Suppose a certain assignment has a 60% passing rate. We randomly sample 200 people that took the assignment. What is the approximate probability that at least 65% of 200 randomly sampled people will pass? Use normal approximation, find the nearest answer.

A: 0.074

B; 0.809

C; 0.926

D; 0.191

To find sin(t), cos(t), and tan(t) for the terminal point P(x, y) = (1/5, -2/6), we can use the trigonometric definitions based on the coordinates of the point.

First, let's find the values of sin(t) and cos(t):

sin(t) = y/r

cos(t) = x/r

where r is the distance from the origin to the point P, given by the formula:

r = sqrt(\(x^2\)+ \(y^2\))

In this case, x = 1/5 and y = -2/6. Let's calculate the values:

r = sqrt((\(1/5)^2\) + \((-2/6)^2\)) = sqrt(1/25 + 4/36) = sqrt(36/900 + 100/900) = sqrt(136/900) = sqrt(17/225) = sqrt(17)/15

sin(t) = (-2/6) / (sqrt(17)/15) = (-2/6) * (15/sqrt(17)) = -5/sqrt(17)

cos(t) = (1/5) / (sqrt(17)/15) = (1/5) * (15/sqrt(17)) = 3/sqrt(17)

Finally, we can calculate tan(t) using the formula:

tan(t) = sin(t) / cos(t)

tan(t) = (-5/sqrt(17)) / (3/sqrt(17)) = -5/3

Therefore, the values are:

sin(t) = -5/sqrt(17)

cos(t) = 3/sqrt(17)

tan(t) = -5/3

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To calculate the duration of the shift, you need to subtract the clock-in time from the clock-out time.

In this case, the shift worker clocked in at 1730 hours (5:30 PM) and clocked out at 0330 hours (3:30 AM). However, since the clock is based on a 24-hour format, it's necessary to consider that the clock-out time of 0330 hours actually refers to the next day.

To calculate the duration of the shift, you can perform the following steps:

1. Calculate the duration until midnight (0000 hours) on the same day:

  - The time between 1730 hours and 0000 hours is 6 hours and 30 minutes (1730 - 0000 = 6:30 PM to 12:00 AM).

2. Calculate the duration from midnight (0000 hours) to the clock-out time:

  - The time between 0000 hours and 0330 hours is 3 hours and 30 minutes (12:00 AM to 3:30 AM).

3. Add the durations from step 1 and step 2 to find the total duration of the shift:

  - 6 hours and 30 minutes + 3 hours and 30 minutes = 10 hours.

Therefore, the duration of the shift was 10 hours.

Answer:

third side = 6

Step-by-step explanation:

Using Pythagoras' identity in the right triangle.

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides.

let the third side be x , then

x² + 8² = 10²

x² + 64 = 100 ( subtract 64 from both sides )

x² = 36 ( take the square root of both sides )

x = \(\sqrt{36}\) = 6

Answer: try b

Step-by-step explanation:

In the study conducted by John Darley and Bibb Latané, the number of people present in the room with the participant served as an independent variable, as it was manipulated by the researchers to observe its effects on helping behavior.

Specifically, the researchers examined how the presence of other people in the room would affect whether or not the participant would choose to help in a given situation. By changing the number of people present in the room, the researchers were able to measure the effects of diffusion of responsibility on helping behavior.

Diffusion of responsibility is a phenomenon in which individuals are less likely to help a victim when they are in the presence of other people, as they assume that someone else will take responsibility. Therefore, the number of people present in the room was an important variable in the study, as it allowed the researchers to measure how the presence of others affected helping behavior.

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The value of the smaller number (x) is approximately 6.67 (rounded to two decimal places).

To solve this problem, let's call the smaller number x and the larger number y.
According to the given information, the sum of the two numbers is 20, so we can write the equation: x + y = 20.
It is also given that one of the numbers (y) is twice the other number (x).

In equation form, we can write: y = 2x.

To find the value of the smaller number (x), we can substitute the value of y from the second equation into the first equation:
x + 2x = 20
Combining like terms, we get:
3x = 20
Dividing both sides by 3, we find:
x = 20/3
So, the value of the smaller number (x) is approximately 6.67 (rounded to two decimal places).

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A regular polygon is a polygon with all sides and angles congruent. It exhibits symmetry and uniformity in its sides and angles, creating a visually appealing shape.

A polygon with all sides and angles congruent is called a regular polygon. In a regular polygon, all sides have the same length, and all angles have the same measure. This uniformity in the lengths and angles of the polygon's sides and angles gives it a symmetrical and balanced appearance.

Regular polygons are named based on the number of sides they have. Some common examples include the equilateral triangle (3 sides), square (4 sides), pentagon (5 sides), hexagon (6 sides), and so on. The names of regular polygons are derived from Greek or Latin numerical prefixes.

In a regular polygon, each interior angle has the same measure, which can be calculated using the formula:

Interior angle measure = (n-2) * 180 / n

Where n represents the number of sides of the polygon.

The sum of the interior angles of any polygon is given by the formula:

Sum of interior angles = (n-2) * 180 degrees

Regular polygons have several interesting properties. For instance, the

exterior angles of a regular polygon sum up to 360 degrees, and the measure of each exterior angle can be calculated by dividing 360 degrees by the number of sides.

Regular polygons often possess symmetrical properties and are aesthetically pleasing. They are commonly used in design, architecture, and various mathematical applications.

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Answer:

roben,dove,raven  ,goose

Step-by-step explaunation:

you need to change them to the same denominator *first*

Answer:

Robin, Raven, Turtle dove, Canada goose.

Step-by-step explanation:

We are given the size of the eggs.

Now, we need to put the sizes of eggs in ascending order.

=> \(\frac{17}{5},\frac{3}{4} ,\frac{6}{5} , \frac{10}{9}\)

Step 1: Make the denominators same.

=> \(\frac{17}{5},\frac{3}{4} ,\frac{6}{5} , \frac{10}{9}\)

=> \(\frac{612}{180} ,\frac{135}{180} ,\frac{216}{180}, \frac{200}{180}\)

Step 2: Order these egg sizes in ascending order.

=> \(\frac{612}{180} ,\frac{135}{180} ,\frac{216}{180}, \frac{200}{180}\)

=> \(\frac{135}{180},\frac{200}{180},\frac{216}{180},\frac{612}{180}\)

Step 3: Match the sizes of the eggs with the bird.

Robin, Raven, Turtle dove, Canada goose.

Final Answer: So, after working on this problem, we can conclude that the ascending order of bird's eggs size is:

Robin, Raven, Turtle dove, Canada goose.

Hoped this helped.

Answer:

D

Step-by-step explanation:

I have done this before
Top row units is 8 i then multiplied both sides so 5*2 which = 10 then multiplied 8*10 to get 80

Answer:

80 square units (D)

Step-by-step explanation:

Base is 16 units, height is 5 units. 16 * 5 = 80

Step-by-step explanation:

2

Example, 2*2=2^2

Hope it helped❤️

Answer:

to the power of 2

for example you can be asked to find the square number of 5 which is the same as 5²= 25

Henry opens a savings account with an annual interest rate of 4.5 percent. After a year, he gets $75,000 in payment. He made a deposit into the savings account of $72,831.68.

Here are the steps on how to calculate the amount Henry invested:

Convert the annual interest rate to a monthly rate.

\(\begin{equation}4.5\% \div 12 = 0.375\%\end{equation}\)

Calculate the number of years.

\(\begin{equation}\frac{18 \text{ months}}{12 \text{ months/year}} = 1.5 \text{ years}\end{equation}\)

Use the compound interest formula to calculate the amount Henry invested.

\(\begin{equation}FV = PV * (1 + r)^t\end{equation}\)

where:

FV is the future value ($75,000)

PV is the present value (unknown)

r is the interest rate (0.375%)

t is the number of years (1.5 years)

\(\begin{equation}\$75,000 = PV \cdot (1 + 0.00375)^{1.5}\end{equation}\)

\$75,000 = PV * 1.0297

\(\begin{equation}PV = \frac{\$75,000}{1.0297}\end{equation}\)

PV = \$72,831.68

Therefore, Henry invested \$72,831.68 in the savings account.

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Answer:

60.96

Step-by-step explanation:

127 times 0.48

Answer:

y=4-(4/5)x or y= -4/5x+4

Step-by-step explanation:

4x+5y=20

5y=20-4x

y=(20-4x)/5

y=(20/5)-(4x/5)

y=4-(4/5)x or y= -4/5x+4

When did not take the reciprocal of the divisor.

Convert Celsius to Fahrenheit ?

Celsius to Fahrenheit conversion will be like one celsius is equal 32 Fahrenheit.

Given,

The temperature fell from 0 Degrees Fahrenheit to 15 and one-half Degrees Fahrenheit below 0 in 5 and three-fourths hours. Wen tried to find the change in temperature per hour.

When she checked the answer by estimating, it did not make sense. What error did When make, Wen incorrectly converted a mixed number to an improper fraction. Wen added the numerators and denominators instead of multiplying. Wen did not take the reciprocal of the divisor

Hence , When did not take the reciprocal of the divisor.

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Hello !

Answer:

\(\Large \boxed{\sf r=\frac{3}{2} }\)

Step-by-step explanation:

Let's remember :

We know that the volume of the sphere is equal to half its surface area.

\(\sf V_{sphere}=\frac{1}{2} A_{sphere}\\\\\sf \frac{4}{3}\pi r^3=\frac{1}{2} 4\pi r^2\\\\\sf \frac{4}{3}\pi r^3=2\pi r^2\)

Let's solve this equation for r.

First, substract \(\sf 2\pi r^2\)  from both sides :

\(\sf \frac{4}{3} \pi r^3-2\pi r^2=0\)

We can now factorize by taking out the highest common factor: 2r²

\(\sf 2r^2(\frac{2}{3} \pi r-\pi )=0\)

We can use the zero-product property.

There are two solutions :

The first solution is absurd : The radius of a sphere cannot be 0.

We conclude that we must keep the second solution.

Have a nice day ;)

Answer:

let (8,3) be (x1,y1)

(2,7) be (x2,y2)

using distance formula

√[(x2-x1)²+(y2-y1)²]

√(2-8)²+(7-3)²

√(36+16)

√52

Answer:

like wise. I too agree with your contribution

Answer:

in decimal form, it is 0.1 in percent form it is 10%

Step-by-step explanation:

Answer:

My username is

Step-by-step explanation:

IloveSatorisamam

Answer: My xbox gamertag is...

Bubbles5306

Step-by-step explanation:

The integral of (6ex)2exdx is 4e3x + C, where C is the constant of integration.

To evaluate the integral, we can use the power rule for integration and then simplify:

∫(6ex)2exdx

= ∫36e3xdx

= (36/3)∫e3xdx

= 12∫e3xdx

= 12(1/3)e3x + C

= 4e3x + C

Overall, A definite integral is the area under a curve between two fixed limits. The definite integral is represented as ∫baf(x)dx ∫ a b f ( x ) d x , where a is the lower limit and b is the upper limit, for a function f(x), defined with reference to the x-axis.

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The amount which Brandon have saved in interest by consolidating the two balances on the card with the lower interest rate is $256.12.

Monthly payment is the payment which has to paid against the loan amount or the borrowed money calculated with interest rate.

It can be calculated with the following formula.

\(M=P\left (\dfrac{r}{1-(1+r)^{-nt}}\right)\)

Here, (P) is the principal amount, (r) is the interest rate and (t) is time.

Brandon has two credit cards and would like to consolidate the two balances into one balance on the card with the lower interest rate.

The table below shows the information about the two credit cards Brandon currently uses.    

Interest rate for the card a is,

\(r=\dfrac{13}{12\times100}=0.01083\)

The time period is 8 years and there are 12 months in one year. Thus, the monthly payment of card A will be,

\(M=1157.98\left (\dfrac{0.01083}{1-(1+0.01083)^{-12(8)}}\right)\\M=19.47\)

In the 8 years, there is total 96 monthly payments. Thus, the total payment by card A is,

\(P_a=19.47\times96=1869.12\)

For the card B the monthly payment is $22.14. Thus the total payment by card B is,

\(P_b=22.14\times96=2125.44\)

The difference in the payment is,

\(d=2125.44-1869.12\\d=256.12\)

Hence, the amount which Brandon have saved in interest by consolidating the two balances on the card with the lower interest rate is $256.12.

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Answer:

C. 256.32

Step-by-step explanation:

Answer:

c. $13. 43

Step-by-step explanation:

Here's the simple interest formula: Interest = P x R x N. P = Principal amount (the beginning balance). R = Interest rate (usually per year, expressed as a decimal). N = Number of time periods (generally one-year time periods).

The system of equations is:

2b + 4.25s = 53.75

b - s = 5  

The number of bagels bought is 12 and the number of sandwiches bought is 7.

2b + 4.25s = 53.75 equation 1

b - s = 5  equation 2

Where:

The elimination method would be used to determine the required values.

Multiply equation 2 by 2

2b - 2s = 10 equation 3

Subtract equation 3 from equation 1 :

6.25s = 43.75

Divide both sides of the equation by 2.25

s = 43.75 / 6.25

s = 7

Substitute for s in equation 1:

2b + 4.25(7) = 53.75

2b + 29.75 = 53.75

2b = 53.75 - 29.75

2b = 24

b = 24 / 2

b = 12

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Dilation and rotation will not produce a congruent triangle

What is rotation ?

The rotation of a point with regard to the origin is described by the rotation formula. To get the position of the point after rotation, apply the rotation formula. Rotation is a circular movement about the specific axis or point of rotation. In general, there are two common directions for rotation: clockwise and anti-clockwise or counter-clockwise.

Rotations, reflections and translations are known as rigid transformations; this means they do not change the size or shape of a figure, they simply move it. These rigid transformations preserve congruence.

Dilation, however, are not rigid transformations, since they change the size of a shape. Dilation would not change the shape, just the size; the angle measures would be the same, and the ratio of corresponding sides would be equal to the scale factor used in the dilation. This would give us a similar, but not congruent, figure.

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Answer:

I don't know what you're asking but if you're asking what the mode is then it's 2, or your mean is 5

Step-by-step explanation:

Answer:

Model is Sam..

so 9 is correct answer..

by the way option A is correct

For the roll of one gaming die, we can compute the following probabilities:

(a) p [5]: The probability of rolling a 5 on one gaming die is 1/6 since there are 6 equally likely outcomes (numbers 1 to 6) and only one of them is a 5.

(b) p [5 then 6]: To calculate the probability of rolling a 5 and then a 6, we multiply the probabilities of each event. The probability of rolling a 5 is 1/6, and assuming the die is fair and independent, the probability of rolling a 6 after rolling a 5 is also 1/6. Therefore, the probability of rolling a 5 then 6 is (1/6) * (1/6) = 1/36.

(c) p [1 or 3 or 6]: The probability of rolling a 1, 3, or 6 can be found by summing the individual probabilities of each event. The die has 6 equally likely outcomes, and 3 of them (1, 3, and 6) satisfy the condition. Therefore, the probability of rolling a 1 or 3 or 6 is 3/6 = 1/2.

In summary, the probability of rolling a specific number on one gaming die is 1/6. The probability of rolling two specific numbers consecutively is the product of their individual probabilities.

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The sequence an = (16n + 20)/(4n + 3) diverges.

To determine convergence or divergence, we can analyze the behavior of the sequence as n approaches infinity. In this case, we have the sequence an = (16n + 20)/(4n + 3). As n becomes larger and larger, the terms in the numerator and denominator grow linearly with n. Therefore, we can simplify the expression by dividing each term by n:

an = (16 + 20/n)/(4 + 3/n)

As n approaches infinity, both (20/n) and (3/n) approach zero. Therefore, the expression simplifies to:

an = 16/4 = 4

Since the coefficient of n is 16, the terms of the sequence increase at a constant rate of 16 for each increase in n. As a result, the terms of the sequence become arbitrarily large without approaching a specific value. Therefore, the sequence an = 16n + 20 diverges, and there is no limit as n approaches infinity.

The resulting value of 4 is a constant and does not depend on n. This means that the terms of the sequence an are all equal to 4, and the sequence does not approach a specific limit as n goes to infinity. Hence, the sequence diverges.

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On solving the provided question, we got to know that - 40/155 adults will not have hypertension (70%),

The probability is calculated by dividing the total number of outcomes by the total number of possible ways an event may occur. Probability and odds are two different ideas. The chances are calculated by dividing the likelihood that a certain event will occur by the likelihood that it won't.

Probabilities are mathematical explanations of the chance that an event will happen or that a proposition is true. The probability of an occurrence is a number between 0 and 1, where 0 often indicates impossibility and 1 normally indicates certainty.

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