Find each angle and arc measure.



m∡RST = ______ degrees

m∡RUT = ______ degrees

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The volume of a right circular cone which has a height of 11.9 ft and a base with a radius of 16.3 ft as required is;

As evident in the task content; the volume of a right circular cone a height of 11.9 ft and a base with a radius of 16.3 ft is to be determined.

Recall, the volume of the cone is;

V = (1/3) × πr²h

V = (1/3) × π × 16.3² × 11.9

V = 3310.9 ft³.

Ultimately, the volume of the right circular cone is; 3310.9 ft³.

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Answer:

3310.9

Step-by-step explanation:

In mathematics, the expression "to the power of" pertains to the exponent, signifying how many times a key number is to be multiplied by itself.

Expressing this idea in English can be done well by using the term "to the power of." To show this, 2 raised to the third power can be interpreted as 2 multiplied by itself three times, resulting in 8.

Therefore, the possible reason behind using the word "power" is probably due to the fact that when the exponent rises, the outcome number is wide, either being greater or smaller, made on the base being above or below 1. This implies that the figure holds more significant value.

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In 58 seconds after starting its descent, the aircraft will touch down.

The plane will land when its altitude y is zero.

So we can set y = 0 in the equation:

0 = 464 - 8x

Solving for x:

8x = 464

x = 58

Therefore, the plane will land 58 seconds after it begins its descent.

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The amount of sand Eloise will put in each sandbox is 7.5 pounds (30 divided by 4).

The minimum time required to depreciate the value of the car is 12 years.

Let us assumed the time to be t. Representing the formula for calculation of time-

Final value = Principal value × [tex] {(1 - rate of depreciation)}^{t} [/tex]

Keeping the values in formula to find the time period

3000 = 18700 × [tex] {(1 - 14.25%)}^{t} [/tex]

Solving the expression

[tex] {(0.8575)}^{t} [/tex] = 3000/18700

Cancelling zeroes common in numerator and denominator

3000/18700 = [tex] {(0.8575)}^{t} [/tex]

Taking log on both sides of the equation

t log 0.8575 = 30/187

Keep the value

t = log 0.8575 30/187

t = 12 years

Hence, it will take 12 years for value depreciation.

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The graph of the inequality is added as an attachment

From the question, we have the following parameters that can be used in our computation:

y < -2 + 7

The above expression is an inequality that implies that

The value of y is less than the sum of -2 and 7

Next, we plot the graph

See attachment for the graph of the inequality

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The equations that can be used to solve for y, the length of the room are y * (y - 5) = 750, y^2 - 5y = 750 and (y + 25)(y – 30) = 0

From the question, we have the following parameters that can be used in our computation:

Area = 750

Length = y

Width = y - 5

The area is the product of the length and the width

So, we have

y * (y - 5) = 750

When expanded. we have

y^2 - 5y = 750

Lastly, we have

(y + 25)(y – 30) = 0 -- when factored

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Answer: a. d. f.

Step-by-step explanation:

Answer:

The style of William Holman Hunt's The Awakening Conscience (1853) is Pre-Raphaelite.

The largest interior angle of the triangle is the angle A

The side lengths of the triangles are given as

b = 10 cm

a = 14 cm

The other side length is not given

So, we solve the question using the two side lengths

Having said that:

The general rule is that; the higher the side length, the larger the angle

14 cm is greater than 10 cm

This means that the angle A is greater than the angle B

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The equation for total cost of buying and shipping the records is

76.4x + 80

We have,

She buys 3 in good condition

So, the cost for 3 good condition

= 3 (10.5x)

= 31.5 x

and, She buys 1 in Fair condition

So, the for 1 fair condition

= 5x

and, She buy 2 new condition then the price is

= 39.9 x

So, the equation for total cost of buying and shipping the records is

= 31.5x + 5x + 39.9x + 8

= 76.4x + 8

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The angle that is an obtuse angle (that is, greater than 90° but less than 180°) is 120°. The correct option is B. 120°

An obtuse angle is an angle that is greater than 90° but less than 180°. Thus, if x is an obtuse angle, the range of values for x are

90° < x < 180°

From the given question, we are to determine the angle which obtuse.

In the given figure, to determine the angle which is obtuse, we will determine the angle that is greater than 90° but less than 180°.

The angle that is greater than 90° but less than 180° is 120°.

Thus,

The obtuse angle is the angle that measures 120°

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The function to determine the length of the candle, y, after burning for x number of hours is y = 9-x/2

Given that, a candle is nine inches long and the packaging states the candle burns down at the rate of 1/2 an inch per hour.

We need find function to determine the length of the candle, y, after burning for x number of hours.

Since, the melting rate of the candle is 1/2 per hour,

So, the function will be =

y = 9-x/2

Hence, the function to determine the length of the candle, y, after burning for x number of hours is y = 9-x/2

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The base of the natural logarithm ln(x) expression is 10

From the question, we have the following parameters that can be used in our computation:

ln(x)

The base of the above expression is not stated

The general rule of logarithm is that when the base of the expression is not stated, then the base is 10

If the base of the expression is stated, then the expression would take the form

lnₐ(x), where the base is represented with the variable a

This means that the base of the natural logarithm ln(x) expression is 10

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Using an equation, the number of children, parents, and grandparents in attendance were:

An equation is an algebraic statement showing the equality or equivalence of two or more mathematical expressions.

Mathematical expressions combine variables, numbers, values, and constants using mathematical operands.

The total number of people in attendance at the family reunion = 400

Let the number of grandparents = x

Let the number of parents = 2x

Let the number of children = 2x + 50

x + 2x + 2x + 50 = 400

5x = 350

x = 70

Grandparents = 70

Parents = 140 (2 x 70)

Children = 190 (2 x 70 + 50)

Total = 400 (70 + 140 + 190)

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The distance between the areas of the two states is A = 1.727 x 10⁵ km²

Given data ,

Let the area of Nebraska = 2 x 10⁵ km²

Let the area of Massachusetts = 2.73 x 10⁴ km²

The difference between the areas of Nebraska and Massachusetts A =  the area of Nebraska - the area of Massachusetts

On simplifying the exponents , we get

A = 2 x 10⁵ km² - 2.73 x 10⁴ km²

Taking the common factor , we get

A = 10⁴ ( 20 - 2.73 )

A = 10⁴ ( 17.27 )

A = 1.727 x 10⁵ km²

Hence , the area is A = 1.727 x 10⁵ km²

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The area of the entire rectangle as polynomial is x^2 + 8x + 12

From the question, we have the following parameters that can be used in our computation:

Height = x + 2; Width = x + 6

Broken rectangles

The area of the rectangle is the product of the dimensions

Adding the heights and the width of the individual rectangles, we have

Height = x + 2; Width = x + 6

So, the area is

Area = (x + 2)(x + 6)

Expand

Area = x^2 + 8x + 12

Hence, the area expression is x^2 + 8x + 12

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92 more students favor visiting Florida than Colorado

From the question, we have the following parameters that can be used in our computation:

Students = 400

Florida = 38%

Colorado = 15%

The percentage difference is

Difference = 38% - 15%

So, we have

Difference = 23%

This means that

Students = 23% * 400

Evaluate

Students = 92

Hence, the number of students is 92

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The angles that you get when a circle is divided into 4 equal parts, would be four 90 degree angles.

The reason these angles are called 'right angles' is because they create an exact 90-degree angle, signifying one fourth of a complete circle. Every specific angle is named as a 'quadrant,' as it covers a quarter or a quadrant of the circle.

These four perpendicular angles stand side by side - having in common not just one diameter of the circle but also a shared vertex, which is at the center of the circle. Together, they share uniformly the circle into four unique sections - each turning toward a distinct quadrant of the circle parallel to their placement.

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The given reflection transformation is a rigid transformation, such that the dimensions are preserved

The statements that are true about the image of triangle ABC following a reflection Bout the the line y = 2·a are;

AB = RS

ΔABC ≅ ΔRST

m∠BAC ≅ m∠SRT

Reasons:

The given parameters are;

Triangle ΔABC is reflected across the line y = 2·x

Given that a reflection is a rigid transformation, we have;

The distance between two points on a preimage is the same as the distance between the corresponding points on the image;

Therefore;

ΔABC is congruent to ΔRST by Side-Side-Side SSS, rule of congruency, such that we have;

AB ≅ RS, BC ≅ ST, and AC ≅ RT

m∠BAC ≅ m∠SRT

m∠BCA ≅ m∠STR

m∠BAC ≅ m∠SRT

Therefore;

The true statements are;

AB = RS

ΔABC ≅ ΔRST

Therefore;

m∠BAC ≅ m∠SRT given that ΔABC ≅ ΔRST

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complete question:

Triangle ABC is reflected across the line y=2x to map onto triangle RST. Select all statements that are true.

Question 3 options:

AB=RS

AB=2RS

ΔABC~ΔRST

△ABC≅ΔRST

m∠BAC=m∠SRT

m∠BAC=2m∠SRT

Answer:

Step-by-step explanation:

To answer this question, we need to calculate the mean and median of the given data set and then see how the additional earnings affect them.

First, let's calculate the mean of the original data set:

Mean = (50 + 82 + 39 + 50 + 31 + 70) / 6 = 322 / 6 = 53.67

Next, let's calculate the median of the original data set. To do this, we need to arrange the data set in order:

31, 39, 50, 50, 70, 82

The median is the middle value, which is 50.

Now, let's add Becky's earnings of $23 to the data set:

31, 39, 50, 50, 70, 82, 23

The new data set has 7 values. Let's calculate the new mean:

Mean = (50 + 82 + 39 + 50 + 31 + 70 + 23) / 7 = 365 / 7 = 52.14

The new mean is less than the original mean, so we can eliminate options A and C.

Now let's calculate the new median. We need to arrange the data set in order:

23, 31, 39, 50, 50, 70, 82

The median is still 50.

Therefore, the answer is option D: The mean decreases and the median remains the same.

Answer:

53,352 cm

Step-by-step explanation:

1. The first step is to draw the rectangle draw one rectangle over the other and start labeling the sides.

2. After labeling use the rectangle prism formula: L times W times H in this case it would be 38 times 18 times 13 this is equal to 8,892.

3. From there, we know that there are six sides so we can multiply this value by 6 so it would be 8,892 times 6 = 53,352 cm.

If I made a mistake or if have any questions feel free to tell me!

-Mathematics and Science Major for Middle School Students at Harvard University

The total amount of FICA tax that was deducted from the executive's paychecks for the year 2018 is $10,860.80.

The FICA tax is imposed on both employees and employers to fund Social Security and Medicare which are federal programs that provide benefits for retirees, the disabled and children of deceased workers.

The Social Security tax will be calculated on the maximum taxable earnings of $128,400:

= $128,400 x 6.2%

= $7,961.20

The Medicare tax will be calculated on the entire earnings:

= $200,000 x 1.45%

= $2,900.

The total FICA tax will be:

= Social Security tax + Medicare tax

= $7,960.80 + $2,900

= $10,860.80.

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Answer:79

Step-by-step explanation:

Answer:

b[tex]\sqrt{a}[/tex]

Step-by-step explanation:

using the rule of radicals

[tex]\sqrt{ab}[/tex] = [tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] , then

[tex]\sqrt{ab^2}[/tex]

= [tex]\sqrt{a}[/tex] × [tex]\sqrt{b^2}[/tex]

= [tex]\sqrt{a}[/tex] × b

= b[tex]\sqrt{a}[/tex]

Answer:

452 square centimeters.

Step-by-step explanation:

To find the area of a circle, we use the formula:

A = πr^2

Where A is the area of the circle, r is the radius, and π is a mathematical constant (approx. 3.14).

Given that the radius of the circle is 12 cm, we can substitute r = 12 in the formula:

A = π(12)^2

A = 3.14 x 144

A = 452.16

Therefore, the area of the circle is approximately 452.16 square centimeters. However, we need to round the answer to the nearest whole number.

Since the decimal part of the answer is less than 0.5, we round the answer down to the nearest whole number. Therefore, the area of the circle nearest the whole number is 452 square centimeters.

Answer:

B. 122.88

Step-by-step explanation:

Since t is the number of years since 1910, we can find the t value we need for the equation by subtracting 1910 from 1980:

t = 1980 - 1910 = 70

Now, we can plug in 70 for t to find the amount of currency in 1980:

[tex]M(t)=2.08(1.06)^t\\M(70)=2.08(1.06)^7^0\\M(70)=122.8779348\\M(70)=122.88[/tex]

Thus, the amount of currency in 1980 according to the model was $122.88 billion