Find the area of the trapezoid

Log () helps to determine the single number to be multiplied.

Log stands for logarithm in algebra. The inverses of equations using exponents are called logarithms. Logs can be used to determine how many times one number needs to be multiplied to get another in its most basic form. For instance, to get 100 in the base-10 system, 10 must be multiplied by 10. In a base-10 system, the logarithm of 100 is therefore 2.

Log () expresses the power or exponent that a base number must be raised to or multiplied by in order to create another number in an ideal world. In situations where the user has data values that are significantly greater or lower than the other values, log scales are quite helpful. When displaying major percentage variations between data points, the user can also utilize a log scale.

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The population of the city grew from 2010 to 2020 by 13.37%.

A percentage is a number that tells us how much out of 100 and can also be written as a decimal or a fraction.

We have to given that;

In 2010, the population of a city was 237,000.

And, From 2010 to 2015, the population grew by 7.6%. From 2015 to 2020, it fell by 4.7%.

We know that;

Where, A = P (1+r)ⁿ

A = final population.

P = Initial population.

r = rate

n = time

Hence, The population in 2015 is, =

A = 237,000(1 + 0.076)⁵

A = 341829.629

And, The population in 2020 =

A = P (1 - r)ⁿ

A = 341829.629 (1 - 0.047)⁵

A = 268704.047

So, Percent grow = (268704.047 - 237,000) / 237,000 × 100

                           = 31704.047 / 237,000 × 100

                            = 13.37 %

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Answer:

x=5, y=3

Step-by-step explanation:

y=x−2;4x+y=23

Step: Solve y=x−2 for y:

Step: Substitute x−2 for y in 4x+y=23:

4x+y=23

4x+x−2=23

5x−2=23(Simplify both sides of the equation)

5x−2+2=23+2(Add 2 to both sides)

5x=25

5x/5 = 25/5(Divide both sides by 5)

x=5

Step: Substitute 5 for x in y=x−2:

y=x−2

y=5−2

y=3(Simplify both sides of the equation)

Answer:

102.3 kilometers per hour

Step-by-step explanation:

A car travel the distance of D equals 450 km for T equals 4.4 hours at a constant rate. What is the speed of the car in kilometers per hour

The formula to calculate Speed = Distance (Kilometers)/ Time(hours)

The speed of the car = 450km/4.4 hours

102.27272727 kilometers per hour

Approximately = 102.3 kilometers per hour

Answer:

C(t) = 5t for 0 < t ≤ 3

C(t) = (8t-9) for 3 < t ≤ 6

C(t) = 44 for 6 < t ≤ 10

C is given in thousands of dollars and t is given in months.

Total lump sum to be paid at the end of the 6 months for the total 10 months that the construction company works on the parking garage = $44000

Step-by-step explanation:

We will do a piecewise analysis for this cost function.

How to obtain the total cost changes with each time interval.

In the first 3 months,

C(t) = 5t for 0 < t ≤ 3

Note that C is given in thousands of dollars

In the next 3 months,

C(t) = (8t-9) for 3 < t ≤ 6

- Here, it gets a little complex, we use the upper limit of the previous interval and the lower limit of this new interval to get the constant to be subtracted from the normal 8t that characterizes this interval.

8(3) = 24

5(3) = 15

constant = 24 - 15 = 9

In the last 4 months,

C(t) = 44 for 6 < t ≤ 10

- For the last four months, it is a single sum of $5000 plus the [8(6) - 9] from the previous inteval

C = [8(6) - 9] + 5 = 39 + 5 = 44

So, the cost of parking, tracked month after month gives

T | Cost (in thousands of dollars)

1 | 5

2 | 10

3 | 15

4 | 23

5 | 31

6 | 39

7 | 44

8 | 44

9 | 44

10 | 44

Total lump sum to be paid at the end of the 6 months for the total 10 months that the construction company works on the parking garage = $44000

Hope this Helps!!!

This is not my answer yet is a stollen verrified one.

Answer:56

Step-by-step explanation:

Let ttt be the initial number of trees.

Hint #22 / 5

MacDonald now has t-5t−5t, minus, 5 trees and each one produced 210210210 oranges this harvest.

The total number of oranges produced is 210(t-5)210(t−5)210, left parenthesis, t, minus, 5, right parenthesis.

Hint #33 / 5

Since the trees produced a total of 417904179041790 oranges, let's set this equal to 417904179041790:

\qquad210(t-5)=41{,}790210(t−5)=41,790210, left parenthesis, t, minus, 5, right parenthesis, equals, 41, comma, 790

Now, let's solve the equation to find the initial number of trees (t)(t)left parenthesis, t, right parenthesis.

Hint #44 / 5

\begin{aligned}210(t-5)&=41790\\&\\ \dfrac{210(t-5)}{\blue{210}}&=\dfrac{41790}{\blue{210}}&&\text{divide both sides by $\blue{210}$}\\ \\ t-5&=199\\ \\ t-{5}\pink{+5}&=199\pink{+5}&&\pink{\text{add }} \pink{5} \text{ to both sides}\\ \\ t&=204\end{aligned}

210(t−5)

210

210(t−5)

​

t−5

t−5+5

t

​

=41790

=

210

41790

​

=199

=199+5

=204

​

​

divide both sides by 210

add 5 to both sides

​

Hint #55 / 5

The equation is 210(t-5)=41790.210(t−5)=41790.210, left parenthesis, t, minus, 5, right parenthesis, equals, 41790, point

MacDonald's farm initially had 204204204 orange trees.

Related content

Here's link[tex]^{}[/tex] to the answer:

bit.[tex]^{}[/tex]ly/3gVQKw3

Answer:

16. C

17. A

Step-by-step explanation:

16 - sin38=x/200

17- tanx=(36)/(32)

The best answer from the choices provided is a = plus-or-minus 16 . Option C

A quadratic equation can be defined as an equation that can be rearranged in a standard form

Such that;

These quadratic equation are also described as polynomial equation having its highest degree as 2.

From the information given, we have that;

3a² - 21 = 27

collect like terms

3a² = 27 + 21

Add the values

3a² = 48

Divide both sides by 3

a² = 48/3

a² = 16

Hence, the value is a² = 16

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Answer:  First, let's consider the rotation of 180 degrees clockwise. This can be thought of as a reflection over the x-axis, followed by a reflection over the y-axis.

The reflection over the x-axis will negate the y-coordinate, while the reflection over the y-axis will negate the x-coordinate. So after the rotation, the coordinates of point C will become (-5,-5)

Next, we'll consider the translation 5 units up. Translating a point up means that we'll add 5 to its y-coordinate. So the coordinates of point C'' will become (-5,-5) + (0, 5) = (-5, 0)

So the coordinates of C'' are (-5,0)

Therefore the answer is B.

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Other two are not true! A is untrue bc .90 pefer silver calculators. C-  .25 want model 55, and .32 for Model 77

Answer:

7.42

Step-by-step explanation:

y = (40.81/5.5)x

y = 7.42x

If the pickup charge for taxi is $3.50 and additional charge of $0.75 per mile , then the cost for riding 5 miles is $7.25  and cost for riding m miles is $[tex]3.50+0.75m[/tex]   .

The pickup charge that taxi service charges is = $3.50  ;

the additional charge for per miles driven is = $0.75  ;

we have to find the cost for riding 5 miles ;

So , the total cost for riding 5 miles is = [tex]Pickup Charge + (Additional Charge)\times(Number Of Miles Driven)[/tex] ;

substituting the values , the total cost equation becomes ;

[tex]Total Cost = 3.50 + 0.75\times5[/tex]

= [tex]3.50+3.75[/tex]

= 7.25

So , the cost for 5 miles is = $7.25  ;

to find cost for driving "m" miles ,we substitute the number of miles = m;

[tex]Total Cost = 3.50+0.75\times m[/tex]

= [tex]3.50+0.75m[/tex]

Therefore , the cost for riding m miles is $ [tex]3.50+0.75m[/tex] .

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Answer:

8.8

Step-by-step explanation:

Normally, to find the distance between two points, you would use the distance formula, but these two points have the same x-coordinate, meaning they will form a vertical line when connected. To find the length of a vertical line you find the distance between the y-coordinates, in this case -4.7 and 4.1. Finding the distance is the same as finding the absolute value of the difference:

|4.1 -(-4.7)|

|4.1 + 4.7|

|8.8|

8.8

so for given expression x⁴-2x³-x²-2x+1 = (x-1)² - (2x+1)

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

An algebraic expression in mathematics is an expression created using variables, constant algebraic numbers, and algebraic operations. A good example of an algebraic expression is 3x2 2xy + c.

we can start by squaring the equation x²+(1/x)=3

so we have x⁴ + 2x² + (1/x)² = 9

x⁴ + 2x² + 1 = 9x²

x⁴ - 7x² + 1 = 0

Now we can factor it

(x²-1)(x²-1) = 0

so x² = 1

now we can substitute x² = 1 in the equation x⁴-2x³-x²-2x+1

x⁴-2x³-x²-2x+1 = x⁴-2x³-1-2x+1

= x⁴-2x³-2x-1

= (x⁴-2x³) - (2x+1)

= x⁴-2x³-2x-1

= (x²-x)² - (2x+1)

= (x-1)² - (2x+1)

so x⁴-2x³-x²-2x+1 = (x-1)² - (2x+1)

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Answer:

[tex]\begin{bmatrix}-1 & 2 \\ \frac{3}{2} & -\frac{5}{2} \end{bmatrix}[/tex]

Step-by-step explanation:

Inverse of a matrix is given by,

[tex]\begin{bmatrix}a & b\\ c & d\end{bmatrix}=\frac{1}{ad-bc}\begin{bmatrix}d & -b\\ -c & a\end{bmatrix}[/tex]

By using this property,

[tex]\begin{bmatrix}5 & 4\\ 3 & 2\end{bmatrix}^{-1}=\frac{1}{(5\times 2-4\times 3)}\begin{bmatrix}2 & -4\\ -3 & 5\end{bmatrix}[/tex]

              [tex]=-\frac{1}{2}\begin{bmatrix}2 & -4\\ -3 & 5\end{bmatrix}[/tex]

              [tex]=\begin{bmatrix}-1 & 2 \\ \frac{3}{2} & -\frac{5}{2} \end{bmatrix}[/tex]

Therefore, inverse of the given matrix will be [tex]\begin{bmatrix}-1 & 2 \\ \frac{3}{2} & -\frac{5}{2} \end{bmatrix}[/tex]

The required two numbers are 9 and 41.

The equation is defined as a mathematical statement that has a minimum of two terms containing variables or numbers that are equal.

Let x be the lesser number, and y be the greater number.

From the question, we know that:

x + y = 50 (Equation 1: The sum of the two numbers is 50)

y = 5x - 4 (Equation 2: The greater number is four less than five times the lesser number.)

The equation is to solve for one of the variables, and then substitute that value into the other equation to find the other variable.

Then, two numbers are x = 9 and y = 41.

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Answer:

So the correct expansion of (4x + 1)(2x7 - 2) is 8x^27 - 8x2 + 2x7 - 2

Step-by-step explanation:

When expanding an algebraic expression like (4x + 1)(2x7 - 2), you can use the distributive property to find the product of each term in the first set of parentheses with each term in the second set of parentheses, and then add them together. The distributive property is the process of multiplying one term in the parentheses by each of the terms outside the parentheses.

Here is the correct expansion of (4x + 1)(2x7 - 2):

(4x + 1)(2x7 - 2) = 4x(2x7) + 4x(-2) + 1(2x7) + 1(-2)

= 8x^27 + -8x2 + 2x71 + -21

= 8x^27 + -8x2 + 2x7 + -2

= 8x^27 - 8x2 + 2x7 - 2

So the correct expansion of (4x + 1)(2x7 - 2) is 8x^27 - 8x2 + 2x7 - 2

It's important to note that you can also use FOIL method which is the acronym for the steps of the distributive property, First, Outside, Inside, Last.

As per the conditions given by the question, the 95% confidence interval of the true proportion who said that they would take a ride in a self-driving car is (53.3856%, 62.6144%).

Now, According to the question:

What is confidence interval?

A confidence interval describes the likelihood that a population parameter would fall between a set of values for a given percentage of the time. Confidence ranges that include 95% or 99% of anticipated observations are frequently used by analysts.

To find the 95% confidence interval of the true proportion, we need to use the following formula:

point estimate +/- (margin of error * z-score)

The point estimate in this case is the sample proportion, which is 58%. The margin of error is 2.4%, and the z-score for a 95% confidence interval is 1.96.

Plugging these values into the formula, we get:

58% +/- (2.4% * 1.96)

This simplifies to:

58% +/- 4.6144%

So the 95% confidence interval is:

(53.3856%, 62.6144%)

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Answer:

v = 4

Step-by-step explanation:

⭐What is the midsegment of  a triangle?

⭐What are some properties of the midsegment?

Thus, we have to make an equation using the properties of the midsegment to solve for v.

Working:

[tex]SU = \frac{1}{2}(QR)[/tex]

[tex]19v - 38 = \frac{1}{2}(-5v + 96)[/tex]

[tex]38v - 76 = -5v + 96[/tex] . . . . .  multiply both sides by 2 to get rid of the fraction

[tex]43v = 172[/tex] . . . . . add 5v and 76 to both sides

∴ [tex]v = 4[/tex] . . . . . . . . . divide both sides by 43 to isolate v

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Answer:

151 in^3

Step-by-step explanation:

please find the image required to answer this question in the attached image

The rocket consists of two shapes - a cone and a cylinder

the volume of the plastic = volume of cone + volume of cylinder

volume of a cylinder = nr^2h

Volume of a cone 1/3(nr^2h)

n = 22/7

r = radius

the diameter is the straight line that passes through the centre of a circle and touches the two edges of the circle.

A radius is half of the diameter

Radius = 5/2 = 2.5

Height of cone = 11 - 6 = 5

Volume of plastic = (22/7) x (2/5^2) x 6  + (1/3) x (22/7) x (2/5^2) x 5 = 117.9 + 32.7 = 150.6 in^3 = 151

Answer:

H i think hope it helps you

thank you

Answer:

x=

y=31

Step-by-step explanation:

hope this helps

Answer:

-8:1

Step-by-step explanation:

How to solve the function operation :D

Simplify 7-15= -8

Then simplify 3-2= 1

Total= -8:1

A high school statistics class wants to conduct a survey to determine what percentage of students in the school would be willing to pay a fee for participating in after-school activities. Twenty students are randomly selected from each of the freshman. sophomore. junior, and senior classes to complete the survey.  This plan is an example of Stratified random  type of sampling .

What does "stratified random sampling" mean?

A population is divided into smaller subgroups known as strata as part of a sampling technique called stratified random sampling.

           During stratified random sampling, also known as stratification, groups of people are divided into groups based on shared traits or characteristics, such as level of education or income.

What is a good illustration of a stratified sampling technique?

A stratified sample is one that guarantees that the various strata (subgroups) of a given population are fairly represented in the sample population as a whole.

                                   One could, for instance, divide a sample of persons into age-related subgroups, such as 18–29, 30-39, 40–49, 50–59, and 60 and above.

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Answer:

C = 31

Step-by-step explanation:

always do the parenthesis first so (2+4) = 6

3² + 4(6) x 6 ÷ 8 + 4 (Use PEMDAS)

9 + 4(6) x 6 ÷ 8 + 4, multiply 4 and 6

9 + 24 x 6 ÷ 8 + 4, multiply 24 and 6

9 + 144 ÷ 8 + 4, divide 144 and 8

9 + 18 + 4, now just add

31.

Answer:

c) 31

Step-by-step explanation:

9 + 4(6) * 6 / 8 + 4

9 + 24 * 6 /8 + 4

9 + 144 / 8 + 4

9 + 18 + 4

= 31