what is 7/8 of 16 times in half of 30?
​

Answer: 70˚

Step-by-step explanation:

Goal: find the other angles in the triangle and subtract them from 180 to find x:

180 - 105 = 75˚

the other angle is 35˚, (alternate interior angles).

.: x = 180 - 75 - 35 = 70˚

The acceleration was -26.04 m/s².

Equations of motion are a set of equations which describes the basic motion concepts like velocity, position, time and acceleration.

There are mainly three equations of motion.

v = u + at

s = ut + [tex]\frac{1}{2}[/tex] at²

v² = u² + 2as

v is the final velocity, u is the initial velocity, a is the acceleration, t is the time and s is the displacement.

Given,

Initial velocity of the motorist, u = 90 km/h = 90 × (5/18) m/s = 25 m/s

Final velocity of the motorist, v = 0 m/s (since the bike stopped)

Stopping distance, s = 12 m

Using the third equation of motion,

v² = u² + 2as

0² = 25² + (2a × 12)

24a = -625

a = -625 / 24 = -26.04 ≈ -26 m/s²

Hence the acceleration of the motorist was -26 m/s².

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The required Length of the DC is 30.47 Units.

A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or formerly rectangled triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and various angles of the right triangle.

We have;

In ΔABD, ∠BAD = 54° and in ΔBDC, ∠BCD = 28°.

Then, In ΔABD

Sin∅ = BD/20

Sin(54°) = BD/20

BD = 0.809(20)

BD = 16.18

in ΔBDC

tan(28°) = BD/DC

DC = BD/tan(28°)

DC = 16.18/0.531

DC = 30.47 Units.

Thus, required Length of the DC is 30.47 Units.

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Answer:

[tex]4x^{2} y^{3}[/tex]

Step-by-step explanation:

[tex]\frac{36x^{4}y^{5}}{(3xy)^{2}}[/tex]

In the denominator, all the terms in the brackets or parenthesis will be squared:

= [tex]\frac{36x^{4}y^{5}}{9x^{2} y^{2}}[/tex]

Law of indices is applied:

                                                    [tex]\frac{a^{n}}{a^{m}}[/tex]= [tex]a^{n - m}[/tex]

= [tex]4x^{4 - 2} y^{5 - 2}[/tex]

= [tex]4x^{2} y^{3}[/tex]

∴Option B

The logarithm is the inverse function to exponentiation. That means the logarithm of a number x to the base b is the exponent to which b must be raised, to produce x.

For example, since 1000 = 10³, the logarithm base 10 of 1000 is 3, or log₁₀ = 3

a. log(2^100) = 100 log(2) ≈ 30.103

b. log(100^2) = 2 log(100) = 2 log(10^2) = 2 × 2 = 4

c. log(3.0862.062) = log(3.086) + log(2.062) ≈ 0.488 + 0.316 = 0.804

(Note: The multiplication of 3.086 and 2.062 can be done using a calculator.)

d. log(55^(-3.1)) = -3.1 log(55) ≈ -3.1 × 1.740 = -5.394

e. log(5/1) = log(5) - log(1) ≈ 0.699 - 0 = 0.699

f. log(1/5) = log(1) - log(5) ≈ 0 - 0.699 = -0.699

g. log(1/81^2) = log(1) - 2 log(81) = -2 log(9^2) = -2 × 2 log(9) ≈ -2 × 0.954 = -1.908

(Note: We can use the property that log(a^b) = b log(a) to simplify the expression.)

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Answer:

x = 32

Step-by-step explanation:

First we would move the x's to the left and the numbers to the right. When doing so they switch from being positive to negative or from negative to positive.

3/4x = 27-3

Now we would try to simplify it as much as we can. Here I would make 3/4 a decimal and subtract 37-3

0.75x = 24

Now we can divide 24 by 0.75 to find x

x = 32

x = 32.

[tex]\frac{3}{4} x+3=27[/tex]

[tex]\frac{3}{4} x+3-3=27-3\\ \\\frac{3}{4} x+3-3=27-3\\ \\\frac{3}{4} x=24[/tex]

[tex]\frac{\frac{3}{4} x}{\frac{3}{4}} =\frac{24}{\frac{3}{4}}\\ \\x=24*\frac{4}{3}\\ \\x=\frac{24*4}{3} \\ \\x=\frac{96}{3} \\\\x=32[/tex]

If "32" is our correct answer, then substituting it by variable "x" on the original equation should make the equation return the same number on both sides of the equal (=) symbol. Let's test it!

[tex]\frac{3}{4} (32)+3=27\\ \\\frac{3*32}{4}+3=27\\ \\\frac{96}{4}+3=27\\ \\24+3=27\\ \\27=27[/tex]

That's correct!

x = 32.

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Answer:

x=9

Step-by-step explanation:

Since y=5x, you plug it into the other equation's y and it'd look like this 5x=4x+9. Then you subtract 4x on both sides and that would leave you with an x=9.

Answer:

Step-by-step explanation:

To find the angle that Mrs. Becker is looking down at, we can use the tangent function. We know the height of her eyes (6 feet) and the distance from her eyes to the ladybug (100 feet), so we can use the formula:

tan(angle) = height/distance

First, we'll solve for the angle:

angle = tan^-1(height/distance)

angle = tan^-1(6/100)

Using a calculator, we can find that the angle is approximately 0.0349 radians, or approximately 2 degrees.

So, Mrs. Becker is looking down at an angle of approximately 2 degrees.

Here are three statements explaining why each of the objects doesn't belong with the others:

Sphere:

Cylinder:

Pyramid:

Cube:

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Answer:

11xy(121x²-y²)

Step-by-step explanation:

When factorizing, you should always look for what each term has in common.

First, let's look at the coefficients (numbers) in each term: 1331 and 11. Both are divisible by 11, so let's factorize out 11:

1331x³y-11y³x

11(121x³y-y³x)

Looking at the terms in the bracket, we see they both have 'x's in common (121x³y has three x's multiplied in and y³x has one). Let's factorize out this x:

11(121x³y-y³x)

11x(121x²y-y³)

We can also see both terms in the brackets have 'y's in common (121x²y has one y and y³ has three multiplied in). Let's factorize out this y:

11x(121x²y-y³)

11xy(121x²-y²)

Since there is nothing in common left between the terms, we can say the expression is fully factorized!

The divisor in the situation given is 14.

We can write the division algorithm as -

dividend = (divisor × quotient) + remainder

Given is that in a division the dividend is 872 the quotient is 62 and the remainder is 4

We can write -

dividend = (divisor × quotient) + remainder

872 = (d x 62) + 4

62d = 868

d = 868/62

d = 14

Therefore, the divisor in the situation given is 14.

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{Question in english -

if in a division the dividend is 872 the quotient is 62 and the remainder is 4 what is the divisor}

The height of the plane to the nearest metres is 1023 metres. Therefore, the answer is A.

A pilot flying over the gulf of Mexico sees an island at an angle of depression of 12 degrees. At this time the horizontal distance from the plane to the island is 4812 metres .

Therefore, the height of the plane can be found as follows:

The situation forms a right angle triangle.

Using trigonometric ratios,

tan 12 = opposite / adjacent

tan 12° = x /  4812

cross multiply

x =  4812 tan 12°

x =  4812 × 0.21255656167

Therefore,

x = 1022.82217476

x = 1023 metres.

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The city that you should live in if you want a greater variability in temperature is city Y.

In order to determine the city that has the greater variability in temperature, the interquartile range has to be determined. The interquartile range is used to measure the variation in a dataset.

The interquartile range is the difference between the third quartile and the first quartile.

interquartile range = third quartile - first quartile

Interquartile range for City X = 50 - 30 = 20

Interquartile range for City Y = 50 - 25 = 25

The interquartile range for city Y is greater than that of city X. This means that city Y has a greater variation in temperature.

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Answer:3.25

Step-by-step explanation:

Divide 325/100=3.25

Answer: 30 in

Step-by-step explanation:

To figure out perimeter, you have to add up all of the sides.

The sides of the triangle are 7, 10, and 13 in.

7+10+13=30

The answer is 30 inches.

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Answer:

Step-by-step explanation:

Step 1: Define each variable

Let's define some variables to make the calculations easier:

t1 = the median monthly rent in 1990, which is $447

t2 = the median monthly rent in 2002, which is $658

Δ = the change in median monthly rent, which is t2 - t1

Step 2: Calculate the change in median monthly rent

Δ = t2 - t1 = $658 - $447 = $211

This means that the median monthly rent increased by $211 from 1990 to 2002.

Step 3: Divide the change by the original amount

To find the percentage increase, we need to divide the change by the original amount and multiply by 100:

Δ / t1 * 100 = ($211 / $447) * 100 = 47.2%

This means that the median monthly rent increased by 47.2% from 1990 to 2002.

Step 4: Round to the nearest tenth of a percent

The final answer is 47.2%, rounded to the nearest tenth of a percent.

The percent increase in the median monthly rent prices from 1990 to 2002 was 47.2%.

Answer:

Step-by-step explanation:

The equation that represents the town's population after 4 years can be found using the formula:

P = P0 * (1 - r)^t

Where P is the population after t years, P0 is the initial population (4.11 x 10^4), r is the annual shrink rate as a decimal (9.6% as 0.096), and t is the number of years (4).

P = 4.11 x 10^4 * (1 - 0.096)^4

P = 4.11 x 10^4 * 0.6994^4

P = 4.11 x 10^4 * 0.4139

P = 1.70 x 10^4

So the town's population after 4 years is 1.70 x 10^4.

Answer:

Let P(t) be the population of the town after t years. We know that P(0) = 4.11 x 10^4. Then, the rate of change of the population is given by -0.096P(t), so we can write the differential equation:

dP/dt = -0.096P(t)

To find the population after 4 years, we need to solve this differential equation with the initial condition P(0) = 4.11 x 10^4. We can do this by separating variables and integrating both sides:

∫(dP/P) = -0.096 ∫dt

ln|P(t)| = -0.096t + C

where C is a constant of integration that can be found using the initial condition. Solving for P(t), we get:

P(t) = Ce^(-0.096t)

where C = e^(ln|P(0)|) = e^(ln|4.11 x 10^4|) = 4.11 x 10^4

Substituting in t = 4, we get:

P(4) = 4.11 x 10^4 e^(-0.096 × 4) = 4.11 x 10^4 e^(-0.384)

So, the equation representing the town's population after 4 years is:

P(t) = 4.11 x 10^4 e^(-0.096t)

According to the information, the graph would be as shown in the attached image (4 * 1/3 = 1 1/3)

According to the information we must take into account that a complete hexagon represents an integer. So one third of the hexagon would be the rhomboid. So, to graph this equation, we must replace the values with the corresponding figures.

In this case we must multiply the rhomboid by four, the rhomboid represents 1 of 3 elements that make up a hexagon. Therefore, if we have 4 rhomboids, we would have a hexagon and a rhomboid.

Note: This question is incomplete. Here is the complete information:

Image attached

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Answer:

41 inches

Step-by-step explanation:

to find the perimeter of any shape, add the length of all the sides together

Answer:

2.016, 2.16, 2.1682, 2.2

How to put anything from least to greatest?

The decimals that you have put are the following:

2.16

2.1682

2.2

2.016

How to do it:

If you look at the decimals the last one, 2.016 does not have a 1 or a 2 instead it has a 0 so that would be a our first decimal in the least to greatest form.

We can also include the third one 2.2 is the only one that has a 2 so now we know that 2.2 will go last.

Lets compare the first and second ones which are 2.16 and 2.1682 and I think we obviously know that the answer is 2.1682 because it is greater then 2.16.

So now here are the decimals from least to greatest:

2.016, 2.16, 2.1682, 2.2

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Answer: your mom

Step-by-step explanation:

Answer:The first question requires the calculation of the 6.5% of $400, which is equal to $26.

The second question requires the calculation of 12.5% of $100, which is equal to $12.50.

For the third question, 130 is 20% of 650.

For the fourth question, $5.40 is 120% of $4.50.

For the fifth question, $8.40 is 30% of $28.

For the sixth question, 56% of 39 is $21.84

For the seventh question, $495 is 55% of $900.

For the last question, 144 is 60% of 240.

Step-by-step explanation:

Answer:

Step-by-step explanation:

26

12.5

20%

120%

30%

12.23

900

60%

Answer:

y = -1/3 x + 3

Step-by-step explanation:

To find the equation of the line that passes through the two points (-3,4) and (3,2) in slope-intercept form, we'll first find the slope of the line using the formula:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are the two given points.

Plugging in the given points, we get:

m = (2 - 4) / (3 - (-3)) = -2 / 6 = -1/3

Next, we'll use the point-slope form of a line to find the equation of the line:

y - y1 = m(x - x1)

where (x1, y1) is one of the given points, and m is the slope of the line.

We'll use the first given point, (-3,4), so we have:

y - 4 = -1/3 (x - (-3))

Expanding the right side of the equation, we get:

y - 4 = -1/3 x + 1

Finally, we'll rearrange the equation to get it in slope-intercept form, which is:

y = -1/3 x + b

where b is the y-intercept. To find b, we'll plug in one of the given points and solve for b:

y = -1/3 x + b

4 = -1/3 * (-3) + b

4 = 1 + b

b = 4 - 1

b = 3

So the equation of the line in slope-intercept form is:

y = -1/3 x + 3

The constant of proportionality in the equation is 0.3.

Firstly, there is proportional relationship.

Two values x  and  y are said to be in a proportional relationship if x=ky, where x and y are variables and k is a constant.

The constant k is called constant of proportionality.

WE are given that number of candies sold can be determined by the equation: T = 0.3c, where T is number of candies and c is the number of children.

0.3 = constant of proportionality

0.3 = p / n

which is the ratio of p to n

The constant of proportionality is the ratio between the two quantities that are directly proportional.

Therefore,

0.3 is the constant of proportionality in the equation.

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Answer:

y = 36

Step-by-step explanation:

Given logarithmic equation:

[tex]\log_4(y-9)+\log_43=\log_481[/tex]

[tex]\textsf{Apply the \textbf{log product law}}: \quad \log_ax + \log_ay=\log_axy[/tex]

[tex]\implies \log_4\left(3(y-9)\right)=\log_481[/tex]

[tex]\textsf{Apply the \textbf{log equality law}}: \quad \textsf{If $\log_ax=\log_ay$ then $x=y$}[/tex]

[tex]\implies 3(y-9)=81[/tex]

Divide both sides of the equation by 3:

[tex]\implies \dfrac{3(y-9)}{3}=\dfrac{81}{3}[/tex]

[tex]\implies y-9=27[/tex]

Add 9 to both sides of the equation:

[tex]\implies y-9+9=27+9[/tex]

[tex]\implies y=36[/tex]

Therefore, the solution to the given logarithmic equation is y = 36.

On solving the prοvided question, we can say that 4.75 miles were ran on day four.

A mathematical equation is a formula that jοins two statements and uses the equal symbol (=) tο indicate equality. A mathematical statement that establishes the equality of twο mathematical expressions is known as an equatiοn in algebra.

Fοr instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences οn either side of a letter is described by a mathematical formula. Often, there is only οne variable, which alsο serves as the symbol. for instance, 2x – 4 = 2.

On day one, Justin ran two miles.

He ran two miles on the second day, or 75% of it. Divide by 100 and multiply by 75 to get the percentage of two miles that is 75%.

On the secοnd day, I ran 1.5 miles, or 2 / 100, or 0.02 x 75. (I've run 3.5 miles so far)

He ran 1.5 miles further on the third day than the previous one:

1.5 + 1.5 = 3 (6.5 miles jogged sο far) (6.5 miles jogged so far)

The total number of miles run was 9.25, thus tο find the solution, we must subtract 6.5 from 9.25.

4.75 miles were ran οn day four, or 9.25 minus 6.5.

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The values for the sets are -

A∪B = { 1 , 2 , 4 , 6 , 8 , 9 , 10 , 12 , 14 , 15 , 16 , 17 , 19 , 20 } and n(A∪B) = 14.

A∩B = { 10 , 12 , 14 , 16 } and n(A∩B) = 4

What is sets?

A set is a precisely defined collection or aggregate of all feasible objects with predetermined qualities that are specified in accordance with a precisely defined rule. Elements of sets are the items used to compare sets.

The set S is - S = { 1 , 2 , 3 , ... , 18 , 19 , 20 }

The set A is - A = { 1 , 2 , 4 , 10 , 12 , 14 , 16 }

The set B is - B = { 6 , 8 , 9 , 10 , 12 , 14 , 15 , 16 , 17 , 19 , 20 }

A∪B is the set of elements of S that are part of A or B, or both.

A∪B = { 1 , 2 , 4 , 6 , 8 , 9 , 10 , 12 , 14 , 15 , 16 , 17 , 19 , 20 }

Count the number of elements present in set A∪B.

Therefore, n(A∪B) value is 14.

A∩B is the set of elements of S that are common to A and B.

A∩B = { 10 , 12 , 14 , 16 }

Count the number of elements present in set A∩B.

Therefore, n(A∩B) value is 4.

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Step-by-step explanation:

The transformation from the function f(x) = |x| to the function g(x) = |x| + 4 can be thought of as a vertical shift upward by 4 units. The shape of the absolute value function remains unchanged, but the entire graph is shifted upward along the y-axis by 4 units. This can be visualized by observing that for any value of x, g(x) = f(x) + 4.

So, the transformation of f(x) to g(x) is a vertical shift upward by 4 units

Answer:

190°

Step-by-step explanation:

Subtract 360° (this is one complete rotation)

"coterminal" is the exact same angle, but 360° bigger (or smaller)

550° - 360°

= 190°

The answers are mentioned below.

In physics, displacement is defined as the change in position of an object from its initial position to its final position, measured as a straight line distance in a specific direction. It is a vector quantity, which means it has both magnitude (the distance between the starting and ending points) and direction. Displacement is different from distance, which is the actual length of the path traveled by an object regardless of its starting and ending points.

i. The person's displacement from the starting point can be calculated using the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. In this case, the person has walked a distance of 500 yards south and 300 yards west, which forms a right triangle. Therefore, the displacement can be calculated as the square root of (500^2 + 300^2) = 583.1 yards (rounded to the nearest hundredth).

ii. To be looking back at point A from point B, the person would have to look in the direction opposite to the direction in which they walked from A to B. Since the person first walked due south and then due west, the direction in which they would have to look to be looking back at point A is north-east. This can be calculated using trigonometry, where the tangent of the angle formed between the line connecting A and B and the due south line is equal to 300/500. Therefore, the angle formed is the arctangent of (300/500) = 31.39 degrees. However, the true bearing is measured from the north and therefore, the true bearing would be 360 - 31.39 = 328.61 degrees (rounded to the nearest hundredth).

iii. If a friend is standing at point A looking at point B, they would be looking in the direction of the line connecting points A and B. To determine the true bearing, we need to find the angle formed between the due north line and the line connecting A and B. This angle can be calculated as the arctangent of (500/300) = 59.04 degrees. However, the true bearing is measured from the north and therefore, the true bearing would be 90 + 59.04 = 149.04 degrees (rounded to the nearest hundredth).

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i. The person's displacement from the starting point can be calculated using the Pythagorean theorem, the person has walked a distance of 500 yards south and 300 yards west, which forms a right triangle. Therefore, the displacement can be calculated as the square root of (500² + 300²) = 583.1 yards

In physics, displacement is defined as the change in position of an object from its initial position to its final position, measured as a straight line distance in a specific direction. It is a vector quantity, which means it has both magnitude (the distance between the starting and ending points) and direction. Displacement is different from distance, which is the actual length of the path traveled by an object regardless of its starting and ending points.

i. The person's displacement from the starting point can be calculated using the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. In this case, the person has walked a distance of 500 yards south and 300 yards west, which forms a right triangle.

Therefore, the displacement can be calculated as the

√(500² + 300²)

= 583.1 yards (rounded to the nearest hundredth).

ii. To be looking back at point A from point B, the person would have to look in the direction opposite to the ²in which they walked from A to B. Since the person first walked due south and then due west, the direction in which they would have to look to be looking back at point A is north-east. This can be calculated using ², where the tangent of the angle formed between the line connecting A and B and the due south line is equal to 300/500.

Therefore, the angle formed is the arctangent of (300/500) = 31.39 degrees. However, the true bearing is measured from the north and therefore, the true bearing would be

360 - 31.39

= 328.61 degrees (rounded to the nearest hundredth).

iii. If a friend is standing at point A looking at point B, they would be looking in the direction of the line connecting points A and B. To determine the true bearing, we need to find the angle formed between the due north line and the line connecting A and B. This angle can be calculated as the arctangent of (500/300) = 59.04 degrees.

However, the true bearing is measured from the north and therefore, the true bearing would be

90 + 59.04

= 149.04 degrees (rounded to the nearest hundredth).

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