Final answer:
To find (fg)(x), multiply f(x) and g(x) by substituting g(x) into f(x) and simplifying the expression.
Explanation:
To find (fg)(x), we need to multiply f(x) and g(x). This can be done by substituting g(x) into f(x) and simplifying the expression.
f(x) = 4x² - 5
g(x) = x + 3
(fg)(x) = f(x) * g(x) = (4x² - 5) * (x + 3) = 4x³ + 12x² - 5x - 15
Therefore, the expression (fg)(x) simplifies to 4x^3 + 12x² - 5x - 15.
The shape of the distribution of the time required to get an oil change at a 10-minute oil-change facility is unknown. However, records indicate that the mean time for an oil change is 11.4 minutes, and the standard deviation for oil- change time is 3.2 minutes.
(a) To compute probabilities regarding the sample mean using the normal model, what size sample would be required?
(b) What is the probability that a random sample of n=45 oil changes results in a sample mean time of less than 10 minutes?
Answer:
a) sample size ≥ 30
b) 0.0017
Step-by-step explanation:
a) The central limit theorem states that for population with mean μ and standard deviation σ and take sufficiently large random samples from the population. This will hold provided the sample size is sufficiently large (usually n > 30) for a normal population.
Therefore the sample size should be greater or equal to 30 i.e n ≥ 30.
b) Given that n = 45, μ = 11.4 minutes and σ = 3.2 minutes, the z score (z) is given by the equation:
[tex]z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]
Substituting values to get:
[tex]z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n} } }= \frac{10-11.4}{\frac{3.2}{\sqrt{45} } }=-2.93[/tex]
Using the z table:
P(x < 10) = P(z < -2.93) = 0.0017
the probability that a random sample of n=45 oil changes results in a sample mean time of less than 10 minutes is 0.0017
For part (a), a sample size larger than 30 would be sufficient for using the normal model. For part (b), we'd use the standard error and z-score to find the corresponding probability for the sample mean time being under 10 minutes with a sample size of 45.
Explanation:The questions revolve around the normal distribution model, which is a concept in Statistics, and the sample size needed to use the normal model to make inferences about a population (in this case, the duration of oil changes). For part (a), we must note that the Central Limit Theorem allows us to assume the distribution of sample means will approximate a normal distribution if the sample size is large enough (mostly, n > 30 is sufficient).
Thus, for this particular scenario, a sample size greater than 30 would be adequate. For part (b), using the standard error (standard deviation / sqrt(n)) with n = 45, we can find the z score = (X - μ) / standard error, where X is 10. We consult a normal distribution table or use software to find the probability associated with this z-score, which would be the answer.
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Anyone can help me with all of these answers 1-10 ( 18 Points ) ?
Answer:
1) 14
2) 8
3) 5
4) 11
5) 10
6) 6
7) 10
8) 17
9) 26
10) 18
Step-by-step explanation:
Merry Early Christmas :)
In the United States, 13 out of 20 cans are recycled. What percent of cans are recycled?
Answer:
65%
Step-by-step explanation:
Divide 13 by 20:
0.65
Times 100:
65
So 65%
Assume you have sea water that weighs 64 lb/ft³ and contains 35 parts per thousand (0.0035) dissolved salt by weight. How many cubic feet of the sea water would you need to place in an exaporation basin to collect 125 lb of sea salt?
Answer:
558.036 lb
Step-by-step explanation:
Let x is the amount of the sea water to collect 125 lb of sea salt
As given: 64 lb/ft³ has 0.0035 dissolved salt by weight
So the formula to find out the amount of the sea water is:
64 lb/ft³ * 0.0035 *x ft³ = 125 lb
<=> x = [tex]\frac{125}{64*0.035}[/tex] = 558.036 lb
Hope it will find you well.
Evaluate: log216
Select the appropriate response
A) 0
B) -1
C) 7
Answer:
4
Step-by-step explanation:
log2(16)
log2(2^4)
4 log2(2)
4 × 1
4
It should be 4
Calculate how many infected people there will be on April 25 if on March 22 there were 69 cases, use equation 15.4x+72, plug x value and simplify to get y value
Answer:
There will be 1134.6 infected people on April 25 if on March 22 there were 69 case.
Step-by-step explanation:
Given : Equation [tex]15.4x+72[/tex]
To find : Calculate how many infected people there will be on April 25 if on March 22 there were 69 case ?
Solution :
Equation [tex]y=15.4x+72[/tex]
Plug the x value in the equation,
[tex]y=15.4(69)+72[/tex]
[tex]y=1062.6+72[/tex]
[tex]y=1134.6[/tex]
Therefore, there will be 1134.6 infected people on April 25 if on March 22 there were 69 case.
Test the claim about the population mean μ at the level of significance α. Claim: μ ≠ 0; α = 0.05; σ = 2.62 Sample statistics: = -0.69, n = 60 Fail to reject H0. There is enough evidence at the 5% level of significance to support the claim. Reject H0. There is enough evidence at the 5% level of significance to reject the claim. Reject H0. There is enough evidence at the 5% level of significance to support the claim.
Answer:
Correct option:
Fail to reject H₀. There is enough evidence at the 5% level of significance to support the claim.
Step-by-step explanation:
The claim to be tested is:
Claim: μ ≠ 0.
The information provided is:
α = 0.05
σ = 2.62
Sample statistics: = -0.69
n = 60
As the population standard deviation is provided, it can be determined that a z-test for single is used to performed the test.
Decision rule:
If the p-value of the test is less than the significance level, α then the null hypothesis will be rejected and vice-versa.
Compute the p-value as follows:
[tex]p-value=2P(Z<-0.69)\\=2\times [1-P(Z<0.69)]\\=2\times [1-0.7549]\\=0.4902[/tex]
*Use a z-table for the probability.
The p-value = 0.4902 > α = 0.05.
The null hypothesis was failed to rejected at 5% level of significance.Thus, it can be concluded that there is enough evidence at the 5% level of significance to support the claim.
can anybody help please?
Answer:
AB = 24 cm, BC = 6 cm
Step-by-step explanation:
The perimeter of PQRS = 2(8) + 2(2) = 16 + 4 = 20 cm
Given the perimeter of ABCD is 60 cm, then
scale factor = [tex]\frac{60}{20}[/tex] = 3
That is the dimensions of ABCD are 3 times those of PQRS, so
AB = 3 × 8 cm = 24 cm
BC = 3 × 2 cm = 6 cm
Answer:
AB = 24 cm.
BC = 6 cm.
Step-by-step explanation:
The outer rectangle is a dilation of the inner rectangle centered at the origin. Therefore:
The inner and outer rectangles are similar so the ratio of length to width of the outer rectangle is the same as the ratio of length to width of the inner one.
so AB / BC = 8/2 = 4
AB = 4BC -------------(1)
Also as the perimeter = 60
2AB + 2BC = 60.............(2)
Substituting AB = 4BC in equation (2):
2(4BC) + 2BC = 60
10BC = 60
BC = 6 cm.
and AB = 4*6 = 24 cm.
Sven observes a bird on top of a light pole. His eye level is 6 feet off of the ground. Sven is 48 feet from the pole. If the distance to the bird from Svens eyes is 50 feet, how tall is the pole?
The height of the pole is 20ft.
Step-by-step explanation:
Let the height of the pole be '(h+6)'
Distance between the pole and Sven = 48ft.
Height of Sven = 6 ft.
Distance between the bird and his eyes = 50 ft.
We can find the value of 'h' using pythogoras theorem,
h = √(2500-2304)
h = √(196)
h = 14 ft.
The height of the pole = h + 6
= 14 + 6
= 20ft.
The height of the pole is 20ft.
GEOMETRY! PLEASE SHOW YOUR WORK.
Given:
The base of the given triangle has two part:
Left( left side of the hypotenuse) = 25
Right ( right side of the hypotenuse) = x
The altitude (h) = 60
To find the value of x.
Formula:
By Altitude rule we know that, the altitude of a triangle is mean proportional between the right and left part of the hypotenuse,
[tex]\frac{left}{altitude} =\frac{altitude}{right}[/tex]
Now,
Putting,
left = 25, altitude = 60 and right = x we get,
[tex]\frac{25}{60} = \frac{60}{x}[/tex]
or, [tex](25)(x)=(60)(60)[/tex] [ by cross multiplication]
or, [tex]x= \frac{3600}{25}[/tex]
or, [tex]x=144[/tex]
Hence,
The value of x is 144.
Answer:
x = 144
Step-by-step explanation:
Height Theorem
60² = 25·x
3600 = 25x
x = 3600 : 25
x = 144
I NEED HELP OBN THIS BADLY WILL GIVE YOU CROWN
A jug contained 3 1/4 pints of milk at the start of a baking class. At the end of the class, only 3 fluid ounces were left.
How many fluid ounces of milk were used during the class?
10 fl oz
23 fl oz
49 fl oz
101 fl oz
what’s the coordinate grid ?
Answer:
linear and lateral
Step-by-step explanation:
thsts it
Final answer:
A coordinate grid, also known as a Cartesian coordinate system, is a mechanism used in mathematics to define every point in a plane with a pair of numerical values indicating horizontal and vertical positions from an origin. Systems like UTM and SPC are derived from this concept, using a grid to simplify plotting and calculations on a plane surface.
Explanation:
A coordinate grid, or a Cartesian coordinate system, is a tool used in mathematics to specify each point uniquely in a plane by a pair of numerical coordinates. These are typically written as an ordered pair (x, y) where 'x' represents the horizontal displacement and 'y' represents the vertical displacement, both measured from a specific origin point. This system of geometry was developed by René Descartes, hence the name Cartesian.
For example, the origin of a coordinate system is the starting point where both x and y are zero, designated as (0,0). If we move to the right, x increases, and if we move up, y increases. Conversely, moving to the left decreases x and moving down decreases y. So, for instance, the point (3,4) is located 3 units to the right of the origin and 4 units above it.
Plane coordinate systems, like the Universal Transverse Mercator (UTM) and the State Plane Coordinate (SPC) systems, simplify calculations by using a grid pattern superimposed on a flattened representation of the Earth's surface, facilitating easier and more precise location plotting than spherical coordinate systems like latitude and longitude.
The lifetime of a battery has the exponential distribution with mean 6.9 months. If it fails, I immediately replace it with another – if I have one. I need a year’s supply of the battery. In addition to the one in the flashlight, how many extra should I bring with me? 1, 2, or 3?
Answer:
You should carry 2 other batteries.
Step-by-step explanation:
If the average life of each battery tends to last 6.9 months, and what you need is a year of battery supply, you probably need to carry two batteries.
The battery inside the flashlight has probably already spent much of its half-life.
We are told that the flashlight already has a battery inside, the batteries are discharged inside the flashlight even if the flashlight is not being used.
Which means that the average life of that battery is wearing out.
It would take 2 more batteries in addition to the one already inside the flashlight to supply the need for these for a year.
You have $30 dollars saved up. Every week you spend $6 at the arcade. Write an equation in slope intercept form that shows how much money you have (y) after x weeks.
Answer:
y = -6x + 30
Step-by-step explanation:
The inicial value you have is $30, so this will be the value of y after 0 weeks, that is, x = 0
After one week, you spend $6, so you will have y = 30 - 6 = 24 when x = 1.
With these pair of values, we can find the linear equation:
y = ax + b
for x = 0, y = 30:
30 = a*0 + b
b = 30
for x = 1, y = 24:
24 = a*1 + 30
a = 24 - 30 = -6
So, our equation is:
y = -6x + 30
help with #22 please
Answer:
side c = 10.2
A = 52.6°
B = 37.4°
Step-by-step explanation:
c² = 8.1² + 6.2²
c² = 104.05
c = 10.20049018
Using cosine law:
8.1² = 10.2² + 6.2² - 2(10.2)(6.2)cos
cosA = 7687/11648
A = 52.57199409
A = 52.6°
B = 180 - 90 - 52.6 = 37.4°
How do i solve this problem while creating a quadratic equation ?
Answer:
f(x) = -15x² + 50x
Step-by-step explanation:
You're given the rocket start at ground level, so we can assume,
f(0) = 0
after 1 second the rocket is 35 feet up.
f(1) = 35
and after 2 second the rocket is 40 ft up.
f(2) = 40
Now you have 2 values to plug in your formula to solve.
Plug in f(x) = ax² + bx + c and solve:
f(0) = a(0)² + b(0) + c = 0
f(1) = a(1)² + b(1) + c = 35
f(2) = a(2)² + b(2) + c = 40
a(0)² + b(0) + c = 0
a(1)² + b(1) + c = 35
a(2)² + b(2) + c = 40
0 + 0 + c = 0 , we got c=0, so substitute it
a + b + c = 35
4a + 2b + c = 40
Solve for a and b
c = 0
a + b + 0 = 35
4a + 2b + 0 = 40 , solve it using elimination
-2a - 2b + 0 = -70
4a + 2b + 0 = 40
2a + 0 = -30
a = -15 , we got a, solve for b now
a + b + 0 = 35
(-15) + b + 0 = 35
b = 50
Now we got c=0, a=-15, and b=50, plug it back in your equation
f(x) = -15x² + 50x + 0
Students set a goal of collecting 900 cans for the canned food drive. The number of cans they have collected so far is 82% of their goal. How many cans have they collected so far?
Answer:
738 cans.
Step-by-step explanation:
To calculate 82% of 900, take 0.82 *900. Your answer will be 738.
Answer:
738 cans
Step-by-step explanation:
900 x .82=738
in what quradrant does the terminal side of 0 lie when tan 0 < 0 and sin 0 < 0
Answer:
Step-by-step expla0000000000000000000000000nation:
I need help with this question about similar triangles
Answer:
ST = 12 units
Step-by-step explanation:
Δ RAS and Δ TES are similar triangles, thus the ratios of corresponding sides are equal, that is, noting that SR = 21 - ST, thus
[tex]\frac{ST}{SR}[/tex] = [tex]\frac{TE}{AR}[/tex] substitute values
[tex]\frac{ST}{21-ST}[/tex] = [tex]\frac{8}{6}[/tex] ( cross- multiply )
6ST = 8(21 - ST)
6ST = 168 - 8ST ( add 8ST to both sides )
14ST = 168 ( divide both sides by 14 )
ST = 12
Please help me answer this
Answer:
B. 3
Step-by-step explanation:
If a toy helicopter is moving at 12 m/s, how much energy does 3kg toy have?
9514 1404 393
Answer:
216 J
Step-by-step explanation:
The kinetic energy is given by ...
KE = 1/2mv^2
KE = (1/2)(3 kg)(12 m/s)^2 = 216 kg·m²/s² = 216 J
The kinetic energy of the toy is 216 joules.
__
Its potential energy depends on its height.
Answer:216 J Is the answer I just checked
Step-by-step explanation:
Find the midpoint of the line segment with end coordinates of:
(
0
,
2
)
and
(
2
,
8
)
The midpoint is just the average of the coordinates,
M = (1/2) ( (0,2) + (2,8) ) = ((0+2)/2, (2+8)/2) = (1, 5)
Answer: (1,5)
Answer:
(1,5)
Step-by-step explanation:
(0,2) and (2,8)
Midpoint: (0+2)/2, (2+8)/2
2/2, 10/2
(1,5)
Of the 60 students in a school, 24 are currently studying chemistry. Exactly 16 of the girls in the school are not currently studying chemistry. The number of girls in the school is 33. How many boys are currently studying chemistry
Answer:
7 boys.
Step-by-step explanation:
Given:
Total number of students in the school = 60
Total number of girls in the school = 33
Total number of students currently studying chemistry = 24
Total number of girls not currently studying chemistry = 16
Question asked:
How many boys are currently studying chemistry ?
Solution:
Total number of girls in the school = 33
Total number of girls not currently studying chemistry = 16
Total number of girls currently studying chemistry = Total number of girls in the school - Total number of girls not currently studying chemistry
Total number of girls currently studying chemistry = 33 - 16 = 17
Now:-
Total number of boys and girls currently studying chemistry = 24
Total number girls currently studying chemistry = 17
Total number of boys currently studying chemistry = Total number of boys and girls currently studying chemistry - Total number girls currently studying chemistry
Total number of boys currently studying chemistry = 24 - 17 = 7
Therefore, 7 boys are currently studying chemistry.
Complete the steps to derive the standard form of the equation of a
circle centered at Alh, k).
1. What is segment AB to circle A?
Check
Answer:
a radius
x-h
y-k
x-h, y-k
Step-by-step explanation:
The standard form of the circle is given by ( x - h )² + ( y - k )² = r²
What is a Circle?A circle is a closed figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle
The circumference of circle = 2πr
The area of the circle = πr²
where r is the radius of the circle
The standard form of a circle is
( x - h )² + ( y - k )² = r²,
where r is the radius of the circle and (h,k) is the center of the circle.
The equation of circle is ( x - h )² + ( y - k )² = r²
For a unit circle , the radius r = 1
x² + y² = r² be equation (1)
Now , for a unit circle , the terminal side of angle θ is ( cos θ , sin θ )
Given data ,
Let the equation of circle be C
Let the center of the circle be represented as A ( h , k )
Now , the radius of the circle is = r units
And , standard form of a circle is
( x - h )² + ( y - k )² = r²
when it is a unit circle , the center is at ( 0 , 0 )
S0 , the equation of circle is x² + y² = r²
Hence , the standard form of circle is ( x - h )² + ( y - k )² = r²
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A monkey collects 60 coconuts and wants to store them in stacks that each contain the same number of coconuts. Describe all the different stacks the monkey can make, including the number of coconuts in each stack. Then find the prime factorization of 60. The monkey can make 1 stack of , 2 stacks of , 3 stacks of , 4 stacks of , 5 stacks of , 6 stacks of , 60 stacks of , 30 stacks of , 20 stacks of , 15 stacks of , 12 stacks of and 10 stacks of . The prime factorization of 60 is
Answer:
1 stack of 60
2 stacks of 30
3 stacks of 20
4 stacks of 15
5 stacks of 12
6 stacks of 10
60 stacks of 1
30 stacks of 2
20 stacks of 3
15 stacks of 4
12 stacks of 5
Prime Factorisation
[tex]60=2^{2}*3*5[/tex]
Step-by-step explanation:
To find the number of stacks you can make just divide the total by the size of the stacks. This also works in reverse.
To find the prime factorisation you just find the factors of the number by dividing it by the largest prime possible.
The monkey can arrange the 60 coconuts into different numbers of stacks, from 1 stack of 60 coconuts to 60 stacks of 1 coconut. The prime factorization of 60 is 2^2 x 3 x 5.
Explanation:The monkey, who has collected 60 coconuts, can distribute them in various different ways. The distribution depends on the number of coconuts in each stack as well as the total number of stacks. Here are the various possibilities:
1 stack with 60 coconuts 2 stacks with 30 coconuts each 3 stacks with 20 coconuts each 4 stacks with 15 coconuts each 5 stacks with 12 coconuts each 6 stacks with 10 coconuts each 10 stacks with 6 coconuts each 12 stacks with 5 coconuts each 15 stacks with 4 coconuts each 20 stacks with 3 coconuts each 30 stacks with 2 coconuts each 60 stacks with 1 coconut each
Now, for the prime factorization of 60. This involves breaking down 60 into its smallest prime factors, which are 2, 3, and 5. Thus, the prime factorization of 60 is: 22 x 3 x 5
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5. Alisha's average math test score was 82. Which of the following students has the same average
math test score as Alisha?
F. Jenny earned 492 points on 6 tests.
G. Frankie earned 352 points on 4 tests.
H. Benicio earned 468 points on 6 tests.
1. Dontonio earned 344 points on 4 tests.
(20 Points)
Answer:
F. Jenny earned 492 points on 6 tests.
Jenny has the same average
math test score as Alisha i.e. 82.
Step-by-step explanation:
Points earned by Jenny = 492
no. of maths tests attempted by Jenny = 6
average maths test score = 492/6
=82
How do I solve this
Answer:
c = 30 inch
Step-by-step explanation:
perpendicular (p) = 18 inch
base(b) = 24 inch
hypotenuse (h) = ?
we know by using Pythagoras theorem
h² = p² + b²
h² = 18² + 24²
h² = 324 + 576
h² = 900
h= √900
therefore h = 30 inch
Hope it will help you. :)
Darian drove 274.5 miles in 4.5 hours. What was his average speed?
Answer:
61 miles per hour
Step-by-step explanation:
because you need to divide 274.5 by 4.5 to get the average speed per hour.
Answer:
61 miles per hour
Step-by-step explanation:
To find the average speed, divide the miles by the hours
miles/hours
274.5/4.5
61
So, the average speed is 61 miles per hour
Step 1: 5 = negative 2 (negative StartFraction 3 Over 10 EndFraction) + b. Step 2: 5 = StartFraction 6 Over 10 EndFraction + b. Step 3: 5 minus StartFraction 6 Over 10 EndFraction = StartFraction 6 Over 10 EndFraction minus StartFraction 6 Over 10 EndFraction + b. Step 4: StartFraction 50 Over 10 EndFraction minus StartFraction 6 Over 10 EndFraction = b. Step 5: StartFraction 44 Over 10 EndFraction = b. Step 6: y = negative 2 x minus 4.4.
A student used the slope-intercept form to write the equation of a line that has a slope of -2 and passes through the point (StartFraction negative 3 Over 10 EndFraction, 5). The student’s work is shown to the left.
Analyze the steps to identify the error.
Step1: student switched the x and y values
Step 3: student needed to add StartFraction 6 Over 10 EndFraction to both sides
Step 5: student subtracted incorrectly
Step 6: student needed to add the b value
Answer:
D.) Step 6: student needed to add the b value.
Step-by-step explanation:
I got it wrong and it gave me the right answer, which is what i provided, D.
Answer: Step6
Step-by-step explanation:
The wholesale price for a chair is $108. A certain furniture store marks of the wholesale price by 27%. Find the price of the chair in the furniture store. Round your answer to the nearest cent as necessary.
Answer:
The price of chair in furniture house is $137.16
Step-by-step explanation:
We are given the following in the question:
Wholesale price of chair = $108
Marked percentage = 27%
We have to find the price of the chair in the furniture store.
Increased price =
[tex]=27\%\times 108\\\\=\dfrac{27}{100}\times 108\\\\=29.16\$[/tex]
Price of chair in furniture house =
= Wholesale price + Increased price
[tex]=108 + 29.16\\=137.16\$[/tex]
Thus, the price of chair in furniture house is $137.16