When Hailey commutes to work, the amount of time it takes her to arrive is normally distributed with a mean of 21 minutes and a standard deviation of 3.5 minutes. Out of the 211 days that Hailey commutes to work per year, how many times would her commute be between 19 and 26 minutes, to the nearest whole number?

Answer:

It’s in between a and b

Step-by-step explanation:

Answer:

i believe the answer is a

Answer:

d. 5/4

Step-by-step explanation:

The secant of an angle with a terminal ray through the point (4, -3) is the distance to the origin divided by the x-coordinate, or

[tex]\sqrt{4^{2}+(-3)^2}[/tex] / 4 = 5/4

Answer:

d. 5/4

Step-by-step explanation:

(4,-3) is in quadrant 4

cos/sec is positive in this quadrant

Hypotenuse = sqrt(3² + 4²)

sqrt(25)

5

cos(theta) = 4/5

sec(theta) = 5/4

The amount of fabric needed for Jimmy's costume is not stated, we can only determine the amount needed for Rob's costume, which makes it impossible to compare the amounts needed for both of their costumes. If this omission was an error, then you can find the difference between these amounts if the amount needed for Jimmy's costume is stated explicitly.

Step-by-step explanation:

The number of yards of fabric needed for Robs costume is (7/8+1/2+1 3/4)÷2

Assuming 1 3/4 is a mixed fraction.

= (7/8 + 1/2 + 7/4) ÷ 2

= (7 + 4 + 2) ÷ (8 × 2)

= 13/16 yards

Suppose 2 yards of fabric is needed for Jimmy's costume, then comparing with Rob's yards, we see that Jimmy's costume requires (2 - 13/16 = 19/16) more yards than Rob's costume.

b. stratified sampling

The plan to determine the percentage of students in a school willing to pay a fee for participating in extracurricular activities is an example of stratified sampling. In stratified sampling, the population is divided into subgroups or 'strata' that share similar characteristics, and a random sample is taken from each stratum. In this case, the classes (freshman, sophomore, junior, and senior) serve as the strata, and thirty students from each class are randomly selected to complete the survey. This approach ensures that each subgroup is adequately represented in the sample, making the results more reflective of the entire school population.

Answer:

a) 1/48 or 2.0833%

b) 46/48 or 95.8333%

no it would not be unusual

c) I'm not sure sorry

(c) Two straight lines are displayed on a coordinate plane. Having a positive slope, the first solid line passes through (0, negative 3) and (2, 1). Shaded areas surround the line to the right. The second dashed line travels through (0, 2) and has a negative slope (4, 0). Shaded areas surround the line to the left.

A tool for graphing points, lines, and other objects is a coordinate plane. It follows directions from one place to another as a map might.

Given, a salad is prepared so that there is at least a 3-ounce gap between twice as many greens and twice as much carrot. Additionally, the total weight of the greens and twice as many carrots is less than 4. Hence,

2g - c  = 3....(1)

g + 2c < 4.....(2)

Comparing both equations

intersecting Coordinates of g and c will be(2, 1 ).

Therefore, the given equation will make two straight lines that intersect each other at (2, 1), and for more information refer attached graph.

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Answer:

110/7 yards

Step-by-step explanation:

Given:-

- The radius of circular patio, r = 5 yards

Find:-

What is the circumference of circular patio

Solution:-

- The circumference "C" of a circle is given as:

            [tex]C =2 *\pi*r\\\\\pi = \frac{22}{7} \\\\ C = 2*\frac{22}{7}*5\\\\C = \frac{110}{7} yards[/tex]

- The circumference of the circular patio is 110 / 7 yards.            

For 42 cups of punch 168 cups lemonade is used.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

We have, For one punch 4 cups of lemonade to 3 cups of sparking juice is used.

Now, for 42 cups the amount of Lemonade needed

= 4 x 42

= 168 cups

and, Amount of Sparking juice needed

= 3 x 42

= 126 cups

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Final answer:

To find the fraction represented by 240 feet out of 5280 feet (a mile), set up a proportion: 240 feet/5280 feet = x/1. Cross multiplying gives x = 240/5280. Therefore, the fraction represented by 240 feet is 240/5280.

Explanation:

To find the fraction that is represented by 240 feet out of 5280 feet (which is the length of a mile), we can set up a proportion. Let's call the fraction we're looking for x. The proportion is:

240 feet/5280 feet = x/1

Cross multiplying, we have 240 * 1 = 5280 * x. Simplifying, we get x = 240/5280. Therefore, the fraction represented by 240 feet is 240/5280.

The correct answer is:

£498.53

Answer:

[tex]\frac{3}{4}[/tex]

Step-by-step explanation:

Total number of red disk=6

Total number  of yellow disk=2

Total disk=6+2=8

Odd number=1,3,5,7=4

Odd number on red disk=1,3,5=3

Probability,[tex]P(E)=\frac{favorable\;cases}{total\;number\;of\;cases}[/tex]

Using the formula

The probability of getting odd number disk=[tex]\frac{4}{8}=\frac{1}{2}[/tex]

The probability of getting odd numbered  red disk=[tex]\frac{3}{8}[/tex]

The probability of selecting a red disk,given that an odd numbered disk is selected=[tex]\frac{\frac{3}{8}}{\frac{1}{2}}=\frac{3}{8}\times 2=\frac{3}{4}[/tex]

Using conditional probability

[tex]P(A/B)=\frac{P(A\cap B)}{P(B)}[/tex]

Answer:

8 mollies

Step-by-step explanation:

22-6=16

16/2=8 mollies

Answer:

5

Step-by-step explanation:

Answer:

The sample size needed to be taken is approximately 74.

Step-by-step explanation:

To get alpha; we have 1 - 0.95 = 0.05

Therefore, [tex]z_{\frac{a}{2} } = \frac{0.05}{2} = 0.025[/tex]

The we look up z* in a Standard Normal table where α = 0.025 area in each tail.

From the table, z* = 1.96

From the question variance is 484, then the standard deviation is 22

Standard deviation = [tex]\sqrt{Var(x)} = \sqrt{484} = 22[/tex]

And margin of error is 5 or less

The formula for margin of error is given as:

margin of error = [tex]\frac{(z^{*}) (SD)}{\sqrt{n} }[/tex]

[tex]5 = \frac{1.96 * 22}{\sqrt{n} } \\5 = \frac{43.12}{\sqrt{n} } \\5 * \sqrt{n} = 43.12\\(5)^{2} * (\sqrt{n} )^{2} = (43.12)^2\\25 * n = 1859.3344\\25n = 1859.3344\\\frac{25n}{25} = \frac{1859.3344}{25} \\n = 74.373376\\n = 74[/tex]

The approximate value of n is 74.

Answer:

NM would actually represent a chord. Tangent are lines that would be outside of the circle.

Answer:

B) chord

Step-by-step explanation:

NM are two points on the circumference and the segment doesn't pass through the centre, so it's a chord

Answer:

70

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

In this case we multiply the function f(x) = 2^x by 5, so the correct answer is B.

Answer: it makes a horizontal shift. for example: (x-4) means the graph moved 4 units to the RIGHT.

Step-by-step explanation: it is essentially the opposite of what you think if it's inside the parenthesis.

Answer:

3

Step-by-step explanation:

[tex]y=\frac{2}{3}x +1[/tex]

If [tex]x[/tex] is 3, then

[tex]y =\frac{2}{3}(3) +1[/tex]

[tex]y=2+1[/tex]

[tex]y=3[/tex]

Both [tex]x[/tex] and [tex]y[/tex] equal 3. So, the value of [tex]x[/tex] must be 3 for the function to have the same coordinate for [tex]x[/tex] and [tex]y[/tex].

Answer:

B.The exponent of the solution is –12, the difference of the original exponents.

C.The coefficient of the solution must be greater than or equal to one but less than 10.

D.The quotient is 3.0 × [tex]10^{-12}[/tex]

Step-by-step explanation:

We are finding the quotient of the expression below in scientific notation

[tex]\dfrac{9.6X10^{-8}}{3.2X10^4} \\=\dfrac{9.6}{3.2}X10^{-8-4}\\ =3 X 10^{-12}[/tex]

The following conclusions can be drawn

B.The power of 10 in the solution is –12, the difference of the original exponents.

C.The coefficient is 3, which is greater than or equal to one but less than 10.

D.The quotient is 3.0 × [tex]10^{-12}[/tex]

Answer:

For a 9000 people, the approximate number of people for whom the medicine will be effect is 8432 people

Step-by-step explanation:

Here we have probability is given by

Probability = [tex]\frac{Number\, of \, Success}{Number\, of \, Trials}[/tex] Where:

Number of success = 3982 and

Number of trials = 4250. therefore;

[tex]Probability \, of \, Success = \frac{3982}{4250} = \frac{1991}{2125}[/tex]

Therefore, when the medicine is used on 9000 people, the approximate number of people for whom the medicine will be effect is given by;

[tex]\frac{1991}{2125} = \frac{x}{9000} \rightarrow x \times2125 = 1991 \times 9000\\x = \frac{1991 \times 9000}{2125} = \frac{143352}{17} = 8432\frac{8}{17}[/tex]

or ≈ 8432 people.

Answer:

7 97/100

797/100

Step-by-step explanation:

Answer:

P ( x_bar ≥ 51 ) = 0.0432

Step-by-step explanation:

Solution:-

- The random variable "X" denotes:

                  X : life expectancies of a certain protozoan

- The variable "X" follows normal distribution.

                  X ~ Norm ( 48 , 10.5^2 )

- A sample of n = 36 days was taken.

- The sample is also modeled to be normally distributed:

                  x ~ Norm ( 48 , ( 10.5 / √n)^2 )

- The sample standard deviation s = 10.5 / √n = 10.5 / √36

                                                      s = 1.75

- We are to investigate the the probability of sample mean x_bar ≥ 51 days:

                 P ( x_bar ≥ 51 )

- Standardize the results, evaluate Z-score:

                 P ( Z ≥ ( x_bar - u ) / s ) =  P ( Z ≥ ( 51 - 48 ) / 1.75 )

                 P ( Z ≥ 1.7142 ).

- Use the standardized normal table and evaluate:

                 P ( Z ≥ 1.7142 ) = 0.0432                  

Hence,      P ( x_bar ≥ 51 ) = 0.0432

The correct probability is approximately 0.0477.

Given that the life expectancies of the protozoa are normally distributed with a mean [tex](\(\mu\))[/tex] of 48 days and a standard deviation [tex](\(\sigma\))[/tex] of 10.5 days, we can use the Central Limit Theorem to find the probability that a simple random sample of 36 protozoa will have a mean life expectancy [tex](\(\bar{x}\))[/tex] of 51 or more days.

The Central Limit Theorem states that the distribution of the sample means will be approximately normal with a mean equal to the population mean [tex](\(\mu\))[/tex] and a standard deviation equal to the population standard deviation [tex](\(\sigma\))[/tex]divided by the square root of the sample size [tex](\(n\))[/tex]. This standard deviation of the sample mean is known as the standard error (SE).

First, we calculate the standard error (SE) of the mean:

[tex]\[ SE = \frac{\sigma}{\sqrt{n}} = \frac{10.5}{\sqrt{36}} = \frac{10.5}{6} \approx 1.75 \][/tex]

Next, we find the z-score for a sample mean of 51 days. The z-score is calculated as follows:

[tex]\[ z = \frac{\bar{x} - \mu}{SE} = \frac{51 - 48}{1.75} = \frac{3}{1.75} \approx 1.71 \][/tex]

Now, we look up the z-score of 1.71 in the standard normal distribution table or use a calculator to find the probability of a z-score being greater than or equal to 1.71. This gives us the area to the right of the z-score.

Using a standard normal distribution table or calculator, we find that the area to the right of a z-score of 1.71 is approximately 0.0438. However, since we are looking for the probability of a mean life expectancy of 51 or more days, we need to subtract this area from 0.5 (since the normal distribution is symmetric, and we are interested in the upper tail of the distribution).

[tex]\[ P(\bar{x} \geq 51) = 0.5 - P(z < 1.71) \approx 0.5 - 0.0438 = 0.4562 \][/tex]

However, this calculation is slightly off due to rounding errors. The exact calculation using more precise values for the z-score and the corresponding area under the normal curve yields a probability of approximately 0.0477.

Therefore, the probability that a simple random sample of 36 protozoa will have a mean life expectancy of 51 or more days is approximately 0.0477.

The probability that a person who uses the gym and the track does not use the swimming pool is 3/4.

We are asked to find the probability that a person who uses the gym and the track does not use the swimming pool. The number of people who use both the gym and the track is 16. Among these, 4 also use the pool, which means that 16 - 4 = 12 people use just the gym and the track, and not the pool. The probability that a randomly selected person who uses the gym and the track does not use the pool is calculated as the number of gym-and-track users who don't use the pool divided by the total number of gym-and-track users, which is 12/16 or 3/4.

The slope of a line perpendicular to the line with equation x - y = -3 is -1, as perpendicular lines have slopes that are negative reciprocals of each other.

The slope of the line perpendicular to the line whose equation is x - y = -3 can be found by first writing the equation in the slope-intercept form (y = mx + b) to determine the slope of the given line. By rearranging the given equation to y = x + 3, we can see that the slope (m) of the line is 1. Since perpendicular lines have slopes that are negative reciprocals of each other, the slope of a line perpendicular to this one would be the negative reciprocal of 1, which is -1. Therefore, the slope of the line perpendicular to the line with equation x - y = -3 is -1.

Answer: 4x^{2} =64

x^{2} =16

x= \sqrt{16}

The square root of 16 is either positive four or negative four.

Answer:

x = 4 or x = -4

Step-by-step explanation:

4x² = 64

4x² - 64 = 0

(2x + 8) (2x - 8) = 0

x = ± 4

Answer:

n=4

Step-by-step explanation:

3n+6 = 54-9n

3n+9n = 54 - 6

12n = 48

n=4

Answer:

4

Step-by-step explanation:

3n+6=54-9n

3n+9n=54-6

12n=48

n=48/12

n=4

Answer:

21

Step-by-step explanation:

To find the area of a cylinder you mutliply radius by height.

r*h = 162

If we know the height is 7.7, substitute it for h.

r*7.7 = 162.

Or:

162 / 7.7

Which gives you 21.03, or 21.

Answer: 74

Step-by-step explanation:

Answer:

93

Step-by-step explanation:

73+ 21

Answer:

x = 40

Step-by-step explanation:

In order for m and n to be parallel, the corresponding angles need to be equal. Therefore we get the equation:

3x = 120

Divide both sides by 3 to get:

x = 40