What is the Area of the Figure?

Answer: 3/8

Step-by-step explanation:1/2 divided by 4/3 is equal to 1/2 x 3/4 (you cannot divide by a fraction, you must multiply by it’s reciprocal- flip it, or cross multiply. Here we are flipping it)

Now multiply across the top ( numerators)

And then across the bottom (denominators)

1x3=3

2x4=8

Answer is 3/8

Complete Question

Your PI claims that the proportion of Morpho butterflies in a population that are blue is 0.3 .A sample is independently obtained from this population. Of 200 sampled Morphos, 50 turn out to be blue.Given only this information, carry out a hypothesis test to evaluate the claim. What is closest to the p-value that you obtain?

A 0.019

B 0.038

C 0.070

D 0.139

Answer:

The correct answer is  D

Step-by-step explanation:

From the question we are told that  

    The population proportion of blue butterflies is  \(p = 0.3\)

    The  sample  size is  \(n = 200\)

     The  sample mean is  \(\= x = 50\)

The  Null Hypothesis is mathematically represented as

        \(H_o : p = 0.3\)

The  Alternative  Hypothesis is mathematically represented as

       \(H_a : p \ne 0.3\)

Now the sample proportion is mathematically represented as

         \(\r p = \frac{\= x}{n}\)

substituting values

        \(\r p = \frac{50 }{200 }\)

         \(\r p = 0.25\)

Generally the test statistics is mathematically represented as

         \(z = \frac{\r p - p }{\sqrt{\frac{p(1-p)}{n } } }\)

substituting values            

         \(z = \frac{ 0.25 - 0.3 }{\sqrt{\frac{0.3(1-0.3)}{200 } } }\)

        \(z = -1.54\)

The  p-value for a two-tailed test  is  mathematically represented as

for lower -tail test

\(p-value = P(Z \le z | H0\ is \ true) = cdf(z )\)

 for higher-tail test

\(p-value = P(Z \ge z | H0\ is \ true) = 1- cdf(z )\)

for this test i assumed a 0.05 level of significance

Now  

  \(cdf(z)\) is the cumulative distribution function for test statistics under the null hypothesis

Which can be calculated using MInitab (A statistics calculator )

  for lower-tail test

     The p-value is not significant

 for higher-tail test

p-value is

      \(1- cdf(-1.54) = 0.125\)

The probability of pulling out a number which is divisible by 2 or 3 will be 7/10 which is not given here. So, option D will be the answer.

How do we find Probability?

The measurement through which we find the likelihood of an event to occur is called probability. We cannot predict a lot of events with total certainty. And thus, the chance of a event to occur (i.e. how likely they re going to happen) can be predicted using probability.

Probability of any event to happen can be find as: No of favorable outcomes/Total number of outcomes.

Here,

The total no of outcomes = 1,2,3,4,5,6,7,8,9,10

No of favorable outcomes ={2,3,4,6,8,9,10} = 7

Therefore, P(E) = 7/10

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Answer:

y- intercept = - 6

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here slope m = 2 , then

y = 2x + c ← is the partial equation

to find c substitute (5, 4 ) into the partial equation

4 = 2(5) + c = 10 + c ( subtract 10 from both sides )

- 6 = c

that is the y- intercept c = - 6

Answer:

The amount of money after 8 years is $8448.69

Step-by-step explanation:

The rule of the compound interest is  

\(A=p(1+r)^{t}\) , where

∵ There is $7500 in an account

∴ P = 7500  

∵ The account paying 1.5% compound interest

∴ r = 1.5% = 1.5/100 = 0.015  

∵ The money will invest for 8 years

∴ t = 8

→ Substitute all of these values in the rule above to find A  

∵  \(A=7500(1+0.015)^{8}\)

→ Use your calculator to find the answer  

∴ A = 8448.69

∴ The amount of money after 8 years is $8448.69

Answer:

( 0 , 1 ) ,  ( 1 , 0 )

( − 5 , 9 ) ,  ( 3 , 0 )

( 0 , 9 ) ,  ( 8 , 6 )

Step-by-step explanation:

Answer:

The third one 54

Step-by-step explanation:

I hope it helps.

Check the picture below.

Answer:

Step-by-step explanation:

Students use algebra to solve equations (of the form px + q = r and p(x + q) = r where p, q, and r are specific rational numbers); using techniques of making zero (adding the additive inverse) and making one (multiplying by the multiplicative inverse) to solve for the variable.

Students identify and compare the sequence of operations used to find the solution to an equation algebraically, with the sequence of operations used to solve the equation with tape diagrams. They recognize the steps as being the same.

Students solve equations for the value of the variable using inverse operations; by making zero (adding the additive inverse) and making one (multiplying by the multiplicative inverse).

An arithmetic sequence is a sequence of integers with its adjacent terms differing with one common difference.

We know that,

An arithmetic sequence is a sequence of integers with its adjacent terms differing with one common difference.

The explicit formula for any arithmetic series is given by the formula,

a_n = a_1 + (n-1)d

where d is the difference and a₁ is the first term of the sequence.

The major distinction between recursive and explicit formulas is that a recursive formula returns the value of a particular term depending on the preceding term, whereas an explicit formula returns the value of a given term based on its location.

When the value of the first term and the common difference is known then an explicit formula is used, while the recursive formula will be used when the value of the previous value is known and the value of the common difference is known.

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complete question:

what is the difference between the explicit formula and recursive formula for sequences when would you use one over the other​

The probability that the shipment will be rejected is 0.15.

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty.

Probability defines the likelihood of occurrence of an event. There are many real-life situations in which we may have to predict the outcome of an event. We may be sure or not sure of the results of an event. In such cases, we say that there is a probability of this event to occur or not occur. Probability generally has great applications in games, in business to make probability-based predictions, and also probability has extensive applications in this new area of artificial intelligence.

Probability of shipment been rejected;

Sample space = 68

To be tested = 10

Therefore, n(S) = 68

n(A) = 10

Probability Formula;

P(shipment rejected) = (n(A))/(n(s))

P(shipment rejected) = 10/68

P(shipment rejected) = 0.15

The probability that the shipment will be rejected after random testing will be 0.15.

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Answer:

\(n \leq -48\)

Step-by-step explanation:

Step 1:  Convert to an expression

8 - 1/4 n is greater than or equal to 20

\(8 - \frac{1}{4}n \geq 20\)

Step 2:  Subtract 8 from both sides

\(8 - 8 - \frac{1}{4}n \geq 20 - 8\)

\(- \frac{1}{4}n \geq 12\)

Step 3:  Multiply both sides by -4

\(- \frac{1}{4}n * -4 \geq 12 * -4\)

Since we are multiplying by a negative we flip the greater than equal sign to a less than equal sign.

\(n \leq -48\)

Answer:  \(n \leq -48\)

Answer: 1.1

Step-by-step explanation: 1.083, if rounding to one decimal place look at the next digit, so in this case the 8. If the digit is 5 or higher, round the tenth up. If the number is 4 or below, round down. So you will end up with 1.1

Step-by-step explanation:

Make a 10 strategy?

Answer:

4(−10−9x)

Step-by-step explanation:

Answer:

55

Step-by-step explanation:

if x=9 and y  = 6x + 1

then  all what you have to do is that you should substitute x by 9 in y equation as the following,

y =  6*(9) + 1 =54 + 1 = 55

Answer:

55

Step-by-step explanation:

Given,

y = 6(x)+1

Substituting x= 9 on the given expression,

Hence y = 55.

Consequently, spot B's updated coordinates are (-4,-1).

To find a point's coordinates inside a coordinate system, you do the opposite. Move either upward or downward in a straight path starting at the location until you approach the x-axis. There is your x-coordinate displayed. Repeat the prior procedure while staying on a straight line to find the y-coordinate.

To translate a point in the coordinate plane, we need to subtract the horizontal and vertical distances by which we want to move it from the original coordinates. In this case, we want to move point B 4 units left and 3 units down. So:

New x-coordinate of B = Old x-coordinate of B - Horizontal distance = 0 - 4 = -4

New y-coordinate of B = Old y-coordinate of B - Vertical distance = 2 - 3 = -1

Therefore, the new coordinates of point B are (-4,-1).

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Kindly note that the question says 4; maybe the final question was intended to be the probability that he gets exactly 2 of the 4 correct. However. If it is the other way round. This a e procedure used in the solution should also be followed.

Answer:

0.21

Step-by-step explanation:

Number of options = 4

One correct answer per option ; hence, the probability of success, p = 1/4 = 0.25

Using the binomial probability relation :

P(x =x) = nCx * p^x * (1 - p)^(n - x)

x = 2 ; n = 4

p = 0.25 ; 1 - p = 0.75

P(x = 2) = 4C2 * 0.25^2 * 0.75^2

P(x = 2) = 6 * 0.0625 * 0.5625

P(x = 2) = 0.2109375

P(x = 2) = 0.21 (2 decimal places)

Note : if the question was 3, then put, n = 3 instead of 4

Answer:

312.5

Step-by-step explanation:

P=5000

r=12.5%=0.125

t=6month=0.5years

I=P•r•t

I=(5000)(0.125)(0.5)

I =$312.5

The rest wavelength of the emission line observed at 2148 nanometers in the galaxy 100 million light-years away is approximately 2103 nanometers.

The rest wavelength of an emission line can be determined by applying the concept of redshift, which is a phenomenon observed in astrophysics where light from distant objects is shifted towards longer wavelengths due to the expansion of the universe.

In this case, the emission line is observed at 2148 nanometers (or 2.148 micrometers) in a galaxy located 100 million light-years away. To calculate the rest wavelength, we need to consider the redshift factor. Redshift, denoted by z, is defined as the observed wavelength divided by the rest wavelength minus 1.

Given that the observed wavelength is 2.148 micrometers and the galaxy is located 100 million light-years away, we need to convert the distance into a redshift factor using the cosmological relationship between redshift and distance. Assuming a standard cosmological model, we can use the Hubble constant to estimate the redshift.

The Hubble constant represents the rate at which the universe is expanding. Taking a typical value of the Hubble constant as 70 kilometers per second per megaparsec, we find that the redshift factor, z, is approximately 0.021.

To determine the rest wavelength, we rearrange the redshift equation as \((observed wavelength) = (1 + z) \times (rest wavelength)\). Substituting the values, we get \((2.148 micrometers) = (1 + 0.021) \times (rest wavelength).\)

Simplifying the equation, we find the rest wavelength to be approximately 2.103 micrometers or 2103 nanometers.

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Answer:

2√2 units.

Step-by-step explanation:

To find the length of the line joining points A(3, 5) and B(1, 3), we can use the distance formula. The distance formula is given by:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Substituting the coordinates of points A and B into the formula, we have:

d = sqrt((1 - 3)^2 + (3 - 5)^2)

  = sqrt((-2)^2 + (-2)^2)

  = sqrt(4 + 4)

  = sqrt(8)

  = 2sqrt(2)

Therefore, the length of the line joining points A and B is 2√2 units.

Answer:

13 (A)

Step-by-step explanation:

take 38 and subtract 15, that leaves you with 13

Answer:

Step-by-step explanation:

Answer:

mark the answer below as brainliest x

Step-by-step explanation:

Answer:The 95% Rule states that approximately 95% of observations fall within two ... about 95% will be within two standard deviations of the mean, and about 99.7% will be ... Suppose the pulse rates of 200 college men are bell-shaped with a mean of 72 ... 1.2 - Samples & Populations ... 3.5 - Relations between Multiple Variables.

Step-by-step explanation:

The final velocity of the parameters is 13.5m/s

In this question, the given parameters are represented as

Formula: v = u + at

Initial velocity = 3m/s

Acceleration = 1.5m/s²

Time = 7 seconds

When these parameters are represented using their required notation, we have the following representations

u = 3m/s

a = 1.5m/s²

t = 7 s

Next, we substitute the above parameters in the above equation

So, we have the following representation

v = 3 + 1.5 * 7

Evaluate the products

This gives

v = 3 + 10.5

Evaluate the sum

So, we have the following representation

v = 13.5

The notation v represents the final velocity

Hence, the final velocity is 13.5m/s

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Answer:

4/ 100000

hope it was useful for you

stay at home stay safe

pls mark me as brain.....m

keep rocking

Answer: D = √2

(please respond if im wrong)

Step-by-step explanation:

The fold is made along BE. A folds onto A′.

A′B = AB =√2 ⇒ A′C = 1

(by Pythagoras)

ΔA′BC

is therefore a right-angled isosceles triangle.

⇒∠BA′C=45∘ ⇒∠EA′D=45∘

⇒ ED = A′D = √2−1

Answer:

a. 0.0385

b. 3.44% probability that more than 50% of the college students from the sample spent their spring breaks relaxing at home

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

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 pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean \(\mu = p\) and standard deviation \(s = \sqrt{\frac{p(1-p)}{n}}\)

In this question:

\(p = 0.43, n = 165\)

a. Calculate the appropriate standard error calculation for the data.

\(s = \sqrt{\frac{0.43*0.57}{165}} = 0.0385\)

b. What is probability that more than 50% of the college students from the sample spent their spring breaks relaxing at home?

This is 1 subtracted by the pvalue of Z when X = 0.5. So

\(Z = \frac{X - \mu}{\sigma}\)

By the Central Limit Theorem

\(Z = \frac{X - \mu}{s}\)

\(Z = \frac{0.5 - 0.43}{0.0385}\)

\(Z = 1.82\)

\(Z = 1.82\) has a pvalue of 0.9656

1 - 0.9656 = 0.0344

3.44% probability that more than 50% of the college students from the sample spent their spring breaks relaxing at home