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For the two given functions, the compositions are:
(f o g)(x) = √(2x + 3)(g o f)(x) = 2*√x + 3How to find the two compositions?
Here we have two functions:
f(x) = √x
g(x) = 2x + 3
Now we want to get the compositions:
(f o g)(x) = f( g(x))
So here we just need to evaluate f(x) in g(x), we will get:
(f o g)(x) = √g(x) = √(2x + 3)
The other composition is:
(g o f)(x) = g(f(x)) = 2*f(x) + 3 = 2*√x + 3
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Related Questions
Simplify 2+^3 ÷ 2- ^3
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We want to simplify the following expression:
[tex]\frac{2+\sqrt[]{3}}{2-\sqrt[]{3}}[/tex]This means that we want to "remove" the denominator".
STEP 1If we observe the denominator:
[tex](2-\sqrt[]{3})[/tex]If we multiply it by
2 + √3, then
[tex]\begin{gathered} (2-\sqrt[]{3})(2+\sqrt[]{3}) \\ =4-\sqrt[]{3}^2=4-3=1 \end{gathered}[/tex]STEP 2We know that if we multiply both sides of a fraction by the same number or expression, the fraction will remain the same, then we multiply both sides by 2 + √3:
[tex]\frac{2+\sqrt[]{3}}{2-\sqrt[]{3}}=\frac{(2+\sqrt[]{3})(2+\sqrt[]{3})}{(2-\sqrt[]{3})(2+\sqrt[]{3})}[/tex]For the denominator, as we analyzed before
[tex](2-\sqrt[]{3})(2+\sqrt[]{3})=1[/tex]For the denominator:
[tex](2+\sqrt[]{3})(2+\sqrt[]{3})=(2+\sqrt[]{3})^2[/tex]Then,
[tex]\frac{2+\sqrt[]{3}}{2-\sqrt[]{3}}=\frac{(2+\sqrt[]{3})(2+\sqrt[]{3})}{(2-\sqrt[]{3})(2+\sqrt[]{3})}=\frac{(2+\sqrt[]{3})^2}{1}=(2+\sqrt[]{3})^2[/tex]STEP 3Now, we can simplify the result:
[tex]\begin{gathered} (2+\sqrt[]{3})^2=(2+\sqrt[]{3})(2+\sqrt[]{3}) \\ =2^2+2\sqrt[]{3}+(\sqrt[]{3})^2+2\sqrt[]{3} \\ =4+4\sqrt[]{3}+3 \\ =7+4\sqrt[]{3} \end{gathered}[/tex]Answer: 7+4√315. Find m<1.
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Observing the given figure n< 1 can be found using the Vertical angel theorem to be 132.75 degrees
What is vertical angle theorem?The vertical angle theorem is used when two straight lines intersect, at their point of intersection four angles are formed. The angles opposite to each other are equal
How to find m< 1 using vertical angle theoremThe figure shows
(x² - 6x)⁰
(x/2 + 42)°
From vertical angle theorem
(x² - 6x)⁰ = (x/2 + 42)°
solving for x by multiplying out by 2
2x² - 12x = x + 84
2x² - 12x - x - 84 = 0
2x² - 13x - 84 = 0
factorizing the parabolic equation gives
(x + 4)(2x-21)
using the positive value of x
x = 21/2
substituting x = 21/2 into (x/2 + 42) gives
= 47.25
sum of angles at a point = 360 degrees
2 * 47.25 + 2 * m< 1 = 360
2 * m< 1 = 360 - 94.5
m< 1 = 265.5/2
m< 1 = 132.75
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-2(k - 5) + 2K = 5k +5A)k=0B)k=4C)k1D)k=2
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The equation we have is:
[tex]-2(k-5)+2k=5k+5[/tex]Now we can simply the equation by multiply the -2 into the parenthesis
[tex]\begin{gathered} -2k+10+2k=5k+5 \\ 10=5k+5 \end{gathered}[/tex]now we can solve for k
[tex]\begin{gathered} 10-5=5k \\ 5=5k \\ \frac{5}{5}=k \\ 1=k \end{gathered}[/tex]mark has a bag containing a mixture of 30 green and white marbles.
Answers
SOLUTION:
From the experiment performed;
Mark got 10 green marbles and 5 white marbles after 15 trials. Since the number of green marbles gotten in the experiment is more than the white, the conclusion best supported by the experiment is ;
The bag contains more green than white marbles.
the circle below has center E. Suppose that m
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Notice that the triangle △GEF is an isosceles triangle, since GE=EF (both sides are radii of the circle).
Since △GEF is an isosceles triangle with GE=EF, then the measure of the angles opposed to those sides is the same:
[tex]m\angle GFE=m\angle EGF[/tex]Since the line FH is tangent to the circle, the angle ∠HFE is a right angle.
Since ∠HFG and ∠GFE are adjacent angles, then:
[tex]m\angle\text{HFG}+m\angle\text{GFE}=m\angle\text{HFE}[/tex]Substitute m∠HFG=62 and m∠HFE=90 to find m∠GFE:
[tex]\begin{gathered} 62+m\angle\text{GFE}=90 \\ \Rightarrow m\angle GFE=28 \end{gathered}[/tex]Since the sum of the internal angles of any triangle is 180 degrees, then:
[tex]m\angle\text{GFE}+m\angle\text{EGF}+m\angle\text{FEG}=180[/tex]Substitute the values of m∠GFE and m∠EGF:
[tex]\begin{gathered} 28+28+m\angle\text{FEG}=180 \\ \Rightarrow\angle FEG=124 \end{gathered}[/tex]Therefore:
[tex]\begin{gathered} \text{m}\angle\text{FGE}=28 \\ m\angle FEG=124 \end{gathered}[/tex]I need help with my statistics homework " -compute the range ,sample variance,and sample standard deviation cost."
Answers
We need to find the range, sample variance, and sample standard deviation cost.
The range is already given: $247. It can be found by subtracting the least from the greatest value:
[tex]466-219=247[/tex]Now, in order to find the sample variance and the sample standard deviation, we first need to find the mean of the sample:
[tex]\text{ mean }=\text{ }\frac{415+466+400+219}{4}=\frac{1500}{4}=375[/tex]Now, we can find the sample variance s² using the formula:
[tex]s²=\frac{\sum_{i\mathop{=}1}^n(x_i-\text{ mean})²}{n-1}[/tex]where n is the number of values (n = 4) and the xi are the values of the sample.
We obtain:
[tex]\begin{gathered} s²=\frac{(415-375)²+(466-375)²+(400-375)²+(219-375)²}{4-1} \\ \\ s²=\frac{40²+91²+25²+(-156)²}{3} \\ \\ s²=\frac{1600+8281+625+24336}{3} \\ \\ s²=\frac{34842}{3} \\ \\ s²=11614 \end{gathered}[/tex]Now, the sample standard deviation s is the square root of the sample variance:
[tex]\begin{gathered} s=\sqrt{11614} \\ \\ s\cong107.8 \\ \\ s\cong108 \end{gathered}[/tex]Therefore, rounding to the nearest whole numbers, the answers are:
Answer
range: $247
s² = 11614 dollars²
s ≅ $108
Complete the square for each expression. Write the resulting expression as a binomial. x^2+14x+____
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To complete the square is take the second term in the expression, divided it by 2 and then squared it. This will be the number that we have to add to the original expression.
(14/2)^2=49
so, completing the expression:
x^2+14x+49
Then, the new expression can be factored into a single term squared:
x^2+14x+49= (x+7)^2
What is the equation of the line that is parallel to the graph of y = 2x - 5 and passes through the point (8, 10)?
Answers
We know that the equation of a line is given by
[tex]y-y_1=m(x-x_1)[/tex]To find it we need the slope m and a point that the line passes thorugh. In this case we have the point (8,10) but we don't know the slope. What we know is that the line we are looking for is parallel to the line
[tex]y=2x-5[/tex]We also know that for two lines to be parallel they have the same slope. Then, if we fin the slope of the line y=2x-5, we have the slope of the line we are looking for. To find the slope of the line y=2x-5 we note that it is written in the slope-intercept form
[tex]y=mx+b[/tex]From this we know that the slope is multiplying the x variable when it is written in that form. Hence m=2.
Then the line we are looking for has an slope of 2 and passes through the point (8,10). Pluggin the values in the equation of a line we have.
[tex]y-10=2(x-8)[/tex]Writting it in the slope intercept form we have
[tex]\begin{gathered} y-10=2(x-8) \\ y-10=2x-16 \\ y=2x-16+10 \\ y=2x-6 \end{gathered}[/tex]Then the line parallel to y=2x-5 and passes through the point (8,10) is
[tex]y=2x-6[/tex]A Norman window has the shape of a rectangle surmounted by a semicircle. If the perimeter of the window is 17.6 ft. give the area A of the window in square feet when the width is 4.1 ft. Give the answer to two decimals places.
Answers
To find the area of the window you need to find the area of rectangular part and the area of semicircle part.
To find the area of the rectangular part you need to find the height of the rectangle, use the perimeter to find it:
Perimeter of the given window is equal to: The circunference or perimeter of the semicircle (πr) and the perimeter of the rectangular part (w+2h)
[tex]P=\pi\cdot r+w+2h[/tex]The radius of the semicircle is equal to the half of the width:
[tex]\begin{gathered} r=\frac{4.1ft}{2}=2.05ft \\ \\ w=4.1ft \\ \\ P=17.6ft \\ \\ 17.6ft=\pi\cdot2.05ft+4.1ft+2h \end{gathered}[/tex]Use the equation above and find the value of h:
[tex]\begin{gathered} 17.6ft-\pi\cdot2.05ft-4.1ft=2h \\ 7.06ft=2h \\ \\ \frac{7.06ft}{2}=h \\ \\ 3.53ft=h \end{gathered}[/tex]Find the area of the rectangular part:
[tex]\begin{gathered} A_1=h\cdot w \\ A_1=3.53ft\cdot4.1ft \\ A_1=14.473ft^2 \end{gathered}[/tex]Find the area of the semicircle:
[tex]\begin{gathered} A_2=\frac{\pi\cdot r^2}{2} \\ \\ A_2=\frac{\pi\cdot(2.05ft)^2}{2} \\ \\ A_2=6.601ft^2 \end{gathered}[/tex]Sum the areas to get the area of the window:
[tex]\begin{gathered} A=A_1+A_2 \\ A=14.473ft^2+6.601ft^2 \\ A=21.074ft^2 \end{gathered}[/tex]Then the area of the window is 21.07 squared feetThe dimensions and the weight of several solids are given. Use the density information to determine what element is the solid made up of.
Answers
Given:
Dimensions and weight of a solid is given.
Height (h) of a cylinder (in cm) =
[tex]h=5[/tex]Radius (r) of a cylinder (in cm) =
[tex]r=5[/tex]Mass (m) of solid (in grams)=
[tex]m=3090.5[/tex]Density of several elements is given.
Cobalt=8.86, Copper=8.96, Gold=19.3, Iron=7.87, Lead 11.3, Platinum=21.5, Silver=10.5, Nickel=8.90.
Required:
What element is the solid made up of.
Answer:
Let us find the volume (V) of cylinder (in cubic cm).
[tex]\begin{gathered} V=\pi\times r^2\times h \\ V=3.14\times\left(5\right)^2\times5 \\ V=3.14\times25\times5 \\ V=392.5 \end{gathered}[/tex]Using formula of density (D), we get,
[tex]\begin{gathered} D=\frac{m}{V} \\ D=\frac{3090.5}{392.5} \\ D=7.87 \end{gathered}[/tex]Hence, the density of the solid is 7.87 grams per cubic cm.
From the given information of density of several elements, we see that the solid is made up of Iron.
Final Answer:
The solid is made up of Iron.
Pls help with the question in the picture. 20 Points and brainliest.
Answers
Answer:
∠ UTV = 66°
Step-by-step explanation:
the central angle USV is twice the angle on the circle ∠ UTV , subtended on the same arc UV , that is
10x + 82 = 2(10x + 16) ← divide both sides by 2
5x + 41 = 10x + 16 ( subtract 5x from both sides )
41 = 5x + 16 ( subtract 16 from both sides )
25 = 5x ( divide both sides by 5 )
5 = x
Then
∠ UTV = 10x + 16 = 10(5) + 16 = 50 + 16 = 66°
the bearing from S to R is 160° what is the bearing of S from R
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.
The bearing of S from R is given as;
[tex]90+90+90+70=340\degree[/tex]Question 6 (1 point)Below are four scenarios where counting is involved. Select those scenarios in whichPERMUTATIONS are involved. There may be more than one permutation.How many possible ways can a group of 10 runners finish first, second andthird?How many ways can 2 females and 1male be selected for a conference from alarger group of 5 females and males?How many 3 letter arrangements of the word OLDWAYS are there?How many 5-card hands from a standard deck of cards would result in allspades?Previous PageNext PagePage 6 of 12
Answers
Step 1: Definition
Arranging people, digits, numbers, alphabets, letters, and colors are examples of permutations. Selection of menu, food, clothes, subjects, the team are examples of combinations.
Step 2:
How many possible ways can a group of 10 runners finish first, second and third?
PERMUTATION because it involved arrangement
Step 3:
How many ways can 2 females and 1 male be selected for a conference from a larger group of 5 females and males?
NOT PERMUTATION because it involved selection, hence it is a combination.
Step 4:
How many 3 letter arrangements of the word OLDWAYS are there?
PERMUTATION because it involved arrangement
Step 5:
How many 5-card hands from a standard deck of cards would result in all spades?
NOT PERMUTATION because it involved selection, hence it is a combination.
Complete the steps to find the value of x .
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Which linear inequality is represented by the graph?1. y≤ 2x+42. y≤ x+33. y²x+34. y≥ 2x+3
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Given a graph represented a linear inequality.
First, we will find the equation of the shown line.
As shown, the line passes through the points (0, 3) and (2, 4)
the general equation of the line in the slope-intercept form will be:
[tex]y=mx+b[/tex]Where (m) is the slope and (b) is the y-intercept
b = y-intercept = 3
We will find the slope as follows:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{4-3}{2-0}=\frac{1}{2}[/tex]So, the equation of the line will be:
[tex]y=\frac{1}{2}x+3[/tex]As shown, the point (0, 0) lying in the area of the solution
So, the linear inequality will be as follows:
[tex]y\leq\frac{1}{2}x+3[/tex]What is the difference between the inverse function of quadratic and exponential
Answers
Answer:
Quadratic functions are those where their rate of change changes at a constant rate. Exponential functions are those where their rate of change is proportional to itself.
Step-by-step explanation:
An example of a quadratic function would be the shape that a ball makes when you throw it. Gravity causes a constant acceleration, the ball slows down as it is moving up, and then it speeds up as it comes down.
An example of an exponential function would be the population of a bacterium as long as there is enough space and nutrients or how your money grows with compound interest in a bank.
The post office offers flat-rate mailing of packages: $1.50 for a package weighing less than 4 oz, $2.50 for a package weighing 4 oz to less than 8 oz, and $3.50 for a package weighing 8 oz to 12 oz. write an equation that would represent the situation.
Answers
To solve the problem, we will define a function that given the weight of the package, will determine the cost of the mailing. Let x be the weigth of the package in oz and let f(x) be the cost of mailing the package. We are told that if the weight is less than 4, then the rate is 1.50. So, in math notation that would be f(x) = 1.50 if x<4. Now, we are told that if the package weights between 4 and less than 8, then the rate is 2.50. So, that is f(x) = 2.50 if 4<=x<8. Finally, we are told that if the package weights between 8 and 12, the cost is 3.50. So f(x) = 3.50 if 8<=x<=12. So the final math expression for f(x) is
1.50 if x<4
f(x) = 2.50 if 4<=x<8
3.50 if 8<=x<=12.
help meeeeeeeeeeee pleaseee
Answers
Equations (f∙g)(x) and (g∙f)(x) have the same product which is 5x² - 19x - 4.
What exactly are equations?In a mathematical equation, the equals sign is used to express that two expressions are equal.An equation is a mathematical statement that contains the symbol "equal to" between two expressions with identical values.Such as 3x + 5 = 15 as an example.There are many different types of equations, including linear, quadratic, cubic, and others.The three primary forms of linear equations are point-slope, standard, and slope-intercept.So, (f∙g)(x) and (g∙f)(x):
Where, f(x) = 5x + 1 and g(x) = x - 4:(f∙g)(x):
5x(x - 4) + 1(x - 4)5x² - 20x + x - 45x² - 19x - 4(g∙f)(x):
x(5x + 1) - 4(5x + 1)5x² + x - 20x - 45x² - 19x - 4Therefore, equations (f∙g)(x) and (g∙f)(x) have the same product which is 5x² - 19x - 4.
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I was getting helprd earlier but the last part didn't show up nor did the text messages. heres the question."Frieda Friendly works for a local car dealership. She noticed 3/4 of the cars are sedans and that half are white. What fraction of the dealership's car are white sedans?" *the picture is just the last question*
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3/4 of the cars are sedans
Half are white ( 1/2)
Multiply the fraction of cars that are sedans (3/4) by the fraction that are white (1/2)
[tex]\frac{3}{4}\times\frac{1}{2}=\frac{3}{8}[/tex]Just divide the fraction to obtain the decimal:
3/8 = 0.375
Multiply by 100 to obtain the percent:
0.375 x 100 = 37.5%
Rain equation for the line that is parallel to the given line and that passes through the given point
Answers
From the properties of line
If two lines are parallel, then thier slope are equal.
The general equation of line with slope m is; y = mx + b
The given equation of line us y = -5x + 3, slope of the given line is (-5)
The line is passes through the point (-6,3) and slope (-5)
The general equation of line is;
[tex]y-y_1=m(x-x_1)[/tex]Substitute the coordinates as;
[tex]x_1=-6,y_1=3[/tex]Thus;
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-3=-5(x+6) \\ y-3=-5x-30 \\ y+5x-3+30=0 \\ 5x+y+27=0 \\ y=-5x-27 \end{gathered}[/tex]Answer : y = -5x - 27
,,,
Given:• UZ | VW• UV ZUZ306Nw4511Which is closest to mZW?26.630°60°63.49
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From the image, given that UZ is parallel to VW, UV is congruent to UZ. We can redraw the image to include some extra details.
The image is below;
With the image above, we can the find the angle W, using tangent function of trigonometry.
This is seen below;
[tex]\begin{gathered} \tan w=\frac{opposite}{\text{Adjacent}} \\ \text{opposite =30ft} \\ \text{Adjacent}=15ft \\ \therefore\tan w=\frac{30}{15} \\ \tan w=2 \\ w=\tan ^{-1}2 \\ w=63.4^0 \end{gathered}[/tex]The angle closest to m
Answer: 63.4
There is sales tax of $9.00 on an item t that costs $ 120.00 before tax. The sales tax on a different item is $ 19.05. How much does the second item cost before tax?
Answers
SOLUTION:
Step 1:
In this question, we are given that:
There is sales tax of $9.00 on an item that costs $ 120.00 before tax.
The sales tax on a different item is $ 19.05.
We are meant to find how much the second item cost before tax.
Step 2:
Assuming that there is an equal percentage of tax,
and let the second item cost before tax be y,
then we have that:
[tex]\frac{9}{120}\text{ = }\frac{19.05}{y}[/tex]Cross-multiply, we have that:
[tex]\begin{gathered} 9\text{ x y = 19.05 x 120} \\ 9y\text{ = 2286} \\ \end{gathered}[/tex]Divide both sides by 9, we have that:
[tex]\begin{gathered} y\text{ = }\frac{2286}{9} \\ y\text{ = 254} \end{gathered}[/tex]CONCLUSION:
The cost of the second item before tax = $ 254
A car can travel 43/1/2 miles on 1/1/4 gallons of gas. What is the unit rate for miler per gallon
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The unit rate for the car is 34.8 miles per gallon.
How to get the unit rate for mile per gallon?
The unit rate will be given by the quotient between the distance traveled and the gallons of gas consumed to travel that distance.
Here we know that the car travels 43 and 1/2 miles on 1 and 1/4 gallons of gas, then the quotient is:
U = (43 + 1/2)/(1 + 1/4) mi/gal = (43.5)/(1.25) mi/gal = 34.8mi/gal
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Write an equation of a line in SLOPE INTERCEPT FORM that goes through (-5,-3) and is parallel to the line y = x +5.
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Since the slope of the line y=x+5 is m=1, then if the other line is parallel to y=x+5, then it must have the same slope, this is, m'=1.
Now we can use the point-slope formula to get the equation of the line:
[tex]\begin{gathered} m^{\prime}=1 \\ (x_0,y_0)=(-5,-3) \\ y-y_0=m(x-x_0) \\ \Rightarrow y-(-3)=1\cdot(x-(-5))=x+5 \\ \Rightarrow y+3=x+5 \\ \Rightarrow y=x+5-3=x+2 \\ y=x+2 \end{gathered}[/tex]therefore, the equation of the line in slope intercept form that goes through (-5,-3) and is parallel to the line y=x+5 is y=x+2
LM is a perpendicular bisector of NP. The length of LN is 12w + 7, and rhe length of LP is 15w - 5. What is the length of LN?(every capital letter has a line over it and i cant add that. Ex. There would be a line over LP. Because its a line. But i dont know to do that so im adding this!)
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LN = LP
So, we can say:
12w + 7 = 15w - 5
Solving for w,
7 + 5 = 15w - 12w
12 = 3w
w = 12/3
w = 4
Length of LN is 12w + 7
plug in w = 4 to get:
12 (4) + 7
48 + 7 = 55
Length of LN is 55
Give the slope and the y-intercept of the line y=– 8x+7. Make sure the y-intercept is written as a coordinate.
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Solution
We have the following function given:
y =-8x+7
If we compare this with the general formula for a slope given by:
y= mx+b
We can see that the slope m is:
m =-8
And the y-intercept would be: (0,7)
А.Translate the triangle.Then enter the new coordinates.A'([?], []).(4,-1) B'([ ], [])C'([],[ ](1,-3)(5,-4)<-2,3)B.
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Given the triangle shown in the picture, you know its vertices:
[tex]A\mleft(4,-1\mright);B\mleft(5,-4\mright);C\mleft(1,-3\mright)[/tex]You have the following translation vector:
[tex]\langle-2,3\rangle[/tex]Therefore, you can identify that to find the Image (the figure translated) of the Pre-Image (the original figure) ABC, you have to translate each vertex 2 units left and 3 units up. Then, you get:
[tex]\begin{gathered} A^{\prime}(4-2,-1+3)=A^{\prime}(2,2) \\ \\ B^{\prime}(5-2,-4+3)=B^{\prime}(3,-1) \\ \\ C^{\prime}(1-2,-3+3)=C^{\prime}(-1,0) \end{gathered}[/tex]Then, the answer is:
[tex]undefined[/tex]The bank requires that customers select a PIN (personal identification number) so ATM’s can be accessed. The PIN must be 3 digits followed by one letter. How many different PIN numbers can be selected if the first digit cannot be zero?
Answers
Answer:
A lot
Step-by-step explanation:
use random numbers from 1 to 9 and or 0, after the first natural number. And different letters, so there is no specific amount to say that can be used.
3. Suppose an investment of $5000 doubles every 12 years. How much is the investment worth after: 24 years?
Answers
Money = $5000
time = 12 years
investment after 24 years
If the investment doubles every 12 years after 24 years the total amount of money will be $10000.0
Which set of ordered pairs does not show y as a function of x? A. {(3,-2); (5,-3); (7,-4); (9,-5)} B. O {(3,-2); (6,-2); (9,-2); (12,-2)} c.{(4, -2); (5,-3); (6,-4); (7,-5)} D.O{(4, -2); (5,-3); (4,-8); (5,-9)}