How is the area of the figure estimated?

The margin of error is a measure of the degree of uncertainty associated with the point estimate of a population parameter. Confidence intervals are constructed to estimate the true value of a population parameter with a certain level of confidence.

The margin of error and the width of the confidence interval are related, in that a larger margin of error implies a wider confidence interval.

When constructing a one-sample z-confidence interval to estimate the population proportion, the margin of error increases as the sample size increases. This is because larger sample sizes provide more information about the population and, as a result, the estimate becomes more precise. Conversely, as the sample size decreases, the margin of error increases, making the estimate less precise.

The margin of error also increases as the population proportion approaches 0.50. This is because when p=0.50, the population is evenly split between the two possible outcomes. As a result, more variability is expected in the sample proportions, leading to a larger margin of error.

Finally, the margin of error decreases as the confidence level (1-a) increases. This is because a higher confidence level requires a wider interval to account for the additional uncertainty associated with a higher level of confidence. In conclusion, the margin of error in one-sample z confidence intervals is affected by sample size, population proportion, and confidence level.

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The probability that a card player is dealt a 13-card hand from a well-shuffled, standard deck of cards and the hand is void in at least one suit is approximately 0.3643.

To calculate this probability, we can consider the complement event, which is the probability that the hand is not void in any suit.

The number of ways to select a 13-card hand from a 52-card deck is given by the binomial coefficient C(52, 13).

The number of ways to select a 13-card hand without a specific suit (let's say hearts) is given by the binomial coefficient C(39, 13), as there are 39 cards remaining in the deck after removing the 13 hearts.

Since there are four suits (hearts, diamonds, clubs, and spades), we can calculate the number of ways to select a 13-card hand without any suit by multiplying C(39, 13) by 4.

The probability that the hand is not void in any suit is then given by the ratio of the number of ways to select a 13-card hand without any suit to the number of ways to select any 13-card hand:

P(not void in any suit) = (4 * C(39, 13)) / C(52, 13)

Finally, we can find the probability that the hand is void in at least one suit by subtracting the probability of not being void in any suit from 1:

P(void in at least one suit) = 1 - P(not void in any suit)

Calculating this probability gives us approximately 0.3643.

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The maximum weight that the balloon can lift is 5020.31 Newtons.

We have to give that,

A 3.2 kg balloon is filled with helium with a density of 0.179 kg/m³.

And, the balloon is a sphere with a radius of 4.9 m.

Since The formula for the volume of a sphere is,

\(V = \dfrac{4}{3} \pi r^3\)

Here, \(g = 9.8 \text{m/s}\)

\(\rho_{air} = 1.225\) kg/m³

So, Buoyant force on the ballons is,

\(F_B = V \times \rho_{air} \times g\)

Substitute all the given values,

\(F_{B} = \dfrac{4}{3} \times\pi \times (4.9)^3 \times 1.225 \times 9.8\)

\(F_B = 5916.15 \text{N}\)

So, the maximum weight that the balloon can lift is calculated as,

\(W +M_b +V \times \rho_{He} \times g = F_B = V \times \rho_{air} \times g\)

\(W = F_B - (M_bg +V \times \rho_{He} \times g)\)

Where, \(M_b\) is the mass of balloons.

Substitute all the values,

\(W = 5916.15 - [(3.2 \times 9.8) + \dfrac{4}{3} \pi (4.9)^3 \times (0.179) \times(9.8)]\)

\(W = 5916.15 - 31.36 - 864.48\\\)

So, the maximum weight that the balloon can lift is,

\(W = 5020.31\)

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Answer:

he bought 6 hats.

Step-by-step explanation:

im just gonna go through this 1 at a time. starting at 1.

12 + (14x9) = 138

(12x5)+(14x5) = 130

(12x4)+(14x6) = 132

(12x8)+(14x2) = 124

(12x6)+(14x4) = 128

Answer: 7 necklaces

Step-by-step explanation: So we're looking at 3blue+2red is less than or equal to the 22 blue beads and 15 red beads. The closest you could get is using 21 blue beads and 14 red beads which is 7 necklaces.

There will be 2 beads left over.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

The number of blue and red beads in a necklace.

= 3 blue beads and 2 red beads

Number of blue beads = 22

The number of necklaces that can be made from the blue beads.

= 7

3 x 7 = 21

One blue bead remains.

Number of red beads = 15

The number of necklaces that can be made from the blue beads.

= 7

2 x 7 = 14

One red bead remains.

Thus,

There will be 2 beads left over.

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Answer:

20 greater than or equal to 4x + 7

Step-by-step explanation:

hope this helps!

Answer:

A

Step-by-step explanation:

We are given two functions:

\(\displaystyle f(x)=\frac{x-16}{x^2+6x-40}\text{ and } g(x)=\frac{1}{x+10}\)

And we want to find:

\(f(x)+g(x)\)

Thus:

\(\displaystyle =\frac{x-16}{x^2+6x-40}+\frac{1}{x+10}\)

We can factor the denominator of the first term:

\(\displaystyle =\frac{x-16}{(x+10)(x-4)}+\frac{1}{x+10}\)

In order to add the two terms, we must have a common denominator. To achieve this, we can multiply to second term by (x - 4). Therefore:

\(\displaystyle =\frac{x-16}{(x+10)(x-4)}+\frac{1}{x+10}\Big(\frac{x-4}{x-4}\Big)\)

Multiply:

\(\displaystyle =\frac{x-16}{(x+10)(x-4)}+\frac{x-4}{(x+10)(x-4)}\)

Combine:

\(\displaystyle =\frac{(x-16)+(x-4)}{(x+10)(x-4)}\)

Simplify:

\(\displaystyle =\frac{2x-20}{(x+10)(x-4)}\)

We can expand the denominator:

\(\displaystyle =\frac{2x-20}{x^2+6x-40}\)

Therefore, our answer is A.

Answer:

A

Step-by-step explanation:

Answer:

50 per hour

Step-by-step explanation:

Answer:

x = 2

Step-by-step explanation:

\(\frac{x}{2x+1} = \frac{16}{40}\)

Step 1: Cross multiply

We want to eliminate all denominators, so we multiply the opposite numerators and denominators

\(\frac{x}{2x+1} = \frac{16}{40}\\\\\\x\cdot40 = 16(2x + 1)\\\\\\40x = 32x + 16\)

Step 2: Solve for x

Now we want x by itself, and we have to solve for x.

             \(40x = 32x + 16\\\\\\40x - 32x = 16\\\\\\8x = 16\)

             \(8x = 16\\\\8(x) = 16\\\\x = 16/8\\\\x = 2\)

-Chetan K

Answer:

x=2

Step-by-step explanation:

40*x=16(2x+1)  (we cross multiply)

40x=32x+16

8x=16

x=2

Answer:I think its 67.2

Step-by-step explanation:

Answer:

eu acho que o resultado é 67.2

e um belo dia abençoado

The least amount Kayla's grandfather can spend on the wood for the toy box is $138.

To determine the least amount Kayla's grandfather can spend on the wood for the toy box, we first need to find the surface area of the box, which is 2 ft tall, 2.5 ft wide, and 4 ft long.

The surface area of a rectangular box can be calculated using the formula: SA = 2lw + 2lh + 2wh, where l is the length, w is the width, and h is the height.

Plugging in the values, we get:
SA = 2(4)(2.5) + 2(4)(2) + 2(2.5)(2) = 20 + 16 + 10 = 46 square feet.

Since the wood costs $3 per square foot, the least amount Kayla's grandfather can spend on the wood is:
Cost = 46 square feet * $3 per square foot = $138.

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Answer:

\(\boxed{Probability = 48}\)

Step-by-step explanation:

Probability of getting a tails = 0.3

If it is flipped 160 times, the probability of getting a tails will be

=> 0.3*160

=> 48

Given:

Principal = $54,000

Time = 9 years

Rate of compound interest = 12% per annum.​

To find:

The compound interest.

Solution:

The formula for amount is:

\(A=P\left(1+\dfrac{r}{n}\right)^{nt}\)

Where, P is principal, r is the rate of interest in decimal, n is the number of time interest compounded and t is the number of years.

The interest is compounded annually, so \(n=1\).

Substituting \(P=54000,\ t=9,\ n=1,\ r=0.12\) in the above formula, we get

\(A=54000\left(1+\dfrac{0.12}{1}\right)^{1(9)}\)

\(A=54000\left(1.12\right)^{9}\)

\(A=149746.252902\)

\(A\approx 149746.25\)

The amount after 9 years is $149746.25.

Now, the compound interest is:

\(C.I.=A-P\)

Where, C.I. is compound interest, A is amount and P is principal.

\(C.I.=149746.25-54000\)

\(C.I.=95746.25\)

Therefore, the compound interest is $95746.25.

A scatterplot that shows the number of hours studied on the x-axis and the number of errors on the y-axis would best support the teacher's observation.

Error in math is an incorrect answer to a mathematical equation or problem. It can be caused by a variety of factors, such as inaccurate calculations, misreading instructions, or not understanding the problem. Error in math can be frustrating and can lead to poor grades, but it can also be an opportunity for learning and growth. With the proper guidance and understanding, students can learn from their mistakes and become better mathematicians.

The scatterplot would likely show a negative correlation, with the number of errors decreasing as the number of hours studied increases. This indicates that as students study more, their performance on multiplication tests improves. It could also show an outlier or two, which could indicate that some students are able to learn multiplication facts more quickly than others.

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Answer:

E is the correct choice

Step-by-step explanation:

i hope this helps

The value of the composite function f(g(-3) is -32

From the question, we have the following parameters that can be used in our computation:

f(x) = x + 4. q(x) = 12x

The above are individual functions

This means that

f(g(x)) = 12x + 4

For f(g(-3)), we have

f(g(x)) = 12 * -3 + 4

Evaluate

f(g(x)) = -32

Hence, the value of the composite function is -32

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Alrighty, so,  you know how young children often believe that a taller container will have a greater volume than a shorter container? Even after seeing that both containers hold the same amount, some children will still think the taller container holds more. It may take measuring the water a few times before they get it.

If it overflows, the first container is bigger, or is able to hold more water. If all of the water from the first container can be poured into the second container without completely filling it, then the second container holds more water.

The tallest container holds the most liquid. Identical containers can have a different capacity.

Answer:

D

Step-by-step explanation:

Edge

Answer:

D

Step-by-step explanation:

The weakest correlation among the given options is a) -0.15.

Correlation measures the relationship between two variables, and it ranges from -1 to +1. The value of the correlation coefficient tells us the strength and direction of the relationship. If the correlation coefficient is closer to -1 or +1, it indicates a strong relationship, whereas a value closer to 0 suggests a weak relationship. In this case, -0.15 is the value that is closest to 0, which implies the weakest correlation. A negative correlation coefficient suggests an inverse relationship, which means that as one variable increases, the other variable decreases. Conversely, a positive correlation coefficient implies a direct relationship, which indicates that as one variable increases, the other variable also increases. Therefore, among the given options, -0.15 represents the weakest correlation, which indicates a weak inverse relationship between the two variables being studied.

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Answer:

y=50 x=80

Step-by-step explanation:

z(3rd spot)=y=50

x=180-2*50=80

Answer:

y=50 cause it is isosceles and then you do 180-100 because 50+50=100 and a triangle =180. so angle x is 80

Answer:

70

Step-by-step explanation:

70/10 = 7

Answer:

13/2<x<12

or  (13/2, 12)

Step-by-step explanation:

break the promblem into two seperate equations and solve.

Answer:

( z - 5 ) ( z - 5 )

Step-by-step explanation:

z² − 10z + 25

= z² − 5z - 5z + 25

= z ( z - 5 ) - 5 ( z - 5 )

= ( z - 5 ) ( z - 5 )

If x and y are directly proportional, that means Y = kX. The variable k here is a constant. When we say x is tripled, k must be 3.

What does it mean directly proportional?

When two quantities are directly proportional, it indicates that if one increases by a specific percentage, the other also increases by the same percentage.

Let's have an example. Let's assume that x is 5. If we triple 5, it would equal to 15.

y = 3(5)

15 = 15

Therefore, the answer to this problem would be:

It is tripled

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Answer:

Equation for Angle 3- 90-38=52

Angle 3= 52

Angle 5= 38

Angle 6= 52

Step-by-step explanation:

Angle is 90 degrees.

Angle 2 is 38 degrees.

If you are just looking at the bottom half(Angle 6, Angle 1, and Angle 2) They are all supposed to add up to equal 180 degrees because it is a supplementary angle.

So you add 90 and 38 and it gives you 52(Angle 6).
90+38+52=180

Then a complementary angle is two angles that equal 90 degrees.

So if you take Angle 2(38 degrees) and subtract it from 90, you get 52. Which is Angle 3.

You do the same with Angle 6 and Angle 5.

Angle 6(52 degrees) subtract from 90 and you get 38.

Then you add 38 and 52 and you get 90.

Then 180-90=90, so Angle 4 is 90 degrees.

We want to find a number that is multiple of all the denominators of the fractions we have. For example, in the cases:

we have two denominators: 5 and 3

And for

we have 3 and 12

2/5 + 1/3:

We can find a common denominator by simply multiplying all the denominators. In this case the common denominator would be

5 x 3 = 15

then,

and

then we have that

1/3 + 3/12:

We can find a common denominator by simply multiplying all the denominators. In this case the common denominator would be

3 x 12 = 36

then

1/3 + 3/12:

We can find the denominator by finding the multiples of both denominators:

multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24...

multiples of 12: 12, 24, 36, 48, ...

We find some the numbers that both multiples share:

multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24...

multiples of 12: 12, 24, 36, 48, ...

We choose the first common multiple, and this is the common denominator. In this case it is 12. Since

3 x 4 = 12, then

Answer:

non linear

Step-by-step explanation:

Answer:

Linear

Step-by-step explanation:

Answer:

a = -0.5

b = −1.73

c = −0.70

d = \(-\frac{\sqrt{2} }{2}\) ≈ -0.70710678

Step-by-step explanation:

EXPLAIN Q(a):

sin(−30)

Use the property sin(−x)=−sin(x).

−sin(30)

Get the value of sin(30) from trigonometric values table.

-0.5

Answer:

no she dont

Step-by-step explanation:

she gotta have 125 cus theres 5 20's in 100 and theres only 4 5's in 20