if tan theta equals 21/20 then find : sec theta​

To given expression |x + 3| simplifies solution is x + 3.

What is expression?

In mathematics, an expression is a combination of symbols, numbers, and operators that represent a quantity or a mathematical relationship. It can be a single number or a combination of numbers, variables, and operators that can be evaluated to give a numerical result.

If x > 2, then the expression |x + 3| can be simplified as follows:

|x + 3| = x + 3

since x + 3 is already non-negative when x > 2.

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The population of bacteria after I days is P(I) = 3700 * e^(0.11 * I) and  percentage rate of change per hour is 0.4285%

Exponential growth is a pattern of data that shows greater increases with passing time, creating the curve of an exponential function.

The population of bacteria in the petri dish is growing exponentially at a rate of 11% per day. This means that the daily growth rate r is 0.11, or 11/100.

The formula for exponential growth is:

P(t) = P0 * e^(rt)

Where:

P(t) is the population after t days

P0 is the initial population

r is the growth rate per day

e is the mathematical constant approximately equal to 2.71828

Using the given information, we have:

P0 = 3700

r = 0.11

So, the formula for the population of bacteria after I days is:

P(I) = 3700 * e^(0.11 * I)

To find the percentage rate of change per hour, we need to convert the daily growth rate to an hourly growth rate. There are 24 hours in a day, so the hourly growth rate h is:

h = (1 + r)^(1/24) - 1

Substituting the value of r, we get:

h = (1 + 0.11)^(1/24) - 1

Simplifying this expression, we get:

h = 0.004285

So, the hourly growth rate is 0.4285%, or 0.004285 expressed as a decimal.

Therefore, the population of bacteria after I days is:

P(I) = 3700 * e^(0.11 * I)

And the percentage rate of change per hour is:

0.4285% (rounded to the nearest hundredth of a percent)

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The percentage rate of change per hour is approximately 0.46%.

How to calculate percentage?

The formula for exponential growth is:

N(t) = N0 * e raise to the power (r*t)

where:

N(t) is the population at time t

N0 is the initial population

r is the growth rate

e is the mathematical constant approximately equal to 2.71828

t is the time elapsed

In this case, we have:

N0 = 3700

r = 11% per day, or 0.11/24 = 0.0045833 per hour (since there are 24 hours in a day)

t is the time elapsed in days

To convert the time elapsed in days to hours, we can multiply t by 24. Therefore, the function for the population of bacteria after t days is:

f(t) = 3700 * e raise to the power (0.004583324t)

To round the coefficients in the function to four decimal places, we can use the round() function in Python:

f(t) = round(3700 * e**(0.004583324t), 4)

To determine the percentage rate of change per hour, we can calculate the percentage increase in the population per hour using the formula:

Percentage increase = (e raise to the power (r*h) - 1) * 100

where:

r is the growth rate per day

h is the time elapsed in hours

In this case, we have:

r = 11% per day, or 0.11/24 = 0.0045833 per hour

h = 1 hour

Plugging these values into the formula, we get:

Percentage increase = (e raise to the power (0.0045833*1) - 1) * 100 = 0.4646%

Therefore, the percentage rate of change per hour is approximately 0.46%.

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The probability that the amount dispensed per box will have to be increased is 0.

To answer this question, we need to know the target amount that should be distributed per carton.

Assuming that the target amount is also 1 pound, we can use the concept of the normal distribution to estimate the likelihood that we will have to increase the amount distributed per case.

hence the probability of having to increase the amount is 0.

z = (target volume - mean) / standard deviation

z = (1 - 1) / 0.2

z = 0

A Z-score of 0 indicates that the target volume is equal to the mean. A standard normal distribution table or calculator can be used to find the probability that the amount should be increased.

However, the target amount is equal to the mean value,

In summary, without knowing the target amount to be dispensed in each case, it is not possible to determine the potential for volume increases.

If the target amount is to be £1 and the mean and standard deviation is also £1 and 0.2 respectively, then the probability of having to increase the amount is 0.

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Answer:

To find the slope between two points (x1, y1) and (x2, y2), we use the formula:

slope = (y2 - y1) / (x2 - x1)

Using the given points P(-11, -24) and Q(21, 40), we can substitute the values into the formula:

slope = (40 - (-24)) / (21 - (-11))

slope = 64 / 32

Therefore, the slope between points P(-11, -24) and Q(21, 40) is 2.

Answer:

2

Step-by-step explanation:

To find the slope, we can use the slope formula

m = ( y2-y1)/(x2-x1)

    = ( 40 - -24)/(21 - -11)

    = ( 40+24)/(21+11)

    = 64/32

    = 2

The first, second, and third one.

The area of a triangle whose sides have lengths √70,√70,√and 28 is 10.45.

What is the area of the triangle?

A triangle is a polygon that has three sides and three vertices. It is one of the basic figures in geometry.

The area of the triangle is defined as the product of half the base and the height of the triangle.

The area of the triangle =  (0.5)x b x h

Length of its base = b units

Its height = h units long,

Given;

The sides of the triangle √70,√70,√28

Now,

H²=70-28/4

H²=70-7

H=7.9

[tex]Area= b *\frac{ h}{2}[/tex]

[tex]=\sqrt{28}\frac{7.9}{2}[/tex]

=10.45

Therefore, the area of the triangle will be 10.45.

The complete question is-

What is the area of a triangle whose sides have length √{70},√{70}, and √{28} ?

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The explicit rule is 2000 + 3500n

The salesperson has earned $33500 after 9 months since starting the job.

What is Linear Equation?

A linear equation is a mathematical equation that involves two variables and forms a straight line when graphed. It can be represented in the form of y = mx + b, where m is the slope and b is the y-intercept.

The explicit rule for the amount of money the salesperson has earned since starting the job can be given by:

Earnings = 2000 + 3500n

Where n represents the number of months since the salesperson started the job.

To find out how much money the salesperson has earned after 9 months, we can substitute n = 9 in the above formula:

Earnings = 2000 + 3500(9)

= 2000 + 31500

= $33500

Therefore, the salesperson has earned $33500 after 9 months since starting the job.

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Answer:

the solution for x is (53 - b)/a.

Answer:

There are 20 students. Of those 20 students, 4 knew 15 capitals. We have:

4/20 = 20/100 = 20% of the students knew 15 capitals.

The volume of the cone is approximately700π/3 inches³.

What exactly is a cone?

A cone is a three-dimensional geometric shape that tapers smoothly from a flat, circular base to a point called the apex or vertex. The base can be any shape, but a circular base is the most common. A cone has a curved surface that extends from the base to the apex, and the distance from the apex to the base along a straight line passing through the center of the base is called the height of the cone.

Now,

As the Volume of cone is given by:

V = (1/3)πr²h

where r is the radius of the base, h is the height, and π is the mathematical constant pi.

In this case, we know that the diameter of the base is 20 inches, which means that the radius is 10 inches. We also know that the height is 21 inches. Therefore, we can plug in these values into the formula to find the volume:

V = (1/3)π(10²)(21) = (1/3)π(100)(21) = 700π/3 inches

Therefore, the volume of the cone is approximately700π/3 inches³, expressed in terms of pi and rounded to the nearest cubic inch.

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The range of the depths of the 10 artifacts is 18.5 inches.

The range in statistics is a measure of variability, which represents the difference between the largest and smallest values in a data set. To calculate the range, we simply subtract the smallest value from the largest value. In this case, the largest value is 38.5 inches, and the smallest value is 20.7 inches.

Therefore, the range of the depths of the artifacts in the remote area is:

Range = 38.5 - 20.7

Range = 17.8

So the range of depths is 17.8 inches. This tells us that there is quite a bit of variability in the depths at which the artifacts were found. The smallest depth was 20.7 inches, while the largest depth was 38.5 inches.

This information could be useful for archaeologists or other researchers who are interested in understanding the distribution of artifacts in the area, as well as the possible reasons for why some artifacts were found at certain depths while others were found at different depths.

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Direct variation equation relating s and t as: S = 0.5t and t=32 when s=16.

What is direct variation equation?

A direct variation equation is a mathematical equation that describes a relationship between two variables that varies proportionally. In other words, if one variable increases or decreases, the other variable also increases or decreases in proportion to it.

Given, S varies directly as t, and S = 8 when t = 16.

Let's find the constant of variation (k) using the given information:

k = S/t = 8/16 = 0.5

So, the constant of variation is 0.5.

Using the constant of variation, we can write a direct variation equation relating s and t as:

S = kt

Substituting k = 0.5 in the above equation, we get:

S = 0.5t

When S = 16, we can find t as follows:

16 = 0.5t

t = 16/0.5

t = 32

Therefore, when S = 16, t = 32.

Therefore, direct variation equation relating s and t as: S = 0.5t and t=32 when s=16.

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Answer:

the final answer is 80800 exactly

Answer: $80 880 US$

Step-by-step explanation:

Add all up

Answer:

187,550,190

Step-by-step explanation:

The number which could be added to both sides of the quadratic equation to complete the square is; -2.25.

What in mathematics is a quadratic equation?

ax² + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a 0. The fundamental theorem of algebra ensures that it has at least one solution because it is a second-order polynomial problem. Real or complicated solutions are also possible.

The quadratic equations give in the task content is; 1=x²-3x. Hence, to express the equation by completing the square method; we have;

1 - 2.25 = (x -3/2)² - 2.25

Hence, the number which should be added to both sides of the equation is; -2.25.

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Answer:

Therefore, the staff should order 320 blue bags, 360 black bags, and 120 gray bags.

Step-by-step explanation:

To determine how many bags of each color to order, we need to estimate the proportion of students who prefer each color based on the sample of 120 students. We can then use these proportions to predict the number of bags of each color needed for all 800 students. Here's how we can do it:

Determine the number of students in the sample who prefer each color:

Let B be the number of students who prefer blue

Let K be the number of students who prefer black

Let G be the number of students who prefer gray

Based on the sample of 120 students, we know:

B + K + G = 120

Estimate the proportion of students who prefer each color:

The proportion of students who prefer each color in the sample is:

p(B) = B/120

p(K) = K/120

p(G) = G/120

Predict the number of bags of each color needed for all 800 students:

The predicted number of bags of each color needed for all 800 students is:

Bags of blue = p(B) * 800

Bags of black = p(K) * 800

Bags of gray = p(G) * 800

So, using the sample results, we get:

Bags of blue = (48/120) * 800 = 320

Bags of black = (54/120) * 800 = 360

Bags of gray = (18/120) * 800 = 120

The chi-square goodness-of-fit test is not an appropriate statistical test to use in this situation.

A statistics teacher wants to know if the student birth month is distributed equally across all months. He uses school records to determine the birth month of all the students at the school and calculates a chi-square statistic to test this hypothesis.

This is not an appropriate use of a chi-square goodness-of-fit test because chi-square goodness-of-fit tests are used to compare the distribution of categorical data to a theoretical distribution.

The chi-square goodness-of-fit test compares observed frequencies of categorical data to expected frequencies based on a theoretical distribution. It is used to determine if a sample of data comes from a specific population or not.

In this case, the teacher is not comparing observed frequencies to expected frequencies, but instead is testing the hypothesis that the distribution of student birth months is equal across all months.

This is not a proper use of a chi-square goodness-of-fit test because the hypothesis being tested is not related to the expected frequencies of a categorical variable. Therefore, the chi-square goodness-of-fit test is not an appropriate statistical test to use in this situation.

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It would be very surprising to observe a random sample of 30-time intervals between eruptions with a mean of 97 minutes, given the population mean and standard deviation.

Based on the information provided, we know that the mean time between eruptions of Old Faithful is 85 minutes and the standard deviation is 21 minutes. We are also given a sample of 30-time intervals between eruptions, and we want to determine whether it would be surprising to observe a sample mean of 97 minutes.

To answer this question, we need to calculate the standard error of the mean (SEM), which is given by the formula:

SEM = σ / sqrt(n)

where σ is the population standard deviation (21 minutes), and n is the sample size (30). Plugging in the values, we get:

SEM = 21 / sqrt(30) ≈ 3.84

Next, we calculate the z-score for a sample mean of 97 minutes, using the formula:

z = (x - μ) / SEM

where x is the sample mean (97 minutes), μ is the population mean (85 minutes), and SEM is the standard error of the mean (3.84 minutes). Plugging in the values, we get:

z = (97 - 85) / 3.84 ≈ 3.13

Finally, we can look up the probability of observing a z-score of 3.13 or more extreme in a standard normal distribution table (or using a calculator or software). The probability turns out to be very small, less than 0.01.

Therefore, Given the population mean and standard deviation, it would be very unexpected to find a random selection of 30-minute gaps between eruptions with a mean of 97 minutes. This suggests that the sample may not be representative of the population, or there may be some other factors affecting the intervals between eruptions.

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Answer: y= -6

Step-by-step explanation: use the slope formula and slope intercept; y=mx+b

Answer:mason must need 33.6 m of materail to make  8 curtains.

so he need to 17.6m of material

Step-by-step explanation:

The area of triangle in given figure is = 60 cm²

A triangle is a three-sided polygon that is formed by connecting three non-collinear points in a plane.The sum of the interior angles of a triangle is always 180 degrees, and the length of each side can be determined by the application of the Pythagorean theorem or other trigonometric functions, depending on the given information. Triangles can also be classified based on the size of their angles and the lengths of their sides, which give rise to various types of triangle such as equilateral, isosceles, scalene, acute, right, and obtuse triangles.

According to quesrtion

Given height = 3cm

Base = 10cm

if the height is quadrupled then height = 4 × 3 = 12cm

Area = 1/2 × base × height

= 1/2 × 70 × 12

to solve this we get

Area = 60cm²

So, the area of this triangle is 60cm²

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The least number of packs of nails Jess needs to buy is 1.

To find the least number of packs of nails Jess needs to buy, we need to find the lowest common multiple (LCM) of the pack sizes of hammers and nails.
Step 1: Identify the numbers
Hammers come in packs of 3, and nails come in packs of 6.
Step 2: Find the LCM of 3 and 6
List the multiples of each number:
Multiples of 3: 3, 6, 9, 12, ...
Multiples of 6: 6, 12, 18, 24, ...
The lowest common multiple of 3 and 6 is 6.
Step 3: Determine the number of packs of nails.

Since the LCM is 6 and nails come in packs of 6, Jess needs to buy 1 pack of nails to have the same number of each item.

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Answer:

The outlier in this graph is (4, 55)

Step-by-step explanation:

Outliers can be seen graphically when we first draw a line of best fit. When we draw the line of best fit it connects through the middle of the string of points near the top of our graph. We can see that any given point on the graph is either on the line of best fit or very close to it. This can be said about all points but one... the point (4,55). This point lies far away from the line we've created and can be identified as an outlier for this reason.

The amount Mariano must make from his job is

$2,500 ($12,500 * 0.2) =  $2500.

A number can be divided by five or multiplied by 0.2 to determine 20% of that amount.

Mariano, for instance, would have to pay $12,500 ($15,000 - $800 - $1,700)

if he had to pay $15,000 for a year of classes at the University of Texas at Brownsville but had also been awarded a grant for $800 and a scholarship for $1,700.

We can divide $12,500 by 5 or multiply it by 0.2 to calculate how much he must make from his employment to cover 20% of the remaining expenses.

The amount Mariano must make from his job is

$2,500 ($12,500 * 0.2) =  $2500.

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Emily has to pay $41.31 for the shirt after adding coupon and discount.

How to find the Cost Price (CP) of any discounted item?

Lets say CP = 54 and the discount is of 15% i.e. marked price

So, Marked Price= 85% of CP = 45.9

Lets apply the additional coupon of 10% on Marked Price.

Therefore, the payment amount = 90% of MP

payment amount = $41.31

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The probability that Sean will make more than Evan on a randomly selected week is approximately 0.3446 or 34.46%.

To calculate the probability that Sean will make more than Evan in a randomly selected week, we need to compare their incomes in terms of standard deviations from the mean.

First, we need to calculate the difference between their means:

Mean difference = Sean's mean income - Evan's mean income = $225 - $240 = -$15

Next, we need to calculate the standard deviation of the difference between their incomes:

Standard deviation of difference = √[(Sean's standard deviation)^2 + (Evan's standard deviation)^2] = √[(35)^2 + (15)^2] = 37.42

Now, we can use a z-score table to find the probability that Sean's income will be higher than Evan's income:

Z-score = (Sean's income - Evan's income - Mean difference) / Standard deviation of difference = (225 - 240 - (-15)) / 37.42 = 0.40

From the z-score table, we find that the probability of a z-score of 0.40 or higher is 0.3446.

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Answer:

AB = 6.71 to nearest hundredth.

Step-by-step explanation:

To get from A to B we move 3 units to the right then 6 units up.

This form a right angled triangle so we use Pythagoras theorem:

AB^2 = 3^2 + 6^2

         =  9 + 36

         = 45

So AB = √45

           = 3√5  = 6.7082

To find the third side length, we can use the fact that the sum of the lengths of any two sides of a triangle is greater than the length of the third side. So we can write: (z + 13) + (2z + 6) > third side Simplifying the left side, we get: 3z + 19 > third side Now we also know that the perimeter of the triangle is the sum of the lengths of all three sides, so we can write: (z + 13) + (2z + 6) + third side = 8z + 11 Simplifying this equation, we get: 3z + 19 + third side = 8z + 11 Subtracting 3z + 19 from both sides, we get: third side = 5z - 8 Therefore, the

value of side x in the triangle is 6 ( simplest radical form with a rational denominator is 6/1).

A right triangle is a triangle that has one angle measuring 90 degrees, which is also called a right angle. The hypotenuse is the side that faces the right angle, while the legs are the other two sides.

Trigonometric functions are a set of mathematical functions used to relate the angles and sides of a right triangle. Sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent are the six fundamental trigonometric functions (cot).

In the given right angles triangle

Using trigonomteric function

Tan30°=√12/x

1/√3=√12/x

x=√12×√3

x=√36

x=6

Hence, value of side x in the triangle is 6.

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