The values for x = 1, then y = 38.23 and for x = 8, then y^ = 55.375.
Given that, [tex]y = b_{0}+ b_{1}x[/tex]
x y xy xx yy
-2 0 0 4 0
0 7 0 0 49
4 15 60 16 225
8 18 144 64 324
9 24 216 81 576
19 64 420 165 1174 - Total(T)
n = 5
Given line is [tex]y = b_{0}+ b_{1}x[/tex]
Solve for the value of [tex]b_{0}[/tex]
[tex]b_{0} = \frac{Ty*Txx-Tx*Txy}{nTx^{2} -(Tx)^{2} }[/tex]
[tex]= \frac{64*165-19*420}{5*165-(19)^{2} }\\ \\= \frac{10560-7980}{825-361}\\ \\= \frac{2580}{64} = 40.135[/tex]
Solve for the value of [tex]b_{1}[/tex]
[tex]b_{1} = \frac{nTxy-Tx*Ty}{nTx^{2} -(Tx)^{2} }\\ \\= \frac{5*420-19*64}{5*165 - (19)^{2} }\\ \\= \frac{2100-1216}{464}\\ \\= \frac{884}{464} = 1.905[/tex]
Therefore, y = 40.135 + 1.905x
To solve for x = 1
y = 40.135 + 1.905(1)
= 38.23
To solve for x = 8
y^ = 40.135 + 1.905(8)
= 55.375
Hence the answer is the values for x = 1, then y = 38.23 and for x = 8, then y^ = 55.375.
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e and all other answers should be rounded to X = 28 X
Since we're in a right triangle, we'll have that:
[tex]\cos 26=\frac{x}{28}[/tex]Solving for x :
[tex]\cos 26=\frac{x}{28}\rightarrow28\cos 26=x\rightarrow x=25.17[/tex]Therefore, x = 25.17
Please answer all questions. Please show your work in the answers.I skated 3 miles in 5 minutes.a. How many miles per minute is that?b. I skated 3 miles in 5 minutes. How many minutes per mile is that?c. If I skated 3 miles in 5 minutes, how far will I skate in an hour?ML and MC live 37 miles apart from each other. ML drives at a speed of 8 miles per hour, and MC drives at a speed of 4 miles per hour. How long does it take until ML and MC meet?Protein bar A has 15 grams of protein in a 40 gram bar. Protein bar B has 20 grams of protein in a 60 gram bar. Which bar has more protein per gram?
1)
a) In order to find the value of miles per minute, we just need to divide the number of miles by the number of minutes:
[tex]\frac{3\text{ miles}}{5\text{ minutes}}=\frac{3}{5}\text{ miles/minute}[/tex]So the result is 3/5 miles per minute.
b) In order to find the number of minutes per mile, since we have the value of miles per minutes, we just need to invert the fraction:
[tex]\frac{3\text{ miles}}{5\text{ minutes}}=\frac{5\text{ minutes}}{3\text{ miles}}=\frac{5}{3}\text{ minutes/mile}[/tex]So the result is 5/3 minutes per mile
c)
In order to calculate the distance after 1 hour (60 minutes), we can use a rule of three:
[tex]\begin{gathered} 5\text{ minutes}\to3\text{ miles} \\ 60\text{ minutes }\to x \\ \\ \frac{5}{60}=\frac{3}{x} \\ \frac{1}{12}=\frac{3}{x} \\ x=3\cdot12=36\text{ miles} \end{gathered}[/tex]So the result is 36 miles.
2)
Since they are going towards each other, the relative speed is the sum of their speeds:
[tex]V=8+4=12\text{ mph}[/tex]Now, to find the time, we just need to divide the distance by the speed:
[tex]t=\frac{37}{12}=3.083=3\text{ hours 5 minutes}[/tex]So the amount of time is 3 hours and 5 minutes.
3)
In order to find which bar has more protein, let's compare the fractions that represents the amount of protein in each bar:
[tex]\begin{gathered} \text{bar A: 15/40 of protein} \\ \text{bar B: 20/60 of protein} \\ \\ \frac{15}{40}=\frac{45}{120} \\ \frac{20}{60}=\frac{40}{120} \\ \frac{45}{120}>\frac{40}{120} \end{gathered}[/tex]So protein bar A has more protein per gram.
6000 divided by 80 (explain and do work)
we can cancel a zero, because it is a common number
we take 60 because 6 is less than 8, 7x8 is very close to 60 obtain the result and substract from 60
go down the zero and look for a number that multiplied by 8 make 40
so,8x5=40
the solution of the division is 75
Answer:
75
Step-by-step explanation:
6 / 8 = 7.5
so 6000/80 = 75
How can I draw a frequency table to represent the information given? how can I calculate the realtive frequency of a size 6 shoe? How can I calculate the probability that if a pupil is chosen at random, that he/she wears a size 7 shoe?
SOLUTION
The relative frequency of size 6 shoe is given as
[tex]\frac{3}{30}=\frac{1}{10}=10\%[/tex]The probability of picking a shoe size of 7 is
[tex]\frac{6}{30}=\frac{1}{5}[/tex]Write the equation of an absolute value function that has been stretched by a factor of 2, reflected across x axis, and shifted 6 units to the right
The absolute value function is the function;
[tex]y=|x|[/tex]STEP 1: To stretch this function vertically by a factor of 2 would mean multiplying the function by 2, we have as a result;
[tex]y=2|x|[/tex]STEP 2: To reflect the function over the x-axis, this means that the entire function is multiplied by a negative sign, we have as a result;
[tex]y=-2|x|[/tex]STEP 3: To shift a function horizontally by 6 units to the right means subtracting 6 from every x- value. we have as a final result;
[tex]y=-2|x-6|[/tex]Therefore, the equation of an absolute value function that has been stretched by a factor of 2, reflected across x-axis, and shifted 6 units to the right is;
[tex]y=-2|x-6|[/tex]coordinate of the vertices after a rotation 270 grades counterclockwise around the origin d (2 2) F (3 4)E(9 2)
If the point (x, y) is rotated 270 degrees counterclockwise around the origin
Then its image is (y, -x)
We change the sign of the x-coordinate and switch the two coordinates
Since point D = (2, 2), then
Its image is D' = (2, -2)
Since point E = (9, 2), then
Its image E' = (2, -9)
Since point F = (3, 4), then
Its image F' = (4, -3)
Hello! I'm a little stumped on this one I think it should be scatter plot
We have a data set that includes the test scores of a class.
We can represent this data, as it is univariate, with a box-and-whisker plot. This will let us graph the distribution of the scores.
A circle graph is only applicable if we group the data in classes. The same for the histogram.
They are not suitable for individual data points that are not grouped.
A scatter plot is also not suitable, as it needs ordered pairs. It will show the relation between two variables, and in this case we have only one variable in the data set.
Answer: box-and-whisker plot.
Your baseball team is holding a silent auction as a fundraiser dinner to pay for the team uniforms. The list shows all the expenses for the silent actions A tablet costs $320Orioles tickets that cost $150A gift card that costs $30The cost of the food is $400The meme era of the baseball team will be selling tickets to the silent auction. A ticket to the silent auction includes chances to win prizes and dinner. The ticket cost is set so 50 tickets will pay for the cost of the prizes and food.Build a function that can be used to find the total profit f(x), the baseball team earns by selling x tickets
The first step to determine the function is to find the total cost of the auction. This is done by adding all the prizes and the cost of the food.
[tex]\begin{gathered} \text{ cost}=320+150+30+400 \\ \text{ cost}=900 \end{gathered}[/tex]The total cost of the auction is $900. Since the cost of 50 tickets should be able to cover the cost, we need to divide the total cost by the number of tickets to determine the cost of each ticket.
[tex]\begin{gathered} x=\frac{900}{50} \\ x=18 \end{gathered}[/tex]Each ticket must be sold as $18. The whole function is:
[tex]f(x)=18\cdot x-900[/tex]If ZY = 26, what is the length of the diameter of circle X?
Given ZY = 26
To find the length of the diameter of circle X.
From the figure shown, it can be observed that ZY is the radius of circle Y.
If ZY is the radius of circle Y, the diameter of circle Y is ZX, which is twice the radius of circle Y.
[tex]\begin{gathered} ZX=2\times ZY \\ ZY=26 \\ ZX=2\times26 \\ ZX=52 \end{gathered}[/tex]ZX is the radius of the circle X.
If ZX is the radius of circle X, the diameter of circle X would be twice the radius of circle X.
[tex]\begin{gathered} D_{\text{circel X}}=2\times ZX \\ ZX=52 \\ D_{\text{circle X}}=2\times52 \\ D_{\text{circle X}}=104 \end{gathered}[/tex]Hence, the length of the diameter of circle X is 104 units
Rich works 140 hours in a month. if his schedule stays the same ,how many hours he work in 3/4 of a month
Let's identify first what informations were given in the scenario:
What is Given: Rich works: 140 hours in a month.
What is being asked: How many hours he work in 3/4 of a month?
To be able to determine how many hours did Rich works in 3/4 of a month, we generate this equation:
[tex]Rich^{\prime}s\text{ work hours in 3/4 month = (Work hours in a month)(3/4)}[/tex][tex]\text{ = (140)(3/4) = }\frac{140\text{ x 3}}{4}[/tex][tex]\text{ = }\frac{420}{4}[/tex][tex]\text{Rich's work hours in 3/4 month = 105 hours}[/tex]Therefore, Rich works 105 hours in 3/4 of a month.
12. Find the weighted average of the student's grades listed below, using the given percentage value for each category.AssignmentScore (%)WeightTest 18330%Test 29430%Homework8410%Quizzes8710%Final Exam7920% %
To find the weighted average we just need to sum all the scores multiplied by their respective weight.
To find 30% of a value, is the same as multiplying by 30 and dividing by 100. As a decimal, this can be represented as 0.3.
[tex]\frac{30}{100}=0.3[/tex]Now, doing the sum multiplying the scores by their respective weights, we have:
[tex]\begin{gathered} \bar{x}=83\times0.3+94\times0.3+84\times0.1+87\times0.1+79\times0.2 \\ \bar{x}=24.9+28.2+8.4+8.7+15.8 \\ \bar{x}=86 \end{gathered}[/tex]The weighted average of this student is 86.
Determine if the following statements are true or false. False [481] = |-481 -21 = -21 976976 1-94 = 94
I understand that you typed by error a square bracket instead of an absolute value vertical bar, right?
|481| = 481 this is a TRUE statement
|-21| = - 21 This is a FALSE statement since |-21| = 21
|976| = - |976| This is a FALSE statement, since |976| = |976| and not equal to the negative of it.
Is the last expression
|-94| = 94?
If such is the case, the statement is TRUE, since the absolute value of a number is ALWAYS the positive of that number.
|-94| = 94 TRUE statement.
The roots of x2 - 4x = 5, in ascending order, are ? and ?
For finding the roots of the function, we have to writte the equation in this form:
[tex]ax^2+bx+c=0[/tex]So in our problem will be:
[tex]x^2+(-4)x-5=0[/tex]Now we can use the cuadratic equation that is:
[tex]\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]and in our problem will be:
[tex]\begin{gathered} \frac{4\pm\sqrt[]{16^{}-4(1)(-5)}}{2(1)} \\ \frac{4\pm\sqrt[]{16^{}+20}}{2} \\ \frac{4\pm\sqrt[]{36}}{2} \\ \frac{4\pm6}{2} \end{gathered}[/tex]Now we can find our two solutions or roots, one with the + and the other with the -
1)
[tex]\begin{gathered} x=\frac{4+6}{2} \\ x=\frac{10}{2} \\ x=5 \end{gathered}[/tex]2)
[tex]\begin{gathered} x=\frac{4-6}{2} \\ x=\frac{-2}{2} \\ x=-1 \end{gathered}[/tex]so the roots are going to be: -1, 5
Find the volume of a cone with a base radius
Solution
Step 1:
Write the formula for the volume of a cone.
[tex]\begin{gathered} Volume\text{ of a cone = }\frac{1}{3}\pi r^2h \\ \text{r = radius} \\ \text{h = height} \end{gathered}[/tex]Step 2:
Given data
r = 6 in
h = 8 in
Step 3
Substitute in the formula to find the volume.
[tex]\begin{gathered} Volume\text{ of a cone = }\frac{1}{3}\pi r^2h \\ \text{= }\frac{1}{3}\times\pi\times6^2\times8 \\ =\text{ }\frac{1}{3}\times\pi\times36\times8 \\ =\text{ }\frac{288\pi}{3} \\ =\text{ 96}\pi\text{ in}^3 \end{gathered}[/tex]Final answer
[tex]Volume\text{ of the cone = 96}\pi\text{ in}^3[/tex]Factor the trinomial100y^2 - 52y +1
Solution
- The question tells us to factor the following trinomial:
[tex]100x^2-52x+1[/tex]- We simply need to rewrite the x-term and factorize the result
- This is done below:
[tex]\begin{gathered} 100x^2-52x+1 \\ 100x^2-50x-2x+1 \\ \text{Factorize} \\ 50x(2x-1)-1(2x-1) \\ \\ (2x-1)\text{ is co}mmon\text{ so we factorize it out} \\ \\ (2x-1)(50x-1) \end{gathered}[/tex]Final Answer
The factored trinomial is
[tex](2x-1)(50x-1)[/tex]can you please help me this is my last one!
281 is the same (equal) as the total (sum) of f and 270
281 = f +270
use the Pythagorean theorem to find the length of the hypotenuse in the Triangle
Answer:
10 units
Explanation:
The Pythagorean theorem says that the hypotenuse c of a triangle is equal to:
[tex]c=\sqrt[]{a^2+b^2}[/tex]Where a and b are the length of the other sides of the triangle.
So, replacing a by 6 and b by 8, we get that the hypothenuse is equal to:
[tex]\begin{gathered} c=\sqrt[]{6^2+8^2} \\ c=\sqrt[]{36+64} \\ c=\sqrt[]{100} \\ c=10 \end{gathered}[/tex]Therefore, the length of the hypothenuse is 10 units
If AC=20, AE = 25, and AB= 5, what is the length of AD?
Answer:
it is 5 because if ab=5 and ac=20
The students in a first-grade class were all asked to time how long (in seconds) they could hold their breath. The resultswere tallied and are presented in the following histogram.How many of those students held their breath greater than 12.5 and less than 15.5 seconds?
ANSWER:
13 students
STEP-BY-STEP EXPLANATION:
To find the answer we must add the number of students between the values 12.5 and 15.5, just like this:
[tex]\begin{gathered} 12.5-13.5=2\text{ students} \\ 13.5-14.5=5\text{ students} \\ 15.5-15.5=6\text{ students} \\ \text{Total}=\text{ }12.5-15.5=2+5+6=\text{ 13 students} \end{gathered}[/tex]The graph of the function F is shown above. What is limF(x)?
Answer:
4
Explanation:
To evaluate a limit, we look at both right and left limi s. If the left and right limits both approach the ssme value, then the limit exists. t
As can be observed from the graph, as we reach x = 2 from the right, the functionseems to reach y = 4. In other other words,
[tex]\lim_{x\to2^+}f(x)=4[/tex]Note the tiny plus sig in the limit . This tells us that we are approaching the limit from the right.
Now let us take a look atthe rleft-hand limit.
Now as we approach x = 2 from the left we see that the function seems to take the value y =4. In other words,
[tex]\lim_{x\to2^-}^f(x)=4.[/tex]Note also the tiny negative sign in the limit. This tells us that we are approaching the limit from the left.
Now both the left and the right-hand limits approach the same value; therefore, the limit exists and its value is the following.
[tex]\boxed{\lim_{x\to2}f(x)=4.}[/tex]The number of kilograms of water in a human body varies directly as the mass of the body. A 66 kg person contains 44 kg of water. How many kilograms of water are in a 144 kg person?
Given:
A 66 kg person contains 44 kg of water.
To find:
The number of kilograms in a 144kg person.
Explanation:
According to the problem, 66 kg person contains 44 kg of water.
For 1 kg person contains,
[tex]\begin{gathered} 1kg\text{ of person}=\frac{44}{66}kg\text{ of water} \\ =\frac{2}{3}kg\text{ of water} \end{gathered}[/tex]Then, for 144kg of a person contains,
[tex]\begin{gathered} 144kg\text{ of a person}=144\times\frac{2}{3}kg\text{ of water} \\ =96kg\text{ of water} \end{gathered}[/tex]Therefore, 144kg per person contains 96 kg of water.
Final answer:
144kg per person contains 96 kg of water.
Which expression best completes the following definition of a complexnumber?where a and bare real numbers and iThe set of all numbers in the formequals -1.
we are given that a and b are real numbers . and that i is a square root of -1
so we expect a and be to be real numbers , this can be expressed as
a + b (i)
so option B is correct .
1. A ball is thrown with an initial velocity of 86 feetper second 4 feet from the ground. The functionn(t) = -16t2 + 86t + 4 represents the height, h, of theball t seconds after it was thrown. After how manyseconds will the ball hit the ground?A. 4.7 secondsB. 4.9 secondsC. 5.2 secondsD. 5.4 secondsА A
D. 5.4 seconds
1) Since the course of that ball is described by the function h(t) = -16t² +86t +4.
So we can sketch out:
When the ball hits the ground, we'll have to find out the 2nd root of that function since when t=0, h =4. So let's find out the roots:
[tex]\begin{gathered} h(t)\text{ =-16t²+86t+4} \\ \Delta=(86)^2-4(-16)(4) \\ \Delta=7396+256 \\ x=\frac{-86\pm\sqrt[]{7652}}{2(-16)} \\ x_1=5.42 \\ x_2=-0.046 \end{gathered}[/tex]3) Since just the positive answer is interesting, then we can state that the answer is D (rounded off to the nearest tenth
A rectangular piece of metal has an area of 112 square centimeters. Its perimeter is 46 centimeters. What are the dimensions of the piece?
Let the length of rectabgle be l and width of rectangle be b.
The equation for the area of rectangle is,
[tex]l\cdot b=112[/tex]The equation for perimeter of rectangle is,
[tex]\begin{gathered} 2(l+b)=46 \\ l+b=23 \\ l=23-b \end{gathered}[/tex]Substitute 23 - b for l in the equation lb
How many period s of the function are there between
The period of a tangent function y = atan(bx) is the distance between any two consecutive vertical asymptotes. And it is given by:
[tex]period=\frac{\pi}{|b|}[/tex]So, given the function y = tan x, we have that b = 1, therefore the period is:
[tex]\text{period}=\frac{\pi}{|1|}=\pi[/tex]Next, between the given points:
[tex]\begin{gathered} -\frac{5\pi}{2}=-2.5\pi \\ and \\ \frac{7\pi}{2}=3.5\pi \end{gathered}[/tex]There are:
[tex]3.5\pi-(-2.5\pi)=6\pi[/tex]Since the period is π, so:
[tex]\frac{6\pi}{\pi}=6[/tex]Answer: 6
how did the temperature change? First, it went up by 25% then went down by 40%
Answer:
24.6%
Step-by-step explanation:
24.6 is the answer
Answer:
The temperature decreased by 25%.
Step-by-step explanation:
The mean phone bill is $______The median phone bill is $______Determine the mode phone bill. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
Given: $36.52,$42.30.$39.78. $38.26. $44.39, $49.55
to find: Mean , Median and mode
soluiton:
Since, formula for mean
[tex]=\frac{su\text{m of all terms}}{nu\text{mber of terms}}[/tex]Here, sum of all terms = 36.52 + 42.30 + 39.78 + 38.26 + 44.39 + 49.55 = 250.8
number of terms = 6
Thus,
[tex]\operatorname{mean}=\frac{250.8}{6}=41.8[/tex]Hence, mean of phone bill is $41.8
Since, number of terms = 6 which is even
so, median
[tex]=\mleft\lbrace\frac{\frac{n}{2}+(\frac{n}{2}+1)th\text{ term}}{2}\mright\rbrace[/tex]arranging the terms in ascending order: 36.52 , 38.26, 39.78, 42.30, 44.39, 49.55
Now, median
[tex]\begin{gathered} =\mleft\lbrace\frac{3rd+4th\text{ term}}{2}\mright\rbrace \\ =\frac{39.78+42.30}{2} \\ =41.04 \end{gathered}[/tex]Hence, median of the phone bill is $41.04
Mode:
Given terms are 36.52 , 38.26, 39.78, 42.30, 44.39, 49.55
If no value or number in the data set appears more than once, then it has no mode
Hence, the phone bill has no mode
Net Worth Statement Assets House (current value) Checking account Automobile Investments Total Assets Value $85,000 $2,500 $18,500 $7,000 $113,000 Llabilities Mortgage Credit card debt Total Liabilities $62,000 $9,500 $71,500 Based on the information in the statement, what is Phillip's net worth? A $184,500B $41,500 C $71,500D $41,500
Value of total assests is ;
$85,000 +$2,500 +$18,500 +$7000=$113,000
Value of total liabilities = $62,000 + $9,500 = $71,000
Net worth = $ 113,000-$71,500 =$41,500
12. Zea has a credit limit of $2,000 on her credit card. Each month, she charges
about $200 and makes a payment of $125.
a. Estimate the number of months that Zea can continue this pattern until
she reaches her credit limit.
9001
b. Consider that part of the $125 Zea pays each month will be for finance
charges. How will the number of months from part a be affected by these
charges?
Answer:
Step-by-step explanation:
1. It will take Zea 27 months to reach her credit card limit.
2. The number of months will be less than 27.
{(-2, 5), (-1, 2), (0, 1), (2,5)}
Which points are on the graph of the inverse?
Select each correct answer.
(5,2)
(2, 1)
-
(-5, 2)
let's recall that the domain of a function is the range of its inverse function, namely, the inverse has a pair that's just the same but flipped sideways, Check the picture below.