What is the measure of angle x?

A. 60 degrees
B. 70 degrees
C. 80 degrees
D. 100 degrees

Answer: 10 pens

Step-by-step explanation: Because you have to add the 3 black pens to 7 blue pens = 10

The solution to the given differential equation is \(y = a_0x^{[0]} + a_1x^{[1]} + a_2x^{[2]}\), where a_0, a_1, and a_2 are constants.

To fathom the given differential equation, xy'' + y' = 0, we will begin by expecting a control arrangement of the frame y = ∑(n=0 to ∞) a_nx^n, where a_n speaks to the coefficients to be decided.

Separating y with regard to x, we get:

\(y' = ∑(n=0 to ∞) a_n(nx^[(n-1))] = ∑(n=0 to ∞) na_nx^[(n-1)]\)

Separating y' with regard to x, we get:

\(y'' = ∑(n=0 to ∞) n(n-1)a_nx^[(n-2)]\)

Presently, we substitute these expressions for y and its subsidiaries into the differential condition:

\(x(∑(n=0 to ∞) n(n-1)a_nx^[(n-2))] + (∑(n=0 to ∞) na_nx^[(n-1))] =\)

After improving terms, we have:

\(∑(n=0 to ∞) n(n-1)a_nx^[(n-1)] + ∑(n=0 to ∞) na_nx^[n] =\)

Another, we compare the coefficients of like powers of x to zero, coming about in a boundless arrangement of conditions:

For n = 0: + a_0 = (condition 1)

For n = 1: + a_1 = (condition 2)

For n ≥ 2: n(n-1)a_n + na_n = (condition 3)

Disentangling condition 3, we have:

\(n^[2a]_n - n(a_n) =\)

n(n-1)a_n - na_n =

n(n-1 - 1)a_n =

(n(n-2)a_n) =

From equation 1, a_0 = 0, and from equation 2, a_1 = 0.

For n ≥ 2, we have two conceivable outcomes:

n(n-2) = 0, which gives n = or n = 2.

a_n = (minor arrangement)

So, the solution to the given differential equation is \(y = a_0x^{[0]} + a_1x^{[1]} + a_2x^{[2]}\), where a_0, a_1, and a_2 are constants.

Learn more about differential equations here:

https://brainly.com/question/28099315

#SPJ1

The Slope-Intercept form of an equation of the line is:

Where "m" is the slope and "b" is the y-intercept.

Given this line:

You need to solve for "y" in order to write it in Slope-Intercept form:

So you can identify that the slope of that line is:

By definition, the slopes of perpendicular lines are opposite reciprocals. Then, you can determine that the slope of the other line is:

Knowing that it passes through this point:

You can substitute the coordinates into the equation and solve for "b":

Knowing the value of "b" and knowing the slope, you can determine that the equatio of the line in Slope-Intercept for

The percent of the square shaded is 37.5 without including the % sign.

The square is divided into 4 equal parts

1/4 of the square is fully shaded

The other 1/4 is shaded half

Hence,

When the square is divided into 8 equal parts, 3 parts are shaded

Percent of square shaded= Parts shaded/ Total parts × 100

= 3/8 × 100

= 0.375 × 100

= 37.5%

Ultimately, 37.5 is the percent of the square shaded.

Read more on percentage:

https://brainly.com/question/843074

#SPJ1

a. The equator has the smallest circumference of all the circles of latitude or longitude.

The equator is an imaginary circle that is located at 0 degrees latitude and circles the Earth's surface at its widest point. Since the Earth is roughly spherical in shape, the equator represents the largest circle of latitude. However, it has the smallest circumference of all the circles of latitude or longitude because it is located at the widest point of the Earth, and its radius is equal to the Earth's radius.

In contrast, the circles of latitude and longitude located at higher latitudes have smaller radii and therefore larger circumferences than the equator. Similarly, circles of latitude and longitude located at lower latitudes have larger radii and smaller circumferences than the equator. Therefore, the equator has the smallest circumference of all the circles of latitude or longitude on the Earth's surface.

Learn more about circumference here:

https://brainly.com/question/15533071

#SPJ4

The term which is used for describing the number of voters who casted their votes using the ballots is called as voter turnout.

The process of selecting a candidate for a suitable post who takes care of the policies which will be framed for the people is called as voting. In this process, the members/ citizens casts their vote in the favor of their suitable candidate. Many times voters are not valid and their votes are considered as null and void.

The voter turnout is either the percentage of registered voters, eligible voters, or all voting-age people ( this varies from place to place depending upon the minimum voting age required). The voter turnout is also referred to the number of people who go to it or take part in it. High voter turnout is generally considered a sign of a healthy democracy.

Learn more about voter turnout at:

brainly.com/question/29639449

#SPJ4

The overall shape of the distribution of soldiers' foot lengths was likely symmetric or approximately bell-shaped.

The distribution of soldiers' foot lengths can be described as symmetric or bell-shaped. The majority of foot lengths cluster around the center, with fewer foot lengths deviating significantly. The center of the distribution, representing the average foot length, can be determined using the mean.

Analyzing the shape through a histogram or box plot helps identify symmetry. A symmetric shape with a peak in the middle and evenly tapering tails indicates a bell-shaped distribution.

Understanding the distribution's shape and center allows us to infer the overall characteristics of the soldiers' foot lengths.

To know more about symmetric visit -

brainly.com/question/31583674

#SPJ11

Answer:

I think it is a

Step-by-step explanation:

Maximum number of distinct majors/groups: 84 therefore, the 85th student must be the same as one of the 84 students.

Date of anticipated graduation: May 15, 2020, or Spring 2020 for graduation (expected). Instead of expected or anticipated, you can use the word pending if you're presently working to finish your final semester.

Employers may be able to see that you are actively pursuing your degree even though you haven't graduated by seeing your anticipated graduation date on your resume.

To know more about Graduation degree visit:-

https://brainly.com/question/15183117

#SPJ4

The equation that represents this situation, if k is the number of hours Keith worked is C. k + 3 = 12

A statement that affirms the equivalence of two expressions that are joined by the equals sign "=" is known mathematically as an equation. If Jason worked 12 hours, 3 more than Keith did, and k is the amount of hours Keith worked, then k + 3 = 12 is the proper equation to reflect the circumstance.

According to this calculation of the equation, the total number of hours Keith worked (k) plus the additional three hours equals 12, which agrees with the fact that Jason put in three more hours of labour than Keith did and worked for a total of 12 hours.

Complete Question:

Jason worked 3 more hours than Keith. Jason worked 12 hours. Which equation represents this situation, if k is the number of hours Keith worked?

A. 12 + k = 3

B. 12k = 3

C. k + 3 = 12

D. 3k = 12

Read more about equation on:

https://brainly.com/question/17145398

#SPJ4

The distance between the two points is sqrt(41) units.To find the distance between two points, we can use the distance formula:d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

where (x1, y1) and (x2, y2) are the coordinates of the two points.

In this case, the two points are (-3, 2) and (2, -2). We can plug these values into the formula:

d = sqrt((2 - (-3))^2 + (-2 - 2)^2)

Simplifying:

d = sqrt((2 + 3)^2 + (-4)^2)

d = sqrt(25 + 16)

d = sqrt(41)

So, the distancedistance between the two points is sqrt(41) units.

To learn more about distance click here:brainly.com/question/13034462

#SPJ11

Answer: as per question statement

we need to set up an equation first

p(t)=1200e(0.052*t)

they have given that it is relative to 1200 that means it starts to increase from 1200 at t=0 initially 1200 bacteria were present

we need to find population at t=6

we need to plug t=6 in p(t).

P(6)=1200e(0.052*6)=1639.38

1638.38 bacteria were present at that time t=6

Step-by-step explanation: I hope this helps.

Using the Shell Method, the volume of the solid obtained by rotating the region underneath the graph of y=1/√(x^2+6) over the interval [0,7], about the line x=0, is approximately 125.979 cubic units.

To find the volume using the Shell Method, we divide the region into infinitely thin vertical strips, or shells, and integrate their volumes. Each shell has a height equal to the function y=1/√(x^2+6) and a thickness of dx.

The radius of each shell is the distance from the axis of rotation (x=0) to the corresponding x-coordinate. In this case, the radius is simply x.

The volume of each shell can be calculated as 2πx * (1/√(x^2+6)) * dx, where 2πx represents the circumference and (1/√(x^2+6)) represents the height.

To find the total volume, we integrate the volume expression with respect to x over the interval [0,7]:

V = ∫[0,7] 2πx * (1/√(x^2+6)) * dx.

Evaluating this integral yields approximately 125.979 cubic units.

Therefore, the volume of the solid obtained by rotating the region underneath the graph of y=1/√(x^2+6) over the interval [0,7], about the line x=0, is approximately 125.979 cubic units.

Learn more about shell method here:

https://brainly.com/question/30401636

#SPJ11

The critical value of t with df as 7 is 2.36, and the critical value of t with df as 102 is 2.62

In a hypothesis test, the critical value is a value that is used to decide whether to accept the null hypothesis or not. It is based on the level of significance that was selected, which is the highest likelihood that a Type I error could occur.

a)

On referring to the t-distribution table, which is statistical software, or a calculator to find the critical value of t for a 95% confidence interval with degrees of freedom (df) = 7. The two-tailed confidence level of 0.95 is the essential value. We discover that the crucial value of t for a 95% confidence interval with df = 7 is roughly 2.365 using a t-distribution table or program.

b)

The t-distribution table, statistical software, or a calculator are used in a similar manner to estimate the critical value of t for a 99% confidence interval with df = 102. The crucial value is equal to the 0.99 two-tailed confidence level. The crucial value of t for a 99% confidence interval with df = 102 is roughly 2.62, according to a t-distribution table or computer programme.

Read more about critical value on:

https://brainly.com/question/31529419

#SPJ4

The 23rd term in the sequence 163, 159, 155, 151, ... is 75.

An arithmetic sequence is a sequence of numbers where the difference between any two consecutive terms is constant. This means that you can find any term in the sequence by adding the common difference to the previous term.

The general formula for an arithmetic sequence is:

a_n = a_1 + d(n - 1)

Use code with caution. Learn more

where:

a_n is the nth term in the sequence

a_1 is the first term in the sequence

d is the common difference

n is the number of the term

The sequence is a decreasing arithmetic sequence, which means that each term is less than the previous term by a constant amount. In this case, the constant amount is 4. This is a decreasing arithmetic sequence, where each term is 4 less than the previous term. The first term is 163, so the 23rd term will be 163 - 4 * 22 = 75.

Learn more about Arithmetic sequence here:

brainly.com/question/28882428

#SPJ11

Answer:

The answer is option D.

Equation of a line is y = mx + c

m = slope

c = intercept on y axis

y-4= -2/3 (x-6)

y = -2/3x + 4 + 4

y = -2/3x + 8

From the above equation

m= -2/3

Since the lines are perpendicular the slope of the line is the negative inverse of the original line.

so m = 3/2

Equation of the line using point (-2 , -2) is

y + 2 = 3/2(x+2)

y = 3/2x + 3 - 2

y = 3/2x + 1

That's the last option

Hope this helps

The linear equation with the given characteristics is given by:

\(y = \frac{3}{2}x + 1\)

It is given by:

y = mx + b.

In which:

When two lines are perpendicular, the multiplication of their slopes is -1, hence:

\(-\frac{2}{3}m = -1\)

\(2m = 3\)

\(m = \frac{3}{2}\)

Then:

\(y = \frac{3}{2}x + b\)

It passes through the point (-2, -2), hence:

\(-2 = \frac{3}{2}(-2) + b\)

\(-3 + b = -2\)

\(b = 1\)

Hence, the equation is:

\(y = \frac{3}{2}x + 1\)

More can be learned about linear equations at https://brainly.com/question/24808124

The annual cost recovery deduction would be $25,641 ($1,000,000 ÷ 39).

a. If the building is classified as residential rental real estate, the cost recovery deduction for 2021 would be calculated using the straight-line method of depreciation over a 27.5 year recovery period, since that is the applicable recovery period for residential rental real estate.

To calculate the annual cost recovery deduction, you would divide the building's depreciable basis (which is its original cost minus the value of the land) by 27.5.

So, assuming that the value of the land is negligible, the depreciable basis for the building would be $1,000,000, and the annual cost recovery deduction would be $36,364 ($1,000,000 ÷ 27.5).

b. If the building is classified as nonresidential real estate, the cost recovery deduction for 2021 would be calculated using the straight-line method of depreciation over a 39 year recovery period, since that is the applicable recovery period for nonresidential real estate.

Using the same depreciable basis of $1,000,000 (assuming again that the value of the land is negligible), the annual cost recovery deduction would be $25,641 ($1,000,000 ÷ 39).

To know more about annual cost refer here

https://brainly.com/question/13993790#

#SPJ11

There are 36 '5' letter words that can be formed from the letters of "formulated" with 2 vowels, 3 consonants, and a vowel at the end.

The word "formulated" has 4 vowels and 6 consonants. If each 5 letter word must contain 2 vowels and end with a vowel, there are two options for the last letter, "e" or "a". To form a 5 letter word with 2 vowels and 3 consonants, we need to choose 2 vowels from the 4 vowels in "formulated" and 3 consonants from the 6 consonants in "formulated". The order of the chosen letters does not matter, as we will arrange them later. Thus, we can use the combination formula to find the number of ways to choose the vowels and consonants: C(4, 2) * C(6, 3) = 6 * 20 = 120. Finally, we need to arrange these 5 letters in a specific order: consonant-consonant-vowel-consonant-vowel. There are 3 choices for the first consonant, 2 choices for the second consonant (since it cannot be the same as the first), 2 choices for the vowel (either "e" or "a"), 3 choices for the third consonant (since it cannot be the same as the first or second), and 1 choice for the final vowel. Thus, the total number of 5 letter words that can be formed from the letters of "formulated" with 2 vowels, 3 consonants, and a vowel at the end is 3 * 2 * 2 * 3 * 1 = 36.

Learn more about combination here:

https://brainly.com/question/29594894

#SPJ11

Answer:

Options (1) and (5)

Step-by-step explanation:

Given function 'f' representing the relation between temperature of the oven after 't' minutes is,

f(t) = 0.25t² + 65

Option (1).

f(0) means that when the cake was placed in the oven, its temperature was 65°.

True.

f(0) = 0 + 65 = 65

Option (2).

To find the temperature after 15 minutes, we need to find 't' when f(t) = 15

False.

We have to find the value of f(15) to find the temperature of the oven after 15 minutes.

Option (3).

Temperature of the cake was 81° F when it was kept in the oven for 8 minutes.

Given statement is False.

It should be represented by,

f(8) = 81

Option (4).

After 10 minutes,the temperature of the cake was 71.25 degree F.

False.

By putting t = 10 in the function,

f(10) = 0.25(10)² + 65

       = 25 + 65

       = 90° F

Option (5).

The temperature of the cake when the baker takes it out of the oven, can be represented by,

f(30) = 290

True.

f(30) = 0.25(30)² + 65

       = 225 + 65

       = 290

Answer:

x = > 2

Step-by-step explanation:

This is the answer because:

1) >2 means x is any number greater than 2

2) For example, 2 x 3 = 6 +  7 = 13

3) 13 is greater than 11

Hope this helps!

Answer:

12.5%

Step-by-step explanation:

12.5% of 120 is 15 so if you take 15 divided by 120 you would get 0.125 and turned into a percentage is the 12.5%

Answer:

227.50

Step-by-step explanation:

Answer:

11 out of 22 marbles

Step-by-step explanation:

Just add up the red and green marbles to get the top # and then add up all the colored marbles to get the bottom #.

Hope this helps :) Please give brainliest!

The location of the coordinate of the point D' following the dilation of the quadrilateral ABCD by a scale factor of 1/3 would be; (2, -1)

A dilation transformation is one in which the image obtained from the original geometric figure is resized proportionately by a scale factor.

The coordinates of the vertices of the quadrilateral ABCD are;

A(-3, -3), B(0, 0), C(6, 3), and D(6, -3)

The scale factor of the required dilation = 1/3

The coordinates of the point (x, y) following a dilation by a scale factor of k with the center of dilation at the origin is; (k·x, k·y), therefore;

The coordinates of the image, D', of the point D(6, -3), following a dilation of the quadrilateral ABCD by a scale factor of (1/3) with the center of dilation located at the origin, will be;

Location of D' = ((1/3)×6, (1/3)×-3) = (2, -1)

Learn more on dilation transformation here: https://brainly.com/question/29488640

#SPJ1

The probability that X is greater than 145.28 is approximately 0.0465.

Given that X is normally distributed with mean (μ) of 110 and standard deviation (σ) of 21. We are to find the probability that X is greater than 145.28. It can be calculated as follows: We can calculate the Z-score value with the help of the following formula, Z = (X - μ) / σWhere X is the random variable value, μ is the mean, and σ is the standard deviation. Substituting the values in the formula, we get: Z = (145.28 - 110) / 21Z = 1.68476 Using the Z-table, we can find the probability that X is greater than 145.28 as follows: From the Z-table, we get: P(Z > 1.68) = 0.0465

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.

Know more about probability here:

https://brainly.com/question/31828911

#SPJ11

Answer:

10 hours......is answer

The sum of the infinite geometric series –288 –216 –144 –72 is -1152.

The sum of an infinite number of terms having a constant ratio between successive terms is called as infinite geometric series.

Given series, -288, -216, -144, -72, ...

The sum of the infinite geometric series can be calculated as:

Sum = \(\dfrac{a}{1 -r}\)

Here, 'a' is the first term of the series and 'r' is the common ratio.

a = -288

The common difference can be calculated as:

r = \(\dfrac{(-216)}{(-288)}\)

= \(\dfrac{3}{4}\)

Substitute the values in the sum formula:

Sum = \(\dfrac{-288}{1 - \dfrac{3}{4}}\)

It can be simplified as:

Sum =  -288 \(\times\) 4

             = -1152

So, the sum of the infinite geometric series is -1152.

Learn more about geometric series here:

https://brainly.com/question/30264021

#SPJ12

Answer:

I have no idea!!!!!!!!!!!!!

Answer:

50.05 feet

Step-by-step explanation:

The tower have 32.57 feet, and you can find it using the same method than I used in your other question

Now you find the length of the guy wire using the Pythagorean theorem:

38²+32.57² = guy wire²

2504.8 = guy wire²

guy wire = √2504.8

guy wire = 50.05 feet