Values of the given expression are:
(a) (f∘g)(−2) = -7
(b) (g∘f)(−2) = -78
To evaluate the expression, we need to find the values of (f∘g)(−2) and (g∘f)(−2).
(a) (f∘g)(−2) means that we need to first plug in -2 into the g(x) function, and then plug in the result into the f(x) function.
So, g(-2) = 3 - (-2)^2 = 3 - 4 = -1
Now, we plug in -1 into the f(x) function:
f(-1) = 2(-1) - 5 = -2 - 5 = -7
Therefore, (f∘g)(−2) = -7.
(b) (g∘f)(−2) means that we need to first plug in -2 into the f(x) function, and then plug in the result into the g(x) function.
So, f(-2) = 2(-2) - 5 = -4 - 5 = -9
Now, we plug in -9 into the g(x) function:
g(-9) = 3 - (-9)^2 = 3 - 81 = -78
Therefore, (g∘f)(−2) = -78.
In conclusion, the values of the expression are a) (f∘g)(−2) = -7 and b) (g∘f)(−2) = -78.
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5. About What percent of students said they like Cookie Cake?
How many students answered this survey over their favorite Cake?
Types of Cake
Cookie Cake
Chocolate Cake
Vanilla Cake
Marble Cake
Number of
students
5
6
8
5. 20% of students said that they enjoy Cookie Cake.
6. 25 students answered a survey regarding their favorite cake.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
The % formula is used to calculate a percentage of a whole in terms of 100.
Percentage = (Value/Total Value) × 100
Percentage of students said they like Cookie Cake:
5/(5 + 6 + 8 + 6) × 100%
5/25 × 100%
20%
The total number of students who answered this survey about their favorite Cake:
5 + 6 + 8 + 6
25
Thus, 25 students answered a survey regarding their favorite cake.
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Find all real zeros (if any ) and state the multiplicity of each. f(x)=x^(4)(x-2)^(4)(x+8)^(2)
The real zeros of this function are 0 (multiplicity 4),-8 (multiplicity 2), and 2 (multiplicity 4).
The real zeros of the function occur when any of the factors is equal to zero:
x^(4) = 0, (x-2)^(4) = 0, or (x+8)^(2) = 0
To find the real zeros of the given function, we need to set the function equal to zero and solve for x:
f(x) = x^(4)(x-2)^(4)(x+8)^(2) = 0
The process to find these zeros is as follows:
1. Set f(x) = 0 and solve for x
2. Factor the polynomial and solve each factor:
f(x) = 0 => x^(4)(x-2)^(4)(x+8)^(2) = 0
=> x4 = 0
=> x = 0 (multiplicity 4)
=> (x-2)4 = 0
=> x = 2 (multiplicity 4)
=> (x+8)2 = 0
=> x = -8 (multiplicity 2)
The multiplicity of a zero is the number of times it appears as a factor in the function. In this case, the zero 0 has a multiplicity of 4, the zero 2 has a multiplicity of 4, and the zero -8 has a multiplicity of 2.
Therefore, the real zeros and their multiplicities are:
0 with a multiplicity of 4
2 with a multiplicity of 4
-8 with a multiplicity of 2
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(1 point) The radius of the circle with a central angle of 6 radians that intercepts an arc with length 88 cm is _____ cm. The radius of the circle with a central angle of 120° that intercepts an arc with length 17 miles is_____ miles.
The radius of the first circle is 14.67 cm and the radius of the second circle is 8.11 miles.
The radius of a circle can be found by using the formula s = rθ, where s is the length of the arc, r is the radius, and θ is the central angle in radians. Rearranging the formula, we can find the radius by dividing the length of the arc by the central angle: r = s/θ.
For the first part of the question, we are given an arc length of 88 cm and a central angle of 6 radians. Plugging these values into the formula, we can find the radius:
r = 88 cm / 6 radians = 14.67 cm
For the second part of the question, we are given an arc length of 17 miles and a central angle of 120°. However, we need to convert the central angle from degrees to radians before plugging it into the formula. We can do this by multiplying the angle in degrees by π/180:
120° × π/180 = 2π/3 radians
Now we can plug the values into the formula to find the radius:
r = 17 miles / (2π/3) radians = 8.11 miles
So the radius of the first circle is 14.67 cm and the radius of the second circle is 8.11 miles.
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PLEASE HELP ASAP
how much percent is 2882.45 of 3374.60?
( include working out and show answer as percentage )
Answer:
97271.1577
Step-by-step explanation:
multiply 3374.60 by 2882.45%
Avogadro borrows $2,500 from Leonardo and agrees to pay him back $2,700 after
180 days. Assume a 360-day year for each of the following.
(a) Find the annual simple interest rate for this transaction.
(b) After waiting 60 days, Leonardo sells the loan to Wolfgang, agreeing that Wolfgang will
receive the $2,700 loan repayment from Avogadro when it is due. Given that Wolfgang
earns 20% annual simple interest on the deal, how much did he pay Leonardo for the
loan?
a) The annual simple interest rate for this transaction is 16%.
b) Wolfgang paid $3,000 for the loan.
The annual simple interest rate is the percentage of the principal amount that is charged as interest for one year. It can be calculated using the formula I = P*R*T, where I is the interest, P is the principal amount, R is the annual interest rate, and T is the time in years.
(a) In this case, the principal amount is $2,500, the interest is $2,700 - $2,500 = $200, and the time is 180/360 = 0.5 years. We can plug these values into the formula and solve for R:
$200 = $2,500*R*0.5
$200 = $1,250*R
R = $200/$1,250
R = 0.16
The annual simple interest rate for this transaction is 16%.
(b) To find out how much Wolfgang paid for the loan, we can use the same formula and solve for P. The interest is $2,700 - $2,500 = $200, the annual interest rate is 20%, and the time is 120/360 = 0.3333 years:
$200 = P*0.20*0.3333
$200 = 0.06666*P
P = $200/0.06666
P = $3,000
Wolfgang paid $3,000 for the loan.
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Give three points that are equivalent to the polar point (7,40°). Write the three points in polar form, with the angles in degrees.
Three points that are equivalent to the polar point (7,40°) are (7,400°), (7,-320°), and (7,760°). These points are equivalent because they all have the same magnitude of 7, but their angles differ by multiples of 360°.
In polar form, these points are written as:
- (7,400°) = 7cis(400°)
- (7,-320°) = 7cis(-320°)
- (7,760°) = 7cis(760°)
These points are equivalent because the angle in polar coordinates is measured modulo 360°. This means that any angle that differs by a multiple of 360° will be equivalent. For example, 40° is equivalent to 400° because 400° - 40° = 360°. Similarly, -320° is equivalent to 40° because -320° + 360° = 40°, and 760° is equivalent to 40° because 760° - 720° = 40°.
In conclusion, the three points that are equivalent to the polar point (7,40°) are (7,400°), (7,-320°), and (7,760°), and they are written in polar form as 7cis(400°), 7cis(-320°), and 7cis(760°).
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find the value of largest rectangular parallelopiped that can be incribed in the ellipsoid
The value of the largest rectangular parallelopiped that can be inscribed in the ellipsoid is (2a)*(2b)*(2c).
To find the value of the largest rectangular parallelopiped that can be inscribed in the ellipsoid, we need to use the formula for the volume of a parallelopiped. The formula is:
V = l*w*h
Where V is the volume, l is the length, w is the width, and h is the height.
Since we are looking for the largest rectangular parallelopiped, we need to maximize the volume. This can be done by finding the maximum values of the length, width, and height.
The maximum values of the length, width, and height can be found by using the semi-axes of the ellipsoid. The semi-axes of the ellipsoid are given by:
a = √(x^2/a^2 + y^2/b^2 + z^2/c^2)
Where a, b, and c are the semi-axes of the ellipsoid, and x, y, and z are the coordinates of the point on the surface of the ellipsoid.
The maximum values of the length, width, and height can be found by setting the derivatives of the volume with respect to x, y, and z to zero:
∂V/∂x = 0
∂V/∂y = 0
∂V/∂z = 0
Solving these equations will give us the maximum values of the length, width, and height. Once we have these values, we can plug them into the formula for the volume of a parallelopiped to find the largest volume.
The largest volume of the rectangular parallelopiped that can be inscribed in the ellipsoid is given by:
V = (2a)*(2b)*(2c)
Where a, b, and c are the semi-axes of the ellipsoid.
Therefore, the value of the largest rectangular parallelopiped that can be inscribed in the ellipsoid is (2a)*(2b)*(2c).
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If z varies jointly as x and y, and z=6 when x=4 and y=10, find z when x=20 and y=8
If z varies jointly as x and y, then the value of z when x = 20 and y = 8 is 24.
When a variable varies jointly as two other variables, it means that the variable is directly proportional to the product of the two other variables.
In this case, we can use the formula:
z = kxy
where k is a constant of proportionality.
We can find the value of k by using the given values of z, x, and y:
6 = k(4)(10)
6 = 40k
k = 6/40
k = 3/20
Now that we know the value of k, we can use the formula to find z when x = 20 and y = 8:
z = (3/20)xy
z = (3/20)(20)(8)
z = (3)(8)
z = 24
Therefore, the value of z when x = 20 and y = 8 is 24.
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At an animal shelter, a guinea pig eats cabbage at the constant rate. The table shows the
proportional relationship between minutes and pieces of cabbage eaten. 4
3
5
7
9
11
X
11
+6
.6
9
+6
-6
+6
6
18
30
42
54
66
y
The situation can be clearly represented by the equation y = 6x.
What is an equation?Equation: A declaration that two expressions with variables or integers are equal. In essence, equations are questions, and attempts to systematically identify the solutions to these questions have been the driving forces behind the creation of mathematics. Simple algebraic equations with merely addition or multiplication to differential equations, exponential equations with exponential expressions, and integral equations are examples of different types of equations. They are employed to represent a number of physics laws.
As per the given data:
Relation between different cabbage eaten and minutes is given.
To find the proportional relation:
Let's consider y as pieces of cabbage eaten.
and x as the time in minutes
If the relation is y = ax
From the table
18 = a × 3 ; a = 6
30 = a × 5 ; a = 6
42 = a × 7 ; a = 6
∴ y = 6x
Hence, the situation can be clearly represented by the equation y = 6x
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Line AB contains point A (-4, 1) and point B (-1, 3). Find the coordinates of A' and B' after a dilation with a scale factor of 2 with a center point
of dilation at the origin. (1 point)
OA (-8, 2) and B (-2, 6)
OA' (-8, 2) and B (2,-6)
OA (8,-2) and B (2,-6)
OA' (-5, -2) and B (-2, 6)
The coordinates of A' and B' after a dilation with a scale factor of 2 with a center point of dilation at the origin is: OA (-8, 2) and B (-2, 6)
What is the coordinates of A' and B'?To find the coordinates of A' and B' after a dilation with a scale factor of 2 with a center point of dilation at the origin, we can use the following formula:
A' = k * (A - O) + O
B' = k * (B - O) + O
where k is the scale factor, O is the center point of dilation, and A and B are the original points.
In this case, k = 2 and O = (0, 0). So we have:
A' = 2 * (-4, 1 - (0, 0)) + (0, 0) = (-8, 2)
B' = 2 * (-1, 3 - (0, 0)) + (0, 0) = (-2, 6)
Therefore, the coordinates of A' and B' after the dilation are (-8, 2) and (-2, 6), respectively.
So, the answer is option (A) OA (-8, 2) and B (-2, 6).
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2 The difference between -6.4 and a
number is 8.5.
Find two possible values for the number.
Answer: -14.9 and 2.1
Step-by-step explanation:
If you take -6.4 - 8.5 in one direction you get -14.9 .
And if you add them together (-6.4 + 8.5) you get 2.1,
those are two possible values depending on if you add or subtract the 8.5 .
Draw the image of the following figure after a dilation centered at the origin with a scale factor of 3/2
The image of the figure under a dilation with scale factor 3/2 is attached
How to determine the image of the figureFrom the question, we have the following parameters that can be used in our computation:
Center = (0, 0).
Point = (6, 12), (8, 12) and (8, 8)
Scale factor = 3
A dilation with center (0, 0) and scale factor k multiplies the coordinates of a point by k.
So, to find the image of the point under the dilation with scale factor 3/2, we multiply each coordinate by 3/2:
Image = [(6, 12), (8, 12) and (8, 8)] * 3/2
Image = [(9, 18), (12, 18) and (12, 12)]
Hence, the image of the figure is attached
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Convert the rectangular coordinates to polar coordinates with r > 0 and 0 < θ (-5,0) (r, θ) = (________)
The answer is (r, θ) = (5, π).
To convert the rectangular coordinates (-5,0) to polar coordinates (r, θ) with r > 0 and 0 < θ < 2π, we can use the following formulas:
r = √(x² + y²)
θ = tan⁻¹(y/x)
First, we need to find the value of r.
r = √((-5)² + (0)²)
r = √(25 + 0)
r = 5
Next, we need to find the value of θ.
θ = tan⁻¹(0/(-5))
θ = tan⁻¹(0)
θ = 0
However, since we need 0 < θ < 2π and the point (-5,0) is in the second quadrant, we need to add π to our θ value.
θ = 0 + π
θ = π
So, the polar coordinates of the point (-5,0) are (r, θ) = (5, π).
Therefore, the answer is (r, θ) = (5, π).
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Solve for x.
please help me
Answer:
Your answer is x = 7.
Step-by-step explanation:
<HFG + <YFG = 180°
180° - <HFG = <YFG
<H + <G + <HFG = 180°
<H + <G = 180° - <HFG
<H + <G = <YFG
(6x + 8) + (65°) = (3+16x)
6x + 8 + 65 = 16x + 3
Get x on one side and the other numbers on the other side.
8 + 65 - 3 = 16x - 6x
70 = 10x
x = 7
You can plug in x into the angle to solve for their angles.
Answer:
x = 7
Step-by-step explanation:
∠HFG must equal to 180° - ∠YFG. Because there are 180° in a triangle, we can subtract the known value, 65°, and be left with 115°.
From there, an equation can be formed.
115° = 6x + 8 + 180 - (3+16x)
115°= 6x + 188 - 3 - 16x
115°= 185 - 10x
-70° = -10x
x = 7
Question 4 \( 1 \mathrm{pts} \) The norm of vector \( v=\left[\begin{array}{c}4 \\ \sqrt{3} \\ \sqrt{6}\end{array}\right] \) is \( \|v\|=? ? ? \) ? \[ \begin{array}{l} 50 \\ \sqrt{13} \\ 4+\sqrt{3}+\s
\(\|v\|=\sqrt{50}\)
The norm of vector \(v\) is \( \|v\|=\sqrt{4^2 + \sqrt{3}^2 + \sqrt{6}^2}=\sqrt{50} \). Therefore, the answer is \(\|v\|=\sqrt{50}\).
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following relation. - 6x2 - 5y = 4x + 3y Determine the implied domain of the function found in the first step. Express your answer in interval notation. Points
The implied domain of the function y = (-6x^2 - 4x)/8 is found to be (-∞, ∞).
The first step in determining the implied domain of the function is to isolate the dependent variable, in this case y, on one side of the equation.
We can do this by adding 5y to both sides of the equation and subtracting 4x from both sides of the equation:
-6x^2 - 4x = 8y
Next, we can divide both sides of the equation by 8 to get y by itself:
(-6x^2 - 4x)/8 = y
Now we have the function in terms of y:
y = (-6x^2 - 4x)/8
The implied domain of the function is the set of all x-values for which the function is defined.
In this case, there are no restrictions on the values of x that can be used in the function, so the implied domain is all real numbers.
Therefore, the implied domain of the function y = (-6x^2 - 4x)/8 is (-∞, ∞).
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Can someone help with this question? its math
Answer:
x < 5
Step-by-step explanation:
2x - 3 < x + 2 ≤ 3x + 5
2x - 3 < x + 2 and x + 2 ≤ 5
x < 5 and x ≤ 3
Answer: x < 5
Radius of a circle 6 feet what is the circumference use 3. 14
Answer: 37.68 feet
Step-by-step explanation:
Circumference = 2 x π x r
Plug in values:
C = 2 x 3.14 x 6
C = 12 x 3.14
C = 37.68
The circumference is 37.68 feet
Hope this helps!
How many gallons of a 3% salt solution must be mixed with a 7% salt solution to obtain 100 gallons of a 5% salt solution?
O 50 gal of 3%
75 gal of 3%
O 25 gal of 3%
60 gal of 3%
Answer:
You need to add 50 gallons of the 3% solution to the 50 gallons of the 7% solution and that will give 100 gallons of a 5% solution.
What is the slope of the line graphed below?
Answer:
B
Step-by-step explanation:
I think so because the rise is going downward, which means it’s a negative number. Therefore m= -1/4
help please!!!!!!!!$!!!
The solids are similar. Find the missing dimension.
d
12ft.
8in.
3ft.
Answer:
32 in
Step-by-step explanation:
You want the missing diameter of the smaller of two similar cylinders, where the larger is 12 ft in diameter and 3 ft high, while the smaller is 8 inches high.
Similar figuresThe linear dimensions of similar figures have the same ratio.
The ratio of the diameter to the height of the larger figure is ...
(12 ft)/(3 ft) = 4
The smaller figure will also have a diameter that is 4 times the height:
d = 4 × 8 in = 32 in
The missing dimension is 32 inches.
Please help me with this math thank u
Consider the expression |x+3|5x-2|-(x+3)(4x+3)| a. Rewrite the expression in the form (x+3)|ax+b|
The expression |x+3|5x-2|-(x+3)(4x+3)| can be rewritten as (x+3)|x-5|.
Consider the expression |x+3|5x-2|-(x+3)(4x+3)|. To rewrite this expression in the form (x+3)|ax+b|, we will need to use the distributive property and combine like terms.
First, let's distribute the (x+3) term:
|x+3|5x-2| - (x+3)(4x+3) = |5x^2 + 13x - 2| - |4x^2 + 15x + 9|
Next, let's combine like terms:
|5x^2 + 13x - 2| - |4x^2 + 15x + 9| = |x^2 - 2x - 11|
Now, we can factor the expression inside the absolute value:
|x^2 - 2x - 11| = |(x+3)(x-5)|
Finally, we can rewrite the expression in the form (x+3)|ax+b|:
|(x+3)(x-5)| = (x+3)|x-5|
So, the expression |x+3|5x-2|-(x+3)(4x+3)| can be rewritten as (x+3)|x-5|.
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t \( \vec{u}=\left[\begin{array}{c}1 \\ -3 \\ 2\end{array}\right] \) and \( \vec{v}=\left[\begin{array}{c}2 \\ 0 \\ -1\end{array}\right] \) Compute the cross product: \[ \vec{u} \times \vec{v}=\left[\
1 & -3 & 2
2 & 0 & -1
The cross product of two vectors can be calculated using the formula:
\[ \vec{u} \times \vec{v} = \left[ \begin{array}{ccc}
\vec{i} & \vec{j} & \vec{k}\\
u_{1} & u_{2} & u_{3} \\
v_{1} & v_{2} & v_{3}
\end{array} \right] \]
For your given vectors, we can calculate the cross product as follows:
\[ \vec{u} \times \vec{v} = \left[ \begin{array}{ccc}
\vec{i} & \vec{j} & \vec{k}\\
1 & -3 & 2 \\
2 & 0 & -1
\end{array} \right] \]
Which simplifies to:
\[ \vec{u} \times \vec{v} = \left[ \begin{array}{c} 6 \\ 2 \\ -1 \end{array} \right] \]
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Based on the results in the table, about how
many times should Jaylon and Paula expect the
pointer to land on 4 out of a total of 130 spins
Jaylon and Paula should expect the pointer to land on 4 around 30 and 43 times respectively.
What is the experimental probability?A probability calculated by a series of tests is known as experimental probability.
The given table is as follows:
1 2 3 4
Jaylon: 6 8 9 7
Paula: 8 5 7 10
To determine the experimental probability of the pointer landing on 4 for Jaylon, we add up the number of times the pointer landed on 4 for Jaylon and divide by the total number of spins:
Experimental probability for Jaylon = (number of times the pointer landed on 4 for Jaylon) / (total number of spins)
= 7 / 30
Similarly,
Experimental probability for Paula:
= 10 / 30
Expected number of times the pointer will land on 4 = (experimental probability) x (total number of spins)
For Jaylon: (7 / 30) × 130 = 30.33
For Paula: (10 / 30) × 130 = 43.33
Therefore, Jaylon and Paula should expect the pointer to land on 4 around 30 and 43 times respectively.
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The missing table has been attached below.
Complete the array to find 208 ÷ 8. Show your work.
Answer:
One possible way to complete the array is:
8 | 2 0 8
|
------
|
2 | 2 6
5 | 5 2
1 | 1 7
6 | 2 0
The answer is 26, so 208 ÷ 8 = 26.
To complete the array, we start by dividing the hundreds digit (2) by 8, which gives 0 with a remainder of 2. We write the remainder (2) in the ones place of the first row. Then we bring down the tens digit (0) and add it to the remainder to get 20. We divide 20 by 8, which gives 2 with a remainder of 4. We write the remainder (4) in the tens place of the second row, and bring down the ones digit (8) to the ones place of the second row. Finally, we add the digits in the second row to get 26, which is the quotient of the division
Step-by-step explanation:
What is the center of this ellipse?
(x-3)^2/4 + (y - 1)^2/9 = 1
The center of the ellipse is,
⇒ (3, 1)
What is an expression?An expression which is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division is called an mathematical expression.
We have to given that;
The equation of ellipse is,
⇒ (x - 3)²/4 + (y - 1)²/9 = 1
Now, We know that;
General form of the ellipse is,
⇒ (x - h)²/a + (y - k)²/b = 1
Where, (h, k) = the center of the ellipse.
Hence, We get;
The equation of ellipse is,
⇒ (x - 3)²/4 + (y - 1)²/9 = 1
By comparing;
The center of the ellipse is,
⇒ (h, k) = (3, 1)
Thus, The center of the ellipse is,
⇒ (3, 1)
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Use long division to find the quotient
(2x^3-5x^2+3x-6) divided by (x+4)
Using long division the quotient of (2x^3-5x^2+3x-6) divided by (x+4) is 2x^2 - 13x + 55.
What is quotient?Quotients are often used in algebra and other branches of mathematics to solve equations and expressions involving division. They are also commonly used in everyday life, such as when calculating the cost per unit of a product, or the average speed of a journey.
For example, if we divide 10 by 2, the quotient would be 5, since 10 divided by 2 equals 5. Similarly, if we divide 12 by 3, the quotient would be 4, since 12 divided by 3 equals 4.
Now let find the quotient using long division:
2x^2 - 13x + 55
_______________________
x + 4 | 2x^3 - 5x^2 + 3x - 6
- (2x^3 + 8x^2)
---------------
- 13x^2 + 3x
- (-13x^2 - 52x)
---------------
55x - 6
- (55x + 220)
-----------
-226
Therefore, the quotient is 2x^2 - 13x + 55 and the remainder is -226.
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Find the output,
�
bb, when the input,
�
aa, is
6
66. �
=
−
1
−
7
�
b=−1−7a
Step-by-step explanation:
uuoflfjtnhgdhdurjsjueiei3io ghy
