is the value of the digit 5 in 0.5is 1/10 times as much as the value in 0.05

Answer:

The required line is Parallel to y = 7x - 8

This means their slopes are equal

So m = 7

Now writing the equation of straight line,

[y - (-2)] = m(x - 5)

y + 2 = 7(x - 5)

y + 2 = 7x - 35

7x - y - 37 = 0

Hope This Helps Y

On solving the provided question, we can say that  inches if a cylinder's enlarged capacity is 45 in3, its compressed volume is 6 in cubic .

One of the most fundamental curved geometric forms is the cylinder, which is often a three-dimensional solid. It is referred to as a prism with a circle as its base in elementary geometry. Several contemporary fields of geometry and topology also define a cylinder as an indefinitely curved surface. A three-dimensional object known as a "cylinder" consists of curving surfaces with circular tops and bottoms. A cylinder is a three-dimensional solid figure that has two bases that are both identical circles joined by a curving surface at the height of the cylinder, which is determined by the distance between the bases from the center. Examples of cylinders are cold beverage cans and toilet paper wicks.

In a certain engine, the compression ratio is 7.5: 1.

A cylinder's enlarged volume is 45 in3 in.

We must determine the cylinder's compressed volume.

Let v represent the cylinder's compressed volume.

The aforementioned circumstance can be described as

7.5 : 1 = expanded volume : compressed volume

7.5/1 = 45/v

7.5 = 45/v

v = 45/7.5

v = 6 cubic inches .

Therefore, if a cylinder's enlarged capacity is 45 in3, its compressed volume is 6 in cubic .

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Answer:

10.5

Step-by-step explanation:

Missing number, 9.8, 9.1

We see that each time it subtracts 0.7

We take

9.8 + 0.7 = 10.5

So, the missing number is 10.5

The expression becomes: p^(1/2) = p^(1/2 * 1) = p^(1/2) Now we can simplify p^(1/2) as p^1/2 which equals the square root of p.

The property of exponents that must be applied to the expression p^(1/2) to derive p as the result is the Power of a Power Property.

The Power of a Power Property states that when a power is raised to another power, the exponents are multiplied.

For instance, consider the expression p^(1/2). We can apply the Power of a Power Property to this expression as follows: p^(1/2) = (p^(1/2))^1 By applying the Power of a Power Property, the exponent (1/2) is multiplied by the exponent 1, giving a result of 1/2.

Therefore, the expression becomes: p^(1/2) = p^(1/2 * 1) = p^(1/2)Now we can simplify p^(1/2) as p^1/2 which equals the square root of p.

So we have derived p as the result using the Power of a Power Property.

In summary, we must apply the Power of a Power Property to the expression p^(1/2) to derive p as the result.

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Answer:

y=1/4 x is a function, because when you plot it, each input (x) only has one output (y).

Step-by-step explanation:

Answer: 162°

Step-by-step explanation:

To find the answer to this question, we need to find what 45% of 360 degrees (a circle) is.

First, a percent divided by 100 becomes a decimal.

       45% / 100 = 0.45

Next, "of" means multiplication in mathematics.

       0.45 * 360 = 162

The central angle will be 162°.

The statements true of function f given by f(Θ) = tan(Θ):

A: Since the tangent function has a repeating pattern, it is a periodic function.

B: The domain of the tangent function is restricted because it has vertical asymptotes at certain values of Θ (specifically, odd multiples of π/2).

C: The range of the tangent function is not all real numbers, but rather all values except for its vertical asymptotes.

D: The period of the tangent function is 2π, because the pattern repeats every 2π radians.

E: The period of the tangent function is not π.

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For part (a) the answer is 400 grams for part (b) 198.63 grams and for part (c)  20 years.

During exponential decay, a quantity falls slowly at first before rapidly decreasing. The exponential decay formula is used to calculate population decline and can also be used to calculate half-life.

We have an equation for radioactive decay:

\(\rm m(t) = 400e^{-0.035t}\)

a) Plug t = 0

\(\rm m(0) = 400e^{-0.035\times 0}\)

m(0) = 400 grams

b) plug t = 20 years

\(\rm m(20) = 400e^{-0.035\times 20}\)

After solving:

m(20) = 198.63 grams

c) Plug m(t) = m(0)/2 = 400/2 = 200 grams

\(\rm 200 = 400e^{-0.035t}\)

x = 19.80 years ≈ 20 years

Thus, for part (a) the answer is 400 grams for part (b) 198.63 grams and for part (c)  20 years.

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9514 1404 393

Answer:

  (x -6)^2 +(y -6)^2 = 10

Step-by-step explanation:

To use the standard form equation for a circle, we need to know the center and the square of the radius. The center can be read from the graph as (6, 6). The square of the radius can be found using the distance formula.

  d^2 = (x2-x1)^2 +(y2-y1)^2

The radius is the distance between the two points shown, so we have ...

  d^2 = (7-6)^2 +(9-6)^2 = 1^2 +3^2 = 10

__

The equation of a circle centered at (h, k) with radius r is ...

  (x -h)^2 +(y -k)^2 = r^2

For (h, k) = (6, 6) and r^2 = 10, the equation is ...

  (x -6)^2 +(y -6)^2 = 10

Answer:

Agree with the answer above

Step-by-step explanation:

Actual time is much longer than the 50-year timeframe suggested by the speaker.

How to verify the statement?

This claim is based on the assumption that the rate of pollution reduction from each factory remains constant at 80%, and the number of factories increases by 3% per annum.

To verify this claim, we can use the following formula to calculate the expected total pollution after n years:

Total pollution after n years = \(Present \: pollution \: level x (1 + 0.03)^n \times (1 - 0.8)^n\)

Here, the first factor represents the increase in pollution due to the growth in the number of factories, and the second factor represents the reduction in pollution due to the 80% reduction in pollution from each factory.

We can set the expected total pollution after n years equal to the present pollution level and solve for n:

\(Present \: pollution \: level = Present \: pollution \: level \times (1 + 0.03)^n \times (1 - 0.8)^n\)

Simplifying this equation, we get:

\(1 = 1.03^n \times 0.2^n\)

Taking the logarithm of both sides of the equation, we get,

\(n \times log(1.03) + n \times log(0.2) = 0 \\ n \times (log(1.03) + log(0.2)) = 0 \\ n = \frac{0} { (log(1.03) + log(0.2))} \\ n = 271.56\)

Therefore, according to this calculation, it would take approximately 272 years for the total annual pollution to return to its present level if the number of factories in the country increases by 3% per annum, and they all immediately reduce the amount of pollution they produce by 80%. This is much longer than the 50-year timeframe suggested by the speaker.

It is important to note that this calculation assumes that the pollution reduction from each factory remains constant at 80% and does not take into account any other factors that may affect pollution levels, such as changes in technology or regulations. Therefore, this should be considered as a rough estimate and not as an exact prediction.

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Correct question is "A speaker claimed that if the number of factories in the country increases by 3% per annum, then even if they all immediately reduced the amount of pollution they produce by 80%, the total annual pollution will be back to its present level in about 50 years. Verify the statement. (use logarithm)"

The image coordinates of NMO after the translation is option d: N′(−5, −6), M′(−2, −5), and O′(−3, −7).

To get the image coordinates of the preimage translated -2 units to the left, we simply subtract -2  from the y-coordinates of each vertex:

N' = (Nx - (-2), Ny) = (−5 , 2- (-2)) = (−5, 4)

M' = (Mx - (-2), My) = (−2 , 1 - (-2)) = (−2, 3)

O' = (Ox - (-2), Oy) = (−3 , 3- (-2)) = (−3, 5)

Therefore, based on the above, the image coordinates of NMO after the translation are N′(−5, 4), M′(-2,3 ), O′(−3, 5)

So the reflected vertices are:

The distance from N to the line y = -2 is 4, and -6 - (-2) = -4, so one need to move down 4 units to have  a y-coordinate of -6.

The distance from M to the line y = -2 is 3, and -5 - (-2) = -3, so  one need to move down 3 units to have a y-coordinate of -5.

The distance from O to the line y = -2 is 5, and -7 - (-2) = -5, so  one need to move down 5 units to have  a y-coordinate of -7.

So it will be: N′ (−5, −6), M′(−2, −5), O′(−3, −7)

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Answer:

---------------------

Given triangle MNO with vertices:

It is reflected in line y = - 2.

This reflection doesn't affect the x-coordinates of the vertices and the y-coordinates change.

Since y = - 2 is the line of symmetry,  it also represents midpoints of the segments formed by corresponding endpoints of image and preimage.

Using midpoint equation, find the y-coordinates.

So the coordinates of the image are:

This is matching the option D.

See attached for visual representation of the problem.

Answer:

-1

Step-by-step explanation:

Im pretty sure this is the right answer :)

Solution

We are given two ranks

First, in 2018, rank of 145 out of 435 students

Secondly, in 2019, rank of 160 out of 404 students.

(A) In which year did you have the higher percentile ranking?

To answer this, we need to calculate the percentiles for the two rankings and comapre them

By comapring the percentile ranking, we realize that year 2019 has higher percentile (39.6%) comapred to year 2018 (33.33%)

(B)

If you had the data on the cumulative GPA of each student at the end of the spring semester in 2018, what would the mean and the median each tell you and how would you compute each measure?

The mean and the median tells us about the measure of the center of the dataset

To compute the mean, we us the formula

1. Bank 1 is the best option for opening a savings account for one year, as it offers the highest total amount after one year.

2. Bank 1 is the best option for opening a savings account for one year, as it offers the highest total amount after one year.

We will use the formula A = P(1 + r/n)^(nt).

Bank 1:

= 3675(1 + 0.0236/4)^(4*1)

= 3762.50058402

= $3762.50

Bank 2:

= 3675(1 + 0.0236/1)^(1*1)

= 3696.6825

= $3696.68

Bank 3:

= 3675(1 + 0.0236/2)^(2*1)

= 3718.49292675

= $3718.49

To calculate which bank is the best option to open a savings account for twelve years, we can use the same formula and plug in t = 12:

Bank 1:

= 3675(1 + 0.0236/4)^(4*12)

= 4874.02928821

= $4874.03

Bank 2:

= 3675(1 + 0.0236/1)^(1*12)

= 4862.06398635

= $4862.06.

Bank 3:

= 3675(1 + 0.0236/2)^(2*12)

= 4870.00654814

= $4870.00

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9514 1404 393

Answer:

  -5/y

Step-by-step explanation:

The wording "the quotient of A and B" is used to signify A/B.

Here, we want the quotient of -5 and y:

  -5/y

The value of X in the given system of matrix is,

\(X=\left[\begin{array}{ccc}\frac{-97}{145}&\frac{-45}{145} \\\\\frac{20}{29}&\frac{21}{29}\\\end{array}\right]\)

Matrices are one of the most powerful tools in mathematics. The evolution of the concept of matrices is the result of an attempt to obtain compact and simple methods of solving the system of linear equations.

We have 2 by 2 matrix in the form,

\(\left[\begin{array}{ccc}9&9\\-9&-9\\\end{array}\right] X+\left[\begin{array}{ccc}6&3\\7&9\\\end{array}\right] =\left[\begin{array}{ccc}-1&8\\-4&6\\\end{array}\right] X\\\\Assume, X=\left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right] \\\\\)

After multiplication,

\(9a+9c+6=-a+8c\\\\-9a-9c+7=-4a+6c\\\\9b+9d+3=-b+8d\\\\-9b-9d+9=-4b-6d\\\\\)

After solving the given system of equations

\(a=\frac{-97}{145}\\\\b=-\frac{54}{145}\\\\c=\frac{20}{29}\\\\d={21}{29}\\\\Hence, \\X=\left[\begin{array}{ccc}\frac{-97}{145}&\frac{-45}{145} \\\\\frac{20}{29}&\frac{21}{29}\\\end{array}\right]\)

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(a) √2 · √8. The simplified surd expression is 4.

(b) √80. The simplified surd expression is  4√5.

(c) √5/√20. The simplified surd expression is  1/2.

(d) √20. The simplified surd expression is  2√5.

The given surd expression is simplified as follows;

(a) √2 · √8

we can simplify it as;

√2 · √8 = √(2 x 8) = √16 = 4

(b) √80

we can simplify it as;

√80 = √ (16 x 5) = √16  x √5 = 4√5

(c) √5/√20

we can simplify it as;

√5/√20  x  √20 / √20

= (√5  x √20 ) /(20)

= √100 / 20

= 10/20

= 1/2

(d) √20

we can simplify it as;

√20 = √4  x √5 = 2√5

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Based on the information given, the price of the zero coupon bond is $692.04.

To calculate the price of a zero coupon bond, we need to use the following formula:

\(\sf P =\dfrac{F}{1+r\div n}^{(nt)\)

Where:

Also, the annual interest rate is 7.50%, which is the market interest rate, and the compounding is semiannual, which means n = 2. Finally, the time to maturity is 5 years.

Plugging in the values into the formula, we get:

\(\sf P = \dfrac{1000}{(1+0.075\div2)^{(2\times5)}}\)

\(\sf P = \dfrac{1000}{(1.0375)^{10}}\)

\(\sf P = \dfrac{1000}{1.4450}\)

\(\sf P = \$692.04 \ \ (rounded \ to \ the \ nearest \ cent)\)

Therefore, the price of the zero coupon bond is $692.04.

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The system of equations has an infinite number of solutions.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 8 is an equation.

We have,

3x + 2y = 6 ____(1)

6x + 4y = 12 _____(2)

Applying the substitution method.

3x + 2y = 6

x = (6 - 2y)/3 in (2)

6 (6 - 2y)/3 + 4y = 12

2 (6 - 2y) + 4y = 12

12 - 4y + 4y = 12

12 = 12

This means,

It has an infinite number of solutions.

Thus,

An infinite number of solutions.

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The complete question is:

Graph the system of equations

3x + 2y = 6

6x + 4y = 12

and find the solution to the system.

Answer:

74480 A

Step-by-step explanation:

0.28 x 266000 = 74480

brainliest maybe?

Answer:

b < 3

Step-by-step explanation:

3 ( b - 5 ) < - 2b

3 ( b ) - 3 ( 5 ) < - 2b

3b - 15 < - 2b

3b + 2b < 15

5b < 15

b < 15/5

b < 3

The market equilibrium is the point where the demand and supply functions are equal

The producer's surplus at market equilibrium for a product is #105

The functions are given as:

\(p = 121 - x^2\)

\(p = x^2 + 6x + 65\)

Equate both functions

\(x^2 + 6x + 65 = 121 - x^2\)

Collect like terms

\(x^2 + x^2 + 6x + 65 - 121 = 0\)

Evaluate the like terms

\(2x^2 + 6x -56 = 0\)

Divide through by 2

\(x^2 + 3x -28 = 0\)

Expand

\(x^2 + 7x - 4x - 28 = 0\)

Factorize

\(x(x + 7) - 4(x +7)= 0\)

Factor out x + 7

\((x - 4)(x +7)= 0\)

Solve for x

x = 4 or x = -7

The number of units cannot be negative,

So, we have:

x = 4

Substitute 4 for x in \(p = 121 - x^2\)

\(p = 121 - 4^2\)

p = 105

Hence, the producer's surplus at market equilibrium for a product is #105

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Answer:

We use the rule,

\((a^b)^c = a^{bc}\)

a. (10^7)²

\((10^7)^2 = 10^{(7)(2)} = 10^{14}\)

10^14

b. (10^9)³

\((10^9)^3 = 10^{(9)(3)} = 10^{27}\)

10^27

c. (10^6)³

\(10^{(6)(3)}= 10^{18}\)

10^18

d. (10^2)³

\(10^{(2)(3)} = 10^{6}\)

10^6

e. (10³)²

\(10^{(3)(2)}=10^{6}\)

10^6

f. (10^5)^7

\(10^{(5)(7)} = 10^{35}\)

10^35

Step-by-step explanation:

Answer:

x = 13 or x = 1

Step-by-step explanation:

To solve the equation (x - 7)^2 = 36, we can take the square root of both sides:

(x - 7)^2 = 36

sqrt((x - 7)^2) = sqrt(36)

x - 7 = ±6

Solving for x, we get:

x - 7 = 6 or x - 7 = -6

x = 13 or x = 1

Therefore, the values of x that satisfy the equation are x = 13 and x = 1. The values x = -29 and x = 42 do not satisfy the equation.

Answer:

            P = 4x  +  10

Step-by-step explanation:

perimeter of a rectangle = 2( width + length )

   P = 2 ( x - 2  +  x + 7 )

   P = 2 ( x + x  +  7 - 2 )

        P = 2 ( 2x +  5 )

            P = 4x  +  10

If he wants an average of 84, he needs to get at least 93 points.

Remember that the average value between 3 values A, B, and C is:

(A + B + C)/3

Here we know that the first two scores are 76 and 83 points, let's say that the third score is x, if we want to have an average of 84 or more, then we need to solve:

(76 + 83 + x)/3 = 84

159 + x = 252

x = 252 - 159

x = 93

So he needs to get at least 93 points in the next exam.

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