Answer:
The probability that defect length is at most 20 mm (or less than 20 mm) is 0.0505
Step-by-step explanation:
Mean defect length = u = 32
Standard deviation = [tex]\sigma[/tex] = 7.3
The distribution is normal and we have the value of population standard deviation so we will use the concept of z-score and probability from z-table to find the said probability.
We have to find the probability that the defect length is at most 20 mm. At most 20 mm means equal to or lesser than 20 mm. Since the normal distribution is a continuous distribution, the probability of at most is approximately equal to probability of lesser than.
If X represents the distribution of defect lengths, then we can write:
P(X ≤ 20) ≅ P(X < 20)
We can find the probability of defect length being lesser than 20 mm by converting it to z-score and find the corresponding probability from the z-table.
The formula to calculate the z-score is:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
Substituting the values, we get:
[tex]z=\frac{20-32}{7.3}=-1.64[/tex]
Therefore, P(X < 20) is equivalent to P(z < -1.64)
From z-table we can find the probability of z being lesser than - 1.64, which comes out to be:
P(z < -1.64) = 0.0505
Therefore, we can conclude that:
The probability that defect length is at most 20 mm (or less than 20 mm) is 0.0505
*) Name this triangle by looking at its side lengths.
Answer
equilateral
Step-by-step explanation:
rate and choose brainliest
A model rocket is launched with an initial upward velocity of 15 m the Rockets height is H equals 50 T minus 5T squared
Answer:
Step-by-step explanation:
What are you looking for as an answer?
2. The radius or diameter of a circle is given. Find the remaining measure.
a) d = 9 m
b)r = 28.5 yd
Answer:
r = 4.5m
d = 57 yds
Step-by-step explanation:
The radius is 1/2 of the diameter
d= 9 meter
r = d/2 =9/2 = 4.5 m
The diameter is twice the radius
r = 28.5 yds
d = 2r = 2*28.5 =57 yds
Answer:
a) r=4.5 m
b) d= 57 yd
Step-by-step explanation:
a)
The diameter is twice the radius, which can be written as:
d=2r
We know the diameter is 9, so we can substitute that in for d.
9=2r
To solve for r, we need to isolate the variable. To do this, divide both sides by 2
9/2=2r/2
4.5=r
So, the radius is 4.5 meters
b)
The diameter is twice the radius, or
d=2r
We know the radius is 28.5, so we can substitute that in for r
d=2*28.5
Multiply
d=57
So, the diameter is 57 yards
1. How many ways are there to make an octagon with 19 different sticks when order DOESN’T matter?
2. How many ways are there to make an octagon with 19 different sticks when order MATTERS?
Answer:
1. 75582
2. 3047466240
Step-by-step explanation:
1. If order does not matter, this is a combination problem. You are choosing 8 sticks from a set of 19. (Octagons have 8 sides.)
The formula for combinations of n things chosen r at a time "n choose r" is
[tex]_nC_r = \frac{n!}{r!(n-r)!}[/tex]
[tex]_19C_8=\frac{19!}{8!(19-8)!} = \frac{19!}{8!11!}=75582[/tex]
2. If order matters, there are more possibilities. This is a permutation problem. The number of permutations of 19 things taken 8 at a time, "19 permute 8" is
[tex]_nP_r=\frac{n!}{(n-r)!} \\ _{19}P_8=\frac{19!}{(19-8)!} = 3047466240[/tex]
Ralph began work at 7 p.m .By 10 p.m ralph packed 18 boxes .At the same Ralph began work at 7 p.m .By 10 p.m ralph packed 18 boxes .At the same rate ,how many boxes will he pack by 12 midnight ,how many boxes will he pack by 12 midnight
g A window is being built and the bottom is a rectangle and the top is a semi-circle. If there is 12 meters of framing materials, what must the dimensions of the window be to let in the most light?
Answer:
Semicircle of radius of 1.6803 meters
Rectangle of dimensions 3.3606m x 1.6803m
Step-by-step explanation:
Let the radius of the semicircle on the top=r
Let the height of the rectangle =h
Since the semicircle is on top of the window, the width of the rectangular portion =Diameter of the Semicircle =2r
The Perimeter of the Window
=Length of the three sides on the rectangular portion + circumference of the semicircle
[tex]=h+h+2r+\pi r=2h+2r+\pi r=12[/tex]
The area of the window is what we want to maximize.
Area of the Window=Area of Rectangle+Area of Semicircle
[tex]=2hr+\frac{\pi r^2}{2}[/tex]
We are trying to Maximize A subject to [tex]2h+2r+\pi r=12[/tex]
[tex]2h+2r+\pi r=12\\h=6-r-\frac{\pi r}{2}[/tex]
The first and second derivatives are,
Area, A(r)[tex]=2r(6-r-\frac{\pi r}{2})+\frac{\pi r^2}{2}}=12r-2r^2-\frac{\pi r^2}{2}[/tex]
Taking the first and second derivatives
[tex]A'\left( r \right) = 12 - r\left( {4 + \pi } \right)\\A''\left( r \right) = - 4 - \pi[/tex]
From the two derivatives above, we see that the only critical point of r
[tex]A'\left( r \right) = 12 - r\left( {4 + \pi } \right)=0[/tex]
[tex]r = \frac{{12}}{{4 + \pi }} = 1.6803[/tex]
Since the second derivative is a negative constant, the maximum area must occur at this point.
[tex]h=6-1.6803-\frac{\pi X1.6803}{2}=1.6803[/tex]
So, for the maximum area the semicircle on top must have a radius of 1.6803 meters and the rectangle must have the dimensions 3.3606m x 1.6803m ( Recall, The other dimension of the window = 2r)
The problem is to maximize the area of a window consisting of a rectangle and a semi-circle on top, given a fixed perimeter of framing material, which is a high school level optimization problem in geometry and calculus.
Explanation:The question addresses the problem of finding the dimensions of a window with the most amount of light passing through, given a fixed amount of framing material. This is a classic problem in mathematics involving optimization under constraints, specifically related to geometry and calculus.
Let the width of the rectangle be x meters, and its height be y meters. Since the top of the window is a semi-circle, its diameter is equal to the width of the rectangle, meaning the radius of the semi-circle is x/2 meters. The perimeter of the entire window consists of the two sides and the bottom of the rectangle, and the circumference of the semi-circle. The total length of framing material is 12 meters, hence:
2y + x + (π(x/2)/2) = 12
Since the area of rectangle A = x*y and the area of the semi-circle is (x/2)²)/2, we want to maximize the total area A = x*y + (x/2)²)/2.
Using calculus, one can differentiate the area with respect to x or y and set the derivative equal to zero to find the maximum value. Assuming the student knows basic differentiation and solving equations, they can arrive at the optimal dimensions to let in the most light.
please help
its a quizziz question
what is the probability of drawing a 5 from 10 cards numbered 1 through 10 and rolling a 2 on a dice
Answer:
1/60 probabiliity
Step-by-step explanation:
You have two independent events that you want to put together.
Let Pr. mean "probability"
Pr(5 from 10 cards and 2 on a dice ) = Pr(5 from 10 cards) * Pr( 2 on a dice)
Pr(5 from 10 cards and 2 on a dice ) =(1/10) * (1/6)
= 1/60
Pr(5 from 10 cards and 2 on a dice ) =0.0167
or 1.67% probability
What is the difference in surface areas, in square feet, of the two boxes?
Rectangular Prism: 3 ft by 4.5 ft by 2 ft
Cube: 3 ft
Final answer:
The difference in surface areas of the two boxes is 3 square feet.
Explanation:
The difference in surface areas between two boxes is computed by first finding the surface area of each box and then subtracting the smaller surface area from the larger one.
Rectangular Prism:
For the rectangular prism with dimensions 3 ft by 4.5 ft by 2 ft, the surface area (SA) is calculated using the formula SA = 2lw + 2lh + 2wh.
The surface areas of the rectangular prism are:
Top and Bottom: 2(3 ft × 4.5 ft) = 27 ft²Front and Back: 2(3 ft × 2 ft) = 12 ft²Sides: 2(4.5 ft × 2 ft) = 18 ft²Total surface area of the rectangular prism = 27 ft² + 12 ft² + 18 ft² = 57 ft²
Cube:
For the cube with a side of 3 ft, the surface area is found using the formula SA = 6s².
Thus:
Total surface area of the cube = 6(3 ft × 3 ft) = 54 ft²
Difference in Surface Area:
Difference in surface areas = Surface area of the rectangular prism - Surface area of the cube = 57 ft² - 54 ft² = 3 ft².
8x-3(-z-y)
X= 1
Y=3
Z=-2
Answer:
11
Step-by-step explanation:
8x - 3(-z - y)
Substitute
8(1) - 3(-(-2) - 3)
Simplify
8 - 3(-1)
Multiply
8 + 3
Add
11
Answer:
Here; 8x-3(-z-y) =
so your asking 8x-3(-z-y) right?
Let's simplify step-by-step.
8x−3(−z−y)
awnser again xD
=8x+3y+3z
Ebru has a standard deck of cards. The deck has 52 total cards and contains 4 suits: hearts, clubs, diamonds, and spades. Each suit contains cards numbered 2-10, a jack, a queen, a king, and an ace.
Ebru randomly selects a card. Let A be the event that the card is a 2 and B be the event that it is a spade. Which of the following statements are true? Choose all that apply.
a.) P(A | B)=P(A) the conditional probability that Ebru selects a 2 given that she has chosen a spade is equal to the probability that Ebru selects a 2
b.) P(B | A)=P(B) the conditional probability that Ebru selects a spade given that she has chosen a 2 is equal to the probability that Ebru selects a spade.
c.) Events A and B are independent events.
d,) The outcomes of events A and B are dependent on each other.
e.) P(A and B)=P(A)⋅P(B) the probability that Ebru selects a card that is a 2 and a spade is equal to the probability that Ebru selects a 2 multiplied by the probability that she selects a spade.
In Ebru’s deck of cards, the probabilities of choosing a 2 and choosing a spade are respectively 1/13 and 1/4. However, these events are not independent, so the probabilities impact each other. The statements (a), (b), (c), and (e) are not true, while (d) is true.
Explanation:The deck of 52 cards contains 4 suits and each suit has 13 cards, meaning there are 4 cards of 2 and 13 spades in total. We can use these numbers to calculate the probabilities.
P(A)=4/52=1/13, the probability that Ebru selects a 2.P(B)=13/52=1/4, the probability that Ebru selects a spade.
When it comes to P(A | B)=P(A) and P(B | A)=P(B), these would hold true if A and B were independent events, meaning the occurrence of one does not affect the probability of the other happening. However, these events are not independent. If Ebru picks a 2, the chances of her picking a spade change, and similarly whether she picks a spade affects the chances of her picking a 2.
So that means (a) and (b) are not true, while (c) is not true because events A and B do indeed influence each other, making (d) true. If A and B were independent, then (e) would be true as the probability of both events A and B happening would be multiplied. However, in this case, they influence each other so (e) is not true.
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From this analysis, the true statements are a, b, c, and e. The decision of a card being a 2 and the choice of a card being a spade are independent events. The outcomes are not dependent on each other.
Explanation:From a standard deck of cards, we have 4 cards that are 2s (one in each of the four suits: hearts, clubs, diamonds, and spades) and 13 cards that are spades (including numbered 2-10, a jack, a queen, a king, and an ace). Therefore, the probability P(A) that Ebru selects a 2 is 4 out of 52 (or 1/13), and the probability P(B) that she selects a spade is 13 out of 52 (or 1/4).
a) P(A | B) refers to the probability that Ebru selects a 2 given that she has already chosen a spade. In this case, there is only one 2 among the 13 spades, so P(A | B) = 1/13 which is equal to P(A). Hence, statement a is true.
b) P(B | A) is the probability that Ebru selects a spade having already chosen a 2. There is one spade among the 4 twos, so P(B | A) = 1/4, which is equal to P(B). Hence, statement b is true.
c) We can see that both P(A | B) = P(A) and P(B | A) = P(B). Therefore, events A and B are independent, making statement c true.
d) Because A and B are independent, statement d, which suggests that they are dependent, is false.
e) For independent events, P(A and B) = P(A) * P(B), which is (1/13) * (1/4), so statement e is true.
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The endpoints of one side of a regular octagon are (-2,-4) and (4.-6). What 6
is the perimeter of the octagon? *
To find the perimeter of the regular octagon, we use the distance formula to calculate the length of one side given the endpoints and then multiply that length by eight, as there are eight equal sides in a regular octagon.
Explanation:The question revolves around finding the perimeter of a regular octagon given the coordinates of one of its sides. First, we must determine the length of the side using the distance formula between the two given endpoints (-2,-4) and (4,-6). The distance formula is √((x2 - x1)^2 + (y2 - y1)^2), where (x1, y1) and (x2, y2) are the coordinates of the endpoints. After calculating the length of one side, we multiply this by 8 (since an octagon has eight equal sides) to get the perimeter.
The calculation is as follows:
Calculate the length of one side: √((4 - (-2))^2 + (-6 - (-4))^2) = √((6)^2 + (-2)^2) = √(36 + 4) = √40Multiply this length by 8 to find the perimeter: 8 * √40 = 8 * 2√10 = 16√10The perimeter of the octagon is 16√10 units.
Next time you see an elderly man, check out his nose and ears! While most parts of the human body stop growing as we reach adulthood, studies show that noses and ears continue to grow larger throughout our lifetime. In one study1examining noses, researchers report "Age significantly influenced all analyzed measurements:" including volume, surface area, height, and width of noses. In a test to see whether there is a positive linear relationship between age and nose size, the study indicates that "p0.001."
State the hypothesis
Answer:
See explaination
Step-by-step explanation:
Please kindly check attachment for the step by step solution of the given problem.
Final answer:
The hypothesis of the study is that there's a positive correlation between nose size and age, with age significantly influencing nose measurements. The strong significance level indicates a likely true relationship. This context involves genetics, evolutionary biology, and human anatomy, illustrating the complexity of evolutionary change.
Explanation:
The hypothesis being tested in the study is that there is a positive linear relationship between age and nose size. This study examines various measurements of the nose, including volume, surface area, height, and width, and assesses how these dimensions change with age. The significance level of p<0.001 suggests a very strong chance that the observed relationship is not due to random variation, but indeed reflects a true correlation between nose size and age.
Genetics and evolutionary biology play crucial roles in this context, with the Price equation outlining how certain traits might evolve over time even in the absence of natural selection. Importantly, reification can lead to misconceptions as it implies that there is a direct correspondence between a named entity, like 'nose genes', and physical traits.
An understanding of human anatomy, like the relationship between the nasal aperture and the overall size of the nose—exampled by the large noses of Neanderthals, reflects broader principles of evolutionary change and adaptation. This complex interplay of genetics, physical development, and evolutionary factors highlights the importance of incremental transformations and selection in shaping human features over time.
What is the formula for this question?
Answer:
2.7
Step-by-step explanation:
This can be modeled using exponential growth/decay.
A = P (1 + r)ⁿ
where A is the final amount,
P is the initial amount,
r is the rate of growth/decay,
and n is the number of cycles.
For half life problems, r = -½, and n = t / T, where t is time and T is the half life.
A = P (1 − ½)^(t/T)
A = P (½)^(t/T)
Given that P = 9, t = 10000, and T = 5730:
A = 9 (½)^(10000/5730)
A ≈ 2.7
There are approximately 2.7 mg of ¹⁴C left.
What is the solution to the system of equations graphed below?
y= -3/2x+12
y= 5x+ 28
Given:
The system of equations is [tex]y=-\frac{3}{2}x+12[/tex] and [tex]y=5x+28[/tex]
We need to determine the solution to the system of equations.
Solution:
The solution to the system of equations is the point of intersection of these two lines.
Let us solve the system of equations using substitution method.
Thus, we have;
[tex]5x+28=-\frac{3}{2}x+12[/tex]
Simplifying, we get;
[tex]\frac{13}{2}x+28=12[/tex]
[tex]\frac{13}{2}x=-16[/tex]
[tex]13x=-32[/tex]
[tex]x=-2.462[/tex]
Thus, the value of x is -2.462
Substituting x = -2.462 in the equation [tex]y=5x+28[/tex], we get;
[tex]y=5(-2.462)+28[/tex]
[tex]y=-12.31+28[/tex]
[tex]y=15.69[/tex]
Thus, the value of y is 15.69.
Therefore, the solution to the system of the equations is (-2.462, 15.69)
A piece of scenery for the school play is in the shape of a 5 foot long rectangle. The designer decides to increase the length. There will be 3 identical rectangles with a total length of 17 feet. By how much did the designer increase the length of each rectangle?
Answer:
Step-by-step explanation:
The school play ground is.
5ft long rectangle
The designer want to increase the length,
Then, there will be 3 identical rectangle of total length of 17ft
By how much did he increase the of each rectangle
Original, the length of the rectangle is 5ft, now, we want to design three rectangle. This three identical rectangle will have total length of (5+5+5)ft,
The original length of the three rectangle is meant to be 15ft,
Now he increase the length to 17ft,
This shows that he has increase all the three rectangle by 2ft.
So, each rectangle is expected to be increased by ⅔ft
So, he increased each rectangle length by ⅔ft.
Mathematically,
Let the increase be x
Then, he increase each length by x, so the new length is
5+x
Then, there are 3 rectangles, so their total length after increase is 3×(5+x)
And this total length after increase is give as 17ft
Then,
3(5+x) = 17
Solving this
15 + 3x = 17
3x = 17-15
3x = 2
x = ⅔ ft
So, the mathematical model of the increase is 3(5+x) = 17 and the increase is ⅔ft
Claim: Most adults would erase all of their personal information online if they could. A software firm survey of 522 randomly selected adults showed that 64% of them would erase all of their personal information online if they could. Find the value of the test statistic.
Answer:
6.3972
Step-by-step explanation:
This is a normal distribution problem.
-We claim that most adults are more likely to erase their data;
[tex]p_o>0.5\\\\H_o:p>0.5[/tex]
-The test statistic for a stated hypothesis for proportions is given by the formula:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o(1-p_o}{n}}}[/tex]
Given the size of the random sample is 522 and that 62% of them are susceptible to erasing their data.
-Let [tex]\hat p[/tex] be the sample proportion. The value of the test statistic :
[tex]z=\frac{0.64-0.5}{\sqrt{\frac{0.5\times 0.5}{522}}}\\\\=6.3972[/tex]
Hence, the test statistic is z=6.3972
5. Find all three cube roots of the the complex number z = 473 + 4i, and plot
them in the complex plane.
Verify the identity
Answer:
z1 = 7.71 + 0.02 i
z2 = 7.73 + 0.306 i
z3 = 7.78 + 0.59 i
Step-by-step explanation:
To find the roots you use:
[tex]z^{\frac{1}{n}}=r^{\frac{1}{n}}[cos(\frac{\theta+2\pi k}{n})+isin(\frac{\theta+2\pi k}{n})][/tex] ( 1 )
n: the order of the roots
k: 0,1,2,...,n-1
First, you write z in polar notation:
[tex]z=re^{i\theta}\\\\r=\sqrt{(473)^2+(4)^2}=473.01\\\\\theta=tan^{-1}(\frac{4}{473})=0.48\°[/tex]
Thus, by using these values for the angle and r in the expression (1), you obtain:
[tex]k=0\\\\z_1=(473.01)^{1/3}[cos(\frac{0.48+2\pi(0)}{3})+isin(\frac{0.48+2\pi(0)}{3})]\\\\z_1=7.79(0.99+i2.79*10^{-3})=7.71+i0.02\\\\z_2=7.79[cos(\frac{0.48+2\pi(1)}{3})+isin(\frac{0.48+2\pi(1)}{3})]\\\\z_2=7.73+i0.306\\\\z_3=7.79[cos(\frac{0.48+2\pi(2)}{3})+isin(\frac{0.48+2\pi(2)}{3})]\\\\z_3=7.78+i0.59[/tex]
hence, from the previous results you obtain:
z1 = 7.71 + 0.02 i
z2 = 7.73 + 0.306 i
z3 = 7.78 + 0.59 i
I attached and image of the plot
Volume of a prism h=2 w=4 l=3
Answer:
I understand the key where you represented what each of the letters represent but, there is no equation sorry I hope this helped if you would please give me a more specific equation if possible??
Georgia Votes 2000 ~ The 2000 presidential election between Al Gore and George W. Bush was the closest presidential election in the history of the United States. A social historian is investigating the relationship between race and voting results. For a random sample of 50 counties in the state of Georgia, the historian obtains the percentage of county residents who were African American (AA), and the percentage of ballots cast for Al Gore. Percentage AA is the X variable and Percentage vote for Al Gore is the Y variable in this scenario. Using the sample data, the historian finds the equation of the estimated regression line for predicting the Y variable to be yˆ = 25.4495 + 0.6956 x 44.0954% of Georgia's Baker county residents are African Americans. What is the estimated/predicted Percentage vote for Al Gore for this county? Give your answer to 4 decimal places. Note: Numbers are randomized for each instance of this question. Use the numbers given above.
Answer:
The predicted percentage vote for Al Gore for the county with 44.0954% African Americans is 25.76%.
Step-by-step explanation:
The least square regression line is used to determine the relationship between a response variable (or dependent variable) and an explanatory variable (or independent variable).
The least square regression line can be used to predict the future value or estimate the past value of the dependent variable based on the independent variable.
The general form of a least square regression line is:
[tex]y=\alpha +\beta x[/tex]
Here,
y = response variable
x = explanatory variable
α = intercept
β = slope
The least square regression line for predicting the percentage vote for AI Gore (y) from the percentage of county residents who were African American (x) is given by:
[tex]\hat y=25.4495+0.6956 x[/tex]
Compute the predicted value of y for x = 44.0954% = 0.440954 as follows:
[tex]\hat y=25.4495+0.6956 x[/tex]
[tex]=25.4495+0.6956 \times 0.440954\\=25.4495+0.3067276024\\=25.7562276024\\\approx 25.76[/tex]
Thus, the predicted percentage vote for Al Gore for the county with 44.0954% African Americans is 25.76%.
Using the equation of the estimated regression line, the predicted percentage vote for Al Gore in Baker County, Georgia is approximately 56.3555% based on a population that was 44.0954% African American.
Explanation:In this scenario, we have a linear regression line of the form y^ = 25.4495 + 0.6956x, where y^ represents the estimated percentage vote for Al Gore, and x represents the percentage of county residents who are African American. We are given that in Baker County, Georgia, 44.0954% of residents are African American. By substituting this x value into the equation, we can find the predicted y value:
y^ = 25.4495 + 0.6956*(44.0954)
This gives an estimated vote for Al Gore in Baker County as y^ = 56.3555 approximately, to four decimal places. This implies that the model predicts that about 56.3555% of the vote in Baker County went to Al Gore.
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Factor completely 3x2 -21
Answer:
=3(x^2 − 7)
Step by Step explanation:
3x^2 − 21
=3(x^2 − 7)
Answer:
=3(x^2 − 7)
Step-by-step explanation:
Margo must sell at least 38 tubs of cookie dough to support the student council fundraiser. She has already sold
19 tubs of cookie dough. Which inequality best represents the number of tubs of cookie dough Margo still
needs to sell?
Answer:
19 + x ≥ 38
Step-by-step explanation:
Margo must sell at least 19 more tubs of cookie dough to meet her goal for the student council fundraiser, represented by the inequality x ≥ 19
The question asks to find an inequality that represents the number of tubs of cookie dough Margo still needs to sell.
Margo needs to sell at least 38 tubs of cookie dough and has already sold 19, so we subtract the tubs sold from the total needed:
38 - 19 = 19
Now, let x represent the number of tubs Margo still needs to sell.
The inequality that best represents this situation is:
x ≥ 19
This inequality shows that Margo needs to sell at least 19 more tubs to meet her minimum goal for the fundraiser.
The graph below shows three different normal distributions,
50
60
70
80
90
100
Which statement must be true?
Each distribution has a different mean and the same standard deviation
Each distribution has a different mean and a different standard deviation.
Each distribution has the same mean and the same standard deviation
Mark this and return
Save and Exit
mext
Submit
Answer: The answer would be D
Step-by-step explanation:
This is because all of the models on the graph show in the same place having the same middle but at different heights but not the same standard deviation.
Each distribution has the same mean and a different standard deviation is the correct statement about the graph.
Three different normal distributions are given in the graph.
The spread in the given normal curves is due to different standard deviation.
The mean for all the three curves lies at the center of the curve.
Therefore, the graph shows that each distribution has the same mean and a different standard deviation.
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The complete question is given below.
The graph below shows three different normal distributions.
Which statement must be true?
Each distribution has a different mean and the same standard deviation.
Each distribution has a different mean and a different standard deviation.
Each distribution has the same mean and the same standard deviation.
Each distribution has the same mean and a different standard deviation.
The x values are called the ????? of the relation and the y values are called the
???? of the relation.
Answer:
x = domain
y = range
Step-by-step explanation:
What is the diameter of a hemisphere with a volume of 2233\text{ cm}^3,2233 cm 3 , to the nearest tenth of a centimeter?
The diameter of the hemisphere is 20.4 centimeters.
Here's the breakdown of the calculation:
Formula for hemisphere volume: The volume of a hemisphere is equal to two-thirds the volume of a full sphere with the same radius (r).
V_hemisphere = (2/3) * (4/3) * π * r^3
Substituting known values: We know the volume of the hemisphere (V_hemisphere) is 2233 cm^3. Plugging this into the equation:
2233 cm^3 = (2/3) * (4/3) * π * r^3
Solve for radius (r): Isolate r:
r^3 = (2233 cm^3 * 3 / 8 * π) ≈ 1181.36 cm^3
r ≈ 10.3 cm
Calculate diameter: Diameter is twice the radius:
diameter = 2 * radius ≈ 20.6 cm
Therefore, the diameter of the hemisphere is approximately 20.4 centimeters to the nearest tenth of a centimeter.
George jogged downhill at 6 mph and then jogged back up at 4 mph. If the total jogging time was 1.25 hours, how far did he jog in all?
The total distance covered is 6 m
Step-by-step explanation:
Let the total distance be '2d'
Total time = 1.25hrs
Downhill speed = 6 mphr
Uphill speed = 4 mphr
(d/6) +(d/4) = 1.25
(2d + 3d) /12 = 1.25
5d/12 = 1.25
d = 3m
So, 2d = 6 m
The total distance covered is 6 m
Stefan was able to map \triangle ABD△ABDtriangle, A, B, D onto \triangle ABC△ABCtriangle, A, B, C. Stefan concluded: "I was able to map \triangle ABD△ABDtriangle, A, B, D onto \triangle ABC△ABCtriangle, A, B, C using a sequence of rigid transformations, so the figures are congruent." What error did Stefan make in his conclusion? Choose 1 answer: Choose 1 answer: (Choice A) A Stefan didn't use only rigid transformations, so the figures are not congruent. (Choice B) B It's possible to map \triangle ABD△ABDtriangle, A, B, D onto \triangle ABC△ABCtriangle, A, B, C using a sequence of rigid transformations, but the figures are not congruent. (Choice C) C There is no error. This is a correct conclusion.
Answer: Stefan didn’t use only rigid transformations, so the figures are not congruent
Step-by-step explanation:
Stefan didn’t use only rigid transformations, so the figures are not congruent.
What is Congruency?Two triangles are said to be congruent if their sides are equal in length, the angles are of equal measure, and they can be superimposed on each other.
In the given, Δ ABC and Δ ABD are not congruent triangles. if they are congruent then This means that the corresponding angles and corresponding sides in both the triangles are equal.
The following are the congruence theorems or the triangle congruence criteria that help to prove the congruence of triangles;
SSS (Side, Side, Side)
SAS (side, angle, side)
ASA (angle, side, angle)
AAS (angle, angle, side)
RHS (Right angle-Hypotenuse-Side or the Hypotenuse Leg theorem)
As, from the given cases the prediction of congruency of two triangles is incorrect. There is no error he made.
Hence, Stefan didn’t use only rigid transformations, so the figures are not congruent
Learn more about congruency here:
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The probability of winning the shell games if you
randomly pick is 1 in 3. What would be the
approximate probability of winning 4 games in a row?
A.) 33.3%
B.) 1.2%
C.) 16.7%
D.) 1.5%
Final answer:
The approximate probability of winning 4 games in a row when each game has a 1/3 chance of winning is 1.23%.
(Option B)
Explanation:
To find the approximate probability of winning 4 games in a row, we need to multiply the probabilities of winning each game. Since the probability of winning each game is 1/3, we can calculate the overall probability as [tex](1/3)^4[/tex]. Using a calculator, this comes out to be approximately 0.0123 or 1.23%.
Multiplying the individual probabilities of winning each game, given as 1/3, results in the overall probability of winning 4 games in a row, expressed as [tex](1/3)^4[/tex]. Using a calculator, this evaluates to approximately 0.0123, or 1.23%, highlighting the cumulative nature of independent events.
Country A, Country B, and Country C won a total of 130 medals. Country B won 10 more medals than Country C. Country A won 38 more medals than the total amount won by the other two. How many medals did each of the top three countries win?
Answer:
Country A = 84
Country B = 28
Country C = 18
Step-by-step explanation:
Country A, Country B, and Country C won a total of 130 medals;
A + B + C = 130 ......1
Country B won 10 more medals than Country C;
B = C + 10 .......2
Country A won 38 more medals than the total amount won by the other two;
A = B + C + 38 ........3
Substituting equation 3 to 1;
(B+C+38) + B+C = 130
2B + 2C + 38 = 130 .......4
Substituting equation 2 into 4;
2(C+10) + 2C + 38 = 130
4C + 58 = 130
4C = 130-58 = 72
C = 72/4 = 18
B = C + 10 = 18 + 10 = 28
A = B + C + 38 = 18 + 28 + 38 = 84
Country A = 84
Country B = 28
Country C = 18
In a certain town 60% of the households own mutual funds, 40% own individual stocks, and 20% own both mutual funds and individual stocks. The proportion of households that own mutual funds but not individual stocks is:A) 20%.
B) 30%.
C) 40%.
D) 50%
Answer:
C. 40%
Step-by-step explanation:
Using set notations,
Check the attachment for the diagram.
Let the total fund shared by the town be 100% which will be our universal set.
Let X be proportion of households that own mutual funds but not individual
From the venn diagram,
The total number of people that owned mutual fund M = (proportion of households that owned both mutual fund and individual stock) + (proportion of households that own mutual funds but not individual stocks)
If X is the proportion of households that own mutual funds but not individual stocks
The total number of people that owned mutual fund = (proportion of households that owned both mutual fund and individual stock) + X
X = (the total number of people that owned mutual fund)- (proportion of households that owned both mutual fund and individual stock)
X = 60% - 20%
X = 40%
Final answer:
To calculate the proportion of households owning only mutual funds, subtract the percentage owning both mutual funds and individual stocks from the percentage owning mutual funds, giving us 40%. The answer is C) 40%.
Explanation:
The question provided falls under the category of probability and sets in mathematics. It involves understanding how to calculate the proportion of households that own mutual funds but not individual stocks when certain percentages are provided for mutual fund ownership, stock ownership, and those owning both. This is commonly known as a problem involving the use of Venn Diagrams or set theory.
Firstly, it is stated that 60% of households own mutual funds and 40% own individual stocks. Among them, 20% own both mutual funds and individual stocks. To find the proportion of households that own only mutual funds (and not individual stocks), we subtract the percentage that owns both from the percentage that owns mutual funds. Therefore:
Proportion owning only mutual funds = (Percentage owning mutual funds) - (Percentage owning both mutual funds and stocks)
This gives us:
Proportion owning only mutual funds = 60% - 20% = 40%
The correct answer is C) 40%.
A study was conducted to determine whether UH students sleep fewer than 8 hours. The study was based on a sample of 100 students. The sample mean number of hours of sleep was 7 hours and the sample standard deviation was 5 hours.
1. What is the value of the test statistic?
a. 0.5
b. 5.0
c. 1.2
d. -5.0
Answer:
The value of t test statistics is -2.
Step-by-step explanation:
We are given that a study was conducted to determine whether UH students sleep fewer than 8 hours.
The study was based on a sample of 100 students. The sample mean number of hours of sleep was 7 hours and the sample standard deviation was 5 hours.
Let [tex]\mu[/tex] = mean number of hours UH students sleep.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \geq[/tex] 8 hours {means that UH students sleep more than or equal to 8 hours}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] < 8 hours {means that UH students sleep fewer than 8 hours}
The test statistics that would be used here One-sample t test statistics as we don't know about the population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean number of hours of sleep = 7 hours
s = sample standard deviation = 5 hours
n = sample of students = 100
So, test statistics = [tex]\frac{7-8}{\frac{5}{\sqrt{100} } }[/tex] ~ [tex]t_9_9[/tex]
= -2
Hence, the value of t test statistics is -2.