1/3 divided by 3 1/2

All sides of a rhombus have equal measures, so TU = 8. Since a rhombus is a parallelogram, and the diagonals of a parallelogram bisect each other, WU = 10. The diagonals of a rhombus are also perpendicular, meaning they form right angles. Using the Pythagorean theorem, you can find the length of TX. (TX)^2 + (WX)^2 = (WT)^2. Substituting in known values, (TX)^2 + 25 = 64. Solving gives you TX = the square root of 39. TV is double the length of TX, so TV = 2 times the square root of 39.

The probability that a student is a female or major in civil engineering is 62%

At a certain college, 49% of the students are female, and 21% of the students major in civil engineering. Furthermore, 8% of the students both are female and major in civil engineering. What is the probability that a randomly selected female student majors in civil engineering?

Let A represent Female and B represents civil engineering.

The above representation means that the given parameters are:

The required probability is calculated as:

P(A or B) = P(A) + P(B) - P(A and B)

This gives

P(A or B) = 49% + 21% - 8%

Evaluate

P(A or B) = 62%

Hence, the probability that a student is a female or major in civil engineering is 62%

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Answer:

Go here

Step-by-step explanation:

https://brainly.com/question/19678086#:~:text=Step%2Dby%2Dstep%20explanation%3A&text=thats%201%20year.,thats%202%20years.

Answer:

4 years

Step-by-step explanation:

9% of 20,000 is 1,800. So, if you keep subtracting 1,800 from 20,000, it will take 4 times until you get to 12,800, which is as close as you can get to 13,000 in this scenario.

The equation to model the total cost, c, in dollars, of a hamburger with t additional toppings on Mondays is c = 3 + 0.50t.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.

Let the additional topping = t

Therefore, the cost will be expressed as:

c = 1/2(6) + (0.50 × t)

c = 1/2(6) + 0.50t

c = 3 + 0.50t

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The triangle for which angle a =30\degree, angle b=45\degree, and a=20, side a ≈ 20, side b ≈ 28.284, and side c ≈ 38.636

Two angles (a and b) and one side (a) are provided for us to solve the triangle. Let's call the side across from angle a side A, the side across from angle b side B, and the side across from the final angle (angle c) side C.

Here, it is given that,

angle a = 30 degrees

angle b = 45 degrees

side a = 20

angle c = 180 - (angle a + angle b)

angle c = 180 - (30 + 45)

angle c = 180 - 75

angle c = 105 degrees

We know that, a/sin(A) = b/sin(B) = c/sin(C)

a/sin(A) = b/sin(B) = c/sin(C)

20/sin(30) = b/sin(45) = c/sin(105)

b/sin(45) = 20/sin(30)

b = (sin(45) * 20) / sin(30)

b ≈ (0.7071 * 20) / 0.5

b ≈ 14.142 / 0.5

b ≈ 28.284

Now,

c/sin(105) = 20/sin(30)

c = (sin(105) * 20) / sin(30)

c ≈ (0.9659 * 20) / 0.5

c ≈ 19.318 / 0.5

c ≈ 38.636

Thus, side a ≈ 20, side b ≈ 28.284, and side c ≈ 38.636.

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likelihood that the difference between the two sample proportions is smaller than 3 percentage points

To calculate the probability that two sample proportions are less than 3 percentage points apart, we need to use the sampling distribution of the difference between two sample proportions. Let p1 be the true population proportion for one group, and p2 be the true population proportion for another group. The standard deviation of the difference between two sample proportions can be calculated as:

√((p1 × (1-p1))/n1) + ((p2 × (1-p2))/n2)

where n1 and n2 are the sample sizes for the two groups. Since we do not know the true population proportions, we will use the sample proportions from the first sample as estimates. Let p1 be the sample proportion from the first sample, and p2 be the sample proportion from the second sample. Then, the standard deviation of the difference between the two sample proportions can be estimated as:

√((p1 × (1-p1))/n1) + ((p2 × (1-p2))/n2)

We are given that n1 = n2 = 500. Let's assume that p1 = p2 = p, where p is the sample proportion from the first sample. Then, the standard deviation of the difference between the two sample proportions can be estimated as:

√((p(1-p))/500) + ((p(1-p))/500)

= √(2p(1-p))/500

= √(p(1-p)/250)

Now, we want to find the probability that the two sample proportions are less than 3 percentage points apart, which means that the absolute value of the difference between the two sample proportions is less than 0.03.

|p1 - p2| < 0.03

|p1 - p| - |p2 - p| < 0.03

Since p1 - p2 = 0, we can simplify this to:

|p - p2| < 0.015

Using the standard normal distribution, we can calculate the probability that the standardized difference between p and p2 is less than 0.015:

P(|p - p2|/√(p(1-p)/250)] < 0.015/√(p(1-p)/250)

This is equivalent to finding the area under the standard normal distribution curve to the left and right of z = 0.015/√(p(1-p)/250).

However, we do not know the value of p, so we need to consider the worst-case scenario. The maximum value of p(1-p) occurs when p = 0.5, so we can use this value to get the most conservative estimate of the probability.

Using p = 0.5, we get:

P(|p - p2|/√(p(1-p)/250)] < 0.015/√(0.5 × (1-0.5)/250)

= P(|p - p2|/0.0346 < 0.015)

Using a standard normal distribution table or calculator, we can find that the probability that a standard normal variable is less than 0.015 is approximately 0.556.

Therefore, the probability that the two sample proportions are less than 3 percentage points.

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The resultant force acting on the block is 47.6N.

The acceleration of the block will be 23.8 m/s².

The speed of the block after 5 seconds of movement is 119 m/s.

In this question, we need to make use of Newton's second law, hence:

resultant force = mass × acceleration

So, for question a. The value of the resultant force  will be obtained by adding the two forces together:

resultant force = F₁ + F₂

                       = 25N + 22.6N

                        = 47.6N

b.  Its acceleration will be:

acceleration = resultant force / mass

                  = 47.6N / 2kg

                  = 23.8 m/s²

c. The speed of the block after 5 seconds of movement will be:

Velocity  (v) = u + at

velocity = initial velocity + acceleration x time

Based on the block was initially at rest, the initial velocity is 0.

Hence:

V = acceleration x time

    = 23.8 m/s² x 5s

     = 119 m/s

Hence the speed of the block after 5 seconds of movement will be: 119 m/s.

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See full text below

The block in the figure is at rest when the forces begin to act.

F₁ = 25N

F, = 22.6 N

m = 2kg

to. Find the value of the resultant force.

b. Determine its acceleration.

C. Calculate the speed of the block after 5 seconds of movement.

Answer:

D)

Step-by-step explanation:

supplementary angles are straight lines equal to 180 degreea

Answer:

(x - 4)^2 + (y + 3)^2 = 25.

Step-by-step explanation:

The standard form is (x - j)^2 + (y - k)^2 = r^2.

Answer:

A. B. C. D.

Step-by-step explanation:

You can find the angles of all of those easily just from angle 1, but for angle 5 and 6 you can't

to find angle one it's obviously what it says

to find 2 and 4 you do 180-whatever angle one is

to find angle 3 it's the exact same of angle one because they are like opposite or whatever.

Using the probability concept, it is found that there is a 0.97555 = 97.555% probability that client A lives to be 30 years old.

A probability is the number of desired outcomes divided by the number of total outcomes, that is:

\(p = \frac{D}{T}\)

In this problem:

Then:

\(p = \frac{D}{T} = \frac{97555}{100000} = 0.97555\)

There is a 0.97555 = 97.555% probability that client A lives to be 30 years old.

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Answer: The answer is 0.97424

Step-by-step explanation: The other answer... the math is correct, its just that they have read the source table incorrectly.

Age

29-30 = 97,555

30-31 = 97,424

The correct row is 30-31.

97,424 / 100,000 = 0.97424

You can tell this is the case because look at row 0-1.. its a 100% chance of survival. If you read that row as a '1 year old' then 100% of all people survive until they turn 1? Alas, no, this is not true :(

Answer:

10

Step-by-step explanation:

20/2=10

Answer:

sinθ = -5/√61

secθ = √61/6

tanθ = -5/6

Step-by-step explanation:

From the given coordinate (6, -5), x = 6 and y = -5. This shows that the point lies in the 4th quadrant. In the fourth quadrant, only cos θ is positive, both sin θ and tan θ are negative.

Let us get the value of the radius 'r' first before calculating the trigonometry identities.

Using the Pythagoras theorem;

\(r^2 = x^2 + y^2\\r^2 = 6^2 + (-5)^2\\r^2 = 36+25\\r^2 = 61\\r = \sqrt{61}\)

Using SOH, CAH, TOA to get the trigonometry identities;

Given x = 6, y =5 and r = √61

\(sin \theta = opp/hyp = y/r\\sin \theta = 5/\sqrt{61} \\\)

Since sin θ, is negative in the fourth quadrant, \(sin \theta = -5/\sqrt{61} \\\)

\(cos \theta = adj/hyp = x/r\\cos \theta = 6/\sqrt{61} \\\)

\(sec \theta = \frac{1}{cos \theta} \\sec \theta = \frac{1}{6/\sqrt{61} } \\sec \theta = \frac{\sqrt{61} }{6}\)

For tanθ:

\(tan \theta = \frac{opp}{adj} = \frac{y}{x} \\tan \theta = \frac{5}{6}\\\)

Since tan θ, is negative in the fourth quadrant, \(tan \theta = -5/6\)

 \(SIN\Theta=\frac{-5}{\sqrt{61} }\),

\(SEC\Theta=\frac{\sqrt{61} }{6}\)  

\(TAN\Theta=\frac{-5}{6}\).

Given coordinate of point be (6, -5).

So the point lies in the 4th quadrant. In the fourth quadrant, only cos θ is positive, both sin θ and tan θ are negative.

Since (6, -5) is on the terminal side that puts us in the fourth quadrant. If we plot that point and draw a diagonal to it from the origin, we will be able to draw a right triangle with that diagonal as the hypotenuse.That means the adjacent side is 6 and opposite side it -5.

By Pythagorean theorem, we find that the hypotenuse

\(H=\sqrt{6^{2} +(-5)^{2} }\)

\(H=\sqrt{61}\)

We know from trigonometric ratios,

\(SIN\Theta=\frac{Perpendicular}{hypotenuse} \\\)

\(SIN\Theta=\frac{5}{\sqrt{61} }\)

Since \(SIN\Theta\) is negative in 4th quadrant,

so,

\(SIN\Theta=\frac{-5}{\sqrt{61} }\)

Similarly,

\(SEC\Theta=\frac{hypotenuse}{base}\)

\(SEC\Theta=\frac{\sqrt{61} }{6}\)

And,

\(TAN\Theta=\frac{perpendicular}{base}\)

\(TAN\Theta=\frac{-5}{6}\)

Hence,  \(SIN\Theta=\frac{-5}{\sqrt{61} }\), \(SEC\Theta=\frac{\sqrt{61} }{6}\)  and \(TAN\Theta=\frac{-5}{6}\).

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Answer:

Harry made 9 resolutions.

Step-by-step explanation:

Tim made x resolutions.

Harry made five more, x + 5.

Harry and Tim's together was 13.

x + x + 5 = 13

combine like terms.

2x + 5 = 13

subtract 5

2x = 8

divide by 2

x = 4

Tim made 4 resolutions.

Harry made 4 + 5, that is, 9 resolutions.

Check:

Harry and Tim together is 13.

4 + 9 = 13

Harry made 9 resolutions.

Answer:

7x + 10

Step-by-step explanation:

-3 + 7x + 13

(7x) + (-3 + 13)

7x + 10

Answer:25.45

Step-by-step explanation:

52936/1 year x 1 year/52 weeks x 1 week/40hours

The Correct answer is option b. The proportion of this population that lies at or below x=87 is 0.3085.

We can conclude that the proportion of this population that lies at or below x=87 is 0.6915 because the graph shows that the area under the curve to the left of x=87 is 0.3085. However, we cannot conclude that the proportion of this population that lies at or below x=87 is 0.3085 because this statement is contradictory to the information provided in the graph.

The area under the curve to the left of x=87 represents the proportion of the population that lies at or below x=87, so it cannot also be equal to the proportion of the population that lies at or above x=87.

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Answer:

√3/3

Step-by-step explanation:

To obtain Tan θ ;

From trigonometry, tan θ = sin θ / cosθ

Given the paired value : (√3/2, 1/2)

The (cosine, sine ) pair ;

Tan θ = sin (1/2) / cos (√3/2)

Tan θ = (1/2 ÷ √3 / 2) = 1 / 2 * 2 / √3 = 2 / 2√3 = 1 / √3

Tan θ = 1 / √3

Rationlaizing the denominator :

1/√3 * √3/ √3 = √3/√9 = √3/3

Answer:

an= -3+5(n-1)

Step-by-step explanation:

Try writing out the terms and finding a pattern. In this case, inserting any plotted x-value into the sequence -3+5(n-1) produces the correct y-value.

Answer:

A.) an = -3 + 5(n - 1)

Explanation:

Given: (1, -3), (2, 2), (3, 7), (4, 12), (5, 17)

Arithmetic Series: a + (n - 1)d

['a' is first term, 'n' determines term position, 'd' is common difference]

Determine the following:

Putting into equation:

Answer:

you have a 11/17 percent chance of getting an apple

Step-by-step explanation:

if there are 11 apples and 6 oranges. 11 out of 17 times you will get an apple

The ratio of girls to boys in the class is 3:7.

To calculate the ratio of girls to boys in the class, we need to determine the number of girls in the class.

Given that there are 50 students in total and 35 of them are boys, we can find the number of girls by subtracting the number of boys from the total number of students:

Number of girls = Total number of students - Number of boys

Number of girls = 50 - 35

Number of girls = 15

Now that we know there are 15 girls in the class and 35 boys, we can calculate the ratio of girls to boys.

Ratio of girls to boys = Number of girls / Number of boys

Ratio of girls to boys = 15 / 35

To simplify the ratio, we can divide both the numerator and denominator by their greatest common divisor, which in this case is 5:

Ratio of girls to boys = (15 ÷ 5) / (35 ÷ 5)

Ratio of girls to boys = 3 / 7

This means that for every 3 girls, there are 7 boys in the class. The ratio provides a relative comparison of the number of girls to the number of boys, helping to understand the gender distribution within the class.

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The range of u(x) = {-15, -5,1,3,1, -5, -15} and range of v(x)= {-3,-2, -1,0,1,2,3} for the domain of x = { -3,-2,-1,0,1,2,3}

The domain of a function is defined by the set of the values of independent variables and the ranges are the set of values of dependent variables.

The domains act as an input of function where ranges act as an output.

We select domain randomly as domain are the set of independent variables. But how will be the ranges must depend on the function given us.

we are given 2 function u(x) = -2x²+3 and v(x)

for the 1st function the set of domain and ranges are different, but the domain and ranges have the same values for the 2nd function.

we select domain x= {-3, -2, -1, 0, 1, 2, 3}

the ranges for u(x) ={ -15, -5, 1, 3, 1, -5 , -15}

because, u(-3) = -2(-3)²+3 = -15

                u(-2) = -2(-2)²+3 =-5

               u(0) = 3

similarly, for the same set of x value, v(-3) = -3

                                                         v(-2) = -2

                                                         v(0) =0

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For statement 5/3, the reason is the definition of slope. And for statement (5/3)=(15/9), the reason is triangle A is similar to triangle B.

Slope or the gradient is the number or the ratio which determines the direction or the steepness of the line. The slope is also defined as the ratio of the rise to the run.

If the slope of the triangles is equal then triangle A is similar to triangle B.

In the statement  when we simplify

(5/3)=(15/9),

(5/3)=(5/3),

Then the reason for this statement is "If the slope of triangles are equal"

And the definition of slope in general is m = y/x.

Therefore, for statement 5/3, the reason is the definition of slope. And for statement (5/3)=(15/9), the reason is triangle A is similar to triangle B.

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Let’s solve the equation x^2 - 4x = 5 by factoring:

First, we’ll move all the terms to one side of the equation:

x^2 - 4x - 5 = 0

Now, we’ll factor the left side of the equation. We’re looking for two numbers that multiply to -5 and add to -4. Those numbers are -5 and 1. So we can write:

(x - 5) (x + 1) = 0

Now we’ll use the zero-product property to solve for x. This property states that if the product of two numbers is zero, then at least one of the numbers must be zero. So we have:

x - 5 = 0 or x + 1 = 0

Solving each equation separately, we find that x = 5 or x = -1.

So, the solutions to the equation x^2 - 4x = 5 are x = 5 and x = -1.

Answer:

k = -3

k =5

Step-by-step explanation:

\(d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\d = 5\\(-1,1) =(x_1,y_1)\\(2,k)=(x_2,y_2)\\\)

\(5=\sqrt{\left(2-\left(-1\right)\right)^2+\left(k-1\right)^2}\\\\\mathrm{Square\:both\:sides}:\quad 25=k^2-2k+10\\25=k^2-2k+10\\\\\mathrm{Solve\:}\:25=k^2-2k+10:\\k^2-2k+10=25\\\\\mathrm{Subtract\:}25\mathrm{\:from\:both\:sides}\\k^2-2k+10-25=25-25\\k^2-2k-15=0\\\\\mathrm{Solve\:by\:factoring}\\\\\mathrm{Factor\:}k^2-2k-15:\quad \left(k+3\right)\left(k-5\right)\\\mathrm{Solve\:}\:k+3=0:\quad k=-3\\\)

\(\mathrm{Solve\:}\:k-5=0:\quad k=5\\\\k =5 , k=-3\)

A = (-1, 1) and B = (2, k) so:

\(d(A,B)=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}=\sqrt{(2-(-1))^2+(k-1)^2}=\\\\=\sqrt{3^2+(k-1)^2}=\sqrt{9+k^2-2k+1}=\sqrt{k^2-2k+10}\\\\\\d(A,B)=5\\\\\sqrt{k^2-2k+10}=5\quad|(\ldots)^2\\\\\big|k^2-2k+10\big|=25\\\\k^2-2k+10=25\qquad\vee\qquad k^2-2k+10=-25\\\\k^2-2k-15=0\qquad\vee\qquad k^2-2k+35=0\\\\\\\Delta_1=(-2)^2-4\cdot1\cdot(-15)=64>0\qquad\text{two solutions}\\\\\Delta_2=(-2)^2-4\cdot1\cdot35=-136<0\qquad\text{no solutions}\\\\\\k_1=\dfrac{2-\sqrt{64}}{2}=\dfrac{2-8}{2}=\dfrac{-6}{2}=\boxed{-3}\)

\(k_2=\dfrac{2+\sqrt{64}}{2}=\dfrac{2+8}{2}=\dfrac{10}{2}=\boxed{5}\)

The gain on sale of the laptop which Jack purchased in 2012 for $64,000 with a current book value of $18,000 but sold for $28,000 is $10,000.

The book value of an asset is the difference between the original value or purchase cost and the accumulated depreciation.

Accumulated depreciation represents the depreciation from the purchase date to the current period. It can be determined as the difference between the purchase price and the current value.

The purchase price of the laptop in 2012 = $64,000

Current book value = $18,000

Accumulated depreciation = $46,000 ($64,000 - $18,000)

Sales price = $28,000

Gain on sale = $10,000 ($28,000 - $18,000)

Thus, when the laptop is sold by Jack, he realized a gain of $10,000 because the sales price exceeded the current book value.

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