Child Health and Development Studies (CHDS) has been collecting data about expectant mothers in Oakland, CA since 1959. One of the measurements taken by CHDS is the weight increase (in pounds) for expectant mothers in the second trimester. In a fictitious study, suppose that CHDS finds the average weight increase in the second trimester is 14 pounds. Suppose also that, in 2015, a random sample of 45 expectant mothers have mean weight increase of 16.3 pounds in the second trimester, with a standard deviation of 5.9 pounds. A hypothesis test is done to see if there is evidence that weight increase in the second trimester is greater than 14 pounds. Find the p -value for the hypothesis test. The p -value should be rounded to 4 decimal places.

Answer:

0.5188 = 51.88% probability of obtaining a difference between sample means of 110 mg or more

Step-by-step explanation:

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

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.

Central Limit Theorem

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

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

Subtraction of normal sample means:

When we subtract two distribution of the sample means, which are normal, the mean is the subtraction of the means, while the standard deviation is the square root of the sum of standard errors squared.

Sample size of 55 men with mean 785 and standard deviation 489

This means that:

[tex]\mu_A = 785[/tex]

[tex]s_A = \frac{489}{\sqrt{55}} = 65.9367[/tex]

Sample size of 40 women with mean 670 and standard deviation of 419

This means that:

[tex]\mu_B = 670[/tex]

[tex]s_B = \frac{419}{\sqrt{40}} = 66.2497[/tex]

Difference between sample means:

The mean and the standard deviation are, respectively:

[tex]\mu = \mu_A - \mu_B = 785 - 670 = 115[/tex]

[tex]\sigma = \sqrt{s_A^2+s_B^2} = \sqrt{65.9367^2+66.2497^2} = 93.47[/tex]

What is the probability of obtaining a difference between sample means of 110 mg or more?

This is 1 subtracted by the pvalue of Z when X = 110. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{110 - 115}{93.47}[/tex]

[tex]Z = -0.053[/tex]

[tex]Z = -0.053[/tex] has a pvalue of 0.4812.

1 - 0.4812 = 0.5188

0.5188 = 51.88% probability of obtaining a difference between sample means of 110 mg or more

Answer:

26

Step-by-step explanation:

Answer:

27

But tell me the exact question it has on there

Step-by-step explanation:

Answer:

the porbality is 50%, since if we make a diagram a circle and we split it in two the possibility is 50% since the circle is 100%

Step-by-step explanation:

Answer:

volume= 186ft

Step-by-step explanation:

Answer:

122

Step-by-step explanation:

61 x 2 = 122 hope this helps:)

Answer:

B

Step-by-step explanation:

Answer:

Step-by-step explanation:it is b because u multiply.

Answer:

c

Step-by-step explanation:

Answer:

x will be equal to 7 comic books

The number of books Maria is ordering is 7 books

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number of comic books Maria orders be = x

The cost of x books is = y

Now , the equation for the total cost be

y = 8x + 4   be equation (1)

Now , the total cost of all the books be = $ 60

So , substituting the value of y as 60 in equation (1) , we get

60 = 8x + 4

Subtracting 4 on both sides of the equation , we get

8x = 56

Divide by 8 on both sides of the equation , we get

x = 7 books

Therefore , the value of x is 7

Hence , The number of books Maria is ordering is 7 books

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Answer:

C, E, and F

Explanation:

There are two ways to answer this question. First, you could simply input each answer into both equations to see which one works but that would take quite a long time.

A better way is to simply solve each equation for x.

You could rewrite

2x + 7 < -3

as

2x + 7 = -3

and solve:

Subtract 7 from both sides

[tex](2x + 7) -7 = (-3) - 7\\2x = -10[/tex]

Now divide both sides by 2

[tex]\frac{2x}{2} = \frac{-10}{2}\\x = -5[/tex]

Now we can simply replace the equals sign with the inequality

x < -5

Where you can run into trouble is if you have to multiply or divide by a negative number across the equation, you must flip the inequality sign. It's best to leave it there to remind you, but I switched it out just to show that it's no different than a typical algebraic equation.

Now, we know that x can be any value less than -5. Let's find out the same thing for the second equation:

[tex]x - 8 + 3x < -4\\(x + 3x) -8 < -4\\4x - 8 < -4\\(4x - 8) + 8 < (-4) + 8\\4x < 4\\\frac{4x}{4} < \frac{4}{4}\\x < 1[/tex]

Now we know that x must be less than 1 for the second equation. So, now we can choose the answers that are both less than -5 and less than 1.

These answers are:

C. -10

E. -8.24

and

F. -15/2 which is -7.5

NOTE: -5 is equal to but not less than -5 so G is not included.

Answer:

x = 33 , y = 25

Here's your solution

=> let both number be x and y

=> so, x + y = 58

=> x - y = 8

=> solving both equation { add both }

=> 2x = 66

=> x = 33

=> now putting value of x in equation

=> 33 + y = 58

=> y = 58 - 33

=> y = 25

hope it helps

Answer:

[tex]13 \div 24[/tex]

13/24

Step-by-step explanation:

[tex]7 \div 8 - 1 \div 3[/tex]

[tex]taking \: the \: lcm \: of \: 8 \: and \: 3[/tex]

[tex]21 - 8 \div 24[/tex]

[tex]13 \div 24[/tex]

if it helps don't forget to like and mark me

Answer:

i can only say that you should use this forumla, the sins law

sin(a)/A = sin(b)/B = sin(c)/C

Step-by-step explanation:

Answer:

when you calculate the value of w is z= 5

Step-by-step explanation:

Answer:98

Step-by-step explanation:

because it is a rectangle at a slight angle so base * height

Brainlest plz

Answer:I’m not sure but I thinks it’s b might be wrong

Step-by-step explanation:

Answer: 90 degrees to 120

Step-by-step explanation:

The probability of a temperature from 90 degrees to 120 degrees.

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. For an experiment having 'n' number of outcomes, the number of favorable outcomes can be denoted by x. The formula to calculate the probability of an event is as follows.

Probability(Event) = Favorable Outcomes/Total Outcomes = x/n

Experiment: A trial or an operation conducted to produce an outcome is called an experiment.

Sample Space: All the possible outcomes of an experiment together constitute a sample space. For example, the sample space of tossing a coin is head and tail.

Favorable Outcome: An event that has produced the desired result or expected event is called a favorable outcome. For example, when we roll two dice, the possible/favorable outcomes of getting the sum of numbers on the two dice as 4 are (1,3), (2,2), and (3,1).

Trial: A trial denotes doing a random experiment.

Given:

Temperatures from 60 degrees to 160 degrees.

As, per the situation the probability will lie between 60 degree to 160 degree.

Hence, The probability of a temperature from 90 degrees to 120 degrees.

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Answer:x/4+3

Step-by-step explanation:

8/1×1/4=8/4=2

X/1×1/4=x/4

4/1×1/4=1

Answer:

2 + [tex]\frac{1}{4} x[/tex] + 1

Step-by-step explanation:

Answer:

60

Step-by-step explanation:

Answer:

You would have spent $4.50

Step-by-step explanation: Divide 100 by 30 and multiply to 15. So it will look like: 30/100*15= $4.50. I hope this helps

Answer:

15 165

Step-by-step explanation:

m1 + m2 = 180

x-18 +5x = 180

6x = 198

x = 33

m1 = 15

m2 = 165

Answer:

First sample size, [tex]n_{x}[/tex] = 20

Second sample size, [tex]n_{y}[/tex] = 20

Sample mean of first sample, [tex]\bar{x}[/tex] = 5.44

Sample mean of second sample, [tex]\bar{y}[/tex] = 3.49

Sample Standard deviation of first sample, [tex]\sigma_{x}[/tex] = 1.75

Sample Standard deviation of second sample, [tex]\sigma_{y}[/tex] = 1.13

Step-by-step explanation:

Given - The sample mean tip amount for the 20 parties to which the waitress gave her name was $5.44, with a standard deviation of $1.75. These statistics were $3.49 and $1.13, respectively, for the 20 parties to which the waitress did not give her name. The data were not strongly skewed in either group.

To find - Use appropriate symbols for the six numbers reported in this paragraph.

Proof -

First sample size, [tex]n_{x}[/tex] = 20

Second sample size, [tex]n_{y}[/tex] = 20

Sample mean of first sample, [tex]\bar{x}[/tex] = 5.44

Sample mean of second sample, [tex]\bar{y}[/tex] = 3.49

Sample Standard deviation of first sample, [tex]\sigma_{x}[/tex] = 1.75

Sample Standard deviation of second sample, [tex]\sigma_{y}[/tex] = 1.13

Answer:

in triangle ACD

<D =<B=90° inscribed angle from the diameter is 90°

base AC=2×OA=2×15=30unit

perpendicular =CD=12unit

area of triangle ACD

=1/2 base×perpendicular=1/2×30×12=180unit²

In triangle ABC

base=AC=30 unit

perpendicular=BC=18unit

area of traingle ABC =

1/2 base×perpendicular=1/2×30×18=270unit²

Area of quadrilateral =area of traingle [ABC+ACD]

=180+270=450 square unit ans..

Answer:

The integers are 7 and 3

Step-by-step explanation:

if you put x as smaller number and y as bigger number you can write two equations:

x+y^2=52 and y-4=x

In the first polynomial, y can either equal 7 or -8, but the number has to be positive, so it's 7

y-4 to get x, plug 7 in and you get x=3

y=7 and x=3

Answer:

7 and 3

Step-by-step explanation:

We will let x equal the larger one

y will be the smaller one

We can write the two equations

x-y=4

y+x²=52

We will solve this through substitution

we will take the first equation and add y to moth sides

x=4+y

we then substitute this into our second equation

y+(4+y)²=52

distribute the square

y+8y+y²+16=52

y²+9y-36=0

Factor this

(y-3)(y+12)=0

Which means that y is either 3 or -12 but because it said that both numbers are positive we can reject the negative 12 (which means that y is 3)

Plug in y=3 into our first equation

x-3=4

x=7

Answer:

Step-by-step explanation:

You want the  value of theta, I take it.  Add 2 to both sides

2cos(theta) = 2                            Divide by 2

2cos(theta)/2 = 2/2

cos(theta) = 1

So theta = 0 degrees.

So 0,360 .... n*360 is the general solution.

Answer:

18$

Step-by-step explanation:

2 tuna sandwiches= 14$

1 tuna sandwich= 14÷2 = 7$

1 tuna sandwich + 1 chicken sandwich = 16$

7$ +1 cs= 16$

1 chicken sandwich = 16$- 7$

1 chicken sandwich = 9$

2 chicken sandwiches = 9x2 = 18$

Option C is correct. The law of cosines must be used to solve a triangle in the case of SAS rule (Side Angle Side Rule)

For a triangle, ABC with sides a, b, and c respectively, the law of cosines is used on such a triangle if there is a presence of an angle between any two sides.

[tex]c^2 = a^2 + b^2 + 2ab cos C[/tex]

Hence the law of cosines must be used to solve a triangle in the case of SAS rule (Side Angle Side Rule)

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Answer:

C IS THE ANSWER

Answer:

7 1/3

Step-by-step explanation:

Add the whole numbers in the equation:

3+4=7

This will get you 7 1/3