The difference of the equation is A = ( x² - 3x - 12 ) / ( x + 3 ) ( x - 5 ) ( x + 7 )
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
Let the first equation be P = x / ( x² - 2x - 15 )
Let the second equation be Q = 4 / x² + 2x - 35 )
Now , A = P - Q
On simplifying , we get
A = x / ( x² - 2x - 15 ) - 4 / x² + 2x - 35 )
Taking the LCM , we get
A = x ( x + 7 ) - 4 ( x + 3 ) / ( x + 3 ) ( x - 5 ) ( x + 7 )
A = x² + 7x - 4x + 12 / ( x + 3 ) ( x - 5 ) ( x + 7 )
A = ( x² - 3x - 12 ) / ( x + 3 ) ( x - 5 ) ( x + 7 )
Therefore , the value of A is ( x² - 3x - 12 ) / ( x + 3 ) ( x - 5 ) ( x + 7 )
Hence , the equation is A = ( x² - 3x - 12 ) / ( x + 3 ) ( x - 5 ) ( x + 7 )
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A real estate purveyor purchases a 60{,}00060,00060, comma, 000 square foot \left(\text{ft}^2\right)(ft 2 )(, start text, f, t, end text, squared, )warehouse and decides to turn it into a storage facility. The warehouse's width is exactly \dfrac 2 3 3 2 start fraction, 2, divided by, 3, end fraction of its length. What is the warehouse's width? Round your answer to the nearest foot.
Answer:
200 feet
Step-by-step explanation:
Area of the warehouse [tex]=60,000$ ft^2[/tex]
Let the length of the warehouse=l
The warehouse's width is exactly [tex]\dfrac23[/tex] of its length
Therefore: Width of the warehouse[tex]=\dfrac23l[/tex]
Area =Length X Width
Therefore:
[tex]\dfrac23l*l=60000\\$Cross multiply\\2l^2=60000*3\\2l^2=180000\\$Divide both sides by 2\\2l^2 \div 2=180000 \div 2\\l^2=90000\\l^2=300^2\\$Length, l=300 feet\\Recall: Width =\dfrac23l\\$Therefore, Width of the warehouse=\dfrac23*300=200$ feet[/tex]
of 5 points)
2. The two figures are similar. Write the similarity statement. Justify you
37.5
(Score for Question 2:
45
Y
40
30
Z
Answer:
Answer:
f\left(x\right)=x^3-x
Step-by-step explanation:
On a coordinate plane, triangle A B C has points (negative 9, 3), (negative 9, 6), (0, 3) and triangle A double-prime B double-prime C double-prime has points (3, negative 1), (3, negative 2), and (0, negative 1).
Which transformations could be performed to show that △ABC is similar to △A"B"C"?
a reflection over the x-axis, then a dilation by a scale factor of 3
a reflection over the x-axis, then a dilation by a scale factor of One-third
a 180° rotation about the origin, then a dilation by a scale factor of 3
a 180° rotation about the origin, then a dilation by a scale factor of One-third
Answer: D 180 degrees rotation about the origin.then a dilation by a scale factor of one-third.
Step-by-step explanation:
A( -9,3) B(-9,6) C (0,3)
After a rotation of 180 degrees you will have the new points as
A (9,-3) B( 9,-6) C (0, -3)
The you after dilating it by a scale factor of 1/3
you will get the coordinates
A ( 3,-1) B( 3,-2) C(0,-1)
which match is what was given in the question.
Answer:
a 180° rotation about the origin, then a dilation by a scale factor of One-third
Step-by-step explanation:
took the test
Which equation can be used to solve for b?
B
5 cm
С
10 cm
b
30
A
O tan(30)=5/b
O tan(30)=b/5
O tan(30)=10/b
O tan(30)=b/10
Answer:
The answer is option 1.
Step-by-step explanation:
You have to apply Tangent Rule, tanθ = opposite/adjacent:
[tex] \tan(θ) = \frac{oppo.}{adj.} [/tex]
[tex]let \: oppo. = 5 \\ let \: adj. = b \\ let \: θ = 30[/tex]
[tex] \tan(30) = \frac{5}{b} [/tex]
The correct answer is option (A) tan(30)=5/b
Tangent functionThe tangent function is one of the main six trigonometric functions and is generally written as tan x. It is the ratio of the opposite side and the adjacent side of the angle in consideration in a right-angled triangle.How to solve this problem?The steps are as follow:
The right angle triangle is given whose sides are as follow:AB = 10 cm
BC = 5 cm
AC = b cm
To find the tan(30) we will use following formula:tan(x) = opposite side / adjacent side
tan(30) = BC / AC
tan(30) = 5 / b
So, the correct answer is option (A) tan(30)=5/b
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Find the equations for a conical helix that has a radius of 8, a height of 12 and does exactly two complete revolutions (starting at the xy-plane). Include a plot of your conical helix.
Answer:
The equation are
[tex]x =\frac{ 12-z }{h} 8 cos (2 z)[/tex]
[tex]y = \frac{12-z }{12} 8sin (2z)[/tex]
z = z
Step-by-step explanation:
From the question we are told that
The radius of the conical helix is [tex]r= 8[/tex]
The height of the conical helix is [tex]h = 12[/tex]
The angular frequency is [tex]w = 2[/tex]
The plot of the conical helix is shown on the first uploaded image
Generally the parametric equation of a conical helix is mathematically represented as
for x -axis
[tex]x =\frac{ h-z }{h} r cos (wz)[/tex]
substituting values
[tex]x =\frac{ 12-z }{h} 8 cos (2 z)[/tex]
for y-axis
[tex]y = \frac{h-z }{h} rsin (wz)[/tex]
substituting values
[tex]y = \frac{12-z }{12} 8sin (2z)[/tex]
for z-axis
z = z
Solve for n.
11(n – 1) + 35 = 3n
n = –6
n = –3
n = 3
n = 6
Answer:
-3 =n
Step-by-step explanation:
11(n – 1) + 35 = 3n
Distribute
11n -11 +35 = 3n
Combine like terms
11n +24 = 3n
Subtract 11n from each side
11n +24 -11n = 3n -11n
24 = -8n
Divide each side by -8
24/-8 = -8n/-8
-3 =n
Answer: n=-3
Step-by-step explanation:
11n-11+35=3n
24=-8n
n=-3
The radius of a circle is 5 cm. Find its area to the nearest tenth.
Answer:
78.5 cm^2
Step-by-step explanation:
The area of a circle is found by
A = pi r^2
A = pi (5)^2
A = 25pi
Letting pi = 3.14
A = 25(3.14)
A =78.5 cm^2
Letting pi be the pi button
A =78.53981634
Rounding to the nearest tenth
78.5
Answer:
78.5 cm²
Step-by-step explanation:
The area of a circle can be found using the following formula.
a=πr²
We know the radius of the circle is 5 centimeters.
r=5
Substitute 5 in for r.
a=π(5²)
Evaluate the exponent. 5² is equal to 5*5, which equals 25.
a=π(25)
Multiply 25 and pi
a=78.5398163397
Round to the nearest tenth. The 3 in the hundredth place tells use to leave the 5 in the tenths place as is.
a≈78.5
Add appropriate units. Area always uses units², and the units in this case are centimeters.
a≈78.5 centimeters²
The area of the circle is about 78.5 square centimeters.
There is a bag with only red marbles and blue marbles. The probability of randomly choosing a red marble is 2 9 . There are 45 marbles in total in the bag and each is equally likely to be chosen. Work out how many red marbles there must be
Answer:
10 red marbles
Step-by-step explanation:
Total= 45 marbles
Probability of red= 2/9
Number of red= 45*2/9= 10
Each roll of tape is 30.5 feet long. A box contains 454 rolls of tape. How many yards are there in total
Answer:
Answer: 4615.66667
Steps: 1 foot=0.33333
total feets=30.5×454=13847
13847 feets=46.1566667 yards
can someone please help meee!???
In a sample of seven cars, each car was tested for nitrogen-oxide emissions (in grams per mile) and the following results were obtained. 0.10 0.13 0.16 0.15 0.14 0.08 0.15 (a) Construct a 99% confidence interval for the mean nitrogen-oxide emissions of all cars. (b) If the EPA requires that nitrogen-oxide emissions be less than 0.165 g/mi, based on the 99% confidence interval in (a),
The question is incomplete. Here is the complete qeustion.
In a sample of seven cars, each car was tested for nitrogen-oxide emissions (in grams per mile) and the following results were obtained: 0.10 0.13 0.16 0.15 0.14 0.008 0.15
(a) Construct a 99% confidence interval for the mean nitrogen-oxide emissions of all cars.
(b) If the EPA requires that nitrogen-oxide emissions be less than 0.165 g/mi, based on the 99% confidence interval in (a), can we safely conclude that this requirement is being met?
Answer: (a) 0.089 ≤ μ ≤ 0.171
(b) No
Step-by-step explanation:
(a) To determine the confidence interval, first calculate the mean (X) and standard deviation (s) of the sample
X = [tex]\frac{0.1+0.13+0.16+0.15+0.14+0.08+0.15}{7}[/tex]
X = 0.13
s = [tex]\sqrt{\frac{(0.1-0.13)^{2} + (0.13 - 0.13)^{2} + ... + (0.15 - 0.13)^{2}}{7-1} }[/tex]
s = 0.029
The degrees of freedom is
N - 1 = 7 - 1 = 6
And since the confidence is of 99%:
α = 1 - 0.99 = 0.01
α/2 = 0.01/2 = 0.005
The t-test statistics for [tex]t_{6,0.005}[/tex] is 3.707
(Value found in the t-distribution table)
Now, calculate Error:
E = [tex]t_{6,0.005}[/tex] . [tex]\frac{s}{\sqrt{N} }[/tex]
E = 3.707. [tex]\frac{0.029}{\sqrt{7} }[/tex]
E = 0.041
The interval will be:
0.13 - 0.041 ≤ μ ≤ 0.13+0.041
0.089 ≤ μ ≤ 0.171
(b) No, because according to the interval, the nitrode-oxide emissions range from 0.089 to 0.171, which is greater than required by EPA.
i have a problem on statistics
5. Data on household vehicle miles of travel (VMT) are compiled annually by the Federal Highway Administration and are published in National Household Travel Survey, Summary of Travel Trends. Independent random samples of 15 midwestern households and 14 southern households provided the following data on last year’s VMT, in thousands of miles. At the 5% significance level, does there appear to be a difference in last year’s mean VMT for midwestern and southern households? Use both p-value and critical value approach. Assume population variance to be equal
Midwest
16.2 , 14.6 , 11.2 , 24.4 , 9.4 12.9 , 18.6 , 16.6 , 20.3 ,15.1 , 17.3 , 10.8 , 16.6 , 20.9 , 18.3
South
22.2, 19.2 , 9.3 , 24.6 ,20.2 , 15.8, 18.0 , 12.2 , 20.1 , 16.0 , 17.5 , 18.2 , 22.8 , 11.5
Answer:
Step-by-step explanation:
Hello!
The objective is to compare the VMT of mid western households and southwestern households. For this two independent random samples of households from both areas and their VMT were recorded:
Be
X₁: VMT of a mid western household
Midwest
16.2 , 14.6 , 11.2 , 24.4 , 9.4 12.9 , 18.6 , 16.6 , 20.3 ,15.1 , 17.3 , 10.8 , 16.6 , 20.9 , 18.3
n₁= 15
∑X₁= 243.20
∑X₁²= 4175.98
X[bar]₁= 16.21
S₁²= 16.64
S₁= 4.08
X₂: VMT of a southwestern household
22.2, 19.2 , 9.3 , 24.6 ,20.2 , 15.8, 18.0 , 12.2 , 20.1 , 16.0 , 17.5 , 18.2 , 22.8 , 11.5
n₂= 14
∑X₂= 247.60
∑X₂²= 4633.24
X[bar]₂= 17.69
S₂²= 19.56
S₂= 4.42
The parameters of study are the population means, if the claim is that the VMT of households is different in both areas, then you'd expect the population means to be different too.
The hypotheses are:
H₀: μ₁ = μ₂
H₁: μ₁ ≠ μ₂
α: 0.05
Assuming both populations are normal and since both population variances are equal the test to apply is an independent samples t test pooled variance:
[tex]t= \frac{(X[bar]_1-X[bar]2)-(Mu_1-Mu_2)}{Sa*\sqrt{\frac{1}{n_1} +\frac{1}{n_2} } } ~~t_{n_1+n_2-2}[/tex]
[tex]Sa^2= \frac{(n_1-1)S_1^2+(n_2-1)S_2^2}{n_1+n_2-2} = \frac{14*16.67+13*19.56}{15+14-2}= \frac{487.66}{27} = 18.06[/tex]
Sa= 4.249= 4.25
[tex]t_{H_0}= \frac{(16.21-17.69)-0}{4.25*\sqrt{\frac{1}{15} +\frac{1}{14} } }= -0.937= -0.94[/tex]
Critical value approach:
This test is two-tailed, this means that the rejection region is divided in two tails:
[tex]t_{n_1+n_2-2; \alpha /2}= t_{27; 0.025}= -2.052[/tex]
[tex]t_{n_1+n_2-2; 1-\alpha /2}= t_{27; 0.975}= 2.052[/tex]
The decision rule is:
If [tex]t_{H_0}[/tex] ≤ -2.052 or if [tex]t_{H_0}[/tex] ≥ 2.052, reject the null hypothesis.
If -2.052 < [tex]t_{H_0}[/tex] < 2.052, do not reject the null hypothesis.
The calculated value is within the "no rejection region" so the decision is to not reject the null hypothesis.
Using the p-value approach:
The p-value is the probability of obtaining a value as extreme as the calculated value of the statistic under the null hypothesis ([tex]t_{H_0}[/tex]). Just as the significance level, the p-value is two tailed, you can calculate it as:
P(t₂₇ ≤ -0.93) + P(t₂₇ ≥ 0.93)= P(t₂₇ ≤ -0.93) + (1 - P(t₂₇ < 0.93)= 0.1796 + ( 1 - 0.8204)= 0.1796*2= 0.3592
p-value= 0.3592
The p-value is always compared to the significance level, the decision rule for this approach is:
If the p-value ≤ α, reject the null hypothesis.
If the p-value > α, do not reject the null hypothesis.
The p-value is greater than α, so the decision is to not reject the null hypothesis.
At a 5% significance level, there is no significant evidence to reject the null hypothesis. You can conclude that the population means of the VMT for households of the Midwest South ers households.
I hope this mhelps!
29.) in Mongolia the temperature can dip down to - 45°C
in January. The temperature in July may reach 40°C.
What is the temperature range in Mongolia?
Answer:
The temperature range is [tex]95^o[/tex] , going from [tex]-45^0[/tex] to [tex]40^o[/tex]
Step-by-step explanation:
The temperature range is the difference between the maximum and the minimum temperature:
[tex]40^o-(-45^o)=40^o+45^o=95^o[/tex]
The temperature range is [tex]95^o[/tex] , going from [tex]-45^0[/tex] to [tex]40^o[/tex]
Find the median of the following set of data: 4, 7, 2, 1, 4, 6,
2,6
Answer:
(4+4)/2 = 4
Hope this helps
Answer:
4
Step-by-step explanation:
1,2,2,4,4,6,6,7
The median is the number in the middle however there are an even amount of numbers so you get the number between 4 and 4 which is just 4
PLEASE HELP!!!!!
This is edge!
A b c d
Will mark brainliest!!!!
Answer:
D. [tex] \frac{7}{12} \: of \: a \: pound[/tex]
Step-by-step explanation:
[tex]total \: candies = 2 \frac{1}{4} + \frac{2}{3} \\ \\ = \frac{9}{4} +\frac{2}{3} \\ \\ = \frac{9 \times 3 + 2 \times 4}{3 \times 4} \\ \\ = \frac{27 + 8}{12} \\ \\ = \frac{35}{12} \\ \\ share \: of \: brother = \frac{1}{5} \times \frac{35}{12} \\ \\ = \frac{7}{12} \: of \: a \: pound[/tex]
Answer:
[tex]\fbox{\begin{minipage}{10em}Option D is correct\end{minipage}}[/tex]
Step-by-step explanation:
Step 1: Let's find the total amount of candy that Loret and her sister have:
Loret has [tex]2\frac{1}{4}[/tex] pound of candy
Loret's sister has [tex]\frac{2}{3}[/tex] pound of candy
=> Total amount: [tex]A =2\frac{1}{4} + \frac{2}{3} = \frac{9}{4} + \frac{2}{3} = \frac{27}{12} + \frac{8}{12} = \frac{35}{12}[/tex] pound of candy
Step 2: Let's find the amount of candy Loret's brother could get:
If Loret's brother did the chores, he can get [tex]\frac{1}{5}[/tex] total amount of candy that Loret and her sister have.
=> The amount Loret's brother can get:
[tex]B = A*\frac{1}{5} = \frac{35}{12} * \frac{1}{5} = \frac{7}{12}[/tex] pound of candy
=> Option D is correct
Hope this helps!
:)
What is the area of the figure?
A figure can be broken into a rectangle and triangle. The rectangle has a base of 5 feet and height of one-third feet. The triangle has a base of 3 and two-thirds feet and height of 2 feet.
5One-third ft2
6 and two-thirds ft2
7 ft2
9 ft2
plzzzz help in a test!!! i only have 18 pts sry!!!
Answer:
5 one-third ft²
Step-by-step explanation:
rectangle=5ft (base) / 1/3ft (height)
triangle1=3ft (base) / 2ft (height)
triangle2=2/3ft (base) / 2ft (height)
area of rectangle=5x1/3
=5/3ft²
area of triangle1=3x2(1/2)
=3ft²
area of triangle2=2/3x2(1/2)
=2/3ft²
Total area=5/3+6+2/3
=16/3ft² or 5 one-third ft²
Answer:
A
Step-by-step explanation:
took the test on edg 2021
Reflect on the concept of function. What concepts (only the names) did you need to accommodate the concept of function in your mind? What is the simplest function you can imagine? In your day to day, is there any occurring fact that can be interpreted as a function? Is it possible to view a function? What strategy are you using to get the graph of a function?
Answer:
Step-by-step explanation:
For this kind of question you'd be better off if you'd write down and share your own answers to these conceptual questions and then ask for Brainly feedback on what you have written. You'll need to understand the concept of "function" often in algebra and beyond.
What concepts (only the names) did you need to accommodate the concept of function in your mind? input, output, rule, domain, range, mapping, variation (direct and inverse)
Simplest function: y = c (there's only one x-value and y equals that value)
In your day to day, is there any occurring fact that can be interpreted as a function? An electronic parking meter: the amount of time you can park at the meter without risking getting a ticket is dependent upon the number of quarters you insert into the meter, e. g, 15 minutes for 25 centers, 30 minutes for 50 cents, and so on.
Is it possible to view a function? Sure. Graph the function.
What strategy are you using to get the graph of a function? Set up a coordinate plane. Label the horizontal axis "x" and the vertical axis "y". Choose x (input) values that are included in the domain of the function. If the domain includes '0' you will be finding the 'y-intercept' of the function. Write the input and output as a point: (x, y). Plot that point. Choose other x values within the domain and calculate the corresponding y value for each. Plot several more points and draw a line or a curve through them. Of course there are more sophisticated strategies for graphing functions. Remember: If you're working with a function, there is never more than one output or y value for any particular input value.
What’s the correct answer for this? Select two answers that, when combined, show that circles are similar
Answer:
A and F
Step-by-step explanation:
First we'll dilate it by a scale factor of 2. After that, we'll translate in 6 units left and 6 units up to map circle J onto circle K
NEED GEOMETRY HELP ASAP
Answer:
HJ > KP
Step-by-step explanation:
Form the figure attached,
Two triangles PKL and JGH have been given with HG ≅ KL and PL ≅ GJ
m∠HGJ = 90°
m∠KLP = 85°
Since m∠HGJ > m∠PLK
Therefore, measure of opposite sides of these angles have the same relation.
HJ > KP
Evie has two sets of blocks of identical size and shape with the colors given. Evie will randomly select on block from each set. What is the probability she will select an orange block and a red block?
set A has 4 orange blocks and 3 yellow blocks.
set B has 5 blue blocks and 2 red blocks.
3/7
2/7
8/49
6/49
Answer:
[tex]\frac{8}{49}[/tex]
Step-by-step explanation:
Orange: [tex]\frac{4}{7}[/tex]
Red: [tex]\frac{2}{7}[/tex]
[tex]\frac{4}{7} *\frac{2}{7} =\frac{8}{49}[/tex]
Find the range of the following data set.
11,5, 1, 11, 12
01
1.
017
Answer:
range 11
Step-by-step explanation:
The range is the largest number minus the smallest number
The largest number is 12 and the smallest number is 1
12 - 1 = 11
Choose the equation of the graph shown below:
y = |x - 1| - 3
y = |x + 1| - 3
y = |x - 1| + 3
Answer:
y=[x+1]-3 because it's at the end of the line
Please answer this correctly
The right answer is 40 cm
please see the attached picture for full solution
Hope it helps
Good luck on your assignment
A man is giving a dinner party. His current wine supply includes 8 bottles of zinfandel, 10 of merlot, and 12 of cabernet, all from different wineries. a) If he wants to serve 3 bottles of zinfandel and serving order is important, how many ways are there to do this? (2 points) b) If 6 bottles are randomly selected, what is the probability that this results in two bottles of each variety being chosen? (4 points) c) If 6 bottles are randomly selected, what is the probability that all of them are the same variety?
Answer:
a. 336
b. 14.01%
c. 0.2%
Step-by-step explanation:
a. We have that the number of zinfandel bottles is 8 and that the number of zinfandel served is 3, therefore:
n = 8 and r = 3
we can calculate it by means of permutation:
nPr = n! / (n-r)!
replacing:
8P3 = 8! / (8-3)!
8P3 = 336
Which means there are 336 ways.
b. First we must calculate the ways to choose 2 bottles of each variety, through combinations:
nCr = n! / (r! * (n-r)!
We know that there are 8 bottles zinfandel, 10 of merlot, and 12 of cabernet, and we must choose 2 of each, therefore it would be:
8C2 * 10C2 * 12C2
8! / (2! * (8-2)! * 10! / (2! * (10-2)! * 12! / (2! * (12-2)!
28 * 45 * 66 = 83160
Now we must calculate the total number of ways, that is, choose 6 bottles of the 30 total (8 + 10 + 12)
30C6 = 30! / (6! * (30-6)! = 593775
Thus:
83160/593775 = 0.1401
In other words, the probability is 14.01%
c. In this case, we must calculate the number of ways of 8 bottles zinfandel, 10 of merlot, and 12 of cabernet choose 6, that is to say that they are all of the same variety, therefore:
8C6 + 10C6 + 12C6
8! / (6! * (8-6)! + 10! / (6! * (10-6)! + 12! / (6! * (12-6)!
28 + 210 + 924 = 1162
And that divide it by the total amount that we calculated the previous point, 30C6 = 593775
Thus:
1162/593775 = 0.002
In other words, the probability 0.2%
One-third times the difference of a number and 5 is
Which equation best shows this?
3
One possible first step in solving the equation in the above problem is to
The value of the number is
Answer:
the value of x is 3
Step-by-step explanation:
Hope this helps!!!! :)
Answer:
one is a
two is c
three is b
Step-by-step explanation:
Score: 0 of 1 pt
7.4.41
From a standard 52-card deck, how many 5-card hands consist entirely of black cards?
Answer:
so halve the deck is black and halve the deck is red so you have 26 black cards then divide by 5 and you get 5 with 1 card leftover
A researcher wants to test the claim that convicted burglars spend an average of 18.7 months in jail. She takes a random sample of 11 such cases from court files and finds x=20.6 months and s=8 months. Test the claim that u=18.7 months at the 0.05 significance level.
Answer:
[tex]t=\frac{20.6-18.7}{\frac{8}{\sqrt{11}}}=0.788[/tex]
The degrees of freedom are given by;
[tex] df =n-1= 11-1=10[/tex]
And the p value would be:
[tex]p_v =2*P(t_{10}>0.788)=0.449[/tex]
Since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly different than 18.7
Step-by-step explanation:
Information given
[tex]\bar X=20.6[/tex] represent the sample mean
[tex]s=8[/tex] represent the sample standard deviation
[tex]n=11[/tex] sample size
[tex]\mu_o =18.7[/tex] represent the value to test
[tex]\alpha=0.05[/tex] represent the significance level
t would represent the statistic
[tex]p_v[/tex] represent the p value
Hypotesis to test
We want to verify if the true mean is equal to 18.7, the system of hypothesis would be:
Null hypothesis:[tex]\mu =18.7[/tex]
Alternative hypothesis:[tex]\mu \neq 18.7[/tex]
The statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing the info we got:
[tex]t=\frac{20.6-18.7}{\frac{8}{\sqrt{11}}}=0.788[/tex]
The degrees of freedom are given by;
[tex] df =n-1= 11-1=10[/tex]
And the p value would be:
[tex]p_v =2*P(t_{10}>0.788)=0.449[/tex]
Since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly different than 18.7
Three security cameras were mounted at the corners of a triangles parking lot. Camera 1 was 110 ft from camera 2, which was 137 ft from camera 3. Cameras 1 and 3 were 158 ft apart. Which camera had to cover the greatest angle
Answer:
Camera 2nd has to cover the maximum angle, i.e. [tex]78.70^\circ[/tex].
Step-by-step explanation:
Please have a look at the triangular park represented as a triangle [tex]\triangle ABC[/tex] with sides
a = 110 ft
b = 158 ft
c = 137 ft
1st camera is located at point C, 2nd camera at point B and 3rd camera at point A respectively.
We can use law of cosines here, to find out the angles [tex]\angle A, \angle B, \angle C[/tex]
As per Law of cosine:
[tex]cos C = \dfrac{a^{2}+b^2-c^2 }{2ab}\\cos B = \dfrac{a^{2}+c^2-b^2 }{2ac}\\cos A = \dfrac{b^{2}+c^2-a^2 }{2bc}[/tex]
Putting the values of a,b and c to find out angles [tex]\angle A, \angle B, \angle C[/tex].
[tex]cos C = \dfrac{110^{2}+158^2-137^2 }{2\times 110 \times 158}\\\Rightarrow cos C = \dfrac{12100+24964-18769 }{24760}\\\Rightarrow cos C =0.526\\\Rightarrow C = 58.24^\circ[/tex]
[tex]cos B = \dfrac{110^{2}+137^2-158^2 }{2\times 110 \times 137}\\\Rightarrow cos B = \dfrac{12100+18769 -24964}{30140}\\\Rightarrow cos B = \dfrac{5905}{30140}\\\Rightarrow cos B =0.196\\\Rightarrow B = 78.70^\circ[/tex]
[tex]cos A = \dfrac{158^{2}+137^2-110^2 }{2\times 158 \times 137}\\\Rightarrow cos A = \dfrac{24964+18769-12100}{43292}\\\Rightarrow cos A = \dfrac{31633}{43292}\\\Rightarrow cos A = 0.731\\\Rightarrow A = 43.05^\circ[/tex]
Camera 2nd has to cover the maximum angle, i.e. [tex]78.70^\circ[/tex].
express the measure in standard notation 5 gal 6qt 48 oz
Answer: 880 oz
Step-by-step explanation:
We want to write it in the same units, let's use oz as our common unit.
1 gal = 128 oz
then 5 gal = 5*128 oz = 640 oz
1 qt = 32 oz
then 6 qt = 6*32 oz = 192 oz
Then we have:
640 oz + 192 oz + 48 oz = 880 oz
The value of standard notation is,
⇒ 880 oz
We have to given that,
Measures are,
⇒ 5 gal 6qt 48 oz
We have to change it into standard notation as,
We want to write it in the same units, let's use oz as our common unit.
1 gal = 128 oz
then 5 gal = 5 x 128 oz = 640 oz
1 qt = 32 oz
then 6 qt = 6 x 32 oz = 192 oz
Then we have:
⇒ 5 gal 6qt 48 oz
⇒ 640 oz + 192 oz + 48 oz
⇒ 880 oz
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Write the equation of the line shown in the graph above in slope-intercept form. Question 3 options: A) y = –2∕3x + 1 B) y = –x + 2∕3 C) 2x + 3y = 3 D) y = 2∕3x + 1
Answer:
A) y = -2/3x + 1
Step-by-step explanation:
Slope - intercept form is y = mx + b, where m is the slope and b is the y - intercept.
The line is falling from left to right, so it has a negative slope.
y = -mx + b
The line has a slope of -2/3.
y = -2/3x + b
The line has a y - intercept of 1.
y = -2/3x + 1
I hope this helps :)
A) y = -2/3x + 1, the equation of the line shown in the graph above in slope-intercept form.
What is a straight line?A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.
here, we have,
Slope - intercept form is y = mx + b,
where m is the slope and b is the y - intercept.
The line is falling from left to right, so it has a negative slope.
y = -mx + b
As, the line passes through (0,1) and (1.5,0)
The line has a slope of -2/3.
y = -2/3x + b
The line has a y - intercept of 1.
y = -2/3x + 1
hence, A) y = -2/3x + 1, the equation of the line shown in the graph above in slope-intercept form.
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