The value of gf(4) is 18
What is Function?
A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.
Given,
f(x) = x + 2
g(x) = 3x
Now we need Function of a function
i.e. g[f(x)]
Then on g(x) we have to replace the x with f(x)
Thus,
g[f(x)] = 3(x + 2)
= 3x + 6
Now by evaluating at
x = 4 i.e.
gf(4) = 3(4) + 6
gf(4) = 12 + 6
gf(4) = 18
Hence, The value of gf(4) = 18
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need help on this !!!!!!!!!!!
Using the Triangle Inequality Theorem we can state that the range of z is 4 < z < 20.
What is the Triangle Inequality Theorem?The above theorem states that The length of any two sides of a triangle must sum to more than the length of the third side. That is:
12 + 8 > z.............1
12 + z > 8;.............2
8 + z > 12.............3
Solving for (1)
20 > z...............4
Solving for (2)
we have- 12 + z > 8
remove 8 from both sides and we have
4 + z > 0 or z > -4 ...............5
Solving for (3) we have
8 + z > 12
remove 8 from both sides
z > 4 .....................6
Since we can't have a negative value on a triangle, we must deal with expressions 4 and 6 which state:
20 > z; and
z > 4
Another way to write this is:
20 > z > 4; or
4 < z < 20
Hence the range of the unknown side that will form a triangle is:
4 < z < 20
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these researchers said the differences were statistically significant. explain what that means in context.
A statistically significant finding indicates that it is unlikely to just be explained purely by chance or random influences.
Define the term statistically significant?The notion that a set given observed data is not the result of random but can instead be linked to a specific cause is referred to as statistical significance.
A high level of statistical significance signifies that the observed link is unlikely to be coincidental.The calculation for statistical significance is prone to some inaccuracy.When researchers do not utilize precise wording when describing their findings, statistical significance could be misconstrued.Depending on the research, many sorts of significance tests are being used.Statistical significance indicates that a result is unlikely to be attributed purely by chance and random causes.
Thus, in other words, if there is no genuine effect in a research study, a statistically significant conclusion has an extremely low likelihood of occuring.
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A population of values has an unknown distribution with
ll
= 83.3 and o
= 10.4. You intend to draw a random
sample of size n
= 212.
What is the mean of the distribution of sample means?
flie
(Please enter an exact answer.)
What is the standard deviation of the distribution of
sample means?
Ox
(Please report your answer accurate
to 2 decimal places.)
By using the concept of mean and standard deviation, it can be obtained that
The mean of the distribution of sample mean ([tex]\mu_x[/tex]) = 83.3
Standard deviation of distribution ([tex]\sigma_x[/tex]) = 0.714
What is mean and standard deviation?
Suppose there is a data set and an average value of the data set needs to be calculated. To find the average value of the data set, mean is used
For Standard deviation, at first, it is important to know about variance
Variance is the sum of the square of deviation from mean.
Square root of variance is the standard deviation
A population of values has an unknown distribution with
[tex]\mu = 83.3[/tex] and [tex]\sigma = 10.4[/tex], n = 212
So the mean of the distribution of sample mean ([tex]\mu_x[/tex]) = 83.3
Standard deviation of distribution ([tex]\sigma_x[/tex]) = [tex]\frac{10.4}{\sqrt{212}}[/tex] = 0.714
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It take an ant farm 2 day to conume 1/2 of an apple. At that rate, in how many day will the ant farm conume 2 apple?
the ant will take 8 days to consume 2 apples.
Given, an ant takes 2 days to consume 1/2 of an apple.
We have to find the number of days ant will take to consume 2 apples.
So, ant takes 2 days = consumption of 1/2 apple
ant takes 4 days = consumption of 1 apple
Consumption of 1 apple = ant takes 4 days
Consumption of 2 apples = ant takes 4×2 days
Consumption of 2 apples = ant takes 8 days
Hence, the ant will take 8 days to consume 2 apples.
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You go to the store to buy supplies for class. You want to buy a new notebook for $3 and 5
folders. The most you can spend is $10. If you buy all the same type of folders, what are the
individual folder prices you can afford?
(Algebra)
If we buy all the same type of folders, the maximum amount we can afford for an individual folder is $ 3.3
To buy : A notebook for = $ 3
number of folders required = 5
The amount of money we can spend is $ 10
The above mentioned problem is a problem of algebra because we would have to use a variable to find out the unknown value.
The individual folders price can be calculated by the equation
3x = 10
divide both sides by 3 and we will get
x = 3.3
Thus the individual folder prices we can afford is $ 3.3
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if a rectangular prism is 4 cm long, 3 cm wide and 1,5 cm high what is the volume of the prism
Answer: The volume of the prism is [tex]18^{3}[/tex]cm
Step-by-step explanation: The formula to solve for the volume of a rectangular prism is V = lwh. In this case, it's V = 4 x 3 x 1.5 therefore V = 18
What is an equation of the line that passes through the points (-2,7) and (-8,4)
Answer: y = (1/2)x + 8
Step-by-step explanation:
Slope: (4-7)/(-8--2) = (-3)/(-6) = 1/2
y = (1/2)x + b
7 = (1/2)-2 + b
7 = -1 + b
8 = b
y = (1/2)x + 8
What is the volume of this figure?
O 6,720 cm³
O 5,760 cm³
O 3,840 cm³
O I don't know.
The volume of the given figure is 5760 [tex]cm^{3}[/tex].
According to the question,
We have the following information:
We have a figure where two cuboids are joined together. So, the volume of the figure will be the sum of the volume of these cuboids.
We know that the following formula is used to find the value of cuboid:
Volume of cuboid = Length*breadth*height
Volume of larger cuboid = 40*8*12
Volume of larger cuboid = 3840 [tex]cm^{3}[/tex]
Volume of smaller cuboid = 20*8*12
Volume of smaller cuboid = 1920 [tex]cm^{3}[/tex]
Volume of the figure = 3840+1920
Volume of the figure = 5760 [tex]cm^{3}[/tex]
Hence, the correct option is B (the second option).
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Answer:
5760
Step-by-step explanation:
Which of the following numbers is a composite number? A. 9 B. 2 C. 29 D. 5
Answer: A. 9
Step-by-step explanation:
a square with side length 2 and a circle share the same center. the total area of the regions that are inside the circle and outside the square is equal to the total area of the regions that are outside the circle and inside the square. what is the radius of the circle?
The radius of the circle which is overlapping the square is 1.12.
The length of side of the square is 2. Let us say that the radius of the circle is R.
The circle and the square are overlapping on each other.
The area of the region that are outside the circle but inside the square are equal to the area of the region which are inside the circle but outside the square.
Let us name the area of the region that are outside the circle but inside the square as M.
Let us name the area of the region which are inside the circle but outside the square as N.
Let us say that the area that is common in both is C.
The area of the square is 4.
So, according to the question,
M + C = 4
And,
N + C = πR²
And we know, M = N,
So,
C - πR² = C - 4
R = 2/√π
R = 1.12.
So, the radius of the circle is 1.12
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solve the equation:x/-3.5+33=30
Answer:
x=10.5
Step-by-step explanation:
Tyrone is the supply manager of a bakery. He needs to make sure there is plenty of flour on hand for their recipes each month. The bakery begins the month with 215.4 pounds of flour. Tyrone tracks the weekly use, along with the supply delivery received in the middle of the month.
Week Weekly Flour Use (lb)
1 −5812
2 −70.6
3 75310
4 −6778
How much flour does the bakery have on hand at the end of the month? Explain how you found your answer.
The pounds of flour the bakery has at the end of the month is 92.725 lb
How much flour does the bakery have at the end of the month?The negative numbers denote when flour was used while the positive numbers denote when flour was added. The negative numbers would be subtracted while the positive numbers would be added.
For ease of computation, the mixed numbers would be converted to decimals.
-58 1/2 = -58.5
75 3/10 = 75.3
-67 7/8 = -67.875
Pounds of flour the bakery has at the end of the month: 215.4 - 58.5 - 70.6 + 75.3 - 67.875 = 92.725 lb
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If y varies directly as x and y=8 when x=2 find when x=6
The equation is y = 4x. And the value of the function at x = 6 will be 24.
What are ratio and proportion?A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.
If y varies directly to x. Then the relationship between them is written as,
y ∝ x
y = kx
When y = 8 and x = 2, then the value of the constant k is given as,
8 = k (2)
k = 8 / 2
k = 4
Then the equation is written as,
y = 4x
Then the value of the function at x = 6 will be given as,
y = 4 (6)
y = 24
The equation is y = 4x. And the value of the function at x = 6 will be 24.
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Ameekah is working with consecutive integers. If she uses x to represent her first number, what should she use to represent her second number?
x
x + 1
x + 2
2x
She should use (b) x + 1 to represent her second number
How to determine the representation of the second number?From the question, we have the following statements that can be used in our computation:
She uses x to represent her first numberThe numbers are consecutive numbersAs a general rule
Consecutive numbers are number that have a difference of 1 i.e both numbers are next to each other
Take for instance:
2 and 3, 5 and 6, 10 and 11 are all instances of consecutive numbers
Recall that she uses x to represent her first number
This means that the next number is
Next number = First number + 1
Substitute the known values in the above equation, so, we have the following representation
Next number = x + 1
Hence, the second number is (b) x + 1
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A cylinder used for storing spools of thread has a radius of 2 units and a slant height of √29. What is the height of the cylinder?
PLS HELP ASAP!!(show work if can)
Height of cylinder is 5 units
Define Cylinder
One of the most fundamental curvilinear geometric shapes, a cylinder has historically been a three-dimensional solid. It is regarded as a prism with a circle as its base in basic geometry.The volume of the slanted cylinder is V = Base area of cylinder × Height of cylinder⇒ V = (π × radius²) × h
We have given,
Slant height of cylinder = √29
Radius is = 2 units
Now, we to have to calculate the height for that we have the formula
h = √l² - r²
where, l = slant height
r = radius of the circular base
h = height of the cylinder
Now, for the sake of simplicity
h = √l² - r²
h² = l² - r²
Now, plug in the values
h² = (√29)² - 2²
h² = 29 - 4
h² = 25
h = 5
Hence, the height of cylinder is 5 units
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Each tire on the toy car has a diameter of 5. 6cm, the tire spin completely around 15 times when the car was pushed in a straight line. About how far was the car pushed
The distance covered by the car is 264cm.
Here we have to find the distance covered by the car.
Information provided:
Diameter (d) = 5.6cm
radius(r) = 5.6/2
= 2.8cm
Rotation = 15 times
Formula to find the circumference of the tire:
Circumference = 2πr
= 2 × 22/7 × 2.8
= 17.6cm
This is the distance covered by the tire in one rotation.
Distance covered after 15 rotations = 15× 17.6
= 264 cm
Therefore distance covered is 264 cm.
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At a certain gas station, gas costs $2.85 a gallon. Jason paid $25.50 to fill his tank. Write and solve an equation to
find how many gallons of gas he bought?
Answer:
8.95 gallons
Step-by-step explanation:
25.50/2.85 = 8.95
An investor has $100,000 to invest in three types of bonds: short-term, intermediate, and long term. how much should he invest in each type to satisfy conditions?
short-term pay 4% annually, intermediate pays 6% and long term pays 8%. The investor wishes to have a return of $6700 on his investment, with equal amounts invested in intermediate and long term bonds.
I know it will be an x+y+z system. I don't know how to set it up. x+y+z=100,000; .04x+.06y+.08z=6700 and ? or is it something else?
The equation used to solve this problem is x + y + z = 100000, 0.04x + 0.06y + 0.08z = 6700 and y = z
What is an equation?An equation is an expression showing the relationship between two or more numbers and variables.
Let x represent the amount of money invested at 4% (short term), y represent the amount of money invested at 6% (intermediate term) and z represent the amount of money invested at 8% (long term)
Since an investor has $100,000 to invest, hence:
x + y + z = 100000 (1)
Also, the investor wishes to have a return of $6700, hence:
0.04x + 0.06y + 0.08z = 6700 (2)
Equal amounts invested in intermediate and long term bonds. This gives:
y = z (3)
The third equation used to solve this problem is y = z
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on their 560-mi trip, the bruins basketball team spent two more hours on the interstate highway than they did on local highways. they averaged 45 mph on local high-ways and 55 mph on the interstate highways. how many hours did they spend driving on local highways?
They spent 6.5 hours driving on local highways by travellin with diffrent average speeds.
Given that,
The bruins basketball team spent two more hours on the interstate than they did on local roadways during their 560-mile journey. They traveled at an average speed of 55 mph on interstates and 45 mph on local routes.
I=interstate
L=local
using d=rt the first rows gives you d=55t
the second row gives you 560-d=45(t-2)
Since the two distances add up to 560. Add the two distance expression and set their sum equal to the given total
560=55t+45(t-2) which equals
560=55t+45t-90
650=55t+45t
650=100t
6.5=t
Hence on local roadways, they traveled at various average speeds for 6.5 hours.
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Impact Sports is having a sale this week. A portable basketball hoop has an original price of $159. It is on sale for 35% off the original price. What is the sale price of the basketball hoop?
Answer: 150*40/100=60
60+150=210.
Step-by-step explanation:
Monica is 33 years old. Amanda is 18 years older than Brittany and 16 years older than Rita. Brittany is 23 years younger than Monica. How old is Rita?
please help
an urn contains 6 blue balls and 6 orange balls. in how many ways can we select 2 blue balls and 2 orange balls from the urn?
The no. of ways to select the 2 blue balls and 2 orange balls from the urn is 0.4545
No. of Blue balls in the urn = 6
No. of Orange balls in the urn = 6
Total no. of balls in the urn = No. of blue balls + No. of orange balls
= 6 + 6
= 12 balls
No. of blue balls to be selected = 2
No. of orange balls to be selected = 2
No. of balls to be selected = 4
The total. no of ways 4 balls can be selected =[tex]^{12}C_{4}[/tex]
The No. of ways 2 blue balls can be selected = [tex]^{6}C_{2}[/tex]
The No. of ways 2 orange balls can be selected = [tex]^{6}C_{2}[/tex]
Therefore, No. of ways to select 2 blue balls and 2 orange balls from the urn
= [tex]^{6}C_{2} \times ^{6}C_{2} /^{12}C_{4}[/tex]
Probability = No. of ways to select blue balls x No. of ways to select orange balls / Total no. of ways to select balls
P = (15×15)/495
= 225 / 495
P = 0.4545
Therefore, the no. of ways to select blue and orange balls is 0.4545
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The difference between a big shot and a little shot is that a big shot is just a little shot that kept on shooting. what do you think about this quote? answer and ill give you a lot of points 100 for free
Answer:
The quote seems to have a little to much shooting. Don’t you think?
Step-by-step explanation:
Answer:
lair lair
Step-by-step explanation:
Nora leans a 24-foot ladder against a wall so that it forms an angle of 76^{\circ} ∘ with the ground. How high up the wall does the ladder reach? Round your answer to the nearest hundredth of a foot if necessary.
Answer:
23.29 ft
Step-by-step explanation:
The given scenario can be modelled as a right triangle, where the angle between the ground and the ladder is 76°, the side opposite the angle is the height the ladder reaches up the wall, and the hypotenuse is the ladder.
To find how high up the wall the ladder reaches, use the sine trigonometric ratio:
[tex]\sin(\theta)=\sf \dfrac{O}{H}[/tex]
where:
θ is the angle.O is the side opposite the angle.H is the hypotenuse (the side opposite the right angle).The angle of elevation is 76°, so θ = 76°.
Let x be the height the ladder reaches up the wall, so O = x.
H is the length of the ladder, so H = 24.
Substitute the given values into the sine ratio and round the answer to the nearest hundredth:
[tex]\sin(\theta)=\sf \dfrac{O}{H}[/tex]
[tex]\sin(76^{\circ})= \dfrac{x}{24}[/tex]
[tex]\sin(76^{\circ})\cdot 24= \dfrac{x}{24}\cdot 24[/tex]
[tex]24 \sin(76^{\circ})= x[/tex]
[tex]x=24 \sin(76^{\circ})[/tex]
[tex]x=23.28709743...[/tex]
[tex]x=23.29\; \sf ft\;(nearest\;hundredth)[/tex]
Therefore, the ladder reaches 23.29 ft up the wall, rounded to the nearest hundredth.
ella has 1/3 as many trading cards as kip. Adira has 3 more than 50 percent of the number of cards that kip has. Kip has 18 cards. write an expression for the total number of cards the groups has. writ an expression for the total number of cards?
If Adira has 3 more than 50 percent of the number of cards that kip has. Kip has 18 cards. The expression for the total number of cards the groups has is: 1/3 ⋅9+(3+0.5⋅18)+18.
How to determine the expression?Given data:
Number of trading cards = 1/3
Adira number of cards = 23 more than 50%
Kip number of cards = 18 cards
Now let formulate an expression and then make use of the formulated expression to find the number of cards
Hence,
Number of cards = 1/3 ⋅9+(3+0.5⋅18)+18
Number of cards = 1/3 ⋅9+(3+9)+18
Number of cards = 1/3 ⋅9+(12)+18
Number of cards =3 + 12+18
Number of cards = 33 cards
Therefore the expression is : 1/3 ⋅9+(3+0.5⋅18)+18.
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45 strikeouts in 36 inning or 96 strikeouts in 80 innings
Evaluate x³ if x = 6
Show work pls
Answer:
216
Step-by-step explanation:
x^3
6^3
6x6x6
36x6
216
Hopes this helps pleas mark brainliest
Suppose that we use a hypothesis test to evaluate a claim about the proportion of narwhals with tusks longer than 3 meters. If we use a a chi-squared test, would the value of our test statistic be the square of the standardized value of the statistic that we would have used if we had chosen a binomial test instead?
Yes, as the asymptotic chi-squared distribution would emerge from normal approximating the binomial distribution and then squaring it.
Given statement;
Suppose that we use a hypothesis test to evaluate a claim about the proportion of narwhals with tusks longer than 3 meters. If we use a chi-squared test, would the value of our test statistic be the square of the standardized value of the statistic that we would have used if we had chosen a binomial test instead.
→ Yes, since by normal approximation of the binomial distribution and then squaring it would give us the resulting asymptotic chi-squared distribution.
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Find the slope of the line that contains (1, 9) and (6, 6).
Answer:
Step-by-step explanation:
To find the slope, subtract the y values, and divide it by subtracting the x values. The order matters!
(9-6)/(1-6)=-3/5
In the diagram below, \angle C\cong\angle F∠C≅∠F, \angle D\cong\angle G∠D≅∠G. Enter segments in the blanks provided that would result in a true equation.
The sides of similar triangles are proportional, therefore, the true equation would be: FG/CD = EG/BD.
What are Proportional Lengths of Similar Triangles?Two similar triangles have corresponding angle measures that are congruent to each other, but have corresponding side lengths that are proportional to each other.
Similar triangles have the same shape but their sizes are different.
Given that angles C and F are congruent, and angles D and G are congruent, therefore triangle BCD is similar to triangle EFG based on the AA similarity theorem.
Therefore, the corresponding side lengths of both triangles will be proportional, which means that the following equation would be true:
FG/CD = EG/BD
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