Find the perimeter and area of the
polygon with the given vertices.
W(5, — 1), X(5, 6), Y(2, — 1), Z(2, 6)
The perimeter is units. The area is
squareunits.

The correct hypothesis for a one-sample z-test for a population proportion p for germination is p <0.9

A hypothesis is an informed estimate about the solution to a scientific issue that is supported by sound reasoning. It is the expected result of the trial, though it is not evidence in an experiment. Depending on the information collected, it might be supported or might not be allowed at all.

The material provided indicates that the following is the appropriate theories for a one-sample z-test for a population proportion where H0 is p = 0.9 and H1 <0.9. Thus, at the null hypothesis, it is tested if the germination rate is actually of 90%, that is H = 0.9 and at the alternative hypothesis, it is tested if the germination rate is of less than 90%, that is H1 <0.9.

Complete Question:

The germination rate is the rate at which plants begin to grow after the seed is planted. A seed company claims that the germination rate for their seeds is 90 percent. Concerned that the germination rate is actually less than 90 percent, a botanist obtained a random sample of seeds, of which only 80 percent germinated. What are the correct hypotheses for a one-sample z-test for a population proportion p ?.

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y > x - 3

y > x - 1

The above system of inequalities was given from the question

Firstly, we will need to graph the system of inequalities

y > x - 3

Change the inequality sign to equality sign

The equation becomes

y = x - 3

To find y, let x = 0

y = 0 - 3

y = -3

To find x, let y = 0

0 = x - 3

Make x the subject of the formula

0 + 3 = x

x = 3

For the system of inequality, y > x - 3

The points is (3, -3)

For the second system of inequality

y > x - 1

Change the inequality ss

Explanation

The ratio 4:11 is equivalent to 20:55 when multiplying both parts by 5.

I did this so that we have 55 as the second term, to have it match with the 55 of 55:8

Combine the ratios 20:55 and 55:8 to end up with the final answer 20:55:8

It says that we could have 20 orange, 55 blue, 8 yellow. Or we could have 40 orange, 110 blue, 16 yellow, and so on.

Answer:

(a) To prove that if n is an odd integer, then n^2 is an odd integer, we assume that n is an odd integer and prove that n^2 is also an odd integer.

Since n is an odd integer, we can express it as n = 2k + 1, where k is an integer.

Now, let's square both sides of the equation:

n^2 = (2k + 1)^2

Expanding the equation:

n^2 = 4k^2 + 4k + 1

We can rewrite the equation as:

n^2 = 2(2k^2 + 2k) + 1

Let's define a new integer m = 2k^2 + 2k. Since m is an integer, we can rewrite the equation as:

n^2 = 2m + 1

The equation shows that n^2 can be expressed in the form 2m + 1, where m is an integer. Therefore, n^2 is an odd integer.

(b) To prove that for any positive real numbers x and y, xy^2 is positive, we assume that x and y are positive real numbers and prove that xy^2 is also positive.

Since x and y are positive real numbers, they are greater than zero: x > 0 and y > 0.

Multiplying x and y^2, we have:

xy^2 > 0 * y^2

xy^2 > 0

Therefore, xy^2 is positive.

(c) To prove that if x is a real number and x ≤ 3, then 12 - 7x + x^2 ≥ 0, we assume that x is a real number and x ≤ 3, and prove that 12 - 7x + x^2 is greater than or equal to zero.

We start with the quadratic expression 12 - 7x + x^2 and simplify it:

12 - 7x + x^2 = x^2 - 7x + 12

To determine the sign of the expression, we factor it:

x^2 - 7x + 12 = (x - 3)(x - 4)

Since x ≤ 3, both factors (x - 3) and (x - 4) are less than or equal to zero.

Multiplying two negative or non-positive numbers yields a non-negative or positive result:

(x - 3)(x - 4) ≥ 0

Therefore, 12 - 7x + x^2 ≥ 0 when x is a real number and x ≤ 3.

(d) To prove that the product of two odd integers is an odd integer, we assume that m and n are odd integers and prove that their product mn is also an odd integer.

Since m and n are odd integers, we can express them as m = 2k + 1 and n = 2j + 1, where k and j are integers.

Now, let's multiply m and n:

mn = (2k + 1)(2j + 1)

Expanding the equation:

mn = 4kj + 2k + 2j + 1

We can rewrite the equation as:

mn = 2(2kj + k + j) + 1

Let's define a new integer p = 2kj + k + j. Since p is an integer, we can rewrite the equation as:

mn = 2p + 1

The equation shows that mn can be expressed in the form 2p + 1, where p is an integer. Therefore, mn is an odd integer.

(e) To prove that if r and s are rational numbers, then the product of r and s is a rational number, we assume that r and s are rational numbers and prove that their product rs is also a rational number.

Since r and s are rational numbers, we can express them as r = a/b and s = c/d, where a, b, c, and d are integers and b ≠ 0, d ≠ 0.

Now, let's multiply r and s:

rs = (a/b)(c/d)

Multiplying the numerators and denominators:

rs = (ac)/(bd)

Since ac and bd are both integers and bd ≠ 0, rs can be expressed as a fraction with integers in the numerator and denominator. Therefore, rs is a rational number.

a) The n² is an odd integer. b) We have proved that for any positive real numbers x and y, their product xy is also positive.

(a) If n is an odd integer, then n² is an odd integer.

To prove this statement, we will assume that n is an odd integer and show that n² is also an odd integer.

Assumption: n is an odd integer, so n = 2k + 1, where k is an integer.

Proof:

n² = (2k + 1)² [Substituting the value of n from the assumption]

= 4k² + 4k + 1 [Expanding the square]

Now, let's express 4k² + 4k as 2m, where m is an integer:

4k² + 4k = 2(2k² + 2k) = 2m

Substituting this back into the expression for n²:

n² = 2m + 1

We have expressed n² in the form 2m + 1, where m = 2k² + 2k. Since m is an integer, n² can be expressed as 2 times an integer plus 1. Therefore, n² is an odd integer.

Hence, we have proved that if n is an odd integer, then n² is an odd integer.

(b) For any positive real numbers x and y, xy > 0.

To prove this statement, we will assume x and y are positive real numbers and show that their product is also positive.

Assumption: x and y are positive real numbers.

Proof:

Since x and y are positive real numbers, we know that both x and y are greater than zero: x > 0 and y > 0.

Multiplying two positive numbers results in a positive number. Therefore, we have:

x * y > 0

Hence, we have proved that for any positive real numbers x and y, their product xy is also positive.

(c) If x is a real number and x ≤ 3, then 12 - 7x + x^2 ≥ 0.

To prove this statement, we will assume that x is a real number and x ≤ 3, and show that the expression 12 - 7x + x^2 is greater than or equal to zero.

Assumption: x is a real number and x ≤ 3.

Proof:

We can rewrite the expression 12 - 7x + x^2 as (x - 3)(x - 4).

We know that x ≤ 3, so (x - 3) ≤ 0. Similarly, (x - 4) ≤ 0.

Multiplying two non-positive numbers or two non-negative numbers results in a non-negative number. Therefore, we have:

(x - 3)(x - 4) ≥ 0

Hence, we have proved that if x is a real number and x ≤ 3, then 12 - 7x + x^2 ≥ 0.

(d) The product of two odd integers is an odd integer.

To prove this statement, we will assume that m and n are odd integers and show that their product is also an odd integer.

Assumption: m and n are odd integers.

Proof:

Since m and n are odd integers, we can express them as m = 2k + 1 and n = 2l + 1, where k and l are integers.

The product of m and n is:

m * n = (2k + 1)(2l + 1)

= 4kl + 2k + 2l + 1

= 2(2kl + k + l) + 1

Let p = 2kl + k + l. Since k, l, and p are integers, we can rewrite the expression as:

m * n = 2p + 1

We have expressed the product m * n as 2p + 1, where p is an integer. Therefore, the product of two odd integers is an odd integer.

Hence, we have proved that the product of two odd integers is an odd integer.

(e) If r and s are rational numbers, then the product of r and s is a rational number.

To prove this statement, we will assume that r and s are rational numbers and show that their product is also a rational number.

Assumption: r and s are rational numbers.

Proof:

Since r and s are rational numbers, we can express them as fractions: r = a/b and s = c/d, where a, b, c, and d are integers and b, d ≠ 0.

The product of r and s is:

r * s = (a/b)(c/d)

= ac / bd

The product ac and bd is the product of two integers, which is also an integer. Furthermore, since b and d are nonzero integers, their product bd is also nonzero.

Therefore, ac / bd is a fraction where the numerator and denominator are both integers. Hence, the product of r and s is a rational number.

Hence, we have proved that if r and s are rational numbers, then the product of r and s is a rational number.

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Answer:

Option a.

Step-by-step explanation:

Two figures are similar if they have the same shape, but maybe different sizes, so if we have a triangle, and we dilate/contract it with a scale factor K, the original triangle and the dilated/contracted one will be similar.

Two figures are congruent if they have the same shape and size. For example, transformations that do not change the size will make congruent figures, those transformations are reflections, rotations and translations.

Now we need to find a sequence of transformations that would result in the two triangles being similar but no congruent, then we need to find the sequence of transformations that has a dilation/contraction in it.

The only sequence that has a dilation is the first one:

a) Rotation 90° centered about the origin, followed by a dilation of scale factor 3 centered about the origin.

Then option a is the correct one.

Answer:

x ≤ -17

Step-by-step explanation:

Answer:

you cant factor it.

Step-by-step explanation:

Answer:

c. 502.65 in³

Step-by-step explanation:

For a cylinder:

V = πr²h

r = d/2 = 8 in. / 2 = 4 in.

V = 3.14159 × (4 in.)² × 10 in.

V = 502.65 in.³

Answer:

a) $55.000

b) $42.000

c) 88.000

Step-by-step explanation:

Step-by-step explanation:

5a.

8 hours a day, 5 days a week. $11.25 per hour.

his base salary will be

8×5×11.25 = $450.00

and he earns commission on sold products.

$750 sales per day (again 5 days a week).

6.5% = ?

100% = $750

1% = 100%/100 = 750/100 = $7.50

6.5% = 1% × 6.5 = 7.5×6.5 = $48.75

he will therefore earn 450+48.75 = $498.75 per week.

5b.

4 weeks per month.

therefore his monthly income will be 4 times the weekly income :

4×498.75 = $1995.00

Answer:

C

Step-by-step explanation:

:)

Answer:

y= 1.8955223

Step-by-step explanation:

Answer:

  add the values of the symbols or symbol pairs

Step-by-step explanation:

You want to know how to convert Roman Numerals to decimal numbers.

The symbols used in Roman Numerals are {I, V, X, L, C, D, M}. Respectively, they have values {1, 5, 10, 50, 100, 500, 1000}. The values of these symbols are multiplied by 1000 by an overline.

A number can be converted to decimal by working right to left. In general, the value of a symbol is added to the total. When a symbol of lesser value than the previous one is encountered, its value is subtracted. (Usually, the value being subtracted is a power of 10.)

Aliases exist. Without knowledge of the rules the Romans used for writing their numbers, we can invent numbers that can be written two or more ways:

  1950 = MLM = MCML

As we noted above, the form MLM = 1950 would probably not be used, since the subtracted L is not a power of 10.

We expect that 1999 would likely be written MCMXCIX, rather than MIM. That way, the character being subtracted is not less than 10% of the character it is subtracted from.

__

Additional comment

Use of an overline is not the only way that the system is extended to higher values. Different notations are found in different contexts.

The basic idea of Roman Numerals is to express value by the character used, rather than its location in a number. It is not a "place value" system.

There is no zero. There are no negative numbers.

The reference to "symbol pairs" in the Answer section above is to recognize a pair of symbols in which the one on the left is subtracted.

Probability of average height of women is 0.1379

First check to see if the Central Limit Theorem applies. Since n > 30, it does. Next we need to calculate the standard error. To do that we divide the population standard deviation by the square-root of n, which gives us a standard error of 0.646. Next, we calculate a z-score using our z-score formula:

Z=(X−μ)/S.E.

S.E = σn/√n

S.E =3/√ 9

S.E=1

Plugging in gives us:

(64−63)/1 = 1

Finally, we look up our z-score in our z-score table to get a p-value.

The table gives us a p-value of,

P(z<1.0)=1−P(z>1.0)

P(z<1.0)=1−0.8621

P(z<1.0)=0.1379

So, Probability of average height of women is 0.1379

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Answer:

1. Quadrant II

2. Quadrant IV

3. Y-axis

Step-by-step explanation:

The weight of the merchandise that will be billed to the customer is 21 pounds.  Option A is correct answer.

Here's why: To determine the weight to be billed, subtract the weight of the box from the total weight of the package.

23 pounds - 2 pounds = 21 pounds.

This is because the customer is only responsible for paying for the weight of the merchandise, not the weight of the box. Therefore, the weight of the box must be subtracted from the total weight of the package to determine the weight that the customer will be billed for.

Option a is correct answer.

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Answer:

29.3 units^2

Step-by-step explanation:

sorry for no explanation

Answer:

Area of shaded region = 254.5 square units

Step-by-step explanation:

We have 3 semicircles:

d = 18 units

Semicircle 1 = The big semicircle

Semicircle 2 and 3 = The two small semicircles

Semicircle 2 = 18 units

Semicircle 3 = 18 units

Semicircle 1 = Semicircle 2 + Semicircle 3 = 36 units

Radius = Half of the diameter

Semicircle 1 radius = 18 units

Semicircle 2 radius = 9 units

Semicircle 3 radius = 9 units

\(\mathrm{Area\:of\:a\:semicircle = \dfrac{ \pi r^2 }{ 2 }}\)

\(\mathrm{Area\:of\:shaded\:region = Area\:of\:Semicircle\:1 - (Area\:of\:Semicircle\:2 + Area\:of\:Semicircle\:3)}\)

\(\mathrm{Area\:of\:shaded\:region = \dfrac{ \pi r^2 }{ 2 } - ( \dfrac{ \pi r^2 }{ 2 } + \dfrac{ \pi r^2 }{ 2 } )}\)

\(\mathrm{Substitute\:the\:numbers\:into\:the\:equation}\)

\(\mathrm{Area\:of\:shaded\:region = \dfrac{ \pi (18)^2 }{ 2 } - ( \dfrac{ \pi (9)^2 }{ 2 } + \dfrac{ \pi (9)^2 }{ 2 } )}\)

\(\mathrm{Do\:all\:of\:the\:exponents\:first}\)

\(\mathrm{Area\:of\:shaded\:region = \dfrac{ \pi\times324 }{ 2 } - ( \dfrac{ \pi\times81}{ 2 } + \dfrac{ \pi\times81}{ 2 } )}\)

\(\mathrm{Combine\:\dfrac{ \pi\times81}{ 2 }\:and\:\dfrac{ \pi\times81}{ 2 }\:to\:get\:\pi\times81}\)

\(\mathrm{Area\:of\:shaded\:region = \dfrac{ \pi\times324 }{ 2 } - ( \pi\times81 )}\)

\(\mathrm{Divide\: \pi \times324\:by\:2}\)

\(\mathrm{Area\:of\:shaded\:region = { \pi\times162} - \pi\times81}\)

\(\mathrm{Combine\:\pi \times162\:and\:- \pi \times81}\)

\(\mathrm{Area\:of\:shaded\:region = 81\pi}\)

\(\mathrm{Area\:of\:shaded\:region = 254.469004941}\)

Area of shaded region rounded to the nearest tenth is: 254.5 square units

look at the picture for more information

Answer:

8p - 1

Step-by-step explanation:

one less than = - 1

than 8 times p = 8p

put it together= 8p - 1

Answer:

h(0) = 10

h(4) = 16

Step-by-step explanation:

h(0) = 2(0)² - 3(0) + 10 = 10

h(4) = 2^4 = 16

Given:

One hundred adults were surveyed.

The results were that 47 liked comedies, 22 liked actions, 15 liked action, 10 liked horror, and 6 liked a different type of movie.

To find:

The categories which adults like most to defend or challenge the given statement.

Explanation:

According to the results,

Out of 100 adults, 47 liked comedies, and 22 liked actions.

So, they like comedies and action movies most.

Hence, we can agree with the statement that states that adults like comedies and action movies most.

Therefore, we should defend the given statement.

Final answer:

Defend.

Based on the given data, the association between variables A and B appears to be a nonlinear association.

What is the association between variables?

Association between variables refers to the relationship between two or more variables in a dataset. It describes how changes in one variable are related to changes in another variable.

Based on the given data, the association between variables A and B appears to be a nonlinear association. There is no clear linear trend between the two variables, and the values of variable B do not consistently increase or decrease as variable A increases. Instead, the relationship between the variables appears to be more complex, with variable B increasing and then decreasing as variable A increases. A scatterplot of the data would help visualize this relationship.

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9A:

The problem says 35% of the 3560 applications are from boys who lived in other states.

This can be expressed as:

3560*35% = 3560*0.35 = 1246 applications.

9B:

The problem says applications to the university (3560 applications) represented 40% of all applications.

This can be expressed as:

3560 = 40% * A, where A = number of applications received in all.

To find how many applications received in all, just solve for A.

A = 3560 / 0.4 = 8900 applications.

The key to these types of problems is that "of" signals multiplication. For example, 40% of all applications is 40% * all applications.

Answer:

1.5x=3

x=3/1.5

x=2

.....

Answer:

Hello! answer: x = 2

Step-by-step explanation:

1.5 × 2 = 3

therefore x = 2 Hope that helps!

Answer:

all 3 options are true : A, B, C

Step-by-step explanation:

warning : it has come to my attention that some testing systems have an incorrect answer stored as right answer for this problem.

they say that A and C are correct.

but I am going to show you that if A and C are correct, then also B must be correct.

therefore, my given answer above is the actual correct answer (no matter what the test systems say).

originally the information about the alignment of the point F in relation to point E was missing.

therefore, I considered both options :

1. F is on the same vertical line as E.

2. F is not on the same vertical line as E.

because of optical reasons (and the - incomplete - expected correct answers of A and C confirm that) I used the 1. assumption for the provided answer :

the vertical line of EF is like a mirror between the left and the right half of the picture.

A is mirrored across the vertical line resulting in B. and vice versa.

the same for C and D.

this leads to the effect that all 3 given congruence relationships are true.

if we consider assumption 2, none of the 3 answer options could be true.

but if the assumptions are true, then all 3 options have to be true.

now, for the "why" :

remember what congruence means :

both shapes, after turning and rotating, can be laid on top of each other, and nothing "sticks out", they are covering each other perfectly.

for that to be possible, both shapes must have the same basic structure (like number of sides and vertices), both shapes must have the same side lengths and also equally sized angles.

so, when EF is a mirror, then each side is an exact copy of the other, just left/right being turned.

therefore, yes absolutely, CAD is congruent with CBD. and ACB is congruent to ADB.

but do you notice something ?

both mentioned triangles on the left side contain the side AC, and both triangles in the right side contain the side BD.

now, if the triangles are congruent, that means that each of the 3 sides must have an equally long corresponding side in the other triangle.

therefore, AC must be equal to BD.

and that means that AC is congruent to BD.

because lines have no other congruent criteria - only the lengths must be identical.

Answer:

Hey there!

The ratio of ducklings to adult ducks is 5:1.

This means for every six ducks, five are ducklings and one is an adult.

If there are 24 ducks, then 5 times 4 = 20 ducklings and 4 adults.

Thus, there are 20 ducklings.

Hope this helps :)

Answer:

20 ducklings.

Step-by-step explanation:

Answer:

The answer is option D.

Step-by-step explanation:

Area of a circle is πr²

where r is the radius

from the question the area is n cm² which is a variable and not a number therefore cannot be used to determine the radius of the circle.

Hope this helps you

Answer:

thank you

Step-by-step explanation:

Answer:  1.5

Step-by-step explanation: 4.05x3=12.15

                                             2.75x4.5=12.375  

4.5-3=1.5

Answer:

Explanation = The Least Squares Regression Line is the line that makes the vertical distance from the data points to the regression line as small as possible. It's called a “least squares” because the best line of fit is one that minimizes the variance (the sum of squares of the errors).

Step-by-step explanation:

I DON'T HOW ABOUT THE ANSWERS.

BUT I CAN HELP THIS MUCH..

I HOPE THIS HELPS....

THANK U!

Answer:

Daniel has to wait around 5.24 years to withdraw the money.

Step-by-step explanation:

We are given that Daniel wants to open an account to purchase a new computer. He was able to put $750 into an account that pays him 8.5% interest. The cost of the computer he wants is $1,150.00.

Let the Principal sum of money be represented by 'P'.

The rate of interest be represented by 'R'.

The time period be represented by 'T'.

The final amount of money be represented by 'A'.

Assuming the interest given is compound interest.

So, the formula for calculating the amount of money is given by;

                          \(\text{A} = \text{P} \times (1-\text{R})^{\text{T}}\)

Here, A = $1,150, P = $750, R = 8.5% and let the time he have to wait to withdraw the money be 'n'.

So, putting these values in the above formula we get;

\(\text{A} = \text{P} \times (1+\text{R})^{\text{T}}\)

\(\text{\$1,150} = \text{750} \times (1+\text{0.085})^{\text{n}}\)

\((1+\text{0.085})^{\text{n}} = \frac{\$1,150}{\$750}\)

\((1+\text{0.085})^{\text{n}} = 1.533\)

Taking log on both sides;

\(\text{n} \times ln(1+\text{0.085}) = ln(1.533)\)

\(n = \frac{ ln(1.533)}{ ln(1.085)}\)

n = 5.24 years

Hence, he has to wait around 5.24 years to withdraw the money.

Answer: 8 minutes, 16 minutes, 24 minutes, 32 minutes

Step-by-step explanation: 12x2=24. 8x2=16. 12x3=36. 8x3=24. 12x4=48. 8x4=32.

The total time taken to cover 48 blocks at the same speed will be 32 minutes.

Work is the completion of any task for example if you have done your homework in 5 hours then you have done 5 hours.

Another example of work is that if you have done your food by 1 hour it means your work duration is 1 hour so work is basically the time duration of any task which you have done.

Speed of dog;

Speed = 12 block in 8 minutes ⇒ 12/8 blocks/minutes

Now,

At the same speed

Speed = 48 blocks in T time

So,

12/8 = 48/T

By cross multiplication

T = 48 × 8/12

T =  32

Hence "The total time taken to cover 48 blocks at the same speed will be 32 minutes".

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