3. (06.01)The tables below show four sets of data:Set Ax123456789y1098765432Set Bx123456789y34567891011Set Cx123456789y86543.532.522Set Dx123456789y12.52.5345689For which set of data will the scatter plot represent a negative linear association between x and y? (4 points)Set ASet BSet CSet D
Answers
For the given sets of data will the scatter plot represent a negative linear association between x and y
The negative linear means as (x) increase (y) will decrease, this means a neagive slope of the line of the realtion between (x) and (y)
As shown for the given tables
Set B and Set D both (x) and (y) increase
And for set C as x increase y will decrease but with not a linear association
So, the answer will be Set A
Related Questions
help how to answer 4 how to find x and y
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Since:
[tex]\Delta ABC\cong\Delta DEF[/tex]We can use CPCTC ( Corresponding parts of congruent triangles are congruent) so:
[tex]\begin{gathered} m\angle A=m\angle D \\ 60=5y \\ so\colon \\ y=\frac{60}{5} \\ y=12 \end{gathered}[/tex][tex]\begin{gathered} 6x-4=3x+26 \\ 6x-3x=26+4 \\ 3x=30 \\ x=\frac{30}{3} \\ x=10 \end{gathered}[/tex]Label the image correctly (some of the choices are wrong) : True False 4-3-6-4Increasing DecreasingSlope is =Slope is equal to = (make sure you simplify)True or False the line passes through the origin ?
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To solve the exercise, you can take the two points highlighted on the graph and use the slope formula
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \text{ Where} \\ (x_1,y_1),(x_2,y_2)\text{ are two points }through\text{ which the line passes and} \\ m\text{ is the slope of the line} \end{gathered}[/tex]So, if you take
[tex]\begin{gathered} (x_1,y_1)=(-4,2) \\ (x_2,y_2)=(4,-4) \end{gathered}[/tex]the slope of the line will be
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{-4-2}{4-(-4)} \\ m=\frac{-6}{4+4} \\ m=\frac{-6}{8} \\ \text{ Simplifying} \\ m=\frac{2\cdot-3}{2\cdot4} \\ m=\frac{-3}{4} \end{gathered}[/tex]Now, with the point slope equation you can write the equation of the line in its slope-intercept form
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ \text{ Where }(x_1,y_1)\text{ is one point through which the line passes} \end{gathered}[/tex]So, if you take the point (-4,2) you have
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-2=\frac{-3}{4}(x-(-4)) \\ y-2=\frac{-3}{4}(x+4) \\ y-2=\frac{-3}{4}x-\frac{3}{4}\cdot4 \\ y-2=\frac{-3}{4}x-3 \\ \text{ Add 2 on both sides the equation} \\ y-2+2=\frac{-3}{4}x-3+2 \\ y=\frac{-3}{4}x-1 \end{gathered}[/tex]Then, the equation of the line in its slope-intercept form is
[tex]y=-\frac{3}{4}x-1[/tex]And to find out if the line passes through the origin, plug x = 0 into the equation found
[tex]\begin{gathered} y=-\frac{3}{4}x-1 \\ y=-\frac{3}{4}(0)-1 \\ y=0-1 \\ y=-1 \end{gathered}[/tex]That means that the line passes through the point (0, -1) and not through the point (0,0). Therefore, the line does not pass through the origin, and the answer is False.
Finally, since the slope of the line is negative, then the line is decreasing.
Jack just took out a $3,000 loan for a new snowmobile. The simple interest rate on his loan is 40% per year after 4 months how much interest will be charged ?
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The amount of interest that wil be charged after 4 months is $400
Here, we want to calculate the amount of interest that will be charged.
To get this, we simply use the simple interest formula
Mathematically;
[tex]\begin{gathered} \text{simple interest = }\frac{p\text{ }\times\text{ r}\times t}{100} \\ \\ \text{where P is the amount borrowed which is 3,000} \\ \\ r\text{ is the interest rate which is 40\%} \\ \\ t\text{ is the time which is 4 months; we express this as 4/12 = 1/3} \\ \\ \text{Substituting these values, we have;} \\ \\ \text{simple interest = }\frac{3000\text{ }\times40\text{ }\times\frac{1}{3}}{100\text{ }}\text{ = }\frac{1000\text{ }\times\text{ 40}}{100}\text{ = 400} \end{gathered}[/tex]Kerri made 27 of 40 shots. What percentage of shots did she make?
Answers
40 represent 100%
27 represent x
x is the percentage of shots
x can be calculated in the next way
[tex]x=\frac{27\cdot100}{40}=67.5[/tex]the answer is 67.5 %
Please help me I don’t understand this concept on number 4
Answers
This is an example of property tax. This is because he is paying a tax for a property he owns, which is his house.
So the correct answer is option H. Property
I need help finding the five-number summary of the given numbers
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We are given the following numbers
3 8 8 4 2 9 8 7 9 5 9 3 2 5 2 9 8 7 7 9
to calculate the five number summary, it means that we should calculate the following numbers:
- minimum
- percentile 25
- median (or percentile 50)
- quantile 75
- maximum
So, we should first sort this numbers from least to greatest, so it is easier to identify this five numbers. Once sorted we get the following numbers:
2 2 2 3 3 4 5 5 7 7 7 8 8 8 8 9 9 9 9 9
From this arrangement, we can see that the least number (or minimum) is 2 and the greatest number (or maximum) is 9.
Now we need to identify the percentiles 25, 50 and 75.
To calculate this numbers, we must first count the number of data points we have. Once we do so, we get that we have 20 elements.
Now, the term percentile 50 means that we are finding a point such that 50% of the data (the half) is on both sides of the number.
So, since we have 20 data points, we must find a number that splits the data in a way such that 10 points are less than or equal to the number and 10 points are greater than or equal to the number.
So, first, we count 10 numbers from left to right. The 10th number in the sorted sequence is 7, and the 11th number is also 7. So, the number that we are looking for is the average of this two numbers. So we get
[tex]\frac{7+7}{2}=7[/tex]So the percentile 50 is 7.
Now, we need to find the percentile 25 and percentile 75.
The percentile 25 is the number such that 25% of the data is less than or equal to this number.
Note that since we have 20 data points. The 25% of 20 is 5. That is, we should find a number such data 5 data points is on the left of the number and 15 numbers are on the right of the number. If we count 5 numbers, we get the number 3. The 6th number is 4. So, the number we are looking for should be inbetween 3 and 4. ONe way to find this number is to take a weighted average of this numbers. Since we are looking for the percentile 25, we will give a weight of 0.25 to 3 and 0.75 to 4. Then the percentile 25 would be
[tex]0.25\cdot3+0.75\cdot4\text{ =3.75}[/tex]In the same manner, to find the percentile 75, we first identify the 15th and 16th numbers. In this case, the 15th number is 8 and the 16th number is 9. Since we want the percentile 75, we give a weight of 0.75 to 8 and a weight of 0.25 to 9. Then we get
[tex]0.75\cdot8+0.25\cdot9\text{ = 8.25}[/tex]Then, the percentile 75 is 8.25.
Then, the five summary of the data is
- minimum : 2
- percentile 25 : 3.75
- median (or percentile 50): 7
- quantile 75: 8.25
- maximum: 9
Select the correct answer.Convert X = 4 to polar form.O A.r4sinoO B.cos4C.4cosO D.= 4O E.4T =sece
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To convert a rectangular equation in polar form you use the next equations:
[tex]\begin{gathered} x=r\cdot\cos \theta \\ y=r\cdot\sin \theta \end{gathered}[/tex]As the given rectangular equation is x=4 use the first equation and substituthe the x by 4, then solve r:
[tex]\begin{gathered} 4=r\cdot\cos \theta \\ r=\frac{4}{\cos \theta} \end{gathered}[/tex]Then, the correct answer is the option C.
1.Noah has a coupon for 30% off at his favorite clothing store. He uses it to buy a hoodieand a part of jeans.Noah paid $28 for the jeans after using the coupon.If the regular price of an item is x dollars and the item is 30% off, how wouldyou find the new price?
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Step 01:
coupon = 30% off
Step 02:
how to solve this question 3x+7x+1=2(5x+1)+2
Answers
Answer:
The equation has no real solution
Explanation:
Given the equation;
[tex]3x+7x+1=2(5x+1)+2[/tex]Let us simplify the two sides of the equation;
[tex]\begin{gathered} 3x+7x+1=2(5x+1)+2 \\ 10x+1=2(5x)+2(1)+2 \\ 10x+1=10x+2+2 \\ 10x+1=10x+4 \\ 10x=10x+3 \end{gathered}[/tex]Therefore, the equation has no real solution
convert the equation into vertex form, then solve the equation x^2 + 6x + 8 = 0
Answers
The Vertex form of a Quadratic function is:
[tex]f(x)=a\mleft(x-h\mright)^2+k[/tex]Where the vertex of the paraboola is:
[tex](h,k)[/tex]Given the following Quadratic equation:
[tex]x^2+6x+8=0[/tex]You need to convert it into Vertex form by completing the square. The steps are shown below:
- Identify the coefficient of the term with the variable "x". In this case, this is:
[tex]b=6[/tex]- Divide it by 2 and square it:
[tex](\frac{b}{2})^2=(\frac{6}{2})^2=3^2[/tex]- Add and subtract the number obtained (in the right side of the equation):
[tex]x^2+6x+8+3^2-3^2=0[/tex]- Order it and express it as a square of a binomial, you get:
[tex]\begin{gathered} (x^2+6x+3^2)+8-3^2=0 \\ (x+3)^2-1=0 \end{gathered}[/tex]- Add 1 to both sides of the equation:
[tex]\begin{gathered} (x+3)^2-1+1=0+1 \\ (x+3)^2=1 \end{gathered}[/tex]To solve the equation you must take the square root of both sides of the equation:
[tex]\begin{gathered} \sqrt[]{(x+3)^2}=\pm\sqrt[]{1} \\ \\ x+3=\pm1 \end{gathered}[/tex]Finally, subtract 3 from both sides of the equation:
[tex]\begin{gathered} x+3-3=\pm1-3 \\ \\ x=-3\pm1 \\ \\ x_1=-3+1=-2 \\ x_2=-3-1=-4 \end{gathered}[/tex]The answer is:
- Vertex form:
[tex](x+3)^2=1[/tex]- Solutions:
[tex]\begin{gathered} x_1=-2 \\ x_2=-4 \end{gathered}[/tex]in the figure, assume that angles that appear to be right angles are right angles.what is the area of the figure?use 3.14 for pi.the approximate area is ___ square units.
Answers
The figure is divided into a semi circle and a trapezium. Thus, the area of the figure would be the sum of the area of the semicircle and the trapezium
The formula for finding the arae of a semicircle is expressed as
Area = 1/2 x pi x radius^2
From the figure,
radius = 3
pi = 3.14
Area of semicircle = 1/2 x 3.14 x 3^2
Area of semicircle = 14.13
The formula for finding the arae of a trapezium is expressed as
Area = 1/2(a + b)h
where
a and b are the length of the top and bottom
h is the height
From the figure,
a = 8, b = 11, h = 6
Area = 1/2(8 + 11)6
Area = 1/2(19)6
Area of trapezium = 57
Thus, the area of the figure is
14.13 + 57
= 71.13
Rounding to the nearest whole number,
the approximate area is 71 square units
2p The height of a ball Doreen tossed into the air can be modeled by the function h(x)= -4.9x^2 +6x + 5, where x is the time elapsed in seconds, and h(x) is the height in meters. The number 5 in the function represents O (1) the initial height of the ball (2) the time at which the ball reaches the ground O (3) the time at which the ball was at its highest point O (4) the maximum height the ball attained when thrown in the air
Answers
Answer:
(1) the initial height of the ball
Explanation:
The initial height of the ball can be found by putting x = 0 into the equation given. This gives
[tex]\begin{gathered} h(0)=-4.9(0)^2+6(0)+5 \\ h(0)=5. \end{gathered}[/tex]Therefore, we conclude that 5 in the equation represents the initial height of the ball.
Find the real numbers that satisfy the equation below. Express your answer in set-builder notation
Answers
We will have the following:
The values that satisfy the expression are:
[tex]x\ge0[/tex]Check all of the values that have three significant figures. A. 0.690B. 356C. 5.03D. 1408
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we have the following:
0.690, has 3 significant figures
356,
Identify whether each formula defines a rational function. If so, identify two polynomials whose ratio comprises it.
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Given the function below
[tex]k(t)=\frac{4}{t+1}-\frac{3}{t^2}[/tex]A rational function is a fraction where both numerator and denominator are polynomials, i.e
[tex]\begin{gathered} k(t)=\frac{4}{t+1}-\frac{3}{t^2} \\ k(t)=\frac{4t^2-3(t+1)}{t^2(t+1)} \\ k(t)=\frac{4t^2-3t-3}{t^2(t+1)} \end{gathered}[/tex]From the above deduction, both numerator and denominator are polynomials.
Hence, the given expression is a rational function.
The two polynomials whose ratio comprises the given rational function are
The numerator
[tex]4t^2-3t-3[/tex]And the denominator
[tex]t^2(t+1)[/tex]A data set is normally distributed with a mean of 18 and astandard deviation of 2.7. Approximately what percent of the data are greaterthan 12.6?
Answers
Solution:
Given;
[tex]x=12.8,\mu=18,\sigma=2.7[/tex]The z-score is;
[tex]\begin{gathered} z=\frac{x-\mu}{\sigma} \\ \\ z=\frac{12.8-18}{2.7} \\ \\ z=-1.9259 \end{gathered}[/tex]Thus, the approximate percent of the data greater than 12.6 is;
[tex]P(x>12.8)=97.5\text{ \%}[/tex]ANSWER: 97.5%
Do not mind the line I didn’t mean to put that there.
Answers
Answer:
55
Explanation:
Given the expression:
[tex]13+23+12+7[/tex]First, introduce parentheses as follows:
[tex]=13+[(23+12)+7][/tex]Apply the commutative property of addition: 23+12 = 12+23
[tex]=13+[(12+23)+7][/tex]Next, apply the associative property of addition: (12+23)+7=12+(23+7).
[tex]\begin{gathered} =13+[12+(23+7)] \\ =13+[12+30] \end{gathered}[/tex]We can then simplify further:
[tex]=13+42[/tex]By the commutative property of addition: 13+42=42+13
[tex]\begin{gathered} =42+13 \\ =55 \end{gathered}[/tex]The value of the given expression is 55.
ABCD and EFGH are quadrilaterals. GivenABCD – EFGH, describe a sequence of rigidmotions followed by a dilation with center (0,0)that maps ABCD to EFGH. Describe the sequence. Select the correctchoice below and fill in the answer boxes tocomplete your choice.
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
quadrilaterals
ABCD ===> EFGH
sequence = ?
Step 02:
We must analyze the graph to find the correct sequence.
1 . ABCD
reflection y-axis
(x , y) ===> (-x, y)
A ( 2, 0) ===> (-2 , 0)
B (4 , 3) ===> (-4 , 3)
C (2 , 4) ===> (-2 , 4)
D (0 , 3) ===> (0 , 3)
2. translation
letf ===> 6 units
down ===> 8 units
3. dilation
scale factor ===> 1.25
8 * x = 10
x = 10 / 8 = 5 / 4 = 1.25
That is the full solution.
Solve for x3x^2 +2x -5=0
Answers
3x^2 + 2x -5 =0
We can factor this function
( 3x +5) ( x-1) =0
Using the zero product property
3x+5 =0 x-1 =0
3x =-5 x=1
x = -5/3 x=1
X=1
Imagine you are the lead engineer building a freeway. You are able to get yourasphalt from 2 suppliers, Company A and Company B. Company A uses themetric system of measurement and sells their asphalt for a total of $3.85 permeter. Company B measures in the Imperial system and offers their asphalt for atotal of $1.33 per foot. Which company offers the better value deal based onprice?(1 foot = 0.3 meters)
Answers
The first company offers the better value deal based on price
Here, we want to compare the prices from the two companies
We can have the unit in the same system
For the first company, we have a price of $3.85 per meter
We want to convert this price to per foot
From the conversion;
1 foot = 0.3 meters
Thus;
[tex]\begin{gathered} 10\text{ foot = 3 meters} \\ or\text{ 1 meter = }\frac{1}{0.3\text{ }}\text{ fe}et \\ \\ \text{Thus;} \\ 3.85\text{ per meter will be} \\ 3.85\text{ divided by }\frac{1}{0.3} \\ \\ =\text{ 3.85 }\times\frac{0.3}{1} \\ =\text{ 1.155} \end{gathered}[/tex]So, for the first company, the price per foot is $1.155
As we can see, this is lesser than what the second company charges
Thus, the first company offers the better value deal based on price
Prescription for Marilyn JonesPiroxicam 20 milligrams (mg) capsules: take 1 capsule 2 times a dayGlucotrol 2.5 milligrams (mg) tablets: take 1 tablet every morningIsoniazid 100 milligrams (mg) tablets: take 1 tablet 3 times a dayHow many tablets should the pharmacy give Marilyn to fill the Isoniazid for 45 days?
Answers
Let:
a = tablets per day
x = Number of days
y = Total tablets
so:
[tex]\begin{gathered} y=ax \\ where \\ a=3 \\ x=45 \\ so\colon \\ y=3\cdot45 \\ y=135 \end{gathered}[/tex]Answer:
135 tablets
I need help on showing work but it can’t be substitution! :(
Answers
(x - 5)^2 = 81
x^2 - 10x + 25 = 81
x^2 - 10x -56 = 0
The equation of bhaskara is
[tex]x=\frac{-b\text{ }\pm\sqrt[]{b^2-4ac}}{2a}[/tex]In this case, we have, a = 1, b = -10 and c = -56
Therefore:
[tex]x_+=\frac{10\text{ +}\sqrt[]{100+4\cdot56}}{2}=14_{},x_-=\text{ }\frac{10-\sqrt[]{100+4\cdot56}}{2}=\text{ -4}[/tex]ADB ВIf m2ABC = 25°, and m2CBD = 35°,then m ABD = [ ? 1°
Answers
m∠ABD = 60°
Explanation:m∠ABC = 25°
m∠CBD = 35°
From the diagram:
m∠ABC + m∠BCD = m∠ABD
[tex]\begin{gathered} m\angle ABD\text{ = 25 + 35} \\ \angle ABD\text{ = 60}\degree \end{gathered}[/tex]what is the simplified expression for 17.4x+0.8+6x+17.4r+0.8+bx
Answers
You have the following algebraic expression:
17.4x+0.8+6x+17.4r+0.8+bx
In order to simplfy the previous expression, you take into account that you only can sum similar terms. In this case you sum terms with variable x and independet coefficients, just as follow:
17.4x+0.8+6x+17.4r+0.8+bx
= ( 17.4x + 6x + bx ) + (0.8 + 0.8) + 17.4r
= 23.4x + bx + 1.6 + 17.4r
The last expression is the simplified expression.
The graph of y = f’(×), the derivative of f(x), is shown below. List the intervals where the graph of f is increasing.
Answers
The graph of derivative of the function is given.
Required
The intervals where the function is increasing.
ExplanationTo determine the function is increasing, the derivative of the function should be greater than zero.
From the given graph it is clear that the derivative of the function is greater than zero for the interval
[tex](0,4)[/tex]AnswerHence the function is increasing in the interval (0,4).
The correct option is D.
#8Ed earned $183.75 for 15 hours or work. At this rate, how many hours didhe work to earn a paycheck of $465.50?OA 38 hoursOB 12 hoursOC 31 hoursOD 45 hours
Answers
Explanation
you can easily solve this by using a rule of three.
Step 1
Let
x represents the hours he has to work for earn 465.50
then
if
[tex]\begin{gathered} 15\text{ hours}\rightarrow183.75 \\ x\text{ hours}\rightarrow465.5 \end{gathered}[/tex]the proportions or wage per hour is the same so,
[tex]\frac{15}{183.75}=\frac{x}{465.5}[/tex]Step 2
finally, solve for x
[tex]undefined[/tex]Given: points A(5, 1), B(5,5), C(1,3), Q(-6,-5) and R(-4,-5). What coordinates for S would prove AABC~AQRS (T.G.7)(2 point) B с QR O A. (-4,-3) O B. (-5,-8) O C. (-3,-5) o D. (-5,-3)
Answers
Given:
A(5, 1), B(5, 5), C(1, 3)
Q(-6, 5), R(-4, -5), S(__, __)
To find the coordinates of S that would prove that ABC is similar to QRS, we have:
First Find the distance betweem AB and the distance between QR using the distance formula below:
[tex]\begin{gathered} D=\sqrt[]{(x2-x1)^2+(y2-y1)^2} \\ \end{gathered}[/tex]Distance between AB:
[tex]\begin{gathered} AB=\sqrt[]{(5-5)^2+(5-1)^2} \\ \\ AB=\sqrt[]{0+16} \\ \\ AB\text{ = 4} \end{gathered}[/tex]Distance between QR:
[tex]\begin{gathered} QR=\sqrt[]{(-4--6)^2+(-5-}-5)^2 \\ \\ QR=\sqrt[]{(-4+6)^2+(-5+5)^2} \\ \\ QR\text{ = }\sqrt[]{(2)^2+(0)^2} \\ \\ QR=\sqrt[]{4} \\ \\ QR\text{ = 2} \end{gathered}[/tex]Since ABC is similar to QRS, we have:
AB ~ QR
AB = 4
QR = 2
The scale factor is:
[tex]\frac{AB}{QR}=\frac{4}{2}=2[/tex]Since the scale factor is 2, Let's find the coordinates of S:
Find the distance between BC and AC .
Thus, we have:
The coordinates of S that would prove that ABC is similar to QRS is:
(-3, -5)
Choice C is correct
ANSWER:
C. (-3 -5)
What is the equation of the line that passes through the point (6,-3) and has aslope of – 3?
Answers
Answer:
Explanation:
An equation for a line in slope-intercept form is given by
[tex]y=mx+b[/tex]where m is the slope and b is the y-intercept.
Now, we are given that slope m = -3; therefore, we have
[tex]y=-3x+b[/tex]Now we only need to find the y-intercept b.
Luckily, we know that the line passes through the point (6, -3), meaning the above equation must satisfy x = 6, y = -3.
Putting in x = 6 and y= -3 in the above equation gives
[tex]-3=-3(6)+b[/tex][tex]-3=-18+b[/tex]Adding 18 to both sides of the equation gives
[tex]-3+18=-18+b+18[/tex][tex]-3+18=b[/tex][tex]15=b[/tex]Hence, the value of b is 15, and therefore, the equation of the line is
[tex]\boxed{y=-3x+15}[/tex]The admission fee at an amusement park is 1.5 dollars for children and 4 dollars for adults. On a certain day, 282 people entered the park, and the admission fees collected totaled 748 dollars. How many children and how many adults were admitted? Your answer is number of children equals number of adults equals Submit Question M
Answers
We have to calculate the number of children (C) and the number of adults (A) that were admitted.
The number of people, that is the sum of the children and the adults, is 282. Then, we can write:
[tex]C+A=282[/tex]The ticket collection was $748, where each children pay $1.5 and each adult pays $4. Then, we can write:
[tex]1.5\cdot C+4\cdot A=748[/tex]Now, we have a system of 2 equations with 2 unknowns. We can solve it by substitution, using:
[tex]A=282-C[/tex][tex]\begin{gathered} 1.5C+4A=748 \\ 1.5C+4\cdot(282-C)=748 \\ 1.5C+4\cdot282-4\cdot C=748 \\ -2.5C+1128=748 \\ -2.5C=748-1128 \\ -2.5C=-380 \\ C=\frac{-380}{-2.5} \\ C=152 \end{gathered}[/tex]Now that we know the number of children C, we can calculate the number of adults A as:
[tex]A=282-C=282-152=130[/tex]Answer:
Number of children = 152
Numbre of adults = 130
5. Terrence makes $10 per hour at his job. This week he also earned a $30 bonus. What isthe fewest number of hours he must work this week in order to earn at least $245?
Answers
Equations
Terrence earns $10 per hour plus a weekly bonus of $30.
The total earnings can be expressed as a function:
y = 10x + 30
Where y is the total earnings and x is the number of hours Terrence works.
We need to find the number of hours needed for Terrence to make at least $245 this week, that is:
[tex]10x+30\ge245[/tex]Subtracting 30:
[tex]10x\ge245-30[/tex]Operating:
[tex]10x\ge215[/tex]Dividing by 10:
[tex]x\ge21.5[/tex]Assuming the number of hours cannot be decimal, the next integer is the solution.
Terrence must work 22 hours to earn al teast $245