Fill in each blank with ONE word to create a sentence to explain slope in the context of this problem: The amount of blank is blank at a rate of slope number per blank.

The surface area of the right triangular pyramid is, 269.5 square units

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

Dimensions of the right triangular pyramid are,

X = 11 units

Y = 10 units

Z = 13 units

Now, The surface area of the right triangular pyramid is,

Area of Lateral triangle = 1/2 × X × Z

                                    = 1/2 × 11 × 13

                                    = 71.5 unit²

And, Area of Base Triangle = 1/2 ·  base ·  height

                                          = 1/2 ·  X ·  Y

                                          = 1/2 ·  11 units · 10 units

                                          = 55 units²

Now, use the method described above to find the surface area of the pyramid.

Surface Area = 3( Area lateral ) + ( Area base )

                    = 3 ( 71.5 square units ) + ( 55 square units )

                   = 269.5 square units

Thus, The surface area of the right triangular pyramid is, 269.5 square units

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Answer: Jim ran 25 1/4 miles altogether.

Step-by-step explanation: I saw him do it.

Answer:

below

Step-by-step explanation:

Given cos, you will have to use this to calculate sin because csc is  1/ sin

Remember    cos^2 + sin^2 = 1

                        (2/5)^2 + sin^2 = 1

                                  sin^2 = 21/25  

                                    sin = sqrt (21) / 5     (ignoring negative root)

csc = 1/sin = 5 / sqrt(21)

Answer:

Step-by-step explanation 0.4 0.8 5 7 10, 10

An equation to represent one way you can find how many miles Emily’s plane flew each hour is y = 182x.

In Mathematics, a proportional relationship can be defined as a type of relationship that generates equivalent ratios and it can be modeled or represented by the following mathematical expression:

y = kx

Where:

Assuming the variable m represent the miles flown each hour, an equation for the number of miles Emily’s plane flew each hour can be calculated as follows;

y = kx

y = (2184/12)x

y = 182x

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Complete Question:

Emily took an airplane trip. Her plane flew an equal number of miles each hour. Write an equation to represent one way you can find how many miles Emily's plane flew each hour.

Use this to help you:

Air travel time: 12 hours

Destination: 2,184 miles​

By performing subtraction we know that the farmer sold 4.2 kilograms of apples in the market.

One of the four operations used in mathematics, along with addition, multiplication, and division, is subtraction.

Removal of items from a collection is represented by the operation of subtraction.

For instance, in the following image, there are 5 2 peaches, which means that 5 peaches have had 2 removed, leaving a total of 3 peaches.

Subtraction in mathematics is the process of subtracting one integer from another. In other words, the result of subtracting two from five is three. After addition, subtraction is usually the second operation you learn in math class.

So, to find the weight of apples, perform subtraction as follows:

= 6.7 - 2.5

= 4.2 kilograms

Therefore, by performing subtraction we know that the farmer sold 4.2 kilograms of apples in the market.

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The total area is given as 160 sq feet. The total yard that is to be purchased is 18 yards

To get the area of the room we would first have to find the area of the sides.

We can call 1 of the areas S1.

The length l1 = 13

The width w1 = 16

area =

s1 = 13 * 16

We have

s2 with

l2 = 6

w2 = 8

then the area

s2 = 6 * 8

S1 - s2

= 208 - 48 =

160

1 square yard = 9 square foot

17.7778 = 160 square feet

Juan has to purchase approximately 18 yards

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Answer:

A)  (-7, 6)

Step-by-step explanation:

The graph of the inverse function is a reflection in the line y = x.

The mapping rule for a reflection in the line y = x is:

Therefore, if point (6, -7) is on the graph of the function f(x), the point that is on the graph of the inverse function f⁻¹(x) is:

The dot notation of the recurring decimal is 51.674674674674.....

Recurrent decimal, often known as recurring decimal, is a decimal number made up only of digits that repeat after the decimal at regular intervals. As an illustration, 46.374374374, 517.338383, etc. Depending on the sort of digits that follow the decimal point—whether they are recurring, non-repeating, ending, or unending—decimals can be divided into many groups (infinite digits after the decimal point).

Here the given recurring decimal is 51.674,

To write into dot notation , we need to write repeated numbers after digits. Then,

=> 51.674674674674....

Hence the dot notation of the recurring decimal is 51.674674674674.....

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The function has domain = {2, , 5, - 4, - 5} and rangle = {1, 4, 5, 3, - 6} and it is not a function.

Suppose we have an ordered pair (x, y) then the domain of the function is the set of values of x and the range is the set of values of y for which x  is defined.

From the given coordinate plots the ordered pairs are,

(2, 1), (2, 4), (5, 5), (- 4, 3), and (- 5, - 6).

We know a relation is not a function when two distinct ordered pairs have the same x-coordinate.

In this case (2, 1) and (2, 4) have the same x-coordinate and hence it is not a function.

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Answer:The quotient of 8,426 divided by 82 can be found using long division or a calculator. When rounded to the nearest hundredth, the quotient is:

102.85

Therefore, the answer is 102.85.

Step-by-step explanation:

Answer:

Values from the set = 1, 2, 3, 4.

Step-by-step explanation:

Now we have to,

→ Find the required value of x.

The inequation is,

→ 4x - 2 < 15

Then the value of x will be,

→ 4x - 2 < 15

→ 4x < 15 + 2

→ 4x < 17

→ x < 17/4

→ [ x < 4.25 ]

Hence, the answer is x < 4.25.

The exponential function [tex]A = 3.2 \times \frac{1}{2}^{\frac{36}{8}}[/tex] determines the amοunt of substance after 36 years to be 0.2 grams.

The fοrmula for an exponential functiοn is [tex]f(x) = a^x[/tex], where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.

The amοunt of a radioactive substance left after a certain number of half-lives can be calculated using the expοnential equation formula -

[tex]A = A_0 \times \frac{1}{2}^{\frac{t}{T}}[/tex]

where -

A0 is the initial amοunt of the substance

A is the amοunt of the substance remaining after t years

T is the half-life οf the substance

In this case, the half-life is 8 years, sο T = 8.

We want tο know how much of the original 3.2 grams of the substance wοuld be left after 36 years, so t = 36.

We can plug these values intο the formula to get -

[tex]A = 3.2 \times \frac{1}{2}^{\frac{36}{8}}[/tex]

A ≈ 0.2 grams

Therefοre, after 36 years, only about 0.2 grams of the original 3.2 grams of the substance wοuld be left.

The equation that best mοdels this situation is -

[tex]A = 3.3 \times \frac{1}{2}^{\frac{t}{8}}[/tex]

where A represents the amοunt of the substance remaining after t years, in grams.

Therefοre, the equation is [tex]A = 3.2 \times \frac{1}{2}^{\frac{36}{8}}[/tex].

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Set D ∈ {76, 90, 92, 94, 96}

Sets are groups of clearly defined objects or elements in mathematics. A set is denoted by a capital letter, and the cardinal number of a set is enclosed in a curly bracket to indicate how many members there are in a finite set.

As per the given data:

Set D consists of positive two-digit even numbers greater than 74 without the digit 8 in them.

For writing set D in the roster form:

For greater than 74:

{76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98}

Without the digit 8:

{76, 90, 92, 94, 96}

Hence, Set D ∈ {76, 90, 92, 94, 96}

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The population of the country in 2024, as predicted by this function, is 1,847 million. The population of the country in 2051, as predicted by this function, is 2,927 million.

An exponential function is a mathematical function that increases or decreases at a rate proportional to its current value. Exponential functions are used in a variety of sciences and everyday applications. For example, population growth is an exponential function of time because the population increases by a fixed percentage each year.

The exponential function f(x) = 565(1.026)ˣ models the population of a country, f(x), in millions, x years after 1970. Substituting 0 for x, the population of the country in 1970 was 565 million. Substituting 27 for x, the population of the country in 1997 was 1,118 million. The population of the country in 2024, as predicted by this function, is 1,847 million. The population of the country in 2051, as predicted by this function, is 2,927 million.

It appears that the population of the country is growing by a factor of 3 every 27 years. This is evident from the fact that the population in 1997 is 3 times the population in 1970, and the population in 2024 is 3 times the population in 1997. This pattern is expected to continue with the population in 2051 being 3 times the population in 2024.

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Answer:

The scale of measurement used by the researcher is interval scale as the data is continuous and there are equal intervals between the values.

Mean = (1+2+4+5+7+11)/6 = 5

Median = (4+5)/2 = 4.5

Mode = There is no mode in the data set as none of the numbers are repeated.

Range = maximum value - minimum value = 11 - 1 = 10

Sample Variance = ((1-5)^2 + (2-5)^2 + (4-5)^2 + (5-5)^2 + (7-5)^2 + (11-5)^2)/(6-1) = 14.67

Standard Deviation = sqrt(sample variance) = sqrt(14.67) = 3.83

Mean + 2SD = 5 + 2*3.83 = 12.66, rounded to the nearest integer = 13.

According to the Empirical Rule, 68% of the sample lies within 1 standard deviation of the mean. Therefore, we need to find the values that are 1 standard deviation away from the mean:

Lower limit = Mean - SD = 5 - 3.83 = 1.17, rounded to the nearest integer = 1.

Upper limit = Mean + SD = 5 + 3.83 = 8.83, rounded to the nearest integer = 9.

So the number of leaves associated with 68% of the sample is between 1 and 9.

Step-by-step explanation:

Answer: The area of a square is given by the formula A = s^2, where s is the length of a side of the square.

In this case, the length of the field is 5x³y5, so each side of the square is also 5x³y5. Therefore, the area of the square can be found as:

A = (5x³y5)^2

A = 25x^6y^10

So the area of the field in terms of x and y is 25x^6y^10.

Step-by-step explanation:

Answer: The ratios that have a unit rate is 9/8 miles:5/6hours and 7miles: 3/4 hours

Step-by-step explanation:

Unit rate is the ratio of the distance travelled o the time taken.

For us to know which of the ratios has a unit rate greater than 1, we need to divide the distance by the time as shown;

If distance = 9/8 miles and time = 5/6 hours

Hence the ratio that has a unit rate is 9/8 miles:5/6hours

If distance = 7 miles and time = 3/4 hours

The required number line shows that the four numbers between 10 and 20 that have a remainder of 2 when divided by 3.

In math, a number line can be defined as a straight line with numbers arranged at equal segments or intervals throughout. A number line is typically shown horizontally and can be extended indefinitely in any direction.

To show the numbers between 10 and 20 that have a remainder of 2 when divided by 3, we need to start with the first number in that range that has a remainder of 2 when divided by 3, which is 11. Then, we can add 3 to that number to get the next number that has a remainder of 2 when divided by 3, which is 14.

We can continue adding 3 to each previous number to get the rest of the numbers that meet this condition:

11, 14, 17, 20

So, these are the four numbers between 10 and 20 that have a remainder of 2 when divided by 3. We can plot them on the number line as shown.

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The equation for the least squares regression line is y = 0.488x + 8.543.

Least squares regression line is the line of best fit formed when the relationship is linear for the given data points.

Number of data points, N = 5

x : 35         39         63         86         93        Σx = 316

y : 38         20         28         55         56        Σy = 197

x² : 1225   1521    3969    7396     8649       Σ(x²) = 22,760

xy : 1330   780     1764     4730     5208       Σ(xy) = 13,812

Slope of the line, m = [N Σ(xy) - Σx Σy] / [N Σ(x²) - (Σx)²]

                                 = [ (5 × 13812) - (316 × 197) ] / [(5 × 22760) - (316)²]

                                 = 6808/13944

                                 = 0.488

Intercept, b = [Σy - (m Σx)] / N

                   = [197 - (0.488 × 316)] / 5

                   = 8.543

Equation of the line is y = mx + b

y = 0.488x + 8.543

Hence the equation of the line is y = 0.488x + 8.543.

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If point M is the largest integer less than √ 28, the value of point M is found as 5.

A number that contains both positive and negative integers, including zero, is called an integer. There are no fractional or decimal parts in it. Integers include things like -5, 10, 1, 45, 8, 97, and 3,43.

Point M is the largest integer less than √ 28.

√ 28 = 5.29

largest integer which is less than 5.92 is 5.

Thus, if point M is the largest integer less than √ 28, the value of point M is found as 5.

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The amount of space each student will occupy is 0.25 square meters of space in the classroom.

To find the amount of space each student will occupy,

We need to first subtract the area taken up by the teacher's table and shelves from the total area of the classroom.

Then we can divide the remaining area by the number of students.

Let's say the total area of the classroom is A.

Then we have:

A - 350 ( the area available for students)

If each student occupies an area of x, then we have:

40x = A - 350

Substituting the first equation into the second equation, we get:

40x = (A - 350)

We can solve for x by dividing both sides by 40:

x = (A - 350) / 40

We know that there are 40 students, so we can substitute that into the equation:

x = (A - 350) / 40 = (360 - 350) / 40 = 0.25

Therefore, each student will occupy 0.25 square meters of space in the classroom.

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The average speed for the second part of the journey is 100 kilometer per hour.

Average Speed is the ratio of the total distance travelled to the total time taken to travel the distance.

Given that,

Distance travelled by motorist in first part = 90 km

Time taken to travel the distance = 1 1/2 hour = 1.5 hours

Distance travelled in second part of the journey = 50 km

Time taken to travel the distance = 1/2 hour = 0.5 hour

Average speed = Distance / Time

                          = 50 / (1/2)

                          = 100 km/h

Hence the average speed is 100 kilometer per hour.

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Answer:

[tex]\frac{49}{45}[/tex] OR [tex]1\frac{4}{45}[/tex]

Step-by-step explanation:

The requried value of (25-y) half dollars is 12.5 - 0.5y dollars.

Simplification involves applying rules of arithmetic and algebra to remove unnecessary terms, factors, or operations from an expression. The goal is to obtain an expression that is easier to work with, manipulate, or solve.

Here,
Assuming you want to find the value of a certain number of half-dollars when each half-dollar has a value of 50 cents, we can use the following formula:

Value = Number of coins x Value of each coin

Here, the number of half-dollars is (25-y), and the value of each half-dollar is 50 cents or $0.5. So, we can write:

Value of (25-y) half dollars = (25-y) x 0.5

Value of (25-y) half dollars = 12.5 - 0.5y

Therefore, the value of (25-y) half dollars is 12.5 - 0.5y dollars.

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The coordinates of the roots of parabola are (2,0) and (4,0).

An equation that sets a point on a curve at the same distance from both a fixed point and a fixed line is known as a parabola. The focus and directrix of a parabola are its fixed point and fixed line, respectively. Another important thing to keep in mind is that the fixed point does not lie on the fixed line. Every position that is equally far from the focus and directrix of two given points is said to be the locus of a parabola. The vertex of a parabola is the location where it turns sharpest. A parabolic function has a maximum value if it is shaped like a "," else, it has a minimum value.

The roots of the parabola are the coordinates where the graph intersects the x-axis (y = 0).

As you can see, the vertex of the graph is above the x-axis, and opens down, meaning that there are two roots for the graph.

Points of intersection: (2,0),(4,0)

Therefore, the coordinates of the roots are (2,0) and (4,0).

Hence the equation of the parabola will be y=3/4 (x²-1).

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Answer:

9 = 3 x 3

Explanation:

Answer:

18π or

Step-by-step explanation:

To find the area of a semicircle, use the formula of the area of a semicircle.

Area = [tex]\frac{1}{2}[/tex] π r^2

Radius = 6

Area = [tex]\frac{1}{2}[/tex] π 6^2

Area = [tex]\frac{1}{2}[/tex] (36π)
Area = 18π (in terms of π)

Area = 56.52 (in terms of 3.14)