find the value of each trigonometric ratio. Part 1​

Using the normal distribution, the standard deviation of bone density in the reference population is of 5.52 g/cm².

The z-score of a measure X of a normally distributed variable with mean \(\mu\) and standard deviation \(\sigma\) is given by:

\(Z = \frac{X - \mu}{\sigma}\)

For this problem, the parameters are given as follows:

\(X = 948, z = -1.45, \mu = 956\)

Hence we solve for \(\sigma\) to find the z-score as follows:

\(Z = \frac{X - \mu}{\sigma}\)

\(-1.45 = \frac{948 - 956}{\sigma}\)

\(-1.45\sigma = -8\)

\(\sigma = \frac{8}{1.45}\)

\(\sigma = 5.52\)

The standard deviation of bone density in the reference population is of 5.52 g/cm².

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Answer:

ok ok easy lol oh my good what I'm did do have he told ya he bc do is so in by he do oh my God he told

Answer:

23/54 meters

Step-by-step explanation:

Assuming that the scale model is smaller, then the scale model should be 1/27th of the actual thing. Therefore:

11.5/27

= 23/54 meters tall

The radioactive element decays by 2% of its original mass every 3 days. The equation for the mass of the element as a function of time is given by: Mass(t) = Mass(0) * (0.98)^(t/3).

The decay of the radioactive element follows an exponential decay model. The equation for the mass of the element as a function of time can be derived from the given information. Since the element decays by 2% of its original mass every 3 days, we can express this as a decay factor of 0.98 (100% - 2% = 98%). Let Mass(t) be the mass of the element at time t, and Mass(0) be the initial mass of the element. The equation for the mass of the element as a function of time is given by Mass(t) = Mass(0) * (0.98)^(t/3), where t represents the time elapsed in days.

To predict the mass of the element after 10 days, we can substitute t = 10 into the mass equation. Using Mass(0) = 20 grams, we get Mass(10) = 20 * (0.98)^(10/3) ≈ 18.275 grams.

To find the instantaneous decay rate at 10 days, we need to take the derivative of the mass equation with respect to time and evaluate it at t = 10. Taking the derivative of Mass(t) = Mass(0) * (0.98)^(t/3) gives dMass(t)/dt = (Mass(0) * ln(0.98) * (1/3)) * (0.98)^(t/3). Evaluating this at t = 10, we get dMass(10)/dt ≈ -0.012695 grams/day. This represents the rate at which the mass is decreasing at t = 10 days.

To determine when the mass will be only half of its original amount, we need to find the value of t that satisfies Mass(t) = Mass(0)/2. Setting Mass(t) = 10 grams (half of the initial mass of 20 grams), we can solve the equation 10 = 20 * (0.98)^(t/3) for t. By taking the logarithm of both sides and solving for t, we find t ≈ 34.656 days. Therefore, the mass will be halved approximately 34.656 days after the start of the decay process.

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Answer:

12+133

Step-by-step explanation:

Separate this expression into two parts, (6x2) + (-19x-7)

Solve what is in the parenthesis (12) + (133)= 12+133

The simplified expression would also be 145

The expression that is equivalent to 6x² −19x−7 would be (2 x - 7 )  ( 3x - 1)

Those expressions that might look different but their simplified forms are the same expressions are called equivalent expressions.

To derive equivalent expressions of some expressions, we can either make it look more complex or simple. Usually, we simplify it.

We need to find the expression into an equivalent form 6x² −19x−7

This expression could also be given by;

6x² −19x−7

Separate this expression into two parts;

(6x²) + (-19x-7)

Solve the parenthesis ;

3x (2 x - 7 ) -1 (2 x - 7 ) = 0

(2 x - 7 )  ( 3x - 1) = 0

The expression that is equivalent to 6x² −19x−7 would be (2 x - 7 )  ( 3x - 1)

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The amount that each of Xavier Yolando, and Zachary has is   $1.48

We know that what we need to do is to convert the problem to an equation. The first step is always to be able to form the equation from the sentence that we have been given and we must have to look out for the key words in the problem.

We are told that each of them; Xavier Yolando, and Zachary have the same amount thus;

3x = 4.44

x = 4.44/3

x = $1.48

Thus they would all have a sum of $1.48

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Answer:

9

Step-by-step explanation:

It is the greatest exponent.

By answering the above question, we may infer that As a result, the inequality answer is 2 x 1.

A connection between two expressions or values that is not equal is known as an inequality in mathematics. Inequality follows imbalance, therefore. In mathematics, an inequality makes a connection between two values that are not equal. Egality and inequality are different. The not equal symbol is often used to indicate that two values are not equal (). Various inequalities are employed to contrast values of all sizes. By changing the two sides until just the variables are left, one may solve many straightforward inequalities. However a variety of factors support inequality: Negative values are split or added on either side. Switch between the left and right.

We may take 3 off of all sides to find the solution to the inequality 1 x + 3 4:

\(1 < x + 3 < 4 \s-3 -3 -3 \s-2 < x < 1\)

As a result, the answer is 2 x 1.

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Answer:

9.000009000009

Step-by-step explanation:

h

The distinct prime factors of 9999 are 3, 11, and 101. So the sum of each distinct prime factor of 9999 is 115.

To find the sum of the distinct prime factors of 9999, we first need to factorize 9999 into its prime factors.

9999 can be factorized as follows:

9999 = 3 * 3333

= 3 * 3 * 1111

= 3 * 3 * 11 * 101

So, the distinct prime factors of 9999 are 3, 11, and 101.

The sum of these distinct prime factors is:

3 + 11 + 101 = 115

Therefore, the sum of each distinct prime factor of 9999 is 115.

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The term for this kind of sample is cluster sampling

Given

that, At a major ten university, 200 of the 30,000 undergraduate students and 100 of the 5,000 graduate students are chosen to represent a sample of student opinion.

What is cluster sampling ?

Cluster sampling involves breaking up a population into smaller units called clusters. Then, they randomly select a sample from each of these clusters. Cluster sampling is a probability sampling technique that is frequently used to examine large populations, especially those that are widely geographically dispersed.

Researchers frequently refer to pre-existing groups like cities or schools when referring to clusters. With an SRS of 200 students and an SRS score of 100, clusters have been utilized in this instance. Cluster sampling is the name given to this type of sample as a result.

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Answer:

A, 1.8796

Step-by-step explanation:

First, convert everything to inches

6 × 12 = 72

72 + 2 = 74

Now, we convert the inches to centimeters

2.54 × 74 = 187.96

Next, we convert to meters

187.96 ÷ 100 = 1.8796

So, your answer would be A, 1.8796 meters

Have a great day!

To evaluate the function csch(ln), we will first understand the terms involved:

1. ln: This represents the natural logarithm, which is the logarithm to the base e (approximately 2.718).
2. csch: This represents the hyperbolic cosecant function, defined as csch(x) = 1/sinh(x), where sinh(x) is the hyperbolic sine function.

Now, let's evaluate csch(ln):

csch(ln) = 1 / sinh(ln)

It's important to note that the value of sinh(ln) can't be simplified into a more basic expression. To find the numerical value of csch(ln), you can use a calculator or software that supports hyperbolic functions and logarithms.

For example, using a calculator, you can find:

sinh(ln) ≈ 0.1755
csch(ln) = 1 / sinh(ln) ≈ 1 / 0.1755 ≈ 5.701

So, the value of csch(ln) rounded to three decimal places is approximately 5.701.

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Answer: Concave down

Explanation:

An example is shown below. We have the concave down parabola \(y = -x^2+7\) marked in red. The trapezoidal sum is in blue. The three trapezoids combine to something just a bit smaller than the true area under the curve from x = -2 to x = 1. Therefore, this trapezoidal sum is an underestimate of the true area under the curve.

Every part of each trapezoid is completely below the red curve. In other words, no part of the blue pieces spill above the parabola.

The rate at which the gas powered pump deliver water is 160.9 litres per seconds

The gas powered water pump delivers 42.50 gallons of water per minute.

Therefore,

1 gallon = 3.78541 litres

42.50 gallons = ?

cross multiply

volume = 42.50 × 3.78541 = 160.879925 litres

Hence,

60 seconds = 1 minutes

1 second = ?

time = 1 / 60 = 0.01666666666 seconds

Hence,

rate = 160.9 litres per second

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Answer:

4 pounds of mac 3 pounds of potato

Step-by-step explanation:

5+6=11+5+6=22+5+6=33+5=38

To calculate the sensitivity for a cutoff point of 0, we need to determine the proportion of true positives (abnormal cases correctly identified) out of all the abnormal cases. option (a) 60%

The given data shows that out of 100 abnormal cases, 60 were correctly identified with a score of 0. Sensitivity is calculated by dividing the true positives by the total number of abnormal cases and multiplying by 100. Therefore, the sensitivity is (60/100) * 100 = 60%. Hence, option (a) 60% is the correct answer.

Sensitivity, also known as the true positive rate, measures the proportion of true positives correctly identified by a test. In this case, the cutoff point is 0. Looking at the given data, we see that out of the 100 abnormal cases, 60 were correctly identified with a score of 0.

The sensitivity is calculated by dividing the number of true positives (abnormal cases correctly identified) by the total number of abnormal cases and multiplying by 100. In this scenario, the sensitivity is (60/100) * 100 = 60%.

Therefore, the correct answer is option (a) 60%, indicating that 60% of the abnormal cases were correctly identified by the test at the cutoff point of 0.

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Component 3 must be started on day 197 to meet the delivery date of day 200.

To illustrate the backward schedule, we need to start from the delivery date (day 200) and work our way backward, taking into account the lead times and dependencies of each operation.

(a) Backward schedule:

Operation    |  Work Center  |  Time (hours)  |  Start Day

--------------------------------------------------------

Final Assembly |   Work Center 1  |        1       |     200

Sub-assembly 1 |   Work Center 2  |        2       |     199

Component 4     |   Work Center 3  |        3       |     197

Component 2     |   Work Center 4  |        4       |     196

Component 3     |   Work Center 5  |        3       |     ????

(b) To identify when component 3 must be started to meet the delivery date, we need to consider its dependencies and lead times.

From the backward schedule, we see that component 3 is required for sub-assembly 1, which is scheduled to start on day 199. The time required for sub-assembly 1 is 2 hours, which means it should be completed by the end of day 199.

Since component 3 is needed for sub-assembly 1, we can conclude that component 3 must be started at least 2 hours before the start of sub-assembly 1. Therefore, component 3 should be started on day 199 - 2 = 197 to ensure it is completed and ready for sub-assembly 1.

Hence, component 3 must be started on day 197 to meet the delivery date of day 200.

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Step-by-step explanation:

wow, how complicated can one phrase this ...

the point being :

1 ft = 12 in and vice versa (1 in = 1/12 ft)

so, any measurements given in feet but needed in inches need to be multiplied by 12.

and any measurements given in inches but needed in feet need to be divided by 12.

so,

3.5 ft = 3.5×12 = 7/2 × 12 = 7×6 = 42 in

27 in = 27/12 = 9/4 = 2 1/4 or 2.25 ft

Answer:When converting from inches to feet, the measurement in inches, m, of an object varies directly with its measurement in feet, f, with the constant of variation being 12.

What is the equation relating these two quantities?

✔ m = 12f

How many inches would a 3.5-foot object measure?

✔ 42

inches

How many feet would a 27-inch object measure?

✔ 2.25

feet

Step-by-step explanation:

Answer:

I couldn't understand your question, please send once more

Answer: GCF = 3

~~~~~~~~~~~~

Hope this helps!

The exponential function between (-1, 2/5) and (3, 250) is as follows:

\(f(x) = 2 * 5^x\)

By combining the fourth roots from both sides, we arrive at:

b = 5

When we use the expression we discovered for a and this value of b, we get:

a = (2/5) * 5 = 2

As a result, the exponential function between (-1, 2/5) and (3, 250) is as follows:

\(f(x) = 2 * 5^x\)

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input. A function is typically represented as y = f. (x).

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

from the question:

This is the shape of the exponential function:

f(x) = a *\(b^x\)

where a represents the starting point and b represents the exponential function's base.

We must solve the system of equations to determine the values of a and b that meet the requirements:

a * \(b^(-1)\) = 2/5 (equation 1) 

a *\(b^3\)= 250 (equation 2) 

We can solve for an in equation 1 by multiplying both sides by b:

a = (2/5) * b

Substituting this expression into equation 2, we get:

(2/5) * b *\(b^3\) = 250

Simplifying, we get:

\(b^4 = 3125\)

By combining the fourth roots from both sides, we arrive at:

b = 5

When we use the expression we discovered for a and this value of b, we get:

a = (2/5) * 5 = 2

As a result, the exponential function between (-1, 2/5) and (3, 250) is as follows:

\(f(x) = 2 * 5^x\)

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The magnitude of the number of the minutes in the school is 2.

Although the order of magnitude of zero is not specified, it is occasionally stated to have a magnitude of. Zero is less than any other positive number, and so is its order of magnitude, according to this infinitely negative order of magnitude.

There can be no negative magnitude. The component of the vector that lacks direction is its length (positive or negative).

The order of magnitude is the approximate representation of the logarithmic of the order's value and is typically considered to be 10 taken as the base.

On a scale of 10 logarithmic, the difference in the order of magnitude can be quantified.

The value storage is where you may find the number into the various magnetic.

As a result, the number of minutes spent in school is 2.

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Complete question -

What is the Order of Magnitude of the number of minutes in a school day?

The total surface area of the prism will be 290.125 Square units.

The surface area of a rectangular prism is the measure of how much-exposed area a prism has. Surface area is expressed in square units.

The surface area of a rectangular prism is given by:

SA = 2 (lh +wh + lw )

where

l = 3

w = 4.25

h = 18.25

SA = 2 (3x18.25 + 4.25x18.25 + 3x4.25)

SA = 2 (54.75 + 77.5625 + 12.75)

SA = 2 (146.0625)

SA = 290.125 square units

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Answer:

108 ? i think i don't know . srry if im wrong

Step-by-step explanation:

The solution set of given system of inequalities is the intersection region (purple colored region)

The correct graph is given by an option (D)

In this question, we have been given  the system of inequalities.

y ≤ -5x + 4

y ≥ 6x + 3

We need to solve the system of inequalities by graphing.

Consider the graph of given system of inequalities as shown below.

An inequality y ≤ -5x + 4 is represented by a region colored red and the inequality y ≥ 6x + 3 represented by a region colored blue.

The solution set for given inequalities is the set of all points which are common to both the inequalities.

This solution set is represented by purple color.

Therefore, the solution set of given system of inequalities is the intersection region (purple colored region)

The correct graph is given by an option (D)

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The rate of change of area as calculated from the data given is 1934.24 cm^2 / min.

A = A(r)

r = r(t)

A = A(r(t))

Using chain rule to solve this problem we get ,

rate of change of area as ,

dA/dt = (dA/dr)(dr/dt)

A = πr2

⇒ dA/dr = 2πr

dr/dt = 7 cm/min  [given]

(dA/dt) = (2πr)(7 cm/min)

When r = 44 cm,

dA/dt

= 2π (44 cm) (7 cm/min)

≅ 1934.24 cm^2/min.

The chain rule is the formula used to determine the derivative of a composite function, such as cos 2x, log 2x, etc. Another name for it is the composite function rule. Only composite functions are subject to the chain rule.

Therefore, before beginning the chain rule formula, let's examine what a composite function is and how it may be distinguished.

Another chain rule formula looks like this:

(f(g(x)) = f' (g(x)) g') = y' = d/dx (x)

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Answer:

50/100 X 70 = 35

Andie needs to do 5 more jumps.

The volume of a pyramid is 2.4 cm^3.

Let's begin by finding the area of the square base. Since the perimeter of the base is 4.7 cm, the length of one side of the square is 4.7 cm / 4 = 1.175 cm. The area of the square base is then

Area = (side length)^2 = (1.175 cm)^2 = 1.38 cm^2

Now, we can use the formula for the volume of a pyramid

Volume = (1/3) x Base Area x Height

Substituting the values we found, we get

Volume = (1/3) x 1.38 cm^2 x 4.7 cm

Volume = 2.3974 cm^3

Rounding to the nearest tenth of a cubic centimeter, the volume of the pyramid is approximately 2.4 cm^3.

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The given question is incomplete, the complete question is:

Find the volume of a pyramid with a square base, where the perimeter of the base is

4.7 cm and the height of the pyramid is 4.7 cm. Round your answer to the nearest tenth of a cubic centimeter