Translate the triangle then enter the new coordinates

Answer:

x=36 y=71

Step-by-step explanation:

for x use the Z alternate angle

for y use 180 -73-36=71

Answer:

The answer for

x=35

y=15

Step-by-step explanation:

let the first number be x

" second number " be y

x:y=7:3

x-y=20

x=20+y

x:y=7:3

20+y/y=7/3

7y=3(20+y)

7y=60+3y

7y-3y=60

4y=60

divide both sides by 4

y=15

x=20+y

x=20+15

x=35

The perimeter of the semicircle is approximately 66.8 cm.

The diameter of the semicircle is given as d = 26cm.

r = d/2 = 26/2 = 13cm

The circumference of a full circle with radius r is given by:

C = 2πr

Therefore, the circumference of the semicircle is:

C/2 = πr

Substituting the value of r, we get:

πr = π(13) = 13π

The perimeter of the semicircle is therefore:

P = d + C/2 = 26 + 13π

Using the value of π = 3.14, we can approximate the perimeter as:

P = 26 + 13(3.14)

= 26 + 40.82

= 66.82 cm

Rounding to 1 dp

= 66.8 cm

Therefore, the perimeter of the semicircle is approximately 66.8 cm.

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Result:

A (is an angle)  = 70°.

Based on the provided information:

AB = BC

BCD = 110

We can use the information to find the value of A.

Since AB = BC, we can assume that triangle ABC is an isosceles triangle, where AB and BC are the two equal sides. For an isosceles triangle, the angles opposite to the equal sides are also equal.

So, ∠ABC = ∠BCA (opposite angles of an isosceles triangle are equal).

Since BCD = 110, we can deduce that  ∠BCA + ∠ BCD = 180 (sum of angles in a triangle equals 180 degrees).

Substituting the values, we get:

∠BCA + 110 = 180

Subtracting 110 from both sides, we get:

∠BCA = 180 - 110

∠BCA = 70

Now, since ∠ABC = ∠BCA, we have:

∠ABC = 70°

Therefore, A = 70 degrees.

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Answer:

$39.75

Step-by-step explanation:

First, you find the tax by dividing the cost of the plate by 100, and then multiplying your answer by the tax, 6.:

375/100 = 3.75

3.75*6 = 22.5.

Then add the shipping charges, 375 + 22.5 = 397.5. This is the total cost. SInce Frank sold the plate three years later for 10% more than the total cost, you find 10% of the total cost, and then add that 10% to $397.5

397.5/100 = 3.975

3.975*10 = 39.75

39.75 + 397.5 = 437.25.

To find the profit, subtract 397.5 from $437.25:

437.25 - 397.5 = 39.75.

The total profit is $39.75

The probability distribution to use in this problem is the binomial distribution and the probability of success is the probability of selecting a woman, which is 4/10.

The probability distribution that should be used to solve the problem of selecting at least one woman from a group of four women and six men for two executive vacancies is the binomial distribution.

The binomial distribution formula is used to calculate the probability of getting a certain number of successes in a fixed number of trials, given the probability of success in each trial. In this case, the probability of success is the probability of selecting a woman, which is 4/10.

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The amount of mesh required is: 1686.24cm²

The volume is: 5934.66cm³cm³

To calculate the amount of mesh we say

L = πrℓ

where r is the radius of the base, ℓ is the generatrix, and π is approximately 3.14.

Given the diameter of the cone, we can calculate the radius as follows

r = d/2 = 22/2 = 11 cm

We are also given that the generatrix ℓ is 48 cm.

Therefore, the lateral surface area of the cone i is

L = πrℓ = 3.14 x 11 x 48 = 1657.92cm²

To find the volume of the cone, we can use the formula

V = (1/3)πr²h

where h is the height of the cone.

We can use the Pythagorn theorem to find the height of the cone as shown below

h² = ℓ² - r²

h² = 48² - 11²

h² = 2197

h = √2197

h ≈ 46.86 cm

Now we can find the volume of the cone whic is

V = (1/3)πr²h = (1/3) x 3.14 x 11² x 46.86 ≈ 5934.66cm³

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Translation:

Calculate the amount of mesh we will need to build a cone-shaped strainer with a diameter of 22cm and a generatrix of 48cm. What is its volume?

The apple will be at the same height of 20ft as the construction worker at t = 3/4sec and t = 5/4sec.

It is given that h = -16t^2 + vt +c

v = 32ft/sec , c = 5ft , h =20ft

So plugging in these values into the formula we have

20 = -16t^2 + 32t + 5

[tex]$\Rightarrow 16t^2 -32t + 15 =0[/tex]

[tex]$\Rightarrow 16t^2 -20t - 12t + 15 =0[/tex]

[tex]$\Rightarrow 4t(4t - 5) -3(4t - 5) = 0[/tex][tex]$\,\,\,\Rightarrow (4t-3)(4t-5) = 0[/tex][tex]$\Rightarrow 4t-3 =0 \Rightarrow t = 3/4\,\,\textrm{ and } \,\, 4t-5 =0 \Rightarrow t = 5/4[/tex]

So t = 3/4 and at t = 5/4 are two times when the apple will be at an elevation of h = 20ft.

The motion of an object launched into free motion under gravity is called projectile motion. During this motion, the only force acting on the object is gravity, whose value is -32ft/sec^2. During this motion, the y coordinate is given by [tex]y = u_yt -(1/2)gt^2 + y_0 = u_yt - 16t^2 + y_0[/tex]. here  [tex]u_y[/tex] is the vertical component of the initial velocity and [tex]y_0[/tex] is the initial y coordinate. The value of the x coordinate is given by [tex]x = u_xt[/tex], where [tex]u_x[/tex] is the horizontal component of the initial velocity.

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Answer: 5

Step-by-step explanation:

You will use Pythagorean theorem for this problem (a²+b²=c²)

This will be 13² - 12² = a

13² - 12² = 25

you must square root your answer

√25 = 5

x=5

The angle between the z-axis and the given vector r with rightwards arrow on top is 33.69 degrees.

The x-component of the vector is -2, which means that the vector has a component that points in the negative x-direction. The y-component of the vector is 3, which means that the vector has a component that points in the positive y-direction. We can use these components to find the magnitude of the projection of the vector onto the xy-plane, which is given by the Pythagorean theorem:

|proj_r| = √((-2)² + 3²) = √(13)

Next, we need to find the angle between the projection of the vector onto the xy-plane and the positive x-axis. We can do this by taking the arctan of the y-component over the x-component:

theta = arctan(3/-2) = -56.31 degrees

Note that we get a negative angle because the projection of the vector lies in the third quadrant of the xy-plane, which is opposite to the positive x-axis.

Finally, we can find the angle between the z-axis and the vector by subtracting the angle between the projection of the vector onto the xy-plane and the positive x-axis from 90 degrees:

phi = 90 - 56.31 = 33.69 degrees

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Answer:

577.76

Step-by-step explanation:

we know formula for volumne of cylinder

pie × square of radius × height

that is = 3.14× 8^2 × 23

that is = 577.76

The required simplified value of x is x > 6 or x ≤ -1.

We have two inequalities here:
5x - 10 > 20 or 5x - 10 ≤ -15

We can start by solving the first inequality:

5x - 10 > 20

5x > 30

x > 6

So x is greater than 6 for the first inequality to hold.

Next, we can solve the second inequality:

5x - 10 ≤ -15

5x ≤ -5

x ≤ -1

So x is less than or equal to -1 for the second inequality to hold.

Putting it all together, the solution to the system of inequalities is:

x > 6 or x ≤ -1

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The linear equation that models the data based on the information is y = 2.2x + 0.6.

An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.

It is important to note that an equation is the mathematical statement which can be made up of two expressions which are connected by an equal sign.

In conclusion, the linear equation that models the data based on the information is y = 2.2x + 0.6.

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Therefore, we need 40 workers to complete the work in 15 days.

Let's assume that the amount of work required to build the house is the same, regardless of the number of workers. This means that the number of workers and the time required to complete the work are inversely proportional to each other. We can use the following formula:

n1 × d1 = n2 × d2

where n1 is the initial number of workers, d1 is the initial number of days, n2 is the new number of workers, and d2 is the new number of days.

Substituting the given values, we get:

20 × 30 = n2 × 15

Simplifying the equation, we get:

n2 = (20 × 30) ÷ 15

n2 = 40

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First, we need to convert feet to miles and seconds to hours.

1 mile is equal to 5280 feet.

So, 1716 feet is equal to (1716/5280) miles or 0.325 miles.

1 hour is equal to 3600 seconds.

So, 3 seconds is equal to (3/3600) hours or 0.00083333 hours.

Now we can calculate the speed of the plane in miles per hour by using the formula:

Speed (in miles per hour) = Distance (in miles) / Time (in hours)

Speed = 0.325 miles / 0.00083333 hours

Speed = 390 miles per hour (rounded to the nearest whole number)

Therefore, the speed of the plane is 390 miles per hour.

The correct option is D, Per the Central Limit Theorem the mean of the sampling distribution of the sample mean is equal to the population Mean.

The Central Limit Theorem (CLT) is a fundamental concept in probability theory and statistics. It states that if you take repeated random samples of a population, the sample means will follow a normal distribution, regardless of the shape of the population distribution, provided the sample size is large enough. This means that as the sample size increases, the sample mean becomes more and more normally distributed.

The CLT is important because it helps us to understand the properties of large samples, even when the population is not normally distributed. It is used in many areas of research, including social sciences, finance, engineering, and more. The theorem provides a powerful tool for estimating population parameters, such as the mean or variance, and for testing hypotheses about them. It also helps to explain why the normal distribution is so commonly observed in real-world data, and why it is often used as a model for statistical analysis.

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Complete Question:-

Per the Central Limit Theorem the mean of the sampling distribution of the sample mean is equal to the population:

a. Standard deviation divided by n

b. Mean divided by n

c. Standard Deviation divided by the square root of n

d. Mean

Answer:

Since ∠CAB = 90°, we know that AC is the hypotenuse of the right triangle ABC. Let's use the sine function to find the length of BC:

sin(∠ABC) = BC/AC

sin(64°) = BC/9.1

BC = 9.1 * sin(64°)

Now, using the Pythagorean theorem, we can find the length of AB:

AB = sqrt(AC^2 - BC^2)

AB = sqrt(9.1^2 - (9.1*sin(64°))^2)

AB ≈ 5.222

Rounding this to 3 significant figures, we get:

AB ≈ 5.22

Therefore, the length of AB rounded to 3 significant figures is approximately 5.22 units.

The correlation between the distance a student sits from the front of the room and their grades in the course is a negative correlation.

Negative correlation is a type of correlation where one variable increases while the other variable decreases. In this case, as the distance of a student in the class increasing, the grades of the student in decreasing.

This shows that distance and grades may not correlate favorably. The professor's discovery of a negative association may therefore reflect the reality that students become less attentive as they grow farther away from their teachers.

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At 100°C, the nitrogen molecules in the container have an rms speed of 576 m/s. The pressure inside the container,

which is at a pressure of 2.4 atm, is a result of the collisions of these fast-moving molecules with the walls of the container. The area of the wall is 13 cm x 13 cm, which means there is a total surface area of 169 cm^2.

The collisions of the nitrogen molecules with this surface area will result in a force on the wall, which is what creates the pressure.

Overall, the properties of the nitrogen molecules, including their speed and number, contribute to the overall pressure inside the container.

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Answer:

2/3.

Step-by-step explanation:

Total number of possible outcomes on one spin = 9.

Total of non multiples of 3:

1, 2, 4, 5,7 and 8

= 6

Answer is 6/9 = 2/3.

Answer:

B. 2/3

Step-by-step explanation:

Probability is written like a fraction where on the bottom you have ALL the possibilities. There's 9 numbers on the spinner, so there's a total of 9 different ways for it to land.

9 ways total. That goes on the bottom of the fraction.

On top of the fraction you put however many number of ways the event in question can happen. That goes on top.

A multiple of three is 3, 6, 9. There are 3 ways the spinner can land on a multiple of three. So there are 6 ways to land on NOT a multiple of three (1, 2, 4, 5, 7, 8) 6 ways, so 6 goes on top.

6/9 is the answer. But always simplify fractions first, like you do.

6/9 simplifies to 2/3

The answer is

B. 2/3

Answer:

x^2 - x + 6 = 0

x = (-(-1) + √((-1)^2 - 4(1)(6)))/(2 × 1)

= (1 + √(1 - 24))/2

= (1 + √-23)/2

So there are no real solutions to this equation--we have the empty (null) set.

{ }

The number of 2-pointers and 3-pointers are 11 and 4, respectively

Given that the pointers are 2 and 3 where

Let x = 2 pointers

Let y = 3 pointers

Using the above as a guide, we have the following:

2x + 3y = 34

x + y = 15

Multiply the second equation by 2

So, we have

2x + 3y = 34

2x + 2y = 30

Subtract the equations

y = 4

Recall that

x + y = 15

So, we have

x + 4 = 15

Evaluate

x = 11

Hence, the number of 2-pointers is 11

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Answer:

This statement is true.

In the simplex method, choosing the pivot row involves selecting a row with a negative value in the right-hand column and dividing the elements in the last column by the corresponding elements in the selected row to obtain the ratios. The row with the smallest non-negative ratio is then chosen as the pivot row.

By choosing the pivot row in this way, we ensure that the new solution will still be feasible, meaning that all the constraints will still be satisfied. This is because choosing the smallest non-negative ratio ensures that the new solution will not violate any of the non-negativity constraints.

Therefore, requiring that the ratio associated with the pivot row be the smallest non-negative number is an important step in the simplex method to ensure that the iteration will not take us from a feasible point to a non-feasible point.

Step-by-step explanation:

This statement is true when using the simplex method to solve a linear programming problem.

In the simplex method, we start with a feasible solution and iteratively improve it until we reach an optimal solution. At each iteration, we choose a pivot row and a pivot column to pivot around. The pivot row is chosen based on the ratio of the right-hand side value to the coefficient of the entering variable in that row. This ratio is called the pivot ratio.

Choosing the pivot row with the smallest non-negative pivot ratio ensures that we pivot to a new feasible solution. This is because the pivot row represents a constraint in the linear programming problem, and the pivot ratio represents how much we can increase the value of the entering variable while still satisfying that constraint. If the pivot ratio is negative, it means that increasing the entering variable would violate the corresponding constraint, and so we cannot pivot in that direction.

Therefore, by choosing the pivot row with the smallest non-negative pivot ratio, we ensure that we pivot in a direction that preserves feasibility and does not take us to a non-feasible point.

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Antonia's probability of making a free throw is 0.75, and the probability of her missing a free throw is 0.25. Based on the results of a simulation of 10 trials, the experimental probability that Antonia makes both of her next two free throw attempts is 0.6 or 60%.

Using the given information, we know that Antonia's probability of making a free throw is 75%, which is equivalent to 0.75. Therefore, the probability of her missing a free throw is 25%, which is equivalent to 0.25.

Looking at the table of results from the simulation, we can see that there are 6 instances where Antonia made both of her next two free throw attempts (YY), out of a total of 10 trials. Therefore, the experimental probability of Antonia making both of her next two free throw attempts is

Experimental probability = Number of trials where Antonia made both of her next two free throws / Total number of trials

Experimental probability = 6/10

Experimental probability = 0.6

Therefore, based on the results of the simulation, the experimental probability of Antonia making both of her next two free throw attempts is 0.6 or 60%.

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The percent increase in the number of subscribers this year as compare to last year is equal to 12%.

Total number of subscribers last year = 6,100

Total number of subscribers this year = 6,832

The percent increase in the number of subscribers,

=  Difference between number of subscribers this year and last year / number of subscribers last year multiply by 100

The difference between this year's and last year's subscribers is equal to

= 6,832 - 6,100

= 732

The percent increase in the subscribers this year compare to last year is,

= (732 / 6,100) x 100

= 0.12  x 100

= 12%

Therefore, the percent increase in the number of subscribers is 12%.

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Answer: Always True

Step-by-step explanation:

Simplifying each of the following expressions:

a) (√5-√12)²:

First, we can simplify the square of each term using the formula (a-b)² = a² - 2ab + b²:

(√5-√12)² = (√5)² - 2(√5)(√12) + (√12)²

= 5 - 2√60 + 12

Next, we can simplify √60 by factoring out its largest perfect square factor, which is 4:

5 - 2√60 + 12 = 17 - 2√(4*15) = 17 - 4√15

Therefore, (√5-√12)² = 17 - 4√15.

b) (√12+√11)²:

We can simplify this expression using the same formula as before:

(√12+√11)² = (√12)² + 2(√12)(√11) + (√11)²

= 12 + 2√132 + 11

Next, we can simplify √132 by factoring out its largest perfect square factor, which is 4:

12 + 2√132 + 11 = 23 + 2√(4*33) = 23 + 2√132

Therefore, (√12+√11)² = 23 + 2√132.

c) (√6+√7) (√6-√7):

This expression can be simplified using the difference of squares formula, (a-b)(a+b) = a² - b²:

(√6+√7) (√6-√7) = (√6)² - (√7)²

= 6 - 7

= -1

Therefore, (√6+√7) (√6-√7) = -1.

Rationalizing each of the following expressions:

a) 1/√8:

To rationalize the denominator, we can multiply both the numerator and denominator by √8:

1/√8 = (1/√8) * (√8/√8) = √8/8

Therefore, 1/√8 = √8/8.

b) 1/√7-√1:

To rationalize the denominator, we can multiply both the numerator and denominator by the conjugate of the denominator, which is √7+√1:

1/√7-√1 = (1/√7-√1) * (√7+√1)/(√7+√1) = (√7+√1)/(7-1)

= (√7+√1)/6

Therefore, 1/√7-√1 = (√7+√1)/6.

c) 1/√8+3:

To rationalize the denominator, we can multiply both the numerator and denominator by the conjugate of the denominator, which is √8-3:

1/√8+3 = (1/√8+3) * (√8-3)/(√8-3) = (√8-3)/(8-9)

= -(√8-3)

Next, we can simplify √8 by factoring out its largest perfect square factor, which is 4:

-(√8-3) = -

Answer:

25

Step-by-step explanation:

25 sqrt= 5

2+5=7; 7 is a prime number

To find the area of the tile, we need to first find the length of the top horizontal side.

Using the Pythagorean theorem, we can find the length of the diagonal:

d² = 3² + (5+6)²

d² = 9 + 121

d = √130

Now we can use the fact that the diagonal cuts the rectangle into two right triangles to find the length of the top horizontal side:

5x = 3(6)

x = 18/5

Therefore, the length of the top horizontal side is 18/5 centimeters.

Now we can find the area of the tile:

A = (3 + 18/5) * 5/2

A = 15 + 27/5

A = 102/5

Rounding to one decimal place, we get:

A ≈ 20.4 cm²

Therefore, the closest option to the area of the tile shown is 42.5 cm².