Please help! I have little time to do this

The volume of the smaller wedge cut from a sphere of radius 4 by two planes that intersect along a diameter at an angle of π/6 is 1/6.

What is volume ?

Volume is a measurement of three-dimensional space that is occupied. It is frequently expressed quantitatively using SI-derived units, as well as several imperial or US-standard units. Volume and the notion of length are connected.

Consider that the tetrahedron is bounded by the coordinate planes and the plane 8 x+y+z=2

Evaluate the triple integral [tex]\iiint_E d V$.[/tex]

The lower boundary of tetrahedron is the plane z=0 and the upper boundary of tetrahedron is the plane z=2-8 x-y.

And the projection is y=2-8 x.

The x-limits are obtained by taking y=0 and z=0 in 8 x+y+z=2.

[tex]$$\begin{array}{r}8 x=2 \\x=\frac{2}{8} \\x=\frac{1}{4}\end{array}$$[/tex]

Therefore, the region becomes [tex]$R=\left\{(x, y, z) / 0 \leq x \leq \frac{1}{4}, 0 \leq y \leq 2-8 x, 0 \leq z \leq 2-8 x-y\right\}$[/tex].

Therefore, the integral becomes

[tex]$ \iiint_E d V=\int_0^{\frac{1}{4}} \int_0^{2-8 x} \int_0^{2-8 x-y} d z d y d x $[/tex]

[tex]$=\int_0^{\frac{1}{4}} \int_0^{2-8 x}[z]_0^{2-8 x-y} d y d x $[/tex]

[tex]$ =\int_0^{\frac{1}{4}} \int_0^{2-8 x}[2-8 x-y] d y d x $[/tex]

[tex]$ =\int_0^{\frac{1}{4}}\left[2 y-8 x y-\frac{y^2}{2}\right]_0^{2-8 x} d x . $[/tex]

[tex]$ =\int_0^{\frac{1}{4}}\left[2(2-8 x)-8 x(2-8 x)-\frac{(2-8 x)^2}{2}\right] d x $[/tex]

[tex]$ =\int_0^{\frac{1}{4}}\left[32 x^2-16 x+2\right] d x $[/tex]

[tex]$ =\left[32\left(\frac{x^3}{3}\right)-16\left(\frac{x^2}{2}\right)+2 x\right]_0 $[/tex]

[tex]$ =32\left(\frac{\left(\frac{1}{4}\right)^3}{3}\right)-16\left(\frac{\left(\frac{1}{4}\right)^2}{2}\right)+2\left(\frac{1}{4}\right)-0 $[/tex]

[tex]$ =\frac{1}{6} $[/tex]

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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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The expression that is equivalent to the given value would be = 18-i . That is option C.

An equivalent expression is defined as the type of expression that is similar to a given value when simplified.

The given expression = ( 3 + 4i) ( 2 - 3i)

Expand the given expression by removing the brackets as follows:

= =2(3+4i)−3i(3+4i)

=(6+8i)−(9i−12)

= (6+12)+i(8−9)

=18−i.

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New coordinates become (-2,8) (-2,-4) and (4,-4)

What do you mean by scale factor?

Magnification is defined as the scale ratio of a given original object and a new object that is a representation of it but of a different size (larger or smaller).

The new figure obtained is similar to the original figure

The expansion description should state how much the shape was expanded.

Suppose a triangle with the vertices (-1, 4), (-1, -2) and (2, -2) were dilated, with the center of dilation at the origin and with a scale factor of 2.

As we know, if (x,y) point dilated by scale factor a then new coordinates become (ax, ay)

So, if triangle having vertices (-1, 4), (-1, -2) and (2, -2) were dilated, with the center of dilation at the origin and with a scale factor of 2 then new coordinates become (-2,8) (-2,-4) and (4,-4)

Therefore, new coordinates become (-2,8) (-2,-4) and (4,-4)

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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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Answer: 240 miles

Step-by-step explanation:

160m = 4 days

miles 40-1  days

        80-2

        120-3

         160-4

       200-5

          240-6

The average rate of change of g(x) = 3x² - 8x from x= 1 to x = 6 is 13.

The middle number, which is obtained by dividing the sum of all the numbers by the variety of numbers, is the average value in a set of numbers. To calculate the average of a set of data, add up all the values and divide the result by the total number of values.

Given:

g(x) = 3x² - 8x

The intervals, x = 1 to x = 6

Calculate the values of g(6) and g(1) as shown below,

g(6) = 3 × 6² - 8 × 6

g(6) = 3 × 36 - 48

g(6) = 108 - 48

g(6) = 60

And, g(1) = 3 × 1² - 8 × 1

g(1) = 3 - 8

g(1) = -5

Calculate the average rate of change as shown below,

The average rate of change = [g(6) - g(1)] / x₂ - x₁

The average rate of change = [60 - (-5)] / 6 - 1

The average rate of change = 65 / 5

The average rate of change = 13

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Step-by-step explanation:

A)20+10x=y

B)20+10(3)=y

20+30=y

y=50

At the local bunny-hop, the sum of geometric sequences showing the jumps performed by Mr. Meyering is 40

The Sequences of the jump include

20, 10, ...

The common ratio, r is calculated from

first term, a * common ratio, r = second term

20 * r = 10

20r = 10

r = 10/20

r = 1/2

hence r < 1

The sum of gp to infinity for r < 1 is

Sum = a/ (1 - r)

Sum = 20 / (1 - 1/2)

Sum = 20 / 1/2

Sum = 20 * 2

Sum = 40

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Retained profits for the upcoming year: 5551.

The amount of profit a business keeps after paying all of its direct and indirect expenses, income taxes, and dividends to shareholders is known as retained profits. This is the percentage of the company's equity that may be utilized, for example, to fund the purchase of new machinery, research and development, and marketing.

RE=[tex]RE_{0}[/tex]-NI-D

Reserved Earnings

RE stands for initial retained income.

Net income is referred to as NI.

the dividend D

Graham Auto Parts now has $42,700 in sales, $9,700 in EBIT, $6,600 in net income, $1,360 in interest expenditure, and $1,925 in dividends paid. and a $8,000 rise in revenue is anticipated for the following year.

8000/42700 = 0.1873536 is the sales growth rate as a result. Its proportion is 18.73536%.

Now project net income = 6600 * 1.1873536

7837

dividends = 1925*1.1873536 = 2286

7837 - 2286 = 5551

retained earnings for next year 5551

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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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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:

Grandma=P

Wagon=TH

Library= PL

Step-by-step explanation:

its pretty simple

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.

The rate of change is not constant.

What is rate of change ?

A rate of change is a measurement of how one quantity alters in proportion to another. The dependent variable y must be present if independent variable x is. rate of change = y-to-x conversion of change. Change rates may be positive or negative.

We know that the rate of change in a function is given by :-

(change in dependent variable) / (change in independent variable)

Let x denotes the Number of hours and y denotes the Cost of parking .

Here , x- independent variable

y- dependent variable

Now, rate of change = ( change in y) / ( change in x)

                                  = (14-10)/(3-1) = 2

Here , the rate of change = $ 2 per hour.

Again rate of change =  ( change in y) / ( change in x)

                                    = (16-14)/(5-3) = 1

Here , the rate of change = $ 1 per hour.

Since both rate of changes are not equal , it means the rate of change is not constant.

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The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

The equation of the form y = A[tex]2^x[/tex] + K  from the graph above is

y = (-5/3) . [tex]2^x[/tex] - (2/3)

The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

We have,

y = [tex]2^x[/tex]

From the graph, we see that,

x = 0, y = -1

x = 1, y = -4

Now,

The equation in the form of y = A.[tex]2^x[/tex]  + K can be written as,

Taking (0, -1) we get,

-1 = A x 1 + K

-1 = A + K ______(1)

Now,

Taking (1, -4) we get,

-4 = A x 2 + K

-4 = 2A + K _____(2)

From (1) and (2) we get,

A = K - 1 putting in (2) we get,

-4 = 2(K - 1) + K

-4 = 2K - 2 + K

-4 = 3K - 2

3K = -4 + 2

3K = -2

K = -2/3

Now,

A = K - 1

A = -2/3 - 1

A = (-2 - 3) / 3

A = -5/3

Now,

The equation is y = (-5/3) . [tex]2^x[/tex] - (2/3)

Thus,

The equation of the form y = A[tex]2^x[/tex] + K  from the graph above is

y = (-5/3) . [tex]2^x[/tex] - (2/3)

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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]

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:

[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:

a)  $153,850

b)  $779.54

c)  $873.54

Step-by-step explanation:

[tex]\begin{aligned}\textsf{Loan amount}&=\textsf{Cost of property}-\textsf{Down payment}\\&=181000-(181000 \times 0.15)\\&=181000-27150\\&=153850\end{aligned}[/tex]

Therefore, the loan amount is $153,850.

[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Monthly Payment Formula}\\\\$PMT=\dfrac{Pi\left(1+i\right)^n}{\left(1+i\right)^n-1}$\\\\where:\\\\ \phantom{ww}$\bullet$ $P =$ loan amount \\\phantom{ww}$\bullet$ $i =$ interest rate per month (in decimal form) \\\phantom{ww}$\bullet$ $n =$ term of the loan (in months) \\\end{minipage}}[/tex]

Given:

Substitute the given values into the  Monthly Payment formula and solve for PMT:

[tex]\implies \sf PMT=\dfrac{153850 \cdot \frac{0.045}{12}\left(1+\frac{0.045}{12}\right)^{360}}{\left(1+\frac{0.045}{12}\right)^{360}-1}[/tex]

[tex]\implies \sf PMT=\dfrac{153850 \cdot 0.00375\left(1.00375\right)^{360}}{\left(1.00375\right)^{360}-1}[/tex]

[tex]\implies \sf PMT=779.5353492[/tex]

Therefore, the monthly payments would be $779.54.

Given:

Substitute the given values into the Monthly Payment formula and solve for PMT:

[tex]\implies \sf PMT=\dfrac{153850 \cdot \frac{0.055}{12}\left(1+\frac{0.055}{12}\right)^{360}}{\left(1+\frac{0.055}{12}\right)^{360}-1}[/tex]

[tex]\implies \sf PMT=873.5433786[/tex]

Therefore, the monthly payments would be $873.54.

The rectangle has the consecutive integers of 21 inches and 22 inches for its width and length respectively.

Consecutive integers are numbers that follow in a particular order, usually just one after the for example, 1, 2, 3,... and so on.

Let the width of the rectangle be represented by x so that the length will be x + 1 as they consecutive integers

The perimeter of the rectangle will have the equation;

x + x + x + 1 + x + 1 = 86 inches

4x + 2 = 86 inches {collect like terms}

4x = (86 - 2) inches {subtract 2 from both sides of the equation}

4x = 84 inches

x = (84/4) inches {divide through by the coefficient of x}

x = 21 inches

Therefore, the rectangle has width of 21 inches and length of 21 + 1 = 22inches.

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The total area of the space will be equal to 175 square meters.

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Given that Elizaveta painted 35 square meters of wall space. This represents 20% of the total area.

The total area will be calculated as,

20% of area = 35 square meters

100% of the area = ( 35 x 100) / 20

100% of the area = 175 square meters

Therefore, the total area of the space will be equal to 175 square meters.

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Elizaveta painted 35 m2 of wall space. This represents 20% of the total area.

What is the total area of the walls to be painted?f ^(4) 2

All the corresponding pairs of angles and sides of ΔNEM and ΔCDE are congruent.

What is rigid motion?

A geometric figure is moved by rigid motions, but its size and shape remain unchanged. It generates visuals that make sense.

Rigid transformation comes in four different varieties.

1. translate 2. reflect. 3. Rotation 4. Gliding reflection

Here,

We have a series of rigid motion maps ΔNEM  onto ΔCDE.

We have to find the correct statement, so we concluded that all the corresponding pairs of angles and sides of ΔNEM and ΔCDE are congruent.

Hence, ΔNEM and ΔCDE are congruent.

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The question is incomplete , I am answering it with my general knowledge,

Zero exponent

Simplifying an expression with a 0 as the exponent does not need consideration of the base value.

Any non-zero number multiplied by 0 has the value 1.

x0 = 1, where x = 0 and x = 1, 2, 3, and so forth.

Negative exponent

For any positive integer m and non-zero number a,

a⁻ⁿ=1/a⁻ⁿ

This rule states that if the exponent is negative, it can be made positive by writing the same number in the denominator and writing one for the numerator.

When a number is positive, the exponent shows how many times it has been multiplied by itself.

On the other hand, the negative exponent indicates how many times we must divide the base number. The negative exponent, then, tells us how many times to multiply the reciprocal of the base, to put it another way.

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The sampling types in this problem are given as follows:

The sampling types used in this problem are defined as follows:

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Answer:

Step-by-step explanation: the amswer is B trust me

There must be no chance that d and e will happen. If the two occurrences cannot coexist, we can infer that they are not independent.

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.

P(A) = n(A)/n(S)

Where P(A) is the likelihood that an event "A" will occur and n(A) is the number of positive outcomes. The total number of occurrences in the sample space is denoted by n(S).

We must have a similar probability for both events in order for them to be independent. Because of the table, we may test for independence by knowing the likelihood that e and d will occur. When we are told that occurrences d and e are mutually exclusive, the entire table of values becomes somewhat of a red herring. The chance of d given e and the probability of d given d are both equal to zero if two events are mutually incompatible. There must be no chance that d and e will happen. If the two occurrences cannot coexist, we can infer that they are not independent. There is a chance for it.

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Answer:

The total amount of the sales tax: $3.00

The total amount paid: $47.25

Step-by-step explanation:

Tip (In $): 6.75

Sales tax: 3.00

The total amount of food (before additional fees): 37. 50

So, to find the amount (in dollars) of the sales tax and tip, we must use this formula:

Amount = whole number * part percent/100

So, plugging in the numbers to the formula, it would look like this:

37.50 * 18 / 100
That is how to find the tip, you would do the same to find the sales tax. Then, when you get both amounts, you add them to 37.50 (the total before the fees) and get $47.25.