The slope of the line with that passes through the coordinates (2,8) and (12,20) is 6/5.
What is the slope of the line with the given coordinates?Slope is simply expressed as change in y over the change in x.
Slope m = ( y₂ - y₁ )/( x₂ - x₁ )
Given the data in the question;
Point 1( 2,8 )
x₁ = 2y₁ = 8Point 2( 12,20 )
x₂ = 12y₂ = 20Slope m = ?
To find the slope m, plug the given x and y values into the slope formula and simplify.
Slope m = ( y₂ - y₁ )/( x₂ - x₁ )
Slope m = ( 20 - 8 )/( 12 - 2 )
Slope m = ( 12 )/( 10 )
Slope m = 12/10
Slope m = 6/5
Therefore, the slope of the line is 6/5.
Learn more about slope formula here: brainly.com/question/24578307
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The National Oceanic and Atmospheric Administration tracks the amount of oysters harvested from the Chesapeake Bay each year.Years since 1900 2 28 53 67 78 89Oysters (metric tons) 54.2 22.5 7.38 5.28 3.52 2.38Find the exponential regression equation that models this data.Ay=-58(-0.964)OB. y = -58(0.964)Oc.y=58(0.964)*OD.y=58(-0.964)*Reset SelectionPreviouNext
Explanation
We are given the following table:
We are required to determine the exponential regression equation that models the data.
This is achieved thus:
We know that an exponential equation is given as:
[tex]y=ab^x[/tex]Using a graphing calculator, we have:
From the graph, we have:
[tex]\begin{gathered} a=58 \\ b=0.964 \end{gathered}[/tex]Hence, the answer is:
[tex]y=58(0.964)^x[/tex]Solve.(3.3 × 10³) (2 × 10²)
Here are the steps in multiplying scientific notations:
1. Multiply the coefficients first.
[tex]3.3\times2=6.6[/tex]2. Multiply the base 10 by adding their exponents.
[tex]10^3\times10^2=10^{3+2}=10^5[/tex]3. Connect the result in steps 1 and 2 by the symbol for multiplication.
[tex]6.6\times10^5[/tex]Hence, the result is 6.6 x 10⁵.
Kepler's third law of planetary motion states that the square of the time required for a planet to make one revolution about the sun varies directly as the cube of the average distance of the planet from the sun. If you assume that Jupiter is 5.2 times as far from the sun as is the earth, find the approximate revolution time for Jupiter in years.
Show work pls ;-;
By applying Kepler's third law of planetary motion, the approximate revolution time for Jupiter is equal to 12 years.
What is Kepler's third law?Mathematically, Kepler's third law of planetary motion is given by this mathematical expression:
T² = a³
Where:
T represents the orbital period.a represents the semi-major axis.Note: Earth has 1 astronomical unit (AU) in 1 year of time.
For this direct variation, the value of the constant of proportionality (k) is given by:
T² = ka³
k = T²/a³
k = 1²/1³
k = 1.
When the semi-major axis or the distance of Jupiter from Sun is 5.2, we have;
T² = ka³
T² = 1 × 5.2³
T² = 140.608
T = √140.608
T = 11.858 ≈ 12 years.
Read more on Kepler's third law here: https://brainly.com/question/15691974
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the price of a gallon of unleaded gas has risen to $2.92 today. yesterday's price was $2.85. find the percentage increase. round to the nearest 10th of a percent
Given:
[tex]\begin{gathered} P_{\text{today}}=2.92,P_{today}=Price\text{ of a gallon of unleaded gas today} \\ P_{\text{yesterday}}=2.85, \\ P_{yesterday}=Price\text{ of a gallon of unleaded gas today} \end{gathered}[/tex]To Determine: The percentage increase round to the nearest 1oth of a percent
The formula for percentage increase is given below:
[tex]\begin{gathered} P_{in\text{crease}}=\frac{increase}{P_{\text{initial}}}\times100\% \\ In\text{crease}=P_{final}-P_{in\text{itial}} \end{gathered}[/tex]Substitute the given into the formula
[tex]\begin{gathered} P_{\text{yesterday}}=P_{i\text{nitial}}=2.85 \\ P_{\text{today}}=P_{\text{final}}=2.92 \\ \text{Increase}=2.92-2.85=0.07 \end{gathered}[/tex][tex]\begin{gathered} P_{in\text{crease}}=\frac{increase}{P_{\text{initial}}}\times100\% \\ P_{in\text{crease}}=\frac{0.07}{2.85}\times100\% \\ P_{in\text{crease}}=0.02456\times100\% \\ P_{in\text{crease}}=2.456\% \\ P_{in\text{crease}}\approx2.5\%(nearest\text{ 10th)} \end{gathered}[/tex]Hence, the percentage increase to the nearest 10th of a percent is 2.5%
how to calculate 1+2?
A train leaves a station and travels north at a speed of 175 km/h. Two hours later, a second train leaves on a parallel track and travels north at 225 km/h. How far from the station will theymeet?The trains will meet (?) away from the station(Type an integer or a decimal.)
Given,
The speed of first train is 175km/h.
The speed of second train is 225 km/h.
Consider, the time taken by first train to meet is x h.
The time taken by the second train to meet is (x-2) h.
The distance is calculated as,
[tex]\text{Distance}=\text{speed}\times time[/tex]At the meeting point the distance covered by both train is same,
So, taking the distance equation of both trains in equal,
[tex]\begin{gathered} 175\times x=225\times(x-2) \\ 175x=225x-450 \\ -50x=-450 \\ x=9 \end{gathered}[/tex]The first train meet to second train after distance,
[tex]d=175\times9=1575\text{km}[/tex]The second train meet to first train after distance,
[tex]d=225\times(9-2)=1575\text{ km}[/tex]Hence, both train meet after 1575 km from the station.
Suppose A and B are points on the number line. If AB=10 and B lies at -6, where could A be located?
Answer: 16 or 4
Step-by-step explanation:
-6-10=-16
10-6=4
Question : Suppose A and B are points on the number line. If AB=10 and B lies at -6, where could A be located?
Answer: 16
Write an inequality:Carlos was going to sell all of his stamp collection to buy a video game. After selling half of them he changed his mind. He then bought twelve more. How many did he start with if he now has at least 29?
Answer:
He started with at least 34 stamp collection
Explanation:
Let x represent Carlos' initial stamp collection.
From the question, we're told that he sold half of them, bought twelve more, and currently has at least 29, we can go ahead and set up an inequality as shown below;
[tex]\frac{x}{2}+12\ge29[/tex]We can go ahead and solve for x following the below steps;
Step 1: Subtract 12 from both sides of the equation;
[tex]\begin{gathered} \frac{x}{2}+12-12\ge29-12 \\ \frac{x}{2}\ge17 \end{gathered}[/tex]Step 2: Multiply both sides by 2;
[tex]\begin{gathered} \frac{x}{2}\times2\ge17\times2 \\ x\ge34 \end{gathered}[/tex]From the above, we can say that Carlos started with at least 34 stamp collection
Making an inference usingig a two-way frequency tableA group of 150 college students who took math fost term were interviewed. They were asked whether they passed their math course and whether they live oncampus. Their responses are summarized in the following tablePassed math Failed mathve on campus2466Live off campus392152(a) What percentage of the students passed moth? []%(b) What percentage of the students live off campus? []%(c) What percentage of the students who live off campus passed math? []%(d) Is there evidence that students who live off campus tend to pass math more often than average?Yes, because the percentage found in part (e) is much greater than the percentage found in part (0)Yes, because the percentage found in part() is much greater than the percentage found in part (b)No, because the percentage found in part(e) is about the same as the percentage found in part (a).No, because the percentage found in part (5) is about the same as the percentage found in part (b).
1) Considering that there are 150 students
A) Adding 24+39 we got 63 students
150------------100%
63 ----------- x
x=6300/150
x= 42% of the students passed Math.
B) Adding the number of those students who live off-campus 39 +21
150 ----------------100%
60------------------ y
y=6000/150
y=40%
C) 60 students live off-campus 39 succeded. So we can write
60 --------- 100%
39 --------- z
z= 3900/60
z=65% passed math (off-campus)
D) Comparing that 65% of students who live off-campus passed math and that among those who live on campus and that 58% of all students failed
Then we can state:
A)
Find the equation of the line passing through points (6,0) and (-1,14)
Answer:
y = -2x + 12
Step-by-step explanation:
Hope this helps!!
Write the slope-intercept form of the equation of the line with the given characteristics. Perpendicular to y = -5x + 2 and passing through (3,-1).
The slope intercept form of a line can be expressed as,
[tex]y=mx+c[/tex]Here, m is the slope of the line and c is the y intercept.
Comparing the above equation with the given equation of a line y=-5x+2, we get
m=-5.
The slope of a line perpendicular to line with slope m is -1/m.
Hence, the slope of line perpendicular to y=-5x+2 is,
[tex]m_1=\frac{-1}{m}=\frac{-1}{-5}=\frac{1}{5}[/tex]The new line is given to be passing through point with coordinates (x1, y1)=(3, -1).
The point slope form of a line passing through point with coordinates (x1, y1)=(3, -1) and having slope m1 is,
[tex]\begin{gathered} y-y_1=m_1(x-x_1) \\ y-(-1)=\frac{1}{5}(x-3) \\ y+1=\frac{1}{5}x-\frac{3}{5} \\ y=\frac{1}{5}x-\frac{3}{5}-1 \\ y=\frac{1}{5}x-\frac{3-5}{5} \\ y=\frac{1}{5}x-\frac{8}{5} \end{gathered}[/tex]Therefore, the slope-intercept form of the equation of the line perpendicular to y = -5x + 2 and passing through (3,-1) is,
[tex]y=\frac{1}{5}x-\frac{8}{5}[/tex]1. Sketch the graph of y = x that is stretched vertically by a factor of 3. (Hint: Write the equation first, then graph) Sketch both y = x and the transformed graph.
ANSWER and EXPLANATION
We want to stretch the graph of:
y = x
A vertical stretch of a linear function is represented as:
y' = c * y
where c is the factor
The factor from the question is 3.
So, the new equation is:
y' = 3 * x
y' = 3x
Let us plot the functions:
Which equation is equivalent to StartRoot x EndRoot + 11 = 15?
Answer:
x+121=225
Step-by-step explanation:
√x+11=15
to find the equivalent let's square both sides
(√x)²+11²=15²
x+121=225
This answer is the only one that matches the question
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Find 164.4% of 289 round to the nearest tenths
Answer:
475.1
Step-by-step explanation:
Percent means per hundred so 164.4 % means [tex]\frac{164.4}{100}[/tex] When you divide by 100 you move the decimal 2 places to the left
1.644 x 289 = 475.116 This rounded to the nearest tenths is
475.1
cabrinha run 3/10 mile each day for 6 days how many miles did she run in off
3/10 mile per day for 6 days.
To find how many miles did she run multiply the miles per day by 6days:
[tex]\frac{3\text{mile}}{10\text{day}}\cdot6\text{days}=\frac{18}{10}\text{mile}=\frac{9}{5}\text{mile}[/tex]Then, in 6 days she run 9/5 mileFIRST OPTIONS ARE THE NUMBER OF CONVERTIBLES SOLD BY PLATO CARSTHE REVENUE FROM SALES OF CONVERTIBLE CARS BY PLATO CARSTHE REVENUE FROM SALES OF SEDANS BY PLATO CARSTHE TOTAL SALES REVENUE OF PLATO CARS SECOND OPTIONS 0.1070.2250.290.33
Given:
The number in the highlighted cell is 18.
The total sales revenue of pluto cars is 80.
To find the relative frequency from the sales of sedans by Plato cars to the total sales revenue of Plato cars:
The formula for relative frequency is,
[tex]\begin{gathered} RF=\frac{subgroup\text{ fr}equency}{\text{Total frequency}} \\ =\frac{18}{80} \\ =0.225 \end{gathered}[/tex]So, the relative frequency is 0.225.
Hence, the answer is,
The number in the highlighted cell is 18. The relative frequency from the sales of sedans by Plato cars to the total sales revenue of Plato cars is 0.225
What is the slope: (-2, 1) (5,-2)
Answer: slope = -3/7
Step-by-step explanation:
m(slope) = (y2-y1)/(x2-x1)
m = (-2+-1)/(5--2)
m = (-2-1)/5+2)
m = -3/7
(Score for Question 1: ___ of 5 points)1. Wendy wants to find the width, AB, of a river. She walks along the edge of the river 300 ft and markspoint C. Then she walks 80 ft further and marks point D. She turns 90° and walks until her location,point A, and point C are collinear. She marks point E at this location, as shown.AriverAD 80 ft300 ftBE(a) Can Wendy conclude that AABC and AEDC are similar? Why or why not?(b) Suppose DE = 50 ft Calculate the width of the river, AB. Show all your work.Answer
We know that two triangles are similar if two pairs of corresponding angles are equal.
In this case, we have:
• Angles EDC and ABC are right angles. Then, these angles are equal.
,• Angles DCE and ACB are ,vertical angles,. In other words, they are opposite angles made by two intersecting lines. Vertical angles are ,congruent,, then these angles are equal.
AnswerSince the above condition is fulfilled, triangles ABC and EDC are similar.
Part b)When two triangles are similar, their corresponding sides are in the same ratio.
[tex]\frac{a}{e}=\frac{b}{d}=\frac{c}{c^{\prime}}[/tex]Then, we can write and solve the following equation:
[tex]\begin{gathered} \frac{300ft}{80ft}=\frac{c}{50ft} \\ 3.75=\frac{c}{50ft} \\ \text{ Multiply by 50ft from both sides} \\ 3.75*50ft=\frac{c}{50ft}*50ft \\ 187.5ft=c \end{gathered}[/tex]AnswerThe width of the river is 187.5 feet.
What is the image point of (-12, —8) after the transformation R270 oD ?
Answer
(-12, -8) after R270°.D¼ becomes (-2, 3)
Explanation
The first operation represented by R270° indicates a rotation of 270° counterclockwise about the origin.
When a rotation of 270° counterclockwise about the origin is done on some coordinate, A (x, y), it transforms this coordinates into A' (y, -x). That is, we switch y and x, then add negative sign to x.
Then, the second operation, D¼ represents a dilation of the coordinate about the origin by a scale factor of ¼ given.
The coordinates to start with is (-12, -8)
R270° changes A (x, y) into A' (y, -x)
So,
(-12, -8) = (-8, 12)
Then, the second operation dilates the new coordinates obtained after the first operation by ¼
D¼ changes A (x, y) into A' (¼x, ¼y)
So,
(-8, 12) = [¼(-8), ¼(12)] = (-2, 3)
Hope this Helps!!!
9Which is the best name for a quadrilateral with vertices at A(5,-2), B(2,2), C(1,-5), and D(-2,-1)?A parallelogramB squarerhombusD rectangle
Parallelogram. Option A is correct
Explanations:In order to determine the best name for a quadrilateral with the given vertices, we will find the measure of the distance AB, BC, CD, and AD using the distance formula as shown;
[tex]D=\sqrt[]{(x_2-x_1)^2+(y_2-y^{}_1)^2}[/tex]For the measure of AB with coordinates A(5,-2), B(2,2);
[tex]\begin{gathered} AB=\sqrt[]{(5-2)^2+(-2-2^{}_{})^2} \\ AB=\sqrt[]{3^2+(-4)^2} \\ AB=\sqrt[]{9+16} \\ AB=\sqrt[]{25} \\ AB=5 \end{gathered}[/tex]For the measure of BC with coordinates B(2,2) and C(1, -5)
[tex]\begin{gathered} BC=\sqrt[]{(2-1)^2+(2-(-5^{}_{}))^2} \\ BC=\sqrt[]{1^2+7^2} \\ BC=\sqrt[]{50} \\ BC=5\sqrt[]{2} \end{gathered}[/tex]For the measure of CD with coordinates C(1,-5), and D(-2,-1);
[tex]\begin{gathered} CD=\sqrt[]{(1-(-2))^2+(-5-(-1^{}_{}))^2} \\ CD=\sqrt[]{3^2+(-4)^2} \\ CD=\sqrt[]{9+16} \\ CD=\sqrt[]{25} \\ CD=5 \end{gathered}[/tex]For the measure of AD with coordinates A(5, -2), and D(-2,-1);
[tex]\begin{gathered} AD=\sqrt[]{(5-(-2))^2+(-2-(-1^{}_{}))^2} \\ AD=\sqrt[]{(5+2)^2+(-2+1)^2} \\ AD=\sqrt[]{7^2+(-1)^2} \\ AD=\sqrt[]{50} \\ AD=5\sqrt[]{2} \end{gathered}[/tex]For the slopes;
Check if the length AB is perpendicular to AD
[tex]\begin{gathered} m_{AB}=\frac{2+2}{2-5} \\ m_{AB}=-\frac{4}{3} \end{gathered}[/tex]For the slope of AD
[tex]\begin{gathered} m_{AD}=\frac{-1+2}{-2-5} \\ m_{AD}=-\frac{1}{7} \end{gathered}[/tex]Since AB is not perpendicular to AD, hence the quadrilateral is not a rectangle and also not a square or rhombus since all the sides are not equal.
From the given distances, you can see that opposite sides are equal (AB = CD and BC = AD ), hence the best name for a quadrilateral is a parallelogram.
Hi I need help with this
how do i evaluate 8!4!/7!2!
Solution:
Consider the following expression:
[tex]\frac{8!4!}{7!2!}[/tex]Remember that The factorial function is defined by the product:
[tex]n!\text{ = }1\cdot2\cdot3\cdot\cdot\cdot\cdot\cdot\cdot(n-2)\cdot(n-1)\cdot n[/tex]thus, according to this definition, the given expression can be expressed as:
[tex]\frac{8!4!}{7!2!}\text{ = }\frac{(1\cdot2\cdot3\cdot4\cdot5\cdot6\cdot7\cdot8)\text{ (}1\cdot2\cdot3\cdot4\text{)}}{(1\cdot2\cdot3\cdot4\cdot5\cdot6\cdot7)(1\cdot2)}[/tex]now, simplifying the previous expression we obtain:
[tex]\text{= }(8)\text{ (}3\cdot4\text{) = }96[/tex]we can conclude that the correct answer is:
[tex]\text{ }96[/tex]A production applies several layers of a clear acrylic coat to outdoor furniture to help protect it from the weather. If each protective coat is 2/27 inch thick, how many applications will be needed to build up 2/3 inch of clear finish.
We know that
• Each protective coat is 2/27 inches thick.
,• We need to fill 2/3 inches of this protective coat.
To solve this problem, we need to know the total number of the application needed to fill 2/3 inches. We can form the following expression
[tex]\frac{2}{27}x=\frac{2}{3}[/tex]We solve for x
[tex]x=\frac{2\cdot27}{3\cdot2}=\frac{27}{3}=9[/tex]Therefore, we need 9 applications in total.You choose a marble from the bag. What is the probability you will NOT choose blue?1/25/72/72
Given a sample and required to get the probability of a particular outcome, we make a couple of considerations including:
- Sample Space: The universal set
- Required Outcome
We can identify these variables as:
Sample space: total number of marbles = 7
Required outcome: Not blue = 7 - 2 = 5
Probability is given as:
[tex]\begin{gathered} P=\text{ }\frac{\text{number of required outcome}}{Sample\text{ space}}=\frac{5}{7} \\ P=\frac{5}{7} \end{gathered}[/tex]The table shows a function. Is the function linear or nonlinear?x y0 1918 1200
By plotting the points, we get a non-linear function
Four more than three times a number, is less than 30. Which of the following is not a solution?61278
Solution
- To solve the question, we simply need to interpret the question line by line.
- Let the number be x.
- "Four more than three times a number" can be written as:
[tex]\begin{gathered} \text{ Three times a number is: }3x \\ \text{ For more than three times a number becomes: }4+3x \end{gathered}[/tex]- "Four more than three times a number is less than 30" can be written as:
[tex]4+3x<30[/tex]- Now, we can proceed to solve the inequality and find the appropriate range of x. This is done below:
[tex]\begin{gathered} 4+3x<30 \\ \text{ Subtract 4 from both sides} \\ 3x<30-4 \\ 3x<26 \\ \text{ Divide both sides by 3} \\ \frac{3x}{3}<\frac{26}{3} \\ \\ \therefore x<8\frac{2}{3} \end{gathered}[/tex]- This means that all correct solutions to the inequality lie below 8.666...
- This further implies that any number greater than this is not part of the solutions of the inequality.
- 12 is greater than 8.666
Final Answer
The answer is 12
Seventeen percent of people say they've seen a ghost or felt its presence. If 10 people are asked, what is the probability that at least two have seen a ghost or felt its presence?Round your answer to at least three decimals.
Answer: the probability that at least two have seen a ghost or felt its presence is 0.527
Explanation:
In this scenario, it is either a person asked has seen seen a ghost or felt its presence or they have not. These outcomes are independent of each other. Thus, it's a binomial distribution. We would apply the formula for calculating binomial probability which is expressed as
P(x) = nCx * p^x * q^(n - x)
where
p = probability of success
q = 1 - p = probability of failure
n = sample size
x = number of successes
From the information given, we are concerned with the people that say they've seen a ghost or felt its presence. Thus,
p = 17% = 17/100 = 0.17
q = 1 - 0.17 = 0.83
n = 10
x = 2
We want to find P(x ≥ 2)
P(x ≥ 2) = 1 - [P(x = 0) + P(x = 1)
P(x = 0) = 10C0 * 0,17^0 * 0.83^(10 - 0) = 0.1552
P(x = 1) = 10C1 * 0,17^1 * 0.83^(10 - 1) = 0.3178
P(x ≥ 2) = 1 - (0.1552 + 0.3178) = 1 - 0.473
P(x ≥ 2) = 0.527
the probability that at least two have seen a ghost or felt its presence is 0.527
The sides of an L-shaped figure meet all the right angles
ANSWER:
24 ft²
STEP-BY-STEP EXPLANATION:
To determine the area of the figure, we must divide the L-shaped figure into two rectangles just like this:
We calculate the area of each rectangle and the sum of both areas would be the area of the L-shaped figure, in the following way:
[tex]\begin{gathered} A_1=L\cdot W=6\cdot2=12\text{ ft}^2 \\ \\ A_2=L\cdot W=3\cdot4=12\text{ ft}^2 \\ \\ \text{ Therefore:} \\ \\ A_t=A_1+A_2=12+12 \\ \\ A_t=24\text{ ft}^2 \end{gathered}[/tex]The area of the L-shaped figure is equal to 24 ft².
Find the sum of the arithmetic series 31+37 +43 +49 +... where n=8,OA. 416B. 1668OC. 832D. 834Reset Selection
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given details
[tex]\begin{gathered} a_1=31 \\ n=8 \\ d=37-31=6 \end{gathered}[/tex]STEP 2: Write the formula for finding sum of arithmetic series
STEP 3: Find the sum of the series
By substitution,
[tex]\begin{gathered} S_8=\frac{8}{2}[2(31)+(8-1)6] \\ S_8=4(62+42) \\ S_8=4(104)=416 \end{gathered}[/tex]Hence, the sum is 416
Directions:For questions 12-16 simplify using the given replacement valued. There should be no decimals, convert all decimals to fractions. (Do not change whole numbers)I need help with 14
14. Given:
[tex]\frac{3}{2}r-rs+4,r=\frac{6}{7},s=\frac{2}{3}[/tex]Substitute the value of r and s in the given problem.
We get,
[tex]\begin{gathered} \frac{3}{2}(\frac{6}{7})-(\frac{6}{7})(\frac{2}{3})+4=3(\frac{3}{7})-(\frac{2}{7})(2)+4 \\ =\frac{9}{7}-\frac{4}{7}+4 \\ =\frac{5}{7}+4 \\ =\frac{33}{7} \end{gathered}[/tex]Hence, the answer is
[tex]\frac{33}{7}[/tex]