Answer:
To find the formula for (g∘f)(x), we need to first evaluate g(f(x)):
g(f(x)) = g(x+3) = (3(x+3)+5)/3 = (3x+14)/3
So, (g∘f)(x) = (3x+14)/3
To find the domain for (g∘f)(x), we need to consider any restrictions on x that would make the function undefined. The only possible restriction is if the denominator of (3x+14)/3 is zero, which occurs when 3x+14=0. Solving for x, we get x=-14/3. Therefore, the domain of (g∘f)(x) is all real numbers except -14/3, or (-∞, -14/3) U (-14/3, ∞).
find the average rate of change of f(x)=2x^2-2 from 2 to 4
Answer:
average rate of change = 12
Step-by-step explanation:
the average rate of change of f(x) in the interval a ≤ x ≤ b is
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
here the interval is 2 ≤ x ≤ 4 , then
f(b) = f(4) = 2(4)² - 2 = 2(16) - 2 = 32 - 2 = 30
f(a) = 2(2)² - 2 = 2(4) - 2 = 8 - 2 = 6
then
average rate of change = [tex]\frac{30-6}{4-2}[/tex] = [tex]\frac{24}{2}[/tex] = 12
Point P is shown on the number line below. The distance between Point Q and Point P is 6 1/2 uhits. Which number
could represent Point Q?
The number that could represent point Q is to be considered as the option c. 2 1/2.
How to solveCalculation of the number:
Since
p = -4
q could be 6.5 units to the right or to the left of point p.
So, to the right, it should be like
=p + q
= -4 + 6.5
= 2.5
Hence, The number that could represent point Q is to be considered as option c. 2 1/2.
In mathematics, a tool known as a number line offers a graphical representation of numerical values arranged in sequential order from left to right with zero located in the center. This instrument is frequently applied throughout mathematical fields when interpreting negative and positive numbers along with fractions and decimals.
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Use the Pythagorean theorem to find the unknown side of the right triangle.
I need help please
Answer:
[tex]\boxed{17}[/tex]
Step-by-step explanation:
Pythagorean theorem:
[tex]c^2=a^2+b^2[/tex]
where:
[tex]c=[/tex] hypothenuse
[tex]a=[/tex] the small size of the triangle
[tex]b=[/tex] the large size of the triangle
In this problem, we have the values of a and b, so:
[tex]c^2=(8)^2+(15)^2\\c^2=64+225\\c^2=289\\\sqrt{c^2}=\sqrt{289}\\ c=17[/tex]
Therefore the value of the unknown side of the triangle is 17.
Hope it helps.
[tex]\text{-B$\mathfrak{randon}$VN}[/tex]
160/30000 simplified
Answer:160/30000 simplified would be 2/375
Step-by-step explanation:
Exact Form:
[tex]\frac{2}{375}[/tex]
Decimal Form:
0.0053
How many solutions does the equation sin(4x) = 1/2 have on the interval
(0, 2π]?
The equation sin(4x) = 1/2 has two solutions on the interval (0, 2π]: x = π/24 and x = 5π/24.
The equation sin(4x) = 1/2 has two solutions on the interval (0, 2π].
The first solution occurs when 4x = π/6, or x = π/24. This corresponds to an angle of π/24 radians, or 7.5°.
The second solution occurs when 4x = 5π/6, or x = 5π/24. This corresponds to an angle of 5π/24 radians, or 112.5°.
Therefore, the equation sin(4x) = 1/2 has two solutions on the interval (0, 2π]: x = π/24 and x = 5π/24.
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The last 48 boat rentals at a boat rental company were 26 sunfish, 6 kayaks, and 16 rowboats. Use this information to complete parts (a) through (c).
a) Determine the empirical probability that the next boat rental is a sunfish.
b) Determine the empirical probability that the next boat rental is a kayak.
c) Determine the empirical probability that the next boat rental is a rowboat.
The answer is , (a) Empirical probability of sunfish rental = 0.5417 or 54.17% , (b) Empirical probability of kayak rental = 0.125 or 12.5% , (c) Empirical probability of rowboat rental = 0.3333 or 33.33% .
What is Empirical probability?Empirical probability is an estimate of the probability of an event based on the frequency of its occurrence in a sample of data. It is calculated by dividing the number of times the event occurred by the total number of observations in the sample. Empirical probability is often used when there is no theoretical probability available, or when the theoretical probability is difficult to calculate or unknown. It is a useful tool in fields such as statistics, finance, and machine learning.
a) The empirical probability that the next boat rental is a sunfish is the number of sunfish rentals divided by the total number of rentals:
Empirical probability of sunfish rental = number of sunfish rentals / total number of rentals
Empirical probability of sunfish rental = 26 / 48
Empirical probability of sunfish rental = 0.5417 or 54.17%
b) The empirical probability that the next boat rental is a kayak is the number of kayak rentals divided by the total number of rentals:
Empirical probability of kayak rental = number of kayak rentals / total number of rentals
Empirical probability of kayak rental = 6 / 48
Empirical probability of kayak rental = 0.125 or 12.5%
c) The empirical probability that the next boat rental is a rowboat is the number of rowboat rentals divided by the total number of rentals:
Empirical probability of rowboat rental = number of rowboat rentals / total number of rentals
Empirical probability of rowboat rental = 16 / 48
Empirical probability of rowboat rental = 0.3333 or 33.33%
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Find the standard form of the equation of the ellipse with the given characteristics and center at the origin.
The x y-coordinate plane is given. The curve starts at the point (0, 2.5), goes down and right, changes direction at the point (4, 0), goes down and left, changes direction at the point (0, −2.5), goes up and left, changes direction at the point (−4, 0), goes up and right, continuing until it reaches its starting point.
The standard form equation of the ellipse as described in the task content is;
x²/4² + y²/(5/2)² = 1.What is the standard form equation of the ellipse as described?It follows from the task content that the standard form equation of the ellipse is to be determined.
Recall, the equation of an ellipse takes the form;
(x - h)²/a² + (y - k)²/b² = 1
where (h, k) is the center and a represents the distance of the center to each vertex on the major axis and b represents the distance from the center to each vertex on the minor axis.
Therefore, for the given scenario where center is at the origin; the equation of the ellipse is;
x²/4² + y²/(5/2)² = 1
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Find the angle of depression from the top of a lighthouse 400 feet above water level to the water line of a ship 18,410 ft offshore? Round your answer to the nearest hundredth of a degree.
To find the angle of depression, we can use the tangent function in trigonometry. In this situation, we have a right triangle where the height (opposite side) is 400 feet, and the distance (adjacent side) is 18,410 feet.
tan(angle) = opposite / adjacent
tan(angle) = 400 / 18,410
Now, we'll use the arctangent (inverse tangent) function to find the angle:
angle = arctan(400 / 18,410)
angle ≈ 1.25 degrees
The angle of depression from the top of the lighthouse to the waterline of the ship is approximately 1.25 degrees, rounded to the nearest hundredth of a degree.
Break-Even Sales
BeerBev, Inc., reported the following operating information for a recent year (in millions):
Sales $6,512
Cost of goods sold $1,628
Gross profit $4,884
Marketing, general, and admin. expenses 592
Income from operations $ 4,292
Assume that BeerBev sold 37 million barrels of beer during the year, that variable costs were 75% of the cost of goods sold and 50% of marketing, general and administration expenses, and that the remaining costs are fixed. For the following year, assume that BeerBev expects pricing, variable costs per barrel, and fixed costs to remain constant, except that new distribution and general office facilities are expected to increase fixed costs by $21.09 million.
a. Compute the break-even sales (in barrels) for the current year. Round your answer to two decimal places. Enter your answers in millions.
The break even sales for the current year using the contribution per unit is 5.27.
The formula to find the break even sales is,
Break even sales = Fixed costs / Contribution per unit
Now,
Contribution per unit = Sales price per unit - Variable cost per unit.
Sales price = $6,512
Variable cost = (75% × cost of goods sold) + (50% × marketing, general and administration expenses)
= (75% × $1,628) + (50% × $592)
= $1517
Contribution margin = $6,512 - $1517 = $4995
Contribution per unit = $4995 / 37 = $135 per million
Fixed costs = (25% × cost of goods sold) + (50% × marketing, general and administration expenses)
= $703
Break even sales = 703 / 135 = 5.21
Hence the break even sales is 5.27.
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Which type of car had the largest range in monthly sales? Explain how you came up with your answer
Sample Response: I subtracted the highest and lowest numbers. The range for new cars was 31. The range for old cars was 75. The range for used cars was much bigger.
Answer:
Without access to specific data on monthly car sales, it is impossible to determine which type of car had the largest range in monthly sales. However, one possible method for finding this information would be to gather sales data for various car models across multiple months and compare the ranges of their sales figures. Alternatively, one could use industry reports or market analysis to determine which car types tend to have the largest fluctuations in sales from month to month.
Step-by-step explanation:
Without access to specific data on monthly car sales, it is impossible to determine which type of car had the largest range in monthly sales. However, one possible method for finding this information would be to gather sales data for various car models across multiple months and compare the ranges of their sales figures. Alternatively, one could use industry reports or market analysis to determine which car types tend to have the largest fluctuations in sales from month to month.
y<-4x-2 choose the graph that best models the inequality
Answer:the upper right one( the dash line that hit -2
Step-by-step explanation:
Please solve As soon as possible.
Answer:
-|x|+1
Step-by-step explanation:
A STUDY OF INTERIOR DESIGNERS OPIONIONS WITH RESPECT TO THE MOST DESIRABEL PRIMARY COLOR FOR EXECUTIVE OFFICES SHOWED THE FOLLOWING
The probability that a designer does not prefer red is 0.77. The Option 2 is correct.
What is probability?Probability is a measure of how likely an event is to happen. Probability is represented as a fraction and always lies between 0 and 1.
The total number of opinions is:
= 92 + 86 + 46 + 91 + 37 + 46 + 2
= 400
The number of designers who do not prefer red is the sum of the opinions for all colors except red:
= 86 + 46 + 91 + 37 + 46 + 2
= 308
Therefore, the probability that a designer does not prefer red is:
= 308/400
= 0.77.
Full question "A study of interior designers' opinions with respect to the most desirable primary color for executive offices showed that:
Primary Color Number of Opinions
Red 92
Orange 86
Yellow 46
Green 91
Blue 37
Indigo 46
Violet 2
What is the probability that a designer does not prefer red? 1.00 0.77 0.73 0.23".
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George plans to order flowers for his daughter's graduation. A bouquet of 12 roses will cost $61, while a bouquet of 18 roses will cost $79. What is the equation that represents the linear relationship between price and number of roses? Let P represent the price, and r the number of roses.
Answer:
Step-by-step explanation:
Start by finding the slope of the line that passes through both the 12 roses bouquet and the 18 roses bouquet.
point 1: (12,61)
point 2: (18,79)
m=y^2-y^1/x^2-x^1
m=79-61/18-12
m=18/6
m=3
then, using one of the points find the fixed costs
P=m*r+b
using 12,61
61=3*12+b
61-36=b
b=25
Answer:
The general equation that represents the linear relationship is:
P=25+3r
please help me i will give brainiest to whoever answers the questions thank you
PLEASE HELP please help thank you please hurry fast i will give brainiest
Answer:
3) The graph that has three x-intercepts
9) Plot the points on the graphing calculator, and then generate a linear regression equation. That equation is:
y = 2.857x - 1.4286
The closest equation is y = 3x - 2. That equation best represents the regression line for this data.
Find the missing angle measure. Show work.
17.
7
20
24
Solve the remaining parts of the triangle.
19.
B
38
12.5 C
7
13
17.
18.
19, AC=
AB-
mzB
Need help with all these please. Asap urgent help need this done before Monday
To find the missing angle measure, we need to use the fact that the sum of angles in a triangle is 180 degrees. Let's denote the missing angle as x. We know that one angle is 38 degrees and another angle is 12.5 degrees.Therefore, the missing angle measure is 129.5 degrees.
By subtracting these two angles from 180 degrees, we get:
180 - 38 - 12.5 = 129.5
Without additional information, it is not possible to determine the remaining parts of the triangle. We would need the lengths of at least one side or the measures of other angles to solve for the missing parts.
The given information states that AC is equal to AB minus mzB. Without knowing the values of AB and mzB, we cannot determine the exact length of AC. We would need additional information to solve for the length of AC.Therefore, the missing angle measure is 129.5 degrees.
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tion 9, 2.2.5 The histogram to the right represents the weights (in pounds) of members of a certain high-school math team. How many team members are included in the histogram? he histogram represents 20 math team members. www 4- 2- 0- Points: 0 of 1 110 120 130 140 150 160 170
Based on the information provided in the question, we can conclude that the histogram represents 20 math team members.
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[tex]\begin{align}\colorbox{black}{\textcolor{white}{\underline{\underline{\sf{Please\: mark\: as\: brillinest !}}}}}\end{align}[/tex]
[tex]\textcolor{blue}{\small\texttt{If you have any further questions,}}[/tex] [tex]\textcolor{blue}{\small{\texttt{feel free to ask!}}}[/tex]
♥️ [tex]{\underline{\underline{\texttt{\large{\color{hotpink}{Sumit\:\:Roy\:\:(:\:\:}}}}}}\\[/tex]
Reyesburg Corporation is contemplating using a new, more expensive glue in the construction of its laminated veneer lumber. Of importance to the company is
the carrying load of the lumber. The company has tested 34 beams using the new glue, recording for each beam the pressure (in pounds per square foot) at
which the beam breaks. The data collected are presented in the following frequency distribution.
Carrying load
(in pounds per square foot)
860 to 879
880 to 899
900 to 919
920 to 939
940 to 959
Frequency
5
9
12
6
2
Based on the frequency distribution, using the midpoint of each data class, estimate the mean carrying load of the beams tested. For your intermediate
computations, use four or more decimal places, and round your answer to one decimal place.
Based on the given frequency distribution, the estimated mean carrying load of the beams tested is approximately 904.2 pounds per square foot.
Estimate the mean carrying load of the beams tested.To estimate the mean carrying load of the beams tested, we need to find the weighted average of the midpoints of each data class.
First, we need to find the midpoint of each class interval. We can do this by taking the average of the lower and upper limits of each interval:
Midpoint of 860 to 879 = (860 + 879) / 2 = 869.5
Midpoint of 880 to 899 = (880 + 899) / 2 = 889.5
Midpoint of 900 to 919 = (900 + 919) / 2 = 909.5
Midpoint of 920 to 939 = (920 + 939) / 2 = 929.5
Midpoint of 940 to 959 = (940 + 959) / 2 = 949.5
Next, we can find the weighted average of these midpoints, using the frequencies as weights. We can set up a table to organize our calculations:
Data class Midpoint Frequency Midpoint x Frequency
860-879 869.5 5 4,347.5
880-899 889.5 9 8,005.5
900-919 909.5 12 10,914
920-939 929.5 6 5,577
940-959 949.5 2 1,899
Total 34 30,743.5
To find the weighted average, we divide the sum of the products in the last column by the total frequency:
Weighted average = Sum of (Midpoint x Frequency) / Total frequency
Weighted average = 30,743.5 / 34
Weighted average ≈ 904.2
Therefore, based on the given frequency distribution, the estimated mean carrying load of the beams tested is approximately 904.2 pounds per square foot.
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Faber Kozlowski had 6 times as much money as Theriault Luigi. After Faber Kozlowski spent 1/3 of his money and Theriault Luigi spent 4/5 of his money, they had a total of $1155 left.
(a) How much money did Faber Kozlowski and Theriault Luigi have altogether at first?
(b) Theriault Luigi spent 3/4 of his remaining money on a hoodie. What fraction of his original amount of money did he spend on the hoodie?
Answer:
Step-by-step explanation:
Let's use variables to represent the amount of money each person had at first.
Let x be the amount of money that Theriault Luigi had.
Then, according to the problem, Faber Kozlowski had 6 times as much money as Theriault Luigi, which means Faber Kozlowski had 6x dollars.
After Faber Kozlowski spent 1/3 of his money, he had 2/3 of his money left, which is (2/3)(6x) = 4x dollars.
After Theriault Luigi spent 4/5 of his money, he had 1/5 of his money left, which is (1/5)x dollars.
Together, they had a total of $1155 left, which means:
4x + (1/5)x = 1155
Multiplying both sides by 5 to eliminate the fraction gives:
20x + x = 5775
Combining like terms gives:
21x = 5775
Dividing both sides by 21 gives:
x = 275
Therefore, Theriault Luigi had $275 at first, and Faber Kozlowski had 6 times as much, which is $1650 at first.
So, the answer to (a) is $275 + $1650 = $1925.
For (b), Theriault Luigi spent 3/4 of his remaining money on a hoodie, which means he spent (3/4)(1/5)x = 3/20 of his original amount of money on the hoodie.
Therefore, Theriault Luigi spent 3/20 of his original amount of money on the hoodie.
Answer:
(a) $1925
(b) 15%
Step-by-step explanation:
(a)
Let f = original amount of money Faber had.
Let t = original amount of money Theriault had.
"Faber Kozlowski had 6 times as much money as Theriault Luigi. "
f = 6t
"After Faber Kozlowski spent 1/3 of his money"
He has now: 2/3 f
"and Theriault Luigi spent 4/5 of his money"
He has now: 1/5 t
"they had a total of $1155 left"
2/3 f + 1/5 t = 1155
f = 6t
2/3 f + 1/5 t = 1155
2/3 (6t) + 1/5 t = 1155
4.2t = 115
t = 1155/4.2
t = 275
f = 6t = 6(275) = 1650
f + t = 275 + 1650 = 1925
Part (a) answer: $1925
(b)
Original amount: t = 275
He first spent 4/5 of the original amount, so he had 1/5 left.
275/5 = 55
He spent 3/4 of $55 on the hoodie.
3/4 × $55 = $41.25
$41.25/$275 × 100% = 15%
Part (b) answer: 15%
EASY POINTS!
On a map, two cities are 2.8 inches apart. The map has a scale of 1 inch to 25 miles. How far apart, in inches, would the same two cities be on a map that has a scale of 1 inch to 40 miles? Show your work!
Answer:
1.75 inches (pls give brainliest lol!)
Step-by-step explanation:
Let's use a proportion to solve the problem:
On the first map, 2.8 inches represents 25 miles:
2.8 / 1 = 25 / x
Simplifying the equation, we get:
x = 25(2.8)/1 = 70
Therefore, the distance between the two cities in the first map is 70 miles.
Now, let's find the distance between the same two cities on the second map, which has a scale of 1 inch to 40 miles:
We want to find how many inches on the second map represent 70 miles. Let's call this value y.
1 / 40 = y / 70
Solving for y, we get:
y = 70/40 = 1.75
Therefore, the two cities would be 1.75 inches apart on the second map with the 1 inch to 40 miles scale.
f(x)=2(x−7)(x−3) y intercept
The y-intercept of the function F(x) = 2(x - 7)(x - 3) is 42, which means that the graph of the function intersects the y-axis at the point (0, 42).
What is y-intercept?The y-intercept is the point where a function or a curve intersects the y-axis. It is the value of the dependent variable (y) when the independent variable (x) is equal to zero.
According to question:The y-intercept of a function is the point where the graph of the function intersects the y-axis. To find the y-intercept of the function F(x) = 2(x - 7)(x - 3), we need to substitute 0 for x in the equation:
F(x) = 2(x - 7)(x - 3)
So, we have:
F(0) = 2(0 - 7)(0 - 3)
Simplifying this expression, we get:
F(0) = 2(-7)(-3)
F(0) = 42
Therefore, the y-intercept of the function F(x) = 2(x - 7)(x - 3) is 42, which means that the graph of the function intersects the y-axis at the point (0, 42).
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Find the area of the circle. Round your answer to the nearest tenth. Use 3.14 or 22
area: about
mm²
9 mm
for π.
Answer:
254.34
Step-by-step explanation:
πr^2
3.14*81
254.34
Suppose that the polynomial function f is defined as follows.
The zeros of f according to their multiplicity are:
Zero of multiplicity 1: x = -8, x = -3, x = 0, x = 9
Zero of multiplicity 2: None
Zero of multiplicity 3: None
Here,
We have,
The zeros of a polynomial function are the values of x that make the function equal to zero. The multiplicity of a zero is the number of times it appears as a factor in the polynomial.
In the given function f(x), the zeros are the values of x that make the function equal to zero.
We can find these values by setting the function equal to zero and solving for x.
f(x) = 7x(x-9)(x+8)^2(x+3) = 0
Therefore, the zeros of f(x) are x = -8, x = -3, x = 0, and x = 9.
To determine the multiplicity of each zero, we can look at the degree to which the corresponding factor appears in the polynomial.
For example, x = -8 is a zero of multiplicity 2 because it appears as a factor twice in the function, as (x+8)^2.
Similarly, x = -3, x = 0, and x = 9 are zeros of multiplicity 1 because they each appear as a factor once in the function.
There are no zeros of multiplicity 3 or higher in this function, so we can list "None" for those categories.
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Find the slope of the line shown below
The slope of the line which passes through points (-2, 1) and (0, -3) is calculated as: m = -2.
How to Find the Slope of a Line?In order to find the slope of the line given in the graph, pick two points on the line, then plug in their coordinates into the slope formula given as:
Slope (m) = change in y / change in x = y2 - y1 / x2 - x1
We have:
(-2, 1) = (x1, y1)
(0, -3) = (x2, y2)
Plug in the values:
Slope (m) = (-3 - 1) / (0 - (-2))
m = -4 / 2
Slope of the line (m) = -2
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The slope of the line represented by the graph is equal to -2.
How to calculate or determine the slope of a line?In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = rise/run
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
By substituting the given data points into the formula for the slope of a line, we have the following;
Slope (m) = (-3 - 3)/(0 + 3)
Slope (m) = (-6)/(3)
Slope (m) = -2.
Based on the graph, the slope is the change in y-axis with respect to the x-axis and it is equal to -2.
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The slope of the line which passes through points (-2, 1) and (0, -3) is calculated as: m = -2.
How to Find the Slope of a Line?In order to find the slope of the line given in the graph, pick two points on the line, then plug in their coordinates into the slope formula given as:
Slope (m) = change in y / change in x = y2 - y1 / x2 - x1
We have:
(-2, 1) = (x1, y1)
(0, -3) = (x2, y2)
Plug in the values:
Slope (m) = (-3 - 1) / (0 - (-2))
m = -4 / 2
Slope of the line (m) = -2
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The slope of the line represented by the graph is equal to -2.
How to calculate or determine the slope of a line?In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = rise/run
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
By substituting the given data points into the formula for the slope of a line, we have the following;
Slope (m) = (-3 - 3)/(0 + 3)
Slope (m) = (-6)/(3)
Slope (m) = -2.
Based on the graph, the slope is the change in y-axis with respect to the x-axis and it is equal to -2.
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What is the measure of <7 in degrees
A. Cannot be determined
B. 74
C. 16
D. 32
The measurement of angle Y which is a twin angle will be equal to 116 degrees which is option A.
What is an Isosceles Triangle?
The triangle which has any two sides equal in length is called as Isosceles Triangles. Also the two angles which is opposite to the equal sides are equal and third angle is unequal. The unequal side which is present is called the base of the triangle. Measurement of the altitude can be done from base to the vertex (which is topmost) of the triangle.
Here, the value of angle X is given 32 degree.
Therefore the value of angle Z will also be 32 degree (due to the property of isosceles triangle)
By angle sum property:
X+Y+Z=180
32+Y+32=180
Therefore, Y = 116 degree
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What values of y and z make
The values of y and z that make the triangles to be congruent are 13 each
Calculating the values of y and zFrom the question, we have the following parameters that can be used in our computation:
The triangles
For the two triangles to be congruent, the following equations must be true
2y = y + 13
y + 5z - 20 = 2y + z + 19
When the above equations are evaluated, we have
y = 13
Next, we have
4z = y + 39
So, we have
4z = 13 + 39
Add and divide by 4
z = 13
Hence, the values of y and z are 13
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What is the value of sin-1(1)?
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Answer:
Step-by-step explanation:arcsin(1) = pi/2
3.25x×400=2.50x+600 solve to determine when costs are equal
Okay, let's solve this step-by-step:
3.25x×400=2.50x+600
1300x = 1500
x = 500
So when x = 500, the costs are equal.
The federal government recently granted funds for a special program designed to reduce crime in high-crime areas. A study of the results of the program in eight high-crime areas of Miami, Florida, yielded the following results.
Number of Crimes by Area: A, B, C, D, E, F, G, H
Before: 14, 7, 4, 5, 17, 12, 8, 9
After: 2, 7, 3, 6, 8, 13, 3, 5
Has there been a decrease in the number of crimes since the inauguration of the program? Use the .01 significance level.
a. What is the p-value?
The p-value method yields P (T > 2.119) = 0.0359. It may be said that, at a 1% level of significance, there has been no decline in crime since the program's inception.
Explain about the Paired T-Test:The observations for the paired t-test are drawn from a single random pair sample. There are the same number of observations in both samples. Each respondent has two observations for the experimental variable recorded.
The alternative is:
[tex]H_{0} =[/tex]: Since the program's launch, there has been no drop in the number of crimes.
The alternate theory is that:
[tex]H_{a} =[/tex] Since the start of the programme, fewer crimes have been committed.
Mathematically,
[tex]H_{0} =[/tex] μo = 0
[tex]H_{a} =[/tex] μd > 0
Given table:
Number of Crimes Before After d = (before - after) d²
A 14 2 14-2 = 12 14² = 144
B 7 7 17 - 7 = 0 0² = 0
C 4 3 4 - 3 = 1 1² = 1
D 5 6 5 - 6 = -1 -1² = 1
E 17 8 17-8 = 9 9² = 81
F 12 13 12 - 13 = -1 -1² = 1
G 8 3 8 - 3= 5 5² = 25
H 9 5 9 -5 = 4 4² = 16
Total 8 29 269
The formula for the t statistic is:
t = ∑d / √[n(∑d²) - (∑d)²] / (n - 1)
t = 29 / √[8*269 - 29²] / (8 - 1)
t = 2.119
As a result, the test statistic's value is 2.119.
8 – 1 Equals 7 degrees of freedom.The p-value method yields P (T > 2.119) = 0.0359.The p-value is inconsequential since it exceeds the specified significance level of 0.01 in this case.
This indicates that at a 1% level of significance, the null hypothesis cannot be ruled out.
As a result, it may be said that, at a 1% level of significance, there has been no crime decline in since the program's inception.
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Consider the following equation.
-(3/2)^x+12 = 2x- 3
Approximate the solution to the equation above using three terations of successive approximation. Use the graph below as a starting point.
A. X=35/8
B. X=33/8
C. X=69/16
D. X=71/16
The solution of the graph is approximately
D. X=71/16What is solution of the graphThe solution of a graph depends on the type of graph and the problem being represented. In general, a solution of a graph refers to a point or set of points that satisfy the conditions or constraints of the problem.
For the problem, the solution of the graph is the point where the two graphs intersects.
Deducing from the graph this is at point x approximately 4.455 the closest value to this point in the option is x = 71/16
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