Let csc(x) = five-thirds, where 0° < x < 90°. which expression has a value of three-fourths?
a. sec(x)
b. cos(x)
c. cot(x)
d. tan(x)

The speed of the person located at earth's equator traveling due to rotation is, 1670 km/hr.

The person at equator traveling due to it's rotation will cover one complete round of earth in 24 hours. Hence the distance travelled is the circumference of the earth.

The radius of the earth is, 6 378.1 kilometers.

The circumference can be calculated as, 2×π×R

Using R = 6 378.1 kilometers,

Circumference = 2×π×6 378.1 kilometers

Circumference = 40090.91 kilometers.

The distance traveled = 40090.91 kilometers.

Time taken is 24 hrs.

Hence speed = distance/time

Speed = 40090.91/24

Speed = 1670 km/hr

The speed of the person is 1670 km/hr.

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The correct option is cone and plane. A conic section is the intersection of a plane and a cone. The best definition of a conic section is "cone and plane".

The definition of conic section is a conic section is a shape that is formed when a right circular cone intersects a plane. Depending on the angle of the plane concerning the center line of the cone, the conic sections are classified into four types. They are a circle, parabola, ellipse, and hyperbola. Each type of conic section has a unique shape and properties.

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The absolute value of a number expression 3.1 + (-6.3) is 3.2 the answer is 3.2.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

It is given that:

The number expression is:

= 3.1 + (-6.3)

To find the absolute value of 3.1 + (-6.3):

= |3.1 + (-6.3)|

= |3.1 - 6.3|

= |-3.2|

= 3.2

Thus, the absolute value of a number expression 3.1 + (-6.3) is 3.2 the answer is 3.2.

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The given equations are as follows

\(\begin{aligned} A.&&\dfrac x4+1&=-3 \\\\ B.&&x+4&=-12 \end{aligned}\)

(1) First, multiply both sides of equation A by 4, we have

\(4\times\left(\frac{x}{4} +1\right)=4\times(-3)\)

Then, rewrite the left-hand side of the above equation by using the distributive property, we have

\(4\times\frac{x}{4}+4\times1=4(-3)\)

\(\Rightarrow x+4=-12\)

This is the required equation B.

In this way, first use choice D: Multiply both sides by the same non-zero constant, i.e 4.

Then, apply choice A to solve the equation, i.e using the distributive property to solve the left-hand side of the equation.

(2) In the previous answer, equation B has been derived from equation A, hence, both the equations are equivalent.

As both the equations are the same, so both will have the same solution.

Yes, they have the same solution.

Answer:

p= 20

Step-by-step explanation:

360 - 145 -75 = 7p

140 =7p

140 ÷7 =7p ÷7

20 = p

Answer:

p= 20°

Step-by-step explanation:

here's your solution

==> Angle formed around a point = 360°

==> 145° + 75° + 7p° = 360°

==> 220° + 7p° = 360°

==> 7p° = 360° - 220°

==> 7p° = 140°

==> p = 140°/7

==> p= 20°

\(hope \: it \: helps\)

Answer:

negative 70 (-70)

Step-by-step explanation:

below sea level, so below zero, would be -70

Answer:

-70

Step-by-step explanation:

Its below it would be in the negatives

Answer:

(-2, 3)

Step-by-step explanation:

The +5 represents shifting 5 units up, so we can add 5 to the y coordinate.

This gives us (-2, -2+5)=(-2, 3)

Answer:

a) 803.84 square feet

Step-by-step explanation:

\(\sf{area~of~circle~=~\pi r^{2} }\\\sf{radius~ =~half~of~diameter}\)

so 32 / 2 = 16 = radius

\(\sf{radius^{2} = 16^{2}=256}\)

256 x 3.14 (because we are taking π as 3.14)

= 803.84

Hope this helps! If you need any further explanation, let me know!

- profparis

The sample mean of the weight of the loaves in the bakery is 797.3 grams.

Given data:Number of loaves of bread = 10Weights of loaves in grams = {790, 680, 900, 855, 745, 740, 874, 903, 876, 800}

Mean or average weight of the loaves in the bakery can be calculated using the formula;

Mean = (Sum of weights of all loaves) / Number of loavesTherefore,Mean = (790 + 680 + 900 + 855 + 745 + 740 + 874 + 903 + 876 + 800) / 10 = 797.3

So, the sample mean of the weight of the loaves in the bakery is 797.3 grams.

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The probability of more than 18% of a sample of 40 employees at a large biotech firm working from home is 0.2628 or 26.28%.

To calculate the probability, we can use the normal distribution and the z-score formula: z =\((x - μ) / (σ / sqrt(n))\) where x is the sample proportion (in decimal form),\(μ\) is the population proportion (in decimal form), \(σ\) is the population standard deviation (in decimal form), and n is the sample size.

Given that, 19% of the employees at the biotech firm are working from home, we can assume that the population proportion is 0.19. The population standard deviation is not given, so we can use the formula:    \(σ = sqrt(p(1-p))\) where p is the population proportion. Plugging in the values, we get: \(σ = sqrt(0.19(1-0.19)) = 0.3929\) Now, we can plug in the values to find the z-score: z = (0.18 - 0.19) / (0.3929 / sqrt(40)) = -0.7606

Using a z-table, we can find the probability that a z-score is less than -0.7606, which is 0.2234. To find the probability that more than 18% of the sample is working from home, we subtract this probability from 1:   P(x > 0.18) = 1 - P(x <= 0.18) = 1 - 0.2234 = 0.7766.

Hence, the probability of more than 18% of a sample of 40 employees at the biotech firm working from home is 0.7766 or 77.66%.

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Using the given function, it is found that:

The profit when n students are enrolled in the class is given by:

f(n) = 70n - 400.

A profit is made when f(n) > 0, hence:

70n - 400 > 0

70n > 400

n > 5.71.

6 students need to be enrolled for the instructor to make a profit.

A profit of $1,000 is made when f(n) = 1000, hence:

70n - 400 = 1000

70n = 1400.

n = 20.

20 students must be enrolled for the instructor to make a profit of $1,000 a month.

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Atleast 6 students must be enrolled to make a profit and 20 student are needed to make $1,000.00 profit per month.

An equation is an expression that shows the relationship between two or more variables and numbers.

Given the function:

f(n) = 70n - 400

To make a profit, f(n) > 0, hence:

70n - 400 > 0

n > 6

For a profit of $1000:

70n - 400 = 1000

n= 20

Atleast 6 students must be enrolled to make a profit and 20 student are needed to make $1,000.00 profit per month.

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Answer:

b: 8

Step-by-step explanation:

with dilating by 2, the B' figure would be bigger than B

because 4*2 = 8

Answer:

Area= 56 cm²

Step-by-step explanation:

Figure given is a rhombus

Area= 1/2*d1*d2

Answer:

The distance between C and D is 4.2768 inches.

Step-by-step explanation:

As from A to B the distance is 5.625 inches and actual is 1688 miles

so,

1 mile = 5.625/1688 = 0.0033 inches

So, the distance between C and D is 1296 miles

= 1296 x 0.0033 inches = 4.2768 inches  

Answer:

The length of CD is

"The Right Triangle Altitude Theorem says that the product of AD times DB must equal the length of \(CD^{2}\). Since 4 * 6 = 24, CD must be \(\sqrt{24}\).

\(AC^{2} = AD^{2} + CD^{2}\)

\(AC^{2} = 40\)

\(AC = \sqrt{40} = 2\sqrt{10}\)

The uniform continuous probability for the interval (25 < x < 45) within the uniform distribution U(15, 65) can be found by calculating the proportion of the total range that falls within that interval.

To calculate the probability, we need to determine the length of the interval (45 - 25) and divide it by the length of the entire range (65 - 15).

Length of the interval: 45 - 25 = 20

Length of the entire range: 65 - 15 = 50

Now, we divide the length of the interval by the length of the entire range to obtain the probability:

Probability = (Length of interval) / (Length of entire range) = 20 / 50 = 0.4

Therefore, the uniform continuous probability for p(25 < x < 45) within the uniform distribution U(15, 65) is 0.4, rounded to one decimal place.

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The statement many quantitative models of decision making are based on comparing a single measure of effectiveness, generally some form of utility to the decision maker is true. So, the correct optio is option a. true.

Many quantitative models of decision theory, such as Expected Utility Theory and also                                             Multi-Attribute Utility Theory, involve comparing a single measure of effectiveness, typically some form of utility, to the decision maker. This allows for the evaluation and comparison of different options based on their expected outcomes and potential risks.

It helps the decision maker determine the best course of action.

Decision theory is a branch of probability. It is concerned with analytic philosophy. It deals with the decision making processes based on probabilities depending on the various factors and the numerical consequences of the outcome.

Therefore, the statement about the decision theory based on comparing a single measure of effectiveness is true.

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The solution of equation is x=-3

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Given

The equation;√x+3=-6

Now,

√x=-6-3

√x=-9

x=-3

Therefore the answer of the given equation will be -3

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Answer:

\( {x}^{2} + 2x + 2 = 0 \: no \: solution \\x + 5 = 0 - \: \: \: \: \: x = - 5 \\ sox = - 5 \)

\(7\frac{1}{2}\implies 7.5\hspace{5em}1\frac{1}{4}\implies 1.25 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{ \textit{Monday through Friday} }{\stackrel{ days }{(5)}\stackrel{ rate }{(10.80)}\stackrel{ hours }{(7.5)}}~~ + ~~\stackrel{ Saturday }{\stackrel{ days }{(1)}\stackrel{ rate }{(10.80)(1.25)}\stackrel{ hours }{(7.5)}} \\\\\\ 405~~ + ~~101.25\implies \text{\LARGE 506.25}\)

The two (2) possible locations of point F include the following: F. [7, 9.5].

In this scenario, line ratio would be used to determine the coordinates of the point on the directed line segment that partitions the segment into a ratio of 5 to 3.

Mathematically, line ratio can be used to determine the coordinates of F and this is modeled by this mathematical expression:

F(x, y) = [(mx₂ + nx₁)/(m + n)],  [(my₂ + ny₁)/(m + n)]

Given the following parameters:

Point (x, y)= (4, 11)

Point (x, y) = (8, 9)

m:n = 3:1

Substituting the given parameters into the line ratio formula, we have;

F(x, y) = [(mx₂ + nx₁)/(m + n)],  [(my₂ + ny₁)/(m + n)]

F(x, y) = [(3(8) + 1(4))/(3 + 1)],  [(3(9) + 1(11))/(3 + 1)]

F(x, y) = [(24 + 4)/(3 + 1)],  [(27 + 11)/(3 + 1)]

F(x, y) = [(28)/(4)],  [(38)/(4)]

F(x, y) = [7, 9.5]

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Multiply the first equation by 4:

Subtract the second equation:

This is:

Simplify:

Substitute y = 1 in the first equation:

Ans solve for x:

Answer:

x = 3

y = 1

The proportion of a normal distribution located between z = .50 and z = -.50 will be 38.2%.

We have,

A normal distribution located between z = 0.50 and z = -0.50,

So,

Now,

From the Z-score table,

We get,

The Probability corresponding to the Z score of -0.50,

i.e.

P(-0.50 < X < 0) = 0.191,

And,

The Probability corresponding to the Z score of -0.50,

i.e.

P(0 < X < 0.50) = 0.191,

Now,

The proportion of a normal distribution,

i.e.

P(Z₁ < X < Z₂) = P(Z₁ < X < 0) + P(0 < X < Z₂)

Now,

Putting values,

i.e.

P(-0.50 < X < 0.50) = P(-0.50 < X < 0) + P(0 < X < 0.50)

Now,

Again putting values,

We get,

P(-0.50 < X < 0.50) = 0.191 + 0.191

On solving we get,

P(-0.50 < X < 0.50) = 0.382

So,

We can write as,

P(-0.50 < X < 0.50) = 38.2%

So,

The proportion of a normal distribution is 38.2%.

Hence we can say that the proportion of a normal distribution located between z = .50 and z = -.50 will be 38.2%.

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The dimensions of a rectangle with area 1728 square meter whose perimeter is as small(minimum) as possible are 41.57m and 41.56m.

Let the dimension of the rectangle be x and y m.

According to the given question.

The area of the rectangle is 1728 square meter.

⇒ x × y = 1728

⇒ x = 1728/y

Since, the perimeter of the rectangle is the sum of the length of its boundary.

Therefore,

Perimeter of the recatngle with dimensions x and y is given by

Perimeter of the rectangle, P = 2(x + y)

⇒ P = 2(1728/y + y)

⇒ P = 3456/y + 2y

Differentiate the above equation with respect to y

⇒ \(P^{'} = -\frac{3456}{y^{2} } + 2\)

For the minimum(small) perimeter equate the above equation to 0.

⇒ \(-\frac{3456}{y^{2} } + 2 = 0\)

⇒ \(2y^{2} =3456\)

⇒ \(y^{2} = \frac{3456}{2}\)

⇒ y^2 = 1728

⇒ y = √1728

⇒ y = 41.56 m

Therefore,

x = 1728/41.56

⇒ x = 41.57 m

Hence, the dimensions of a rectangle with area 1728 square meter whose perimeter is as small(minimum) as possible are 41.57m and 41.56m.

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For the given functions, (f - g)(x) = f(x) - g(x) = -x² + x + 42. The correct option is B.

To find (f - g)(x), we need to subtract the function g(x) from f(x).

f(x) = 49 - x²

g(x) = 7 - x

Substituting these values, we have:

(f - g)(x) = f(x) - g(x)

           = (49 - x²) - (7 - x)

           = 49 - x² - 7 + x

           = -x² + x + 42

Therefore, the answer is option B: -x² + x + 42.

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The probability values are calculated and listed below

They are both black

Here, we have

Black = 3

Yellow = 5

Sice the balls are not replaced, we have

P(Both black) = 3/8 * 2/7

P(Both black) = 3/28

They are both yellow

Sice the balls are not replaced, we have

P(Both Yellow) = 5/8 * 4/7

P(Both Yellow) = 5/14

The first is yellow and the second is black

Sice the balls are not replaced, we have

P(Yellow and black) = 5/8 * 2/7

P(Both Yellow) = 5/28

One is yellow the other is black

Sice the balls are not replaced, we have

P(One Yellow and One black) = 5/8 * 2/7 * 2

P(One Yellow and One black) = 5/14

They are of the same colour​

Here, we have

P(Same) = 3/28 + 5/14

P(Same) = 13/28

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The equivalent to the product of the expression √(x + 3 ) × √(x - 3 ) is √(  x² - 9  ).

Given the expression in the question;

√(x + 3 ) × √(x - 3 )

To multiply, we use combine using the product rule for radicals.

If two terms are contained in radicals, you can combine them under the same radical symbol if the index is the same.

Hence;

√(x + 3 ) × √(x - 3 ) = √( x + 3)( x - 3 )

Next. we expand the bracket using FOIL method.

√( x + 3)( x - 3 )

√(  x( x - 3 ) + 3( x - 3 ) )

√(  x² - 3x + 3x - 9  )

Simplify

Add -3x and 3x

√(  x² - 9  )

Therefore, the equivalent expression is √(  x² - 9  ).

Option A) √(  x² - 9  ) is the correct answer.

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