Right Angle Trig Including Problem Solving Question 4.1.

What's the X1 value and X2?

The measure of <YZX is 55.2 degree.

The area of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).

Given:

XY= 12.4 cm, YZ= 15.1 cm

In right ΔXYZ with hypotenuse XZ and opposite side XY to ∠YZX then

Using the sine ratio

sin <YZX= 12.4/ 15.1

sin <YZX = 0.8211

<YZX= 55.2

Hence, the measure of <YZX is 55.2 degree

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Answer: 55.2

Step-by-step explanation: just took it

Answer:

x = 2, y = -1/3

Step-by-step explanation:

I'm pretty sure the question is asking for the values of x and y. By finding these values you will need to use elimination.

Equations given:

5x + 3y = 9

2x - 3y = 5

To find x:

5x + 3y + 2x - 3y = 9 + 5  (add to eliminate y to solve for x)

7x = 14

x = 2

To find y:

5(2) + 3y = 9

10 + 3y = 9

3y = -1

y = -1/3

Therefore, x = 2 and y = -1/3

Answer: 180 ft^3

Step-by-step explanation:

Answer: 180 ft is the answer

Step-by-step explanation:

After calculations, it is determined that the required spacing of the closed stirrups is approximately 6 inches.

To determine the required spacing of closed stirrups for the given beam, we need to consider the factored shear and factored torsional moment. The formula for calculating the spacing of closed stirrups is given by:

s = (0.75√(f'c) / fy) * (Av / (bd - 2s))

where:

s = spacing of stirrups

f'c = specified compressive strength of concrete

fy = specified yield strength of steel reinforcement

Av = area of one closed stirrup

b = width of the beam

d = effective depth of the beam

Given information:

Width (b) = 15 in.

Effective depth (d) = 26.5 in.

Factored shear = 80 kips

Factored torsional moment = 50 ft-kips

Stirrup centroid from concrete face = 1.75 in.

No. 4 (no. 13) closed stirrup size = 0.2 square inches

First, we need to calculate the area of one closed stirrup:

Av = (No. of stirrups) * (Area of one stirrup)

Av = (2) * (0.2 square inches)

Av = 0.4 square inches

Next, we can substitute the values into the formula to calculate the spacing (s):

s = (0.75√(f'c) / fy) * (Av / (bd - 2s))

Assuming f'c = 4 ksi (common value for concrete strength) and fy = 60 ksi (common value for steel reinforcement strength), we can calculate:

s = (0.75√(4) / 60) * (0.4 / (15 * 26.5 - 2s))

Simplifying the equation, we get:

s = 0.0986 / (397.5 - 30s)

To solve for s, we can use an iterative approach or trial and error method. By substituting different values of s into the equation, we can find the spacing that satisfies the equation.

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Answer:

The prime factorization of 32 in exponential form is

\(2^5\)

Step-by-step explanation:

The prime factorization of 32 is,

32/2 = 16,

16/2 = 8,

8/2 = 4,

4/2 = 2,

2/2 = 1,

So, we get, 2*2*2*2*2

In exponential form, we get, 2*2*2*2*2 = 2^5

\(2^5\)

The two numbers that satisfy both equations are r = 2.125 and s = -12.

The two numbers can be represented as variables, let's say "r" and "s." We have two equations to solve for these variables:

8r + (1/4)s = 11

4r + (1/8)s = 7

To solve this system of equations, we can use the method of substitution or elimination. Let's use the method of elimination to eliminate the variable "s."

We can multiply the first equation by 2 to eliminate the fractions:

16r + (1/2)s = 22

Now we can subtract the second equation from this new equation:

16r + (1/2)s - (4r + (1/8)s) = 22 - 7

12r + (7/8)s = 15

Multiplying the second equation by 8 to eliminate the fractions:

32r + s = 56

Now we have a new system of equations:

12r + (7/8)s = 15

32r + s = 56

We can solve this system using various methods like substitution or elimination. Let's solve it using the substitution method.

From the second equation, we can express s in terms of r as s = 56 - 32r. Substituting this value in the first equation, we have:

12r + (7/8)(56 - 32r) = 15

Simplifying the equation, we get:

12r + 49 - 28r = 15

-16r = -34

r = 2.125

Now, substituting the value of r back into the equation s = 56 - 32r, we get:

s = 56 - 32(2.125)

s = 56 - 68

s = -12

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Answer:

3cm approx

Step-by-step explanation:

Given data

Volume=  72cm^3

Radius=3cm

Required the height

The expression for the volume is

Volume= πr^2h

substitute

72=3.142*3^2*h

72=28.278h

h= 72/28.278

h=2.54

Hence the height is 3cm approx

Answer:15

Step-by-step explanation: 1st multiple what’s in the parenthesis (3*3= 9 & 4*4= 16

Next write it out 22+(9-16)

Then you subtract 9 from 16 since it’s in parenthesis So it’s 22+(-7) and since you are adding a negative and a positive together you will have to subtract and keep the sign of the larger number so the answer is 15 since u needed to subtract but 22 is the larger number making it positive answer

Answer:

12/8 or 1 1/2 hope this helps

Answer:

I think answer is. Tap in photo

The probability that tails appears on the next toss is 0.5

Given,

In the question:

If I toss a fair coin five times and the outcomes are TTTTT,

To find the probability that tails appears on the next toss is.

Now, According to the question:

The possible ordered outcomes are listed as elements in a sample space, which is commonly indicated using set notation.

A sequence of five fair coin flips has a sample space that contains all potential outcomes. \(2^3\) {H, T}  is the sample of a fair coin toss. {HHHHH, HHHHT, HHHTH, HHTHH, HTHHH,...…TTTTT} .

The probability of a tails result on the next flip is always equal to 0.5 It makes no difference if previous outcomes were {TTTTT} , {HHHHH}  or {THTHT} In each of these and all other circumstances, the probability of the next being tails is still 0.5

Hence,  the probability that tails appears on the next toss is 0.5

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Answer:

-1/2

Step-by-step explanation:

cos (4π/3)= cos (π+π/3)

Answer:

Step-by-step explanation:

\(cos (\frac{4 \pi }{3} )=cos (\pi +\frac{\pi }{3} )=-cos (\frac{\pi }{3} )=-\frac{1}{2}\)

To find the slope of the tangent to the curve 1/x + 1/y = 1 at the point (2, 2).

We need to differentiate the equation implicitly with respect to x and then evaluate it at the given point.

Step 1: Start with the given equation: 1/x + 1/y = 1.

Step 2: Differentiate both sides of the equation implicitly with respect to x.

Differentiating 1/x with respect to x gives -1/x^2. Differentiating 1/y with respect to x gives (dy/dx) / y^2.

Step 3: Combine the derivatives and simplify the equation.

-1/x^2 + (dy/dx) / y^2 = 0.

Step 4: Solve the equation for dy/dx.

(dy/dx) / y^2 = 1/x^2.

dy/dx = y^2 / x^2.

Step 5: Substitute the coordinates of the given point (2, 2) into the equation dy/dx = y^2 / x^2.

dy/dx = (2^2) / (2^2).

dy/dx = 1.

The slope of the tangent to the curve 1/x + 1/y = 1 at the point (2, 2) is 1.

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Answer:

f(- 3) = 18

Step-by-step explanation:

Substitute x = - 3 into f(x) , that is

f(- 3) = 2(- 3)² = 2(9) = 18

Answer:

I answered this already in your last question, it is 6 1/6

Step-by-step explanation:

hope it helps

Answer:

option C is correct.

hope this answer helps you dear..... take care and may u have a great day ahead!

8n + 25 = 65

8n = 65 - 25

8n = 40

8n/ 8 =40/8

n = 5..

firstly I made 8n the subject of the formula by taking 25 to the other side which gives u 8n = 65 - 25and the reason why the sign changed chnged os because when send a number to the other side the sign changes and then i divided both sides by 8

Given that the household is located in the northeast, there is a 0.230 probability that the randomly chosen US household makes more than $75,000.

Given info;

19.1% of US households, according to the US Census Bureau, are in the Northeast. Additionally, 4.4% of households in the US earn $75,000 or more annually and are situated in the northeast.

let, A represents the U.S. households in the Northeast.

     B represents the U.S. households earning $75,000 or more.

To determine the probability that a randomly selected US household earns more than $75,000/year, given that the household is located in the northeast.

P(A) = 19.1% = 0.191

P(A ∩ B) = 4.4% = 0.044

P(B I A) = P(A ∩ B) / P(A)

            = 0.044 / 0.191

            = 0.230

Hence, the probability that a randomly selected US household earns more than $75,000/year, given that the household is located in the northeast is 0.230.

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If the standard deviation of a set of data is 6, then the value of variance is 36

The formula for determining variance is variance = √Standard deviation

Variance of a set of data is equal to square of the standard deviation.

If the standard deviation of a set of data is 6 then we get variance by putting the value of standard deviation in the formula

variance = √Standard deviation

Take square root on both sides

Standard deviation² = 6²

Standard deviation= 36

Hence,  standard deviation of a set of data is 6, then the value of variance is 36

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The width of the concrete path is 0.65 m.

The width of the concrete path is calculated as follows;

let the width of the concrete path = x

The dimensions of the shed with the path around it is determined as;

2x + 4  by 2x + 2

The equation for the area of this path becomes;

(2x + 4)(2x + 2)  - (4 x 2) = 9.5

4x² + 4x + 8x + 8 - 8 = 9.5

4x² + 12x = 9.5

4x² + 12x - 9.5 = 0

solve the quadratic equation using formula method;

a = 4, b = 12, and c = -9.5.

The solution becomes, x = 0.65 m or - 3.65

We will take the positive dimension, x = 0.65 m

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Answer:

A system of linear equations has one solution when the graphs intersect at a point. No solution. A system of linear equations has no solution when the graphs are parallel. Infinite solutions.

Step-by-step explanation:

Answer:

Solution given:

volume of pyramid =⅓area of base×height

=⅓*1*1*1=⅓=0.33yd³

the volume of the pyramid

0.33yd³

The surface area of the right prism with right triangular bases and height of 15 inches is bh + 15(a + b + c).

It can be found by adding the area of the two triangular bases and the area of the three rectangular faces:

Surface area = 2(Area of base triangle) + (Perimeter of base triangle x height of prism)

To find the area of the base triangle, we can use the formula A = 1/2bh, where b is the base of the triangle and h is its height. The perimeter of the triangle is simply the sum of its three sides.

So, if we let the base of the triangle be b, and the height of the triangle be h, then the area of the base triangle is A = 1/2bh. The perimeter of the triangle is P = a + b + c, where a, b, and c are the lengths of its sides.

Thus, the surface area of the prism is given by:

Surface area = 2(1/2bh) + (a + b + c) x 15

Simplifying the expression gives us the final answer:

Surface area = bh + 15(a + b + c)

Therefore, the surface area of the right prism with right triangular bases and height of 15 inches is bh + 15(a + b + c).

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Answer:

Let the inverse of f(x) be h(x):

\({ \tt{h(x) = \frac{1}{4x} }}\)

To find the minimum score required for an A grade, we need to determine the cutoff point that corresponds to the top 13% of scores.

Given that the scores on the test are normally distributed with a mean of 69.5 and a standard deviation of 9.5, we can use the standard normal distribution to calculate the cutoff point. Using a standard normal distribution table or a statistical calculator, we find that the z-score corresponding to the top 13% is approximately 1.04. To find the corresponding raw score, we can use the formula:

x = μ + (z * σ)

where x is the raw score, μ is the mean, z is the z-score, and σ is the standard deviation. Plugging in the values, we have:

x = 69.5 + (1.04 * 9.5) ≈ 79.58

Rounding this to the nearest whole number, the minimum score required for an A grade would be 80. Therefore, a student would need to score at least 80 on the test to achieve an A grade according to the professor's grading scheme.

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Answer:

34

Step-by-step explanation:

Substitute the values.

s = 3 and t = -2

8s-5t

8 (3) - 5(-2)

( 8 x 3 ) - ( 5 x -2 )

24 + 10 [ - x - = + ]

= 34

Answer:

Possible answers could be that you have 400 adults and no children, or you could have 100 children and 340 adults.

Step 1

State the for the sales tax rate

where

Step 2

Get the sales tax rate in percentage by substitution

Answer:

Hope you understand it ^^.

Answer: \(\sqrt{\frac{1-(-15/17)}{2}}\)

Step-by-step explanation:

Note that \(180^{\circ} < \theta < 270^{\circ} \implies 90^{\circ} < \frac{\theta}{2} < 135^{\circ} \implies \sin \frac{\theta}{2} > 0\).

Using the half-angle formula \(\sin \frac{\theta}{2}=\sqrt{\frac{1-\cos \theta}{2}}\),

\(\sin \frac{\theta}{2}=\sqrt{\frac{1-(-15/17)}{2}}=\frac{4\sqrt{17}}{17}\)

Emerson actually hit the ball 32% of the times at bat.

Since in Game 1, Emerson struck out 30 times in 90 times at bat, and in Game 2, he struck out 40 times in 120 times at bat, and in Game 3, Emerson struck out 42 times in 140 times at bat, to determine the percentage of times at bat did Emerson actually hit the ball, the following calculations should be performed:

Therefore, Emerson actually hit the ball 32% of the times at bat.

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No, the probability be found by using the binomial probability formula with x counting the number who are left-handed. The correct option is (c) No, because the 100 adults were selected without replacement, the selections are dependent.

The binomial distribution assumes that the trials are independent, meaning that the outcome of one trial does not affect the outcome of any other trial. However, in this case, the 100 adults were selected without replacement, which means that the outcome of one selection affects the probability of the next selection. Therefore, the trials are dependent, and the binomial probability formula cannot be used.

Instead, we can use the hypergeometric distribution to calculate the probability of at least 30 left-handed adults in a sample of 100 adults selected without replacement from the U.S. population. The hypergeometric distribution takes into account the fact that the selections are dependent and is appropriate for this type of problem.

Therefore, the correct option is (c) No, because the 100 adults were selected without replacement, the selections are dependent.

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