Fraction - Multiplication : (a) 2/9 x 1/13 (b) 12/5 x 35/21

Answer:

A.

Step-by-step explanation:

Volume of sphere = (4/3)πr³

= 4/3(3.14)(d/2)³

= 4/3(3.14)(7/2)³

= 4/3(3.14)(3.5)³

= 4/3(3.14)(42.875)

= (1.33)(3.14)(42.875)

= 179.5 cm³

Answer:

The answer is 179.5 cm^2

Answer:

C) The auditor may or may not achieve the desired risk of assessing control risk too low.

Step-by-step explanation:

In a concept of risk sampling, if the sample size is chosen randomly in accordance with random selection procedures, the auditor may or may not achieve the desired risk of assessing risk too low. In other words the auditor may or may not achieve desired precision. This is because a samole chosen randomly may not represent the true population.

This depends largely on the sample size. If the sample size selected is too small, the allowance for sampling risk will be larger than what is required because it will lead to a large standard error of the mean

Answer:

Random variable: for this case represent the number of complaints in 2007

Population parameter: represent the real proportion of complaints in 2007 p

Hypothesis to verify

We want to check if the true proportion of complaints in 2007 is equal to 0.23, the system of hypothesis are.:  

Null hypothesis:[tex]p=0.23[/tex]  

Alternative hypothesis:[tex]p \neq 0.23[/tex]  

Step-by-step explanation:

Information provided

n=1432 represent the random sample taken

X=321 represent the number of complaints

[tex]\hat p=\frac{321}{1432}=0.224[/tex] estimated proportion of complaints in 2007

[tex]p_o=0.23[/tex] is the value to verify

z would represent the statistic

Random variable: for this case represent the number of complaints in 2007

Population parameter: represent the real proportion of complaints in 2007 p

Hypothesis to verify

We want to check if the true proportion of complaints in 2007 is equal to 0.23, the system of hypothesis are.:  

Null hypothesis:[tex]p=0.23[/tex]  

Alternative hypothesis:[tex]p \neq 0.23[/tex]  

Answer:

Step-by-step explanation:

a. Null hypothesis: P = p

Alternatives hypothesis: P =/ p

Where P is the hypothesized population proportion and p is the sample proportion

b. Performing a test of proportions

Randomization: the sample was randomly selected in the study

The population size is at least 20 times as big as the sample size.

The sample includes both successes and failures with 29 success and 171 failures.

c. To perform the hypothesis test: we have to find the standard deviation first

Sd = sqrt[ P * ( 1 - P ) / n ]

where P is the hypothesized value of population proportion, n is the sample size.

Sd = √[0.12*(1-0.12)/200]

Sd = √[0.12*(0.88/200]

Sd = √[0.12*(0.0044)]

Sd = √0.000528

Sd = 0.023

Then we can find the z score

z = (p - P) / σ where p = 29/200 = 0.145

z = (0.145-0.12)/ 0.023

z = 0.025/0.023

z = 1.09

Calculation the p value using 0.05 level of significance and a two waited test (p value calculator),

A p-value of 0.2757 which is greater than 0.05, thus we will fail to reject the null stating that there is not enough strong evidence that the left-handed rate in the state of Maine is higher than the national average.

Answer:

r = - [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

The common ratio r is the ratio between consecutive terms in the sequence.

r = [tex]\frac{48}{-96}[/tex] = [tex]\frac{-24}{48}[/tex] = [tex]\frac{12}{-24}[/tex] = [tex]\frac{-6}{12}[/tex] = - [tex]\frac{1}{2}[/tex]

Answer:

-1/2 or b on edge

Step-by-step explanation:

Answer:

isosceles triangle

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

No one is there which satisfies the condition

Answer:

0 or 0/9 of the club members

Step-by-step explanation:

The only part of the data of members that have logged more than 1 1/5 but less than 1 3/5 hours is the members that logged 1 2/5 hours. There are no members that have logged 1 2/5 hours so our answer is 0 or 0/9.

Answer:

x=55,y=14

Step-by-step explanation:

<M = <{opposite angles of a parallelogram are congruent and equal}

Hence 3x-55 = 2x=>3x-2x= 55 =>x=55

Simarly;

M+N=180°{ sum of angles in a parallelogram is 180°}

N= 180°-M=>N=180-(3x-55)=180-(3x55-55)= 180- 110=70°

N=70°=>5y=70=>y=70/5=14

therefore x=55,y=14

Answer:

55 and 14

Step-by-step explanation:

i just took the test

Answer:

acute and scalene

Step-by-step explanation:

Answer:no entiendo esta en ingles

Step-by-step explanation:

Answer:

51 = 5x+1

x = 10

Step-by-step explanation:

The angles are vertical angles which means they are equal

51 = 5x+1

Subtract 1 from each side

51-1 = 5x+1-1

50 = 5x

Divide each side by 5

50/5 = 5x/5

10 =x

Answer:

10

Step-by-step explanation:

51 = 5x + 1

5x = 51 - 1

5x = 50

x = 10

Hope this helps!

Answer:

Observational Study

Step-by-step explanation:

An experimental study is a research study in which conditions are under the direct manipulation of the investigator. We use it to mainly test the efficacy of a medical, preventive, or therapeutic measure.

In an observational study, on the other hand,  the researcher observes the effect without trying to influence the outcome in any way.

In this study, the researchers are trying to determine the paired daytime and nighttime counts of the species of fishes made by the same divers in six lakes during September 2015.

This is simply an Observational Study as nothing is done to influence the population count.

Answer:-2

Step-by-step explanation:

Ok so I’m assuming the x stands for the multiplication sign

7/2-4.5*3+8

Use pemdas

Multiplication first

7/2-4.5*3+8

-4.5*3

7/2-13.5+8

Then addition

-13.5+8

Lastly subtraction

7/2-5

-2

Answer:

[tex]f = \frac{1}{ {d}^{2} } [/tex]

Answer:

g-7

Step-by-step explanation:

Multiply the numbers

g-(1*7)

g-7

Answer:

5

Step-by-step explanation:

We know that g is an invertible function and so it must also be a one-to-one function.

This means that each input is paired with exactly one output and that each output is paired with exactly one input.

We know that g(a)=7g and g(5)=7. If the output of 7 is to be paired with exactly one input, then a must be equal to 5.

Answer:

Answer is B

Step-by-step explanation:

This is because you can combine both the green tiles. With the other options, you can't combine them.

(also I did the test )

Answer:

The answer is in ur head lololol

Step-by-step explanation:

Its b

Answer:

5

Step-by-step explanation:

Answer:

they played the pivotal role

Answer:

S ≈ 9.8

Step-by-step explanation:

Finding central angle of circle A first

S=r∅

6.5 = (4)∅

Central angle = 6.5/4

C A = 1.63(in radians)

Now finding Arc EF

S = r∅

S = (6)(1.63)

S = 9.75

S ≈ 9.8

Answer:

h ≈ 77 cm

Step-by-step explanation:

Let us convert the liters to cm³.

Smaller barrel

0.001 litres = 1 cm³

100 litres = 100000  cm³

Larger barrel

0.001 litres = 1 cm³

160 litres = 160000  cm³

For a similar solid figure the cube of their corresponding sides is equal to the volume ratio.

This means

h³/90³ = 100000/160000

cube root both sides

h/90 =  ∛100000 / ∛160000

h/90 = 46.4158883/54.2883523

cross multiply

54.2883523h = 46.4158883 × 90

54.2883523h = 4177.429947

divide both side by  54.2883523

h = 4177.429947/54.2883523

h = 76.9489175858

h ≈ 77 cm

Answer:

Options (C) and (F)

Step-by-step explanation:

Polynomial function is,

f(x) = x³ - x² - 5x - 3

Possible rational roots of the given function will be = [tex]\frac{\pm1, \pm3}{\pm1}[/tex]

By putting x = -1

f(-1) = (-1)³ - (-1)² -5(-1) - 3

     = -1 - 1 + 5 - 3

     = 0

Therefore, x = -1 will a root of the given function.

Now we apply synthetic division to get the other roots,

-1 |  1       -1       -5      -3

      ↓      -1         2      3

     1       -2       -3      0

Therefore, factored form of the polynomial will be (x + 1)(x² - 2x - 3).

Now we will find the roots of (x² -2x - 3).

x² - 2x - 3 = x² - 3x + x - 3

                = x(x - 3) + 1(x - 3)

                = (x + 1)(x - 3)

For roots of the function, f(x) = 0

(x + 1)(x - 3) = 0

x = -1, 3

Therefore, roots of the function are x = -1, 3

Options (C) and (F) are the answers.

Answer:

a) [tex]\frac{dB}{dt} = \frac{5\pi}{4.2} \cdot \cos \left(2\pi\cdot \frac{t}{4.2} \right)[/tex], b) [tex]\frac{dB}{dt}\approx 5.595[/tex]

Step-by-step explanation:

a) The rate of change of the brightness of the Cepheid can be determined by deriving the function in time:

[tex]\frac{dB}{dt} = \left(\frac{2\pi}{4.2} \right)\cdot 0.25\cdot \cos (2\pi\cdot \frac{t}{4.2})[/tex]

[tex]\frac{dB}{dt} = \frac{5\pi}{4.2} \cdot \cos \left(2\pi\cdot \frac{t}{4.2} \right)[/tex]

b) The rate of increase after one day is:

[tex]\frac{dB}{dt} = \frac{5\pi}{4.2} \cdot \left(2\pi \cdot \frac{1}{4.2} \right)[/tex]

[tex]\frac{dB}{dt}\approx 5.595[/tex]

Answer:

x = 6

Step-by-step explanation:

x + 6 = x + x

Combine like terms

x+6 =2x

Subtract x from each side

x+6-x = 2x-x

6 = x

a) The percentage of women meeting the height requirement is approximately 99.99%.

b) The percentage of men meeting the height requirement is approximately 99.95%.

c) The new height requirements are at least 58.5 inches and at most 71.8 inches.

a) To find the percentage of women meeting the height requirement of being between 4ft 9in (57 inches) and 6ft 4in (76 inches), we need to calculate the proportion of women within this range using the normal distribution.

First, we standardize the height requirement using the formula:

Z = (X - μ) / σ

where X is the value (height), μ is the mean, and σ is the standard deviation.

For the lower limit (57 inches):

Z_lower = (57 - 63.3) / 2.7 ≈ -2.33

For the upper limit (76 inches):

Z_upper = (76 - 63.3) / 2.7 ≈ 4.70

Using a standard normal distribution table or calculator, we can find the area between -2.33 and 4.70. This represents the percentage of women meeting the height requirement.

The percentage of women meeting the height requirement is approximately 99.99%.

b) Similarly, for men meeting the height requirement of being between 4ft 9in (57 inches) and 6ft 4in (76 inches), we standardize the values:

For the lower limit (57 inches):

Z_lower = (57 - 67.3) / 2.8 ≈ -3.68

For the upper limit (76 inches):

Z_upper = (76 - 67.3) / 2.8 ≈ 3.11

Using the standard normal distribution table or calculator, we find the area between -3.68 and 3.11.

The percentage of men meeting the height requirement is approximately 99.95%.

c) To find the new height requirements that exclude the tallest 5% of men and the shortest 5% of women, we need to determine the corresponding Z-scores.

For men:

Z_upper_men = Z(0.95) ≈ 1.645

For women:

Z_lower_women = Z(0.05) ≈ -1.645

Using these Z-scores, we can calculate the new height requirements:

For the new lower limit:

X_lower = Z_lower_women * σ + μ

For the new upper limit:

X_upper = Z_upper_men * σ + μ

Substituting the values:

X_lower = -1.645 * 2.7 + 63.3 ≈ 58.53 inches

X_upper = 1.645 * 2.8 + 67.3 ≈ 71.78 inches

Therefore, the new height requirements are at least 58.5 inches and at most 71.8 inches.

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a) The percentage of women meeting the height requirement is 99.99%.

b) The percentage of men meeting the height requirement is 99.95%.

c) The new height requirements are at least 58.5 inches and at most 71.8 inches.

a) For women meeting the height requirement:

Given: Mean (μ) = 63.3 in.

Standard Deviation (σ) = 2.7 in.

So, Minimum height requirement:

= 4 ft 9 in

= 4 * 12 + 9

= 57 inches

and, Maximum height requirement:

= 6 ft 4 in

= 6 * 12 + 4

= 76 inches

We will calculate the Z-scores for these heights using the formula:

Z = (x - μ) / σ

For the minimum height requirement:

[tex]Z_{min[/tex] = (57 - 63.3) / 2.7 ≈ -2.33

For the maximum height requirement:

[tex]Z_{max[/tex] = (76 - 63.3) / 2.7 ≈ 4.70

So, the the area between -2.33 and 4.70.

Thus, the percentage is  99.99%.

b) For men meeting the height requirement:

Given: Mean (μ) = 67.3 in., Standard Deviation (σ) = 2.8 in.

Minimum height requirement: 4 ft 9 in = 57 inches

Maximum height requirement: 6 ft 4 in = 76 inches

For the minimum height requirement:

[tex]Z_{min[/tex]= (57 - 67.3) / 2.8 ≈ -3.68

For the maximum height requirement:

[tex]Z_{max[/tex] = (76 - 67.3) / 2.8 ≈ 3.11

So, the area between -3.68 and 3.11.

Thus, the percentage is 99.95%.

c) For the new height requirements:

For men:

[tex]Z_{upper_{men[/tex] = Z(0.95) ≈ 1.645

For women:

[tex]Z_{lower_{women[/tex] = Z(0.05) ≈ -1.645

For the new lower limit:

[tex]X_{lower} = Z_{lower}_{women} \sigma+ \mu[/tex]

For the new upper limit:

[tex]X_{upper} = Z_{upper}_{men} \sigma+ \mu[/tex]

Substituting the values:

[tex]X_{lower} = -1.645 * 2.7 + 63.3[/tex]

           = 58.53 inches

and, [tex]X_{upper} = 1.645 * 2.8 + 67.3[/tex]

                     = 71.78 inches

Therefore, the new height at least 58.5 inches and at most 71.8 inches.

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Answer:

y = -2x - 10

Step-by-step explanation:

1. rearrange to find the gradient.

the gradient of the original equation is 1/2 hence why a line PERPENDICULAR to that equation would have a gradient of -2.

2. substitute into y - y1 = m (x - x1)

y - (-2) = -2 (x - (-4))

y = -2x - 10

Answer:

It might be 1/3 but I'm not 100% sure

The required scale factor  of ABC to DEF is 1/3.

Scale factor of ABC to DEF to determine.

The scale factor is defined as the ratio of modified change in length to

Here, Triangle ABC is similar to triangle DEF. So, the ratio of the same sides describe the scale factor.
Scale factor = EF/BC
                   = 7/21
                   = 1/3

Thus, the required scale factor  of ABC to DEF is 1/3.

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Answer:

Step-by-step explanation:

Answer: B

Step-by-step explanation: