Find the length of the lettered sides of a right angle triangle if the angle of the interior is 60 90 and 30 degrees. And the height is 8cm and the hypothenus is given as A and the base is given as B

Answer:

the two numbers are 10 and 12.

Step-by-step explanation:

Let’s assume that the two numbers are 5x and 6x respectively. Then we can write:

5x/6x = 5/6

Multiplying both sides by 6x gives:

5x = (5/6) * 6x = 5x - (5/6) * 8

Simplifying gives:

30x = 30x - 20

Therefore, x = 2.

So the two numbers are:

5x = 10

6x = 12

If we subtract 5 from each number, we get:

10 - 5 = 5

12 - 5 = 7

Therefore, the two numbers are 10 and 12.

I hope this helps! Let me know if you have any other questions.

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The probability of selecting a black marble, replacing it, then selecting a red marble is  7.0%.

The probability of selecting a yellow marble, not replacing it, then selecting another yellow marble is 2.2%.

The probability of selecting one yellow marble, not replacing it, then selecting a black marble is  15.6%.

There are 10 marbles in the bag, and 7 of them are black.

If we select a black marble and replace it, then there are still 10 marbles in the bag, but now only 6 of them are black and 1 is red.

Therefore, the probability of selecting a black marble, replacing it, then selecting a red marble is:

P(black, then red) = (7/10) × (1/10) = 0.07

P(black, then red) = 7 %

Therefore, the probability of selecting a black marble, replacing it, then selecting a red marble is approximately 7.0%.

P(yellow, then yellow) = (2/10) × (1/9) = 0.0222...

P(yellow, then yellow) = 2.2%

P(yellow, then black) = (2/10) × (7/9) = 0.1556...

P(yellow, then black) = 15.6%

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An inequality that is represented by this graph include the following: C. y ≤ (4 - x)/2.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (1 - 3)/(2 + 2)

Slope (m) = -2/4

Slope (m) = -1/2.

At data point (2, 1) and a slope of -1/2, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 1 = -1/2(x - 2)

y = -x/2 + 1 + 1

y = -x/2 + 2

y ≤ (4 - x)/2 (since the solid line is shaded below)

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$90m + $500 is the correct expression for the given data.

Troy's grandpa gave him a one-time gift of $700, so let's start there.

Next, let's think about Troy's monthly salary. He receives $40 a month from his grandfather, so in m months he would have gotten 40 million dollars.

He gets $50 a month from his mother, but she just started doing so 4 months after his grandfather, so he would have gotten that amount for (m-4) months. The entire sum he received from his mother would be as follows:

50(m-4)

We can add up the three sums to make the statement for Troy's overall payment after m months simpler:

Total amount = $700 + $40m + $50(m-4)

Condensing the phrase:

Total amount = $700 + $40m + $50m - $200

Total amount = $90m + $500

Therefore, the simplified expression for the amount of money Troy received m months after his mother started giving him money is $90m + $500.

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Answer: 338.5 mm²

Step-by-step explanation:

There are 3 rectangles for the lateral surface area

LA=Ph           lateral surface area is the are around which is found Permiter*height

LA=(7.5+10.5+11)9.5=275.5

Total area = LA + 2B                    B is the area of the base 1/2 bh

A=275.5+2(1/2)(10.5)(6)

=338.5 mm²

The correct equation is the one in option C:

[tex]\frac{7}{12} = \frac{14}{15}*\frac{5}{8}[/tex]

Here we have a quotient between fractions:

[tex]\frac{7}{12} /\frac{5}{8} = \frac{14}{15}[/tex]

To check that, we need to multiply both sides by the denominator 5/8, then we will get:

[tex](\frac{7}{12} /\frac{5}{8} )*\frac{5}{8} = \frac{14}{15}*\frac{5}{8}\\\\\frac{7}{12} = \frac{14}{15}*\frac{5}{8}[/tex]

That is the equation that we can see in option C, so that is the correct option.

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The circle's circumference is approximately 43.96 kilometers.

The circumference of a circle is given by the formula:

C = πd

where C is the circumference, π is the mathematical constant pi (approximately equal to 3.14), and d is the diameter of the circle.

Substituting the given value for the diameter (d = 14 kilometers) into the formula, we get:

C = 3.14 × 14 km

C = 43.96 km

Therefore, the circle's circumference is approximately 43.96 kilometers.

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If you go three times faster than another car, it will take nine times longer to stop your car than the other car.

To understand why, we need to consider the physics of stopping a car. The distance required to stop a car depends on the car's speed and braking ability.

Assuming the braking ability is the same for both cars, we can use the equation:

distance = (speed)² / (2 * deceleration)

where deceleration is the rate at which the car slows down.

Since we are assuming that the other car and your car have the same deceleration, we can write:

We know that your car is going three times faster than the other car, so:

speed your car = 3 * speed other car

Substituting this into the equation for the distance of your car, we get:

distance your car = (3 * speed other car)²/ (2 * deceleration)

distance your car = 9 * (speed other car)² / (2 * deceleration)

Therefore, the distance required to stop your car is nine times greater than the distance required to stop the other car. Since the time to stop is directly proportional to the distance required to stop, it will also take nine times longer to stop your car than the other car.

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The following is the detailed proof of that ∠2 and ∠8 are supplementary.

What are parallel lines?

Parallel lines are two or more lines in a plane which never intersect, no matter how far they are extended. They always remain the same distance apart and have the same slope. Parallel lines can be found in many geometric figures, such as squares, rectangles, and parallelograms.

From the figure we can see that ∠2 and ∠4 are supplementary angles.

That is, ∠2 + ∠4 = 180°.

We can also see that ∠4 = ∠8, because they are corresponding angles.

That means if we substitute ∠8 instead of ∠4 we get,

∠2 + ∠8 = 180°

This gives us the result that ∠2 and ∠8 are supplementary.

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Answer:

x = 7, y = -1

Step-by-step explanation:

3x + 7(x - 8) = 14

3x + 7x - 56 = 14

10x - 56 = 14

10x = 70

x = 7

y = 7 - 8

y = -1

The z-scores for each situation are given as follows:

a) 35% of the data is to the left: z = -0.385.

b) 18% of the data is to the right: z = 0.915.

The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

From the second bullet point, we have that the z-score for which 35% of the data is to the left of the Z-score is z with a p-value of z = 0.35, hence z = -0.385.

The z-score for which 18% of the data is to the right of the data-set, is z with a p-value of 1 - 0.18 = 0.18, hence it is z = 0.915.

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Because "7 feet 14 inches" is not a conventional or usual method to describe measurements, you would use the measurement "8 feet 4 inches" instead.

REASONS FOR USING 8 feet 4 inches:

For a few reasons, the measurement of 8 feet 4 inches is more frequently used than 7 feet 14 inches. First off, compared to 7 feet 14 inches, 8 feet 4 inches is a more common unit of measurement. Based on multiples of 12 inches, the imperial system of measurement is widely used in the United States and other regions of the world. This standard is followed by 8 feet 4 inches because 8 feet is equal to 96 inches and 4 inches is an extra increment. On the other hand, because 7 feet 14 inches is not a common unit of measurement, figuring out the entire length in inches needs an additional step.

Second, when converting to other units of measurement, utilizing 7 feet 14 inches can be confusing. For instance, it would be more challenging to translate 7 feet 14 inches to meters or centimeters than it would be to convert 8 feet 4 inches to meters. This is due to the ease with which 8 feet 4 inches may be converted to inches, which can then be transformed using normal conversion factors to centimeters or meters. However, in order to convert 7 feet 14 inches to inches, an additional step of taking 2 inches away from 8 feet to get to 6 feet 10 inches is needed.

Thirdly, a measurement of 8 feet 4 inches is more accurate than one of 7 feet 14 inches. When 7 feet 14 inches is used, it suggests that the measurement is rounded to the nearest inch, which may result in some measurement error. A more accurate measurement, however, is 8 feet 4 inches, which implies that the post office's length was calculated to the nearest inch.

Using 8 feet 4 inches is also more in line with how dimensions are typically expressed. The simplest version of a measurement should always be used, without any extraneous fractions or decimals. The less usual method of describing an object's length is 7 feet 14 inches, however, this adds an extra fraction to the measurement. Therefore, stating the length of the smallest post office in the United States using 8 feet 4 inches is more accurate and consistent.

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The expression of the given polynomial 4x³ − 3x² + 16x − 12 in the form of

products of binomial terms is given by option c. (x² + 4)(4x − 3).

Polynomial is equal to ,

4x³ − 3x² + 16x − 12

Now to rewrite the polynomial in the form of a products of binomial terms.

Take out the common factors we get,

Common factors between first two terms 4x³ − 3x² is equal to x² .

Common factors between last two terms 16x − 12 is equal to 4

4x³ − 3x² + 16x − 12

⇒ x² ( 4x - 3 ) + 4 ( 4x - 3 )

⇒ ( x² + 4 )( 4x - 3 )

Therefore, the polynomial in the form of products of binomial  is written as option c. (x² + 4)(4x − 3).

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The above question is incomplete, the complete question is:

Given the polynomial 4x³ − 3x² + 16x − 12, rewrite the polynomial as a product of binomials.

a. (x² − 4)(4x + 3)

b. (x² − 4)(4x − 3)

c. (x² + 4)(4x − 3)

d. (x² + 4)(4x + 3)

Answer:

(x2 + 4)(4x − 3)

Step-by-step explanation:

bc i got it right on my quiz

Answer:

r = 22 over 7

Test for symmetry about the vertical line

0 = pie over 2

Therefore, the answer is B

Step-by-step explanation:

I hope this helps :)

A 95% confidence interval estimate can be interpreted to mean that option (a) we are 95% confident that the true population mean is covered by the calculated confidence interval.

A 95% confidence interval is a range of values within which we are 95% confident that the true population mean lies. This means that if we take many random samples from the same population and calculate a 95% confidence interval for each sample, we would expect 95% of these intervals to contain the true population mean.

The 95% confidence level indicates the level of certainty we have in our estimate of the population mean, and it is a common statistical tool used in hypothesis testing and inferential statistics. However, it does not guarantee that the true population mean is within the calculated interval for a particular sample, as there is still a 5% chance of obtaining an interval that does not contain the true population mean.

Therefore, the correct option is (a) We are 95% confident that the true population mean is covered by the calculated confidence interval.

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Answer:

Step-by-step explanation:

127.58

Answer:

50 Starbusts in a bowl

Red = 20% of 50 = 10

Orange = 30% of 50 = 15

Yellow = 24% of 50 = 12

Pink = 50 - 15 - 12 - 10

= 13

Therefore, There are 13 pink Starbusts.

The amount of miles in total that Steph travels each week is 160 miles.

The distance is a length of path joining two or more points of reference. It is measured in meters and a scalar quantity.

From the given information, Steph travels to and from work via Bootie. Then it can be deduced that;

Distance from Crosby to Bootie = 4 miles

Distance from Bootie to Speke = 12 miles

So the distance traveled in one trip = 4 + 12

                                                           = 16 miles

Then distance traveled to and from work each day = 2*16

                                                           = 32 miles

Thus,

Total miles travelled to and from work each week can be determined as;

given that she works for 5 days in a week, then;

total distance per week = distance traveled per day x number of days in a week

                              = 32*5

                              = 160 miles

Therefore, Steph travels a total of 160 miles to and from work each week.

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A displacement vector is a vector that represents the overall change in position of an object, taking into account both the direction and magnitude of the change. It is a measurement of the distance and direction from an object's initial position to its final position.

Distance, on the other hand, is a scalar quantity that refers to the total amount of ground covered by an object, regardless of its direction. It is simply a numerical value indicating the length of the path traveled by an object.

When considering velocity vs speed, velocity is also a vector quantity that includes both the speed and direction of an object's motion. Average velocity is calculated by dividing the total displacement of an object by the time it took to travel that distance.

Average speed, however, is calculated by dividing the total distance traveled by the time it took to travel that distance.

Instantaneous velocity refers to the velocity of an object at a specific point in time, while instantaneous speed refers to the speed of an object at a specific point in time.

Both of these values can be calculated by taking the derivative of the object's position vs time graph. Overall, the difference between displacement and distance is that displacement takes direction into account, while distance does not. And when considering velocity vs speed, velocity includes both direction and speed, while speed only includes the numerical value of the distance traveled over time.

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To find the difference between 87 and 12 12, we need to convert 12 12 to an improper fraction.

12 12 = (12 x 2 + 12) / 2 = 36/2 + 12/2 = 48/2 = 24

Now we can subtract the fractions:

87 - 24/12 = 87 - 2 = 85

Therefore, the difference between 87 and 12 12 is 85.

The gradient of line A is 8, and the gradient of line B is -4.

We have,

To find the gradient of a line, we use the formula:

Gradient = (change in y) / (change in x)

For line A:

Between (1, 2) and (1.5, 6), the change in y is 6 - 2 = 4, and the change in x is 1.5 - 1 = 0.5.

So the gradient between these two points is 4 / 0.5 = 8.

Between (1.5, 6) and (2, 10), the change in y is 10 - 6 = 4, and the change in x is 2 - 1.5 = 0.5.

So the gradient between these two points is 4 / 0.5 = 8.

Since the gradient is constant for a straight line, we can conclude that the gradient of line A is also 8.

For line B:

Between (2, 0) and (1, 4), the change in y is 4 - 0 = 4, and the change in x is 1 - 2 = -1. So the gradient between these two points is 4 / (-1) = -4.

Between (1, 4) and (0, 8), the change in y is 8 - 4 = 4, and the change in x is 0 - 1 = -1. So the gradient between these two points is 4 / (-1) = -4.

Again, since the gradient is constant for a straight line, we can conclude that the gradient of line B is also -4.

Therefore,

The gradient of line A is 8, and the gradient of line B is -4.

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Answer:

----------------------

AAS congruence theorem states that:

We can see two angles and the non-included side are marked as congruent:

Hence the triangles are congruent:

Therefore the correct choice is C.

Answer:

61

Step-by-step explanation:

Quick maths

If the right rectangular-prism has a volume of 1.5 cubic inches, and product of length and width as 1.5, then the height of prism will be 1 inch.

In order to find the height of the "rectangular-prism", we use the formula for the volume of a rectangular prism, which is:

⇒ Volume = length × width × height;

We know that the volume is 1.5 in³ and

The product of the length and width is given to be 1.5,

So we can write : length × width × height = 1.5,  ....equation(1)

length × width = 1.5,

Substituting the product of "length" and "width" in equation(1),

We get,

⇒ 1.5 = 1.5 × height,

⇒ height = 1.5/1.5 = 1 inch.

Therefore, the height of prism will be 1 inch.

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Using equations, we can find that the person was getting 35 as the hourly wage and the bonus was zero.

Equations are mathematical statements with the equals (=) symbol and two algebraic expressions on either side. This illustrates the equality of the relationship between the expressions printed on the left and right sides. The formula LHS = RHS (left hand side equals right hand side) is utilised in all mathematical equations. To determine the value of an unknown variable that represents an unknown quantity, you can solve equations. A statement is not regarded as an equation if it has no "equal to" symbol. It'll be regarded as a term.

The given equation is:

y = 35x

Where, x is hours worked.

And y is total pay.

From the equation, we can get:

The hourly wage for the person is 35 units.

As there are no constants in the equation, we can conclude that the bonus for the person was 0.

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The commutative property of multiplication is used in -8/9x1=1x-8/9=-8/9

The commutative property, which states that changing the order of the factors in a multiplication expression does not change the result.

-8/9 x 1 = 1 x (-8/9)

Then, we can apply the commutative property again to switch the order of the factors:

1 x (-8/9) = (-8/9) x 1

Finally, we can simplify by multiplying the two factors:

(-8/9) x 1 = -8/9

Therefore, we have shown that -8/9 x 1 = 1 x (-8/9) = -8/9 using the commutative property of multiplication.

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We know that (A) ∠h = 28° as the angle pair ∠h and ∠I are alternate angles and hence they are equal.

The intersection of two parallel lines by a transversal produces alternate angles.

Because they are not additional angles, alternate angles often don't add up to 180 degrees, although they can if the transversal is perpendicular to the parallel lines.

So, by observing the figure we can easily state that:

∠h and ∠I are a pair of alternate angles and hence they must be equal.

So, according to this:

∠h = 28°

Therefore, we know that (A) ∠h = 28° as the angle pair ∠h and ∠I are alternate angles and hence they are equal.

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Answer: there's a 50-50 chance of at least two people having the same birthday.

In a group of 50 people, the expected number of days of the year which are one of their birthdays can be determined using the concept of probability which are one of their birthdays is approximately 194 days.

The expected number of days of the year which are one of their birthdays in a group of 50 people can be calculated using the formula E(X) = np, where n is the number of trials and p is the probability of success in each trial. In this case, there are 50 people and 365 days in a year, so each person has a probability of 1/365 of having their birthday on a particular day. Therefore, the expected number of people with a birthday on any given day is 50*(1/365) = 0.137. Since there are 365 possible days, we can multiply this by 365 to get the expected number of days with at least one birthday, which is approximately 50.034 days. So, the expected number of days of the year which are one of their birthdays in a group of 50 people is around 50.034.
In a group of 50 people, the expected number of days of the year which are one of their birthdays can be determined using the concept of probability.
Assuming that each person's birthday is equally likely to fall on any of the 365 days in a year (ignoring leap years), the probability of any particular day being a birthday is 1/365.
Now, the probability of a day not being a birthday for a single person is (364/365). For 50 people, the probability of a day not being any of their birthdays would be (364/365)^50.
To find the expected number of days with at least one birthday, we can calculate the probability of a day having at least one birthday, which is the complement of no birthdays on that day. This probability is:
1 - (364/365)^50
Now, we multiply this probability by the total number of days in a year to find the expected number of days with at least one birthday:
365 * (1 - (364/365)^50) ≈ 194.03
So, in a group of 50 people, the expected number of days of the year which are one of their birthdays is approximately 194 days.

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(a) The initial value of water in the tank is 88 gallons, and the rate of change is -6 gallons per minute (since the water is being drained). Therefore, the function that represents the amount of water in the tank, Y, after X minutes is: Y = -6X + 88.

(b) We know that the amount of water left in the tank is 34 gallons. To find out how long the tank has been draining for, we can plug in 34 for Y in the function and solve for X:

34 = -6X + 88

-6X = -54

X = 9

Therefore, the tank has been draining for 9 minutes.

Answer: $8.64.

Step-by-step explanation:

P = price of the pizza

R = radius of the pizza

We know that the price of the pizza varies directly as the square of its radius. This means that we can write the following equation:

P = kR^2

where k is a constant of proportionality.

We are given that a pizza with a diameter of 20 cm costs $6.00. This means that the radius of the pizza is 10 cm. We can use this information to find the value of k.

6 = k(10)^2

6 = 100k

k = 0.06

Now that we know the value of k, we can find the price of a pizza with a radius of 12 cm.

P = 0.06(12)^2

P = 0.06(144)

P = 8.64

Therefore, a pizza with a radius of 12 cm would cost $8.64.