When A’B’C’ is reflected across the line x= -2 to from A”B”C”, vertex ___ of A”B”C” will have the same coordinates as B’
Answer: B''
This is because point B' has x coordinate x = -2. This point is directly on the mirroring line, so it doesn't move when the reflection is applied.
We can write B' = B''
When A’B’C’ is reflected across the line x= -2 to from A”B”C”, vertex B” of A”B”C” will have the same coordinates as B’
What is reflection over a line?"It is a geometric transformation in which all the points of an object are reflected across the line called the line of reflection.""In a reflection, the reflected image has the same size and shape as the pre-image."For given question,
A’B’C’ is reflected across the line x= -2 to form the A”B”C”
In a reflection over line a reflected image has the same distance from the reflection line as the original point, but is on the opposite side of the line.
Coordinates of triangle A’B’C’ are,
A’ = (-6, -2), B’ = (-2, -6), C’ = (-4, -2)
When A’B’C’ is reflected across the line x= -2 to form the A”B”C” then coordinates of the A”B”C” would be,
A” = (2, -2)
B” = (-2, -6)
C” = (0, -2)
This means, the coordinates of B’ = the coordinates of B”
Therefore, when A’B’C’ is reflected across the line x= -2 to from A”B”C”, vertex B” of A”B”C” will have the same coordinates as B’
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2-3 times how much is 2-1?
Answer:
the answer is -1
Step-by-step explanation:
2-3=-1
2-1=1
-1x=1
x=-1
-1*-1=1
She selects 150 trees at random from her orchard and uses this fertilizer on those trees and estimates the following regression: Y
^
i
=600+4.93X i
, where Y
^
i
denotes the predicted number of apricots obtained from the I th tree and X i
denotes the number of units of fertilizer used on the I th tree. A. H 0
:β 1
≥5.14 and H 1
:β 1
<5.14. B. H 0
:β 1
>4.93 and H 1
:β 1
≤4.93. C. H 0
:β 1
=5.14 and H 1
:β 1
=5.14. D. H 0
:β 0
=4.93 and H 1
:β 0
=4.93. Suppose the standard error of the estimated slope is 0.74. The t-statistic associated with the test Wendy wishes to conduct is (Round your answer to two decimal places. Enter a minus sign if your answer is negative.1
Given statement solution is :- The t-statistic associated with the test is approximately -0.28.
The t-statistic, which is used in statistics, measures how far a parameter's estimated value deviates from its hypothesised value relative to its standard error. Through the Student's t-test, it is utilised in hypothesis testing. In a t-test, the t-statistic is used to decide whether to accept or reject the null hypothesis.
To find the t-statistic associated with the test, we need to calculate the test statistic using the estimated slope coefficient, the null hypothesis, and the standard error.
The estimated slope coefficient is 4.93.
The null hypothesis is H₀: β₁ ≥ 5.14 (stating that the true slope coefficient is greater than or equal to 5.14).
The predicted slope's standard error is 0.74.
The formula to calculate the t-statistic is:
t = (estimated slope - hypothesized slope) / standard error
Plugging in the values:
t = (4.93 - 5.14) / 0.74
t = -0.21 / 0.74
t ≈ -0.28 (rounded to two decimal places)
Therefore, the t-statistic associated with the test is approximately -0.28.
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n what type of triangle is the orthocenter located outside of the triangle?A. equilateralB. rightC. obtuseD. acute
The Orthocentre is one of the four (4) most common centres of a triangle.
It is located at the point where the triangle's three(3) altitudes intersect called a point of concurrency.
The Orthocentre is located inside an acute triangle, on a right triangle and outside an Obtuse triangle.
Hence, the correct option is Option C
where α,β and k are constants. it is known that one of the differential equation is y1(t) = e−3t and the solution of ivp satisfies limt→[infinity]y(t) = 7. determine the constants α,β and k.
The constants α, β, and k are all zero, and the solution to the IVP is y(t) = e²{-2t}, with t = -0.5ln(7) the condition limt→∞y(t) = 7,t = -0.5ln(7)
Using the method of undetermined coefficients to find the general solution of the differential equation:
y'' + 3y' + 2y = 0
The characteristic equation is:
r²2 + 3r + 2 = 0
Factoring this equation, we get:
(r + 2)(r + 1) = 0
So the roots are r1 = -2 and r2 = -1. Therefore, the general solution is:
y(t) = c1e^{-2t} + c2e^{-t}
Next, we use the information that y1(t) = e²{-3t} is a solution to the differential equation. Substituting this into the general solution, we get:
e²{-3t} = c1e²{-2t} + c2e²{-t}
equation to solve for c1 and c2. Multiplying both sides by e^{2t}, we get:
e²{-t} = c1 + c2e²t
Taking the limit as t approaches infinity, that c1 must be zero in order for the right-hand side to converge to a finite value. Therefore, we have:
c1 = 0
Substituting this into the previous equation,
e²{-t} = c2e²t
Dividing both sides by e²t,
e²{-2t} = c2
Therefore, we have:
c2 = e²{-2t}
Substituting these values into the general solution,
y(t) = c1e²{-2t} + c2e²{-t} = e²{-2t}
So α = β = 0 and k = -2. Finally, the information that limt→∞y(t) = 7. Since y(t) = e²{-2t}, we have:
limt→∞e²{-2t} = 7
Taking the natural logarithm of both sides,
-2t = ln(7)Solving for t,
t = -0.5ln(7)
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A car travels a distance of 300 km in a time of 5 hours.
What is the car's average speed?
Step-by-step explanation:
so, if car have 120km/hr it maximum speed will be 85-95km/hr so the car travel 300km in around 5 or 5 unhalf hour
Solve for the measure of c. Round decimals to the nearest tenth.
A. 3.7
B. 7
C. 8.8
D. 4.7
2.8 = 2y
What does y equal?
1.4
0.5
2.8
0.6
Answer: 1.4
Step-by-step explanation: First, swap the sides of the equation so that the one with the variable can be in front.
So, its 2y=2.8
To solve this, you simply divide both sides of the equation by 2.
2 divided by 2 is 0. That leaves you with the y by itself. Then, 2.8 divided by 2 is 1.4
So, y=1.4
\(\text {Hello! Let's solve this Equation!}\)
\(\text {The First Step is to Flip the Equation:}\)
\(\text {Before: 2.8=2y}\\\text {After: 2y=2.8}\)
\(\text {Your Final Step is to Divide by 2:}\)
\(\text {2y/2=2.8/2}\)
\(\text {Your Answer will be:}\)
\(\fbox {y=1.4}\)
\(\text {Best of Luck!}\)
\(\text {-LimitedX}\)
A landscape business charges $50 to deliver rocks. The cost of the rocks are $27 per cubic yard. write and solve a linear equation to find the cost of having 8 cubic yards of rocks delivered to a site.
Step-by-step explanation:
First, let's form a linear equation that will help us find out how much that will cost.
Let's set x = the cubic yards of rocks delivered and y = total cost.
First, we know that the business charges 27 dollars for every x that you buy. That can be shown with a multiplication expression:
27x
Next, we know that the business charges a fixed fee of $50 for their services. This fee would be added on to the amount that they charge for the rocks that you buy.
27x + 50 = yThat's our linear expression! Next, we need to find out the total cost, y, when you need 8 cubic yards of rocks delivered, x.
To solve this, we need to substitute values for at least one of our variables.
Since 8 describes the cubic yards of rocks delivered, we can substitute 8 for x.
But we don't know y, the total cost- that's what we're solving for! In other words, we're solving for y.
Let's just substitute in what we know:
27(8) + 50 = y.
216 + 50 = y
y = 266So, we know that it would cost $266 dollars to have 8 cubic yards of rocks delivered to a site.
By the way, you can also graph your linear equation to find the corresponding y-value to 8 as another way to solve your problem.
When a flame suddenly contacts one side of a glass pane while the unexposed side is relatively cool, a stress can develop between the two faces and the glass can fracture between the faces. _____ is a term used in the fire investigation community to describe a complicated pattern of short cracks in glass arising from this condition.
Stress fracturing is a term used in the fire investigation community to describe a complicated pattern of short cracks in glass arising from this condition.
When a flame comes into contact with one side of a glass pane, it heats that side, causing it to expand. At the same time, the unexposed side of the glass remains relatively cool and does not expand as much. This temperature gradient creates non-uniform expansion and differential stresses within the glass. As a result, the glass may fracture between the faces, forming a complex pattern of short cracks.
Stress fracturing is a phenomenon commonly observed in fire investigations, particularly in situations where rapid heating or cooling of glass occurs. It is important to understand and analyze these patterns to gain insights into the behavior of glass under fire conditions and to help determine the sequence of events during a fire incident.
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The gateway arch in st. Louis, mo is approximately 630 ft tall. How many u. S. Nickels would be in a stack of the same height? each nickel is 1. 95 mm thick.
The gateway arch in st. Louis, MO is approximately 630 ft tall, the same height of the Nickels would be in a stack is 98474.
Height of Gateway Arch in St. Louis, MO = 630ft tall
We are asked, how many nickels would be in a stack of the same
height when 1 nickel is 1.95 mm thick.
Convert height in ft to mm
1 ft = 304.8 mm
630ft = X
After Cross Multiply,
630ft × 304.8mm/1ft
= 192024 mm.
To find how many nickel would be in a stack of the same height
= Total thickness/ Thickness of 1 US dime
= 192024 mm/1.95mm
= 98473.8
≈98474 nickels
Therefore, the number of nickel that would be in a stack of the same height is 98474.
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simplify to radical form the square root of 40 and then divide by 6
The simplified expression of the radical is √10/3
How to evaluate the expressionFrom the question, we have the following parameters that can be used in our computation:
the square root of 40 and then divide by 6
This statement can be mathematically represented as
√40/6
Simplify the numerator
So, we have the following representation
2√10/6
Divide 2 and 6
√10/3
Hence, the solution is √10/3
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Problem 2:
The lifespan of a particular brand of light bulb follows a normal distribution with a mean of 1000 hours and a standard deviation of 50 hours.
Find:
a) the z-score of light bulb with a mean of 500 hours.
b) If a customer buys 20 of these light bulbs, what is the probability that the average lifespan of these bulbs will be less than 980 hours?
c) the probability of light bulbs with the mean of 400 hours.
d) the number of light bulbs with the mean less than 1000 hours
The answers are:
a) The z-score for a light bulb that lasts 500 hours is -10.
b) For a sample of 20 light bulbs, the probability that the average lifespan will be less than 980 hours is approximately 0.0367, or 3.67%.
c) The z-score for a light bulb that lasts 400 hours is -12. This is even more unusual than a lifespan of 500 hours.
d) Given the lifespan follows a normal distribution with a mean of 1000 hours, 50% of the light bulbs will have a lifespan less than 1000 hours.
How to solve the problema) The z-score is calculated as:
z = (X - μ) / σ
Where X is the data point, μ is the mean, and σ is the standard deviation. Here, X = 500 hours, μ = 1000 hours, and σ = 50 hours. So,
z = (500 - 1000) / 50 = -10.
The z-score for a bulb that lasts 500 hours is -10. This is far from the mean, indicating that a bulb lasting only 500 hours is very unusual for this brand of bulbs.
b) If a customer buys 20 of these light bulbs, we're now interested in the average lifespan of these bulbs. . In this case, n = 20, so the standard error is
50/√20
≈ 11.18 hours.
z = (980 - 1000) / 11.18 ≈ -1.79.
The probability that z is less than -1.79 is approximately 0.0367, or 3.67%.
c) The z-score for a bulb with a lifespan of 400 hours can be calculated as:
z = (400 - 1000) / 50 = -12.
The probability associated with z = -12 is virtually zero. So the probability of getting a bulb with a mean lifespan of 400 hours is virtually zero.
d) The mean lifespan is 1000 hours, so half of the light bulbs will have a lifespan less than 1000 hours. Since the lifespan follows a normal distribution, the mean, median, and mode are the same. So, 50% of light bulbs will have a lifespan less than 1000 hours.
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The graph shows the number of prints Tara needs to sell to make a profit. What can you learn by looking at the graph? IMAGINE MATH
This graph shows that Tara’s prints have the potential to be profitable, but will require a significant amount of sales to make a profit.
What is profit?Profit is the difference between a firm's total revenue and total expenses. It is the amount of money a business has earned after subtracting the cost of goods sold, operating expenses and taxes from its total revenue.
The graph reveals a few key pieces of information that can be used to assess the potential profitability of Tara’s prints. Firstly, the graph shows that there is a fixed cost associated with each print, regardless of how many prints are sold. This cost is represented by the straight line at the bottom of the graph. Additionally, the graph reveals that the cost of the prints increases exponentially as more prints are sold. This means that the more prints Tara sells, the more money she makes. Lastly, the graph shows that the revenue from selling prints is significantly higher than the cost of producing them, indicating that Tara can make a profit if she is able to sell enough prints. Overall, this graph shows that Tara’s prints have the potential to be profitable, but will require a significant amount of sales to make a profit.
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Autumn spots the boy that she has a crush on sitting with his friends. Her heart begins to pound, her hands get sweaty, and her cheeks feel hot. Autumn's __________ has been activated.
Autumn's physiological response, characterized by her increased heart rate, sweaty hands, and flushed cheeks, indicates that her sympathetic nervous system has been activated.
Autumn's physiological response, such as an increased heart rate, sweaty hands, and flushed cheeks, is a typical manifestation of the fight-or-flight response, which is controlled by the sympathetic nervous system. In this situation, Autumn's body is reacting to a perceived threat or a stressful stimulus, which in this case is the presence of the boy she has a crush on.
When the sympathetic nervous system is activated, it triggers the release of stress hormones like adrenaline, which leads to various physiological changes in the body. These changes include increased heart rate, dilation of blood vessels, increased blood flow to the muscles, and sweating, all of which prepare the body for action in response to a perceived threat. This response is part of the body's automatic reaction to stressful or arousing situations and helps to mobilize the body's resources to deal with the perceived threat or challenge.
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a force is applied tyo a 2kg radio controlled model car parallel to the x axis as it moves along a straight track. The x-component of the forces varies with the x-coordinate of the car as shown in the figure.
no title provided
Calculate the work done by the force F when the car moves from x=4.0m to x=7.0m.
W=___J
Calculate the work done by the force F when the car moves from x=0 to x=7.0m.
W=___J
Calculate the work done by the force F when the car moves from x=7.0m to x=2.0m
W=___J
Therefore, According to the given information: W = 30 J (x=4.0m to x=7.0m), W = 40 J (x=0 to x=7.0m and x=7.0m to x=2.0m)
To calculate work, we use the formula W = F * d * cos(theta), where F is the force applied, d is the distance moved, and theta is the angle between the force and displacement vectors. Since the force is parallel to the x-axis, theta = 0 and cos(theta) = 1.
For the first question, the force is constant between x=4.0m and x=7.0m, so we can use W = F * d = (10 N)(3.0 m) = 30 J.
For the second question, we need to split the distance into segments where the force is constant. From x=0 to x=2.0m, the force is 0 N, so no work is done. From x=2.0m to x=4.0m, the force is 5 N, so W = (5 N)(2.0 m) = 10 J. From x=4.0m to x=7.0m, the force is 10 N, so W = (10 N)(3.0 m) = 30 J. Adding these up gives W = 40 J.
For the third question, we use the same approach as the second question but in reverse. From x=7.0m to x=4.0m, the force is 10 N, so W = (10 N)(3.0 m) = 30 J. From x=4.0m to x=2.0m, the force is 5 N, so W = (5 N)(2.0 m) = 10 J. From x=2.0m to x=0, the force is 0 N, so no work is done. Adding these up gives W = 40 J.
Therefore, According to the given information: W = 30 J (x=4.0m to x=7.0m), W = 40 J (x=0 to x=7.0m and x=7.0m to x=2.0m)
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an organization will give a prize to a local artist. the artist will be randomly chosen from among 7 painters, 4 sculptors, and photographers. what is the probability that the artist chosen will be a painter or a 5 photographer? write your answer as a fraction.
The probability that the artist chosen will be a painter or a photographer is 3/4
What is probability?Probability is the function that measures the chances that an outcome of a random event will be as expected. In this way you can measure how likely it is that an event will happen.
To solve this exercise the formula and the procedure that we have to use for probability is:
probability= (achieving success / possible outcomes)
Achieving success = 7 painters + 5 photographer = 12
Possible outcomes = 7 painters + 5 photographer + 4 sculptors = 16
Applying the formula to calculate the probability we get:
probability= (achieving success / possible outcomes)
probability= 12/16
Simplifying:
probability= 3/4
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................................................................................................
Answer: A is the answer (7,9)
Perform the following mathematical operation and report the answer to the appropriate number of significant figures. We know the least precise place value is the 10's place.
67.4+43+30+42.10=?
Answer:182.5
Step-by-step explanation: 67.4 + 43 = 110.4
110.4 + 30 + 42.10
110.4 + 30 = 140.4
140.4 + 42.10
140.4 + 42.10 = 182.5
182.5
Round 182.5 → 182 (Decimals: 0)
Write a function called count characters that counts the number of times each character appears in a user-supplied string s
This output shows the counts of each character in the string "hello world". The letter 'l' appears 3 times, the letter 'o' appears 2 times, and so on.
Here's an example Python function called count_characters that counts the number of times each character appears in a user-supplied string s:
def count_characters(s):
Given a string s, returns a dictionary containing the count of each character in the string.
char_count = {}
for char in s:
if char in char_count:
char_count[char] += 1
else
char_count[char] = 1
return char_count
This function creates an empty dictionary called char_count to store the counts of each character. It then loops through each character in the string s and checks if it's already in the char_count dictionary. If it is, it increments the count for that character. If it's not, it adds the character to the dictionary with a count of 1. Finally, the function returns the char_count dictionary.
You can call this function like this:
string = "hello world"
char_count = count_characters(string)
print(char_count)
Output:
python
{'h': 1, 'e': 1, 'l': 3, 'o': 2, ' ': 1, 'w': 1, 'r': 1, 'd': 1}
This output shows the counts of each character in the string "hello world". The letter 'l' appears 3 times, the letter 'o' appears 2 times, and so on.
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What is the surface area of the pyramid?
Answer:
56 inches squared
Step-by-step explanation:
(4x6) ÷ 2 = 12
12 x 4 = 48
4 x 4 = 16
48 + 16 = 56
Majed made 208$ for 13 hours of work. At the same rate, how much would he make for 7 hours of work
Answer:
230
Step-by-step explanation: because he worked 13 hours early at the same rate
Answer:
$230
Step-by-step explanation:
Question 10 Not yet answered Points out of 1.5 Flag question Use the following cash flow data to calculate the project's NPV: WACC: 10.00% tax rate: 35% Year 0 1 2 3 Cash flows -$1,050 $450 $460 $470 Be sure to show both your answer and the TVM function inputs on the calculator to receive credit. Be sure to use 4 decimal places (25.25% or 0.2525).
Answer:
The NPV of the project is $75.40.
Step-by-step explanation:
To calculate the Net Present Value (NPV) of the project, we need to discount the cash flows to their present value using the Weighted Average Cost of Capital (WACC) and the provided tax rate.
Using a financial calculator or spreadsheet, we can calculate the NPV as follows:
Inputs:
WACC = 10.00%
Tax rate = 35%
Year 0 cash flow = -$1,050
Year 1 cash flow = $450
Year 2 cash flow = $460
Year 3 cash flow = $470
Calculations:
Calculate the present value of each cash flow using the formula:
PV = CF / (1 + r)^n, where CF is the cash flow, r is the discount rate, and n is the time period.
Year 0: PV0 = -$1,050 / (1 + 0.10)^0 = -$1,050
Year 1: PV1 = $450 / (1 + 0.10)^1 = $409.09
Year 2: PV2 = $460 / (1 + 0.10)^2 = $375.21
Year 3: PV3 = $470 / (1 + 0.10)^3 = $341.10
Calculate the after-tax cash flows by multiplying each cash flow by (1 - tax rate):
After-tax cash flow = Cash flow * (1 - tax rate)
Year 0 after-tax cash flow = -$1,050 * (1 - 0.35) = -$682.50
Year 1 after-tax cash flow = $450 * (1 - 0.35) = $292.50
Year 2 after-tax cash flow = $460 * (1 - 0.35) = $299.00
Year 3 after-tax cash flow = $470 * (1 - 0.35) = $305.50
Calculate the NPV by summing up the present values of the after-tax cash flows:
NPV = PV0 + PV1 + PV2 + PV3
NPV = -$1,050 + $409.09 + $375.21 + $341.10 = $75.40
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A special deck of cards has 9 green cards , 11 blue cards , and 7 red cards . When a card is picked, the color is recorded. An experiment consists of first picking a card and then tossing a coin.
a. How many elements are there in the sample space?
b. Let A be the event that a green card is picked first, followed by landing a head on the coin toss.
P(A) = Round your answer to 4 decimal places.
c. Let B be the event that a red or blue is picked, followed by landing a head on the coin toss. Are the events A and B mutually exclusive?
- Yes, they are Mutually Exclusive
- No, they are not Mutually Exclusive
d. Let C be the event that a green or blue is picked, followed by landing a head on the coin toss. Are the events A and C mutually exclusive?
- Yes, they are Mutually Exclusive
- No, they are not Mutually Exclusive
a. There are 54 elements in the sample space.
b. P(A) = 0.2778
c. No, events A and B are not mutually exclusive.
d. No, events A and C are not mutually exclusive.
a. To find the total number of elements in the sample space, we need to multiply the number of cards by the number of possible outcomes from the coin toss. Therefore, the sample space has 54 elements (9+11+7) x 2.
b. The probability of event A is the probability of picking a green card first (9/27) multiplied by the probability of getting a head on the coin toss (1/2). Therefore, P(A) = (9/27) x (1/2) = 0.2778 (rounded to 4 decimal places).
c. Events A and B are not mutually exclusive because it is possible to pick a red or blue card and still have a head on the coin toss. Therefore, there are some elements in the sample space that belong to both events.
d. Events A and C are not mutually exclusive because it is possible to pick a green card and still have a head on the coin toss. Therefore, there are some elements in the sample space that belong to both events.
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Write the mission power of 10 in exponent form 0.007 X_____=7
On solving the provided question we cans ay that - the value of the following exponent is \(10^-5\)
what are exponents?Exponentiation, often known as "b raised to the nth power," is a mathematical operation denoted by the symbol bn that involves two numbers: a base number, b, and an exponent, or power, n. Exponents show how many times a number has been multiplied by itself. As an illustration, 2-3 (written as 23) denotes: 2 x 2 x 2 = 8. 23 is not equivalent to 2 + 3 = 6. Recall that an integer raised to the power of one equals itself. A approach to express huge numbers as powers is through the use of exponents. Exponent, then, is the quantity that indicates how many times a number has been multiplied by itself. As an illustration, 6 is multiplied by 4 to provide 6 x 6 x 6 x 6. It may be expressed as 64. 4 is where
here,
\(10^-5\) = \(\frac{1}{10^5}\)
= 1/100000
=0.00001
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Determine the equation of the line that passes through (-8,9) and (2,-6)
Express you answer as a fraction in lowest terms.
The equation of the line that passes through the points (-8, 9) and (2, -6) is y = (-3 / 2)x - 3.Given two points (-8, 9) and (2, -6). We are supposed to find the equation of the line that passes through these two points.
We can find the equation of a line that passes through two given points, using the slope-intercept form of the equation of a line. The slope-intercept form of the equation of a line is given by, y = mx + b,Where m is the slope of the line and b is the y-intercept.To find the slope of the line passing through the given points, we can use the slope formula: m = (y2 - y1) / (x2 - x1).Here, x1 = -8, y1 = 9, x2 = 2 and y2 = -6.
Hence, we can substitute these values to find the slope.m = (-6 - 9) / (2 - (-8))m = (-6 - 9) / (2 + 8)m = -15 / 10m = -3 / 2Hence, the slope of the line passing through the points (-8, 9) and (2, -6) is -3 / 2.
Now, using the point-slope form of the equation of a line, we can find the equation of the line that passes through the point (-8, 9) and has a slope of -3 / 2.
The point-slope form of the equation of a line is given by,y - y1 = m(x - x1)Here, x1 = -8, y1 = 9 and m = -3 / 2.
Hence, we can substitute these values to find the equation of the line.y - 9 = (-3 / 2)(x - (-8))y - 9 = (-3 / 2)(x + 8)y - 9 = (-3 / 2)x - 12y = (-3 / 2)x - 12 + 9y = (-3 / 2)x - 3.
Therefore, the equation of the line that passes through the points (-8, 9) and (2, -6) is y = (-3 / 2)x - 3. Thus, the answer is (-3/2)x - 3.
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The production rate per hour of a purse factory that can manufacture 200 purses in 8 hours.
Answer:
>:)
Step-by-step explanation:
200 purses, 8 hours
200/8 = 25
25 purses per hour!
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Answer: The Factory manufactures 25 purses per hour
Step-by-step explanation:
200 purses / 8 hours
25 purses per hour
a) about what percentage of scores were between between 68 and 82? 68 % b) about what percentage of scores were between 61 and 75?
Therefore , the percentage of case 1 is 68% and percentage of case 2 is 47.4%
What is percentage?One percent (symbolized as 1%), being the hundredth component, is represented as 100 percent, while 200 percent signifies twice the amount specified. As an illustration, 1% of 1,000 chickens is equal to 1/100 of 1,000, or 10 birds, and 20% of the quantity is equal to 20% of 1,000, or 200.
Here,
Given: Total number of freshman =500
mean =75 and standard deviation =7
a) the percentage of scores that fell between 68 and 82
340 is the number of freshman whose scores that fell between 68 and 82
thus,
percentage = 340 /500 * 100
=> percentage = 68%
b)the percentage of scores that fell between 61 and 75
237 is the number of freshman whose scores that fell between 61 and 75
thus,
percentage = 237/500 * 100
=> percentage = 47.4%
Therefore , the percentage of case 1 is 68% and percentage of case 2 is 47.4%
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Let A={1,2,3,4,5,6} and B={4,6,8}. Which of the following is an element of A∩B?Select the correct answer below:3682
Given the following set:
A = {1,2,3,4,5,6}
B = {4,6,8}
∩ means "intersection" of two sets. In other words, the data that the two sets have in common.
Checking the given sets,
A = {1,2,3,4,5,6}
B = {4,6,8}
A∩B or A and B have a common data of 4 and 6. These two are the intersections of A and B.
Among the given choices, only Choice B is correct which is 6.
Therefore, the answer is CHOICE B : 6
How do you find an expression for a cubic function f if f(5) = 300 and f(−5) = f(0) = f(6) = 0?
The expression for the cubic function f is -5x^3 + 20x^2 - 25x.
To find an expression for a cubic function f(x) given specific values, we can start by using the general form of a cubic function: f(x) = ax^3 + bx^2 + cx + d.
We are given three points on the graph of the function: (5, 300), (-5, 0), and (0, 0), as well as (6, 0) which gives us a fourth point.
Substituting the x and y values into the equation, we get the following system of equations:
For point (5, 300):
300 = a(5^3) + b(5^2) + c(5) + d
For point (-5, 0):
0 = a(-5^3) + b(-5^2) + c(-5) + d
For point (0, 0):
0 = a(0^3) + b(0^2) + c(0) + d
For point (6, 0):
0 = a(6^3) + b(6^2) + c(6) + d
Simplifying these equations, we obtain a system of linear equations in terms of a, b, c, and d. Solving this system will give us the coefficients for the cubic function.
After solving the system, we obtain the expression for the cubic function:
f(x) = -5x^3 + 20x^2 - 25x
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