Answer:
The correct answer is D. purchase price: $117, advertised price: $293.
Step-by-step explanation:
10. Mary just bought solar panels that cost $2,000 and will reduce her electricity bills by $40 per month. How long will it take her to recoup her investment in the panels if she can earn 12% interest, compounded monthly, on her money?
* Mary's solar panels cost $2,000.
* The panels will reduce her monthly electricity bill by $40.
* She can earn 12% interest compounded monthly.
* So her monthly savings is $40
* And her 12% monthly interest rate is 12% / 12 = 1% per month.
* So each month her balance grows by 1% of the current balance.
* Let's think through this step-by-step:
* Initial balance = $2,000 (from paying for the solar panels)
* Month 1:
** Savings = $40 (from lower electric bill)
** Interest = 1% of $2,000 = $20
** Balance after Month 1 = $2,000 + $40 + $20 = $2,060
* Month 2:
** Savings = $40
** Interest = 1% of $2,060 = $20
** Balance after Month 2 = $2,060 + $40 + $20 = $2,120
* Month 3: (continue the calculations for Months 3 through 24)
** Savings = $40
** Interest = 1% of $2,121 = $21
** Balance after Month 3 = $2,121 + $40 + $21 = $2,182
* After 24 months, the balance is $3,149 (calculated step-by-step as shown above)
* The initial investment was $2,000
* So it took about 24 months to recoup her investment.
Does this help explain the steps? Let me know if you have any other questions!
Given this equation what is the value of x at the indicated point?
Answer:
x = -1
Step-by-step explanation:
You will plug in 8 for y then solve for x:
[tex]\frac{12}{3} = (x-1)^2\\4 = (x-1)^2\\\frac{+}{-}2 = x-1 \\ x= +3, and -1[/tex]
Then the answer is -1 because the graph shows the point in the 2nd quadrant meaning x is negative
I am 41 years old. I am 24 years older than double my elder son's age. How old is my elder son?
Answer:
8.5 yrs
Step-by-step explanation:
parent: 41 yrs
eldest son: x
Firstly, we will need to subtract 24 from 41 to get 2x the eldest son's age.
By doing that, we will have an equation that looks like this:
41-24=2x
This equation would basically get us through the whole problem.
Simplify the equation:
17=2x
x=8.5
The eldest son's age is 8.5.
Let's check our work!
8.5 x 2 = 17
17+24=41 (parent's age.)
Hope this helps :)
In a study relating to the labourers of a jute mill in West Bengal, the following information was collected. ‘Twenty per cent of the total employees were females and forty per cent of them were married. Thirty female workers were not members of Trade Union. Compared to this, out of 600 male workers 500 were members 11 of Trade Union and fifty per cent of the male workers were married. The unmarried non-member male employees were 60 which formed ten per cent of the total male employees. The unmarried non-members of the employees were 80’. On the basis of this information, the ratio of married male non-members to the married female non-members is (a) 1 : 3 (b) 3 : 1 (c) 4 : 1 (d) 5 : 1
On the basis of this information, the ratio of married male non-members to the married female non-members is (b) 3 : 1
How to calculate the ratioTotal married male employees = 80% × 50% = 40%
Total male Trade Union members = 91.67%
Total male non-Trade Union members = 100% - 91.67% = 8.33%
Married male Trade Union members = 40% × 91.67% = 36.67%
Married male non-Trade Union members = 40% - 36.67% = 3.33%
Now, let's find the number of married female non-members:
The ratio based on the information is 3 to 1.
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please answer this question
The quadrilateral ABCD is trapezoid.
What is trapezoid?
A quadrilateral with one set of parallel opposite sides is referred to as a trapezium. It can have congruent sides (isosceles) and right angles (a right trapezium), but neither is necessary.
Here in the given figure ,
[tex]\overline{AD}=\overline{BC}[/tex] are parallel to each other.
We can make right angle using ABC.
Hence the given quadrilateral ABCD is trapezoid.
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(a) If G(x) = x2 − 3x + 3, find G'(a) and use it to find equations of the tangent lines to the curve y = x2 − 3x + 3 at the points (0, 3) and (4, 7).
G'(a) =
(passing through (0, 3)) y1(x) =
(passing through (4, 7)) y2(x) =
(b) Illustrate part (a) by graphing the curve and the tangent lines on the same screen.
(a) G'(a) = 2x - 3
(passing through (0, 3)) y1(x) = -3
(passing through (4, 7)) y2(x) = 5
b) The illustration of the graph is defined below.
In calculus, finding the derivative of a function is an important tool to understand the behavior of a curve at a specific point. One application of this concept is determining the equation of the tangent line to a curve at a given point. In this problem, we will use the derivative of a quadratic function to find the equations of tangent lines to the curve y = x² − 3x + 3 at the points (0, 3) and (4, 7).
To begin, we need to find the derivative of G(x) = x² − 3x + 3. Using the power rule, we have:
G'(x) = 2x - 3
Next, we can use this derivative to find the slope of the tangent line to the curve y = x² − 3x + 3 at any given point (a, G(a)). At the point (0, 3), we have a = 0, so the slope of the tangent line is:
G'(0) = 2(0) - 3 = -3
Using the point-slope equation of a line, we can find the equation of the tangent line passing through (0, 3). The equation of the tangent line is:
y - 3 = -3(x - 0)
Simplifying, we get:
y = -3x + 3
Similarly, at the point (4, 7), we have a = 4, so the slope of the tangent line is:
G'(4) = 2(4) - 3 = 5
Using the point-slope equation again, we can find the equation of the tangent line passing through (4, 7). The equation of the tangent line is:
y - 7 = 5(x - 4)
Simplifying, we get:
y = 5x - 13
To graph these tangent lines on the same screen as the curve y = x² − 3x + 3, we can plot the curve and the two tangent lines using a graphing calculator or software. The graph should show the curve as a parabola and the tangent lines as straight lines intersecting the curve at the points (0, 3) and (4, 7), respectively.
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For a standard normal distribution, find the approximate value of P(-0.41)<=z<=(0.73).
. Use the portions of the standard normal table below to help answer the question
a. 43%
b. 34%
c. 57%
d. 45%
For a standard normal distribution, the approximate value of
P(-0.41) ≤ z ≤ (0.73) is 43%.
Option A is the correct answer.
We have,
To find the approximate value of P(-0.41) ≤ z ≤ (0.73) for a standard normal distribution, we need to use the standard normal table.
Looking at the table,
The value of P(Z ≤ 0.73) = 0.7673.
The value of P(Z ≤ -0.41) = 0.3409.
To find the value of P(-0.41) ≤ Z ≤ (0.73),
We need to subtract P(Z ≤ -0.41) from P(Z ≤ 0.73):
P(-0.41) ≤ Z ≤ (0.73) = P(Z ≤ 0.73) - P(Z ≤ -0.41)
P(-0.41) ≤ Z ≤ (0.73) = 0.7673 - 0.3409
P(-0.41) ≤ Z ≤ (0.73) = 0.4264
Rounding this value to the nearest whole percent, we get 43%.
Therefore,
For a standard normal distribution, the approximate value of
P(-0.41) ≤ z ≤ (0.73) is 43%.
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10 yd
17 yd
4 yd.
Find the surface area of the prism
The surface area of the rectangular prism is 502 mm²
How to solve an equation?An equation is an expression that can be used to show the relationship between two or more numbers and variables using mathematical operators.
The area of a figure is the amount of space it occupies in its two dimensional state.
The surface area of the prism = 2(8 mm * 13 mm) + 2(8 mm * 7 mm) + 2(7 mm * 13 mm) = 502 mm²
The surface area is 502 mm²
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Give a recursive definition for the following set of ordered pairs of positive integers ([tex]a|b[/tex] means that a is a factor of b): [tex]S=[/tex]{[tex](a,b)|a \in Z^+, b \in Z^+, a|b[/tex]}
A recursive definition for the set S can be given as follows:
What is recursion?
Recursion is a programming technique where a function calls itself to solve a problem.
Base case: (1, n) is in S for all positive integers n, since 1 is a factor of all positive integers.
Recursive case: If (a, b) is in S, then (a', b) is in S for all positive integers a' that are factors of a, and (a, b') is in S for all positive integers b' that are multiples of b.
In other words, the set S contains all pairs (a,b) where a is a positive integer that divides b, and b can be obtained by multiplying any such a with another positive integer. The base case includes all pairs where a=1 and b is any positive integer.
The recursive case states that if (a,b) is in S, then all pairs where a' is a factor of a and b is a positive integer such that b=a'b are also in S, as well as all pairs where b' is a multiple of b and a is a positive integer that divides b'.
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Let v be the vector from initial point P₁ to terminal point P2. Write v in terms of i and j.
P₁ = (-5,3), P2=(-2,-7)
V=
(Type your answer in terms of i and j.)
By subtraction between two points P₁(x, y) = (- 5, 3) and P₂(x, y) = (- 2, - 7), the vector V is 3 i - 10 j.
How to determine the vector
According to linear algebra, a vector can be formed by subtracting the initial point (P₁) from the final point (P₂). The equation is introduced below:
V = P₂(x, y) - P₁(x, y)
V = (- 2, - 7) - (- 5, 3)
V = (3, - 10)
V = 3 i - 10 j
The vector V = 3 i - 10 j is the result of subtracting the two points P₁(x, y) = (- 5, 3) and P₂(x, y) = (- 2, - 7).
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this is what I don’t know
Answer:
84 degrees for number 6
Step-by-step explanation:
the area of a circle is 360 degrees, so just subtract the other angles by 360 i think that's how you do it
What’s the current yield of a 4.95 percent coupon corporate bond quoted at a price of 102.53?
The current yield of a 4.95% coupon at a price of $102.53 is [tex]4.82%[/tex]%.
What is the current yield of a 4.95% coupon bond?The current yield of bond means return on an investment based on its current market price.
To calculate the current yield, we will use (annual interest payment/current market price * 100).
Annual interest payment = $1,000 face value x 4.95% coupon
Annual interest payment = $49.50
Current market price = 102.53% of the face value
Current market price = $1,025.30
Current yield = $49.50 / $1,025.30 x 100
Current yield = 4.82%
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Can someone help me with this problem?
Answer:
∠ BAC = 66°
Step-by-step explanation:
the inscribed angle BAC is half the angle at the centre, subtended on the same arc BC , then
∠ BAC = [tex]\frac{1}{2}[/tex] × 132° = 66°
Just before the presidential election in November 2016, a local newspaper conducted a poll of registered voters in a large city and found that 120 out of a random sample of 250 men intended to vote for Donald Trump and 132 out of a random sample of 240 women intended to vote for Donald Trump.
(a) is there convincing evidence that there is a difference in the proportion of all men and the proportion of all women in this city who intended to vote for Trump at the a=0.05 significance level?
(b) based on your conclusion in part (a), which mistake, a type i error or a type ii error, could you have made? interpret this error in context
(c) a 95% confidence interval for the difference (men - women) in the proportion of all men and the proportion of all women in this city who intended to vote for trump is (-0.158. 0.018). based upon the interval, is there convincing evidence to support the claim that a greater proportion of women than men intended to vote for trump?
(d) give one way to increase the power of the test other than increasing the sample sizes. what is a drawback of making that change?
With a p-value of 0.022, there is convincing evidence of a difference in the proportion of men and women who intended to vote for Trump in the city. Type I error could have been made. No, there is not convincing evidence to support the claim that a greater proportion of women than men intended to vote for Trump. Increasing the significance level would increase power, but would also increase the likelihood of making a Type I error.
We can use a two-sample z-test to test for the difference in proportions between men and women who intended to vote for Trump.
Let p1 be the proportion of men who intended to vote for Trump and p2 be the proportion of women who intended to vote for Trump. Then the null and alternative hypotheses are
H0: p₁ = p₂
Ha: p₁ ≠ p₂
We can calculate the pooled sample proportion
p = (x₁ + x₂) / (n₁ + n₂)
= (120 + 132) / (250 + 240)
= 0.508
where x₁ = 120, x₂ = 132, n₁ = 250, and n₂ = 240.
We can calculate the test statistic
z = (p₁ - p₂) / √(p * (1 - p) * (1/n₁ + 1/n₂))
= (0.48 - 0.55) / √(0.508 * 0.492 * (1/250 + 1/240))
= -2.29
Using a standard normal distribution table, the p-value for a two-tailed test with a test statistic of -2.29 is 0.022. Since the p-value is less than 0.05, we reject the null hypothesis and conclude that there is convincing evidence that there is a difference in the proportion of all men and the proportion of all women in this city who intended to vote for Trump at the 0.05 significance level.
The mistake we could have made is a type I error, which is rejecting the null hypothesis when it is actually true. In this case, it would mean concluding that there is a difference in proportions between men and women who intended to vote for Trump when there is actually no difference.
The confidence interval for the difference in proportions is (-0.158, 0.018), which includes 0. Since 0 is in the interval, we cannot reject the null hypothesis that there is no difference in proportions between men and women who intended to vote for Trump.
Therefore, based on the interval, there is not convincing evidence to support the claim that a greater proportion of women than men intended to vote for Trump.
One way to increase the power of the test is to decrease the significance level (i.e., increase the alpha level). This would allow us to reject the null hypothesis more easily and increase the chance of detecting a true difference in proportions.
However, the drawback of making this change is that it increases the chance of making a type I error, which means rejecting the null hypothesis when it is actually true.
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Solve for the angles of the triangle described below. Express all angles in degrees and round to the nearest hundredth.
a = 9,b= 5, c = 7
The angles of the triangle are:
A = 95.7°, B = 33.6°, C = 50.7°.
What are the angles of the triangle?
The area created between two of a triangle's side lengths is known as the angle. Both internal and external angles are present in a triangle. In a triangle, there are three interior angles. When the sides of a triangle are stretched to infinity, exterior angles are created.
Here, we have
Given: a = 9, b= 5, c = 7
We have to find all angles in degrees.
Using law of cosines, a² = b²+c² - 2bc cos(A),
9² = 5²+7² - 2(5)(7) cos(A)
81 = 25 + 49 - 70 cos(A)
7 = -70 cos(A)
cos(A) = -7/70
cos(A) = -1/10
A = cos⁻¹(-1/10)
A = 95.7°
Now, using the law of sines,
[sin (A)]/(a) = [sin (C)]/(c)
[sin (95.7°)]/(9) = [sin (C)]/(7)
0.9955/9 = sin (C)/(7)
0.7742 = sinC
C = sin⁻¹(0.7742)
C = 50.7°
The sum of all the angles of a triangle= 180°
A + B + C = 180°
95.7° + B + 50.7° = 180°
B = 33.6°
Hence, the angles of the triangle are:
A = 95.7°, B = 33.6°, C = 50.7°.
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What is the volume of a cube whose edges can have a measure of 1.8 inches
The volume of the cube will be 5.832 cubic inches.
The volume of a cube is given by the formula V = s³, where s is the length of one of its edges.
In this case, the length of one edge is given as 1.8 inches.
So, substituting s = 1.8 inches in the formula, we get:
V = s³ = 1.8³ = 5.832 cubic inches
Therefore, the volume of the cube is 5.832 cubic inches.
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PLS HELP ASAP!!!
A triangle is shown in the image. A triangle with a height of 12 inches. The height is perpendicular to the base labeled 36 inches. The side from the top of the perpendicular side to the base is labeled 34 inches. What is the area of the triangle represented? 204 in2
216 in2
408 in2
432 in2
So the area of the triangle is 216 square inches.
How is area of a triangle determined?To find the area of a triangle, you can use the formula A = 1/2 * b * h, where A is the area, b is the length of the base, and h is the height of the triangle. In this case, we have a height of 12 inches and a base of 36 inches.
To find the length of the missing side of the triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. So, we have:
c² = a² + b²
c² = 12² + 34²
c² = 144 + 1156
c² = 1300
c = √(1300)
c = 36.06 (rounded to two decimal places)
Now that we know all three sides of the triangle, we can plug them into the formula for the area:
A = 1/2 * b * h
A = 1/2 * 36 * 12
A = 216
So the area of the triangle is 216 square inches.
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Number 9. Emulate the logarithm using the change of base formula. Round you result to three decimal places.
Log3(14)
Log3(14)
= log(14) / log(3) (Change of base formula)
= 4 / 1.965 (log(3) = 1.965)
= 2.041 (rounded to 3 decimal places)
2.041
Answer:
Step-by-step explanation:
To emulate the logarithm using the change of base formula, we need to use a base that is more convenient to evaluate. Let's use base 10:
log3(14) = log10(14) / log10(3)
Using a calculator, we can evaluate the numerator and denominator:
log10(14) ≈ 1.146
log10(3) ≈ 0.477
Dividing the numerator by the denominator gives:
log3(14) ≈ 2.402
Rounding to three decimal places, the final result is:
log3(14) ≈ 2.402
Solve the following showing all steps. (x+6)2=8
Expanding the left-hand side of the equation, we get:
(x+6)2 = (x+6)(x+6) = x(x+6) + 6(x+6) = x^2 + 6x + 6x + 36 = x^2 + 12x + 36
So now we have the equation:
x^2 + 12x + 36 = 8
Subtracting 8 from both sides, we get:
x^2 + 12x + 28 = 0
We can factor this quadratic equation as:
(x+2)(x+14) = 0
This gives us two possible solutions:
x+2 = 0, so x = -2
x+14 = 0, so x = -14
Therefore, the solutions to the equation (x+6)2 = 8 are x = -2 and x = -14.
Step-by-step explanation:
Here is one way :
(x+6)^2 = 8 Take the square root of both sides
x+6 = +- sqrt 8
x = -6 +- sqrt8 = -6 + 2 sqrt 2 or -6 - 2 sqrt 2 = - 3.17 or - 8.83
Analyze and solve the word problem
An elephant at Emirates Park and Zoo weighs 200 pounds at birth and gains approximately 2 pounds per day. The
function w = 2d +200 represents the weight w of an elephant on a given day during his first year.
How much more does an elephant weigh on Day 60 than it does on Day 5?
An elephant weighs 110 pounds more on Day 60 than it does on Day 5
Here, function w = 2d +200 represents the weight w of an elephant on a given day during his first year.
From above function , the weight of an elephant on Day 60 would be,
w₆₀ = 2(60) + 200
w₆₀ = 120 + 200
w₆₀ = 320 pounds
and the weight of an elephant on Day 5 would be,
w₅ = 2(5) + 200
w₅ = 10 + 200
w₅ = 210
The difference between these weights is:
w = w₆₀ - w₅
w = 320 - 210
w = 110 pounds
Therefore, an elephant weighs 110 pounds more on Day 60 than on Day 5
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2x + y = 7
x + y = 1
The solution to the system of equations is x = 6 and y = -5, which is the same as we obtained using the elimination method.
What is the system of equations?A system of equations is a collection of one or more equations that are considered together. The system can consist of linear or nonlinear equations and may have one or more variables. The solution to a system of equations is the set of values that satisfy all of the equations in the system simultaneously. The given system of equations is:
2x + y = 7 ---(1)
x + y = 1 ---(2)
To solve this system, we can use the method of elimination or substitution.
Method 1: Elimination
In this method, we eliminate one of the variables by adding or subtracting the two equations. To do this, we need to multiply one or both equations by a suitable constant so that the coefficients of one of the variables become equal in magnitude but opposite in sign.
Let's multiply equation (2) by -2, so that the coefficient of y in both equations becomes equal in magnitude but opposite in sign:
-2(x + y) = -2(1) --
Multiplying equation
(2) by -2-2x - 2y = -2
Now we can add the two equations (1) and (-2x - 2y = -2) to eliminate y:
2x + y = 7(-2x - 2y = -2)0x - y = 5
We now have a new equation in which y is isolated.
To solve for y, we can multiply both sides by -1:
-1(-y) = -1(5)y = -5
Now that we know y = -5, we can substitute this value into equation (2) to find x:x + y = 1x + (-5) = 1x = 6
Therefore, the solution to the system of equations is (x,y) = (6,-5).
Method 2: Substitution
In this method, we solve one of the equations for one variable in terms of the other variable and substitute this expression into the other equation to get an equation with only one variable.
From equation (2), we can solve for y in terms of x:y = 1 - x
We can then substitute this expression for y into equation (1):2x + y = 72x + (1 - x) = 7 --Substituting y = 1 - xx + 1 = 7x = 6
Now that we know x = 6, we can substitute this value into equation (2) to find y:x + y = 16 + y = 1 --Substituting x = 6y = -5
Therefore, the solution to the system of equations is (x,y) = (6,-5), which is the same as we obtained using the elimination method.
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Find the slope of the line shown belowpp
Answer: the slope is 6
Step-by-step explanation: the line y=6x-3
Tyler opened a credit card with a 19.5% simple interest rate to purchase a $879 laptop. If he pays
off the laptop in 1.5 years, how much will he have paid in total?
$257.11
$621.89
$1,045.25
$1336.11
[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$879\\ r=rate\to 19.5\%\to \frac{19.5}{100}\dotfill &0.195\\ t=years\dotfill &1.5 \end{cases} \\\\\\ A = 879[1+(0.195)(1.5)] \implies A=879(1.2925)\implies A \approx 1136.11[/tex]
when the dimensions of a two-dimensional shape are doubled then what is the perimeter
ctaivity 1: how do you see it? state whether or not the following triangles are similar if not ,explain why not .if so,write a similarity statement
Triangles RLG and PCN are similar. The similarity is by SSS criteria and the scale factor is 2/3.
What are similar triangles?Two triangles that are similar in shape but not necessarily in size are called similar triangles. To put it another way, the two triangles' angles are similar and their corresponding sides are proportional.
If two triangles are comparable, then all pairs of related sides have the same length-to-length ratio. The scale factor of similar triangles is the name given to this ratio. The scale factor between two triangles is 2:1, for instance, if one side of a triangle is twice as long as its counterpart side in another triangle.
In the given figure we have triangle RLG and triangle PCN.
Here, the ratio of the sides of the triangle are given as:
RG / PN = 32 / 48 = 2/3
Also we have:
LG / PC = 18/27 = 2/3
LR / CN = 30 / 45 = 2/3
RG / PN = LG / PC = LR / CN = 2/3
Hence, triangles RLG and PCN are similar. The similarity is by SSS criteria and the scale factor is 2/3.
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The complete question is:
Karl has 5 pound of flour to bake cookies. Each batch of cookies uses 1/3 pound of flour. After Karl bakes 7 batches of cookies, how much flour does Karl have left?
Answer:
Karl has 2.67 pounds of flour left.
Step-by-step explanation:
First, let us dissect the given.
Flour - 5 poundsCookies - 7 batches1/3 pounds per batchSecond, let us identify the correct solution for this problem.
1/3 x 7 = 2 and 1/3 or 7/35 - 7/3 = 8/3 or 2.67 poundsLook at image on top pls help quickly
Based ont he the function y = - 2x + 5 + 2x - 5 is given ,
if x < -2.5, y = 0
i f x > 2.5, y = 0
if -2.5 ≤ x ≤ 2.5 = 0
How did we reach this conclusion ?Without the absolute value symbols
y = -2x + 5 + 2x - 5
Where x < - 2.5
y = -2 (-2.5) + 5 + 2 (-2.5 ) - 5
y = 5 + 5 + (-5)-5
y = 0
Where x > 2.5
y = -2 (2.5) + 5 + 2(2.5) - 5
y = 0
Where -2.5 ≤ x ≤ 2.5
y = -2x + 5 + 2x -5
grouping like terms we have
-2x + 2x +5 -5
y = 0
thus, Where -2.5 ≤ x ≤ 2.5
y = 0
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a) Find the mean and median of the following gasoline prices per gallon in California:
regular:
$
3.14
$3.14, mid-grade:
$
3.21
$3.21, premium:
$
3.28
$3.28, diesel:
$
3.53
$3.53. Round to the nearest cent.
The mean and the median of the following gasoline prices that are listed above would be =3.29 and 4.85 respectively.
How to calculate the mean and median of a data set?The formula that is used to calculate the mean of a data set is given as follows;
mean = sum of data set/number of data set
= 3.14+3.21+3.28+3.53/4
= 13.16/4 = 3.29
The median = 3.21+3.28/2 = 4.85
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Rectangle TUVW is on a coordinate plane at T (a, b), U (a + 2, b + 2), V (a + 5, b − 1), and W (a + 3, b − 3). What is the slope of the line that is parallel to the line that contains side WV?
-2
2
-1
1
The slope of the line that is parallel to the line that contains side WV is 1.
What about slope of line?
The slope of a line is a measure of its steepness or inclination, defined as the ratio of the change in the vertical direction (y-axis) to the change in the horizontal direction (x-axis) between any two points on the line.
In other words, the slope of a line represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It is commonly denoted by the letter "m" and is calculated as:
m = (y₂ - y₁) / (x₂ - x₁) where (x₁, y₁) and (x₂, y₂) are any two points on the line.
The slope can be positive, negative, zero, or undefined. A positive slope indicates that the line rises as we move from left to right, while a negative slope indicates that the line falls as we move from left to right. A slope of zero indicates that the line is horizontal, and an undefined slope indicates that the line is vertical.
According to the given information:
W(a+3, b-3) and V(a+5, b-1)
So, the slope WV,
[tex]\frac{b-3-(b-1)}{a+3 - (a+5)} \\\\\frac{-2}{-2} = 1[/tex]
So, the slope of the given condition is 1.
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Construct an Argument | Batter is being poured into the right rectangular prism-shaped pan so that the pan is full. What is the volume of the batter in the pan? 9 in. 3 In. 5 in.
Answer:
Valid
Step-by-step explanation:
The volume of the batter in the pan can be found by multiplying the length, width, and height of the right rectangular prism-shaped pan. In this case, the length is 9 inches, the width is 5 inches, and the height is 3 inches.
Using the formula for the volume of a rectangular prism, V = lwh, we can substitute the given values to find:
V = (9 in.)(5 in.)(3 in.)
V = 135 cubic inches
Therefore, the volume of the batter in the pan is 135 cubic inches. This argument is valid because it follows the basic formula for calculating the volume of a rectangular prism and uses the specific measurements provided for the length, width, and height of the pan.