A diagram shows the dimensions for a local botanical garden. Measure the parallelogram to the nearest 1/4 inch. What is the area of the botanical garden diagram in square inches?

Answer:

a) The null hypothesis is [tex]H_{0}: \mu = 8.5[/tex] and the alternate hypothesis is [tex]H_{a}: \mu \neq 8.5[/tex]

b) A test statistic of -2.06 should be used.

Step-by-step explanation:

Question a:

One water-treatment plant has a target pH of 8.5.

At the null hypothesis, we test if the mean is close to the target. So, the null hypothesis is:

[tex]H_{0}: \mu = 8.5[/tex]

At the alternate hypothesis, we test if it differs from 8.5, so the alternate hypothesis is:

[tex]H_{a}: \mu \neq 8.5[/tex]

Question b:

The test statistic is:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

8.5 is tested at the null hypothesis:

This means that [tex]\mu = 8.5[/tex]

The mean and standard deviation of 1 hour's test results, based on 17 water samples at this plant, are 8.42 and 0.16, respectively.

This means that [tex]n = 17, X = 8.42, \sigma = 0.16[/tex]

Value of the test statistic:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{8.42 - 8.5}{\frac{0.16}{\sqrt{17}}}[/tex]

[tex]z = -2.06[/tex]

A test statistic of -2.06 should be used.

Answer:

x=70°

Step-by-step explanation:

x+110=180 linear pair

x=180-110=70

Answer:

The 98% confidence interval for the mean magnesium ion concentration is between 122 ppm and 220 ppm. As the lower bound of the interval is below 195, it is not reasonable to conclude that the mean magnesium ion concentration may be greater than 195

Step-by-step explanation:

The six measurements are:

202, 164, 157, 177, 113, 213

Sample mean:

Sum of all values divided by the number of values which is 6. So

[tex]S_m = \frac{202+164+157+177+113+213}{6} = 171[/tex]

Sample standard deviation:

Square root of the difference squared between each value and the mean, and divided by 1 subtracted by the sample size. So

[tex]s = \sqrt{\frac{(202-171)^2+(164-171)^2+(157-171)^2+(177-171)^2+(113-171)^2+(213-171)^2}{5}} = 35.69[/tex]

Confidence interval

We have the standard deviation for the sample, which means that the t-distribution will be used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 6 - 1 = 5

98% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 5 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.98}{2} = 0.99[/tex]. So we have T = 3.365

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 3.365\frac{35.69}{\sqrt{6}} = 49[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 171 - 49 = 122 ppm

The upper end of the interval is the sample mean added to M. So it is 171 + 49 = 220 ppm

The 98% confidence interval for the mean magnesium ion concentration is between 122 ppm and 220 ppm. As the lower bound of the interval is below 195, it is not reasonable to conclude that the mean magnesium ion concentration may be greater than 195

Step-by-step explanation:

[tex]C=2\pi r[/tex]

[tex]C=2*\pi *28[/tex]

[tex]C=56\pi[/tex]

Yes, it is because the circumference is always [tex]2\pi[/tex] times the amount of the radius.

Answer:

30 pages in this book

Step-by-step explanation:

20% is equal 6 pages

so 80% is equal (80/20)*6+6=30

Answer:

420 + 69 = 489

Step-by-step explanation:

HOPE THIS HELPS

brainliest pls :)

Answer:

489

Step-by-step explanation:

420 + 69 = 489

Answer:

8:15

or 8/15

Step-by-step explanation:

8 out of 15

Answer:

8:15

Step-by-step explanation:

There are 8 red apples and total of 15 apples

Answer:

180 - 35 - 74 = 71 degrees is the angle value that is right next to 35 degree angle.

35 + 71 = 106

180 - 106 = 74.

So w = 74 degrees.

Answer:

[tex]\dfrac{5}{7}[/tex]

Step-by-step explanation:

Given numbers are :

0.30 cm and 0.42 cm

We need to find the ratio of the above whole numbers.

Taking 0.3 cm on the numerator and 0.42 cm on the denominator. So,

[tex]\dfrac{0.3}{0.42}=\dfrac{\dfrac{3}{10}}{\dfrac{42}{100}}\\\\=\dfrac{3}{10}\times \dfrac{100}{42}\\\\=\dfrac{10\times 3}{42}\\\\=\dfrac{10}{14}\\\\=\dfrac{5}{7}[/tex]

So, the required fraction is equal to [tex]\dfrac{5}{7}[/tex].

Answer:

Step-by-step explanation:

C sampling

Answer:

Step-by-step explanation:

Answer:

531441

Step-by-step explanation:

using multiplicative law of indices

2 by 3 Is 6

so, -9⁶=531441

9514 1404 393

Answer:

  a.  24 = 8·3

  b.  336 = 8·x

Step-by-step explanation:

A division equation can be rewritten as a multiplication equation by multiplying both sides by the denominator (divisor).

  a/b = c   ⇔   a = bc

__

a.  24/3 = 8   ⇒   24 = 3·8

b.  336/8 = x   ⇒   336 = 8x

The population of The Colony after 2 hours is d. 64​

The given parameters are:

Initial, a = 1

Rate, b = 2 every 20 minutes

An exponential function is represented as:

y = ab^x

So, we have:

y = 1 * 2^x

y = 2^x

There are six 20 minutes in 2 hours.

This means that:

x = 6

So, we have:

y = 2^6

Evaluate

y = 64

Hence, the population of The Colony after 2 hours is d. 64​

Read more about exponential functions at

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Answer:

An expression is a number, a variable, or a combination of numbers and variables and operation symbols.

An equation is made up of two expressions connected by an equal sign.

Step-by-step explanation:

Answer:

the answer to the question is c

The equivalent expression to the equation is A = √ ( x² - 9 )

Equations are statements in mathematics that have two algebraic expressions on either side of the equals (=) sign.

It displays the similarity of the connections between the phrases on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are examples of the parts of an equation. When creating an equation, the "=" symbol and terms on both sides are necessary.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

A = √ ( x + 3 ) .√( x - 3 )

Now , on simplifying the roots of the equation , we get

A = √ ( x + 3 ) ( x - 3 )

The value of ( a + b ) ( a - b ) = a² - b²

So , on further simplification , we get

A = √ ( x² - 9 )

Therefore , the equivalent expression of A is √ ( x² - 9 )

Hence , the equation is A = √ ( x² - 9 )

To learn more about equations click :

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Answer:

A

Step-by-step explanation:

950 is 95% of 1000

so he lost 5 percent, which can be represented as -5.0%

Answer:

Step-by-step explanation:

because the value went down.. we know the the rate of return , is negative.  then we just have to think about , how much is 50 of 1000 ??  well 10 is 10% of 100 right?  so 100 is 10% or 1000,  right?  sooo  half of 100, or 50, is 5% of 1000,  

so -5% is the return on investment (roi)

Answer: (a)

Step-by-step explanation:

Given

The pattern is 2, 4, 16, 256...

From the pattern, we can see that the next term is square of the previous i.e.

[tex]\Rightarrow 4=2^2\\\Rightarrow 16=4^2\\\Rightarrow 256=16^2[/tex][tex]\Rightarrow 4=2^2\\\Rightarrow 16=4^2\\\Rightarrow 256=16^2[/tex]

So, for the [tex]n^{th}[/tex] term, the function is [tex]f(n)[/tex]

For the next term, it is [tex]f(n+1)[/tex]

So,

[tex]\Rightarrow f(n+1)=[f(n)]^2[/tex]

Answer:

A is correct

Step-by-step explanation:

[tex]\frac{0.20}{1min}[/tex] = [tex]\frac{12.00\\}{1 hour}[/tex]  

We can scale the ratio to give the most accurate answer.

0.20 X 60 = 12.00

*pls give brainlist*

Answer:

96

Step-by-step explanation:

4×8×3=96 is the surface area

Answer:

a = 25/2

Step-by-step explanation:

5 = (2/5)*a // - (2/5)*a

5-((2/5)*a) = 0

(-2/5)*a+5 = 0

5-2/5*a = 0 // - 5

-2/5*a = -5 // : -2/5

a = -5/(-2/5)

a = 25/2

a = 25/2

Answer:

a=41.2

Step-by-step explanation:

a^2 + (30)^2. =51^2

a^2+900=2601

-900. -900

a^2= +\- square root 1701

a=41.243181

a=41.2

Answer: x=13

Step-by-step explanation: Hope this help :D

Answer:

One Solution

__________

x = 13

__________

Explanation:

| x – 13 | – 5 = -5

[Add 5 to both sides to isolate | x – 13 | and cancel out –5]

| x – 13 | – 5 + 5 = -5 + 5

[Reduce]

| x – 13 | = 0

[An absolute value can include both a positive and negative value so |x| = n → x = ±n ]

x – 13 = ± 0

[Add 13 to both sides to get the value of x]

x – 13 + 13 = 13 ± 0

x = 13 ± 0

[Adding or subtracting zero will leave you with the same number]

x = 13

Answer:

C

Step-by-step explanation:

7.67 is greater than 7.66666...

9514 1404 393

Answer:

  27

Step-by-step explanation:

The measure of an inscribed angle is half the measure of the arc it subtends.

  ∠P = (RT)/2

  ∠P = 54/2

  ∠P = 27

Answer:

3

Step-by-step explanation:

I believe the answer is 3 because:

- 6 + 9 = 3

minus and plus are equal to minus therefore we minused it and there is no minus sign with 3 because we always use the sign which is with the greater number.

— hope this helped :)!

Answer:

60m2

Step-by-step explanation:

(12x4)+(4x3)=60

Please give brainliest if this helps :)

Answer:

y = ½x + 8

Step-by-step explanation:

The equation of the function can be written in the slope-intercept form y = mx + b.

m = slope = change in y/change in x

b = y-intercept = the value of y when x is zero

✔️From the table, when x = 0, y is 8.

Therefore,

y-intecept (b) = 8

✔️Find the slope (m) using two of the given pairs of values from the table, (-4, 6) and (2, 9):

m = (9 - 6)/(2 -(-4))

m = 3/6

m = ½

✔️Next is to plug in the values of m and b into y = mx + b.

Thus:

y = ½x + 8

Answer:

I think it would be 6800 square in because you just have to multiply 16 by 425.... Sorry if it is wrong

Step-by-step explanation:

Answer:

me no sabo

Step-by-step explanation:

Answer:

pill

Step-by-step explanation: