I need help on answering 3. (d) I have two choices it can be which is false and sometimes true.
Answers
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.
Related Questions
A box is filled with 3 yellow cards, 2 blue cards, and 7 brown cards. A card is chosen at random from the box. What is the probability that it is a yellow or abrown card?Write your answer as a fraction in simplest form.
Answers
We need to find the probability of the card chosen at random is yellow or brown.
So, since there are 3 yellow cards and 7 brown cards, the total numbers of cards that are yellow or brown is:
[tex]3+7=10[/tex]Now, the probability that the chosen card is yellow or brown can be found by dividing the above value by the total number of cards in the box.
The total number of cards in the box is:
[tex]3+7+2=12[/tex]Thus, that probability is given by:
[tex]\frac{10}{12}=\frac{10\div2}{12\div2}=\frac{5}{6}[/tex]Therefore, the answer is:
[tex]\frac{5}{6}[/tex]P(x) =x and q(x) = x-1Given:minimum x and Maximum x: -9.4 and 9.4minimum y and maximum y: -6.2 and 6.2Using the rational function [y=P(x)/q(x)], draw a graph and answer the following: a) what are the zeroes?b) are there any asymptotes? c) what is the domain and range for this function?d) it it a continuous function?e) are there any values of y= f(x)/g(x) that are undefined? Explain
Answers
we have the following function
[tex]\frac{p(x)}{g(x)}=\frac{x}{x\text{ -1}}[/tex]where x is between -9.4 and 9.4 and y is between -6.2 and 6.2.
We will first draw the function
from the graph, we can see that the zeroes are all values of x for which the graph crosses the x -axis
In this case, we see that that the only zero is at x=0.
Now, we have that the asymptotes are lines to which the graph of the function get really close to. On one side, we can see that as x goes to infinity or minus infinity, the values of the function get really close to 1. So the graph has a horizontal asymptote at y=1. Also, we can see that as x gets really close to 1, the graph gets really close to the vertical line x=1. So the graph has a vertical asymptote at x=1.
Recall that the domain of a function is the set of values of x for which the function is defined. From our graph, we can see that graph is not defined when x=1. So the domain of the function is the set of real numbers except x=1. Now, recall that the range of the function is the set of y values of the graph. From the picture we can see that the graph has a y coordinate for every value of y except for y=1. So, this means that the range of the function is the set of real numbers except y=1.
From the graph, we can see that we cannot draw the graph having a continous drawing. That is, imagine we take a pencil and start on one point on the graph on the left side. We can draw the whole graph on the left side, but we cannot draw the graph on the right side without lifting the pencil up. As we have to "lift the pencil up" this means that the graph is not continous
Finally note that as we have a vertical asymptote at x=1 and horizontal asymptote at y=1 we have that when y is 1 or x is 1, the function y=f(x)/g(x) is undefined
After adding the two equations to eliminate x you are left with 4y=-8
Answers
solve for y
[tex]\begin{gathered} \frac{4y}{4}=-\frac{8}{4} \\ y=-2 \end{gathered}[/tex]then, solve for x
[tex]\begin{gathered} 2x-2=4 \\ 2x-2+2=4+2 \\ 2x=6 \\ \frac{2x}{2}=\frac{6}{2} \\ x=3 \end{gathered}[/tex]x = 3
y = -2
The round off errors when measuring the distance that a long jumper has jumped is uniformly distributed between 0 and 5.3 mm. Round values to 4 decimal places when possible.
The mean of this distribution is _____
The standard deviation is _____
The probability that the round off error for a jumper's distance is exactly 0.4 is P(x = 0.4) = ____-
The probability that the round off error for the distance that a long jumper has jumped is between 0 and 5.3 mm is P(1.2 < x < 3.4) = ____
The probability that the jump's round off error is greater than 4.16 is P(x > 4.16) = ____
P(x > 4.2 | x > 1.8) = ___
Find the 85th percentile____
Find the maximum for the lower quartile. ____
Answers
Using the uniform distribution, it is found that:
The mean is of 2.65 mm.The standard deviation is of 1.53 mm.P(X = 0.4) = 0.P(1.2 < x < 3.4) = 0.4151 = 41.51%.P(X > 4.16) = 0.2121 = 21.51%.P(X > 4.2|x > 1.8) = 0.3257 = 32.57%.85th percentile: 4.505 mm.Lower quartile: 1.325 mm.Uniform probability distributionThe uniform distribution has two bounds, a and b, and all outcomes in the distribution are equally as likely.
In this problem, the bounds are as follows:
a = 0, b = 5.3.
Hence the mean is:
M = (a + b)/2 = (0 + 5.3)/2 = 2.65 mm.
The standard deviation is of:
[tex]S = \sqrt{\frac{(b - a)^2}{12}} = \sqrt{\frac{5.3^2}{12}} = 1.53[/tex]
The uniform distribution is continuous, hence the probability of an exact value is of 0.
The probability of finding a value between c and d is:
[tex]P(c \leq X \leq d) = \frac{d - c}{b - a}[/tex]
Hence:
P(1.2 < x < 3.4) = (3.4 - 1.2)/(5.3 - 0) = 0.4151 = 41.51%.
The probability of finding a value above x is:
[tex]P(X > x) = \frac{b - x}{b - a}[/tex]
Hence:
P(X > 4.16) = (5.3 - 4.16)/(5.3 - 0) = 0.2121 = 21.51%.
P(x > 4.2 | x > 1.8) makes the lower bound 1.8, hence:
P(X > 4.2|x > 1.8) = (5.3 - 4.16)/(5.3 - 1.8) = 0.3257 = 32.57%.
The 85th percentile is found as follows:
0.85 x (5.3 - 0) = 4.505 mm.
The lower quartile is the 25th percentile, hence:
0.25 x (5.3 - 0) = 1.325 mm.
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What is the greatest common factor of 9 and 72?
Answers
The Greatest Common Factor of 9 and 72 is: 9
SOLUTION
Problem Statement
The question asks us to find the greatest common factor of 9 and 72.
Method
In order to solve this question, we just need to follow these steps:
1. Write out the prime factors of 9 and 72
2. Choose the common factors from both expressions.
3. Multiply the common factors.
Implementation
1. Write out the prime factors of 9 and 72:
[tex]\begin{gathered} 9=1\times3\times3 \\ \text{The common factors of 9 are: 3 and 3} \\ \\ 72=1\times2\times2\times2\times3\times3 \\ \text{Common factors of 72 are: 1,2, 2, 2 and 3, 3} \end{gathered}[/tex]2. Choose the common factors from both expressions.:
We need to examine the two expressions for 9 and 72 above. Choose the common values.
[tex]\begin{gathered} 3\times3\text{ is common to both 9 and 72} \\ i\mathrm{}e\text{.} \\ 9\text{ is common to both 9 and 72} \\ 3\text{ is common to both 9 and 72 as well} \\ 1\text{ is also common to both 9 and 72} \end{gathered}[/tex]3. Multiply the common factors.:
[tex]\begin{gathered} \text{Thus, choosing the greatest values from 1,3 and 9.} \\ \therefore\text{The Greatest Common Factor = 9} \end{gathered}[/tex]Final Answer:
The Greatest Common Factor of 9 and 72 is: 9
Classify the triangle with side lengths 8,13,20. a) Acute b) Right c) Obtuse
Answers
for right angles triangle,
hyposenuse square should be equal to sum of square of other two sides
it fails that law so its not right angled triangle
Find the mean for this set of data. Write your answer as a decimal roundedto the nearest TENTH.32, 23, 34, 29, 15, 17, 23
Answers
Given:
The set of data is given as
[tex]32,23,34,29,15,17,23[/tex]Required:
To find the mean.
Formula:
[tex]\text{Mean(}\bar{\text{X}})=\frac{\Sigma x}{n}[/tex]Explanation:
Mean is the ratio of the sum of the values and the number of values.
No of values in the given data is 7.
[tex]n=7[/tex][tex]\begin{gathered} \text{Mean}=\frac{32+23+34+29+15+17+23}{7} \\ =\frac{173}{7} \\ =24.7 \end{gathered}[/tex]Final Answer:
[tex]\text{Mean}=24.7[/tex]
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Answers
There are two families who visit a park and pay the entrance fee. The distribution of each family and the total cost paid at the entrance by each are given:
Family 1:
[tex]\begin{gathered} NumberofAdults(A_1\text{ )= 2} \\ NumberofChildren(B_{1\text{ }})\text{ = 3} \\ TotalEntryCost(C_1)\text{= }20\text{ pounds} \end{gathered}[/tex]Family 2:
[tex]\begin{gathered} NumberofAdults(A_2\text{ ) = 1} \\ NumberofChildren(B_2\text{ )= 4} \\ TotalEntryCost(C_2\text{ )= 15 pounds} \end{gathered}[/tex]Now we will define the ticket rates for adults and children at this park:
[tex]\begin{gathered} \text{Adult Rate = x} \\ \text{Children Rate = y} \end{gathered}[/tex]Next step is to express the total entry cost born by each family. This is done by multiplying the rate of each age group with the respective distribution of age group comprising each family.
Family 1:
[tex]\begin{gathered} C_1\text{ = x}\cdot A_1\text{ + y}\cdot B_1 \\ 20\text{ = 2}x\text{ + 3}y\text{ }\ldots.\text{ Eq1} \end{gathered}[/tex]Family 2:
[tex]\begin{gathered} C_2\text{ = x}\cdot A_2\text{ + y}\cdot B_2 \\ 15\text{ = x + 4y }\ldots Eq\text{ 2} \end{gathered}[/tex]We have two equation with two unknowns representing the cost charged for adults ( x ) and cost charged for children ( y ) at the park entrance.
We will solve the equation simultaneously ( Eq1 and Eq2 ) by using the process of Elimination:
[tex]\begin{gathered} 20\text{ = 2x + 3y} \\ -2\cdot(15\text{ = x + 4y) = -30 = -2x -8y} \end{gathered}[/tex][tex]\begin{gathered} 20\text{ = 2x + 3y} \\ -30\text{ = -2x -8y} \\ ========== \\ -10\text{ = 0 -5y} \\ \textcolor{#FF7968}{y}\text{\textcolor{#FF7968}{ = 2}} \end{gathered}[/tex]Plug the value of ( y ) in either of the two equations and solve for ( x ):
[tex]\begin{gathered} 15\text{ = x + 4(2)} \\ x\text{ = 15 - 8} \\ \textcolor{#FF7968}{x}\text{\textcolor{#FF7968}{ = 7 }} \end{gathered}[/tex]Therefore, the rates charged for each age group are:
[tex]\begin{gathered} \text{\textcolor{#FF7968}{Adult ticket = x = 7 pounds}} \\ \text{\textcolor{#FF7968}{Child ticket = y = 2 pounds}} \end{gathered}[/tex]Answer:yes
Step-by-step explanation:
Question 3 of 14What are the factors of the product represented below?TILESX2 X2 X2 X2X X X XA. (2x + 1)(4x + 3)B. (4x + 2)(3x + 1)C. (8x + 1)(x+2)D. (4x + 1)(2x + 3)
Answers
Hi!
To solve this exercise, we can analyze the sides of this rectangle, which indicate the size of each side.
Let's do it:
On the superior side, we have: x+x+x+x+1, which means 4x+1, right?
On the left side, we have: x+x+1+1+1, or 2x+3
So, we can say that the factors of this rectangle are (4x+1)*(2x+3), last alternative.
Madison is in the business of manufacturing phones. She must pay a daily fixed cost of $400 to rent the building and equipment, and also pays a cost of $125 per phone produced for materials and labor. Make a table of values and then write an equation for C,C, in terms of p,p, representing total cost, in dollars, of producing pp phones in a given day.
I need the equation
Answers
Here is the completed table:
Number of phones manufactured Total cost of Manufactured phones
0 $400
1 $525
2 $650
3 $775
The equation that represents the total cost is C = $400 + $125p .
What is the total cost?The equation that represents the total cost is a function of the fixed cost and the variable cost. The fixed cost remains constant regardless of the level of output. The variable cost changes with the level of output.
Total cost = fixed cost + total variable cost
Total cost = fixed cost + (variable cost x total output)
C = $400 + ($125 x p)
C = $400 + $125p
Total cost when 0 phones are made = $400 + $125(0) = $400
Total cost when 1 phone are made = $400 + $125(1) = $525
Total cost when 2 phones are made = $400 + $125(2) = $650
Total cost when 3 phones are made = $400 + $125(3) = $775
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For the following function, briefly describe how the graph can be obtained from the graph of a basic logarithmic function. Then, graph the function and state the domain and the vertical asymptote. f(x) = 7 - In x Describe how the graph of f(x) can be obtained from the graph of a basic logarithmic function. The graph of f(x) = 7 - In x is a transformation of the graph of f(x) = In x by a reflection across the and then a translation units. Use the graphing tool to graph the equation.
Answers
Answer
1) Graph is shown below in the 'Explanation'.
2) Domain: x > 0
In interval notation,
Domain: (0, ∞)
3) Vertical asymptote: x = 0
Horizontal asymptote: y = 7
4) The transformations required to turn f(x) = In x into f(x) = 7 - In x include
A reflection of f(x) = In x about the x-axis.
Then, this reflected image is then translated 7 units upwards.
Explanation
The graph of function is attached below
For the domain and asymptote,
Domain
The domain of a function refers to the values of the independent variable (x), where the dependent variable [y or f(x)] or the function has a corresponding real value. The domain is simply the values of x for which the output also exists. It is the region around the x-axis that the graph of the function spans.
We know that the logarithm of a number only exists if the number is positive.
So,
Domain: x > 0
In interval notation,
Domain: (0, ∞)
Asymptote
Asymptotes are the points on either the x-axis or the y-axis where the graph of the function doesn't touch.
They are usually denoted by broken lines.
For this question, we know that the value of f(x) cannot go beyond f(x) = 7 and x = 0
Vertical asymptote: x = 0
Horizontal asymptote: y = 7
For the transformation
When a function f(x) is translated horizontally along the x-axis by a units, the new function is represented as
f(x + a) when the translation is by a units to the left.
f(x - a) when the translation is by a units to the right.
When a function f(x) is translated vertically along the y-axis by b units, the new function is represented as
f(x) + b when the translation is by b units upwards.
f(x) - b when the translation is by b units downwards.
So, if the original function is
f(x) = In x
f(x) = -In x
This reflects the original function about the x-axis.
Then,
f(x) = 7 - In x
This translates the reflected function by 7 units upwards.
help meeeeeeeeee pleaseee !!!!!
Answers
The simplified answer of the composite function is as follows:
(f + g)(x) = 2x + 3x²(f - g)(x) = 2x - 3x²(f. g)(x) = 6x³(f / g)(x) = 2 / 3xHow to solve composite function?Composite functions is a function that depends on another function. A composite function is created when one function is substituted into another function.
In other words, a composite function is generally a function that is written inside another function.
Therefore,
f(x) = 2x
g(x) = 3x²
Hence, the composite function can be simplified as follows:
(f + g)(x) = f(x) + g(x) = 2x + 3x²
(f - g)(x) = f(x) - g(x) = 2x - 3x²
(f. g)(x) = f(x) . g(x) = (2x)(3x²) = 6x³
(f / g)(x) = f(x) / g(x) = 2x / 3x² = 2 / 3x
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If cos A = 3/√13 and angle A is not in quadrant I, determine the exact value of sin A.
Answers
To determine the exact value of sin A we get -2/√13
What is determinant?
the determinant is a scalar of value that is a function of to the entries of a square matrix. It is allows characterizing of some properties of to the matrix and the linear map of represented by the matrix.
It is a scalar value which is associated with the square matrix.
Sol-Cos A =3/√13
angle A is not in quadrant I
So angle A is in quadrant IV
Thus,
Sin A =-√(√13)^2-3^2/√13
=-√13-9/√13
=-√4/√13
=-2/√13
Thus the answer is -2/√13.
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Quadrilateral MNOP is dilated by a scale factor of % to create quadrilateral M'N'O'P. The perimeter of quadrilateral MNOP is x units. What is the perimeter in units of quadrilateral M'N'O'P'? A. x units B. ( V2 x units COM X units D. 8/7 x units
Answers
If the perimeter of the quadrilateral MNOP is x
And a scale factor of a dilated image is
[tex]\frac{7}{8}[/tex]If the perimeter of M'N'O'P' = y
Then
[tex]\text{scale factor = }\frac{perimeter\text{ of y}}{perimeter\text{ of x}}\text{ = }\frac{7}{8}[/tex]Cross multiplying,
[tex]perimeterofy=M^{\prime}N^{\prime}O^{\prime}P^{\prime}=\frac{7}{8}\text{ x units}[/tex]The perimeter of M'N'O'P' = 7/8 x units
Option A is correct
y = -2x + 5a. What is the slope? b. What is the vertical intercept? c. What is the horizontal intercept? d. Graph the equation
Answers
Given: The equation below
[tex]y=-2x+5[/tex]To Determine: The slope, the vertical and horizontal intercept, and the graph of the equation
Solution
The general slope-intercept form of a straight line is as shown below
[tex]\begin{gathered} y=mx+c \\ Where \\ m=slope \\ c=vertical-intercept \end{gathered}[/tex]Let us compare the general slope-intercept form of a straight line to the given
[tex]\begin{gathered} y=mx+c \\ y=-2x+5 \\ slope=m=-2 \end{gathered}[/tex]The vertical intercept is the point where the x values is zero
[tex]\begin{gathered} y=-2x+5 \\ x=0 \\ y=-2(0)+5 \\ y=0+5 \\ y=5 \end{gathered}[/tex]The vertical intercept is y = 5, with coordinate (0, 5)
The horizontal intercept is the point where the y value is zero
[tex]\begin{gathered} y=-2x+5 \\ y=0 \\ 0=-2x+5 \\ 2x=5 \\ x=\frac{5}{2} \end{gathered}[/tex]The horizontal intercept is x = 5/2, with coordinate (5/2, 0)
The graph of the equation is as shown below
Answer Summary
(a) slope = -2
(b) Vertical intercept, y = 5
(c) Horizontal intercept, x = 5/2
Mathematics literacy Finance Break-even analysis homework (1.1 and 1.2 only)
Answers
We are given a set of data with the employee number and the corresponding weekly wage.
Part 1.1 To determine the wage per hour we need to find the quotient between the weekly wage and the number of hours worked per week.
In the case of employee 1, we have that his weekly wage was 1680, therefore, the weekly payment per hour is:
[tex]p=\frac{1680}{42}=40\text{ per hour}[/tex]The weekly payment is $40 per hour.
Part 1.2 We have that employee number 4 work a total of 6 hours each day of the week. Since there are 7 days per week we have that the total number of hours during the week is:
[tex]h_4=(6day)(7)=42\text{ }hours[/tex]Now, we multiply by the rate of payment per week, therefore, his weekly pay must be:
[tex]p_4=(42hours)(40\text{ per hour\rparen}=1680[/tex]Therefore, the weekly wage of 4 is 1680.
Part 1.3 To determine the number of hours that employee 8 we must have into account that the number of hours per week by the rate of pay per hour is the total weekly wage, therefore:
[tex](40\text{ per hour\rparen}h_8=2000[/tex]Now, we divide both sides by 40:
[tex]h_8=\frac{2000}{40}=50hours[/tex]Therefore, employee 8 worked 50 hours.
Part 1.4 Since the weekly payment is proportional to the number of hours this means that the employee that worked the least number of hours is the one with the least weekly wage.
We have that employee 5 has the smaller wage, therefore, employee 5 worked the least number of hours.
Part 1.5 we are asked to identify the dependent variable between weekly wage and the number of hours worked.
Since the number of hours does not depend on any of the other considered variables this means that this is the independent variable. Therefore, the dependent variables is the weekly wage. The correct answer is A
Part 1.6 The modal value of a set of data is the value that is repeated the most. We have that the weekly wage that is repeated the most is 1600 since it is the wage of employees 2 and 7. Therefore, the modal value is 1600
Part 1.7 The range of a set of data is the difference between the maximum and minimum values. The maximum wage is 2000 and the minimum is 1160, therefore, the range is:
[tex]R=2000-1160=840[/tex]The range is 840
Type the correct answer in each box use numerals instead of words What are the values of the function
Answers
Given the following function:
[tex]h(x)=\begin{cases}{3x-4;x<0} \\ {2x^2-3x+10;0\leq x<4} \\ {2^x};x\ge4\end{cases}[/tex]We will find the value of the function when x = 0 and when x = 4
First, when x = 0, the function will be equal to the second deifinition
So, h(0) will be as follows:
[tex]h(0)=2(0)^2-3(0)+10=10[/tex]Second, when x = 4, the function will be equal to the third definition
So, h(4) will be as follows:
[tex]h(4)=2^4=16[/tex]So, the answer will be:
[tex]\begin{gathered} h(0)=10 \\ h(4)=16 \end{gathered}[/tex]give the answer as a mixed number and as an improper fraction (number 1)
Answers
Answer:
Jossie has filled 59/30 of the 3 baskets.
Step-by-step explanation:
If Jossie has filled 3/5 of one, 7/10 of another, and 2/3 for the last one. The proportion of the total baskets:
[tex]\frac{3}{5}*\frac{2}{2}+\frac{7}{10}+\frac{2}{3}=\frac{6}{10}+\frac{7}{10}+\frac{2}{3}[/tex]Compute.
[tex]\frac{13}{10}+\frac{2}{3}=\frac{39+20}{30}=\frac{59}{30}[/tex]Jossie has filled 59/30 of the 3 baskets.
Check PictureGraph the polynomial given below by first selecting the number of points, then moving the points. You will need a point for each x intercept, and one for the y intercept.f(x)=17(x−1)(x+3)(x+7)
Answers
ANSWER
Graph:
EXPLANATION
Given:
[tex]f(x)\text{ = }\frac{1}{7}\left(x−1\right)\left(x+3\right)\left(x+7\right)[/tex]Desired Outcome:
Graph the polynomial
Plotting a few selected points using the table below
Mrs. Williams estimates that she will spend $65 onschool supplies. She actually spends $73. What is thepercent error? Round to the nearest tenth ifnecessary.
Answers
We can calculate the percent error as the absolute difference between the predicted value ($65) and the actual value ($73) divided by the actual value and multiplied by 100%.
This can be written as:
[tex]e=\frac{|p-a|}{a}\cdot100\%=\frac{|65-73|}{73}\cdot100\%=\frac{8}{73}\cdot100\%\approx11.0\%[/tex]Answer: the percent error is approximately 11.0%
Please help me answer the following question with the picture below.
Answers
Answer:
9x+b
Step-by-step explanation:
A linear function has a slope of 11. Interpret this slope with a complete sentence using the words“inputs” and “outputs”. (1 point)As the inputs________,_______
Answers
Answer
the inputs increase by 1 and the outputs increase by 11
Step-by-step explanation:
The standard form of a linear function is written as
y = mx + c
where m = slope
Since the slope is 11
y = 11x + c
This implies that the inputs increase by 1 and the outputs increase by 11
Which phrase represents this expression?
5 + 4 ÷ 2
Responses
the product of 5 and the quotient of 4 and 2
the product of 5 and the quotient of 4 and 2
the product of 5 and 4 is divided by 2
the product of 5 and 4 is divided by 2
the sum of 5 and 4 is divided by 2
the sum of 5 and 4 is divided by 2
the sum of 5 and the quotient of 4 and 2
Answers
Reason
According to the PEMDAS rule, we multiply and divide before add and subtract
So we find the “quotient” or divide 4 by 2 first. Then we add 5 to the quotient which is a “sum” of 5 and quotient
Where do the graph shifted if the function changes from Y=x^2 to Y=(x+h)^2
Answers
The independent variable x is shifted (x + h). This is a value of h units to the right since it is the sum to the variable x.
So, the graph to find where the graph shift, we need to find the difference between these two values:
[tex](x+h)^2-x^2=x^2+2hx+h^2-x^2=2hx+h^2[/tex]Then, the graph is shifted
[tex]2hx+h^2[/tex]This is from my prep guideI will provide the answer options in another picture
Answers
In order to determine the corresponding graph to the given function f(x), consider the y-intercept of the function (the value of the y-coordinate of the curve when x = 0).
The y-intercept is the value of f(x) for x= 0. Replace x = 0 into the given function:
[tex]f(0)=(\frac{1}{2})^{0+1}+3=\frac{1}{2}+3=\frac{7}{2}[/tex]Then, the point of intersection of the curve with the y-axis is (0 , 7/2) or (0 , 3.5).
You can notice that from the given answer choices, that option two (up right side) has the required y-intercept. Then, that graph matches with the given function.
Find the slope, if it exists, of the line containing the pair of points. (−2,−6) and (−15,−7)
Answers
The linear regression for a given data set has the form
[tex]y=a+bx[/tex]where the values a and b can be solved using the equation
[tex]\begin{gathered} a=\frac{(\sum y)(\sum x^2)-(\sum x)(\sum xy)}{n(\sum x^2)-(\sum x)^2} \\ b=\frac{n(\sum xy)-(\sum x)(\sum y)}{n(\sum x^2)-(\sum x)^2} \end{gathered}[/tex]Based on the given data set, we have n equals 5. We will solve for the values of the summation first. We have the following
[tex]\begin{gathered} \sum y=4+4+6+6+8=28 \\ \sum x=1+3+5+7+9=25 \\ \sum xy=(1\cdot4)+(3\cdot4)+(5\cdot6)+(7\cdot6)+(8\cdot9)=160 \\ \sum x^2=1^2+3^2+5^2+7^2+9^2=165^{} \\ (\sum x)^2=25^2=625 \end{gathered}[/tex]Using these values to compute for the values of a and b, we get
[tex]\begin{gathered} a=\frac{(28\cdot165)-(25\cdot160)}{5(165)-625}=\frac{31}{10}=3.1 \\ b=\frac{5(160)-(28\cdot25)}{5(165)-625}=\frac{1}{2}=0.5 \end{gathered}[/tex]Take note that the problem wants us to reduce the numbers to the nearest tenth. Hence, the linear regression for the given data set is written as
[tex]y=3.1+0.5x[/tex]Determine if the correlation between the two given variables is likely to be positive or negative, or if they are not likely to display a linear relationship.A child’s age and the number of hours spent napping-positive-negative-no correlation
Answers
We know that a a childresn spend more hours napping when they are youngers therefore we have a negative correlation
Use the following function rule to find f(48).
f(x) = 12 + x/4
Answers
Answer:
See image
depending on what is in the numerator of your question:
24 OR 15 SEE IMAGE!
Step-by-step explanation:
f(48) just means to use 48 in place of x in your work.
f(x) = 12 + x/4
f(48) = 12 + 48/4
Hopefully, your text/worksheet/screen is clear on which problem you are doing.
I need the slope the y intercept is -2 and the x intercept is -1
Answers
The x intercept is the value of x when y = 0
Given that x intercept = - 1, the coordinate is (- 1, - 0)
The y intercept is the value of y when x = 0
Given that y intercept = - 2, the coordinate is (0, - 2)
Slope = (y2 - y1)/(x2 - x1)
x1 = - 1, y1 = 0
x2 = 0, y2 = - 2
Slope = (- 2 - 0)/(0 - - 1)
slope = - 2/1
slope = - 2
the triangle in the figure had a hypotenuse equal to 40 units what is the approximate length of x
25.7 units
30.6 units
47.7 units
52.2 units
(Srry I’m spamming I know nothing on this test)
Answers
If the triangle in the figure has a hypotenuse equal to 40 units, then the approximate length of x is 30.64 units
The length of the hypotenuse = 40 units
The angle = 50 degrees
Here we have to apply the trigonometric function
we know
sin θ = Opposite side / Hypotenuse
cos θ = Adjacent side / Hypotenuse
tan θ = Opposite side / Adjacent side
Here we have to use the equation of sin θ
Substitute the values in the equation
sin 50 = x/40
x = 40×sin 50
x = 30.64 units
Hence, if the triangle in the figure has a hypotenuse equal to 40 units, then the approximate length of x is 30.64 units
Learn more about trigonometric function here
brainly.com/question/14746686
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