Write an equation for the function that includes the points ( 1, 4/5) and ( 2, 2/3).
Answers
Answer:
f(x) = -2/15x + 14/15
Step-by-step explanation:
Slope = (2/3 - 4/5)/(2 - 1)
= (10/15 - 12/15) = -2/15
Plug in a known point (into y=mx+b) to find y-intercept:
4/5 = -2/15(1) + b
12/15 = -2/15 + b
b = 14/15
Formulate:
f(x) = -2/15x + 14/15
Related Questions
i need help. please
Answers
Answer:
what are we supposed to do
Step-by-step explanation:
im confused
Pls helpppppppppppppppppppppp
Answers
Answer:
0.875
Step-by-step explanation:
7/8 in decimal form is 0.875.
Are the graphs of the lines in the pair parallel? Explain.y=−32x+2
3x+2y=8
Answers
Answer:
no
Step-by-step explanation:
if to re-write the second equation:
y= -3/2 x+8
and to compare it with the first one, then -3/2≠-32.
It means, the given lines are not parallel.
The advertisement above shows the terms of a certificate of deposit (CD) at a local bank.
Suppose Robert invests $1,200 in the CD for a period of 3 years. How much interest will he earn? How much will Robert have after 3 years?
Answers
Answer:
1. The interest is $ 117.
2. The amount is $ 1,317.
Step-by-step explanation:
The following data were obtained from the question:
Principal (P) = $ 1,200
Rate (R) = 3.25%
Time (T) = 3 years
Interest (I) =..?
Amount (A) =...?
1. Determination of the interest.
Principal (P) = $ 1,200
Rate (R) = 3.25%
Time (T) = 3 years
Interest (I) =..?
I = P × R × T / 100
I = 1200 × 3.25 × 3 / 100
I = $ 117
Therefore, the interest is = $ 117
2. Determination of the amount.
This can be obtained as follow:
Interest (I) = $ 117
Principal (P) = $ 1,200
Amount (A) =?
Amount (A) = principal (P) + interest (I)
A = P + I
A = 1200 + 117
A = $ 1,317
Therefore, the amount at the end of 3 years is $ 1,317
The ______ sum of squares measures the variability of the observed values around their respective
treatment means
error
Answers
The variability of a observed values all around respective treatment means is measured by the "error" sum of squares.
Explain the term error sum of squares?SSE, also referred to as residual sum of squares, stands for sum of squares error. It is the discrepancy between the actual value and the value projected.
The product of a score's deviation from the mean and this same difference. The amount of variance in the dependent variable which can be affected by the independent is reflected with in denominator of a F ratio in a variance analysis. Additionally known as residual sum of squares and sum of squared errors (SSE).Thus, the variance of the observed values surrounding the means of the corresponding treatments is measured by the "error" sum of squares.
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The correct question is-
The ______ sum of squares measures the variability of the observed values around their respective treatment means.
Connecticut families were asked how much they spent weekly on groceries. Using the following data, construct and interpret a 95% confidence interval for the population mean amount spent on groceries (in dollars) by Connecticut families. Assume the data come from a normal distribution
210 23 350 112 27 175 275 50 95 450
Answers
Answer:
The 95% confidence interval for the population mean amount spent on groceries by Connecticut families is ($73.20, $280.21).
Step-by-step explanation:
The data for the amount of money spent weekly on groceries is as follows:
S = {210, 23, 350, 112, 27, 175, 275, 50, 95, 450}
n = 10
Compute the sample mean and sample standard deviation:
\(\bar x =\frac{1}{n}\cdot\sum X=\frac{ 1767 }{ 10 }= 176.7\)
\(s= \sqrt{ \frac{ \sum{\left(x_i - \overline{x}\right)^2 }}{n-1} } = \sqrt{ \frac{ 188448.1 }{ 10 - 1} } \approx 144.702\)
It is assumed that the data come from a normal distribution.
Since the population standard deviation is not known, use a t confidence interval.
The critical value of t for 95% confidence level and degrees of freedom = n - 1 = 10 - 1 = 9 is:
\(t_{\alpha/2, (n-1)}=t_{0.05/2, (10-1)}=t_{0.025, 9}=2.262\)
*Use a t-table.
Compute the 95% confidence interval for the population mean amount spent on groceries by Connecticut families as follows:
\(CI=\bar x\pm t_{\alpha/2, (n-1)}\cdot\ \frac{s}{\sqrt{n}}\)
\(=176.7\pm 2.262\cdot\ \frac{144.702}{\sqrt{10}}\\\\=176.7\pm 103.5064\\\\=(73.1936, 280.2064)\\\\\approx (73.20, 280.21)\)
Thus, the 95% confidence interval for the population mean amount spent on groceries by Connecticut families is ($73.20, $280.21).
0
Explain how to use a graph of the function f(x) to
find f(3)
Answers
Answer:
Step-by-step explanation:
f(3) is another notation for x = 3
on a graph, find 3 on the x axis then move up or down to find its y value
There are 7 red marbles and 9 blue marbles in a bag. What is the ratio of all marbles in the bag to blue marbles? What is the ratio of red marbles to blue marbles?
Answers
Answer:
Answer to the 1st question is: 16/9 or 16:9 (whichever form you use)
Answer to the 2nd question is: 7/9 or 7:9
Step-by-step explanation:
Key skills needed: Number theory, Ratios, and Fractions
1) Let's look at the first question. A ratio is usually a number of something over a number of another thing. One such example is 5 apples : 4 oranges (or 5 apples/ 4 oranges - whichever form you write in).
Based on that let's look at the first problem. We want to find the ratio of all the marbles in the bag to the blue marbles. So it would be --> the total # of marbles over the number of blue marbles. The total number of marbles is 7+9= 16. This would be our first number, or the numerator. The number of blue marbles is 9. This would be our 2nd number, or the denominator of the ratio.With this information --> The ratio would be 16/9 or 16:92) Now let's look at the 2nd question. The number of red marbles to the number of blue marbles is the ratio we need to find.
The number of red marbles is 7. This would be our first number or the numerator. The number of blue marbles is 9. This would be our second number or the denominator. Therefore, the ratio would be --> 7/9 or 7:9Hope you understood and have a nice day!! :D
The rear windshield wiper of a car rotated 120 degrees,as shown. Find the area cleared by the wiper. 25inch,120 degrees, 14inch
Answers
The rear windshield wiper of a car rotated 120 degrees, as shown in the figure. The area cleared by the wiper blade is approximately 205.875 square inches.
The problem states that a car’s rear windshield wiper rotates 120 degrees, as shown in the figure. Our aim is to find the area cleared by the wiper.
The wiper's arm is represented by a line segment and has a length of 14 inches.
The wiper's blade is perpendicular to the arm and has a length of 25 inches.
Angular degree measure indicates how far around a central point an object has traveled, relative to a complete circle. A full circle is 360 degrees, and 120 degrees is a third of that.
As a result, the area cleared by the wiper blade is the sector of a circle with radius 25 inches and central angle 120 degrees.
The formula for calculating the area of a sector of a circle is: A = (θ/360)πr², where A is the area of the sector, θ is the central angle of the sector, π is the mathematical constant pi (3.14), and r is the radius of the circle.
In this situation, the sector's central angle θ is 120 degrees, the radius r is 25 inches, and π is a constant of 3.14.A = (120/360) x 3.14 x 25²= 0.33 x 3.14 x 625= 205.875 square inches, rounded to the nearest thousandth.
Therefore, the area cleared by the wiper blade is approximately 205.875 square inches.
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The director of a community recreation center conducted a six-week study to examine the effects of four types of exercise—strength training, flexibility training, aerobics, and jogging—on maximal oxygen consumption. From the 40
members who participated, the director randomly assigned 10 members to each exercise type. Maximal oxygen consumption was measured for each member at the beginning of the study and again at the end of the six weeks. The director examined the change in maximal oxygen consumption for each member. Which of the following statements is a correct description of a feature of the study?
a. The study has replication because there are four types of exercise.
b. The study has replication because it was conducted over a six-week period.
c. The response variable is the type of exercise with the greatest change in maximal oxygen consumption.
d. The treatments in the study are strength training, flexibility training, aerobics, and jogging.
e. The experimental units are the four different types of exercise.
Answers
Answer: The treatments in the study are strength training, flexibility training, aerobics, and jogging.
Step-by-step explanation:
A correct description of a feature of the study is that the treatments in the study are strength training, flexibility training, aerobics, and jogging.
It should be noted that the study has no replication. Also, the experimental units are the 40 members that participated.
Therefore, the correct option is D.
For F(x)=x^2+8 and g(x)=x^2-8 , find
( f o g) (x)
(g o f) (x),
(f o g)(2)
thanks!!
Answers
The final answer is (f o g)(x) = x^4 - 16x^2 + 72
(g o f)(x) = x^4 + 16x^2 + 56
(f o g)(2) = 24
To find the composite functions (f o g)(x) and (g o f)(x), we need to substitute one function into the other.
(f o g)(x):
To find (f o g)(x), we substitute g(x) into f(x):
(f o g)(x) = f(g(x))
Let's substitute g(x) = x^2 - 8 into f(x) = x^2 + 8:
(f o g)(x) = f(g(x)) = f(x^2 - 8)
Now we replace x in f(x^2 - 8) with x^2 - 8:
(f o g)(x) = (x^2 - 8)^2 + 8
Simplifying further:
(f o g)(x) = x^4 - 16x^2 + 64 + 8
(f o g)(x) = x^4 - 16x^2 + 72
Therefore, (f o g)(x) = x^4 - 16x^2 + 72.
(g o f)(x):
To find (g o f)(x), we substitute f(x) into g(x):
(g o f)(x) = g(f(x))
Let's substitute f(x) = x^2 + 8 into g(x) = x^2 - 8:
(g o f)(x) = g(f(x)) = g(x^2 + 8)
Now we replace x in g(x^2 + 8) with x^2 + 8:
(g o f)(x) = (x^2 + 8)^2 - 8
Simplifying further:
(g o f)(x) = x^4 + 16x^2 + 64 - 8
(g o f)(x) = x^4 + 16x^2 + 56
Therefore, (g o f)(x) = x^4 + 16x^2 + 56.
(f o g)(2):
To find (f o g)(2), we substitute x = 2 into the expression (f o g)(x) = x^4 - 16x^2 + 72:
(f o g)(2) = 2^4 - 16(2)^2 + 72
(f o g)(2) = 16 - 64 + 72
(f o g)(2) = 24
Therefore, (f o g)(2) = 24.
In summary:
(f o g)(x) = x^4 - 16x^2 + 72
(g o f)(x) = x^4 + 16x^2 + 56
(f o g)(2) = 24
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graph the line y= -2x- 3
Answers
Answer:
i hope this helps
Step-by-step explanation:
Answer: the line will go through (0, -3) and for every x value it will go down one
Step-by-step explanation:
Example: (0, -3), (1, -5), (2, -7)
Are all intersecting lines perpendicular? Draw a picture to help explain your answer
Answers
Not all intersecting lines are perpendicular.
What are perpendicular lines?Perpendicular lines require a 90-degree angle of intersection, creating the formation of right angles.
Nonetheless, unlike perpendicular lines that necessitate exactly 90 degrees of intersections, other types of driven lines can be at varying angles beside these.
As such, it is critical to highlight that in general intersecting lines come with different angles of intersection, and only those featuring exact 90-degree angle of intersection become normal cases of intersecting lines, becoming one among many subtypes existing today.
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A rectangular prism has a width of x2 inches and a length of xy2 inches and a height of xy inches.
Which expression represents the volume of the rectangular prism in cubic inches?
2x^2y^2
2xy^3 + 2x^2y
2x^4y^3
x^3y^2
Answers
In this case, the width is x^2 inches, the length is xy^2 inches, and the height is xy inches.
Substituting these values into the formula, we get:
V = (xy^2)(x^2)(xy)
Simplifying, we get:
V = x^4y^3
Therefore, the expression that represents the volume of the rectangular prism in cubic inches is x^4y^3.
What is 2.5 × 15.625
Answers
Answer:
39.0625
Step-by-step explanation:
Answer:
39.0625
Step-by-step explanation:
Paul paid $663 for a new freezer. He paid for the freezer with his credit card, which has an interest rate of 15.28% compounded monthly, and made monthly payments for five years until the freezer was paid off. He kept the freezer for seven years, and it used an average of $2.14 of electricity per week. Paul made no other purchases or payments with his credit card until the freezer was paid off. Between the interest and the electricity, which component of the lifetime cost of the freezer was greater, and how much greater was it? (Round all dollar values to the nearest cent.)
a.
The interest cost $106.60 more than the electricity.
b.
The interest cost $173.24 more than the electricity.
c.
The electricity cost $489.76 more than the interest.
d.
The electricity cost $115.96 more than the interest.
Answers
Answer:
c
Step-by-step explanation:
The electricity cost $489.76 more than the interest.
Thus, option C is correct.
What is Interest cost?Interest cost is the total measure of interest a borrower pays on an obligation commitment over the existence of the getting. Interest is paid on the obligation notwithstanding reimbursement of head.
The formula will be:
I = A - P
I = 663(1 + 0.1528/12)^(5*12) - 663
I = 663(1 + 0.1528/12)^60- 663
I = 1416.51 - 663
I = $753.51
The bill for electricity for 7 years and 52 weeks per year will be
= 7 x 52 x 2.14
= $778.96
The electricity cost is bigger than the interest:
$778.96 is bigger than $753.51 by $25.45:
$778.96 - $753.51 = $25.45.
Therefore, option C is correct.
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What does the circled portion represent in the confidence interval formula?
p±z.
O Sample proportion
O Margin of error
p(1-p)
n
Confidence interval
O Sample Size
Answers
The circled portion in the confidence interval formula p ± z represents the Margin of Error, which plays a crucial role in interpreting the range of plausible values for the population parameter.
In the confidence interval formula p ± z, the circled portion represents the Margin of Error.
The Margin of Error is a critical component of a confidence interval and quantifies the level of uncertainty in the estimate.
It indicates the range within which the true population parameter is likely to fall based on the sample data.
The Margin of Error is calculated by multiplying the critical value (z) by the standard deviation of the sampling distribution.
The critical value is determined based on the desired level of confidence, often denoted as (1 - α), where α is the significance level or the probability of making a Type I error.
The Margin of Error accounts for the variability in the sample and provides a measure of the precision of the estimate.
It reflects the trade-off between the desired level of confidence and the width of the interval.
A larger Margin of Error indicates a wider confidence interval, implying less precision and more uncertainty in the estimate.
Conversely, a smaller Margin of Error leads to a narrower confidence interval, indicating higher precision and greater certainty in the estimate.
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If average of 3a and 4b is less than 50 and a is tiwce b,what is largest possible integer value of a?
Answers
28 the answer is 28 because 3+4 =7 and 7x7 = 49 so 4x7 = 28
I need help to find the slope of the line
Answers
A standard number cube is rolled . What is the probability of getting a factor of 4?A standard number cube is rolled . What is the probability of getting a factor of 4?
Answers
Answer:
1 out is six
Step-by-step explanation:
there are six numbers on a dice cube to get four that is a one out of six.
Answer:
3/6, 1/2 or 50%
Step-by-step explanation:
The answer would be 3/6
because there are 3 factors of 4 and there are 6 total sides so the answer would be 3/6 or 1/2 or 50%
Solve for a
4-(2a+7)=9
Answers
Answer:
a = -6
use pemdasp:arenthesis
e:xponents
m:ultiplication/
d:ivision
a:ddition/
s:ubtraction
Equation given:
4 -(2a + 7) = 9
When there is a minus (-) next to the parenthesis, there is an invisible negative one (-1).
4 -1(2a + 7) = 9
Distribute:
4 -2a -7 = 9
There is a like-term which is 4 and -7. 4 -7 = -3
Combine like-terms:
-3 -2a = 9
Solve the two-step equation:
-3 -2a = 9
Turn -3 to +3 and add 3 to 9
-3 -2a = 9
+3 +3
--------------
-2a = 12
Divide -2a to 12
12/-2 = -6
a = -6
Match the information on the left with the appropriate equation on the right.
An equation perpendicular to y = - 3x + 1 through the point
(3,-2)
An equation through the point ( - 2, 3) and parallel to
y = - 3x - 1
Answers
Can someone please HELP ME WITH THIS IM STUCK
Answers
Answer:
$4240
Step-by-step explanation:
investment = $4000
intrest = $4000×6%
=4000×6÷100
=240
total=$4000+$240
=$4240
F(x)=(x+2)^2 (x-3) graph the function
Answers
The value of the equation f ( x ) is
f ( x ) = x³ + x² - 8x - 12
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
f ( x ) = ( x + 2 )²( x -3 ) be equation (1)
Now , on simplifying the equation , we get
f ( x ) = ( x + 2 )²( x -3 )
f ( x ) = ( x² + 4x + 4 ) ( x - 3 )
Now , multiplying each term with ( x - 3 ) , we get
f ( x ) = ( x - 3 ) x² + ( x - 3 ) 4x + ( x - 3 ) 4
f ( x ) = x³ - 3x² + 4x² - 12x + 4x - 12
On simplifying the equation ,we get
f ( x ) = x³ + x² - 8x - 12
Now , the value of the equation f ( x ) = x³ + x² - 8x - 12
On graphing the equation , we get
The graph of the equation f ( x ) = x³ + x² - 8x - 12 is shown below
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Help this is due today!!!!
Answers
Its the first one, hope u pass lol
Answer:
The second option: 3.5x+685\(\leq \\\)85
Step-by-step explanation:
The addition fee is 6 meaning adding not subtracting. Cancel out the first and last one. Then, it says without going over. Meaning it could equal exactly $85. Which means \(\leq\). So it would be the second option.
-1/4 plus 3/5
Answer or else
Answers
The algebric expression -1/4 + 3/5 is equal to 7/20 when simplified.
To solve the expression -1/4 + 3/5, we need to find a common denominator for the fractions and then perform the addition.
The common denominator for 4 and 5 is 20. We can rewrite the fractions with this denominator:
-1/4 = -5/20
3/5 = 12/20
Now that the fractions have the same denominator, we can add them:
-5/20 + 12/20 = (-5 + 12)/20 = 7/20
Therefore, -1/4 + 3/5 is equal to 7/20.
To further simplify the fraction, we can check if there is a common factor between the numerator and denominator. In this case, 7 and 20 have no common factors other than 1, so the fraction is already in its simplest form.
Thus, the final answer is 7/20.
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The cellular phone service for a business executive is $35 per month plus $0.40 per minute of phone use over 900 min. For a month in which the executive's cellular phone bill was $87.80, how many minutes did the executive use the phone?
Answers
The number of minutes that the executive use the phone is 131 minutes.
How to calculate the number of minutes?From the information, the cellular phone service for a business executive is $35 per month plus $0.40 per minute of phone use.
Let the number of minutes be m.
This will be illustrated as:
35 + 0.40m = 87.80
Collect like terms
0.40m = 87.80 - 35
0.40m = 52.80
Divide
m = 52.40 / 0.40
m = 131
The number of minute is 131 minutes.
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In an insect colony, there are 280 insects after 6 days. If there were initially 90 insects, how long will it take the population to grow to 500 insects?
Answers
Answer:
3 days
Step-by-step explanation:
Population growth of the insects after 6 days
= 280-90
= 190
(500-90)÷190=410÷190
=3 days (rounded up)
44444444444444444444
Answers
Answer:
whatcha asking here buddy?
Step-by-step explanation:
Answer: err u said u will make me the brainlies so I have answered
#3 Preimage point B is
located at (5,-4).
B' is located at (20, -16).
Write the algebraic rule for
the transformation.
Answers
The algebraic rule for the transformation is B' = (Bx + 15, By - 12)
Given data ,
To determine the algebraic rule for the transformation from point B to point B', we need to find the equations that relate the coordinates of the preimage point B to the image point B'.
Let's denote the translation amounts in the x-direction and y-direction as (dx, dy). The coordinates of B' can be obtained by adding these translation amounts to the coordinates of B:
B' = (Bx + dx, By + dy)
Given that B is located at (5, -4) and B' is located at (20, -16), we can calculate the translation amounts:
dx = 20 - 5 = 15
dy = -16 - (-4) = -12
Hence , the algebraic rule for the transformation is B' = (Bx + 15, By - 12)
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