The required value of the given function is (f ⋅ g)(4) = 130.
What are the functions?The function is defined as a mathematical expression that defines a relationship between one variable and another variable.
The functions are given in the question, as follows:
f(x)=3x+1 and g(x)=x²-6
(f ⋅g)(x) is the composition of the functions f and g, which means f(x) × g(x).
(f ⋅ g)(x) = f(x) × g(x)
So, substituting x = 4:
(f ⋅ g)(4) = f(4) × g(4)
= (3 × 4 + 1)×(4² - 6)
= 13 × 10
= 130
So, (f ⋅ g)(4) = 130.
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35x10. I need help please help thank you
Answer:350
Step-by-step explanation: 35x10 =350
Ai Mi goes out to lunch. The bill, before tax and tip, was $16. A sales tax of 6% was added on. Ai Mi tipped 14% on the amount after the sales tax was added. What was the total cost of the meal, plus tax and tip? Round to the nearest cost.
Answer:
$18.97
Step-by-step explanation:
You want to know Ai Mi's bill if her $16 lunch had 6% tax added, and she tipped 14% on the amount with tax.
TaxAdding tax multiplies the bill by (1 +6%) = 1.06.
TipAdding the tip on the amount with tax multiplies that amount by (1 +14%) = 1.14.
Total costThe total cost of Ai Mi's lunch is ...
($16(1.04))(1.14) ≈ $18.97
The total cost with tax and tip was $18.97.
<95141404393>
(0.4)^4 it’s for k12
Answer:
the answer would be
0.0256
solve for the rate (as a %). round to the nearest tenth of a percent when necessary. what is the rate if the base is $23,500 and the portion is $6,227.50?
Rate of the given base $23,500 and the portion $6227.50 is equal to 26.5 percent ( nearest tenth ).
As given in the question,
Given base of the required rate is equal to $23,500
Portion of the given base used is equal to $6227.50
Formula to calculate the rate percent is given by :
Rate percent = [(Portion of the given base used) / ( Base) ] × 100
Substitute the value in the formula we get,
⇒ Rate percent = ( 6227.50 / 23,500 ) × 100
⇒ Rate percent = 26.5%
Therefore, rate percent of the given base and the portion used is equal to 26.5%.
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Which is a better buy: 5 shirts for 100 shekels, or 8 shirts for 128 shekels? Solve by comparing unit costs. Show your work and explain your reasoning.
Answer: 8 shirts for 128 shekels
Step-by-step explanation:
First, we can set up fractions and simplify to find the cost of one shirt.
5shirts/100shekels = 1shirt/20 shekels
8 shirts/128 shekels = 1shirt/16 shekels
Ultimately, whichever cost per shirt is lower is going to be the better buy. Since 16shekels/shirt is less than 20shekels/shirt, you are ultimately buying more shirts for a lower cost. Hope this helps
M114) solve
cos (2x) = √2 - cos (2x)
Answer:
To solve the equation cos (2x) = √2 - cos (2x), we can first isolate the variable on one side of the equation.
cos (2x) = √2 - cos (2x)
add cos(2x) to both sides
2*cos(2x) = √2
divide both sides by 2
cos(2x) = √2/2
Now we can use the identity cos 2x = 2cos^2 x - 1, so
2cos^2 x - 1 = √2/2
Square both sides
4cos^2 x - 2 = 2 - 1
4cos^2 x = 1
Divide both sides by 4
cos^2 x = 1/4
Since cos^2 x = 1/4, then cos x = +/- √(1/4) = +/- 1/2
So x = pi/3 + 2npi or x = 5pi/3 + 2n*pi
the height of a cylinder is increasing at a constant rate of 9 inches per second. the volume remains a constant 1318 cubic inches. at the instant when the radius of the cylinder is 99 inches, what is the rate of change of the radius? the volume of a cylinder can be found with the equation v
The rate of change of the radius is -9/(2π*99) inches/second.
The volume of a cylinder can be found with the equation V = πr^2h, where V is the volume, r is the radius, h is the height and π is a constant. We know that the volume is constant at 1318 cubic inches and we know that the height of the cylinder is increasing at a constant rate of 9 inches per second.
V = πr^2h
1318 = π * 99^2 * h
Now we can differentiate this equation with respect to time.
dV/dt = 2πr*dr/dt * h + πr^2 * dh/dt
where dV/dt is the rate of change of the volume, dr/dt is the rate of change of the radius and dh/dt is the rate of change of the height.
Now we know that dV/dt = 0, dh/dt = 9 and we know the value of r, we can substitute these values in the above equation and solve for dr/dt
0 = 2π * 99 * dr/dt * h + π * 99^2 * 9
dr/dt = -9/(2π*99) inches/second
The rate of change of the radius is -9/(2π*99) inches/second at the instant when the radius of the cylinder is 99 inches.
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if i rolled one die 10 times, what is the mode of the values listed that i rolled? 5, 5, 4, 6, 3, 2, 2, 3, 1, 5 responses 2 2 3 3 4 4 5 5 6 6
mode is 5 and 2 because 2 and 5 occurs more times than other number
Mode: The most frequent number—that is, the number that occurs the highest number of times. Example: The mode of {4 , 2, 4, 3, 2, 2} is 2 because it occurs three times, which is more than any other number.
The total outcomes = 7
This is because the cube was rolled 7 times
The value recorded are
2, 1
4, 5
3, 2
2,2
1,3
6,2
5,3
From all the outcomes, the only possible out comes that shows that the sum of two numbers is more than 5 are
4, 5
6, 2,
5,3
Probability = possible outcomes / total outcomes
Possible outcomes = 3
Total outcomes = 7
Probability = 3/7
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a set s of distinct positive integers has the following property: for every integer x in s, the arithmetic mean of the set of values obtained by deleting x from s is an integer. given that 1 belongs to s and that 2002 is the largest element of s, what is the greatest number of elements that s can have?
The greatest number of elements that s can have is 2002, and the set s = {1,2,3,4,5,...,2002}
The property of the set s states that for every element x in s, the arithmetic mean of the set obtained by deleting x from s is an integer.
To understand this property, we can start by considering the case when the set s has only two elements, say x and y. In this case, the arithmetic mean of the set obtained by deleting x from s is y, and the arithmetic mean of the set obtained by deleting y from s is x. As both x and y are integers, this property holds true.
When the set s has three elements, say x, y, and z. The arithmetic mean of the set obtained by deleting x from s is (y+z)/2. as y and z are integers, (y+z) is always even, thus (y+z)/2 is always an integer. The same applies to the arithmetic mean of the set obtained by deleting y and z.
As we can see, this property holds true for any set of distinct positive integers, no matter the number of elements.
Given that 1 belongs to s and that 2002 is the largest element of s, we can use the property of the set to find the greatest number of elements that s can have.
The arithmetic mean of the set obtained by deleting 1 from s is (x+y+z+...+2002)/(n-1) = (x+y+z+...+2002)/n + 1/n. as x, y, z... 2002 are integers, (x+y+z+...+2002) is always an integer, thus (x+y+z+...+2002)/n is always an integer. Then, as 1/n is always an integer, (x+y+z+...+2002)/n + 1/n is always an integer.
Therefore, the greatest number of elements that s can have is 2002, and the set s = {1,2,3,4,5,...,2002}
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A town with 1800 homes was surveyed. of the 360 who answered the survey, 48 did not have computers at home. On the basis of the survey, estimate how many total homes do not have computers at home.
URGENT!!!!!!!
Answer:
here
Step-by-step explanation:
18000 divided by 360, then multiply that new number with 48. i believe that is the correct math...
Answer:
240
Step-by-step explanation:
48/360*1800
240
Will give brainly. Thanks
Answer: The domain and range is equal to all positive real numbers.
Explanation: The domain and range of the function shown is equal to all positive real numbers because there is no such a value that the function can have an indeterminate situation and also there is no such another positive value that the function cannot have as a result.
Help please this got me confused
Answer:
Step-by-step explanation:
X=32
where M is we can see that those 3 sections add up to make 180.
Therefore 180-96=84 and 84/2=42 so the angles by 84 on both side is 42 since we know that LM and MN is the same we can then determine that the angles in the middle triangle add up to make 180. By looking at the proofs at the top NO and LM are the same so both the bottom angles in each triangle is 42. So we know that 84 is the addition of both the bottom angles 180 - 84 is 96. We set that equal to 3x. 3x=96 Divide both sides by 3 x is equal to 32.
work out 4x(2x10^2) answer in standard form
Answer:
Step-by-step explanation:
nai dunga
Factorise fully x²+X
Answer:
x(x+1)
Step-by-step explanation:
x^2+x=x(x+1)
Answer: x (x + 1)
Step-by-step explanation: Factor out the X
Please see attachment
The fill ups are as follow.
1. vertical Opposite Angle.
2. alternate Interior Angle.
3. b || c, Co- interior angle.
4. a || c, corresponding Angle.
5. Linear pair.
What are parallel line?The fundamental characteristics listed below make it simple to recognise parallel lines.
Straight lines that are always the same distance apart from one another are called parallel lines.No matter how far apart they are from one another, parallel lines can never intersect.Given:
First, <3 = <9 because they vertical Opposite Angle.
Second, <2 = <10 are equal because of alternate Interior Angle.
Third, If <9 and <8 are supplementary then line b || line c because they are Co- interior angle.
Fourth, if <11 = <7 then a || c because they corresponding Angle.
Fifth, < and <6 are supplementary because they are Linear pair of Angle.
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A chord of the circle with centre O and radius 10 cm, subtends an angle
of 120° at the centre of the circle. Find the area of the major sector and
the area of minor segment.
(Use = 3.14 √3 = 1.732
Answer:
Step-by-step explanation:
Erica is considering moving into a one-bedroom apartment in Hyde Park. The
apartment has a rent of $960 and has the following fees.
- Application fee: 6.5% of one month's rent
Credit application fee: $15
- Security deposit: 2 month's rent
- Lease protection: the last month's rent
Broker's fee: 7% of one year's rent
- First month's rent
How much is Erica expected to pay up front in order to move into this apartment?
PLEASE PLEASE HELP
What is ½ as a percentage?
Answer:
50%
1 2 = 1 × 50 2 × 50 = 50 100 . . So the answer is 50%.
please mark me as a brainalist
two regular hexagons are joined together
work out angle x
Answer:
Step-by-step explanation:
120 degrees per angle - It says that it's a *regular* hexagon
what is the slope of y = 17x - 39
Answer:
The slope is 17
Step-by-step explanation:
The slope in a point-slope form equation is always the coefficient of x, which in this case is 17.
Answer the screenshot
Answer: Undefined
Step-by-step explanation:[tex]\sqrt{x}[/tex]
This seems to be undefined.
Let's make a chart:
x #s | y #s
1
2
0
-1
-2
-------------------------------------
Let's take a number out of the chart to act as x:
f(x)=[tex]\sqrt{-2^4 -16}[/tex] -> f(x)=[tex]\sqrt{-16-16}[/tex] -> [tex]\sqrt{-32}[/tex]
Since the answer is negative, the answer should be the one that says undefined.
---- SORRY IGNORE WHAT I TYPED I JUST REALIZED IT IS WRONG PLS DELETE THIS
Draw the first through the fifth generations of squares, triangles and trapezoids. count how many of each shape are needed to create each generation. explain the pattern that you have observed. if a pattern does hold for each generation, how many tiles would be required at the 20th generation? how do you determine if the generation you are building is similar (by mathematical definition) to the other generations? what happens to area when you double the dimensions of a given polygon? triple them? describe the pattern and give the value needed for the 20th generation.
At the 20th generation, 400 squares, 400 triangles, and 400 trapezoids are needed.
The pattern for the first through the fifth generations of squares, triangles, and trapezoids is that each generation is made up of the previous generation's shapes, but with each shape having an additional set of smaller shapes attached to each side.
For example, in the first generation, there is only one square. In the second generation, four smaller squares are attached to the sides of the first square. In the third generation, nine smaller squares are attached to the sides of each of the four squares in the second generation, and so on.
The number of shapes needed to create each generation can be found using the formula:
(n^2)
Where n is the generation number.
For example, in the first generation, only 1 square, 1 triangle and 1 trapezoid is needed, in the second generation, 4 of each are needed, in the third generation, 9 of each are needed, and so on.
If this pattern holds for each generation, the number of tiles required at the 20th generation can be found by substituting n = 20 into the formula:
(20^2) = 400
To determine if the generation you are building is similar (by mathematical definition) to the other generations, you would need to check whether the ratio of corresponding sides is the same for each shape in the generation.
When you double the dimensions of a given polygon, the area is multiplied by four. When you triple the dimensions of a given polygon, the area is multiplied by nine.
The pattern for the number of shapes needed to create each generation follows the pattern of a square of n^2. Therefore, the number of tiles required at the 20th generation can be found by substituting n = 20 into the formula, n^2 = 20^2 = 400.
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The two rectangles are similar. Use a proportion to find the missing side.
Answer: 9 cm
Step-by-step explanation: Let's create a proportion. 20/50 = x/22.5. Using cross-multiplying, we get 22.5 x 20 = 50 times x. We can simplify this equation to get 450 = 50x. To get x by itself, we divide both sides of the equation by 50, leaving us with 9 = x, or 9 cm
(Variance of a linear combination) Let X,Y be random variables and a,b,c be constants. Show that: var (aX + bY + c) = a^2 var X + b^2 varY + 2ab cov(X,Y) (Hint: write the variance as a covariance and use bilinearity twice)
To show that var(aX + bY + c) = a^2 var X + b^2 varY + 2ab cov(X, Y), we can start by using the definition of variance, which is var(X) = E[(X - E[X])^2], and the definition of covariance, which is cov(X, Y) = E[(X - E[X])(Y - E[Y])].
Variance is a measure of the spread of a random variable's possible values. It is defined as the expected value of the squared deviation of a random variable from its mean. For a random variable X, the variance is denoted as Var(X) or σ^2(X) and is calculated as:
Var(X) = E[(X - E[X])^2]
Using these definitions, we can write:
var(aX + bY + c) = E[(aX + bY + c - E[aX + bY + c])^2]
Using the properties of expectations and bilinearity, we can simplify this to:
var(aX + bY + c) = E[(a(X - E[X]) + b(Y - E[Y]))^2]
Expanding the square and using bilinearity again, we get:
var(aX + bY + c) = a^2 E[(X - E[X])^2] + b^2 E[(Y - E[Y])^2] + 2ab E[(X - E[X])(Y - E[Y])]
Since the expectations of (X - E[X])^2 and (Y - E[Y])^2 are equal to var(X) and var(Y) respectively, we can substitute these values into the above equation to get:
var(aX + bY + c) = a^2 var X + b^2 varY + 2ab cov(X,Y)
Therefore, we have shown that var(aX + bY + c) = a^2 var X + b^2 varY + 2ab cov(X,Y)
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What is the imaginary line that divides a shape into two equal halves called?
The imaginary line which divides any shape into two equal halves is known as line of symmetry.
As given in the question,
To divides the given shape into two equal parts :
The imaginary line which is used to divide any given shape into two equal halves is known as line of symmetry.The line of symmetry is also called by another name ' mirror line'.It is called a mirror line as it represents the mirror reflection of the given shape by dividing into two equal parts.Therefore, the imaginary line used to divide the given shape into two equal halves is called line of symmetry.
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a lot of 50 electrical components numbered 1 to 50 is drawn at random, one by one, and is divided among five customers. (a) suppose that it is known that components 3, 18, 12, 26, and 46 are defective. what is the probability that each customer will receive one defective component? (b) what is the probability that one customer will have drawn five defective components? (c) what is the probability that two customers will receive two defective components each, two none, and the other one?
The probability of getting one defective component per customer is very low, less than 1/14,254. The probability of getting five defective components to a single customer is also low, 1/14,254. And the probability of getting two defective components to two different customers and the rest of the customers getting none is 10/14,254.
(a) The probability that each customer will receive one defective component is the probability that the five defective components will be drawn in a specific order, divided by the total number of ways the 50 components can be drawn. There are 5049484746 ways that the 50 components can be drawn, and 5! (5 factorial) ways that the defective components can be drawn in a specific order. So the probability is (5!)/(5049484746) = 1/14,254.
(b) The probability that one customer will have drawn five defective components is the probability that all five defective components will be drawn in a row, divided by the total number of ways the 50 components can be drawn. There are 5049484746 ways that the 50 components can be drawn, and 5! (5 factorial) ways that the defective components can be drawn in a row. So the probability is (1!)/(5049484746) = 1/14,254,
(c) The probability that two customers will receive two defective components each, two none, and the other one, is the probability that the five defective components will be drawn in a specific order and then divided among the five customers in a specific way, divided by the total number of ways the 50 components can be drawn. The number of ways to divide the defective components among the customers is 5!/(2!2!1!) = 10. There are 5049484746 ways that the 50 components can be drawn, and 5! (5 factorial) ways that the defective components can be drawn in a specific order, so the probability is (105!)/(50494847*46) = 10/14,254.
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What are two possible transformations that together could have been used to create the red figure from the blue figure?
mc023-1 (see picture for graph )
A. a translation of 2 units up followed by a translation of 4 units right
B. a rotation of 90 degrees counterclockwise about the origin followed by a translation of 2 units up
C. a reflection across the y axis followed by a translation of 2 units up
D. a translation of 2 units up followed by a reflection across the x axis
Answer:
(c) a reflection across the y-axis followed by a translation 2 units up
Step-by-step explanation:
You want to know transformations that will give the red figure from the blue one.
ObservationThe red figure is reversed left-to-right with respect to the blue figure, so a reflection across a vertical line is required. The only answer choice that has such a reflection is ...
C. a reflection across the y axis followed by a translation of 2 units up
Is √20 greater than, less than, or equal to 4?
Answer: It is greater than 4.
Step-by-step explanation: It is equal to 2 root 5. But if you convert to a decimal you get 4.4721 which is greater than 4.
The formula to find the square root is: y=√a
Find the product of the root of 6x^2 = 17x - 42
Solving the provided question, can say can't calculate square root. The solution to this equation could not be determined, quadratic equation can be factorized.
What is quadratic equation?A quadratic equation is x ax2+bx+c=0, which is a quadratic polynomial in a single variable. a 0. The Fundamental Theorem of Algebra ensures that it has at least one solution since this polynomial is of second order. Solutions may be simple or complicated. An equation that is quadratic is a quadratic equation. This indicates that it has at least one word that has to be squared. The formula "ax2 + bx + c = 0" is one of the often used solutions for quadratic equations. where are numerical coefficients or constants a, b, and c. where the variable "X" is unidentified.
the quadratic equation we have is ,
[tex]6x^2 = 17x - 42[/tex]
[tex]6x^2 - 17x + 42 = 0\\[/tex]
can't calculate square root. The solution to this equation could not be determined.
so this quadratic equation can be factorized.
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Find a vector equation and parametric equations for the line segment that joins p to q. p(1, −1, 7), q(7, 6, 1) vector equation r(t) = <1+6t,−1+7t,7−6t> parametric equations (x(t), y(t), z(t)) =
Vector equation: r(t) = <1, -1, 7> + t<6, 7, -6>
Parametric equations:
x(t) = 1 + 6t
y(t) = -1 + 7t
z(t) = 7 - 6t
The vector equation and parametric equations describe the line segment that joins the two points p and q.
The vector equation is given by r(t) = <1, -1, 7> + t<6, 7, -6>
Here, <1, -1, 7> is the vector that represents the point p, and <6, 7, -6> is the direction vector of the line segment.
The variable t is a scalar parameter that describes the position of any point on the line segment.
The parametric equations are x(t) = 1 + 6t, y(t) = -1 + 7t, z(t) = 7 - 6t.
These equations express the coordinates of any point on the line segment in terms of the parameter t. So we can substitute any value of t between 0 to 1 in this equation to get the coordinates of a point on the line segment.
For example, if we substitute t = 0, we get x(0) = 1, y(0) = -1, z(0) = 7
which gives us the coordinates of point p.
Similarly, if we substitute t = 1, we get x(1) = 7, y(1) = 6, z(1) = 1
which gives us the coordinates of point q.
So, the line segment is defined by the set of all points whose coordinates are given by these equations for values of t between 0 and 1.
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