The two composite functions have their values to be (w o s)(x) = 7x² - 49x + 33 and (s o w)(x) = (7x - 2)² - 7(7x - 2) + 5
How to determine the composite functions?Composite function 1
The given parameters are
w(x) = 7x - 2
s(x) = x² - 7x + 5
To calculate (w o s)(x), we make use of
(w o s)(x) = w(s(x))
So, we have
(w o s)(x) = 7s(x) - 2
Substitute s(x) = x² - 7x + 5
(w o s)(x) = 7(x² - 7x + 5) - 2
Expand
(w o s)(x) = 7x² - 49x + 35 - 2
Simplify
(w o s)(x) = 7x² - 49x + 33
Composite function 2
Here, we have
w(x) = 7x - 2
s(x) = x² - 7x + 5
To calculate (s o w)(x), we make use of
(s o w)(x) = s(w(x))
So, we have:
(s o w)(x) = w(x)² - 7w(x) + 5
Substitute w(x) = 7x - 2
(s o w)(x) = (7x - 2)² - 7(7x - 2) + 5
So, the composite functions are (w o s)(x) = 7x² - 49x + 33 and (s o w)(x) = (7x - 2)² - 7(7x - 2) + 5
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Suppose you open a bank account and deposit $50. Then, every month you deposit $20. Write anequation that relates the total number of dollars deposited, T, and the month, m.Which equation below relates the total number of dollars deposited, T, and the month, m?
Let:
T = Total number of dollars deposited
m = Number of months
b = Initial deposit
So:
[tex]\begin{gathered} T(m)=20m+b \\ where \\ b=50 \\ so\colon \\ T(m)=20m+50 \end{gathered}[/tex]Hello! I need help with this:Calculation of the confidence interval Statistics.The confidence interval should be calculated for the percentage of people who chose the answer spruce:Sample: 313Answers:Spruce - 272Pine - 41Confidence level - 0.9
We have to calculate a 90% confidence interval for the proportion that chose the answer "Spruce".
The sample proportion is p = 0.869:
[tex]p=\frac{X}{n}=\frac{272}{313}\approx0.869[/tex]The standard error of the proportion is:
[tex]\begin{gathered} \sigma_p=\sqrt{\frac{p(1-p)}{n}} \\ \\ \sigma_p=\sqrt{\frac{0.869\cdot0.131}{313}} \\ \\ \sigma_p\approx\sqrt{0.0003637} \\ \sigma_p\approx0.019 \end{gathered}[/tex]The critical z-value for a 90% confidence interval is z = 1.645.
The margin of error (MOE) can be calculated as:
[tex]MOE=z\cdot\sigma_p=1.645\cdot0.019\approx0.031[/tex]Then, the lower and upper bounds of the confidence interval are:
[tex]\begin{gathered} LL=p-z\sigma_p=0.869-0.031=0.838 \\ UL=p+z\sigma_p=0.869+0.031=0.900 \end{gathered}[/tex]Answer: The 90% confidence interval for the population proportion is (0.838, 0.900).
5 1/7 * 4 2/3 equals
We have to solve this operation with mixed numbers.
We can solve this applying the distributive property or by converting the mixed numbers into fractions.
We will solve this converting the numbers into fractions:
[tex]\begin{gathered} (5+\frac{1}{7})\cdot(4+\frac{2}{3}) \\ \frac{5\cdot7+1}{7}\cdot\frac{4\cdot3+2}{3} \\ \frac{35+1}{7}\cdot\frac{12+2}{3} \\ \frac{36}{7}\cdot\frac{14}{3} \\ \frac{36}{3}\cdot\frac{14}{7} \\ 12\cdot2 \\ 24 \end{gathered}[/tex]Answer: 24
I need help on answering 3. (d) I have two choices it can be which is false and sometimes true.
Question:
Solution:
If x represents a positive integer, then the point x is a natural number, that is, x is greater than zero, in particular, if x is a number greater than zero it can be a number greater than any number after zero. For example, it can be greater than 1.
Then the question d is ALWAYS TRUE.
a triangle with an area of 8 in^2 is dilated by a factor of 3. the area of the dilated triangle is ___ in^2(no image included)
we have:
[tex]A=\frac{1}{2}(b\times3)(h\times3)=\frac{1}{2}(9bh)=\frac{9}{2}bh[/tex]therefore:
[tex]A=72[/tex]answer: 72 in^2
A particular lawn requires 6 bags of fertilizer. A lawn next door requires 4 bags of fertilizer. How big is the lawn next door?A. 10 feet square feetB. 24 feet square feetC. 50 feet square feetD. Not enough information is given
Answer:
D. Not enough information is given
Explanation:
To know the size of the lawn next door, we would need a relation between the square feet and the number of bags of fertilizer.
Since all we know is the bags of fertilizer for the particular lawn and the lawn next door, we can say that we didn't have enough information to answer the question.
Therefore, the answer is:
D. Not enough information is given
Is ⅓ greater that 3/9?
1/3 and 3/9
Simplify 3/9 by 3
(3/3) / (9/3 ) = 1 /3
So, both fractions are equal
1/3 is not greater than 3/9
How to fill out an income summary
Answer: Pick a Reporting Period. ...
Generate a Trial Balance Report. ...
Calculate Your Revenue. ...
Determine the Cost of Goods Sold. ...
Calculate the Gross Margin. ...
Include Operating Expenses. ...
Calculate Your Income. ...
Include Income Taxes.
I only need part bb) A foam protector is covered with PVC material to make it waterproof. Find the total surface area of a protector which is covered by PVCmaterial.
Assuming all the parts are covered, inluding the internal part, we have to find the surface area of the whole protector.
So, let's list which areas we need:
- We need the lateral areas of the external parts, which are 4 rectangles.
- We need the top and bottom areas, which are both area of squares minus the area of the cicle of the hole.
- We need the interior aread, which is the same as the lateral area of a cylinder.
For the external part, we only need the dimensions of each rectangle. since they have the same length and the other sides are the sides of the squares, they are all the same.
The area of each of them is:
[tex]A_{\text{rectangle}}=300mm\cdot1.8m=0.3m\cdot1.8m=0.54m^2[/tex]Since we have 4, the total exterior lateral area is:
[tex]A_{\text{lateral}}=4\cdot0.54m^2=2.16m^2[/tex]For the top and bottom, both are the same, a square of 300 mm x 300 mm with a hole of 150 mm diameter.
First, let's get all to meters: 0.3 m x 0.3 m and 0.15 m diameter. The radius of the circle is half the diameter, so:
[tex]r=\frac{0.15m}{2}=0.075m[/tex]The area of a circle given its radius is:
[tex]A=\pi r^2[/tex]So, the area of both the top and bottom is the area of the square minus the area of the circle and double all of this:
[tex]\begin{gathered} A_{\text{top/ottom}}=2((0.3m)^2-\pi(0.075m)^2) \\ A_{\text{top/ottom}}=2(0.09m^2-0.005625\pi m^2) \\ A_{\text{top/ottom}}=2(0.09-0.005625\pi)m^2 \end{gathered}[/tex]We deal with π later on.
For the lateral area of the cylinder, we can remember that it is the same as the area of a rectangle with on dimension being the length of the cylinder and the other being the circumference of the top/bottom.
the circumference of a circle is:
[tex]C=2\pi r[/tex]The radius is the same as the hole, and the length is 1.8m, so the lateral area of the cylinder is:
[tex]\begin{gathered} A_{\text{cylinder}}=1.8m\cdot2\pi(0.075m) \\ A_{\text{cylinder}}=(1.8\cdot0.15\pi)m^2 \\ A_{\text{cylinder}}=(0.27\pi)m^2 \end{gathered}[/tex]So, the total surface area is the sum of all of these:
[tex]A=2.16m^2+2(0.09-0.005625\pi)m^2+(0.27\pi)m^2[/tex]Now, we just need to evaluate:
[tex]\begin{gathered} A=2.16m^2+2\cdot0.072328\ldots m^2+0.848230\ldots m^2 \\ A=2.16m^2+0.144657\ldots m^2+0.848230\ldots m^2 \\ A=3.152887\ldots m^2 \\ A\approx3.15m^2 \end{gathered}[/tex]So, the lateral area is approximately 3.15 m².
Hello I would like to know what is the answer to the question 3/4x 3 < 6
determin wether true or false. (2 points) True False The functions f(x) = x – 5 and g(x) = -3x + 15 intersect at x = 5. The functions f (x) = 3 and g(x) = 11 – 2. intersect at x = 3. O The functions f (x) = x + 3 and g(x) = -x + 7 intersect at x = 2. The functions f (x) = {x – 3 and g(x) = -2x + 2 intersect at x = -2.
To find the intersection point between f(x) and g(x) we will equate their right sides
[tex]\begin{gathered} f(x)=x-5 \\ g(x)=-3x+15 \end{gathered}[/tex]Equate x - 5 by -3x + 15 to find x
[tex]x-5=-3x+15[/tex]add 3x to both sides
[tex]\begin{gathered} x+3x-5=-3x+3x+15 \\ 4x-5=15 \end{gathered}[/tex]Add 5 to both sides
[tex]\begin{gathered} 4x-5+5=15+5 \\ 4x=20 \end{gathered}[/tex]Divide both sides by 4 to get x
[tex]\begin{gathered} \frac{4x}{4}=\frac{20}{4} \\ x=5 \end{gathered}[/tex]Then the first one is TRUE
For the 2nd one
f(x) = 3, and g(x) = 11 - 2x
If x = 3, then substitute x by 3 in g(x)
[tex]\begin{gathered} g(3)=11-2(3) \\ g(3)=11-6 \\ g(3)=5 \end{gathered}[/tex]Since f(3) = 3 because it is a constant function and g(x) = 5 at x = 3
That means they do not intersect at x = 3 because f(3), not equal g(3)
[tex]f(3)\ne g(3)[/tex]Then the second one is FALSE
For the third one
f(x) = x + 3
at x = 2
[tex]\begin{gathered} f(2)=2+3 \\ f(2)=5 \end{gathered}[/tex]g(x) = -x + 7
at x = 2
[tex]\begin{gathered} g(2)=-2+7 \\ g(2)=5 \end{gathered}[/tex]Since f(2) = g(2), then
f(x) intersects g(x) at x = 2
The third one is TRUE
For the fourth one
[tex]f(x)=\frac{1}{2}x-3[/tex]At x = -2
[tex]\begin{gathered} f(-2)=\frac{1}{2}(-2)-3 \\ f(-2)=-1-3 \\ f(-2)=-4 \end{gathered}[/tex]g(x) = -2x + 2
At x = -2
[tex]\begin{gathered} g(-2)=-2(-2)+2 \\ g(-2)=4+2 \\ g(-2)=6 \end{gathered}[/tex]Hence f(-2) do not equal g(-2), then
[tex]f(-2)\ne g(-2)[/tex]f(x) does not intersect g(x) at x = -2
The fourth one is FALSE
A father is buying cheeseburgers for his children. Each cheeseburgercosts $3.50. He spends $17.50 on cheeseburgers. Which equation canyou use to determine how many cheeseburgers he bought?O 17.50 = 3.50cO 3.50 = 17.500O 3.50 + 17.50 =cO 17.50 -3.50 = C« PreviousNext
Each cheese burger costs $3.50
c reprsents the number of cheese burgers
$17.50 is the total cost spent on c cheeseburgers
If you multiply the value of each cheeseburger by the number bought, you'll obtain the total cost:
3.50c=17.50
The correct option is number 1
Triangle ABC is similar to triangle DEF. Find the measure of side DE. Round youranswer to the nearest tenth if necessary.C7BF27E15DAD
Given:
Triangle ABC is similar to triangle DEF.
[tex]\frac{DE}{AB}=\frac{EF}{BC}[/tex][tex]\begin{gathered} \frac{DE}{15}=\frac{27}{7} \\ DE=\frac{27}{7}\times15 \\ DE=57.9 \end{gathered}[/tex]Frank makes 8 dollars for each hour of work. Write an equation to represent his total pay p after working h hours
The equation will be
P = 8h
here, P = total pay
h= working hours.
Find f(-4) and f(3) for the following funxripnf(x)=3x
Given the function:
[tex]f(x)=3x[/tex]• You need to substitute this value of "x" into the function:
[tex]x=-4[/tex]And then evaluate, in order to find:
[tex]f(-4)[/tex]You get:
[tex]f(-4)=3(-4)[/tex][tex]f(-4)=-12[/tex]Remember the Sign Rules for Multiplication:
[tex]\begin{gathered} +\cdot+=+ \\ -\cdot-=+ \\ -\cdot+=- \\ +\cdot-=- \end{gathered}[/tex]• Substitute this value of "x" into the function:
[tex]x=3[/tex]Then:
[tex]f(3)=3(3)[/tex]Evaluate, in order to find:
[tex]f(3)[/tex]You get:
[tex]f(3)=9[/tex]Hence, the answer is:
[tex]\begin{gathered} f(-4)=-12 \\ f(3)=9 \end{gathered}[/tex]the table below shows changes in the population densities of the zebra and you knew I'd muscles from 1991 to 2015, in six-year intervals.1. based on the data shown in the table calculate the percent change in the population density of zebra mussels from 1997 to 2003
The table below shows changes in the population densities of the zebra and you knew I'd muscles from 1991 to 2015, in six-year intervals.
1. Based on the data shown in the table calculate the percent change in the population density of zebra mussels from 1997 to 2003
_____________________
1997 (3 250)
2003 (2 500)
Percentage change= 100 *(new value- old value)/old value
Percentage change = 100 *(2500- 3250)/ 3250 = 100* (-0.2308)
Percentage change = -23.08%
__________________________________
Answer
The percent change in the population density of zebra mussels from 1997 to 2003 is -23.08%
There was a decrease of 23. 08%
A hot chocolate recipe calls for 2.5 gallons of milk. How many quarts of milk are needed for the recipe
Answer: 10
Step-by-step explanation: a gallon has 4 quarts, 4x2.5=10
10 quarts is 2.5 gallons.
9 - 6 - 19 c) y - 12 OC p = b) y 24 c) = 9
x=70, y= -50 and x=80
1) Let's solve each equation, plugging in the given value for x
y=5x -300
a) y=50
y=5x -300 Plug y=50
50=5x -300 Add 300 to both sides
50+300=5x
350 = 5x Divide both sides by 5
x=70
b) x = 50
y=5x -300 Plug x=50
y=5(50) -300 Distribute the factor
y= 250 -300
y= -50
c) y=100
y=5x -300 Plug y=100
100 = 5x -300 Add 300 to both sides
400 = 5x
x =80
Hence, the answer is
x=70, y= -50 and x=80
Find the equation of a line that is parallel to the line x = 10 and contains the point (-8,1)the equation of the line is =
The given line is x = 10, which is a vertical line. All vertical lines have the form x = k, where k is a real number.
So, a parallel line passing through (-8,1) would be x = -8.
Hence, the answer is x = -8.You deposit $400 into a savings account that earns interest annually. The function g(x) = 400(1.05)x can be used to find the amount of money in the savings account, g(x), after x years. What is the range of the function in the context of the problem?
ℝ
[0, 400]
[0, ∞)
[400, ∞)
Answer:
Step-by-step explanation:
The constant percent rate of change in the case of a deposit of $400 into a savings account is compounded annually.
With an example, what is compound interest?
When you add the interest you have already earned back into your principal balance, you are earning compound interest, which increases your profits.
Consider that you have $1,000 in a savings account earning 5% interest annually. If you made $50 in the first year, your new balance would be $1,050.
Principal - $400
rate of interest is compounded annually
g(x) = 400( 1.03)ˣ equation 1.
Formula used
A = P( 1 + r )ⁿ
here n = x
Solution:
Putting the value of n, and principal in the formula
A = P( 1 + r )ⁿ ................... equation 2
now comparing both equation 1 and equation 2,
400( 1.05)ˣ = 400( 1 + r )ˣ
( 1.05)ˣ = ( 1 + r )ˣ
1.05 = 1 + r
r = 1.05 - 1
r = 0.05
r % = 0.05 × 100
r % = 5 %
thus, the constant percent rate of change = 5 %
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Find the values of x and y
Since the "x" values are vertical angles, and so are the "y" values, you must make them equal. If this is confusing, look at steps below (The order of solving the "x" or "y" values don't matter. I will write both ways down (in point form --> [tex](x,y)[/tex] and as just "x=..." "y=..."
First step is to make the "y" values equal each other
[tex]5y = 7y-34\\-2y = -34\\2y = 34\\\\y=17[/tex]
Next to solve make the "x" values equal each other
[tex]8x+7 = 9x-4\\-x = -11\\x = 11[/tex]
Final Answer:
[tex](11,17)[/tex]
x = 11; y = 17
Hope this helps :)
The pyramid has a square base with side
length 2 cm and height 3 cm. What is the
volume of the chocolate to the nearest
tenth?
A 12 cm
B 6 cm3
C 4 cm
D 2 cm
E 1.3 cm3
The radius of cylinder is r = 3 in.
The height of cylinder is h = 10 in.
The formula for the volume of cylinder is,
[tex]V=\pi\cdot(r)^2\cdot h[/tex]Substitute the values in the formula to determine the volume of cylinder.
[tex]\begin{gathered} V=\pi\cdot(3)^2\cdot10 \\ =282.743 \\ \approx282.7 \end{gathered}[/tex]So volume of cylinder is 282.7 in^3.
Option H is correct.
Bell Ringer -- Find the distance of each side of the triangle: A(-10, 6) B(-6, 9) C(-6, 6)
Answer:
It is c) (-6, 6)
A model rocket is launched with an initial upward velocity of 156 ft/s. The rocket's height h (In feet) after t seconds is given by the following.
h=156t-16t²
Find all values of t for which the rocket's height is 60 feet.
Round your answer(s) to the nearest hundredth.
(If there is more than one answer, use the "or" button.)
Explanation
Check
ground
t = 0 seconds
☐or D
X
5
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I need help
The quadratic equation that gives the height of the rocket, h = 156·t - 16·t² is evaluated at h = 60 feet to give the two times the rocket's height is 60 feet as 0.40 seconds and 9.35 seconds.
What is a quadratic equation?A quadratic equation is an equation of the second degree that can be expressed in the form; a·x² + b·x + c = 0, where the letters, a, and b represents the coefficients of x and c is a constant.
The initial velocity of the rocket = 156 ft./s upwards
The given equation of the rocket is: h = 156·t - 16·t²
The times when the rocket height is 60 feet are found by plugging in the value h = 60, in the equation of the vertical height of the rocket as follows:
h = 60 = 156·t - 16·t²
156·t - 16·t² - 60 = 0
4·(39·t - 4·t² - 15) = 0
Therefore: [tex]39\cdot t - 4\cdot t^2 - 15 = \dfrac{0}{4} =0[/tex]
39·t - 4·t² - 15 = 0
-4·t² + 39·t - 15 = 0
From the quadratic formula which is used to solve the quadratic equation of the form; f(x) = a·x² + b·x + c, is presented as follows;
[tex]x = \dfrac{-b\pm\sqrt{b^2-4\cdot a \cdot c} }{2\cdot a}[/tex]
The solution of the equation, -4·t² + 39·t - 15 = 0, is therefore:
[tex]t = \dfrac{-39\pm\sqrt{(39)^2-4\times (-4) \times (-15)} }{2\times (-4)}= \dfrac{-39\pm\sqrt{1281} }{-8}[/tex]
Therefore, when the height of the rocket is 60 feet, the times are: [tex]t = \dfrac{-39-\sqrt{1281} }{-8}\approx 9.35[/tex] and [tex]t = \dfrac{-39+\sqrt{1281} }{-8}\approx 0.40[/tex]
The times when the height of the rocket is 60 feet, the times are:
t ≈ 9.35 s, and t ≈ 0.40 s
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You and 2
2
friends have a job cleaning houses. You split the total money you make so that you each get the same amount. On the first day, you earn $93
$
93
. The second day, you earn $75
$
75
. The third day, you earn $108
$
108
. How much money do you each get for 3
3
days of work?
The amount of money that each person would get for the three days of work is $92.
How much would each person get?The first step is to add all the money earned on the three days together. Addition is the process of determining the sum of two or more values.
Total amount earned in the 3 days = amount earned on the first day + amount earned on the second day + amount earned on the third day
= $93 + $75 +$108 =$276
The next step is to divide the total amount of money earned in the three days by the total number of people that would share the money. Division is the process of determining the quotient of a number.
The amount of money gotten by each person = total earnings / total number of people
$276 / 3 = $92
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A total of $6000 is invested: part at 5% and the remainder at 10%. How much is invested at each rate if the annual interest is $590
If a total of $6000 is invested, part at 5% and remainder at 10%, then the amount invested on 10% interest is $5800 and the amount invested on 5% interest is $200
The total amount = $6000
Consider the amount invested on 10% interest as x
The amount invest on 5% interest = (6000-x)
The the equation will be
x×(10/100) + (6000-x)(5/100) = 590
0.1x + 0.05(6000-x) = 590
0.1x + 300 - 0.05x = 590
0.05x +300 = 590
0.05x = 590-300
0.05x = 290
x = 290/0.05
x = $5800
The amount invested on 10% interest = $5800
The amount invested on 5% interest = 6000-5800
= $200
Hence, if a total of $6000 is invested, part at 5% and remainder at 10%, then the amount invested on 10% interest is $5800 and the amount invested on 5% interest is $200
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Use the table to write an equation that relates the cost of lunch Y and the number of students X
In order to determine what is the equation which describes the values of the table, consider that the general form of the equation is:
y = mx
where m is the constant of proportionality between both variables x and y.
To calculate m you calculate the quotient between any pair of data from the table.
If you for example use the following values:
Students = 8.00
Lunch cost = 2
the constant of proportionality is:
m = 8.00/2 = 4.00
Next, you replace the value of m in the equation y=mx:
y = $4.00x
the top of the hill rises 67 feet above checkpoint 4, which is -211. What is the altitude of the top of the hill?
Answer:
-144 feet
Step-by-step explanation:
-211 plus the added 67 feet it is above equals an altitude of -144ft
Consider the following word problem:Two planes, which are 1180 miles apart, fly toward each other. Their speeds differ by 40 mph. If they pass each other in 2 hours,what is the speed of each?Step 1 of 2: Use the variable x to set up an equation to solve the given problem. Set up the equation, but do not take steps to solve it.
So we have two planes flying toward each other. Let's use v for the speed of the slower plane. Then the speed of the faster plane is v+40. If we pass to the reference system of the slower plane we have that its speed is 0 and the speed of the other plane is v+v+40=2v+40. So basically we have a problem where one of the planes is stationary whereas the other approaches at 2v+40mph and it takes it 2 hours to travel 1180 miles. Remember that the speed is equal to the distance traveled divided by the time it took the plane to travel that distance. Then we get:
[tex]\begin{gathered} 2v+40\frac{mi}{h}=\frac{1180mi}{2h}=590\frac{mi}{h} \\ 2v=590\frac{mi}{h}-40\frac{mi}{h}=550\frac{mi}{h} \\ v=\frac{550\frac{mi}{h}}{2}=275\frac{mi}{h} \end{gathered}[/tex]Then we get:
[tex]v+40\frac{mi}{h}=275\frac{mi}{h}+40\frac{mi}{h}=315\frac{mi}{h}[/tex]Then the speeds of the planes are 275mph and 315mph.
Multiply.-4u? ( – 5u?)Simplify your answer as much as possible.X $
SOLUTION:
Simplify;
[tex]-4u^2(-5u^3)[/tex]Using product rule;
[tex](-\times-)(4\times5)(u^2\times u^3)[/tex]From Indices law;
[tex]a^b\times a^c=a^{b+c}[/tex]Thus;
[tex]\begin{gathered} (-\operatorname{\times}-)(4\times5)(u^2\times u^3)=(+)(20)(u^{2+3}) \\ =20u^5 \end{gathered}[/tex]FINAL ANSWER:
[tex]\begin{equation*} 20u^5 \end{equation*}[/tex]