt{(\text{Leg of right triangle}_{2} )^{2}}[/tex]
[tex]\rightarrowtail2\sqrt{3 \tim \times 2} = \text{Leg of right triangle}_{2}[/tex]
[tex]\rightarrowtail\boxed{2\sqrt{6} \ \text{units} = \text{Leg of right triangle}_{2}}[/tex]
A rectangular deck has a length of 12 feet and a perimeter of 36 feet. Include units with your answers.
The deck's width is____________________.
The deck's area is_______________________.
PLS HELPPPPPP
Answer:
The deck's width is 9 feet
The deck's area is 18 feet
Correct po yan
Hope it helps po
Answer:
Deck Width: 6 Feet
Deck Area: 72 Feet Squared
Step-by-step explanation:
[l = length, w = width, f = feet, p = perimeter, a = area]
A = l x w
P = 2l + 2w [l = 12f, p = 36f]
P = 2l + 2w
=> 36f = 2 (12f) + 2w
=> 36f = 24f + 2w
=> 36f - 24f = 2w
=> 12f = 2w
=> 2w/2 = 12f/2
=> W = 6f
Therefore: Width = 6 Feet
A = l × w
A = 12f × 6f
A = 72f^2
Therefore: Area = 72 Feet Squared