Answer:
To prove that triangle ABF is congruent to triangle EDG, we need to show that the three sides of triangle ABF are congruent to the corresponding three sides of triangle EDG.
Since we are given that BC is congruent to DC, AB is congruent to ED, and AG is congruent to EF, we can conclude that the three sides of triangle ABF are congruent to the corresponding three sides of triangle EDG. Therefore, triangle ABF is congruent to triangle EDG.
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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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
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 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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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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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)
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 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}.
What needs to be known to determine the critical values for an independent-samples t test?
the sample size of the power analysis
degrees of freedom for the smallest group
total degrees of freedom
degrees of freedom for the largest group
Total degrees of freedom needs to be known to determine the critical values for an independent-samples t-test. So, option 3 is correct.
What is meant by critical value?To evaluate whether the null hypothesis should be rejected or not, a critical value is a value that is contrasted with a test statistic in hypothesis testing. The null hypothesis cannot be rejected if the test statistic's value is not more extreme than the crucial value.
In the sampling distribution of a test statistic, a crucial value delimits areas. Both hypothesis tests and confidence intervals take these values into consideration. When conducting hypothesis testing, crucial values are used to assess whether the findings are statistically significant.
A t-test with independent samples.
To compute the critical values, one must therefore be aware of the degrees of freedom and significance level.
Therefore, total degrees of freedom needs to be known to determine the critical values for an independent-samples t-test.
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What are the 5 transformations of a linear function?
The 5 transformations of a linear function are translation , reflection , dilation , vertical transformation and horizontal transformation.
In the question ,
we have to write the different types of transformation .
A transformation is defined as an alteration in the parent function’s graph .
there are basically 3 main types of transformations .
(i) the first type is Translations ,
the translation causes the graph to shift left, right, up, or down so many units.
(ii) the second type is Reflection ,
the Reflections cause the graph to rotate/flip over the x-axis or y-axis.
(iii) the third type is Dilation ,
In dilation the shape of a graph is changed by a certain factor. that is the graphs will look narrower or wider .
the other two transformations are
(iv) vertical transformation : it affects the y axis .
(v) horizontal transformation : it affects the x axis .
Therefore , the 5 types of transformation are explained above.
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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:
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."
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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an arched window is in the shape of a rectangle surmounted by a semicircle. if the perimeter is 5 m, what should the radius of the semicirculoar part be if the window is to admit as much light as possible?
The radius of the semicircle surmounted on the rectangle with perimeter 5m is equal to 5 / ( 4 + π )meters
As given in the question,
Let '2x' be the side where semicircle surmounted on rectangle.
And y be the width of the rectangle.
Total perimeter = 5m
⇒ Perimeter of three sides rectangle + circumference of semicircle with radius 'x' = 5
⇒ 2y + 2x + πx = 5
⇒ 2y + x ( 2 + π ) = 5
⇒ y = (1/2)[5 - x ( 2 + π )]
Let 'A' be the total area
Total area of the shape = area of rectangle + area of semicircle
⇒A = 2xy + (1/2)πx²
⇒A = 2x( (1/2)[5 - x ( 2 + π )]) + (1/2)πx²
⇒A = 5x - x²(2 + π) + (1/2)πx²
⇒A = 5x - 2x² - (1/2)πx²
For maximum light
dA/dx = 0
dA/dx = 5 -4x -πx
⇒5 - 4x - πx = 0
⇒x = 5 / ( 4 + π )meters
Therefore, the radius of the semicircular part to have maximum light is equal to 5 / ( 4 + π )meters.
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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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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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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
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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The population of a small town, P, as a function of time, t, in years past 1940 is given below.
P = 2,323 + 200t
For which of the following years was the population of the town 7,723?
A.
1967
B.
1927
C.
1937
The population grew to the number 7,723 in 27 years past 1940, i.e., 1967.
What is the linear function?
In mathematics, the term linear function refers to two distinct but related notions: In calculus and related areas, a linear function is a function whose graph is a straight line, that is, a polynomial function of degree zero or one.
We have,
The population of a small town, P, as a function of time, t, in years past 1940 is:
P = 2,323 + 200t
Let t be the year in which the population reached a count of 7,723. Solve for t:
P = 2,323 + 200t
7,723 = 2,323 + 200t
7,723 - 2,323 = 200t
5,400 = 200t
t = 5400/200
t = 27 years
Hence, The population grew to the number 7,723 in 27 years past 1940, i.e., 1967.
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a designer of custom windows wishes to build a norman window with a total outside perimeter of 60 feet. how should the window be designed to maximize the area of the window? a norman window contains a rectangle bordered above by a semicircle
The Dimensions are 16.402 in wide by 8.401 in tail
Can the perimeters of two dissimilar shapes match each other?
Be aware that shapes with similar areas might have dissimilar perimeters, and vice versa. The perimeter of shapes that have the same area are not always the same. Similar to how not all forms with the same perimeter have the same area.Perimeter of custom windows = Perimeter of (rectangle+ semicircle)
Perimeter of rectangle = 2xy
Perimeter of semicircle = 1/2 πx²
A = 2xy + 1/2 πx²
2x + 2y + πx = 60
y = (60 - 2x -πx) / 2
A = 2x([60 - 2x - πx] /2) + 1/2(πx²)
0 = 60 - 4x - πx
x = 60 / (π+4)
x = 8.401
Hence, Dimensions are 16.402 in wide by 8.401 in tail.
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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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Expressing trig ratios as fractions in simplest terms ?
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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What is the solution y 2 3x 3 x =- 2?
The solution of the equation y = (2/3)x + 3 is 5/3
The given equation is
y = (2/3)x + 3
The slope of the line is the change in y coordinates with respect to the change in x coordinates.
This is the linear equation in the the slope intercept form
y = mx + b
Where m is the slope of the line
b is the y intercept
y is the y coordinates
x is the x coordinates
The value of x = -2
Substitute the value of x in the equation
y = (2/3) × -2 + 3
Do the arithmetic operations
= -4/3 + 3
Add the numbers
= 5/3
Therefore, the solution is 5/3
I have solved the question in general, as the given question is incomplete
The complete question is:
What is the solution of the equation y = (2/3)x + 3x, when x = -2?
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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
Find the z-score for the given shaded region under the standard normal distribution. Round your answer to two decimal places
The Z - score for the given shaded region under the standard normal distribution = - 0.61
What is Standard Normal Distribution ?A normal distribution with a mean of zero and a standard deviation of one is known as the standard normal distribution. The standard deviation shows how far a given measurement deviates from the mean, and the standard normal distribution is centered at zero.
According to the given information
P(Z > z) = 0.73
= 1 - P(Z < z) = 0.73
= P(Z < z ) = 1 - 0.73
= P(Z < z ) = 0.27
= P(Z <-0.61 ) = 0.27
z = -0.61 (using standard normal (Z) table )
The Z - score for the given shaded region under the standard normal distribution = - 0.61
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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]
what is the equation of the least squares regression line that describes the relationship between operating cost per hour and number of passenger seats in the plane? define any variables used in this equation.
The equation of the Least squares regression line is:
y(hat) = a + bx ,
⇒y(hat) = 1136+14.673x,
y(hat) = cost per hour and x= number of seats
If the data show a slimmer relationship between the two variables, the line that best fits this linear relationship is called the least-squares regression line, which minimizes the vertical distance between the data points and the regression line. The term "least squares" is used because it is the smallest sum of squared errors, also known as "variance".
In regression analysis, the dependent variable is plotted on the vertical Y-axis and the independent variable is plotted on the horizontal X-axis. These labels form the equation of the best-fit line determined by the least-squares method.
Operating costs are related to the day-to-day maintenance and management of your business. Operating expenses include direct cost of goods sold (COGS) and other operating expenses, often referred to as selling, general and administrative expenses (SG&A). These costs include rent, labor costs, other overhead costs, raw material costs, and maintenance costs. Operating expenses do not include non-operating expenses related to financing such as interest, investments and foreign currency translation. Operating expenses are deducted from revenue to determine operating profit and reflected in the company's income statement.
Operating cost=Cost of goods sold + Operating expenses
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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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