Question 4 of 10 The function a(b) relates the area of a trapezoid with a given height of 12 and one base length of 9 with the length of its other base. It takes as input the other base value, and returns as output the area of the trapezoid. a(b)-12.b+9 Which equation below represents the inverse function b(a), which takes the trapezoid's area as input and returns as output the length of the other base?​

The number that will produce the greatest number of rectangular arrangements is 6.

From the information, when forming a marching band the leader wants the number so the greatest number of arrangements can be made and she has to choose between 18 and up to 42 members.

It should be noted that the question simony relate to the highest common factor of the values that are given. This will be illustrated as:

18 = 1, 2, 3, 6, 9 and 18

42 = 1, 2, 3, 6, 7, 14 and 42

Therefore, the highest common factor is 6 and this is the greatest number.

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A fraction which is not equivalent to 12/20 is: D. 2/3

A fraction simply refers to a numerical quantity which isn't expressed as a whole number. This ultimately implies that, a fraction is simply a part of a whole number.

In Mathematics, a fraction comprises two (2) main parts and these include the following:

Next, we would evaluate the given fractions as follows:

Dividing the fraction by 2, we have:

12/20 = 6/10

Dividing the fraction by 3, we have:

12/20 = 4/5

Dividing the fraction by 4, we have:

12/20 = 3/5

Multiplying the fraction by 2, we have:

12/20 = 24/40

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Answer:

omg what is standard deviation that was on my psat today

The water level compared to normal at the end of April is 23 13/42 inches below normal.

From the information, the water level in a lake was 22 inches below normal at the beginning of March and rhe water level decreased by 3 1/6 inches in March and increased by 1 6/7 inches in April.

The water level compared to normal at the end of April will be:

= -22 - 3 1/6 + 1 6/7

= - 22 - 3 7/42 + 1 36/42

= -22 - 1 13/42

= -23 13/42

There, it is 23 13/42 below normal.

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Answer: μ=​20, σ=4.0

Step-by-step explanation:

The interest that they will they have to pay if it takes them 4 years and 3 months to repay the loan is $1377.

From the information, Isaac's parents borrow $3600.00 from the bank for new appliances for their kitchen and the simple interest rate is 9% per year.

Principal = $3600

Rate = 9%

Time = 4 years 3 months = 4.25

It should be noted that simple interest is calculated as:

= Principal × Rate × Time / 100

= (3600 × 9 × 4.25) / 100

= 137700 / 100

= $1377

Therefore, the interest is $1377.

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The most appropriate choice for right rectangular prism will be given by

a) Dimension of the prism = [tex]\frac{4}{3}[/tex] ft [tex]\times[/tex] [tex]1[/tex] ft [tex]\times[/tex] 1 ft

b) There are 36 unit cubes

c) Volume of prism = [tex]\frac{4}{3}[/tex] [tex]ft^3[/tex]

What is a right rectangular prism?

A geometrical figure which has 6 faces, 12 edges and 8 vertices is called a right rectangular prism.

If l is the length, b is the breadth and h is the height of right rectangular prism, volume will be l [tex]\times[/tex] b [tex]\times[/tex] h .

a)  The right rectangular prism is filled with [tex]\frac{1}{3}[/tex] ft of unit cubes

   Length of right circular prism = [tex]4 \times \frac{1}{3} = \frac{4}{3}[/tex]  ft

   Breadth of right circular prism = [tex]3 \times \frac{1}{3} = 1[/tex] ft

   Height of right circular prism = [tex]3 \times \frac{1}{3} = 1[/tex] ft

   Dimension of the prism = [tex]\frac{4}{3}[/tex] ft [tex]\times[/tex] [tex]1[/tex] ft [tex]\times[/tex] 1 ft

b) Number of unit cubes = [tex]4 \times 3 \times 3[/tex]

                                         = 36 ft

c) Total volume = [tex]\frac{4}{3} \times 1 \times 1[/tex]

                          = [tex]\frac{4}{3}[/tex] [tex]ft^3[/tex]

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Complete Question

The diagram has been attached here

Answer:

it is 1,152

Step-by-step explanation:

4×3=12×96=1,152

Answer:a

Step-by-step explanation:

the total number of students in class is given by the equation x - 1 / 2 x - 1 / 4 x - 1 / 7 x = 3 and is equal to 28.

Let the total number of students be x

Mathematics = 1 / 2 x

natural philosophy = 1 / 4 x

Silence = 1 / 7 x

Remaining = 3

So, we get the equation as:

x - 1 / 2 x - 1 / 4 x - 1 / 7 x = 3

(28 x - 14 x - 7 x - 4 x) / 28 = 3

3 x / 28

x = (3 × 28) / 3

x = 28

Number of students in class = 28.

Therefore, the total number of students in class is given by the equation x - 1 / 2 x - 1 / 4 x - 1 / 7 x = 3 and is equal to 28.

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Answer:

i cannot see the lines very well, but i can tell you how to find slope

Step-by-step explanation:

slope is rise/run. find where the line hits a intersection on the graph, and count the squares across the graph where it hits another intersection. it should not be on the line though, because that is only the run. then count how many squares up it takes till you touch where the line hits another intersection. that is the rise. then divide the rise by the run.

It should be noted that translating the phrase into an algebraic expression the sum of b and 9 will be b + 9.

It should be noted that an algebraic expression in mathematics simply refers to the expression which is made up of constants and variables.

From the information given, we want to translate the sum of b and 9 into an expression. This will be:

= b + 9

Therefore, the expression is b + 9.

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The maximum height the ball reaches is 80 feet

The ball stayed in the air for 1 second

A function can be defined as a law, rule or expression that shows the relationship between two known variables:

Given the function:

h(t) = -16t² + 96

Where;

To determine the maximum height in feet that the ball reached, we have to substitute the value of t as

We have:

h(1) = -16(1)² + 96

expand the bracket

h = -16 + 96

Add the values

h = 80 feet

The time it took the ball to stay in the air would be 1 second, this is so because the ball reached it maximum height as t = 1 sec

Hence, the maximum height is 80 feet

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Given ratio:

Multiply both sides by the L.C.M of their denominator

The L.C.M of 2 and 4 is 4

Hence:

[tex]\frac{2.4}{10^{4} }[/tex] is the simplest form of scientific notation.

In mathematical notation, operations, unnamed numbers, relations, and any other mathematical objects are represented by symbols that are combined into expressions and formulae. Using scientific notation, one can express extremely big or extremely small values. When a number between 1 and 10 is multiplied by a power of 10, the result is represented in scientific notation. For instance, 650,000,000 can be expressed as 6.5 108 in scientific notation. A system of symbols for designating unique items. Example: In mathematics, the symbol "∞" stands for "infinity." There are many notations in mathematics.

Given Data

8.1×10^−7

3×10^−3

Dividing

[tex]\frac{8.1(10}{3(10}[/tex]⁷₃

[tex]\frac{8.1}{3}[/tex] × 10⁻⁷⁻⁽⁻³⁾

2.7 × 10⁻⁴

[tex]\frac{2.4}{10^{4} }[/tex]

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Answer:

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The plot of the points on a coordinate plane is added as an attachment

The coordinate of the point on a coordinate plane is given as

Point = (-3 1/2, -1 1/4)

As a general rule, we express the above coordinate as follows:

(x, y) = (-3 1/2, -1 1/4)

The next step is to remove the bracket

So, we have the coordinates into x and y coordinates

This is represented as

x = -3 1/2 and y = -1 1/4

The interpretation of the above equations is:

Next, we plot the points

See attachment for the plot of the points on a coordinate plane

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The 2 events are independent​ because the outcome of the first draw doesn't affect the outcome of the second.

ANSWER

independent​

The value of x for the given parallel line d || e is x = 20.

From the given question;

The lines d || e.

Thus, both sum of both angles will be 180 by linear pair.

2x - 3 + 7x + 3 = 180

Solving;

9x = 180

x = 20

Thus, the value of x obtained for the given parallel lines is 20.

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The price of the house will double the original value in 35 years

The given parameters from the question are

Initial value of the house = $265,100

Rate of gain = 2% of its value every year

An exponential function is represented as

y = a *(1 + r)^x

Where

This means that

a = 265,100

r = 2%

So, we have

y = 265,100 *(1 +2%)^t

When the price doubles, we have

2 * 265,100 = 265,100 *(1 +2%)^t

Divide both sides by 265,100

So, we have

2  = (1 +2%)^t

Evaluate the sum

So, we have

2 = 1.02^t

Take the logarithm of both sides

t * log(1.02) = log(2)

Divide

t = log(2)/log(1.02)

Evaluate

t = 35

Hence, the number of years is 35

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Using system of equation, the solution shows that it will take 50 weeks before Jacob and Diego will be tied in the race to complete community service hours for scouting.

As given,

let us assign the unknown quantity (number of weeks) a variable x.

Jacob plans to devote 5 hours per week from now onwards. Hence his volunteer hours will cumulate to 5x+50 as he has already completed 50 weeks.

Diego plans to devote 6 hours per week from now onwards. Hence his volunteer hours will cumulate to 6x.

For Jacob and Diego to tie in the race, their volunteer hours should be equal.

Solution of the  system of equation is given by:

6x = 5x+50

=> 6x-5x = 50

=> x = 50

Therefore, using system of equation, the solution shows that it will take 50 weeks before Jacob and Diego will be tied in the race to complete community service hours for scouting.

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The area under the standard normal curve between z=0 and z=3 is 0.4987.

It should be noted that because the normal distribution is symmetrical on both sides of the mean and is a continuous probability distribution, the right side of the center is the opposite of the left side.

The normal distribution was first termed by early statisticians who observed that the same shape repeatedly appeared in many distributions. The characteristics of normal distributions are as follows: Bell-like in its symmetry. The distribution's mean and median, which are both at its center, are equal.

The area will be illustrated as:

P(0 < Z < 3)

From the distribution table. In this case, it's important to look at the normal distribution table under the z score for the values of zero less than Z and Z less than 3. This will be:

= 0.9987 - 0.5

= 0.4987

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Given the set of data:

12, 4, 11, 3, 4, 0, 13, 13, 2, 6, 11, 0, 10, 11, 3, 4, 0, 10, 13, 2, 11, 9.

Let's complete the given frequency table using the set of data given.

Frequency can be said to be the number of times a number occurs in a set of data.

hus, we have:

• 0 - 2

ubmbers between 0 - 2 in the data set: 0, 2, 0, 0, 2 ==> 5 times

• 3 - 5

3 - 5: 4, 3, 4, 3, 4, ==> 5 times

• 6 - 8:

6 - 8: 6, ==> 1 time

• 9 - 11:

: 9 - 119, 11, 11, 10, 11, 10, 11, 9 ==> 7 times

• 12 - 14:

12 - 134: 12, 13, 13, 13 =3 ==> 4 times.

Therefore, the complete table is:

Answer:

[tex]5 \times 10^4[/tex]

Step-by-step explanation:

Let the number of grains of rice be g.

[tex]\frac{g}{1}=\frac{1}{2 \times 10^{-5}} \\ \\ g=\frac{1}{2} \times 10^5 \\ \\ =5 \times 10^4[/tex]

The statement that is not true is that at this rate, it would take less than 10 mins for the temperature of the liquid to rise to 52 degrees.

We know that in a graph we see the presentation of a data set by the use of the Cartesian coordinates. There is the vertical axis and there is the horizontal axis. The vertical axis is the axis where we have to plot the time while the vertical axis is the axis where we have to plot the temperature as we can see from the image attached to this answer.

The graph as show has to the points which are; (0, 0) and (6.5, 26). Thus we can use the both points to obtain the slope of the graph and this would give us;

m = 26 - 0/ 6.5 - 0

m = 4

This implies that the rate at which the temperature rise with time is 4 degrees centigrade per hour. In a quarter hour, the temperature would rise to;

y = mx

y = 4(15)

y = 60 degrees centigrade.

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(a)

The angle R of triangle PQR is congruent to the angle U of triangle STU. So

(b)

The angle H of triangle GHJ is congruent to angle Q of triangle PQR and angle Q of triangle PQR is congruent to angle T of triangle STU, which means

So,

(c)

The side QR of triangle PQR is congruent to the side TU of triangle STU. So

(d)

The side JG of triangle GHj is congruent to side RP of triangle PQR and side RP of triangle PQR is congruent to side US of triangle STU. So

Answer:

Step-by-step explanation:

1)

f(x) = m*x + b

x = 0

5 =m*0 + b

b = 5

2)

2 = m*2 + 5

2*m = - 3

m = - 3/2

3)

f(x) = - 3/2*x + 5

The true statements about the solutions to this number line include the following:

A. -1 is a solution.

E. -1.5 is a solution.

F. All negative numbers are solutions.

A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numbers (numerical values) that are placed at equal intervals along its length.

This ultimately implies that, a number line can be used to determine the difference between two numbers such as 23 and 12. Also, a number line typically increases in numerical value towards the right and decreases in numerical value towards the left.

In conclusion, we can reasonably infer and logically deduce that an inequality which represent the solutions to this number line in interval notation is given by: -1 ≤ x ≤ ∞.

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Answer:

18.25%

Step-by-step explanation:

730/4000 = 0.1825

The equation of the line is x + 3y = 2

Linear equations are equations that have constant average rates of change.

The given parameters are

Slope, m = -1/3

Points (x, y) = (1, 1/3)

A linear equation is represented as

y = slope * (x - x₁) + y₁

Where

(x₁, y₁) = (1, 1/3)

Substitute (x₁, y₁) = (1, 1/3) and Slope, m = -1/3 in the equation y = slope * (x - x₁) + y₁

So, we have

y = -1/3* (x - 1) + 1/3

Multiply through by 4

So, we have

3y = -(x - 1) + 1

Remove the brackets

3y = -x + 1 + 1

So, we have

x + 3y = 2

Hence. the linear equation is x + 3y = 2

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