Answers
[tex]\begin{cases} f(x)=5x-2\\\\ g(x)=x^2-5x+11\\\\ (f\circ g)(x)=f(~~g(x)~~) \end{cases} \\\\[-0.35em] ~\dotfill\\\\ g(1)=(1)^2 -5(1)+11\implies g(1)=7 \\\\\\ f(~~g(1)~~)\implies f(~~7~~)=5(7)-2\implies \stackrel{(f\circ g)(1)}{f( ~~ 7 ~~ )}=33[/tex]
Related Questions
At a restaurant, you order a moal that costs $12. You leave a 15% tip. The sales tax is 9%. What is the total costof the meal In dollars
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SOLUTION:
Case: Percentages
Given:
Meal cost= $12
tip= 15%
sales tax= 9%
Method:
To find the Total cost of the meal,
We calculate the actual cost of the tip
[tex]\begin{gathered} 15\%\times12 \\ \frac{15}{100}\times12 \\ \frac{180}{100} \\ 1.8 \end{gathered}[/tex]The actual cost of the tip was $1.80
We then calculate the actual cost of the sales tax
[tex]\begin{gathered} 9\%\times12 \\ \frac{9}{100}\times12 \\ \frac{108}{100} \\ 1.08 \end{gathered}[/tex]The cost of sales tax is $1.08
The total cost of the mean is:
[tex]\begin{gathered} 12+1.80+1.08 \\ =14.88 \end{gathered}[/tex]Final answer:
The total cost of the meal is $14.88
(5 x 2c) + 50 ÷ 5 = 30
Solve for C
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Answer: The correct answer is c=4/x^2
Step-by-step explanation:
Solve for c:
5x^2c+50/5=30
Add -10 to each side:
5cx^2+10+(−10)=30+(−10)
5cx^2=20
Divide both sides by 5x^2:
(5cx^2)/(5x^2)=20/(5x^2)
c=4/x^2
Length = 2.4 yards; Height = 3.6 yards; Width = 4.2 yards. Find the surface area of a rectangular prism
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Ok, so
Remember that the surface area of a rectangular prism can be found using:
[tex]SA=2lw+2wh+2lh[/tex]If we replace our values:
l = 2.4
h = 3.6
w = 4.2
We got that:
[tex]\begin{gathered} SA=2(2.4)(4.2)+2(4.2)(3.6)+2(2.4)(3.6) \\ SA=20,16+30,24+17,28 \\ SA=67,68 \end{gathered}[/tex]Then, the surface area of this rectangular prism is 67.68 yd2.
what are the domain and range of this exponential functions y=4×+8
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The given function is
[tex]y=4^{x+8}[/tex]The domain of the function would be all real numbers.
But the range would be all real numbers greater than zero because the function approximates to y = 0 but it doesn't go through.
Hence, the answer is the first option.2. Solve: x/4.6 = 3.5 x/4.6 = 3.5 X M Check: Right Hand Side
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Starting with the equation:
[tex]\frac{x}{4.6}=3.5[/tex]Multiply both sides by 4.6:
[tex]\frac{x}{4.6}\cdot4.6=3.5\cdot4.6[/tex]Simplify the left hand side:
[tex]x=3.5\cdot4.6[/tex]Simplify the right hand side:
[tex]x=16.1[/tex]The answer is: 16.1.
To check your answer, substitute x=16.1 into the first equaton to see if you obtain the same number in both sides:
[tex]\frac{16.1}{4.6}=3.5[/tex]Simplify the left hand side:
[tex]3.5=3.5[/tex]Quadrilateral DEFG has vertices D(-1,2), E(-2, 0), F(-1,-1) and G(1, 3). A
translation maps quadrilateral DEFG to quadrilateral D'E'F'G'. The image of D is D'(-2,-2).
What are the coordinates of E, F, and G′ ?
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Answer:
E' = (-3, -4)
F' = (-2, -5)
G' = (0, -1)
Step-by-step explanation:
Given vertices of quadrilateral DEFG:
D = (-1, 2)E = (-2, 0)F = (-1, -1)G = (1, 3)A translation is a type of transformation and moves a figure left, right, up or down.
Every point on the original figure is translated (moved) the same distance in the same direction.
Therefore, to calculate the mapping rule that translates DEFG to D'E'F'G', compare the coordinates of D with the coordinates of D'.
D = (-1, 2)D' = (-2, -2)The x-coordinate has be translated 1 unit to the left.
The y-coordinate has been translated 4 units down.
Therefore, the mapping rule is:
(x, y) → (x-1, y-4)To find the coordinates of E', F' and G', apply the mapping rule to the given vertices of the pre-image:
⇒ E' = (-2-1, 0-4) = (-3, -4)
⇒ F' = (-1-1, -1-4) = (-2, -5)
⇒ G' = (1-1, 3-4) = (0, -1)
-2/5y=4 what is y???????
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Answer:
-10
Step-by-step explanation:
solve for y by simplifying both sides of the equation, then isolating the variable.
Nate is 22 years old. Karina is 13 years old. How many years ago was Nate's age 4 times Karina'sage?
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Nate current age = 22 years
Karina current age = 13 years
let
x = the years ago
[tex]\begin{gathered} 4(13-x)=22-x \\ 52-4x=22-x \\ 52-22=-x+4x \\ 30=3x \\ x=\frac{30}{3} \\ x=10 \end{gathered}[/tex]The answer is 10 years ago.
A line passes though two points A(-2, 2). B(-1, 2). What is the slope:
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The slope of the line that passes through points (-2, 2) and (-1, 2) is 0.
What is the slope of the line with the given coordinates?Slope is simply expressed as change in y over the change in x.
Slope m = ( y₂ - y₁ )/( x₂ - x₁ )
Given the data in the question;
Point A(-2, 2)
x₁ = -2y₁ = 2Point B( -1, 2 )
x₂ = -1y₂ = 2To determine the slope, plug the given x and y coordinates into the slope formula and simplify.
Slope m = ( y₂ - y₁ )/( x₂ - x₁ )
Slope m = ( 2 - 2 )/( -1 - (-2) )
Slope m = ( 0 )/( -1 + 2 )
Slope m = ( 0 )/( 1 )
Slope m = 0
Therefore, the slope of the line is 0.
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homework help
give two examples of when you might estimate differences in everyday life.
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Some examples of the use of estimates in our everyday lives are given below:
Making an estimate when shopping so as not to exceed budgetMaking an estimate of the number of shoppers in a shopping mallWhat is an Estimate?This refers to the rough calculation that is done to judge the value of a thing or the data outcome of a proposition.
Hence, when it comes to estimation or rough calculation of values or numbers, it is important that it is done as accurately as possible within the limits of current available data or data projections.
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The radius of a circle is 6 feet. What is the area of a sector bounded by a 66° arc?Give the exact answer in simplest form. ____ square feet. (pi, fraction,)
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where:
r= radius = 6 ft
Θ = angle = 66°
Replacing:
[tex]A=\frac{66\cdot\pi}{360}\cdot6^2[/tex]A= 33/5 π
help me please
thank you
Answers
Answer:
Domain: [tex](-\infty, \infty)[/tex]
Range: [tex][0, \infty)[/tex]
Step-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
Determine the value of x using a trigonometric ratio.Question options:A) 4.98B) 8.49C) 4.18D) 10.11
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We know that the hypotenuse is 6.5 units long, and x is the opposite leg to angle 50.
To find the value of x, use the sine trigonometric reason.
[tex]\begin{gathered} \sin 50=\frac{x}{6.5} \\ x=6.5\cdot\sin 50 \\ x\approx4.98 \end{gathered}[/tex]Therefore, the answer is A) 4.98.Given Point A, what is the coordinate for A' after the following transformation has occurred?(x, y) + (2 - 5, -y + 2)A (5,7)Al
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In order to perform the given transformation, we just have to replace the x and y-coordinates into the transformation rule, like this:
A(5, 7), by replacing 5 for x and 7 for y into (x - 5, -y + 2), we get:
(5 - 5, -7 + 2) = (0, -5)
A(5, 7) -> A'(0, -5)
Then, the coordinates of the new point A' are (0, -5)
What two numbers multiply to -25 adds up to 2
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what principal will amount to $1750 if invested at 3% interest compounded quarterly for 5 years
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The formula for calculating compound interest is expressed as
A = P(1 + r/n)^nt
Where
A is the total amount after t years
P is the principal or initial amount invested
r is the interest rate
n is the number of compouding periods in a year
t is the number of years
From the information given,
A = $1750
r = 3% = 3/100 = 0.03
t = 5
n = 4 because it was compounded quarterly
By substituting these values into the formula, we have
1750 = P(1 + 0.03/4)^4 * 5
1750 = P(1 + 0.03/4)^20
1750 = P(1.0075)^20
Dividing both sides by (1.0075)^20, it becomes
P = 1750/(1.0075)^20
P = 1507.0822
Approximating to the nearest whole number,
Principal = $1507
There are 360° in a circle graph. If 50° of the graph represents rent and 7° of the graph represents savings, what fractional portion of the whole graph is not represented by rent and savings?
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Based on the circle graph and portions that are represented by rent and savings, the fractional portion of the graph that is not represented by rent and savings is 84.2%
How to find the fractional portion?First, find the degrees in the circle graph that is not represented by rent and savings. This is:
= Total number of degrees in circle graph - degrees represented by rent and savings
= 360 - 50 - 7
= 303 °
The fractional portion which isn't represented by either rent or savings is:
= Degrees not represented by rent or savings / Total number of degrees x 100%
= 303 / 360 x 100%
= 84.2%
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Geena's hair grew 1 1/8 inches in 2 months. How many inches will her hair grow in 1 month?
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Answer: 9/16 or 0.5625 or (3/4)^2 inches per month
Step-by-step explanation:
divide by two
(1 1/8) / 2
9/16 or 0.5625 or (3/4)^2
{-3,0,3} what is it closed under addition, multiplication,both or neither
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{-3,0,3} is closed under multiplication.
What are functions of different types of brackets?Curly brackets are often used to denote sets in writing. For instance, a set of the integers 3, 4, 5, and 6 is denoted by "3, 4, 5, 6." In a calculus or physics lecture, angular brackets like 1,3> may denote an inner product, and square brackets may denote a matrix. Mathematicians often use brackets to group similar phrases or numbers together, which is a very important use of these symbols. An expression or thing encompassed by brackets is implied to be given precedence over other things by the presence of brackets. The most popular method for enclosing extra information from a third party is to use square brackets (someone other than the original author). In writing, a list of equal options is frequently denoted by curly brackets.
The set consist of numbers -3, 0 and 3 so if we use any combination of those 3 numbers under some operation and get as result one of those 3 numbers that means set is closed under that operation.
for multiplication you get:
0 × 3 = 0
0 × -3 = 0
-3 × 3 = -9
So all combinations used and answers are 0 and -9 which means set is closed under multiplication.
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VOn December 13, 2007, one U.S. dollar was worth 0.69 euro.(a) On that date, how many dollars was 71.33 euro worth?Round your answer to the nearest hundredth of a dollar.dollars(b) On that date, how many euro was 117.99 dollars worth?Round your answer to the nearest hundredth of a euro.I need help with both of these math problems.
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Given
One US dollar was worth 0.69 euro.
To find:
a) How many dollars was 71.33 euro worth?
b) How many euro was 117.99 dollars worth?
Explanation:
It is given that,
One US dollar was worth 0.69 euro.
Then,
a) Let x be the number of dollars.
That implies,
Since 1 dollar=0.69euro.
Then,
[tex][/tex]
I need to know how to do the whole thing and understand it.
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We are given the data on the number of candies handed by neighborhood A and neighborhood B.
Let us first find the mean and variance of each neighborhood.
Mean:
[tex]\bar{x}_A=\frac{\sum x}{N_1}=\frac{12}{6}=2[/tex][tex]\bar{x}_B=\frac{\sum x}{N_2}=\frac{20}{6}=3.33[/tex]Variance:
[tex]s_A^2=\frac{\sum x^2}{N_1}-\bar{x}_A^2=\frac{28}{6}-2^2=0.667[/tex][tex]s_B^2=\frac{\sum x^2}{N_2}-\bar{x}_B^2=\frac{80}{6}-3.33^2=2.244[/tex]A. Null hypothesis:
The null hypothesis is that there is no difference in the mean number of candies handed out by neighborhoods A and B.
[tex]H_0:\;\mu_A=\mu_B[/tex]Research hypothesis:
The research hypothesis is that the mean number of candies handed out by neighborhood A is more than neighborhood B.
[tex]H_a:\;\mu_A>\mu_B[/tex]Test statistic (t):
The test statistic of a two-sample t-test is given by
[tex]t=\frac{\bar{x}_A-\bar{x}_B}{s_p}[/tex]Where sp is the pooled standard deviation given by
[tex]\begin{gathered} s_p=\sqrt{\frac{N_1s_1^2+N_2s_2^2}{N_1+N_2-2}(\frac{N_1+N_2}{N_1\cdot N_2}}) \\ s_p=\sqrt{\frac{6\cdot0.667+6\cdot2.244}{6+6-2}(\frac{6+6}{6\cdot6})} \\ s_p=0.763 \end{gathered}[/tex][tex]t=\frac{2-3.33}{0.763}=-1.74[/tex]So, the test statistic is -1.74
Critical t:
Degree of freedom = N1 + N2 - 2 = 6+6-2 = 10
Level of significance = 0.05
The right-tailed critical value for α = 0.05 and df = 10 is found to be 1.81
Critical t = 1.81
We will reject the null hypothesis because the calculated t-value is less than the critical value.
Interpretation:
This means that we do not have enough evidence to conclude that neighborhood A gives out more candies than neighborhood B.
can someone help me
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The answer is f(-2) = 30
The question requires us to substitute the value of x into the function.
if the function is:
[tex]f(x)=-2x^3+2x^2-2x+2[/tex]then f(-2) means we only need to substitute -2 for x into the equation given.
[tex]\begin{gathered} f(-2)=-2(-2)^3+2(-2)^2-2(-2)+2 \\ (-2)^3=-8_{} \\ (-2)^2=4 \\ -2(-2)=4 \\ \\ f\mleft(-2\mright)=-2\mleft(-8\mright)+2\mleft(4\mright)+4+2 \\ f(-2)=16+8+4+2 \\ f(-2)=30 \end{gathered}[/tex]Therefore,
The final answer is f(-2) = 30
Change the exponential expression to an equivalent expression involving a logarithm.
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Since the exponential and natural logarithm are inverses each other, we can apply natural logarithm to both sides and get
[tex]x=\ln 8[/tex]or equivalently,
[tex]\ln 8=x[/tex]Threfore, the answer is the last option
The price of a gallion of unleaded gas has risen to $2.89 today. Yesterday's price was $2.84. Find the percentage increase, Round your answer to the nearesttenth of a percentX5 ?
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Answer:
1.8%
Explanation:
Given the original price as $2.84 and the new price as $2.89, let's go ahead and determine the increase in price as seen below;
[tex]\begin{gathered} \text{Increase }=\text{ New price - Original price} \\ =2.89-2.84 \\ =0.05 \end{gathered}[/tex]We'll use the below formula to determine the percentage increase;
[tex]\begin{gathered} \text{Percentage Increase }=\frac{Increase}{\text{Original price}}\times100 \\ =\frac{0.05}{2.84}\times100 \\ =0.0176\times100 \\ =1.8\text{\%} \\ \end{gathered}[/tex]What is the equation for this graph?
Answers
Answer:
[tex]y=\frac{2}{3}x+4[/tex]
Step-by-step explanation:
please help. i don’t under any of this and it’s due today
Answers
GIVEN:
We are given the exponential relationship as shown below;
[tex]g(x)=4(0.6)^x[/tex]Required;
To determine the characteristics of the graph as indicated.
(1) The range of the function; The range of the function is determined as follows;
[tex]\begin{gathered} For\text{ }the\text{ }function;\text{ }c\times n^{ax+b}+k \\ \\ Range=g(x)>k \end{gathered}[/tex]In this question, the value of k is nil or zero. Therefore, we have
[tex]\begin{gathered} Range: \\ \\ g(x)>0 \\ \\ That\text{ }is; \\ \\ y>0 \end{gathered}[/tex]O is the center of the regular pentagon below. Find its perimeter. Round to the nearest tenth if necessary.
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Answer:
To find the perimeter of the regular pentagon.
O is the center of the regular pentagon from the figure.
we know that, There are 360 degrees around a point, the angle formed over each side are equal that is eual to 360/5 =72
In the triangle made by the side and line joinging center, we get
[tex]72+x+x=180[/tex]whereb x is the angle made by the line joining to the center and one of the side.we get,
[tex]\begin{gathered} 72+2x=180 \\ 2x=108 \end{gathered}[/tex][tex]x=54[/tex]Consider the right angled triangle,
we know that,
[tex]\tan \theta=\frac{opposite\text{ side}}{Adjacent\text{ side}}[/tex]we get,
[tex]\tan 54\degree=\frac{10}{y}[/tex][tex]1.376=\frac{10}{y}[/tex][tex]y=\frac{10}{1.376}[/tex][tex]y=7.26[/tex]Side of a pentagon (s)= 2x7.26=14.52
Perimeter of a pentagon is,
[tex]=5s[/tex][tex]=5\times14.52[/tex][tex]=72.6[/tex]Perimeter of a pentagon is 72.6 units.
need answer asap ty
multiplying integers
(-5) (-12) =
-9 × (-6) =
(-7) (8) =
11 × -8 =
(-12) (4) =
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question 1 =60
2=54
3=-56
4=-88
5=-48
how to solve linear equations for example 7x-(x-3)=4x-2
Answers
7x-(x-3)=4x-2
We need to solve first the brackets
7x-x+3=4x-2
Next, we need to put all the terms with x on one side and all the terms without x on the other side, remember is you change the side of a term the sign will be the opposite that's why 4x change to -4x on the other side
7x-x-4x=-2-5
then we sum of the term
2x=-7
the term with x the 2 is multiplying x so on the other side change to divide the seven
x=-7/2
Bath and Body works is having a sale. Their Body Mists are 65% off. If the original price is $14.50, how much would you spend if you bought 5 body mists? Write an equation(s) to represent the problem and solve.
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Body mists are 65% off
The original price is $14.50
So, the 60% of 14.50 is
[tex]\begin{gathered} 60\text{ percent of 14.50 dollars is =}\frac{60\times14.50}{100} \\ 60\text{ percent of 14.50 dollars is}=8.7\text{ dollars} \end{gathered}[/tex]Since the 8.7 dollars is off so, the net price is 14.50-8.7
The prics of one body mists after 60% off is $5.8
Let the x is the amount spend in the 5 body mists
Since the prics of 1 body mists is $5.8
So, the price of 5 body mists is : 5 times of $5.8
[tex]\begin{gathered} \text{The price of 5 body mists =5}\times5.8 \\ \text{The price of 5 body mists=}29\text{ dollars} \\ \text{ Since we assume that the price of the 5 body mists is x } \\ So,\text{ x = 29 Dollars} \end{gathered}[/tex]Answer : x = $29
