1. Write two expressions that are equivalent to the expression listed below. You can use the equation editor to input your answers.
(x^{1/3)²

Based on given question question, following are the answers of blanks based on Midpoint Theorem.

1.) Definition of midpoint

The midpoint theorem states that the line segment joining the midpoints of any two sides of a triangle is parallel to the third side and equal to half of the third side.

2.) ∠ECD ≅ ∠BCA [Vertically opposite angle]

Vertical angles are a pair of non-adjacent angles formed by the intersection of two straight lines. In simple words, vertical angles are located across from one another in the corners of the "X" formed by two straight lines. They are also called vertically opposite angles as they are situated opposite to each other.

3.) ∠D ≅ ∠A [Alternate interior angle]

When two parallel lines are crossed by a transversal, the pair of angles formed on the inner side of the parallel lines, but on the opposite sides of the transversal are called alternate interior angles. These angles are always equal.

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The value when 7 is divided by 292 is given as 0.023972(approximation)

One of the fundamental mathematical operations is division, which involves breaking a bigger number into smaller groups with the same number of components. How many groups will be created, for instance, if 30 students need to be separated into groups of five for a sporting event? The division operation may be used to quickly and simply fix such issues. In this case, we must divide 30 by 5. 30 x 5 = 6 will be the outcome. There will thus be 6 groups with 5 students each. The initial number, 30, which is obtained by multiplying 6 by 5 may be used to confirm this figure.

The names of the phrases connected with the division process are referred to as division parts. The division is made up of the following four components: dividend, divisor, quotient, and remainder.

In the problem 7 is the Dividend and 292 is the divisor so

[when we add decimal 0 is added to the number and for each 0 in the quotient 0 is also added to the number if the zero is after the decimal]

      292 ) 700( 0.023972

              - 584                

                 1160

                - 976    

                  2840

                 -2628    

                    2120

                   -2044  

                       760

                      - 584

                         176

7 divided by 292 is 0.023972 (approx.)

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Step-by-step explanation:

what is the. meaning of this

The required answer for the given mathematical operation is 182.5

What are arithmetic operations?

A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.

Given, 67.4 + 43 + 30 + 42.10

        = 110.4 + 30 + 42.1

        = 140.4 + 42.1

        = 182.5

Hence, the required answer for the given mathematical operation is 182.5

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The estimated price of a new car in 4 years time if the inflation rate is 12.3% is 393050

In economics, "inflation" refers to a significant increase in the price of goods and services throughout an economy. This is why growing prices often cause inflation. Deflation, which is a sustained decline in the average level of prices for goods and services, is the reverse of inflation. The most common measure of inflation is the annualized percentage change in an index of general prices, also known as the inflation rate.

Given,

The cost of the car bought by a women=350000

Time=4 years

And inflation rate=12.3%

We know that,

Inflation rate=((B-A)/A)×100

Here A denotes the standing price

So, A=350000

B denotes estimated price

So, B=x

12.3=((B-350000)/350000)×100

43050=B-350000

B=393050

Therefore, the estimated price of a new car in 4 years time if the inflation rate is 12.3% is 393050.

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Answer:

f(3) = 10

Step-by-step explanation:

f (x) = x +7

plug in 3

f (3) = 3 + 7

add

f(3) = 10

Therefore, the new volume comes out to be 787.22 cm3.

The volume of a substance is a measurement of how much space it occupies. Matter is a term used to describe a physical substance that has mass and occupies space. In physical disciplines like chemistry, cubic meters are the standard unit of volume (m3). This yields other units like the litre (L) and milliliter (mL) (mL).

Here,

When the height was raised here by 13 inches, it was equivalent to adding an additional 13 levels, each measuring 56.23 cm3, to the prism that already existed.

Your new volume would therefore be: => 56.23 cm3 + 13 (56.23 cm3) = > 787.22 cm3.

therefore, the new volume comes out to be 787.22 cm3.

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Answer:

Step-by-step explanation:

3 small tiers + 5 medium tiers= 291 guests

1 small tier+5 medium tiers=247 guests

The 2 cakes have the same medium tiers(5 medium tiers). If we subtract  291-247 we will have the number of guest that  2 small tiers serve.

291-247= 44 guests serve per 2 small tiers

44:2=22 guests serve per one small tier.

So if we subtrack the number of guest that one small tier one the cake that has only one small tier we will obtain the number of guests that the 5 medium tiers serve.

247-22=225 guests serve per 5 medium tiers

225:5= 45 guests per 1 mediem tier.

Sorry, because english isn't my mother tongue.

For diagram 5, X = 76° and from diagram 6 x = 80° in the given triangles

An isosceles triangle is a type of triangle that has any two sides equal in length. The two angles of an isosceles triangle, opposite to equal sides, are equal in measure. In geometry, triangle is a three-sided polygon that is classified into three categories based on its sides, such as:

Scalene triangle (All three sides are unequal)

Isosceles triangle (Only two sides are equal)

Equilateral triangle (All three sides are equal)

Find attachment to understand the explanation

∠A = ∠C ( base angles of an isosceles triangle)

∠A = x and ∠C = 76

Therefore ∠X = 76°

For diagram 6

interior ∠A + exterior ∠A = 180°

but exterior ∠A = 110°

interior ∠A = 180  - 110

interior ∠A = 70°

∠A = ∠C( base angles of isosceles ΔBAC) which is 70°

∠A + ∠B + ∠c = 180

∠B = 180 - 70 - 70

∠B = 40°

but ∠CBA + ∠CBD = 90 because ∠B = 90° and ∠CBA = 40°

∠∠CBD = 90 - 40

∠CBD = 50°

But ∠∠CBD = ∠BDC( base angles of isosceles Δ)

so that

∠BCD + ∠CBD + ∠BDC = 180°( angles in a triangle)

x + 50 + 50 = 180

x = 180 - 100

x = 80°

In conclusion the value of x in the first and second diagrams are 76° and 80° respectively

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The mass of the substance that would remain after 50 years is 49 Kg

We know that the term radioactive decay has to do with the breakdown of a radioactive substance and such  a break down can be modelled by the use of a mathematical function as we can see here.

The mathematical function that we can be  able to use for the modeling is given as;  m(t)=120e^-0.018t where t is the time that is taken in years.

After 50 years we are going to have;

m(t)=120e^-0.018(50)

m(t)= 49 Kg

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Missing parts;

A certain radioactive material decay in such a way There’s a mass in kilograms remains after T years is given by the that the mass in kilograms remains after T years is given by the function m(t)=120e^-0.018t

How much mass remains after 50 years? Round to 2 decimal places.

There is a 0.001 percent chance that this song will be played on no more than two of the seven days.

A probability simple definition is what?

A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

Detailed explanation:

Since this is a combination issue, we must first determine the combination of 7 select 5, and then multiply that result by the chance of each possible outcome:

Pick 5 from a combination of 7:

C(7,5) = 7! / (5! * 2!) = 7*6/2 = 21

This figure indicates that there are 21 alternative ways that the five days we want to be allocated in the seven days could be used.

The likelihood of each event is now:

5 days of song playback: (0.15)5

The song wasn't played for two days: (0.85)2.

Therefore, the final likelihood is

P =(0.15)^5*C(7,5) * (0.85)^2 = 0.001

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The volume of a cone is given by the formula:

V = (1/3) * π * r^2 * h

Where V is the volume, r is the radius of the base, and h is the height of the cone.

In this case, the base diameter and the height of the cone are both equal to x units, so the radius of the base is x/2 units. Therefore, the volume of the cone is:

V = (1/3) * π * (x/2)^2 * x

= (1/3) * π * x^3 / 4

= (π/4) * x^3

The correct expression for the volume of the cone is therefore O πx^3.

The expression that represents the volume of the cone in cubic units is:

V = (1/12) π x³

It is a shape of a Christmas tree where there is a base of radius r and a top point called the apex.

The volume of a cone is 1/3πr²h

We have,

The volume of a cone can be calculated using the formula:

V = (1/3) πr²h

where r is the radius of the base and h is the height.

Since the diameter of the base is equal to x, the radius is equal to half the diameter, which is x/2.

Also, we know that the height of the cone is also equal to x.

Substituting these values into the formula, we get:

V = (1/3)π (x/2)² x

Simplifying this expression, we get:

V = (1/3)π(x²/4)x

V = (1/12)πx³

Therefore,

The expression that represents the volume of the cone in cubic units is:

V = (1/12) π x³

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Answer:

[tex]a_n=9n+26[/tex]

Step-by-step explanation:

An explicit formula for a sequence allows you to find the nth term of the sequence.

To determine if the sequence is arithmetic or geometric, calculate the differences between the terms:

[tex]35 \underset{+9}{\longrightarrow} 44 \underset{+9}{\longrightarrow} 53[/tex]

As the first differences are the same, the sequence is arithmetic with a common difference, d, of 9.

[tex]\boxed{\begin{minipage}{8 cm}\underline{General form of an arithmetic sequence}\\\\$a_n=a+(n-1)d$\\\\where:\\\phantom{ww}$\bullet$ $a_n$ is the nth term. \\ \phantom{ww}$\bullet$ $a$ is the first term.\\\phantom{ww}$\bullet$ $d$ is the common difference between terms.\\\phantom{ww}$\bullet$ $n$ is the position of the term.\\\end{minipage}}[/tex]

Substitute a = 35 and d = 9 into the formula to create an explicit formula for the nth term of the sequence:

[tex]\implies a_n=35+(n-1)9[/tex]

[tex]\implies a_n=35+9n-9[/tex]

[tex]\implies a_n=9n+26[/tex]

Answer:

Step-by-step explanation:

The risk of getting a cold is calculated by dividing the number of people who have a chance of getting a cold by the total number of people. In this case, the risk of getting a cold is 4 people / 20 people = 20%. Therefore, the risk of getting a cold is 20%.

Answer:

18.2

Step-by-step explanation:

20 + (n-1)-.2

n is the number of the term.

-.2 is the common difference

20 + (10-1) -.2

20 + 9(-.2)

20 - 1.8

18.2

The new 2 × 2 system of equation is

2y – 3z = 12

–3y – 8z = 7

What are linear equations ?

If a, b, c and r are real numbers (and if a, b, and c are not all equal to 0) then ax + by + cz = r is called a linear equation in three variables. (The “three variables” are the x, the y, and the z.) The numbers a, b, and c are called the coefficients of the equation.

How do you solve linear equations with 3 variables?

Pick any two pairs of equations from the system. Eliminate the same variable from each pair using the Addition/Subtraction method. Solve the system of the two new equations using the Addition/Subtraction method.

Given Equations:

x-y-2z=4 ............(1)

-x+3y-z=8 ..........(2)

-2x-y-4z=-1 ........(3)

Given Condition 1: use equation (1) with equation (2) to eliminate x

According to the condition,

x-y-2z=4 ........(1)

-x+3y-z=8 ......(2)

On adding (1) and (2), we get

(1-1)x +(-1+3)y +(-1-2)z = 4+8

2y - 3z = 12

Given Condition 2: use equation (1) with equation (3) to eliminate x

x-y-2z=4 .......(1)

-2x-y-4z=-1 ..(3)

on multiplying (1) both the sides with 2 , we get

2x - 2y -4z = 8

On adding with (3), we get

2x - 2y -2z = 8

-2x-y-4z=-1

-3y - 8z = 7

Thus, The new 2 × 2 system of equation is

2y – 3z = 12

–3y – 8z = 7

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The probability of the flights at the airlines at least 4 of the next 5 are overbooked from the given histogram is equal to 0.446.

Histogram is attached.

As given in the question,

Required histogram is attached.

From the attached histogram,

Histogram is attached.

The probability of 4 overbooked flights for the given airlines 'P (4) =  0.332

The probability of 4 overbooked flights for the given airlines 'P(5)' = 0.114

Required probability of at least 4 for the next 5 flights of the given airlines

= P ( x ≥ 4 ) upto next P(5)

= P(4) + P(5)

= 0.332 + 0.114

= 0.446

Therefore, the probability of at least 4 upto next 5 flights of the given airlines from the given histogram is equal to 0.446.

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Answer:

The answer is in the picture

Step-by-step explanation:

The explanation is in the picture

[tex]6\frac{5}{6}-4\frac{1}{3}[/tex] Showing my work using the mixed fraction the answer is [tex]=\frac{5}{2}[/tex]

What do you mean by mixed fraction?

A fraction represented by a quotient and a remainder is a mixed number

Fractions represent parts of a whole.

How can I convert an improper fraction to a mixed number?

Divide the numerator by the denominator.

Keep the denominators the same, take the quotient as an integer, and the remainder as the numerator of the correct fraction.

Given expression:

[tex]6\frac{5}{6}-4\frac{1}{3}[/tex]

⇒ [tex]\frac{41}{6}-\frac{13}{3}[/tex]

⇒ [tex]\frac{41-26}{6}[/tex]

= 15/6

= 5/2

Therefore, [tex]6\frac{5}{6}-4\frac{1}{3}=\frac{5}{2}[/tex]

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Answer:

C. 38 = x + 23

Step-by-step explanation:

X represents the amount she still needs to bake for the party.

38 represents the total amount of cookies she needs to bake.

Because she already made 23 cookies, you add to X

. Each lemon bar must be covered in decorative icing. A picture of the lemon bar is shown below.

Answer: 240 miles

Step-by-step explanation:

160m = 4 days

miles 40-1  days

        80-2

        120-3

         160-4

       200-5

          240-6

On solving the provided question, we got to know that -  the points (0,1) and (1,0) to be used to plot the graph .

An algebraic equation of the form y=mx+b (where m is the slope and b is the y-intercept) with one constant and only one first-order (linear) term is called a linear equation. The above is sometimes called a "linear equation in two variables" where x and y are variables.

To draw a straight line, just two points are needed.

Finding the points where the graph intersects is one approach.

[tex]the intercepts of the x and y axes[/tex]

[tex]Let x = 0 in the y-intercept equation.\\ Let y = 0 in the x-intercept equation.[/tex]

x =0→y=0+y=1⇒y=1←y-intercept

y =0→x+0=1⇒x=1←x-intercept

plot the points (0,1) and (1,0)

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Based on a system of equations, the number of seats in the upper section of the racetrack is 3,600.

A system of equations or simultaneous equations is two or more equations concurrently or simultaneously solved.

There are four methods for solving simultaneous equations:

The charge per lower-section seat = $85

The cost per upper-section seat = $60

The fee per field ticket = $35

Let the number of lower-section seats = x

Let the number of upper-section seats = 3x

Let the number of field tickets = y

Equation 1: x + 3x + y = 22,800 or 4x + y = 22,800

85x + 60(3x) + 35y = 948,000

Equation 2: 85x + 180x + 35y = 948,000

From equation 1, y = 22,800 - 4x ...Equation 3

Substitute Equation 3 in Equation 2 to eliminate y:

85x + 180x + 35(22,800 - 4x) = 948,000

85x + 180x + 798,000 - 140x = 948,000

125x = 948,000 - 798,000

125x = 150,000

x = 1,200

The number of seats for each racetrack section:

Lower section seats, x = 1,200

Upper section, 3x = 3,600 (1,200 x 3)

Field tickets, y = 22,800 - 4x

y = 22,800 - 4(1,200)

= 18,000

Check:

85x + 180x + 35y = 948,000

85(1,200) + 180(1,200) + 35(18,000) = 948,000

102,000 + 216,000 + 630,000 = 948,000

948,000 = 948,000

Total revenue:

Lower section seats = $102,000 (85 x 1,200)

Upper section seats = $216,000 (60 x 3 x 1,200)

Field tickets = $630,000 (35 x 18,000)

Total revenue = $948,000

Thus, based on simultaneous equations, we can conclude that there are 3,600 seats in the upper section.

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Step 1: Figure out when Savannah will double her account value:

We need to solve [tex]140000 = 70000\left(1+\frac{0.01375}{4}\right)^{4t}[/tex].

Divide by 70000:

       [tex]2 = \left(1+\frac{0.01375}{4}\right)^{4t}[/tex]

Take the natural log of both sides and bring the exponent down:

      [tex]\ln(2) = 4t\cdot\ln\left(1+\frac{0.01375}{4}\right)[/tex]

Divide by that mess multiplied by t:

      [tex]\dfrac{\ln(2)}{4\ln\left(1+\frac{0.01375}{4}\right)} = t[/tex]

Throw that into a calculator and you get about 50.497297884.

Depending on how picky your teacher is, we'd need to round this to the next time the interest is compounded, since it's only compounded each quarter, so t = 50.5.  (The fact is that Savannah's account will never exactly double in value.)

Step 2:

Now, we need to evaluate Carter's continuously compounded investment for 50.5 years:

    [tex]B = 70000e^{0.01125\cdot(50.5)}\approx123546.825994[/tex]

    B ≈ 123547 to the nearest dollar.

As a comparison, here's the other calculation with the more precise t value.

    [tex]B = 70000e^{0.01125\cdot(50.497297884)}\approx123543.070375[/tex]

    B ≈ 123543 to the nearest dollar.

Again, I would say the 50.5 calculation is actually more correct, since Savannah's account only compounds the interest each quarter, but you'll have to decide what your teacher would say.

Answer:

$123,543 (nearest dollar)

Step-by-step explanation:

Find the length of time Savannah has to invest her money for it to double.

[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Compound Interest Formula}\\\\$ A=P\left(1+\frac{r}{n}\right)^{nt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $n =$ number of times interest is applied per year \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]

Given:

Substitute the given values into the formula and solve for t:

[tex]\implies 140000=70000\left(1+\dfrac{0.01375}{4}\right)^{4t}[/tex]

[tex]\implies 140000=70000\left(1.0034375\right)^{4t}[/tex]

[tex]\implies2=\left(1.0034375\right)^{4t}[/tex]

[tex]\implies \ln2=\ln\left(1.0034375\right)^{4t}[/tex]

[tex]\implies \ln2=4t\ln\left(1.0034375\right)[/tex]

[tex]\implies t=\dfrac{\ln 2}{4 \ln\left(1.0034375\right)}[/tex]

[tex]\implies t=50.49729788[/tex]

Therefore, it would take approximately 50.5 years for Savannah's principal investment to double.

[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Continuous Compounding Formula}\\\\$ A=Pe^{rt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $e =$ Euler's number (constant) \\ \phantom{ww}$\bullet$ $r =$ annual interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]

Given:

Substitute the given values into the formula along with the found value of t and solve for A:

[tex]\implies A=70000e^{0.01125 \times 50.4972...}[/tex]

[tex]\implies A=123543.0704...[/tex]

Therefore, the amount of money that Carter would have in his account when Savannah's money has doubled in value is $123,543 (nearest dollar).

Answer:

83 degrees

Step-by-step explanation:

17^2 = 8^2 + 16^2 - 2 * 8 * 16 * cos (X)

289 = 64 + 256 - 16 * 16 * cos(X)

289 = 320 - 256 cos(X)

289-320 = -256 cos(X)

- 31 = -256 cos(X)

31 = 256 cos(X)

31/256 = 256/256 cos(X)

0.121094 = cos (X)

x = arccos 0.121094

x = 83.04475538

The amount of money left on the gift card, in term of the number of cups, a Lauren has bought is represented by the equation would be A = 10 - 2a.

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

We are given that from the task content that the total amount of money Lauren has initially is $10.

Hence, each cup of coffee costs $2.

Since the amount of money Lauren has left each time,

That is related to the number of coffee cups bought by the equation;

A = 10 -2a.

where a ranges be between 0 and 5.

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Answer:

[tex]\textsf{Slope form}: \quad y=-\dfrac{4}{5}x-\dfrac{26}{5}[/tex]

[tex]\textsf{Standard form}: \quad 4x+5y=-26[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]

Given equation:

[tex]5x-4y=1[/tex]

Rewrite in slope-intercept form:

[tex]\implies 5x-4y+4y=1+4y[/tex]

[tex]\implies 5x=1+4y[/tex]

[tex]\implies 5x-1=1+4y-1[/tex]

[tex]\implies 5x-1=4y[/tex]

[tex]\implies \dfrac{5}{4}x-\dfrac{1}{4}=\dfrac{4y}{4}[/tex]

[tex]\implies y=\dfrac{5}{4}x-\dfrac{1}{4}[/tex]

Therefore, the slope of the line is ⁵/₄.

If two lines are perpendicular to each other, their slopes are negative reciprocals.

Therefore, the slope of the perpendicular line is -⁴/₅.

Substitute the found slope -⁴/₅ and given point (1, -6) into the slope-intercept formula and solve for b:

[tex]\implies -6=-\dfrac{4}{5}(1)+b[/tex]

[tex]\implies -6=-\dfrac{4}{5}+b[/tex]

[tex]\implies b=-\dfrac{26}{5}[/tex]

Therefore, the equation of the perpendicular line in slope form is:

[tex]y=-\dfrac{4}{5}x-\dfrac{26}{5}[/tex]

[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Standard form of a linear equation}\\\\$Ax+By=C$\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are constants. \\ \phantom{ww}$\bullet$ $A$ must be positive.\\\end{minipage}}[/tex]

Multiply both sides of the equation in slope form by 5:

[tex]\implies y \cdot 5=-\dfrac{4}{5}x\cdot 5-\dfrac{26}{5}\cdot 5[/tex]

[tex]\implies 5y=-4x-26[/tex]

Add 4x to both sides:

[tex]\implies 5y+4x=-4x-26+4x[/tex]

[tex]\implies 4x+5y=-26[/tex]

Therefore, the equation of the perpendicular line in standard form is:

[tex]4x+5y=-26[/tex]