Cards from an ordinary deck of 52 playing cards are turned face up one at a time. If the first card is an ace, or the second a deuce, or the third a three, or, . . . , or the thirteenth a king, or the fourteenth an ace, and so on, we say that a match occurs. Note that we do not require that (13n + 1)th card be any particular ace for a match to occur but only that it be an ace. Compute the expected number of matches that occur.

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

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%.

Answer: 1 = 57.2

2 = angle S

3 = the triangles are similar (the second choice)

Step-by-step explanation: i got the question right on my work on e d g e n u i t y

Consider the triangles.

Triangle C D E. Angle C is blank, angle D is 87.3 degrees, angle E is 35.5 degrees. Triangle R S T. Angle R is blank, angle S is 57.2 degrees, angle T is 87.3 degrees.

Answer the questions about these triangles.

What is the measure of angle C?

✔ 57.2

Which angle corresponds to angle C?

✔ angle S

What can be concluded about the triangles?

✔ The triangles are similar.

The measure of angle C in triangle CDE is 57.2 degrees, Angle C corresponds to angle R in triangle RST,  and the two triangles are  similar or congruent.

A triangle is a three-sided polygon that consists of three edges and three vertices.

Since the sum of angles in a triangle is always 180 degrees, we can find the measure of angle C in triangle CDE by subtracting the measures of angles D and E from 180 degrees:

Angle C = 180 degrees - Angle D - Angle E

Angle C = 180 degrees - 87.3 degrees - 35.5 degrees

Angle C = 57.2 degrees

Therefore, the measure of angle C in triangle CDE is 57.2 degrees.

Angle C corresponds to angle R in triangle RST, since they are both unknown angles in their respective triangles.

We can conclude that the two triangles are  similar or congruent.

Hence, the measure of angle C in triangle CDE is 57.2 degrees, Angle C corresponds to angle R in triangle RST,  and the two triangles are  similar or congruent.

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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.

Answer:

6

Step-by-step explanation:

A triangular prism, a shape with two identical triangular faces and three identical rectangular faces, has 6 vertices where the edges of these faces meet.

In geometry, a shape's vertices are the points where two or more lines or edges meet. When we consider a triangular prism, we see that it is a figure with two triangular faces and three rectangular faces. Each triangular face has 3 vertices, and since these faces are identical, they share vertices. If you count up all these points, we find that a triangular prism has 6 vertices in total.

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Answer: f(2x)

Step-by-step explanation:

ed 2020

Answer:

x = domain

y = range

Step-by-step explanation:

Answer:

42,690

Step-by-step explanation:

it is the rule of LONG numbers

The value of the car in 2020 is $5532.53

A quantity is subject to exponential decay if it decreases at a rate proportional to its current value.

Given that, You purchase a car in 2010 for $25,000. The value of the car decreases by 14% annually.

The exponential decay is given by =

[tex]A = P(1-r)^t[/tex]

A = final amount

P = principal amount

r = rate of decrease.

t = 10

Therefore,

A = 25000(1-0.14)¹⁰

A = 25000×0.86¹⁰

A = 5532.53

Hence, the value of the car in 2020 is $5532.53

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Answer:

[tex]\hat p = \frac{Lower+Upper}{2}[/tex]

And replacing the info from the problem we have:

[tex]\hat p = \frac{0.018+0.046}{2}= 0.032[/tex]

So then the best estimator for the true proportion p is given by [tex]\hat p = 0.032 [/tex] or equivalent to 3.2 %

Step-by-step explanation:

We want to find a confidence interval for a proportion p who represent the parameter of interest.

The confidence interval would be given by this formula:

[tex]\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]

For this case the 90% confidence interval is given by (1.8%=0.018, 4.6%=0.046) after apply the last formula

Since the confidence interval is symmetrical we can estimate the point estimator of the true percentage with this formula:

[tex]\hat p = \frac{Lower+Upper}{2}[/tex]

And replacing the info from the problem we have:

[tex]\hat p = \frac{0.018+0.046}{2}= 0.032[/tex]

So then the best estimator for the true proportion p is given by [tex]\hat p = 0.032 [/tex] or equivalent to 3.2 %

Answer:

133/1152

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

In this question:

19+15+14 = 48 marbles

Of which 19 are red, 15 are yellow and 14 are blue.

What is the probability of pulling out a blue marble, followed by a red marble, if you replace the blue marble first

Blue marble

48 marbles, of which 14 are blue.

So [tex]P_{A} = \frac{14}{48} = \frac{7}{24}[/tex]

Red marble

48 marbles, of which 19 are red.

So [tex]P_{B} = \frac{19}{48}[/tex]

Both:

[tex]P = P_{A} \times P_{B} = \frac{7}{24} \times \frac{19}{48} = \frac{133}{1152}[/tex]

So the correct answer is:

133/1152

Given:

Given that Steven purchased a box of chocolate shaped like a square pyramid.

The box is 12 inches tall and the area of the bottom of the box is 35 square inches.

We need to determine the expression that is used to find the number of chocolates that the box holds.

Expression:

The expression that is used to find the number of chocolates that the box holds can be determined using the formula,

[tex]V=\frac{1}{3} Bh[/tex]

where B is the area of the base and h is the height of the pyramid.

Substituting B = 35 and h = 12 in the above formula, we get;

[tex]V=\frac{1}{3}(35 \cdot 12)[/tex]

Thus, the expression that is used to find the number of chocolates that the box holds is [tex]\frac{1}{3}(35 \cdot 12)[/tex]

Hence, Option b is the correct answer.

Answer:

Option 2

Step-by-step explanation:

Volume of a pyramid

⅓ × base area × height

⅓ × 35 × 12

12 × 35 × ⅓

Answer:

4 hours

Step-by-step explanation:

We know that there are 24 hours in a day. Therefore, we will subtract from 24.

If mark spends one-third of his day sleeping, then he will be asleep for 8 hours.

[tex]\frac{1}{3}\times24 \\=\frac{24}{3} \\=8[/tex]

We also know that if Mark spends one-sixth of his day at soccer practice, he will have been practicing for 4 hours.

[tex]\frac{1}{6}\times24 \\=\frac{24}{6} \\=4[/tex]

We now simply subtract from 24:

[tex]\text{hours in a day - hours asleep - hours at school - hours practicing} \\24 - 8 - 8 - 4 \\= 4[/tex]

Therefore, Mark will have 4 hours of free time.

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.

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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Initial bacteria count is 3, as it doubles every 12 hours; after 2 days, totaling 48 bacteria.

To solve this problem, we can use the formula for exponential growth, which is  

[tex]- \( N \)[/tex]is the final number of bacteria,

[tex]- \( N_0 \)[/tex] is the initial number of bacteria,

[tex]- \( t \)[/tex] is the elapsed time in hours, and

[tex]- \( d \)[/tex] is the doubling time in hours.

Given that the doubling time is 12 hours and after 2 days (which is 48 hours) there are 48 bacteria, we can plug these values into the formula and solve for [tex]\( N_0 \):[/tex]

[tex]\[ 48 = N_0 \times 2^{(48/12)} \][/tex]

Solving this equation:

[tex]\[ 48 = N_0 \times 2^4 \][/tex]

[tex]\[ 48 = N_0 \times 16 \][/tex]

Now, to find [tex]\( N_0 \)[/tex]:

[tex]\[ N_0 = \frac{48}{16} \][/tex]

[tex]\[ N_0 = 3 \][/tex]

So, there were 3 bacteria at the beginning of the first day.

Answer:

5x+20

Step-by-step explanation:

5(x+4)

Distribute

Multiply 5 by each term inside the parentheses

5*x + 5*4

5x+20

Answer:

I'm just going to take a guess and say 36?

Step-by-step explanation:

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.

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:

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]

Answer:

Prism A

Step-by-step explanation:

Volume of a triangular prism is calculated like this : 1/2 × 7 × 4 × 9 = 126 m^3

Volume of a cuboid is calculated like this : 8 × 8 × 2 = 128 m^3

Answer:

A

Step-by-step explanation:

Answer:

2,5, and 6

Step-by-step explanation:

hope this helps

The solid will be a triangular prism .The solid will have some faces that are rectangles and some faces that are triangles.

The solid will have five faces.

Answer:

the answer is A.Use the numbers in the table to create ordered pairs. and D.Draw a straight line that starts at the origin and connects all the points.

Step-by-step explanation:

I just did it on edgnuity and got it right.

Answer:

The correct answer is A C and D

Step-by-step explanation:

Answer:

Communitive property of addition

Step-by-step explanation:

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

Answer:

a A=$47,887.81

b.A=$46,430.80

Step-by-step explanation:

a. Given the initial amount is $40,000 with a 3-year term and a 6% rate compounded daily.

-Take 1 year=365 days

#First we calculate the effective interest rate corresponding to the daily compounding;

[tex]i_m=(1+i/m)^m-1\\\\=(1+0.06/365)^{365}-1\\\\=0.06183[/tex]

#We use the calculated effective rate, 0.06183, to solve for the future value as:

[tex]A=P(1+i_m)^n\\\\=40000(1.06183)^3\\\\=47887.81[/tex]

Hence, the total future value for a daily compounding is $47,887.81

b. For a sinking fund with a 5% compounded quarterly:

#We calculate the annual effective rate:

[tex]i_m=(1+i/m)^m-1\\\\=(1+0.05/4)^4-1\\\\=0.05095[/tex]

#We use the calculated effective rate, 0.05095, to solve for the future value as:

[tex]A=P(1+i_m)^n\\\\=40000(1.05095)^3\\\\=46430.80[/tex]

Hence, the future value of the sinking fund is $46,430.80

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

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??

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.

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.

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.

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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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