If a triangle has angles of X+2, 2x, and 55. What are the three angle
measurements?
Answer:
41, 43 and 82
Step-by-step explanation:
hope it may help you
These two polygons are similar. In the spaces below, enter the values of a, b, m
Given:
The two polygons are similar.
To find:
The value of [tex]a,\ b,\ m\angle C,\ m\angle D[/tex].
Solution:
We know that the corresponding side of similar figures are proportional. So,
[tex]\dfrac{5}{4}=\dfrac{5.39}{a}[/tex]
[tex]1.25=\dfrac{5.39}{a}[/tex]
[tex]a=\dfrac{5.39}{1.25}[/tex]
[tex]a=4.312[/tex]
Similarly,
[tex]\dfrac{5}{4}=\dfrac{5.83}{b}[/tex]
[tex]1.25=\dfrac{5.83}{b}[/tex]
[tex]b=\dfrac{5.83}{1.25}[/tex]
[tex]b=4.664[/tex]
We know that the corresponding angles of similar figures are congruent and their measures are equal. So,
[tex]m\angle C=99.2^\circ[/tex]
[tex]m\angle D=149^\circ[/tex]
Therefore, [tex]a=4.312\text{ units},\ b=4.664\text{ units},\ m\angle C=99.2^\circ,\ m\angle D=149^\circ[/tex].
(10 points)Assume IQs of adults in a certain country are normally distributed with mean 100 and SD 15. Suppose a president, vice president, and secretary of state are chosen randomly from the adults in the country, with each adult having an equal chance to be assigned each of the 3 jobs. What is the probability that the president will have an IQ of at least 107.5 and that at least one of the other two leaders (vice president and/or secretary of state) will have an IQ of at least 130
Answer:
0.0139 = 1.39% probability that the president will have an IQ of at least 107.5 and that at least one of the other two leaders (vice president and/or secretary of state) will have an IQ of at least 130.
Step-by-step explanation:
To solve this question, we need to use the binomial and the normal probability distributions.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Probability the president will have an IQ of at least 107.5
IQs of adults in a certain country are normally distributed with mean 100 and SD 15, which means that [tex]\mu = 100, \sigma = 15[/tex]
This probability is 1 subtracted by the p-value of Z when X = 107.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{107.5 - 100}{15}[/tex]
[tex]Z = 0.5[/tex]
[tex]Z = 0.5[/tex] has a p-value of 0.6915.
1 - 0.6915 = 0.3085
0.3085 probability that the president will have an IQ of at least 107.5.
Probability that at least one of the other two leaders (vice president and/or secretary of state) will have an IQ of at least 130.
First, we find the probability of a single person having an IQ of at least 130, which is 1 subtracted by the p-value of Z when X = 130. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{130 - 100}{15}[/tex]
[tex]Z = 2[/tex]
[tex]Z = 2[/tex] has a p-value of 0.9772.
1 - 0.9772 = 0.0228.
Now, we find the probability of at least one person, from a set of 2, having an IQ of at least 130, which is found using the binomial distribution, with p = 0.0228 and n = 2, and we want:
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{2,0}.(0.9772)^{2}.(0.0228)^{0} = 0.9549[/tex]
[tex]P(X \geq 1) = 1 - P(X = 0) = 0.0451[/tex]
0.0451 probability that at least one of the other two leaders (vice president and/or secretary of state) will have an IQ of at least 130.
What is the probability that the president will have an IQ of at least 107.5 and that at least one of the other two leaders (vice president and/or secretary of state) will have an IQ of at least 130?
0.3085 probability that the president will have an IQ of at least 107.5.
0.0451 probability that at least one of the other two leaders (vice president and/or secretary of state) will have an IQ of at least 130.
Independent events, so we multiply the probabilities.
0.3082*0.0451 = 0.0139
0.0139 = 1.39% probability that the president will have an IQ of at least 107.5 and that at least one of the other two leaders (vice president and/or secretary of state) will have an IQ of at least 130.
Melinda is playing a game with a number cube. Each face of the cube has a number from 1 to 6. If she tosses a number greater than 4she wins the round. Which statement correctly describes her chances of winning?
A)Melinda will certainly win the round.
B)Melinda will most likely win the round.
C)Melinda has an equal chance of winning or not winning the round.
D)Melinda will most likely not win the round.
Answer:
Step-by-step explanation:
She wins if the numbers 5 or 6 come up. There are 4 other numbers that are equally likely to be face up.
Most of the time she will lose because two out of 6 is much smaller than 4/6. If you were betting on horses, the odds are 1 in 2. That means that who ever you are playing against should put up 2 dollars for every dollar you put up.
That would be a fair game.
Answer:
the correct t answer is d
Cassie took 2 quizzes last week. She scored the same in each quiz.
Her score was -12 from being perfect. What was the difference
between Cassie's score and a perfect score on each quiz?
Help fastttt
Answer:
since her score was -12 from being perfect
if she had scored 12 more points her score would have been perfect .
that is difference between her score and the perfect score o each quiz was 12
using a=15 b=12 c=21 is the triangle ABC a right angle triangle
Write an equation for the line with passing through ( -2, 9) and ( 1, 0)
Answer:
[tex]y=-3x+3[/tex]
Step-by-step explanation:
We start by finding the slope of the line, which is given by the formula:
[tex]m=\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
The points (x1, y1) and (x2, y2) are represented by the pairs given: (-2, 9) and (1, 0). WE can substitute this in and simplify.
[tex]m=\frac{0-9}{1-(-2)} =\frac{-9}{1+2} =\frac{-9}{3} =-3[/tex]
Using the point-slope formula, [tex]y-y_{1} =m(x-x_{1} )[/tex], we can find the equation. We can substitute the point (-2, 9) for (x1, y1):
[tex]y-9=-3(x+2)\\y-9=-3x-6\\y=-3x+3[/tex]
Using the quadratic formula to solve x2 35-x, what are the values of x?
-12-121
-12-11
54.
12/19
51 21
2
Answer:
x = (-1 ± √21) / 2
The first choice
Step-by-step explanation:
x² = 5 - x
Put in standard form
x² + x - 5 = 0
Use quadratic equation
x = ( -b ± √( b² - 4ac) ) / (2a)
Plug in a = 1, b = 1 , c = -5
x = (-1 ± √( 1² - 4*1*(-5)) ) / 2
evaluate
x = (-1 ± √21) / 2
A news report suggested that an adult should drink a minimum of 4 pints of water per day.
Based on this report, determine the minimum amount of water an adult should drink,
in fluid ounces, per week.
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Answer:
448
Step-by-step explanation:
(4 pt/da)×(7 da/wk)×(16 oz/pt) = 448 oz/wk
That would be 448 fluid ounces per week.
Plzzz help me please ??
A. 4/7 Answer:
B. 60/7 or (8 and 4/7)
Step-by-step explanation:
A. 4 divided by 7 is the same as 4/7
B. 4/7 • 15/1= 60/7
Greg is installing a tile floor in a room that is 10 feet long by 15 feet wide. He will use 1-foot square tiles. He has two different types of tile: plain and hand-painted. Plain tiles cost $0.79 per tile. Hand-painted tiles cost $5.00 per tile. What is the maximum number of hand-painted tiles that Greg can use to keep the total cost under $200?
Answer:
The maximum number of hand-painted tiles that Greg can use to keep the total cost under $ 200 is 19.
Step-by-step explanation:
Since Greg is installing a tile floor in a room that is 10 feet long by 15 feet wide, and he will use 1-foot square tiles, and he has two different types of tile: plain and hand-painted, and plain tiles cost $ 0.79 per tile, while hand-painted tiles cost $ 5.00 per tile, to determine what is the maximum number of hand-painted tiles that Greg can use to keep the total cost under $ 200, the following calculation must be performed:
10 x 15 = 150
150 x 0.79 + 0 x 5 = 118.5
130 x 0.79 + 20 x 5 = 202.7
131 x 0.79 + 19 x 5 = 198.49
Therefore, the maximum number of hand-painted tiles that Greg can use to keep the total cost under $ 200 is 19.
Find the missing coordinates.
Answer:
1) (2, 1)
2) (2, -2)
3) (-1, -1)
4) (-5, -5)
Answer:
1. Pairs A(2, 5), B(6, 5), and C(6, 1)
missing coordinate is (2,1)
2. Pairs A(2, 3), B(7, 3), and C(7, -2)
missing coordinate is (2,-2)
3. Pairs A(-5, -1), B(1, -1), and C(1, -5)
missing coordinate is (-5,-5)
4. Pairs A(-1, 4), B(7, 4), and C(7, -1)
missing coordinate is (-1,-1)
Hope this is correct!! Have a nice day!!<3
A rectangular garden covers 80 yd?. The length is 7 yd longer than the width. Find the length and width.
Round your answers to the nearest tenth of a yard.
Answer:
The width of the rectangle is 6,105 yards, and the length of the rectangle is 13,105 yards.
Step-by-step explanation:
Given that a rectangular garden covers 80 square yards, and the length is 7 yd longer than the width, to find the length and width of the rectangle the following calculation must be performed, knowing that the area of a rectangle arises from multiplying its width by its length:
X x (X + 7) = 80
5 x 12 = 60
6 x 13 = 78
8 x 14 = 112
6.1 x 13.1 = 79.91
6,105 x 13,105 = 80
Therefore, the width of the rectangle is 6,105 yards, and the length of the rectangle is 13,105 yards.
What is the height of the trapezoid?
Answer:
4 inches
Step-by-step explanation:
The line that is perpendicular to the bottom of the trapezoid is the height.
A population analysist is using the formula Pn = 25.8(1.0219)h to predict the population for Ghana, a country in Africa. What does the number in in parenthesis tell us?
Answer:
Kindly check explanation
Step-by-step explanation:
Given the formula :
Pn = 25.8(1.0219)^h to predict the population of Ghana ;
The equation given is in the form of an exponential function:
The general form of an exponential distribution :
y = ab^x
a = Initial value ; b = constant multiplier or growth or Decay factor
Comparing :
The number in parenthesis = 1.0219 = b
b = Decay or growth factor :
Since b > 1 ; then We have a growth factor;
b = 1 + rate
1.0219 = 1 + rate
Rate = 1.0219 - 1
Rate = 0.0219
Hence, the population is growing at a rate of about (0.0219)*100% = 2.19%
How to calculate raw score from standard score and percentile rank?
Answer:
Step-by-step explanation:
Decide which project the most profitable is by:
(a) Determining the NPV at a discount rate of 6.5%. (8 marks)
(b) The IRR. ?
Answer:
Project A :
NPV : $703,888.64
IRR : 44.882%
Project B:
NPV : $5,241.26
IRR : 49.662%
Project B is more profitable
Step-by-step explanation:
The NPV gives the difference between the present value of cash inflow and cash outflow over a certain period of time.
The Internal rate of return is the discount rate which makes the NPV of an investment 0. It is used to estimate the potential return on an investment. Investments with higher IRR are said to be better than those with lower IRR value.
Using the net present value, (NPV) Calculator, the NPV for project A is : $703,888.64
The IRR of project A is : 44.882%
The NPV for Project B is : $5,241.26
The Internal rate of return (IRR) : 49.662%
From the Internal rate of return value obtained, we can conclude that, project B is more profitable as it has a higher IRR than project A.
how to calculate surface area
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Explanation:
Divide the figure into areas for which you have a surface area formula. Use the appropriate formula for each area, then add up the results.
Formulas are available for surface areas of a cone, cylinder, sphere, pyramid, rectangular prism, and for plane shapes that are circles, ellipses, triangles, rectangles, trapezoids, and regular polygons.
Most of the figures for which you are asked to find the area will decompose to some subset of these shapes. Take care to identify the relevant dimensions of each of the constituent parts of the area, and to make sure that all parts are accounted for. Do not allow your parts of the area to overlap, unless you intend to account for that overlap by subtracting the area that is counted more than once.
Also, use your common sense. A semicircle will have half the area of a circle, for example.
In some cases, it may be expedient to compute the area of a larger figure than the one you have, then subtract the part of that area that is missing from your figure.
Someone help me please this is an emergency T.T
Answer:
x < 3
Step-by-step explanation:
The graph of f(x) is above the graph of g(x) for values of x less than 3.
Answer: x < 3
3. The simple interest on $6,000 for 4 years is $1,680. *
Determine if the triangles are congruent. If they are, state how you know. NO LINKS!!!!
Part 1c. Show your work please.
Answers:
Each pair of triangles are congruent. The congruence reasoning is shown below.
ASASSSHA======================================
Further Explanation:
ASA is where we have the marked side between two marked angles. This is slightly different from AAS or SAA. The order is important. The diagram shows how the angles pair up (eg: the double arc angles are the same measure). Using ASA is enough to prove the triangles congruent.SSS is used here because we have three pairs of congruent sides. The unmarked sides overlap perfectly, so we consider this a shared side. They are congruent to each other (because of the reflexive property). So we have enough info to show that the triangles are congruent.HA stands for hypotenuse angle. It's probably not that often used. It only applies to right triangles. The two overlapped segments are the hypotenuse of each right triangle, so that takes care of the "H" of "HA". The A part refers to the congruent acute angles (not the right angles). Therefore, the triangles are congruent by the HA theorem.Abbreviations:
ASA = angle side angle
SSS = side side side
HA = hypotenuse angle
Determine the value of x.
Answer:
Step-by-step explanation:
(B). 2√2
What is the value of tan(π6)
The measure of angle S is 65 degrees.
What is the measure of angle R?
RS
A
115°
B.
230°
с
65°
D
25°
Answer:
A. 115°
Step-by-step explanation:
180° - 65° = 115°
Given that events A and B are independent with P(A) = 0.55 and P(B) = 0.72,
determine the value of P(AB), rounding to the nearest thousandth, if necessary.
Answer:
Step-by-step explanation:
For independent events,
P(AB)=P(A)orP(B)
= P(A)uP(B)
=P(A)×P(B)
= 0.55×0.72
P(AB)=0.396
work out the angle x please help.
Answer:
x is 13°.take the triangle to find the measure of x.180° -(85°+82°)=x
180°-167°=13°
For the given triangle the measure of the angle x is = 3 degrees.
Labeling the given figure,
since angle C and angle B are alternate angles
Therefore,
For the triangle ABE
The interior angle for A = x
The interior angle for B = 180 -98
= 92 degree
Since we know that,
The sum of the two interior angles of a triangle is equal to the exterior angle of the opposite side.
Therefore,
⇒ x + 92 = 180 - 85
⇒ x = 3 degrees.
Hence,
The measure of the angle x is = 3 degrees.
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The graph shows the number of hours that Tammy spends typing for work, x, and the amount of pay that she earns, y.
A graph titled Tammy's Pay with number of hours on the x-axis and pay in dollars on the y-axis. A line goes through points (2, 18) and (8, 42).
What does the y-intercept represent?
Tammy initially had $10 pay.
Tammy will type for 10 minutes each day.
Tammy initially had $4 pay.
Tammy will type for 4 minutes each day.
Answer:
Tammy initially had $4 pay.
Step-by-step explanation:
C on edge 2021
The y-intercept represent Tammy initially had $10 pay.
From the given graph, we can observe that the line passes through the points (2, 18) and (8, 42).
Using the two points on the line, the slope (m) of the line:
m = (change in y) / (change in x)
= (42 - 18) / (8 - 2)
= 24 / 6
= 4
Using slope-intercept form of a line equation: y = mx + b,
y= 4x+ b
Put x=2 and y= 18 we get
18 = 4(2)+b
18 = 8 + b
b= 18- 8
b = 10
Thus, the y-intercept represent Tammy initially had $10 pay.
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what is 1+544 please somone tell me or i wikl fail mah test qwq
Answer:555
Step-by-step explanation:
Answer:
545
Step-by-step explanation:
you are just adding one
544+1=
If f(x) =2x²+5sqrt(x-2), complete the following statement: f(6) =
Answer:
f(6) = 82
Step-by-step explanation:
[tex]f(x) = 2x^2 + 5\sqrt{x-2}[/tex]
[tex]=> f(6) = 2(6)^2 + 5\sqrt{6-2}[/tex]
[tex]= 2 \times 36 + 5 \times \sqrt{4}[/tex]
[tex]= 72 + 5 \times 2[/tex]
[tex]= 72 + 10[/tex]
[tex]= 82[/tex]
If two standard, six-sided die were rolled and the numbers that turned up on each were added together, which of the following would be the probability their sum would be equal to 4?
Answer:
3/36 or 8.333
Step-by-step explanation:
the way you get it is write all the possibilities and that how you get 3/36