Given:
Function A: f(x) = -3x + 2
And the graph of the function B
We will compare the domains of the functions
Function A is a linear function, the domain of the linear function is all real numbers
Function B: as shown in the figure the graph starts at x = 0 and the function is graphed for all positive real numbers So, Domain is x ≥ 0
So, the answer will be the last option
The domain of function A is the set of real numbers
The domain of function B: x ≥ 0
Solve for x. Round to the nearest hundredth. Show all work.
The equation is given as,
[tex]3e^{5x}=1977[/tex]Transpose the term,
[tex]\begin{gathered} e^{5x}=\frac{1977}{3} \\ e^{5x}=659 \end{gathered}[/tex]Taking logarithm on both sides,
[tex]\ln (e^{5x})=\ln (659)[/tex]Consider the formula,
[tex]\ln (e^m)=e^{\ln (m)}=m[/tex]Applying the formula,
[tex]\begin{gathered} 5x=\ln (659) \\ x=\frac{1}{5}\cdot\ln (659) \\ x\approx1.30 \end{gathered}[/tex]Thus, the solution of the given exponential equation is approximately equal to,
[tex]1.30[/tex]Be specific with your answer thank you thank you thank you bye-bye
The y-axis on the graph, that shows us the cost, goes from 2 to 2 units.
To find the cost at option one, the red line, we look in the graph where the line is when x = 80.
For x= 80, y= 58
Now, the same for option 2:
For x = 80, y= 44.
58-44 = 14
Answer: The difference is 14.
find the average rate of change on the interval (SHOW ALL WORK)
First, evaluate the function at the ends of the interval:
[tex]\begin{gathered} g(x)=x^3-2x \\ g(-1)=(-1)^3-2(-1) \\ g(-1)=-1^{}+2 \\ g(-1)=1 \end{gathered}[/tex][tex]\begin{gathered} g(x)=x^3-2x \\ g(2)=2^3-2(2) \\ g(2)=8-4 \\ g(2)=4 \end{gathered}[/tex]Now, the average rate of change will be
[tex]\begin{gathered} \text{Average rate of change }=\frac{g(2)-g(-1)}{2-(-1)} \\ \text{Average rate of change }=\frac{4-1}{2-(-1)} \\ \text{Average rate of change }=\frac{3}{2+1} \\ \text{Average rate of change }=\frac{3}{3} \\ \text{Average rate of change }=1 \end{gathered}[/tex]In terms of trigonometry ratios for triangle BCE what is the length of line CE. Insert text on the triangle to show the length of line CE.When you are done using the formula for the triangle area Area equals 1/2 times base times height write an expression for the area of triangle ABC Base your answer on the work you did above
CE can be written as:
[tex]\frac{BE}{CE}=\frac{CE}{AE}[/tex]Solve for CE:
[tex]\begin{gathered} CE^2=BE\cdot AE \\ CE=\sqrt[]{BE\cdot AE} \end{gathered}[/tex]The area is:
[tex]\begin{gathered} A=\frac{b\cdot h}{2} \\ _{\text{ }}where\colon \\ _{\text{ }}b=AB \\ h=CE=\sqrt[]{BE\cdot AE} \\ so\colon \\ A=\frac{AB\cdot\sqrt[]{BE\cdot AE}}{2} \end{gathered}[/tex]Henry had a batting average of 0.341 last season (out of 1000 at-bats, he had 341 hits). Given that thisbatting average will stay the same this year, answer the following questions,What is the probabilitythat his first hit willoccur within his first 5at-bats? Answer choice. 0.654. 0.765. 0.821. 0.876
The probability of a successful batting is 0.341; we need to find the probability of at least 1 hit within the first 5 at-bats; thus,
[tex]P(Hit)=1-P(NoHit)[/tex]Therefore, we need to calculate the probability of not hitting the ball within the first 5 at-bats.
The binomial distribution states that
[tex]\begin{gathered} P(X=k)=(nBinomialk)p^k(1-p)^{n-k} \\ n\rightarrow\text{ total number of trials} \\ k\rightarrow\text{ number of successful trials} \\ p\rightarrow\text{ probability of a successful trial} \end{gathered}[/tex]Thus, in our case,
[tex]P(k=0)=(5Binomial0)(0.341)^0(0.659)^5=1*1*0.124287...[/tex]Then,
[tex]P(Hit)=1-0.124287...\approx0.876[/tex]Therefore, the answer is 0.876In July, Lee Realty sold 10 homes at the following prices: $140,000; $166,000; $80,000; $98,000; $185,000; $150,000; $108,000; $114,000; $142,000; and $250,000. Calculate the mean and median.
The mean is 143000 and Median is 141000 for data $140,000; $166,000; $80,000; $98,000; $185,000; $150,000; $108,000; $114,000; $142,000; and $250,000.
What is Statistics?A branch of mathematics dealing with the collection, analysis, interpretation, and presentation of masses of numerical data
The mean is give by sum of n numbers to the total number of observations
Mean=Sum of observations/ Number of observations
Given,
10 homes at the following prices: $140,000; $166,000; $80,000; $98,000; $185,000; $150,000; $108,000; $114,000; $142,000; and $250,000.
Sum of observations=$140,000+$166,000+$80,000+$98,000+ $185,000+$150,000+ $108,000+$114,000+$142,000+ $250,000=1433000
n=10
Mean=1433000/10=143000
So mean is 143000
Now let us find the median, Median is the middle most number.
First we have to arrange the observation in ascending order.
$80,000, $98,000, $108,000, $114,000, $140,000, $142,000, $150,000, $166,000, $185,000, $250,000
Now Median= ($140,000+$142,000)/2
=282000/2=141000
Hence Mean is 143000 and Median is 141000.
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Given the functions, f(x) = 6x+ 2 and g(x)=x-7, perform the indicated operation. When applicable, state the domain
restriction.
The domain restriction for (f/g)(x) is x=7
What are the functions in mathematics?a mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable.
What does a domain math example mean?The collection of all potential inputs for a function is its domain. For instance, the domain of f(x)=x2 and g(x)=1/x are all real integers with the exception of x=0.
Given,
f(x) = 6x+2
g(x) = x-7
So,
(f/g)(x) = 6x+2/x-7
Remember that the denominator can not be equal to zero
Find the domain restriction
x-7=0
x=7
Therefore, the domain is all real numbers except the number 7
(-∞,7)∪(7,∞)
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Which expression allows us to find the discount amount of ANY price thatis discounted 25%?*
the expression of the discount amount is
[tex]discountamount=x\times\frac{25}{100}[/tex]here x is the price
and the discount is 25%
Calculate the variance and the standard deviation for the following set of data: 7, 2, 5, 3, 3, 10
We need to know about variance and standard deviation to solve the problem. The variance of the set is 7.67 and the standard deviation is 2.77
Variance is a measure of dispersion which means it measures how far a set of numbers is spread out from the mean value. Standard deviation is the square root of variance. Inorder to calculate the variance we need to calculate the mean of the data set first.
mean=7+2+5+3+3+10/6=30/6=5
variance=[(7-5)^2+(2-5)^2+(5-5)^2+2(3-5)^2+(10-5)^2]/6=4+9+8+25/6=46/6=7.67
standard deviation =[tex]\sqrt{var}[/tex]=2.77
Therefore the variance of the data set is 7.67 and the standard deviation is 2.77
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A committee of six people is chosen from five senators and eleven representatives. How many committees are possiblethere are to be three senators and three representatives on the Committee
SOLUTION
This means we are to select 3 persons from 5 senators and 3 persons from 11 representatives. This can be done by
[tex]^5C_3\times^{11}C_3\text{ ways }[/tex]So we have
[tex]\begin{gathered} ^5C_3\times^{11}C_3\text{ ways } \\ 10\times165 \\ =1650\text{ ways } \end{gathered}[/tex]Hence the answer is 1650 ways
Renta scored 409 points in a video game. This was 223 more points than Sadia score (s). Which equation does not represent this situation? And why?
A) 223 = 409 - s
B) s = 409 - 223
C) s = 409 + 223
D) 223 + s = 409
Answer:C
Step-by-step explanation: S is equal to a number less than 409 and if you add 223 you go over 409
Why did I get this wrong I did 4/3 times 3.14 times 7 to the next power I did all what my teacher told me
Given the figure of a sphere
The radius = r = 7
We need to find the volume of the sphere
The volume =
[tex]\frac{4}{3}\cdot\pi\cdot r^3=\frac{4}{3}\cdot3.14\cdot7^3=1436.0267[/tex]Rounding the answer to the nearest hundredth
So, the volume = 1436.03
I need help with my homework pls be fast it’s 11pm for me and I couldn’t do this earlier because of family business
We have a linear function and we have to find the meaning of the slope.
The function is:
[tex]C=50h+35[/tex]In this function the slope is m=50, as it is the coefficient for h, the number of hours.
The slope usually represents the variation of the result variable (in this case, the cost in dollars) and the independent variable (in this case, h, the number of hours).
Then, we can think of the slope in this model as the marginal hourly rate he charges. This means that any additional hour of work will cost $50 more.
Then, from the options given, the correct one is: the charge per hour [Option D].
What is the radius of a hemispherewith a volume of 281,250 cm??
Given:
The volume of the hemisphere = 281,250
Find-:
Radius of hemisphere
Explanation-:
The volume of the hemisphere is:
[tex]V=\frac{2}{3}\pi r^3[/tex]Given volume is 281250
[tex]\begin{gathered} V=\frac{2}{3}\pi r^3 \\ \\ 281250=\frac{2}{3}\pi r^3 \\ \\ r^3=\frac{281250\times3}{2\times\pi} \\ \\ r^3=134286.9832 \\ \\ r=51.209 \end{gathered}[/tex]So, the radius is 51.209 cm
Every week a company provides fruit for its office employees. They canchoose from among five kinds of fruit. Which probabilities correctly completethis probability distribution for the 50 pieces of fruit, in the order listed?
Given:
Total number of pieces = 50
So, the probabilities are:
Apples
[tex]P(apples)=\frac{8}{50}=0.16[/tex]Bananas
[tex]P(bananas)=\frac{10}{50}=0.2[/tex]Lemons
[tex]P(lemons)=\frac{5}{50}=0.1[/tex]Oranges
[tex]P(oranges)=\frac{15}{50}=0.3[/tex]Pears
[tex]P(pears)=\frac{12}{50}=0.24[/tex]Answer: A.
Christi earns $21 per hour working as a receptionist. If she works 19 hours per week, what is her weekly wage? A) $250 B) $299 C) $350 D) $399
Since Christi earns $21 per hour, to find how much she earns by working 19 hours per week we need to multiply the hourly wage by the number of hours she works in a week:
[tex]21\times19=399[/tex]Her weekly wage is $399
Answer: D) $399
What did the student do incorrectly in this problem? Thanks for the help!
Solution
We have the function
[tex]f(x)=\frac{(5x-2)(x-1)}{(x-1)(x+2)}[/tex]The graph of the function is
Determine the real number x and y if (x-yj)(3+5j) is the conjugate of -6-24j
The values of the variables x and y such that the conjugate of - 6 - j 24 is found are 3 and 3, respectively.
How to find the value of two variables associated with the conjugate of a complex number
Let α + i β be a complex number, whose conjugate is the complex number α - i β. In this problem we find the values of the variables x and y such that:
(x + i y) · (3 + i 5) = - 6 + i 24
3 · x + i 3 · y + i 5 · x + i² 5 · y = - 6 + i 24
(3 · x - 5 · y) + i (5 · x + 3 · y) = - 6 + i 24
Then, we need to solve the following system of linear equations:
3 · x - 5 · y = - 6
5 · x + 3 · y = 24
Now we proceed to solve the system algebraically. Clear x in the first equation:
x = (- 6 + 5 · y) / 3
x = - 2 + (5 / 3) · y
Substitute x on the second equation and clear y:
5 · [- 2 + (5 / 3) · y] + 3 · y = 24
- 10 + (25 / 3) · y + 3 · y = 24
34 / 3 · y = 34
(1 / 3) · y = 1
y = 3
Finally, we substitute on y in the first equation:
x = - 2 + (5 / 3) · 3
x = - 2 + 5
x = 3
The values of the variables x and y are 3 and 3, respectively.
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ind the value of x. Round to the nearest tenth. The diagram is not drawn to scale.
ANSWER
x = 10.2
EXPLANATION
In this problem, we are given a right triangle: one of its non-right interior angles measures 22°. We know that the length of the hypotenuse is 11 units long and we have to find the length of the side adjacent to the given angle, x.
With the given information, we can use the cosine of the angle to find the missing value,
[tex]\cos\theta=\frac{adjacent\text{ }leg}{hypotenuse}[/tex]In this problem,
[tex]\cos22\degree=\frac{x}{11}[/tex]Solving for x,
[tex]x=11\cdot\cos22\degree\approx10.2[/tex]Hence, the value of x is 10.2, rounded to the nearest tenth.
how much would EZ Excavation charge to haul 40 cubic yards of dirt
Given the line on the graph, we have that it passes through the points (1,25) and (2,50), then we can find the relation function with the slope-point equation of the line:
[tex]\begin{gathered} \text{slope:} \\ m=\frac{y_2-y_1}{x_2-x_1} \\ \Rightarrow m=\frac{50-25}{2-1}=\frac{25}{1}=25 \\ y-y_1=m(x-x_1) \\ \Rightarrow y-25=25(x-1) \\ \Rightarrow y=25x-25+25=25x \\ y=25x \end{gathered}[/tex]we have that the cost of the dirt is given by the equation y=25. To find how much would it be for 40 cubic yards of dirt, we make x=40 and we get the following:
[tex]\begin{gathered} x=40 \\ \Rightarrow y=25\cdot40=1000 \\ y=1000 \end{gathered}[/tex]therefore, the cost to haul 40 cubic yards of dirt is $1000
What is the measure of m?n20m5m = [?]✓=Give your answer in simplest form.Enter
STEP - BY - STEP EXPLANATION
What to find?
The value of m.
To find the value of m, we take the proportion of the sides of the triangles.
That is;
adjacent of the bigger triangle/hypotenuse of the bigger triangle = adjacent of the smaller triangle / hypotenuse of the smaller triangle.
That is;
[tex]\frac{m}{20+5}=\frac{5}{m}[/tex][tex]\frac{m}{25}=\frac{5}{m}[/tex]Cross-multiply
[tex]m^2=25\times5[/tex]Take the square root of both-side of the equation.
[tex]m=\sqrt[]{25\times5}[/tex][tex]m=5\sqrt[]{5}[/tex]The point (4, 16) is on the graph of f(x) = 2^x. Determine the coordinates of this point under the following transformations.
f(x) = 2^4x: ____________
The coordinate of the image after the transformation is (4, 65536)
How to determine the coordinate of the image?From the question, the coordinate of the point is given as
(4, 16)
From the question, the equation of the function is given as
f(x) = 2^x
When the function is transformed. we have the equation of the transformed function to be given as
f(x) = 2^4x65536
So, we substitute 4 for in the equation f(x) = 2^4x
So, we have
f(4) = 2^(4 x 4)
Evaluate the products
f(4) = 2^16
Evaluate the exponent
f(4) = 65536
So, we have (4, 65536)
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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.
b. Function h will begin to exceed f and g around x = [. (Round up to the nearest whole number.)
If we evaluate x = 10 on all the functions, we have:
[tex]\begin{gathered} h(10)=1.31^{10}=14.88 \\ f(10)=1.25(10)=12.5 \\ g(10)=0.1562(10)^2=15.625 \end{gathered}[/tex]and then, evaluating x = 11, we get:
[tex]\begin{gathered} h(11)=1.13^{11}=19.49 \\ f(11)=1.25(11)=13.75 \\ g(11)=0.15625(11)^2=18.9 \end{gathered}[/tex]notice that on x = 10, h(x) does not exceed g(x), but on x = 11, h(x) exceeds the other functions. Therefore, h will begin exceed f and g around 11
Drag each tile to the correct box. Not all tiles will be used. Arrange the steps to solve the equation x + 3 − 2 x − 1 = - 2 . Simplify to obtain the final radical term on one side of the equation. Raise both sides of the equation to the power of 2. Apply the Zero Product Rule. Use the quadratic formula to find the values of x. Simplify to get a quadratic equation. Raise both sides of the equation to the power of 2 again.
The value of x = 16 + 4[tex]\sqrt{15}[/tex]
Given,
To solve the equations :
[tex]\sqrt{x+3} - \sqrt{x -1}[/tex] = -2
Solve by the given steps :
Now, According to the question:
Step 1: Simplify to obtain the radical form on one side of the equation:
[tex]\sqrt{x+3} - \sqrt{x -1}[/tex] = -2
Step 2: Raise both sides of the equation to the power of 2
[tex](\sqrt{x+3} - \sqrt{x -1})^2 = (-2)^2[/tex]
x + 3 + 2x - 1 -2 [tex]\sqrt{(x+3)(2x -1)}[/tex] = 4
3x - 2 = 2 [tex]\sqrt{(x+3)(2x -1)}[/tex]
[tex](3x - 2)^2 = [2\sqrt{(x+3)(2x -1)}]^2[/tex]
9[tex]x^{2}[/tex] - 12x + 4 = 4 (2[tex]x^{2}[/tex] + 5x -3)
Step 3: Apply the zero product rule, Simplify to get a quadratic equation :
[tex]x^{2}[/tex] - 32x +16 = 0
Step 4: Use the quadratic formula to find the values of x :
[tex]x^{2}[/tex] - 32x + 16 =0
x = 16 + 4[tex]\sqrt{15}[/tex] and x = 16 - 4[tex]\sqrt{15}[/tex]
x = 16 - 4[tex]\sqrt{15}[/tex] (It is rejected)
So, the value of x = 16 + 4[tex]\sqrt{15}[/tex]
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Answer: Raise both sides of the equation to the power of 2
simplify to obtain the final radical term on one side of the equation
raise both sides of the equation to the power of 2 again
simplify to get a quadratic equation
use the quadratic formula to find the xvalues
Step-by-step explanation:
Acetaminophen and liver damage. It is believed that large doses of acetaminophen
(the active ingredient in over the counter pain relievers like Tylenol) may cause damage to the
liver. A researcher wants to conduct a study to estimate the proportion of acetaminophen users
who have liver damage. For participating in this study, he will pay each subject $20 and provide
a free medical consultation if the patient has liver damage.
(a) If he wants to limit the margin of error of his 98% confidence interval to 2%, what is the
minimum amount of money he needs to set aside to pay his subjects?
(b) The amount you calculated in part (a) is substantially over his budget so he decides to use
fewer subjects. How will this affect the width of his confidence interval?
Using proportions we can conclude that the researcher should recruit a minimum of 1509 subjects.
What is proportion?A proportion is an equation that sets two ratios at the same value. For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls).So, a study is being planned to determine the percentage of acetaminophen users who suffer liver injury.
With,
Level of confidence: 98%E=0.03 is the error margin.Then,
The z-value for 98% confidence is known Zₙ = 2.33.Calculation of the sample size: n = p(1 - p)(Zₙ/E)²In order to obtain the most cautious estimate, we should pick p = 0.5 because the researcher has no preconceived notions about what the sample proportion should be:
n = 0.5(1-0.5)(2.33/0.03)²1508.0277778 = 1509Therefore, using proportions we can conclude that the researcher should recruit a minimum of 1509 subjects.
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The correct question is given below:
It is believed that large doses of acetaminophen (the active ingredient in over the counter pain relievers like Tylenol) may cause damage to the liver. A researcher wants to conduct a study to estimate the proportion of acetaminophen users who have liver damage. If she wants to limit the margin of error of her 98% confidence interval to be no more than 3%, what is the minimum number of subjects that she needs to recruit? [Note: The researcher has no expectations about what the sample proportion should be ahead of time, so she – and you – should use p = 0.5 to get the most conservative estimate.]
The one-to-one functions 9 and h are defined as follows.g={(0, 5), (2, 4), (4, 6), (5, 9), (9, 0)}h(x)X +811
Step 1: Write out the functions
g(x) = { (0.5), (2, 4), (4,6), (5,9), (9,0) }
[tex]h(x)\text{ = }\frac{x\text{ + 8}}{11}[/tex]Step 2:
For the function g(x),
The inputs variables are: 0 , 2, 4, 5, 9
The outputs variables are: 5, 4, 6, 9, 0
The inverse of an output is its input value.
Therefore,
[tex]g^{-1}(9)\text{ = 5}[/tex]Step 3: find the inverse of h(x)
To find the inverse of h(x), let y = h(x)
[tex]\begin{gathered} h(x)\text{ = }\frac{x\text{ + 8}}{11} \\ y\text{ = }\frac{x\text{ + 8}}{11} \\ \text{Cross multiply} \\ 11y\text{ = x + 8} \\ \text{Make x subject of formula} \\ 11y\text{ - 8 = x} \\ \text{Therefore, h}^{-1}(x)\text{ = 11x - 8} \\ h^{-1}(x)\text{ = 11x - 8} \end{gathered}[/tex]Step 4:
[tex]Find(h.h^{-1})(1)[/tex][tex]\begin{gathered} h(x)\text{ = }\frac{x\text{ + 8}}{11} \\ h^{-1}(x)\text{ = 11x - 8} \\ \text{Next, substitute h(x) inverse into h(x).} \\ \text{Therefore} \\ (h.h^{-1})\text{ = }\frac{11x\text{ - 8 + 8}}{11} \\ h.h^{-1}(x)\text{ = x} \\ h.h^{-1}(1)\text{ = 1} \end{gathered}[/tex]Step 5: Final answer
[tex]\begin{gathered} g^{-1}(9)\text{ = 5} \\ h^{-1}(x)\text{ = 11x - 8} \\ h\lbrack h^{-1}(x)\rbrack\text{ = 1} \end{gathered}[/tex]1+——>1/12 write. Fraction to make each number sentence true, answer I got is 1/1
c) Set x to be the number we need to find; therefore, the inequality to be solved is
[tex]\begin{gathered} 1+x>1\frac{1}{2}=1+\frac{1}{2}=\frac{3}{2} \\ \Rightarrow1+x>\frac{3}{2} \\ \Rightarrow-1+1+x>-1+\frac{3}{2} \\ \Rightarrow x>\frac{1}{2} \end{gathered}[/tex]Therefore, any number greater than 1/2 (greater, not equal to) satisfies the inequality; particularly 1/1=1>1/2. Thus, 1/1 is a possible answer
Hello! I think the answer is 398. Would you mind guiding me?
Given -
Total Personal Videos Players = 400
Video Players with no defects = 398
Number of Video Players sent = 2000
To Find -
The number of Video Players with no defects =?
Step-by-Step Explanation -
Total Personal Videos Players = 400
Video Players with no defects = 398
So,
Two video players in every 400 are defected
So,
2000 = 5 × 400
So,
Total number of Video Players with defects = 5 × 2 = 10
Hence,
The number of Video Players with no defects = 2000 - 10 = 1990
Final Answer -
The number of Video Players with no defects = 1990
Madeline is a salesperson who sells computers at an electronics store. She makes a base pay of $80 each day and then is paid a $20 commission for every computer sale she makes. Make a table of values and then write an equation for P, in terms of x, representing Madeline's total pay on a day on which she sells x computers.
I need the equation.
Answer:
I don’t know if I can send it answer
Step-by-step explanation: