According to the given data we have the following function:
f(x)=3x-6
To determine f(8) we would have to plug in into the equation the 8 and then proceed to calculate it, so:
If f(x)=3x-6
Then, f(8)=3(8)-6
f(8)=24-6
f(8)=18
12. A teacher weighed 148 lbs. in 1999 and weighs 190 lbs. In 2020. What was the rate ofchange in weight?
Given,
The weight of the teacher in 1999 is 148 lbs.
The weight of the teacher in 2020 is 190 lbs.
The rate of change in weight is,
[tex]\begin{gathered} \text{Rate of change=}\frac{190-148}{2020-1999} \\ =\frac{42}{21} \\ =2 \end{gathered}[/tex]The teacher gained 2 pounds per year.
Hence, option A is correct.
Find the equation of the line passing through the points (-11,-18) and (-22,-16). Write your answer in the
form y = mx + b.
Answer: y =
Write your answers as integers or as reduced fractions in the form A/B.
Answer:
y=−2/11x−20
Step-by-step explanation:
15% of $764.69rounded to the nearest cent.
Percentage is expressed in terms of 100. To find 15% of 764.69, we would multiply ratio of 15% to 100% by 764.69. Thus, we have
15/100 * 764.69
= 114.7035
I got the picture and will send it to you show the coordinates of the points that create the shape of the image
We have the following:
[tex]\begin{gathered} P(1-1,-3+3)\rightarrow P^{\prime}(0,0) \\ Q(3-1,-1+3)\rightarrow Q^{\prime}(2,2) \\ R(4-1,-3+3)\rightarrow R^{\prime}(3,0) \end{gathered}[/tex]now,
The answer is:
(8-4) mulitiply (3-2)=
Write an equation for the graph below in point-slope form and then solve rewrite in slope-intercept form.
We are given the graph of a line and we are asked to determine its equation in point-slope form.
The general form in slope point form of a line is:
[tex]y-y_0=m(x-x_0)[/tex]Where:
[tex]\begin{gathered} m=\text{ slope} \\ (x_0,y_0)\text{ is apoint in the line} \end{gathered}[/tex]to determine the slope we will use the following formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where:
[tex](x_1,y_1);(x_2,y_2)=\text{ points on the line}[/tex]We will choose two points on the line from the graph:
[tex]\begin{gathered} (x_1,y_1)=(0,1) \\ (x_2,y_2)=(2,2) \end{gathered}[/tex]Now, we plug in the values in the formula for the slope:
[tex]m=\frac{2-1}{2-0}=\frac{1}{2}[/tex]Now, we substitute the value of the slope in the equation of the line:
[tex]y-y_0=\frac{1}{2}(x-x_0)[/tex]Now, we plug in the first point we choose for the line:
[tex]\begin{gathered} y-1=\frac{1}{2}(x-0) \\ \\ y-1=\frac{1}{2}x \end{gathered}[/tex]And thus we have determined the equation of the line in point-slope form.
The slope-intercept form is the following:
[tex]y=mx+b[/tex]To convert this equation to slope-intercept form, we will take the previous equations and we will add 1 to both sides:
[tex]y=\frac{1}{2}x+1[/tex]And thus we have determined the slope-intercept form of the equations of the line.
Evaluate the expression (4x^3y^-2)(3x^-2y^4) for x = –2 and y = –1.
Answer:
3x−2y)(4x+3y)
It can be written as =3x(4x+3y)−2y(4x+3y)
By further calculation =12x
2
+9xy−8xy−6y
2
So we get =12x
2
+xy−6y
2
question 5 only. determine the missing side length QP. the triangles are not drawn to scale.
This is a simple question.
First, we can see both triangles are proportional, it means it has the same relation between its sides even if one is in a large scale and the other on a a small scale.
Now we can identify which side corresponds to which side. Once side AC is the longest one for triangle ABC it means its equivalent for triangle PQR is the side RP, so the equivalent for side AB is side QP. Once we know that we can write the following relation and calculate:
look at the screenshots
Answer:
c for the first one and a for the second
Solve the problem. Use 3.14 as the approximate value of pie
The volume of a cylinder is calculated using the formula:
[tex]V=\pi r^2h[/tex]where r is the radius of the cylinder and h is the height.
From the question, we have the following parameters:
[tex]\begin{gathered} diameter=4.8 \\ \therefore \\ r=\frac{4.8}{2}=2.4 \\ and \\ h=6.66 \end{gathered}[/tex]Therefore, we c n calculae tehe volume of a cylinder to be:
[tex]\begin{gathered} V=3.14\times2.4^2\times6.66 \\ V=120.455424 \end{gathered}[/tex]For four cylinders, the combined volume will be:
[tex]\begin{gathered} V=120.455424\times4 \\ V=481.821696 \end{gathered}[/tex]The volume i 481 .82 cubic inches.
A friend plans to purchase a 72-inch tv at a particular store for a cost of $1500. The store is offering 25% off any one item. He also has an internet coupon for an additional 10% off any discounted price. How much will your friend save (a) in dollar amount and (b) in percent?
the The Solution.
The marked price of the 72-inch TV = $1500
25% discount makes the actual discount to be:
[tex]\begin{gathered} \text{Actual Discount = 25 \% of 1500} \\ \text{ = }\frac{25}{100}\times1500=\text{ \$375} \end{gathered}[/tex]So, the discounted price will now be
Discounted price = 1500 - 375 = $1125
He has an additional 10% internet coupon discount on already dicounted price ($1125) .
[tex]\begin{gathered} \text{Additional discount = 10\% of 1125} \\ \text{ =}\frac{10}{100}\times1125=\text{ \$112.50} \end{gathered}[/tex]a. The friend will save
[tex]\begin{gathered} 375+112.50 \\ =\text{ \$487.50} \end{gathered}[/tex]b. in percentage, he saved
[tex]\frac{487.5}{1500}\times100=32.5\text{ \%}[/tex]Therefore, the correct answers are:
a. $487.50
b. 32.5%
a. Create a perfect square trinomial.
b. Factor the perfect square trinomial you created in 1a.
a. Create a difference of two squares.
b. Factor the difference of two squares you created in 2a.
a. Describe at least one similarity between the perfect square trinomial and the difference of squares. You can use either the form you wrote in 1a and 2a, or you can use their factored form from 1b and 2b. Write your answer using complete sentences.
b. Describe at least one difference between the perfect square trinomial and the difference of squares. You can use either the form you wrote in 1a and 2a, or you can use their factored form from 1b and 2b. Write your answer using complete sentences.
A factored perfect square might look like (x+a)(x+a) or (x-a)(x-a) [or (ax+b)(ax+b) but keep it simple]. Then, distribute.
A factored difference of two squares might look like (x+a)(x-a). Then, distribute.
(pick a number for a)
1.
a. One example of a perfect square trinomial is: x² + 6x + 9.
b. The factored trinomial above is: (x + 3)².
2.
a. One example of a difference of two squares is: x² - 4.
b. The factored difference of squares above is: (x - 2)(x + 2).
3.
a. The similarity is that the first term is positive for both cases.
b. The difference is that the final term is positive for perfect square trinomials and negative for the difference of squares.
Perfect square trinomialsThere are two examples of perfect square trinomials, the square of the sum and the square of the subtraction, as follows:
Square of the sum: (a + b)² = a² + 2ab + b².Square of the subtraction: (a - b)² = a² - 2ab + b².The left side is the factored form and the right side is the expanded form.
Hence one example of a perfect square trinomial is given as follows:
(x + 3)² = x² + 6x + 9.
Difference of two squaresA difference of two squares is factored as follows:
x² - y² = (x + 2)(x - 2)
Hence one possible example is:
x² - 4 = (x + 2)(x - 2).
Compared to the perfect square trinomial, we have that:
The similarity is that the first term in any of the two polynomials will always be positive.The difference is in the last term, for the perfect square it will always be positive (+ b²) and for the difference of two squares it will always be negative (- b²).More can be learned about perfect square trinomials at https://brainly.com/question/14584348
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algebra 2 question..
We are supposed to solve the equation
[tex]6(2x-1)-12=3(7x+4)[/tex]Here, we need to apply the distributive laws on both sides.
Comment: The distributive laws say that
[tex]a(b+c)=ab+ac\text{ and }(b+c)a=ba+ca[/tex]Using this comment we get
[tex]6(2x-1)=6(2x)+6(-1)=12x-6[/tex][tex]3(7x+4)=3(7x)+3(4)=21x+12[/tex]Then, our equation becomes
[tex](12x-6)-12=21x+12[/tex][tex]12x-18=21x+12[/tex]Now, let's apply the rule: terms with x on the right-hand side, and the rest on the left-hand side, to obtain
[tex]-18-12=21x-12x[/tex][tex]-30=9x[/tex][tex]x=\frac{-30}{9}=-\frac{10}{3}[/tex][tex]8.25 \div 6[/tex]8.25 divid by 6
We want to calculate the following number
[tex]\frac{8.25}{6}[/tex]To make the calcul.ation easier, we will transform the number 8.25 into a fraction. Recall that
[tex]8.25=\frac{825}{100}[/tex]So, so far, we have
[tex]\frac{8.25}{6}=\frac{\frac{825}{100}}{6}[/tex]Also, recall that
[tex]6=\frac{6}{1}[/tex]So, we have
[tex]\frac{\frac{825}{100}}{6}=\frac{\frac{825}{100}}{\frac{6}{1}}[/tex]Now, recall that when we divide fractions, we have
[tex]\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a\cdot d}{b\cdot c}[/tex]In this case, we have a=825,b=100,c=6,d=1.
So we have
[tex]undefined[/tex]NO LINKS!! Please help me with this probability question 2a
====================================================
Work Shown:
A = he eats pizza
B = he drinks cola
P(A) = 0.40
P(B) = 0.60
P(A and B) = 0.30
Then apply the conditional probability formula.
P(A given B) = P(A and B)/P(B)
P(A given B) = 0.30/0.60
P(A given B) = 0.5 exactly
P(A given B) = 50%
If we know for certain he drinks cola, then there's a 50% chance of him eating pizza.
Can you Help me with this i cannot do ir
To translate f(x) 4 units down we subtract 4 from f(x):
[tex]f(x)-4.[/tex]Now, to reflect f(x)-4 over the x-axis we multiply by -1:
[tex]-1(f(x)-4)=-f(x)+4.[/tex]Answer:
[tex]g(x)=-\sqrt[3]{x-2}+4.[/tex]Two functions are shown. f(x) = 29(0.5)* g(x) = 18x + 14 What is the value of f(2) + g(4)?
Answer:
93.25
Explanation:
Given the below functions;
[tex]\begin{gathered} f(x)=29(0.5)^x \\ g(x)=18x+14 \end{gathered}[/tex]To be able to find the value of f(2) + g(4), we have to 1st determine the value of f(2) and f(4) as shown below;
[tex]\begin{gathered} f(2)=29(0.5)^2=29\ast0.25=7.25 \\ g(4)=18(4)+14=72+14=86 \end{gathered}[/tex]Let's go ahead and find the value of f(2) + g(4);
[tex]f(2)+g(4)=7.25+86=93.25[/tex]What is the product of 11/12 and its reciprocal?
Answer:
The product of 11/12 is 0.916.This as as a fraction would be 0.916/1.00. This means it's reciprocal is 1.
Step-by-step explanation:
The reciprocal is basically the bottom part, denominator, of the fraction, being siwtched to on top of the fraction (numerator, and vice versa. The fraction would be 0.916/ 1.00 because the closest whole number to 0.916 is 1, meaning the fraction would be 0.916 out of 1. DO NOT MISTAKE THIS FOR 100. When you do the final step, finding the recirprocal of 0.916/1.00, we siwtch the numerator and denominators position, making out answer:
The product of 11/12 is 0.916 which is 0.916/1.00 in fraction form. The reciprocal of this is 1.00/0.916. Hope this helped!
Use the remainder theorem to find P (1) for P(x) = 2x - 3x' + 3x -3.Specifically, give the quotient and the remainder for the associated division and the value of P (1).미미2Quotient = 0Х$2Remainder =0P(1) =
Using the remainder theorem, we must find P(1) for:
[tex]P(x)=2x^4-3x^3+3x-3[/tex]1) Because we want to evaluate P(x) for x = 1, we must compute
[tex]\frac{2x^4-3x^3+3x-3}{x-1}[/tex]2) Now we make the synthetic division by putting a 1 in the division box:
The remainder from the division is:
[tex]R=-1[/tex]The quotient of the division is:
[tex]2x^3-x^2+2x+2[/tex]3) From the synthetic division we get a remainder R = -1, applying the Remainder Theorem we get that:
[tex]P(1)=R=-1[/tex]Summary
The answers are:
1)
[tex]Quotient=2x^3-x^2+2x+2[/tex]2)
[tex]Remainder=-1[/tex]3)
[tex]P(1)=-1[/tex]How to draw the graphs of the following non-linear functions?y=x^2 + 1y=3^x + 1
The first step is to substitute values of x into each equation.
For y = x^2 + 1,
if x = - 2, y = (- 2)^2 + 1 = 4 + 1 = 5
if x = - 1, y = (- 1)^2 + 1 = 1 + 1 = 2
if x = 0, y = (0)^2 + 1 = 0 + 1 = 1
if x = 1, y = (1)^2 + 1 = 1 + 1 = 2
if x = 2, y = (2)^2 + 1 = 4 + 1 = 5
We would plot the corresponding values of x and y on the graph as shown below
For y = 3^(x + 1),
if x = - 2, y = 3^(-2 + 1) = 3^-1 = 0.33
if x = - 1, y = 3^(-1 + 1) = 3^0 = 1
if x = 0, y = 3^(0 + 1) = 3^1 = 3
if x = 1, y = 3^(1 + 1) = 3^2 = 9
if x = 2, y = 3^(2 + 1) = 3^3 = 27
We would plot the corresponding values of x and y on the graph as shown below
n a recent poll, a random sample of adults in some country (18 years and older) was asked, "When you see an ad emphasizing that a product is "Made in our country," are you more likely to buy it, less likely to buy it, or neither more nor less likely to buy it?" The results of the survey, by age group, are presented in the following contingency table. Complete parts (a) through (c).
Purchase likelihood
Total
Total
Question content area bottom
Part 1
(a) What is the probability that a randomly selected individual is years of age, given the individual is to buy a product emphasized as "Made in our country"?
The probability is approximately
0.134.
(Round to three decimal places as needed.)
Part 2
(b) What is the probability that a randomly selected individual is to buy a product emphasized as "Made in our country," given the individual is years of age?
The probability is approximately
a) The probability that a randomly selected individual is 45-54 years of age, given the individual is neither more nor less likely to buy is 0.206
b) The probability that a randomly selected individual is neither more nor less likely to buy, given the individual is 45-54 years of age is 0.309
c) 18-34 year olds are less likely to buy a product emphasized as "Made in our country" than individuals in general.
Hence, the answer is no.
A random sample is one that is drawn at random from the population, meaning that every member of the population has an equal chance of being picked for the sample. The probability sampling approach is the practice of choosing people at random.
a. Total number of individuals that are neither more nor less likely to purchase = 786
Total number of individuals aged 45-54 that are neither more nor less likely to purchase = 162
The probability that a randomly selected individual is 45-54 years of age, given the individual is neither more nor less likely to buy =
= Total number of individuals aged 45-54 neither more or less likely to purchase./ Total number of individuals more or less likely to purchase.
= 162/786
= 0.206
b. Total number of individuals 45-54 years of age = 524
Total number of individuals aged 45-54 that are neither more nor less likely to purchase = 162
The probability that a randomly selected individual is neither more nor less likely to buy, given the individual is 45-54 years of age
= Total number of individuals aged 45-54 neither more or less likely to purchase./ Total number of individuals 45-54 years of age.
= 162/524
= 0.309
c. The number of 18-34 year old individuals more likely to buy = 204
The total number of 18-34 year old individuals = 523
The proportion of 18-34 year old individuals more likely to buy = 204/523
= 0.390
= 39%
The total number of individuals more likely to buy = 1266
The total number of all individuals in the survey = 2123
The proportion of individuals, in general, more likely to buy = 1266/2123
= 0.596
= 59.6%
Therefore, 18-34 year olds are less likely to buy a product emphasized as "Made in our country" than individuals in general.
Hence, the answer is no.
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Your question is incomplete. Please find the missing content below.
In a recent poll, a random sample of adults in some country (18 years and older) was asked, "When you see an ad emphasizing that a product is "Made in our country," are you more likely to buy it, less likely to buy it, or neither more nor less likely to buy it?" The results of the survey, by age group, are presented in the following contingency table. Complete parts (a) through (c).
Purchase likelihood 18-34 35-44 45-54 55 and over Total
More likely 204 318 334 410 1266
Less likely 27 5 28 11 71
Neither more nor less 292 210 162 122 786
Total 523 533 524 543 2123
a) What is the probability that a randomly selected individual is 45-54 years of age, given the individual is neither more nor less likely to buy a product emphasized as "Made in our country"? The probability is approximately _____. (round to three decimal places)
b) What is the probability that a randomly selected individual is neither more nor less likely to buy a product emphasized as "Made in our country", given the individual is 45-54 years of age? The probability is approximately _____. (round to three decimal places)
c) Are 18-34-year-olds more likely to buy a product emphasized as "Made in our country" than individuals in general? Yes or no
A sector of a circle has a central angle of 60∘ . Find the area of the sector if the radius of the circle is 9 cm.
Step-by-step explanation:
area of a sector is theta ÷360 ×πr²
The cost C (in dollars) of producing x units of a product is given by the following. C= 2.6. Square root of x + 600
The marginal cost in dollars of producing x units is given by the next equation:
[tex]C=2.6\sqrt[]{x}+600[/tex]a)
To find the marginal cost (in dollars per unit) when x= 9.
Then, we need to replace x=9 on the derivation of the cost equation:
So:
[tex]\frac{d}{dx}C=\frac{1.3}{\sqrt[]{x}}[/tex]Where:
[tex]\frac{d}{dx}2.6\sqrt[]{x}=2.6\frac{d}{dx}\sqrt[]{x}=2.6\frac{d}{dx}^{}x^{\frac{1}{2}}=2.6\cdot\frac{1}{2}x^{\frac{1}{2}-1}=1.3\cdot x^{-\frac{1}{2}}=\frac{1.3}{\sqrt[]{3}}[/tex]and, the derivate of a constant is equal to zero.
[tex]\frac{d}{dx}600=0[/tex]Replacing x= 9
[tex]\frac{d}{dx}C=\frac{1.3}{\sqrt[]{9}}[/tex]Hence, the marginal cost is equal to:
[tex]\frac{d}{dx}C=0.43[/tex]b) Now, when the production increases 9 to 10. It's the same as the cost of producing one more machine beyond 9.
Then, it would be x=10 on the cost equation:
[tex]C=2.6\sqrt[]{x}+600[/tex][tex]C=2.6\sqrt[]{10}+600[/tex][tex]C=608.22[/tex]and x= 9
[tex]C=2.6\sqrt[]{9}+600[/tex][tex]C=2.6(3)+600[/tex][tex]C=607.8[/tex]Then, we calculate C(10) - C(9) =
[tex]608.22-607.8[/tex][tex]=0.43[/tex]C)
Both results are equal.
Hence, the marginal cost when x=9 is equal to the additional cost when the production increases from 9 to 10.
There are 6 dogs and 2 mice. Write a ratio for the number of ears to th number of paws. * 6:2 3 people are in a room. Write a ratio to represent the number of finger
each dog has 4 paws, then 6 dogs have 6*4 = 24 paws
each mouse has 4 paws, then 2 mice have 2*4 = 8 paws
Total number of paws: 24 + 8 = 32 paws
each dog has 2 ears, then 6 dogs have 6*2 = 12 ears
each mouse has 2 ears, then 2 mice have 2*2 = 4 ears
total number of ears: 12 + 4 = 16 ears
The ratio for the number of ears to the number of paws: 16/32 = 1/2 or 1:2
I need help me answering #10 I'm really bad with ratios. (also sorry for the bad lighting in the picture)
The ratio of Perch to total fish is:
3 ( Number of perch that he caught)
------------------------------------------------------
9 ( The result of the addition of all values)
Simplifying, we have:
1
---
3
So, the answer would be 1 : 3
55mL of hardener to each container of resin. How much hardener should be added to 14 containers of resin?Write your answer in liters.
The amount of hardener added to 1 container of resin = 55mL.
The amount of hardener added to 14 containers is calculated as,
[tex]\begin{gathered} \text{Amount of hardener = 55 }\times\text{ 14 } \\ \text{Amount of hardener = 770 mL} \\ \text{Amount of hardener = 0.770 L} \end{gathered}[/tex]Thus 0.770 litres of hardener must be added to 14 containers of resin.
identify the slope: 6x - 2y = -6
The slope = 3
Explanations:Note that:
The slope - Intercept form of the equation of a line takes the form y = mx + c
where m is the slope and
c is the intercept
The given equation is:
6x - 2y = -6
The equation can be re-written as:
2y = 6x + 6
2y / 2 = 6x/2 + 6/2
y = 3x + 3
The slope, m = 3
The intercept, c = 3
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided
From the given picture we can see
ACB is a right triangle at C
AC = b
CB = a
AB = c
Since mSince a = 5 ft
Then to find b and c we will use the trigonometry ratios
[tex]\begin{gathered} \sin A=\frac{a}{c} \\ \sin 60=\frac{5}{c} \end{gathered}[/tex]Substitute the value of sin 60
[tex]\begin{gathered} \sin 60=\frac{\sqrt[]{3}}{2} \\ \frac{\sqrt[]{3}}{2}=\frac{5}{c} \end{gathered}[/tex]By using the cross multiplication
[tex]\begin{gathered} \sqrt[]{3}\times c=2\times5 \\ \sqrt[]{3}c=10 \end{gathered}[/tex]Divide both sides by root 3
[tex]\begin{gathered} \frac{\sqrt[]{3}c}{\sqrt[]{3}}=\frac{10}{\sqrt[]{3}} \\ c=\frac{10}{\sqrt[]{3}} \end{gathered}[/tex]To find b we will use the tan ratio
[tex]\begin{gathered} \tan 60=\frac{a}{b} \\ \tan 60=\frac{5}{b} \end{gathered}[/tex]Substitute the value of tan 60
[tex]\begin{gathered} \tan 60=\sqrt[]{3} \\ \sqrt[]{3}=\frac{5}{b} \end{gathered}[/tex]Switch b and root 3
[tex]b=\frac{5}{\sqrt[]{3}}[/tex]The exact values of b and c are
[tex]\begin{gathered} b=\frac{5}{\sqrt[]{3}} \\ c=\frac{10}{\sqrt[]{3}} \end{gathered}[/tex]Tristan tried his luck with the lottery. He can win $85 if he can correctly choose the 3 numbers drawn. If order matters and there are 13 numbers in the drawing, how many different ways could the winning numbers be drawn?
The ways to select the winning numbers is 286
How to determine the ways the winning numbers could be drawn?From the question, we have
Total numbers, n = 13Numbers to select, r = 3The winning numbers could be drawn is calculated using the following combination formula
Total = ⁿCᵣ
Where
n = 13 and r = 3
Substitute the known values in the above equation
Total = ¹³C₃
Apply the combination formula
ⁿCᵣ = n!/(n - r)!r!
So, we have
Total = 13!/10!3!
Evaluate
Total = 286
Hence, the number of ways is 286
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what is 5/6 converted to decimal form
5/6 in decimal form is
[tex]\frac{5}{6}=0.8\bar{3}[/tex]