The linear function relating the variables C and S is given as follows:
C(S) = 5000 + 200S.
The graph of the linear function is given by the image at the end of the answer.
How to define the linear function?The linear function in this problem is defined in the slope-intercept as follows:
y = mx + b.
In which the coefficients of the function are defined as follows:
m is the slope, representing the rate of change of the output y relative to the input x.b is the y-intercept, representing the initial value of the output y.In the context of this problem, the variables are given as follows:
Output: Cost.Input: Tons of Sugar.It will cost $5000 to rent trucks, hence the intercept is of:
b = 5000.
It will cost an additional $200 for each ton of sugar transported, hence the slope is of:
m = 200.
Then the equation is defined as follows:
C(S) = 5000 + 200S.
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Each triangle weighs 2.5 pounds, each circle weighs 3 pounds, and x represents the weight of each square. Select all equations that represent the hanger.
Answer: 1
Step-by-step explanation:
The Ponce Inlet lighthouse in Ponce Inlet has a gallery deck where one can view the surrounding area. Kim is standing on the deck, point k, which is 140.75 feet above ground level. Louise point L, is standing 200ft from the base of the lighthouse directly below Kim’s position. Determine the distance, in feet, between point K and point L
The distance between Kim and Louise is 340.75 feet.
What is algebra?Algebra is a study of mathematical expressions, in which numbers and quantities are represented in formulas and equations by letters and other universal symbols.
Given that,
The distance of Kim from the ground level, who is standing on the deck at point K = 140.75 feet.
Also, the distance of Louise at point L, who is standing below Kim's position, = 200 feet.
The distance between point K and L,
= 200 + 140.75
= 340.75 feet
The required distance between K and L is 340.75 feet.
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Whats is 3/2 x 2/3 mas a mixed number
Answer:
3/2*2/3=1
Step-by-step explanation:
3/2*2/3. Everything cancels out, and you are left with 1.
3/2*2/3=6/6=1
Answer:
=1
Using the given fractions,
3/2×2/3
Applying the fractions formula for multiplication,
=3×2/2×3
=6/6
Simplifying 6/6, the answer is
=1
The sample mean is 12.8, and the sample standard deviation is two. The sample size is 20. What distribution should you use to perform a hypothesis test? Assume the underlying population is normal.
A. Student's t-distribution
B. geometric distribution
C. exponential distribution
D. normal distribution
E. binomial distribution
If the sample mean is 12.8, sample standard deviation is 2 and sample size is 20, then the student's t-distribution should be use to perform the hypothesis test
The population mean = 13
The sample mean = 12.8
The standard deviation = 2
The sample size of the population = 20
The given condition is the underlying population is normal.
Here population standard deviation is missing in the given data. So to perform a hypothesis test when the population standard deviation is missing then we have to use the student t-distribution
Therefore, the student's t-distribution should be use to perform the hypothesis test
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Please help I am trash at these ones and I'll keep posting questions like these
The average rate of change between x = -3 and x = 1 is; 9/4
How to calculate the average rate of change?The average rate of change is calculated as the slope of the line between the two given points on the graph.
Now, looking at the graph, we can see that the coordinates of the two given points are;
(-3, -6) and (1, 3)
The formula to calculate the average rate of change which is the slope is;
m = (y₂ - y₁)/(x₂ - x₁)
m = (3 - (-6))/(1 - (-3))
m = 9/4
Thus, that is the average rate of change in conclusion
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A group of hikers started at an elevation of 1,803 feet. A squid is swimming 300 feet below sea level. What is the distance between the hikers and the squid
Answer:
1503
Step-by-step explanation:
1803 - 300
A rectangular board has an area of 648 square centimeters. The triangular part of the board has an area of 162 square centimeters. A dart is randomly thrown at the board. Assuming the dart lands in the rectangle, what is the probability that it lands inside the triangle? round to the nearest whole percent. 18% 25% 35% 50%.
Answer: 25% i believe
Step-by-step explanation:
The probability that it lands inside the triangle is,
P = 25%
What is mean by Probability?The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.
Since, the probability is equal to,
P = size of the event space/size of the sample space
Here, In this problem
size of the sample size = area of the rectangular dartboard = 648 square centimeters
And, size of the event space = area of the triangular part = 162 square centimeters.
Hence, the probability that it lands inside the triangle is,
P = 162 / 648
P = 0.25
P = 25%
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7) Mrs. Bell's favorite coffee place used to charge $2 for a small coffee,
now they charge $5. Find the percent of change in the price.
Answer:
150%
Step-by-step explanation:
2 x 2 = 4
Remainder=1
50% OR 0.5 x 2 = 1
Find the solution to the following system by substitution.
4x + y = 40
y = 4x
OA. (0,40)
OB. (5,20)
O C. (10,40)
D. (10,0)
A line has a slope of
7/10 and includes the points (c, -3) and (10, 4). What is the value of c?
Answer:
0
Step-by-step explanation:
Slope=(y2-y1)/(x2-x1)
=(4-(-3))/(10-c)=7/10
=7/(10-c)=7/10
c=0
What is (-9,8) reflected across the y-axis?
Answer: ( -9, -8)
Step-by-step explanation:
When reflected across the y-axis, the y-coordinate will be the opposite!
So the answer is (-9, -8)
What is the value of x? Responses 12√2 4√3 12 4
Answer:
x = 4[tex]\sqrt{3}[/tex]
Step-by-step explanation:
using the sine ratio in the right triangle and the exact value
sin60° = [tex]\frac{\sqrt{3} }{2}[/tex]
sin60° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{x}{8}[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )
2x = 8[tex]\sqrt{3}[/tex] ( divide both sides by 2 )
x = 4[tex]\sqrt{3}[/tex]
How do you find the roots of a polynomial using synthetic division?
Synthetic division is a yet another way to divide a polynomial by the factor, where k is a constant.
What is a synthetic division?
Synthetic division is usually used to find factors of polynomials of degree 3 that cannot be factored by grouping the polynomial.
Synthetic division is also used to find factor polynomials of degree 4 or higher.
We use synthetic division if and only if no other methods will work since there is a trial and error aspect to using it.
Taking an example:
We have to find the roots of the polynomial, [tex]f(x)= x^3+3x^2-4[/tex]
Substituting x=1 in the above equation, we get,
f(1)= [tex]1^3+3-4[/tex]=0
Thus, (x-1) is a root of the above polynomial.
Dividing the given function by (x-1)
[tex]x^3+3x^2-4/x-1\\=x^2+4x+4\\=(x+2)^2[/tex]
Thus, the roots of the given polynomial are given as, (x-1) and [tex](x+2)^2[/tex].
Hence, this is the synthetic division to find out the roots of the polynomial.
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Multiply 1 3/4 x 7 1/5 Simplify your answer and write it as a mixed fraction.
Answer: 12 3/5
Step-by-step explanation:
1 3/4 x 7 1/5 = 12.6= 12 3/5
The Sugar Sweet Company is going to transport its sugar to market. It will cost $5000 to rent trucks, and it will cost an additional $200 for each ton of sugar transported. Let C represent the total cost (in dollars), and let S represent the amount of sugar (in tons) transported. Write an equation relating C to S, and then graph your equation using the axes below.
The equation relating C and S is given as follows:
C(S) = 5000 + 200S.
The graph of the equation is then given by the image shown at the end of the answer.
How to define the function?The first step in defining the function is verifying the input and the output variables, as follows:
Output: Cost.Input: Tons of Sugar.Then from these variables, we identify the type of function, which is linear, as for each additional ton of sugar, the cost increases by a fixed amount.
This fixed amount is of $200, hence it represents the slope of the function. The fixed fee of $5,000 to rent trucks is the intercept, hence the equation is defined as follows:
C(S) = 5000 + 200S.
And then the graph starting at (0,5000) and connecting point (10, 7000) is given at the end of the answer.
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A 14 seater matatu charges sh 20 per passenger during normal hours and sh 30 per passenger during rush hours. if it made 10 trips and earned sh 3540.how many rush hours trip did it make
Answer:
2
Step-by-step explanation:
A 14 seater matatu makes 1420 = <<1420=280>>280 shillings per trip during normal hours.
It makes 1430 = <<1430=420>>420 shillings per trip during rush hours.
Since the matatu made 10 trips and earned 3540 shillings, then it made 10-3540/280 = <<10-3540/280=12>>12 trips during normal hours.
This means it made 10-12 = <<10-12=2>>2 trips during rush hours. Answer: {2}.
5) Find the perimeter of JKL. j 5x-8 8r-35 I ㅏ N 7y-9 2y + 11 -32- K
=======================================================
Explanation:
Segments JK, KL, and JL are tangent to the circle.
We can break those segments into smaller pieces and notice we have these 3 pairs of congruent tangents:
MJ = NJKN = KOLM = LOLet's use the first equation to solve for x.
MJ = NJ
5x-8 = 8x-35
5x-8x = -35+8
-3x = -27
x = -27/(-3)
x = 9
Use the same idea to find y.
KN = KO
7y-9 = 2y+11
7y-2y = 11+9
5y = 20
y = 20/5
y = 4
Now compute the length of segment KO.
KO = 2y+11 = 2*4+11 = 19 units
Subtract this from LK to find LO
LO = LK - KO
LO = 32 - 19
LO = 13
This makes segment LM to be also 13 units long.
Now use the value of x to find sides MJ and NJ
MJ = 5x-8 = 5*9-13 = 32
NJ = 32 as well
--------------------------------------------------------------
We have these pieces:
MJ = NJ = 32KN = KO = 19LM = LO = 13which give us
JK = NJ+KN = 32+19 = 51KL = KO+LO = 19+13 = 32JL = MJ+LM = 32+13 = 45Therefore, the perimeter of triangle JLK is:
JK+KL+JL = 51+32+45 = 128 units
Consider the following two points:
A (1,3)
B (6,13)
What is the initial value of the linear function through A and B?
Initial value of the linear function through A and B is 3.
Define initial value.The starting output value, or the y-value when x = 0, is the initial value. The rate of change is the rate at which the input or, in the case of a graph, the rate at which y changes in relation to x. A function's starting value in mathematics denotes the function's y-intercept. The constant in an equation can also be used to determine initial values. In graph functions, understanding the y-intercept is beneficial. By substituting 0 0 for x x and finding y y, you may verify the starting value.
Given,
Points
A (1,3)
B (6,13)
Linear function,
f(x) = ax + b
Equating,
f(x) = x + 3
Let x = 0
f(x) = 3
As we know,
The graph of a linear function is a straight line. The following is the form of a linear function. a + bx = y = f(x). One independent variable and one dependent variable make up a linear function. X and Y are the independent and dependent variables, respectively.
Initial value of the linear function through A and B is 3.
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What is the type of scale in which the representative factor is 1 is to 1?
A full size scale is a type of scale in which the representative factor is 1 is to 1
A scale factor is defined as the ratio of the scale of a given original object to the scale of a new object that is its representation but of a different size.
To determine the scale factor, first identify the corresponding sides on the two figures.
Then, divide the new figure's measurement by the original figure's measurement. The resulting value is your scale factor, or how many times your new figure is larger or smaller than the original.
A full size scale is a scale in which the length of the drawing is proportional to the actual length of the object.
As a result, its representative fraction is 1:1 by definition. The drawing is drawn in full size scale with the actual measurement
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What is the average rate of change of the function on the interval from x = 0 to x = 5? f(x)=12(3)x.
the average rate of change of the function on the interval from x = 0 to x = 5 is 580.8
Average rate of change of a function f(x) between x-values x1 and x2 = (f(x2) -f(x1)/ (x2 -x1)
For this given function f(x)=12(3)x then it will mean that
f(x) = 12.3^x and x-values 0 and 5, the average rate of change is
the average rate of change = (f(5) -f(0))/(5 -0) = (2916 -12)/5 = 580.8
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I have a couple of questions but whoever gives me the equation for all 3 and answers 1st will get the brainiest and a ton of points LOL( 50 POINTSSS)
1-what is the equation of the line that passes through (-5,4) and has a slope of 0
2-what is the equation of the line that passes through (-2,0) and has a slope of 2
3-what is the equation of the line that passes through the points (5,3)and has and unidentified slope
Thanksssssss :)
1) The line's equation is y = 4 because it passes through the coordinates (-5,4).
2) The equation of the line is y= 2x + 4
What is slope ?
A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x).
1) A line with a slope of 0 is considered to be horizontal.
The equation is y=4 because along a horizontal line, the y-values remain constant.
The line's equation is y=4 because it passes through the coordinates (-5,4).
2) (x1,y1) = (-2,0) , m=2
y-y1=m(x-x1)
y-0 = 2 (x-(-2))
y=2(x+2)
y= 2x + 4
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square root of 998001
For the number given as - {n} = 998001, its corresponding square root is 999.
What is square root of a number?In mathematics, a square root of a number [x] is a number [y] such that - y² = x. in other words, a number y whose square is x. For example, 4 and −4 are square roots of 16.
y² = x
y = ±√(x)
Given is to find the square root of a number as follows -
998001
The given number is -
998001
We can write it as -
x² = 998001
x = ± 999
Therefore, we get the value of [x] as 999.
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What's the slope of 7x Y =- 4?
To find the slope of a line given an equation in the form of ax + by = c .The slope of 7x + y = -4 is 7.
To find the slope of a line given an equation in the form of ax + by = c, you first need to put the equation into slope-intercept form, which is y = mx + b. To do this, start by subtracting ax from both sides of the equation, leaving you with by = c - ax. Then divide both sides by b, giving you y = (c - ax) / b. This is the equation in slope-intercept form, with m being the slope, which in this case is 7.
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The interpretation of the slope is different in a multiple linear regression model as compared to a simple linear regression model.a. True
b. False
It is true that a multiple linear regression model interprets the slope differently than a simple linear regression model.
The link between two variables is determined through simple linear regression. The slope of a straight line used to represent linear regression indicates how changing one variable impacts another variable.
For the complex relationships between data, multiple linear regression is used. More than one variable may contribute to the explanation of this relationship.
One y-intercept and numerous slopes (one for each variable) make up a multiple regression formula. The formula is understood in the same way as a simple linear regression formula, however more than one variable influences the relationship's slope.
Therefore, the statement is true.
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Which phrase best defines “figurative language”?
writing that is meant to be imaginative and vivid rather than literal
words that create mental pictures of something seen, heard, tasted, smelled, or touched
poems that include many different types of rhymes and rhythms
sentences that are long and reference historical and literary figures
The phrase that best defines “figurative language is A. writing that is meant to be imaginative and vivid rather than literal
What is a figurative language?The use of figurative language, as opposed to literal language, serves the following purpose: it allows the reader to imagine what the author means when he writes a sentence or a statement. Figurative speech strengthens and deepens an author's work.
Figurative language is the use of words in unconventional ways to convey a complicated meaning, colorful writing, clarity, or evocative comparison. It employs a common sentence to allude to something without directly stating it.
Types of Figurative Language include:
Simile. Metaphor. Hyperbole. Personification. Synecdoche. OnomatopoeiaIn conclusion, the correct option is A.
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You are working on an air conditioning system. A roll of cylindrical copper tubing has an outside diameter of 78 inch and an inside diameter of 34 inch. How much refrigerant can 12 feet of the tubing hold?.
557,568 inch³ of refrigerant can be held by the tubing.
Here we have to find how much a refrigerant can hold.
Data given:
outer diameter (d) = 78inch
outer radius(r) = 39 inch
inner diameter (d') = 34 inch
inner radius (r') = 17inch
Height (h) = 12 feet
= 12 × 12
= 144 inch
the formula to find the volume of the cylinder:
volume= пr²h
So here we get
Refrigerant hold = Volume of the outer cylinder - the volume of the inner cylinder
= πr²h - πr'²h
= πh(r² - r'²)
= π ×144 ( 39² - 17²)
= π × 144 ×56 × 22
= 22/7 × 144 × 56 × 22
= 557,568 inch³
Therefore the refrigerant can hold 557,568 inch³.
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what is the probability of getting at least 1 gram more cereal than advertised? there is a 0.1234 probability of getting at least 1 gram more cereal than advertised. there is a 0.0905 probability of getting at least 1 gram more cereal than advertised. there is a 0.5726 probability of getting at least 1 gram more cereal than advertised. there is a 0.7705 probability of getting at least 1 gram more cereal than advertised. there is a 0.8766 probability of getting at least 1 gram more cereal than advertised.
P(Z3)=0.1170 is the likelihood of earning at least 1 gram of extra cereal.A probability seems to be a number that expresses the possibility or probability that a specific event will take place.
How is probability determined?The probability is computed by dividing the total possible outcomes by the number of possible ways the event could occur. Probabilistic and odds are two distinct ideas. Odds are the likelihood that something will occur and the variety of outcomes that can result in success. the overall number of outcomes that could occur. For instance, there is only one way to receive a head and there are a total of two possible outcomes, hence the probability of flipping the coin and getting heads is 1 in 2.
Y=1.8945 grams.
Y = 0.8405 grams.
The z-score is the result of dividing the standard deviation by the value that has been decreased by the mean:
z= σx−μ = 0.85053−1.9845≈1.19
Table A can be used to determine the relevant value:
P(Z≥3)=P(Z>1.19)=1−P(Z<1.19)=1−0.8830=0.1170
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A store is having a sale. They are offering $15 off the
purchase of 4 video games and 10% off if you are a
first time customer.
The discounts could be applied in two different orders.
Which do you PREDICT would save you the most
money?
Use intuition, don't calculate.
You will save more by getting $15 off, then 10% off
You will save more by getting 10% off, then $15 off
You will save the same amount either way
Answer:
You would be saving the same amount of money either way.
Step-by-step explanation:
It's the commutative property.
the incubation period of ebola virus is known to have a normal distribution with a mean of 10 days and a standard deviation of 7 days suppose a group of researchers claimed that the true mean is shorter than 10 days. a test is conducted using a random sample of 23 patients. consider a rejection region suppose the test failed to reject . if the true mean incubation period is 6 days, what is the type ii error probability of the test using (round off to third decimal place)?
The required type ii error probability of the test using is 0.085.
What is probability of the test?It is determined by duplicating the pretest chances by the probability of a positive or negative test (as we will show). Post-test probability is characterized, as the likelihood of the objective problem after a symptomatic experimental outcome is known.
According to question:We have,
standard deviation = 7, mean = 6, size of the sample = 23.
P(type II error) = P(Xbar >=8 given mean =6)
=P(Z>(8-6)×√(23)/7) =P(Z>1.37)=1-P(Z<1.37)
=1-0.9147=0.0853 =0.085
Thus, required probability is 0.085
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PLEAZE HELPP 50 POINTS If the function f(x) =-3x3 +7x represents the movement of a whale in meters what is the average rate of change of the whale for x=1 and X=3 seconds label your answer
Answer:
The average rate of change of a function over an interval is found by taking the difference between the function's values at the endpoints of the interval and dividing by the length of the interval. In this case, we have:
f(1) = -3(1)^3 + 7(1) = -3 + 7 = 4
f(3) = -3(3)^3 + 7(3) = -27 + 21 = -6
The average rate of change over the interval from x=1 to x=3 is therefore (-6 - 4) / (3 - 1) = -10 / 2 = -5.
To label your answer, you could write something like: "The average rate of change of the whale's movement over the interval from x=1 to x=3 seconds is -5 meters/second."