Answers
1) The Linear equation that models the average price of a new home is;
y = -800x + 294000.
2) The prediction of the average price of a new hom in the year 2014 is; $256000
How to solve the equation in slope intercept form?We are told that the average price in the year 2004 was $294000
We are told that y is the average price in a home in the year x, where x = 0 represents the year 2004. Thus, this means that the y-intercept is $294000.
Since the line must pass through the points (0, 294000) and (7, 288400), it means that;
Slope = (288400 - 294000)/(7 - 0)
Slope = -5600/7
Slope = -800
Now, we know that the general formula for equation in slope intercept form is; y = mx + c
where; m is slope and c is y-intercept.
Thus;
1) Linear equation is; y = -800x + 294000.
2) For the average price of a new home in the year 2014, this means that x = 2014 - 2004 = 10 years
Thus;
y = -800(10) + 294000
y = $256000
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Related Questions
Use the number line to find the coordinate of the midpoint of
¯¯¯¯¯
J
P
.
Answers
Answer: -1
Step-by-step explanation:
The midpoint of a segment is the same as the average of the coordinates of the endpoints. So, the midpoint is [tex]\frac{-7+5}{2}=-1[/tex].
Find the difference between 3 /5 of 125 and 5/8 of 144
Answers
The answer to this question will be 15.
3/5 of 125 = 3/5 x 125 = 75
5/8 of 144 = 5/8 x 144 = 90
So, 5/8 of 144 - 3/5 of 125 = 90 - 75 = 15
The difference between 3/5 of 125 and 5/8 of 144 is 15.
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Determine whether each sample method is unbiased or biased. If the method is unbiased, use it to make a prediction. If the method is biased, explain why. 1. A cable company representative randomly calls 250 households to determine how many customers subscribe to the movie channels. Of the 250 households contacted, 22% do not subscribe to movie channels. If there are 5,240 customers, how many do not subscribe to movie channels.
Answers
The representative took a sample to estimate the proportion of customers that do not subscribe to movie channels.
He took a sample from the customer base and the sample proportion he gets is 22% (p = 0.22). This sample proportion is an unbiased estimator of the populations proportion, so we can use it to calculate how many customers do not subscribe to movie channels:
[tex]n=N\cdot p=5240\cdot0.22\approx1153[/tex]Answer: we can estimate that there are 1153 customers that do not subscribe to movie channels.
A tree trunk may be considered a circular cylinder.
Suppose the diameter of the trunk increases 1 inch per
year and the height of the trunk increases 6 inches per
year. How fast is the volume of wood in the trunk
increasing when it is 100 inches high and 5 inches in
diameter?
Answers
The volume of the tree trunk increases 52.64% in one year.
Given,
The height of a tree trunk = 100 inches
The diameter of a tree trunk = 5 inches
Diameter increases 1 inch per year
Height increases 6 inches per year
We have to find the increase in its volume.
Consider the trunk as a circular cylinder.
Volume of circular cylinder = πr²h
Radius, r = 5/2
Height, h = 100
Initial Volume = πr²h
Volume = π × (5/2)² × 100 = π × 6.25 × 100 = 1963.50 cubic inches
After one year
Diameter = 6
Height = 106
Increased Volume = πr²h
Volume = π × (6/2)² × 100 = π × 9 × 106 = 2997.08 cubic inches
The rate of increase in volume = (Increased volume × 100) ÷ Initial volume
= (2997.08 × 100) ÷ 1963.50 = 152.64
That is,
The volume of the tree trunk increases 52.64% in one year.
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Here are the recorded temperatures at the different times on a winter evening
Answers
ANSWER
Tyler was right
EXPLANATION
To answer the question, we have to find the rate at which the temperature dropped between 4pm - 6pm and 6pm - 10pm
By 4pm, the temperature was 25°F and by 6pm, the temperature was 17°F.
The temperature difference is:
T = 17 - 25 = -8°F
There are 2 hours between 4 and 6 pm.
Now, we divide by the number of hours that elapsed:
[tex]\text{Rate = }\frac{-8}{2\text{ hours}}\text{ =}-4\degree F\text{ / hr}[/tex]By 6 pm the temperature was 17°F and by 10pm, the temperature was 8°F.
The temperature difference is:
T = 8 - 17 = -9°F
There are 4 hours between 6 and 10 pm.
Now, divide by the number of hours that elapsed:
[tex]\text{Rate = }\frac{-9}{4}\text{ = }-2.25\degree F\text{ / hr}[/tex]As we can see, the rate at which the temperature dropped between 4pm and 6 pm is more (since it became colder at a faster rate during that period)
Therefore, Tyler was right.
Plant A is 2 inches tall and is growing
at 14 inches per week. Plant B is 12
inches tall but is only growing at
inch per week. How many weeks will it
take for Plant A to be the same height
as Plant B?
Answers
It will take Plant A 5 days to be the same height as Plant B and this can be calculated through unitary method of mathematical calculation.
Unitary Method: What is it?The unitary technique used in here involves at first determining the value of a particular single unit, that is thus followed by the value of the necessary number of units.
What is an example of a unitary method?A single or type of a distinct unit is referred to by the word of unitary.
Therefore, the goal of this strategy is to establish values in reference to a single unit.
The unitary technique, for instance, can be used to calculate how many kilometers a car will go on one liter of gas if it travels 44 km on two liters of fuel.
Plant A initial height = 2 inches
Growth rate = 14 inches/ week
= 2 inches/ day
Plant B initial height = 12 inches
Growth rate = 1 inch/ week
After 5 days we can see that plant A will be
2 + (5 x 2) = 12 inches
this is the same height as that of Plant B.
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Find the common ratio and write out the first four terms of the geometric sequence (1.06)n−1 Common ratio is a1= a2= a3= a4=
Answers
Solution
Step 1
Write the nth term ex[pression and the common ratio formula.
[tex]\begin{gathered} T_n\text{ = \lparen1.06\rparen}^{n-1} \\ Common\text{ ratio = }\frac{2^{nd}term}{1^{st}term} \end{gathered}[/tex]Step 2
[tex]\begin{gathered} T_1\text{ = \lparen1.06\rparen}^{1-1}\text{ = 1} \\ T_2\text{ = \lparen1.06\rparen}^{2-1}\text{ = 1.06} \\ T_3\text{ = \lparen1.06\rparen}^{3-1}\text{ = \lparen1.06\rparen}^2\text{ = 1.1236} \\ T_4\text{ = \lparen1.06\rparen}^{4-1}=\text{ \lparen1.06\rparen}^3\text{ = 1.191016} \end{gathered}[/tex]Step 3
[tex]Common\text{ ratio r = }\frac{1.06}{1}\text{ = 1.06}[/tex]Final answer
A manufacturer of kitchen utensils and gadgets is considering changing the design of their salt and pepper shakers. Their current design is a standard cylinder, while the new design they are considering is an oblique cylinder. The figure shows both designs.Which set of additional details are the minimum required to ensure the new design will have the same volume as the original design?A. The heights of both designs must be the same, and at least one cross-section taken at the same height on both designs must have the same area.B. The heights of both designs must be the same, the base areas of both designs must be the same, and each cross-section taken at the same height on both designs must have the same area.C. The heights of both designs must be the same, and the base areas of both designs must be the same.D. The heights of both designs must be proportional, the base areas of both designs must be proportional, and each cross-section taken at the same height on both designs must have the same radius.
Answers
1) In this problem, we need to keep in mind the formula for the volume of one cylinder:
[tex]V=\pi r²h[/tex]Or in other words, the base area (area of a circle) times the height.
2) Since the point here is not to lose capacity (volume) the new design must keep its base areas as well as their height, so examining the answers we can tell that the answer is:
[tex]C[/tex]
These are the minimum requirements
If a running back runs 28 yards in the first quarter, how many yards can you expect him to gain
throughout the game?
Answers
Answer:
112 yards
Step-by-step explanation:
quarter is 1/4 right¿
28 × 4 = 112
Statically question
Answers
Answer: We have to select the statistical questions out of the given options,
the statistical questions are any questions that involve the use of data, therefore following options are the statistical questions:
[tex]\begin{gathered} \text{ Following Options:} \\ \\ (1)\text{ \lparen2\rparen and }(4) \end{gathered}[/tex]Therefore (1) (2) and (4) use the data, they are the statistical questions.
|4x - 5| = 8A. x= 13/4 or x= -3/4B. x= 3/4 or x= -13/4C. x= 13/4 onlyD. no solutionE. infinitely many solutions
Answers
We will solve this problem thus:
[tex]\begin{gathered} \lvert4x-5\rvert=8 \\ \text{means} \\ 4x-5=+8\text{ or 4x-5= -8} \end{gathered}[/tex]Solving further we will have:
[tex]\begin{gathered} 4x=8+5\text{ or 4x=-8}+5 \\ 4x=13\text{ or 4x = -3} \\ x=\frac{13}{4}\text{ or x=}\frac{-3}{4} \\ \text{The correct answer is option A} \end{gathered}[/tex]pls help 9th grade geometry
Answers
Answer:
< 6 = 58°
< 8 = 58°
< 5 = 122°
<7 = 122°
Step-by-step explanation:
<6 = <8 because corresponding angles are equal
5y + 13 = 7y -5 Subtract 5 y from both sides
13 = 2y -5 Add 5 to both sides
18 = 2y
9 = y
Now that we know that y = 9, we plug it back into either equation
5y + 13
5(9) + 13
45 + 13
58
<5 is supplemental to <6 so 180 - 58 = 122
<8 is supplemental to < 7 so it is 122 also
the sum of -5 and six times a number
Answers
Six times menas multiply by six:
a number = x
The sum of -5 and six times a number
-5 + 6x
[tex] \frac{5}{3}s = \frac{15}{3} + \frac{3}{2}s - \frac{1}{4} [/tex]i dont under stand it and other questions like it because I'm sorta slower than the rest of my class. We're doing Types of Solutions of Linear Equations.
Answers
The question we have to solve is:
[tex]\frac{5}{3}s=\frac{15}{3}+\frac{3}{2}s-\frac{1}{4}[/tex]To solve this equation, we take all the "s"'s to one side and numbers to the other and simplify:
[tex]\begin{gathered} \frac{5}{3}s=\frac{15}{3}+\frac{3}{2}s-\frac{1}{4} \\ \frac{5}{3}s-\frac{3}{2}s=\frac{15}{3}-\frac{1}{4} \\ \frac{5(2)-3(3)}{6}s=\frac{15(4)-1(3)}{12} \\ \frac{1}{6}s=\frac{57}{12} \\ s=\frac{\frac{57}{12}}{\frac{1}{6}} \end{gathered}[/tex]When we want to divide by a fraction, we mulitply by its reciprocal. So,
[tex]\begin{gathered} s=\frac{\frac{57}{12}}{\frac{1}{6}} \\ s=\frac{57}{12}\times\frac{6}{1} \\ s=\frac{57}{2} \end{gathered}[/tex]Select all value of c for which f(x) = g(x)Please look gráficos.
Answers
Statement Problem: Select all values of x for which;
[tex]f(x)=g(x)[/tex]Solution:
The value of x for which the two functions are equal is the x-coordinate of their insections;
The coordinates of the intersections are;
[tex](0,-3)\text{ and }(4,5)[/tex]Thus, the values of x that is correct are;
[tex]x=0,x=4[/tex]Hence, CORRECT OPTIONS are;
[tex]A\text{ and D}[/tex]Please help I don’t get what did teacher even wants bro
Answers
Base of the rectangle is 9 inches.
What is Area of Rectangle ?
You may determine the area of any form by counting how many unit squares fit inside of it.
In this context, a square with a side of 1 unit is referred to as a unit square.
In other words, the area of the rectangle is equal to the number of unit squares inside its perimeter.
Area = base * height
Given,
Area = 108 in²
height = 12 inches
put these values in given formula,
108 = 12 * base
base = 108 / 12
= 9 inches
Therefore, Base of the rectangle is 9 inches.
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Elon has removed two dead batteries from a flashlight and inadvertently mingled them with the two good batteries he intended as replacements. The four batteries look identical. Elon now randomly selects two of the four batteries. What is the probability he selects the two good batteries? (Hint: sampling is without replacement here)
Answers
The probability of the required event is [tex]\frac{1}{2}[/tex]
Number of batteries removed by Elon = 2
And then he mixed these batteries with the other two batteries
Thus total number of batteries = 4
These 4 batteries as given is identical
Now since it is given in the question that there aren't any replacements thus it means that we don't have to apply the Baye's theorem. So we can simply write it as it is mentioned below.
Thus the probability of taking out two batteries which are good without any replacement :
Probability = [tex]\frac{number of outcomes }{total number of favorable outcomes}[/tex]
Given number of outcomes = 2
Total number of favorable outcomes = 4
Thus the probability of the given event is = [tex]\frac{2}{4}[/tex]
Thus P( E ) = [tex]\frac{1}{2}[/tex]
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Two forces 30-lb and 50-lb are pulling an object at an angle of 30°between them. Find the magnitude of the resultant force. Round answer to 2 decimal places.
Answers
Answer: The magnitude of the resultant force is 77.45-lb
Explanation:
Resultant is represented as R
35.4 divided by 0.59
Answers
To do the operation, first the numerator and denominator by 100:
[tex]\frac{35.4\cdot100}{0.59\cdot100}=\frac{3540}{59}[/tex]Now simplify
[tex]\frac{3540}{59}=\frac{59\cdot60}{59\cdot1}=\frac{60}{1}=60[/tex]Therefore,
[tex]\frac{35.4}{0.59}=60[/tex]Answer:
60
Step-by-step explanation: 35.4 / 0.59 = 60
Find X.
Circumscribed Angles
Answers
Answer:
x=20
Step-by-step explanation:
To find x you must first set up an equation. (3x+90+90+120=360) the reason why i did that is because the red boxes indicate that they are 90° angles. They add up to 360 is because the quadrilaterals add up to 360. after solving for x, you should get x = 20.
The tree diagram represents an experiment consisting of two trials
P(A)=
Answers
Based on the parameters in the question, the value of probability P(A) is 0.60
How to determine the probability?The given parameters from the tree diagram are:
Probability of event A: P(A only) = 0.6Probability of event A: P(A and C) = 0.3Probability of event A: P(A and D) = 0.7The probability is calculated using the following probability formula
P(A) = P(A and D) + P(A and C)
Substitute the known values in the above equation
P(A) = 0.6 * 0.7 + 0.6 * 0.3
Evaluate the products
P(A) = 0.42 + 0.18
Evaluate the sum
P(A) = 0.60
Hence, the value of the probability of A is 0.60
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In 4 1/2 hours Greg reads 9 3/4 chapters what is the unit rate in chapters per hour
Answers
2 1/6 is the answer
9 3/4 divided by 4 1/2 = 2 1/6
Can someone please help with my homework?
NASA launches a rocket at t=0 seconds. Its height, in meters above sea level, as a function of time is given by h(t) = −4.9t^2 + 241t + 402 Assuming that the rocket will splash down into the ocean, at what time does splashdown occur?
1. The rocket splashes down after________seconds.
2. How high above sea level does the rocket get at its peak? The rocket peaks at_________ meters above sea level.
Answers
Considering the given quadratic function, it is found that:
1. The rocket splashes down after 50.8 seconds.
2. The rocket peaks at 3365.3 meters above sea level.
When does the rocket splashes down?The height of the rocket after t seconds is given according to the following rule:
h(t) = -4.9t² + 241t + 402.
Which is a quadratic equation with coefficients given by:
a = -4.9, b = 241, c = 402.
It splashes down when it hits the ground, that is, when h(t) = 0, hence:
-4.9t² + 241t + 402 = 0.
Then:
[tex]\Delta = 241^2 - 4(-4.9)(402) = 65960.2[/tex][tex]x_1 = \frac{-241 + \sqrt{65960.2}}{-9.8} = -1.62[/tex][tex]x_2 = \frac{-241 - \sqrt{65960.2}}{-9.8} = 50.8[/tex]Time is a positive measure, hence it splashes down after 50.8 seconds.
What is the maximum height?The height of the rocket is a concave down quadratic equation, hence the maximum height is the y-coordinate of the vertex, given as follows:
[tex]h_{MAX} = -\frac{\Delta}{4a}[/tex]
Both these parameters have been found in the previous item, hence:
[tex]h_{MAX} = -\frac{65960.2}{4(-4.9)} = 3365.3[/tex]
3365.3 meters.
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PLS HELP ASAP WILL GIVE BRAINLIST
Answers
X=2
Y=15
solve for x using the figure below. (view image)
Answers
The value of x in the figure is 3
How to find x from the figure?
Let us re -write the given values as fractions
[tex]\frac{5}{8} =\frac{x+3.25}{10} \\\\[/tex]
By applying cross multiplication method,
5(10) = 8(x+3.25)
50 =8x +26
8x = 50-26
8x = 24
x = 3
Similarly re- writing next set of vales as fractions,
[tex]\frac{2}{5} =\frac{2.5}{x+3.25} \\\\[/tex]
By applying cross multiplication method,
2(x+3.25) = 5(2.5)
2x+6.5 = 12.5
2x = 12.5 - 6.5
2x = 6
x = 3
What is cross multiplication of fractions?
To cross multiply two fractions, multiply the denominator of one by the numerator of the other, and then compare the results. The larger fraction is the one having the larger value.Virtually all fractions that are cross multiplied will have various denominators. It is a quick way to compare fractions by reducing them to a common denominator.To learn more about cross multiplying fractions, refer:
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5. Among 100 students, 60 participated on playing games and 50 participated in music. How many students participated in both the activities? Also find how many students participated in music only?
Answers
40 participated in music only
Basically when you add the no of students doing these both activities you get 110
But there are only 100 students
This means that the 10 students must be doing both
So music only is 50-10 that is 40
savings 50,000 in 30 years with a saving compounded monthly at an interest rate of 6%. How much would I need to deposit a month?
Answers
If the saving compounded monthly at an interest rate of 6%. The amount you need to deposit a month is $8,302.
How to find the compound interest?Using this formula to determine the principal amount
P = A / (1 + r/n) ^nt
Where:
P = principal = ?
A = amount = $50,000
r = interest rate = 6%
t = time = 30
Now let plug in the formula
P = $50,000 / (1 + 0.06/12) ^( 12 × 30 )
P = $50,000 / (1 + 0.005) ^ 360
P = $50,000 / (1.005)^360
P = $50,000 / 6.022575
P = $8,302
Therefore $8,302.10 is the amount deposited.
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I need help with putting 64/128 fully simplified and to a decimal
Answers
Given:
[tex]\frac{64}{128}[/tex]To convert into decimal:
Explanation:
Let us write it as the factored form for each term.
[tex]undefined[/tex][tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{\dfrac{64}{128}}\\\\\mathsf{= \dfrac{64\div8}{128\div8}}\\\\\mathsf{= \dfrac{8}{16}}\\\\\mathsf{= \dfrac{8\div4}{16\div4}}\\\\\mathsf{= \dfrac{2}{4}}\\\\\mathsf{= \dfrac{2\div2}{4\div2}}\\\\\mathsf{= \dfrac{1}{2}}\\\\\\\huge\text{Therefore, the answer simplified is:}\\\huge\boxed{\mathsf{\dfrac{1}{2}}}\huge\checkmark[/tex]
[tex]\mathsf{\dfrac{1}{2}\rightarrow 1\div2 \rightarrow 0.5}\\\\\\\huge\text{Therefore your decimal form of }}\huge\boxed{\boxed{\rm{\dfrac{1}{2}}}}\huge\text{ is:}\\\\\huge\boxed{\mathsf{0.5}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
A rectangular picture measures 32 by 28. when the picture is framed, a margin 2cm wide is left all the way round .1: what is the area of the picture without the frame?2:what is the area of the frame3:what is the area of the margin
Answers
1) The area of the picture without the frame will be A.
[tex]A=32\times28=896cm^2[/tex]So the area without frame is 896 square centimeters.
2) If the frame is 2 cm all around then the length and width increase by 4.
So the length becomes 32+4=36cm and the width becomes 28+4=32.
The area of big rectangle which is the frame is A'.
[tex]A^{\prime}=36\times32=1152cm^2[/tex]So the area of the frame is 1152 square centimeters.
3) The area of the margin will be the difference of the area of the frame and area of the picture, so it will be A'-A
[tex]A^{\prime}-A=1152-896=256cm^2[/tex]So the area of the margin is 256 square centimeters.
26. If 25% of a number p is 19, what is 15% of p?
Answers
Given:
25% of p is 19.
[tex]\begin{gathered} \frac{25}{100}\times p=19 \\ p=19\times\frac{100}{25} \\ p=19\times4 \\ p=76 \end{gathered}[/tex]The expression to calculate the 15% of p is,
[tex]\frac{15}{100}\times p[/tex]Substitute value of p=76 in the above expression.
[tex]\begin{gathered} \frac{15}{100}\times76=\frac{3}{20}\times76 \\ =\frac{228}{20} \\ =11.4 \end{gathered}[/tex]Thus, 15% of p is 11.4.