Answer:
fog(x)=[tex]x^2+8[/tex]
Step-by-step explanation:
Here we are given two functions
f(x) = x+2
g(x)=[tex]x^2+6[/tex]
We are required to find fog(x)
fog(x) is a composite function.
fog(x) = f(g(x))
g(x) = [tex]x^2+6[/tex]
f(g(x)) = f( [tex]x^2+6[/tex] )
f(x)= x+2
Hence we replace x in f(x) with [tex]x^2+6[/tex]
f(g(x))=([tex]x^2+6[/tex])+2
f(g(x))=[tex]x^2+8[/tex]
Hence
fog(x) = [tex]x^2+8[/tex])
Given 4 coordinate points A(2,0), B(4,0), C(5,-2), D(1, -2), click in the figure until the image that is rotated by 180° about
the origin O appears.
The origin O appears rotated by 180° about ’( -2,0), (-4,0), (-5,2) , ’(-1,2).
What is coordinate geometry?Coordinate geometry (or analytic geometry) is described as the examination of geometry and the use of coordinate factors. using coordinate geometry.
Coordinate using the horizontal and vertical distances from the two reference axes. generally represented by way of (x,y) the x-price and y-cost.
Coordinate geometry is used to control and regulate air visitors. The coordinates of the flight are used to describe the plane's modern location. despite the fact that a plane actions a tiny distance (up, down, forward, or backward), the machine updates the coordinates of flight for each small change in its role.
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What is the pattern in the values as the exponents increase?
Answer:
Option D is correct.
Step-by-step explanation:
The first value is 1/32
if we multiply 1/32 with 2 i.e 1/32*2 we get 1/16
So, next value is 1/16
if we multiply 1/16 with 2 i.e 1/16 * 2 we get 1/8
So, next value is 1/8
if we multiply 1/8 with 2 i.e 1/8 * 2 we get 1/4
So, next value is 1/4
if we multiply 1/4 with 2 i.e. 1/4 *2 we get 1/2
so, next value is 1/2
if we multiply 1/2 with 2 i.e 1/2 * 2 we get 1
So, Option D multiply the previous value by 2 is correct.
For a group experiment, your science class measured the fine-particulate
concentrations in the air at random places around campus, and estimated a
sample average of 12 ug/m3 (micrograms per cubic meter). If 196 readings
were taken, and the standard deviation of the sample measurements was
3.5 pg/m3, you are 99.7% confident that actual concentration of fine
particulates at the school is
Answer:
The 99.7% confidence interval for the mean here is
[tex]\rm (11.2, 12.8)\; \mu g\cdot m^{-3}[/tex].
Step-by-step explanation:
The data in this question comes from random samples. In other words, the true population data are not known. Assume that both the sample average and the sample stdev are unbiased estimates for the population mean and stdev.
The sample size 196 is sufficient large, such that the central limit theorem will apply. By the central limit theorem, the distribution of the mean (as well as the sum) of a sufficiently large samples resembles normal distributions. However, since stdev is only an estimate, the confidence interval can only be found using the Student's t-distribution.
What is the confidence interval for the mean of a random variable that follows the t-distribution?
[tex]\displaystyle \left(\bar{x} - t\cdot \frac{s_{n-1}}{\sqrt{n}}, \; \bar{x} + t\cdot \frac{s_{n-1}}{\sqrt{n}}\right)[/tex],
where
[tex]\bar{x}[/tex] is the unbiased estimate of the population mean (a.k.a sample mean.) For this question, [tex]\bar{x} = 12[/tex]. [tex]s_{n-1}[/tex] is the unbiased estimate of the standard deviation (the square root of variance) of the population. For this question, [tex]s_{n-1} = 3.5[/tex].[tex]n[/tex] is the sample size. For this question, [tex]n = 196[/tex].What is not given is
[tex]t[/tex], the test statistics of the t-distribution. This value depends on the confidence level of the estimate (99.7% in this case.)Start by determining the degree of freedom [tex]df[/tex] of [tex]t[/tex]. The degree of freedom for a one-variable estimate is usually equal to [tex]n -1[/tex] (that is: sample size minus one.) For this question, [tex]n = 196[/tex] so [tex]df = 196 - 1 = 195[/tex].
If [tex]T[/tex] represent a random variable that follows the [tex]t_{195}[/tex]-distribution, the value of t shall ensure that
[tex]P(-t \le T \le t) = \text{Confidence Interval} = 0.997[/tex].
The t-distribution is symmetric. As a result,
[tex]\displaystyle P(T > t) = 0.997 + \frac{1}{2}\times (1 - 0.997) = 0.9985[/tex].
Find the value of [tex]t[/tex] either with a t-distribution table or with technology. Keep in mind that for this question, [tex]df = n - 1 = 195[/tex].
[tex]t \approx 3.00549[/tex].
Apply the formula for the confidence interval:
[tex]\displaystyle \left(\bar{x} - t\cdot \frac{s_{n-1}}{\sqrt{n}}, \; \bar{x} + t\cdot \frac{s_{n-1}}{\sqrt{n}}\right)[/tex].
Lower bound:
[tex]\displaystyle \bar{x} - t\cdot \frac{s_{n-1}}{\sqrt{n}} &= 12 - 3.00549\times \frac{3.5}{\sqrt{196}}\approx 11.2[/tex].
Upper bound:
[tex]\displaystyle \bar{x} + t\cdot \frac{s_{n-1}}{\sqrt{n}} &= 12 + 3.00549\times \frac{3.5}{\sqrt{196}}\approx 12.8[/tex].
In other words, the 99.7% confidence interval for the actual concentration is [tex]\rm (11.2, 12.8)\; \mu g\cdot m^{-3}[/tex].
write 5 in the form of a/b using integers to show it as a rational number
Answer:
a = 5, b=1
Step-by-step explanation:
We can rewrite a whole number as a fraction by putting it over 1
5/1 = 5
a = 5, b=1
5/1 is a rational number since it can be written in the form a/b
Evaluate |-7| + 3|4|
A. 0
B.5
C.19
The answer is going to be 19.
Answer:
C. 19
Step-by-step explanation:
Order of operationsPEMDAS
Parenthesis
Exponent
Multiply
Divide
Add
Subtract
[tex]|-7|=7[/tex]
[tex]3|4|=3*4=12[/tex]
Add.
[tex]7+12=19[/tex]
[tex]19[/tex], is the correct answer.
What is answer to the equation 81x=x^2 ?
For this case we have the following equation:
[tex]81x = x ^ 2[/tex]
Rewriting we have:
[tex]x ^ 2-81x = 0[/tex]
We take common factor "x" from both terms:
[tex]x (x-81) = 0[/tex]
It is observed that equality is fulfilled when x = 0 and when x = 81
So, the roots are:
[tex]x_ {1} = 0\\x_ {2} = 81[/tex]
Answer:
[tex]x_ {1} = 0\\x_ {2} = 81[/tex]
What is the solution of sqrt x+2-15=-3
Answer:
Step-by-step explanation:
Without brackets, we are not exactly sure what is under the root sign. There are 3 choices.
sqrt(x) + 2 - 15 = - 3
sqrt(x + 2) - 15 = - 3
sqrt(x + 2 - 15) = - 3
I think the middle one is what you intend. If not leave a note.
sqrt(x + 2) - 15 = - 3 Add 15 to both sides.
sqrt(x + 2) - 15+15 = - 3+15 Combine
sqrt(x + 2) = 12 Square both sides
x + 2 = 12^2 Do the right
x + 2 = 144 Subtract 2 from both sides.
x + 2-2 = 144-2
x = 142
Answer:
142
Step-by-step explanation:
What is the range of this promblem
Answer:
3
Step-by-step explanation:
Range is the largest number minus the smallest number
4-1 = 3
The range is 3
Answer:
3
Step-by-step explanation:
The range of a set of data is the difference between the highest and lowest values in the set.
Sort your data from lowest to highest. You get
1, 2, 3, 4, 4, 4, 4, 4
Highest value = 4
Lowest value = 1
Range = 3 chocolate chips
What is the best approximation of a 15% tip on a $38 car wash?
Answer:
15% of 38= 5.7
Round up to 6
Answer: b) $6
Step-by-step explanation:
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6/y=9/24 whats the proportion?
a= 16
b= 19
c= 20
d=21
Answer:
a = 16
First exclude any restricted values of y.
6/y = 9/24 , y is not equal 0
Simplify the right side of the equation using 3.
6y = 3/8
Cross multiply.
6 x 8 = 3
3 x y = 3y
6 x 8 = 3y
48 = 3y
Switch the sides of the equation.
3y = 48
Divide both sides by 3.
3y/3 = y
48/3 = 16
evaluate the following expression: 2(1,1) -4(0,1). enter your answer as a vector.
Answer:
The answer is (2,-2)
You just distribute the 2 into (1,1) and same with the -4 into (0,1) and add them together
Step-by-step explanation:
ANSWER
[tex]\binom{2 }{ - 2}[/tex]
EXPLANATION
We were given the vector equation:
[tex]2 \binom{1}{1} ) - 4 \binom{0}{1} [/tex]
We perform the scalar multiplications first to get:
[tex]\binom{2 \times 1}{2 \times 1} ) - \binom{4 \times 0}{4 \times 1}[/tex]
Simplify the components of each vector
[tex]\binom{2 }{2} - \binom{0}{4}[/tex]
We subtract the corresponding components of the vector to get:
[tex]\binom{2 - 0}{2 - 4} [/tex]
This simplifies to
[tex]\binom{2 }{ - 2}[/tex]
gradient answer it for bare points
Gradient is the slope of the line.
Use two points of the graphed line to find the slope, which is the change in Y over the change in x.
I'll use the points (4,0) and (6,8)
Slope = (8-0) / 6/4) = 8/2 = 4
The gradient is 4
Emily is a geometry teacher. She asks each student to bring in a cutout of a parallelogram. She tells them that one angle must measure 50° and the length of one side must be 10 centimeters. Emily also states that the parallelogram must not be a rhombus, rectangle, or square. Using this information, each student can prepare (________) parallelogram(s).
A- 0
B- 1
C- 2
D- Infinitely many
Answer:
D
Step-by-step explanation:
There are infinitely many possible parallelograms. The angles are fixed at 50° and 130°, and two parallel sides are fixed at 10 cm, but the other two sides can have any length (except 10 cm).
Use the function f(x) = 15 - x to answer the question.
Evaluate. (f · f)(2)
A) 0
B) 2
C) 4
D) 13
Answer:
B
Step-by-step explanation:
To evaluate (f ￮ f)(2) substitute x = 2 into f(x) and evaluate. Then substitute this value into f(x)
f(2) = 15 - 2 = 13, then
f(13) = 15 - 13 = 2
Hence (f ￮ f)(2) = 2
help me: solve the simultaneous equation y-2x= -8 and x²- 3x - y = 2
Answer:
(2,-4) And (3,-2)
Step-by-step explanation:
Here we have to solve one linear equation and a quadratic equation.
First we find the value of y in terms of x from linear equation and then substitute this value in our quadratic equation to solve it for x , Let us see how :
we have y-2x=8
y=2x-8
Now we substitute this in [tex]x^2-3x-y=2[/tex]
Hence we have
[tex]x^2-3x-(2x-8)=2\\x^2-3x-2x+8=2\\x^2-5x+8=2\\x^2-5x+8-2=0\\x^2-5x+6=0\\x^2-2x-3x+6=0\\x(x-2)-3(x-6)=0\\(x-2)(x-3)=0\\[/tex]
Thus we have
either (x-2)= 0 or (x-3)=0
or x=2 or x=3
Now let us find the value of y by substituting them in y=2x-8 one by one.
y=2(2)-8= 4-8=-4
y+2((3)-8=6-8=-2
Hence our coordinates are
(2,-4) and (3,-2)
Answer:
(2, - 4), (3, - 2)
Step-by-step explanation:
Given the 2 equations
y - 2x = - 8 → (1)
x² - 3x - y = 2 → (2)
Rearrange (1) expressing y in terms of x
y = 2x - 8 → (3)
Substitute y = 2x - 8 in (2)
x² - 3x - 2x + 8 = 2
x² - 5x + 6 = 0 ← in standard form
(x - 2)(x - 3) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 2 = 0 ⇒ x = 2
x - 3 = 0 ⇒ x = 3
Substitute these values into (3) for corresponding values of y
x = 2 : y = (2 × 2) - 8 = 4 - 8 = - 4 ⇒ (2, - 4)
x = 3 : y = (2 × 3) - 8 = 6 - 8 = - 2 ⇒ (3, - 2)
Helpppp me pleaseeeeeee
Answer:
my bad if im wrong but im pretty sure its b
Step-by-step explanation:
What do I do?????❓‼️❓‼️❓‼️❓‼️
Working and answer in the photo above. Hope this helps
Which symbol correctly compares these fractions?
9 36
10 40
Answer:
=
Step-by-step explanation:
9/10 vs 36/40
Multiply 9/10 by 4/4 so the denominators are equal
9/10*4/4 = 36/40
36/40 vs 36/40
They are equal
The solutions to the inequality y s 2x - 4 are shaded on the
graph. Which point is a solution?
O (-1, 1)
O (1,-1)
O (3, 2)
O (2, 3)
5432
Answer:
C. (3, 2)
Step-by-step explanation:
(3, 2) is the solutions to the inequality y ≤ 2x − 4 shaded region.
If my fraction is 10/60 whats my decimal
Answer:
10/60 as a decimal is:
0.166666667
Step-by-step explanation:
To get 10/60 converted to decimal, you simply divide 10 by 60.
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Answer:
0.166666666666667
Step-by-step explanation:
Which description of the graph of the linear equality y > 3x - 8 is correct?
The graph will be a dashed line with a y-intercept of negative eight and a slope of three. The graph will be shaded below
the line
The graph will be a solid line with a y-intercept of three and a slope of negative eight. The graph will be shaded above the
line
The graph will be a solid line with a y-intercept of three and a slope of negative eight. The graph will be shaded below the
line
The graph will be a dashed line with a y-intercept of negative eight and a slope of three. The graph will be shaded above
the line
Answer:
Option The graph will be a dashed line with a y-intercept of negative eight and a slope of three. The graph will be shaded above
the line
Step-by-step explanation:
we have
[tex]y>3x-8[/tex]
The solution of the inequality is the shaded area above the dashed line The equation of the dashed line is [tex]y=3x-8[/tex]
The slope of the dashed line is positive [tex]m=3[/tex]
The y-intercept of the dashed line is -8
see the attached figure to better understand the problem
Answer:
D is the correct answer
Step-by-step explanation:
Express 0.0000594 using scientific notation
Answer:
5.94×10^6
Step-by-step explanation:
you have to move the decimal 6 times before reaching the next number then you have to mutiply it by 10 and put the 6
which of the following is the complex conjugate of the complex number below? 4+51i
a. -4-51i
b. 4+51i
c. 4-51i
d. -4+51i
if you could give a dumbed down explanation as well that would be great
The conjugate of the complex number a+bi is a-bi
you just reverse the sign of the imaginary part of the number; so it is 4 -51i
The complex conjugate of the complex number is Option C. 4-51i
How do you simplify a complex conjugate?To simplify this fraction we multiply the numerator and the denominator by the complex conjugate of the denominator. When we change the sign of the imaginary part, we have the complex conjugate. Another way to think of this is to return all the i with -i. As we can see here, the complex conjugate of 3 - 4i is 3 + 4i.
How do you conjugate complex?You find the complex conjugate simply by reversing the sign of the imaginary part of the complex number. To find the complex conjugate of 4+7i we change the sign of the imaginary part. Thus the complex conjugate of 4+7i is 4 - 7i.
Complex conjugate is when "Each of two complex numbers having their real parts equal and their imaginary parts of equal magnitude but opposite sign."
What is the complex conjugate of z?The notation for the complex conjugate of z is either ˉz or z∗. The complex conjugate has the exact real part as z and the same imaginary part but with the opposite sign.
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write an inequality for the sentence: twice a number, decreased by the quotient of that number and 2, is at least 2
Answer:
2x - (x/2) >12
Step-by-step explanation:
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Solve log x = 4. Please show all the work!
Answer:
x = 10000
Step-by-step explanation:
Using the rule of logarithms
[tex]log_{b}[/tex] x = n ⇔ x = [tex]b^{n}[/tex]
Given
log x = 4 ( noting that log x has base 10 ), then
x = [tex]10^{4}[/tex] = 10000
What are the first two terms of the sequence defined recursively by the formula ^an=(^an-1)^2, when ^a4=1604?
Answer:
The first two terms are √2 and 6.
Step-by-step explanation:
a3^2+4=1604
a3=40
a2^2+4=40
a2=6
a1^2+4=6
a1=√2
The first two terms are approximately a1 ≈ 2.52 and a2 ≈ 6.33.
First Two Terms of the Sequence
To find the first two terms of the sequence defined recursively by the formula an = (an-1)2, given that a4 = 1604, we need to work backwards.
Step-by-Step Explanation:
Given: a4 = 1604.Since an = (an-1)^2, we take the square root of 1604 to find a3:Therefore, the first two terms of the sequence are approximately a1 ≈ 2.52 and a2 ≈ 6.33.
Can someone please help me With BOTH parts of the question ..thanks u
Answer:
-0.89 < -0.51
B. Felipe's Restaurant has less value than Ming's Lodge.
Step-by-step explanation:
If you have a big debt you're going to have less money.
Drag the tiles to the correct boxes to complete the pairs. Match each inequality to the number line that represents its solution. x – 99 ≤ -104 x – 51 ≤ -43 150 + x ≤ 144 75 < 69 – x
Answer:
The four answers in the attached figure
Step-by-step explanation:
Part 1) we have
[tex]x-99\leq-104[/tex]
Solve for x
Adds 99 both sides
[tex]x-99+99\leq-104+99[/tex]
[tex]x\leq-5[/tex]
The solution is the interval ----> (-∞, -5]
All real numbers less than or equal to -5
In a number line, the shaded area at left of x=-5 (close circle)
Part 2) we have
[tex]x-51\leq-43[/tex]
Solve for x
Adds 51 both sides
[tex]x-51+51\leq-43+51[/tex]
[tex]x\leq 8[/tex]
The solution is the interval ----> (-∞, 8]
All real numbers less than or equal to 8
In a number line, the shaded area at left of x=8 (close circle)
Part 3) we have
[tex]150+x\leq144[/tex]
Solve for x
Subtract 150 both sides
[tex]150+x-150\leq144-150[/tex]
[tex]x\leq -6[/tex]
The solution is the interval ----> (-∞, -6]
All real numbers less than or equal to -6
In a number line, the shaded area at left of x=-6 (close circle)
Part 4) we have
[tex]75<69-x[/tex]
Solve for x
Subtract 69 both sides
[tex]75-69<69-x-69[/tex]
[tex]6<-x[/tex]
Multiply by -1 both sides
[tex]-6> x[/tex]
Rewrite
[tex]x < -6[/tex]
The solution is the interval ----> (-∞, -6)
All real numbers less than -6
In a number line, the shaded area at left of x=-6 (open circle)
TO BILL CUSTOMERS FOR WATER USAGE ONE CITY CONVERTS THE NUMBER OF GALLONS USED INTO UNITS THIS RELATIONSHIP IS REPRESENTED BY THE EQUATION G=748 U WHERE G IS THE TOTAL NUMBER OF GALLONS OF WATER USED AND U IS THE NUMBER OF UNITS. DETERMINE WHICH STATEMENT IS TRUE ABOUT RELATIONSHIP SELECT TWO
G IS A DEPENDENT VARIABLE
U IS A DEPENDENT VARIABLE
G IS THE INDEPENDENT VARIABLE
U IS THE INDEPENDENT VARIABLE
THE TWO VARIABLES CANNOT BE LABELED AS INDEPENDENT OR DEPENDENT WITHOUT A TABLE OF VALUES.
THE TWO VARIABLES CANNOT BE LABELED AS INDEPENDENT OR DEPENDENT SINCE ANY VALUE CAN BE SELECTED FOR EITHER
Answer:
1. G IS A DEPENDENT VARIABLE
2.U IS THE INDEPENDENT VARIABLE
Step-by-step explanation:
G is a dependent variable because its values will rely on the values of U multiplied by 748. A dependent variable in most cases is isolated on one side of an equation ( mostly the left-hand side) and it value is affected by the values selected on the other side of the equation.
U is an independent variable because it stands on its own such that it does not rely on the behavior of another variable to determine its value/characteristic.Characteristic here i mean , U is freely selected without considering the behavior of other variable, thus it does not face any restrictions as compared to G.
Solve for x -1/6x=7
Answer:
x= 42/5
alternative forms:
x=8 2/5
x=8.4
Step-by-step explanation:
Start with x-1/6x=7
Multiply both sides by 6 to get 6x-x=42
combine like terms (the Xs) to get 5x (6x-x is 5x)
5x=42
divide both sides by 5 to get x=42/5
Answer:
x = 42/5
Step-by-step explanation:
x -1/6x=7
Get a common denominator
6/6x - 1/6 x = 7
5/6x = 7
Multiply each side by 6/5 to isolate x
6/5 * 5/6x = 6/5*7
x = 42/5