Answer:
at x-intercept, y = 0
4x = 28
x = 7
x intercept = (7,0)
at y-intercept, x = 0
y = 28
y intercept = (0,28)
SAT scores are normally distributed with a mean of 1,500 and a standard deviation of 300. An administrator at a college is interested in estimating the average SAT score of first-year students. If the administrator would like to limit the margin of error of the 88% confidence interval to 15 points, how many students should the administrator sample? Make sure to give a whole number answer.
Answer:
The administrator should sample 968 students.
Step-by-step explanation:
We have to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.88}{2} = 0.06[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a p-value of [tex]1 - 0.06 = 0.94[/tex], so Z = 1.555.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
Standard deviation of 300.
This means that [tex]n = 300[/tex]
If the administrator would like to limit the margin of error of the 88% confidence interval to 15 points, how many students should the administrator sample?
This is n for which M = 15. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]15 = 1.555\frac{300}{\sqrt{n}}[/tex]
[tex]15\sqrt{n} = 300*1.555[/tex]
Dividing both sides by 15
[tex]\sqrt{n} = 20*1.555[/tex]
[tex](\sqrt{n})^2 = (20*1.555)^2[/tex]
[tex]n = 967.2[/tex]
Rounding up:
The administrator should sample 968 students.
The graph shown below expresses a radical function that can be written in
17
the form f(x) = a(x + k)!
C. What does the graph tell you about the
value of k in this function
Answer:
C. [tex]k[/tex] is greater than zero.
Step-by-step explanation:
We know that graph is obtained from the function of the form [tex]f(x) = a\cdot (x+k)^{1/n} + c[/tex]. According to the graph and if [tex]x + k = 0[/tex], we find that:
[tex]x = -k[/tex] (1)
[tex]x < 0[/tex] (2)
By (1) and (2):
[tex]-k < 0[/tex]
[tex]k > 0[/tex]
Hence, correct answer is C.
help
What is 5 added to 3 4?
6. 12
Answer:
8.4
Step-by-step explanation:
jjdijendjndoendidnie
which of these figures has rotational symmetry
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Answer:
A
Step-by-step explanation:
The parallelogram has rotational symmetry of degree 2. It looks the same after rotation by 180°.
_____
Additional comment
When a figure only looks like itself after a full rotation of 360°, it is said to have rotational symmetry of degree 1. All of the figures here will return to their original appearance after one 360° rotation. So, we assume the intent of the question is to identify figures with a rotational symmetry of degree greater than 1.
You have 2 5 sided dice, what's the probability the addition of rolling both
Answer:
7
Step-by-step explanation:
I need help ASAP please
Answer:
5:10
6 (-2,0)
7 (-5,6)
8 (5,3)
9 No, ab=8 CD=6
Step-by-step explanation:
A binomial probability experiment is conducted with the given parameters. Compute the probability of x successes in the n independent trials of the experiment.
n=12, p=0.35, x=2
Answer:
0.1088 or 10.88%
Step-by-step explanation:
q = 1 - 0.35 = 0.65
P(X=2) = 12C2 × (0.35)² × (0.65)¹⁰
= 0.1088
-27
Which of the following is equivalent to
نان-۴
?
N
O
(197)
NI
12
22
(22)
2².2
Answer:
3rd option
Step-by-step explanation:
(1/2)^-2t
= (2^-1)^-2t
= 2^2t
= (2^2)^t
Answered by GAUTHMATH
Question with last attempt is displayed for your review only
Amanda rented a bike from Ted's Bikes.
It costs $9 for the helmet plus $5.25 per hour.
If Amanda paid about $43.13, how many hours did she rent the bike?
Let h = the number of hours she rented the bike. Write the equation you would use to solve this problem.
Answer:
[tex]43.13 = 5.25h + 9[/tex]
Step-by-step explanation:
Let's solve this by making an equation.
$9 for the helmet, and $5.25 per hour.
h will stand for hours, C will stand for Amanda's cost.
[tex]C = 5.25h + 9[/tex]
Now, substitute in what we learned from the problem.
[tex]43.13 = 5.25h + 9[/tex]
This is an equation you can use to solve for the hours.
What are the values of (-2)4 and -24?
1. 8 and -8
2. -8 and -8
3. 16 and -16
4. 16 and 16
Answer:
2.
Step-by-step explanation:
(-2)×4=-8
-2×4=-8
~~~~~~~~
Answer:
16 and 16 is the correct answer
The length of a rectangle is 10 yd less than three times the width, and the area of the rectangle is 77 yd^2. Find the dimensions of the rectangle.
Answer:
W=7 and L=11
Step-by-step explanation:
We have two unknowns so we must create two equations.
First the problem states that length of a rectangle is 10 yd less than three times the width so: L= 3w-10
Next we are given the area so: L X W = 77
Then solve for the variable algebraically. It is just a system of equations.
3W^2 - 10W - 77 = 0
(3W + 11)(W - 7) = 0
W = -11/3 and/or W=7
Discard the negative solution as the width of the rectangle cannot be less then 0.
So W=7
Plug that into the first equation.
3(7)-10= 11 so L=11
Factor 64a^3 -8b^3 Explain all steps.
Answer:
[tex]8(2a- b)(4a^2+ 2ab+ b^2)[/tex]
Step-by-step explanation:
factor out the 8
then you have the sum/difference of cubes..
look that up SOAP: same opposite, always a plus
[tex]64a^3 -8b^3\\8(8a^3 -b^3)[/tex]
[tex]8(2a- b)(4a^2+ 2ab+ b^2)[/tex]
What is 50g as a percentage of one kg?
Answer:
5 %
Step-by-step explanation:
1000 g = 1 kg
50 kg = 0.05 kg
0.05 = 5%
Therefore, 50 g as a percentage of 1kg is 5%.
Find the length of AB
Answer:
C. 44.98
Step-by-step explanation:
Hi there!
We are given the right triangle ABC, m<B=12°, and CB =44
We want to find the length of AB
We can use trigonometry to do it
Let's find the ratio in reference to angle B, as that angle is given.
In reference to angle B the opposite angle is AC, the adjacent side is CB, and the hypotenuse is AB
Now let's recall the 3 most commonly used functions:
[tex]sine=\frac{opposite}{hypoptenuse}[/tex]
[tex]cosine=\frac{adjacent}{hypotenuse}[/tex]
[tex]tangent=\frac{opposite}{adjacent}[/tex]
Let's find the cosine of angle B, as it uses CB and AB, which are the given side and the side we need to find
In that case,
cos(12)=[tex]\frac{CB}{AB}[/tex]
cos(12)=[tex]\frac{44}{AB}[/tex]
Multiply both sides by AB
[tex]AB[/tex]*cos(12)=44
Divide both sides by cos(12)
AB=[tex]\frac{44}{cos(12)}[/tex]
Now plug [tex]\frac{44}{cos(12)}[/tex] into your calculator. Make sure your calculator is on degree mode
AB≈44.98
So the answer is C
Hope this helps!
If (4x-5) :(9x-5) = 3:8 find the value of x.
Answer:
x is 5
Step-by-step explanation:
[tex] \frac{4x - 5}{9x - 5} = \frac{3}{8} \\ \\ 8(4x - 5) = 3(9x - 5) \\ 32x - 40 = 27x - 15 \\ 5x = 25 \\ x = \frac{25}{5} \\ \\ x = 5[/tex]
Step-by-step explanation:
as you can see as i solved above. all you need to do was to rationalize the both equations
Fill in this blank spaces (1,3,5,7,9 , 11, 13, 15) _+_+_=30
Step-by-step explanation:
Just till the number 9 upside down to make it 6 then
6+11+13=30
The sum of three odd numbers can never be even. so I did it in that way.
I HOPE THIS WILL HELP U
STAY SAFE, STAY HAPPY
P,W,R & S form the vertices of a quadrilateral. PQR = 74 degrees
RSP = 121 degrees
Find the value of SPQ
Answer:
∠ SPQ = 75°
Step-by-step explanation:
The sum of the 4 angles in a quadrilateral = 360°
Subtract the sum of the 3 angles from 360 for ∠ SPQ
∠ SPQ = 360° - (90 + 74 + 121)° = 360° - 285° = 75°
find the missing length indicated
explainion:
[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]
Use The (Pythagorean Theorem) to find the length of any side of a right triangle. Form it like its shown in picture above. Follow the instructions that also shown in the picture above.
WILL GIVE BRAINLIEST
Complete the equation describing how
x and y are related.
х
-3
-2
-1
0
1
2
3
y
12
8
4
0
-4
-8
-12
y = [? ]x
Answer:
[tex]y=4x[/tex]
Answer:
y = -4x
hope that helped.........
What is |1-8i|?
A.
B.
C
D
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Answer:
(b) √65
Step-by-step explanation:
The modulus of a complex number is the root of the sum of the squares of the real and imaginary parts.
|1 -8i| = √(1² +(-8)²) = √(1+64) = √65
Shaun is planting trees along his driveway, and he has 66 redwoods and 66 pine trees to plant in one row. What is the probability that he randomly plants the trees so that all 66 redwoods are next to each other and all 66 pine trees are next to each other
Answer:
0.0022 = 0.22% probability that he randomly plants the trees so that all 6 redwoods are next to each other and all 6 pine trees are next to each other.
Step-by-step explanation:
The trees are arranged, so the arrangements formula is used to solve this question. Also, a probability is the number of desired outcomes divided by the number of total outcomes.
Arrangements formula:
The number of possible arrangements of n elements is given by:
[tex]A_n = n![/tex]
Desired outcomes:
Two cases:
6 redwoods(6! ways) then the 6 pine trees(6! ways)
6 pine trees(6! ways) then the 6 redwoods(6! ways)
So
[tex]D = 2*6!*6![/tex]
Total outcomes:
12 trees, so:
[tex]D = 12![/tex]
What is the probability that he randomly plants the trees so that all 6 redwoods are next to each other and all 6 pine trees are next to each other?
[tex]p = \frac{D}{T} = \frac{2*6!*6!}{12!} = 0.0022[/tex]
0.0022 = 0.22% probability that he randomly plants the trees so that all 6 redwoods are next to each other and all 6 pine trees are next to each other.
Find the exact value by using a half-angle identity.
tan seven pi divided by eight
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Answer:
1 -√2
Step-by-step explanation:
[tex]\tan(x/2)=\dfrac{1-\cos(x)}{\sin(x)}\\\\\tan\left(\dfrac{1}{2}\cdot\dfrac{7\pi}{4}\right)=\dfrac{1-\cos\dfrac{7\pi}{4}}{\sin\dfrac{7\pi}{4}}=\dfrac{1-\dfrac{1}{\sqrt{2}}}{-\dfrac{1}{\sqrt{2}}}=\boxed{1-\sqrt{2}}[/tex]
tan(7π/8) = 1 -√2
what percent of 70 is 35
Answer:
50%
Step-by-step explanation:
35 is halve of 70 therefore it is 50%
hope it helps u...........
The rate of change for yyy as a function of xxx is
, therefore the function is
.
For all values of xxx, the function value y\:yy
\:000.
The yyy-intercept of the graph is the function value y=\:y=y, equals
.
When x=1x=1x, equals, 1, the function value y=\:y=y, equals
.
everything seems to be correctly filled.
if you wanted confidence by confirmation: here, take some
It is an exponentially decaying function.
What is an exponential function ?An exponential function is where the independent variable is in the exponent. Generally the the independent variable is in the power of a constant term e.
Exponential functions are of two types one is exponentially growing function and exponentially decaying function.
when the we have a positive exponent the function is exponentially growing and when we have a negative exponent the function is exponentially decaying.
In the given question f(x) = 8e⁻ˣ
when, x = 0 f(x) = 8
f(x) = 8e⁻ˣ
f(0) = 8e⁰
f(0) = 8
Learn more about Exponential functions here :
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What are the first and third quartiles for the following data set?
12, 15, 18, 16, 14, 9, 12, 21
A 9 and 21
C 12 and 17
B 12 and 16
D 15 and 17
Answer:
A
Step-by-step explanation:
I guess that is it may be
Charity is planting trees along her driveway, and she has 6 pine trees and 6 willows to plant in one row. What is the probability that she randomly plants the trees so that all 6 pine trees are next to each other and all 6 willows are next to each other
Answer:
0.0022 = 0.22% probability that she randomly plants the trees so that all 6 pine trees are next to each other and all 6 willows are next to each other.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
In this question, the elements are arranged, so we have to use the arrangements formula.
Arrangements formula:
The number of possible arrangements of n elements is:
[tex]A_{n} = n![/tex]
Desired outcomes:
Pine trees(6!) then the willows(6!) or
Willows(6!) then the pine trees(6!). So
[tex]D = 2*6!*6! = 1036800 [/tex]
Total outcomes:
12 trees, so:
[tex]T = 12! = 479001600 [/tex]
What is the probability that she randomly plants the trees so that all 6 pine trees are next to each other and all 6 willows are next to each other?
[tex]p = \frac{D}{T} = \frac{1036800 }{479001600 } = 0.0022[/tex]
0.0022 = 0.22% probability that she randomly plants the trees so that all 6 pine trees are next to each other and all 6 willows are next to each other.
A hexagonal pyramid is located ontop of a hexagonal prism. How many faces are there?
A. 15
B. 24
C. 6
D. 13
Answer:
15
Step-by-step explanation:
The figure has total 15 faces, the correct option is A.
What is a Hexagon?A hexagon is a polygon with six sides.
A hexagonal pyramid has 8 faces
From (2 hexagonal base + 6 lateral surfaces)
A hexagonal prism has 7 faces
From ( A hexagonal base + 6 lateral faces)
Total faces the figure has is 8 +7 = 15
To know more about Hexagon
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Write the ratio as a fraction in simplest form, with whole numbers in the numerator and denominator. 2.1yd : 1.4yd
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Answer:
3/2
Step-by-step explanation:
Multiplying numerator and denominator by 10 will convert the ratio to a ratio of whole numbers. Then dividing by the common factor of 7 will reduce it to simplest form.
[tex]\dfrac{2.1\text{ yd}}{1.4\text{ yd}}=\dfrac{2.1\times10}{1.4\times10}=\dfrac{21}{14}=\dfrac{3\times7}{2\times7}=\boxed{\dfrac{3}{2}}[/tex]
Reduce 20/60 to its lowest common denominator
Answer:
it is 1/4
Step-by-step explanation:
20/60=10/30=1/3
Answer:
20/60=1/3
Step-by-step explanation:
20/60
HCF=20,
20*1=20, 20*3=60
1/3
or,
Remove the zeros,
2/6
Divide by 2 on both,
1/3
or divide by any common factor on both and keep dividing until u cant no more
20/60=1/3
Assume that the matrices below are partitioned conformably for block multiplication. Compute the product.
[I 0] [W X]
[K I] [Y Z]
Multiplying block matrices works just like multiplication between regular matrices, provided that component matrices have the right sizes.
[tex]\begin{bmatrix}\mathbf I&\mathbf 0\\\mathbf K&\mathbf I\end{bmatrix}\begin{bmatrix}\mathbf W&\mathbf X\\\mathbf Y&\mathbf Z\end{bmatrix} = \begin{bmatrix}\mathbf{IW}+\mathbf{0Y}&\mathbf{IX}+\mathbf{0Z}\\\mathbf{KW}+\mathbf{IY}&\mathbf{KX}+\mathbf{IZ}\end{bmatrix}[/tex]
[tex]\begin{bmatrix}\mathbf I&\mathbf 0\\\mathbf K&\mathbf I\end{bmatrix}\begin{bmatrix}\mathbf W&\mathbf X\\\mathbf Y&\mathbf Z\end{bmatrix} = \begin{bmatrix}\mathbf W+\mathbf 0&\mathbf X+\mathbf 0\\\mathbf{KW}+\mathbf Y&\mathbf{KX}+\mathbf Z\end{bmatrix}[/tex]
[tex]\begin{bmatrix}\mathbf I&\mathbf 0\\\mathbf K&\mathbf I\end{bmatrix}\begin{bmatrix}\mathbf W&\mathbf X\\\mathbf Y&\mathbf Z\end{bmatrix} = \begin{bmatrix}\mathbf W&\mathbf X\\\mathbf{KW}+\mathbf Y&\mathbf{KX}+\mathbf Z\end{bmatrix}[/tex]
(I assume I is the identity matrix and 0 is the zero matrix.)
