Use the Limit Comparison Test to determine the convergence or divergence of the series. 6 + 1 7 + 1 n = 1 6n + 1 zn + 1 lim = L > 0 converges O diverges

Answer:

4

Step-by-step explanation:

-3-(-7) is the same as -3+7, which is also the same as 7-3, which is equal to 4

Answer:

4 is the answer.

Step-by-step explanation:

-3--7

-3+7

4

Hope it helps.

Answer:

x=−3 and y=1

i used substitution.

Step-by-step explanation:

Answer:

5 : 7

Step-by-step explanation:

groom's side: 40

bride's side: 56

ratio groom to bride = 40/56 = 20/28 = 10/14 = 5/7

Answer: 5 : 7

Using the exponent rule \((a^b)^c=a^{bc}\), we can rewrite \((153^2)^7\) as \(153^{(2)(7)}=\boxed{153^{14}}\).

Answer:

Find two points on the line and write them out: (x1,y1) (x2,y2)

Use this formula: y2-y1/x2-x1

The answer you get is the slope which is "m" in y=mx+b

Now in y=mx+b plug in one point's y into y and x into x. 

Find b

Answer:

Use points from the graph to create a table of data points. Then find a rule for the data in the table and write an equation that represents that rule. Lastly, check that the equation holds true for other data points in the table or graph.

Step-by-step explanation:

Answer:

x>11

Step-by-step explanation:

To simplify this inequality, we add 3 from both sides to get x-3+3>8+3. Since -3+3 cancels out to 0, we are left with x>8+3. 8+3=11 so x>11.

Hope this helps! If you need further explanation let me know :)

The number of observations strictly less than 24 is 7.

The five-number summary consists of the minimum value (13), the first quartile (Q1) or 25th percentile (24), the median or second quartile (Q2) or 50th percentile (38), the third quartile (Q3) or 75th percentile (51), and the maximum value (69).

Since Q1 represents the value below which 25% of the observations lie, and the five-number summary indicates that Q1 is 24, it means that 25% of the observations are less than or equal to 24.

Therefore, the number of observations strictly less than 24 is 25% of 33, which equals 7.

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The integer for vector 1 {2,6,-7}, integer for vector 2 is 10,8,-14}, integer for vector 3 is {4,12,-14}, integer for vector 4 is {14,-2,-7} and integer for vector 5 is {22,0,-14}. (all these vectors are in span {V1 and V2})

List five vectors in Span {v_1, v_2}?

1) V1+v2={8,2,-7 }+{-6,4,0 }

={2,6,-7}

2) 2v1+v2={16,4,-14}+{-6,4,0}

={10,8,-14}

3)2v1+2v2={16,4,-14}+{-12,8,0}

={4,12,-14}

4)V1-v2={8,2,-7}-{-6,4,0}

={14,-2,-7}

5)2v1-v2={16,4,-14}-{-6,4,0}

={22,0,-14}

All of these vectors are contained within the span.

{v1,v2}={av1+bv2:ab∈r}

A matrix is a rectangular variety of ordered numbers (real or complex) or functions .Assume we want to express the following information about   Ram and his two friends Rohan and Yash's possession of pens and pencils:
Ram       has      20     pens       and       7       pencils,

Rohan    has      15     pens       and       5       pencils,

Yash       has      12     pens       and       3       pencils

Now, this could be arranged in tabular form as follows,
⎢20  7⎢
⎢15   5⎢                            
⎢12   3⎢        

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The function's formula for the ice sheet's thickness is S(t) = 0.2t + 1.02.

Mathematically, a linear function is sometimes referred to as an expression or the slope-intercept form of a straight line and it can be modeled (represented) by this mathematical expression;

S(t) = mt + b

Where:

After a time of 7 weeks and a rate of decrease of 0.2, the y-intercept or initial amount of ice can be calculated as follows;

S(t) = mt + b

2.42 = 0.2(7) + b

2.42 = 1.4 + b

y-intercept, b = 2.42 - 1.4

y-intercept, b = 1.02.

Therefore, the required linear function is given by S(t) = 0.2t + 1.02.

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Complete Question:

A lake near the Arctic Circle is covered by a thick sheet of ice during the cold winter months. When spring arrives, the warm air gradually melts the ice, causing its thickness to decrease at a rate of 0.2 meters per week. After 7 weeks, the sheet is only 2.42 meters thick.

Let S(t), denote the ice sheet's thickness S (measured in meters) as a function of time t (measured in weeks).

Write the function's formula.

S(t) = ?

Answer:

Answer:

21.9

Step-by-step explanation:

Similarity Theorem

15/13=x/19

1.15384615=x/19

19*1.15384615=x

21.9230769=x

Final Answer

21.9

Proof answer

15/13=21.9/19

1.2= 1.2

The amount of work needed to stretch the spring 18 in. from its natural position is 3.75  ft-lb.

According to the Hooke's Law, the work done on the spring is:

W = 1/2. k . x²

Where:

k = spring constant

x = displacement.

Notice that the work done is directly proportional to x².

Hence,

W₁ : W₂  = x₁² : x₂²

Parameters given:

W₁ = 15 ft-lb

x₁ = 3 ft

x₂ = 18 in. = 1.5 ft

Plug the above parameters into the ratio equation:

15 : W₂  = 3² : (1.5)²

W₂ = (1.5)² . 15 /  3² = 15/4 = 3.75  ft-lb

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The equation of the polynomial is P(x) = (x - 8)(x - 1)(x + 2)

The given parameters are

The sum of multiplicities of the polynomial equation must be equal to the degree.

This means that the multiplicity of the zeros 8, 1 and -2 is 1

The equation of the polynomial is then calculated as

P(x) = (x - zero)^ multiplicity

So, we have

P(x) = (x - 8) * (x - 1) * (x + 2)

This gives

P(x) = (x - 8)(x - 1)(x + 2)

Hence, the equation is P(x) = (x - 8)(x - 1)(x + 2)

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We can use the Pythagorean identity one more time to get:

cos^2(a)t + cos^2(B) + cos^2(y) = 1

What is Trigonometry ?

Trigonometry is the branch of mathematics that studies the relationships between the sides and angles of triangles. Trigonometry is found throughout geometry because every shape with equal sides can be broken down into a collection of triangles.

The identity you want to prove is:

cos^2(a)t cos^2(B) + cos^2(y) = 1

We can start by using the Pythagorean identity for sine and cosine:

sin^2(x) + cos^2(x) = 1

cos^2(x) = 1 - sin^2(x)

We can use this identity to substitute for cos^2(a)t and cos^2(B):

cos^2(a)t cos^2(B) = (1 - sin^2(a)t)(1 - sin^2(B))

Expanding this expression, we get:

cos^2(a)t cos^2(B) = 1 - sin^2(a)t - sin^2(B) + sin^2(a)t sin^2(B)

Now we can substitute this expression back into the original identity:

cos^2(a)t cos^2(B) + cos^2(y) = 1

(1 - sin^2(a)t)(1 - sin^2(B)) + cos^2(y) = 1

Expanding the left side and simplifying, we get:

1 - sin^2(a)t - sin^2(B) + sin^2(a)t sin^2(B) + cos^2(y) = 1

sin^2(a)t sin^2(B) + cos^2(y) = sin^2(a)t + sin^2(B)

Now we can use the Pythagorean identity again:

sin^2(a)t + sin^2(B) = 1 - cos^2(a)t - cos^2(B)

Substituting this expression, we get:

sin^2(a)t sin^2(B) + cos^2(y) = 1 - cos^2(a)t - cos^2(B)

Finally, we can use the Pythagorean identity one more time to get:

cos^2(a)t + cos^2(B) + cos^2(y) = 1

which is the identity we wanted to prove.

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Answer:

4

Step-by-step explanation:

the answer is 4 so d on edge .

Based on the information given regarding the graph, it should be noted that the correct option is graph 4.

It should be noted that a graph is a diagram that shows the relationship between two or more sets of numbers.

From the information given, the system of inequalities and its graph is given is y ≤ –0.75x y ≤ 3x – 2 and the first line has a negative slope and goes through (negative 8, 6) and (0, 0).

Therefore, the section of the graph where the actual solution to the system lie is in graph 4.

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Answer: The median will remain about the same, but the mean will decrease.

Step-by-step explanation:

The Excel function used when deciding to reject or fail to reject the null hypothesis is the T.TEST function.

This function is used to calculate the probability of obtaining the observed results or more extreme results, assuming that the null hypothesis is true. If the probability, also known as the p-value, is less than the significance level, typically 0.05, the null hypothesis is rejected, and it is concluded that there is sufficient evidence to support the alternative hypothesis.

Otherwise, if the p-value is greater than the significance level, the null hypothesis is not rejected, and it is concluded that there is not enough evidence to support the alternative hypothesis.

The p-value is the probability of obtaining a test statistic as extreme or more extreme than the observed value, assuming that the null hypothesis is true. If the p-value is less than or equal to the level of significance (alpha) chosen for the test, typically 0.05 or 0.01, then the null hypothesis is rejected in favor of the alternative hypothesis. If the p-value is greater than the chosen alpha level, then the null hypothesis is not rejected.

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Answer:

I don’t know

Step-by-step explanation:

Answer:

8/15

Step-by-step explanation:

you want to do y2-y1 over x2-x1 and it'll look like this:

0-8=-8

-8-7=-15

The probability that a student scores between 450 and 600 on the SAT math section is approximately 0.4147 or 41.47%.

To find the probability that a student scores between 450 and 600 on the SAT math section, we need to use the properties of the normal distribution. We know that the mean is 511 and the standard deviation is 110.

First, we need to standardize the values of 450 and 600 using the formula:

z = (x - μ) / σ

where x is the value we want to standardize, μ is the mean, and σ is the standard deviation.

For 450:

z = (450 - 511) / 110 = -0.55

For 600:

z = (600 - 511) / 110 = 0.81

Next, we need to find the area under the normal curve between these two standardized values. We can use a table or a calculator to find that the area between z = -0.55 and z = 0.81 is approximately 0.4147.

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Answer:

affixwritersgmaicom

APP 447520635495

The number of large boxes of porridge that William bought, using a system of equations, was of:

8.

A system of equations is a set of equations involving multiple variables that are related, and then operations are made to solve these equations and identify the numeric value of each variable in the context of the problem.

For this problem, the variables are defined as follows:

William buys 5 small boxes of oat porridge, hence:

x = 5.

The total weight of his purchase is of 6825 grams, hence, considering the weight of each box, the following equation is built:

325x + 650y = 6825.

It is already stated on the problem that x = 5, hence the value of y can be obtained as follows:

325(5) + 650y = 6825.

y = (6825 - 325(5))/650

y = 8 large boxes.

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The solution for question a is -2.00. The solution for question b is  0.6687. The solution for question c is 10 students. We can show the working in the following manner.

a. What is the probability of completing the exam in one hour or less (to 4 decimals)?

To answer this question, we need to convert the time of one hour (60 minutes) to a z-score using the mean and standard deviation provided. We have:

z = (60 - 80) / 10 = -2.00

Using a standard normal distribution table or calculator, we can find that the probability of completing the exam in one hour or less is approximately 0.0228, rounded to 4 decimal places.

b. What is the probability that a student will complete the exam in more than 60 minutes but less than 75 minutes (to 4 decimals)?

To answer this question, we need to find the probability of completing the exam in less than 75 minutes and subtract the probability of completing the exam in less than 60 minutes. We have:

z1 = (60 - 80) / 10 = -2.00

z2 = (75 - 80) / 10 = -0.50

Using a standard normal distribution table or calculator, we can find that the probability of completing the exam in less than 75 minutes is approximately 0.6915 and the probability of completing the exam in less than 60 minutes is approximately 0.0228, as calculated in part a.

So, the probability of completing the exam in more than 60 minutes but less than 75 minutes is approximately:

0.6915 - 0.0228 = 0.6687, rounded to 4 decimal places.

c. Assume that the class has 60 students and that the examination period is 90 minutes in length. How many students do you expect will be unable to complete the exam in the allotted time (to the next whole number)?

To answer this question, we need to find the number of students whose exam time is greater than 90 minutes, which is the maximum time allowed. We can use the normal distribution with the given mean and standard deviation to calculate this.

First, we need to find the z-score corresponding to a time of 90 minutes:

z = (90 - 80) / 10 = 1.00

Using a standard normal distribution table or calculator, we can find that the probability of completing the exam in more than 90 minutes is approximately 0.1587.

Therefore, the expected number of students who will be unable to complete the exam in the allotted time is:

60 x 0.1587 = 9.52, which rounds up to 10 students (to the next whole number).

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Answer:

260 cities

Step-by-step explanation:

Multiple 5 and 52

James would visit 260 cities in one year.

Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression for some number of times.

Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.

Given:

1 year = 52 weeks

James visits 5 cities per week.

To find the number of cities in e one year:

Multiply by 52

52 x 5

= 260 cities.

Therefore, he would visit 260 cities.

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Answer:

She earned 1,076 dollars and 25 cents.

Step-by-step explanation:

x =  7.25 * 4,500 / 100

x = 7.25 * 45

x = 326.25

So commission earned is 326.25 $

We need to add this to her base salary for the week, so:

750 + 326.25 = 1, 076.25

Therefore she earned 1,076 dollars and 25 cents.

Hopes this helps ;p

Answer:

12

Step-by-step explanation:

for everyone 1 toy car there is 6 trucks so 2x6 is 12

Answer:

-1

Step-by-step explanation:

Given the equation :

2(3x – 1) > 4x – 6

Open the bracket :

6x - 2 > 4x - 6

Collect like terms

6x - 4x > - 6 + 2

2x > - 4

Divide both sides by 2

2x /2 > - 4/2

x > - 2

Since x > - 2

-10, - 5, - 3 are all < - 2

Hence, the only option greater than - 2 is - 1

Answer:

answer is id.k

Step-by-step explanation:

The correct equation to represent the condition is,

⇒ 2 + 3 1/4x = 1/2 + 5 1/2x

And, The volume of the paint is, 2/3 quartz.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Liam and Evan are mixing paint. Liam uses 2 quarts of yellow paint and adds 3 1/4 jars of blue paint.

And, Evan uses 1/2 quart of yellow paint and adds 5 1/2 jars of red paint. They end up with the same volume of paint.

Let the volume of the paint is, x

Hence, We can formulate;

The correct equation to represent the condition is,

⇒ 2 + 3 1/4x = 1/2 + 5 1/2x

And, Solve for x as;

⇒ 2 + 13/4x = 1/2 + 11/2x

⇒ 2 - 1/2 = 11/2x - 13/4x

⇒ 3/2 = (44 - 26)x / 8

⇒ 12 = 18x

⇒ x = 12/18

⇒ x = 2/3

Hence, The volume of the paint is, 2/3 quartz.

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The particular solution of the differential equation  y''-5y' 4y=8e^x is A*e^x form.

To find the form of the particular solution for the given differential equation, y'' - 5y' + 4y = 8e^x, we will first identify the terms involved and then determine an appropriate trial function for the particular solution.

Given differential equation: y'' - 5y' + 4y = 8e^x

Here, the left side represents a linear differential equation with constant coefficient and the right side is the non-homogeneous term (8e^x).

To find the form of the particular solution, we'll assume a trial function based on the non-homogeneous term. Since the non-homogeneous term is 8e^x, our trial function will have the form:

Trial function: Y_p(x) = A*e^x

Now, we need to find the derivatives of Y_p(x) and substitute them into the differential equation:

First derivative: Y_p'(x) = A*e^x
Second derivative: Y_p''(x) = A*e^x

Substituting these into the differential equation:

(A*e^x) - 5(A*e^x) + 4(A*e^x) = 8e^x

Simplifying the equation:

(A - 5A + 4A)e^x = 8e^x

Now, we compare the coefficients:

A = 8

So, the form of the particular solution for the given differential equation is Y_p(x) = 8e^x

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The growth rate of bacteria in a culture is not specified, so assuming it is exponential, the number of bacteria present after 2 hours will be approximately 1.8 x 10^8.

To solve this problem, we can use the exponential growth formula: N(t) = N0 * e^(rt), where N(t) is the number of bacteria at time t, N0 is the initial number of bacteria, r is the growth rate, and e is the base of the natural logarithm. First, we need to find the growth rate, r. We can use the initial and final number of bacteria and the time interval to do this.

N(t) = N0 * e^(rt)

171 = 38 * e^(49r)

ln(171/38) = 49r

r = ln(171/38)/49

r ≈ 0.069 Now we can use the formula to find N(120) (i.e., the number of bacteria after 2 hours, or 120 minutes):

N(120) = 38 * e^(0.069 * 120)

N(120) ≈ 1.8 x 10^8 Therefore, approximately 1.8 x 10^8 bacteria will be present in the culture after 2 hours.

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Answer:

Step-by-step explanation:

a)  x = time to fill the container

x = (300 l) / (15 l/min) = 20 min

b)  x = (300 l) / (2)(15 l/min) = 10 min   *half the amount of time as with one tap