Answer:
Slope: -7
y-intercept: (0, -9)
Step-by-step explanation:
Adam tabulated the values for the average speeds on each day of his road trip as 60.5, 63.2, 54.7, 51.6, 72.3, 70.7, 67.2, and 65.4 mph. The sample standard deviation is 7.309.Select the 98% confidence interval for Adam’s set of data.a. 46.94 to 71.33b. 46.94 to 79.46c. 55.45 to 79.46d. 55.45 to 70.95
Answer:
Option D, 55.45 to 70.95
Step-by-step explanation:
Alpha = 1 – confidence interval
Alpha = 1 – 0.98 = 0.02
Sample size = n = 8
t (alpha/2) ; (n-1) = t (0.02/2) ; (8-1) = t 0.01, 7 = 2.998
Mean = sum of all frequencies /total number of frequency = 505.6/8 = 63.2
s = 7.309
E = t (0.01;7) * s/sqrt n
Substituting the given values, we get –
E = 2.998 * 7.309 /sqrt (8)
E = 7.75
98% confidence interval
Mean – E and Mean + E
63.2 – 7.75 and 63.2 + 7.75
(55.45, 70.95)
Answer: 55.45 to 70.95
Step-by-step explanation:
An electrician leans an extension ladder against the outside wall of a house so that it
reaches an electric box 30 feet up. The ladder makes an angle of 68° with the ground.
Find the length of the ladder. Round your answer to the nearest hundredth of a foot if
necessary.
Answer: [tex]32.36\ ft[/tex]
Step-by-step explanation:
Given
Ladder is leaned and make an angle of [tex]68^{\circ}[/tex]
Electric box is 30 ft up the ground.
Suppose x is the length of ladder
From the figure, we can write
[tex]\Rightarrow \sin 68^{\circ}=\dfrac{30}{x}\\\\\Rightarrow x=\dfrac{30}{\sin 68^{\circ}}\\\\\Rightarrow x=32.36\ ft[/tex]
The Sine or Sinθ in a right angle triangle is the ratio of its perpendicular to its Hypotenuse. The length of the ladder is 32.356 feet.
What is Sine (Sinθ)?The Sine or Sinθ in a right angle triangle is the ratio of its perpendicular to its Hypotenuse. it is given as,
[tex]\rm{Sine(\theta) = \dfrac{Perpendicular}{Hypotenuse}[/tex]
where,
θ is the angle,
Perpendicular is the side of the triangle opposite to the angle θ,
The hypotenuse is the longest side of the triangle.
As it is given that the height of the electric box from the bottom is 30 feet, while the ladder makes an angle of 68° with the ground.
The length of the ladder can be found using the trigonometric functions, therefore, the length of the ladder can be written as,
[tex]\rm Sine(\theta) = \dfrac{Perpendicular}{Hypotenuse}\\\\\\Sine(\angle C) = \dfrac{AB}{\text{Length of the ladder}}\\\\\\{\text{Length of the ladder}}= \dfrac{AB}{Sine(\angle C) }\\\\\\{\text{Length of the ladder}}= \dfrac{30}{Sine(68^o) }\\\\\\{\text{Length of the ladder}}= 32.356\ feet[/tex]
Hence, the length of the ladder is 32.356 feet.
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Stan knows that segment AB∥segment CD. He wants to use the definition of a parallelogram to prove that quadrilateral ABCD is a parallelogram. Which equation can he use?
Answer:
[tex]\frac{q - r}{m- n} = \frac{p - s}{m - n}[/tex]
Step-by-step explanation:
Given
See attachment for parallelogram
Required
Proof that ABCD is a parallelogram
We know that opposite sides are equal and parallel.
First, we calculate the slope of BC
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
So, we have:
[tex]m = \frac{q - r}{m- n}[/tex]
Next, the slope of AD using:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
So, we have:
[tex]m = \frac{p - s}{m - n}[/tex]
For ABCD to be a parallelogram; then:
[tex]\frac{q - r}{m- n} = \frac{p - s}{m - n}[/tex]
Please help me answer e, f and number 3. See the image below
Answer:
Prat two of e) 6/12 Both the numerator and denominator were multipled by three, the number of boxes we split each box into.
F) we can multiply both the numerator and denominator without changing the values, so 2a/2b or 10a/10b
PLSSSSS
cos36 * cos72=???
I need procedure
cos 36 × cos 72 = 0.25
cos 36 × cos 72 =
0.309 x 0.809 = 0.249 = 0.25
Qual é a frequência de cada gênero de leitura citados?
Answer:
i velo you
Step-by-step explanation:
43
d. 34
Clear my choice
For the discrete series given as, X variable values - 32 with frequemcy 2,37 with frequency 5,
46 with frequency 3 and 48 with frequency 9, mode is
Select one:
O a. 9
O b. 48
O c. 37
O d. 5
Given:
The frequency distribution table is:
Values of variable X Frequency
32 2
37 5
46 3
48 9
To find:
The mode of the given data set.
Solution:
We know that mode is the most frequent value of the data set.
In the given data set highest frequency is 9 that is corresponding to the value 48.
Therefore, the mode of the given data set is 48. Hence, the correct option is (b).
Please!!!!!! I need whole process
Answer:
This is the whole process I guess
6.
40 x 6+ (9+21)
I need help ASAP please due tomorrow show work
i need help with this on my homework
ko iê ế t??????????????? t
which expression is it please help
Answer:
first option is the correct answer.
Step-by-step explanation:
Which of the following is the equation of a line in slope-intercept form for a
line with slope = and yintercept at (0, -1)?
O A. y - x-
1
B. y = 4x-1
O c. y= |x-1
O D. y=x+1
Answer:
y=1/4x - 1
Step-by-step explanation:
going off of the picture, I'd say this is your answer
9 Two people start writing reports on the same day. Both write 200-page reports. Writer A averages 8 pages a day, and writer B averages 5 pages per day. How much sooner will Writer A finish her report than will Writer B?
Answer:
15 days
+
Step-by-step explanation:
A
200 pages / (8 pages / day) =
= 200 pages days / 8 pages =
= 200 days / 8 = 25 days
B
200 pages / (5 pages / day) =
= 200 pages days / 5 pages =
= 200 days / 5 = 40 days
40-25 = 15 days
A will finish 15 days sooner than B.
A will finish her report 15 days sooner than B.
What is the ratio?The ratio is defined as a relationship between two quantities, it is expressed one divided by the other.
Writer A averages 8 pages a day,
Number of pages per day written by writer A = 8 per day
Writer A will finish her report = Total pages / per day written by writer A
⇒ 200 pages / (8 pages / day)
⇒ 200 pages days / 8 pages
⇒ 200 days / 8
⇒ 25 days
Writer B averages 5 pages a day
Number of pages per day written by writer B = 5 per day
Writer B will finish her report = Total pages / per day written by writer A
⇒ 200 pages / (5 pages / day)
⇒ 200 pages days / 5 pages
⇒ 200 days / 5
⇒ 40 days
Difference between both of time when they finished their report = 40-25 = 15 days
Hence, A will finish her report 15 days sooner than B.
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Difference Quotient. Correct answer is shown. It says multiply by conjugate but I don’t understand what that is and how they did it. TIA
9514 1404 393
Answer:
3/(√(3(x+h)) +√(3x))
Step-by-step explanation:
The conjugate of a binomial is the same sum, but with the sign changed. That is (a +b) and (a -b) are a conjugate pair: each is the conjugate of the other.
The purpose of multiplying expressions involving roots or complex numbers by their conjugate is to take advantage of the relation ...
(a +b)(a -b) = a² -b²
Here. you want to eliminate the h from under the radical, so squaring the radical containing h is useful for the purpose. Hence the conjugate gets involved.
"Multiply by the conjugate" means multiply both the numerator and the denominator by the conjugate. (Effectively, multiply by 1.)
__
[tex]\displaystyle\frac{f(x+h)-f(x)}{h}=\frac{\sqrt{3(x+h)}-\sqrt{3x}}{h}\\\\=\frac{(\sqrt{3(x+h)}-\sqrt{3x})(\sqrt{3(x+h)}+\sqrt{3x})}{h(\sqrt{3(x+h)}+\sqrt{3x})}=\frac{3(x+h)-3x}{h(\sqrt{3(x+h)}+\sqrt{3x})}\\\\=\frac{3h}{h(\sqrt{3(x+h)}+\sqrt{3x})}=\boxed{\frac{3}{\sqrt{3(x+h)}+\sqrt{3x}}}[/tex]
_____
Additional comment
In the end, you will want the limit as h → 0, which will be 3/(2√(3x)). You will notice that h=0 no longer makes the denominator zero, so the limit is found by simple evaluation.
When the "binomial" is a complex number of the form a+bi, its conjugate is a-bi, regardless of the sign of b. That is, the conjugate of a complex number is found by negating its imaginary part. The sign of the real part is left alone.
12 Kendrick wants to build a slide for his son in the backyard. He buys a
slide that is 8 feet long. The height of the stairs is 5 feet. Find the
distance from the bottom of the stairs to the base of the slide.
Rounding in the calculation of monthly interest rates is discouraged. Such rounding can lead to answers different from those presented here. For long-term loans, the differences may be pronounced.
To buy a car, you borrow $27,000 with a term of five years at an APR of 6%. What is your monthly payment? (Round your answer to the nearest cent.)
$
How much total interest is paid? (Round your answer to the nearest cent.)
$
Answer:
The correct answer is -
monthly payment = 521.99
total pain intrest = 4319.14
Step-by-step explanation:
Given:
a or the borrowed amount = 27000
r or the interest rate = 6%
n = 5 years or 60 months
Monthly payment = ?
total intreset = ?
Formula:
The formula for the monthly payment is -
[tex]\frac{a}{\frac{{[(1+r)^n]-1}}{[r(1+r)^n]}} = P[/tex]
or, [tex]\frac{ar}{[1-(1+r)^{-60}}[/tex] = P
Where, the amount of the loan = a
r = 0.005 (6% annual rate—expressed as 0.06—divided by 12 monthly payments per year)
n = 60 months
Solution:
Putting all the values in the either of the following formula will give monthly payments:
[tex]\frac{27000}{\frac{{[(1+0.005)^{60}]-1}}{[0.005(1+0.005)^{60}]}} = P[/tex] or [tex]\frac{ar}{[1-(1+r)^{-60}}[/tex]
= 521.9856 or to the nearest cent 521.99.
The total intrest would be -
= (monthly payment*number of month) - amount borrowed
= 521.99*12-27000
= 31319.14-27000
= 4319.14
Please help with question 2
Answer:
Step-by-step explanation:
7*(4) - 2(-3) - (-3)^2
28 + 6 - 9
34 - 9 = 25
what is the inverse of f(x)=2x-4
Step-by-step explanation:
Hey there!
The given function is; f(x) = 2x-4.
To find: f'(X)
Let f(X) be y, then;
y = 2x - 4
Interchanging"X" and "y" we get;
x = 2y - 4
or, X+4 = 2y
or, y = (X+4)/ 2
Therefore, f'(X) = (X+4)/2.
Hope it helps!
If ∠P, ∠Q, and ∠R are given, as well as the value of p, then explain whether the Law of Sines or the Law of Cosines should be used to solve for q.
Law of Sines, two angles and an opposite side are known
Law of Sines, two sides and an opposite angle are known
Law of Cosines, two sides and the included angle are known
Law of Cosines, all sides are known
Answer:
Law of Sines, two angles and an opposite side are known
Step-by-step explanation:
Law of Sines, two angles and an opposite side are known
q/sinQ = p/sinP
q = p/sinP * sinQ
In how many ways can the letters in the word 'Illinois' be arranged?
Answer
How to enter your answer
Answer:
The numbers of ways to permute letters of the word Illinois if the two Ls must be consecutive is 7.
The word ILLINOIS contains 7 letters.
How do you find the number of distinguishable permutations of the letters in a word?To estimate the number of different permutations, consider the total number of letters factorial and divide by the frequency of each letter factorial. The little n's exist the frequencies of each various (different) letter.
We will use the formula for the number of permutations with imperceptible objects. Since the two L's must be consecutive, we consider them to be a single letter LL. Then the word ILLINOIS contains n = 7 letters: 3 I's, 1 LL, 1 N, 1 O, and 1S.
Hence the number of methods to permute letters of the word ILLINOIS if the two L's must be consecutive exists:
[tex]$\frac{7 !}{3 ! 1 ! 1 ! 1 ! 1 !}=7 \cdot 6 \cdot 5 \cdot 4=840 \text {. }$$[/tex]
The word ILLINOIS contains 7 letters.
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What is the value of angle v?
Answer:
x = 5
Step-by-step explanation:
a) The third interior angle of this triangle is 180 - 20 x.
The three interior angles must sum up to 180 degrees.
Therefore, 60 + 7x + 5 + 180 - 20x = 180, or
65 + 180 - 13x = 180, or
65 - 13x = 0
Finally, 13x = 65, and so x = 5
Another name for NQ is? (Geometry)
Answer:
NQ : Summary
CodeNQOne-letter codeXMolecule name2-HYDROXYNAPHTHOQUINONESynonyms2-HYDROXY-1,4-NAPHTHOQUINONESystematic namesProgram Version Name ACDLabs 10.04 2-hydroxynaphthalene-1,4-dione OpenEye OEToolkits 1.5.0 2-hydroxynaphthalene-1,4-dione
Josh ate 7/8 pizza and Jerry ate 1/2 pizza. how much more did Josh eat then Jerry
Step-by-step explanation:
6/5 this is the answer hopes this help
This are 3 different questions please help me
Find the product of -9 and -3.
1. 0-3
2. 27
3. 0-27
4. 3
27 is the answer
gbu...
Answer:
- 9 × - 3 = 27
Step-by-step explanation:
when we multiply two negative numbers then the sign of the product convert to positive sign
I.e( - )×( - )= (+) product
Factor completely, then place the factors in the proper location on the grid. 25a2 +9b2 + 30ab
Answer:
(5a+3b)(5a+3b) or SQ(5a+3b)
Step-by-step explanation:
Now you can plot by referring to the above factors
HELP I NEED TO PASS!!!!!
A. g(x) = 2x-1
B. g(x) = 2x + 1
C. g(x) = 2x –1
D. g(x) = 2x+1
NEED HELP ASAP!!! Giving brainliest!!!!!!!
C.(f-g)(x) = 4x^3 +5x²-7x-1
Step-by-step explanation:
Given information :
[tex]f(x) = 4 {x}^{3} + 5 {x}^{2} - 3x - 6 \\ g(x) = 4x - 5[/tex]
Find :
[tex](f - g)(x) = \\ (4 {x}^{3} + 5 {x}^{2} - 3x - 6) \\ - 4x -5[/tex]
Open bracket and Simplify
[tex]4 {x}^{3} + 5 {x}^{2} - 3x - 6 - 4x + 5 \\ 4 {x}^{3} + 5 {x}^{2} - 7x - 1[/tex]
To the nearest degree, find the measure of angle A.
Cosine(angle) = adjacent leg/ hypotenuse
Cosine( angle ) = 18/20
Angle = arccos(18/20)
Angle = 26 degrees
Answer:
26°
Step-by-step explanation:
For a right triangle, we can use trigonometry equations :-
In this case we need to use cosine equation .
cos A = adjacent side / hypotenuse
cos A = 18 / 20
A = cos × 18/20
A = arccos × 18/20
A = 26°
If you apply these changes to the linear parent function f(x)=x what is the equation of the new function vertically compressed by a factor of 3 reflect over the x axis
Answer:
Because this gravity of. The earth