The number of terms of an Ap is even and the sum of odd terms is 24 the sum of even terms is 30 and the last term exceeds the first by 10 1/2. find the number of term and the series.




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(a) Isla's trading cards are 125% of Lily's trading cards.

(b) Lily's trading cards are 80% of Isla's trading cards.

Given that,

There are 225 trading cards and Lily has 180 trading cards.

To calculate the percentage of Isla's trading cards compared to Lily's,

We can use this formula:

⇒ Isla's trading cards / Lily's trading cards x 100%

Plugging in the values we get:

⇒ (225 / 180) x 100% = 125%

Therefore,

Isla's trading cards are 125% of Lily's trading cards.

b) To calculate the percentage of Lily's trading cards compared to Isla's, we can use the formula:

⇒ Lily's trading cards / Isla's trading cards x 100%

Plugging in the values we get:

(180 / 225) x 100% = 80%

Therefore,

Lily's trading cards are 80% of Isla's trading cards.

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The type of error that could have been committed in this scenario is a Type I error.

In hypothesis testing, a Type I error occurs when the null hypothesis is rejected, even though it is true. It means that the researcher incorrectly concludes that there is a significant result or effect when there is actually no real effect present in the population. In this case, if the researcher rejects the null hypothesis that the dropout rate is 45% and concludes that it is different, she might be committing a Type I error if the null hypothesis is actually true.

A Type II error, on the other hand, occurs when the null hypothesis is not rejected, even though it is false. It means that the researcher fails to detect a significant result or effect when there is actually a real effect present in the population. The question states that the null hypothesis is rejected, so a Type II error is not relevant in this situation.

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Answer:

(a+b)(a+b)

=a^2 + ab + ab + b^2

=a^2 + 2ab + b^2

Answer:

(a+b)² = ( a +b ) (a + b )

= a² + b² + 2ab

The value of a(t) is -1 and b(t) is 55 + \(e^t\)

No, the given equation y' - y = 55 + \(e^t\) is not in the standard form of a first-order linear differential equation.

In the method for solving a first-order linear differential equation, an integrating factor is a function used to transform the equation into a form that can be easily solved.

For an equation in the standard form y' + a(t)y = b(t), the integrating factor is defined as:

μ(t) = e^∫a(t)dt

To solve the equation, you multiply both sides of the equation by the integrating factor μ(t) and then simplify. This multiplication helps to make the left side of the equation integrable and simplifies the process of finding the solution.

To put it in standard form, we need to rewrite it as y' + a(t)y = b(t).

Comparing the given equation with the standard form, we can identify:

a(t) = -1

b(t) = 55 + \(e^t\)

Therefore, The value of a(t) is -1 and b(t) is 55 + \(e^t\)

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The component of a linear programming model that is NOT listed is "Decision variables."

A linear programming model consists of several components that work together to optimize a given objective while considering various constraints. The components of a linear programming model include:

Constraints: These are the limitations or restrictions that define the feasible set of solutions. Constraints restrict the values that decision variables can take.

Objective Function: This function represents the goal or objective of the linear programming problem. It is either minimized or maximized based on specific criteria.

Feasible Region: Also known as the feasible set or feasible solution space, this refers to the collection of all points that satisfy each constraint in the linear programming problem. It represents the set of possible solutions that meet all the given constraints.

However, "Decision variables" is not a component of a linear programming model but rather the unknowns or variables that we want to determine in order to optimize the objective function.

Decision variables are not a component of a linear programming model. The components of a linear programming model include constraints, objective function, and feasible region. The feasible region refers to the collection of all points that satisfy each constraint in the linear programming problem.

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Answer:

They Played 15 games total

Step-by-step explanation:

Make ratios:

9:60 %

x:100 %

Cross multiply: 60 times x =60x and 9x100= 900 = 60x=900

Divide to get x: 60x/60=900/60

x=15

They Played 15 games total

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Answer:

3

8

+

4

0

+

1

2

0

=

3

4

−

7

(

2

0

−

1

9

)

{\color{#c92786}{38x}}+40+{\color{#c92786}{120x}}=34x-7(20-19x)

1

5

8

+

4

0

=

3

4

−

7

(

2

0

9

)

Step-by-step explanation:

Answer:

x = 20

Step-by-step explanation:

\(38x+40+120x=34x-7(20-19x)\\\rule{180}{0.5}\\\text{Simplifying the left:}\\\\38x+120x+40\\\\158x + 40\\\\\text{Simplifying the right:}\\\\34x-7(20-19x)\\\\34x - 140 + 133x\\\\34x + 133x - 140\\\\167x - 140\\\rule{180}{0.5}\\158x + 40 = 167x - 140\\\\158x + 40 - 40 = 167x - 140 - 40\\\\158x = 167x - 180\\\\158x - 167x = 167x - 167x - 180\\\\-9x = -180\\\\\frac{-9x}{-180}\\\\\boxed{x = 20}\)

Hope this helps.

a) The explanatory variable in the study is the format of the stories presented to the four-year-olds: audio, illustrated, and animated. This variable is categorical because it involves distinct categories or formats.

b) The response variable in the study is the brain connectivity measured by the magnetic resonance imaging (MRI) machine. This variable is quantitative as it represents a numerical measurement of brain connectivity.

c) The study includes 27 four-year-olds as the observational units or individuals.

The study aimed to investigate the impact of different story formats on brain connectivity in four-year-olds. The explanatory variable, format, was categorized into three groups: audio, illustrated, and animated.

The response variable, brain connectivity, was measured using an MRI machine. The researchers found a "Goldilocks effect" in the brain connectivity, indicating that the audio format was associated with low brain connectivity, possibly due to the children straining to understand.

On the other hand, the animated format also resulted in low brain connectivity, suggesting that the animation did all the work for the children.

The highest brain connectivity, considered optimal, was observed with the illustrated format, which simulated the experience of reading a book to a child.

The study included 27 four-year-olds as the observational units, providing insights into the relationship between story format and brain connectivity in young children.

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Answer:

the answer to 1 is 24.5

Step-by-step explanation:

i believe

Answer:

Rectangles! Nice.

Step-by-step explanation:

This is a very simple problem. Let's first represent the width of the rectangle as the variable x.

Then, we know that the length of the triangle is x+2. See where I'm going with this?

The formula for the perimeter of an rectangle is \(P=2*Length+2*Width\).

All we have to do next is just input our values for the length and width, and you'll be golden!

\(56=2(x+2)+2(x)\\56=4x+4\)

Next to subtract 4 from both sides and then to divide by 4!

\(52=4x\\x=13\)

There's your answer! Don't know why Brainly is bugged right now.

NOTE: If you can't read the answer above, the width is 13cm. This also means that the length is 15cm.

Hope this helps!

Stay safe!

Answer:

Area:

15 x 9 = 135 divided by 2 = 67.5

The marginal profit function represents the rate of change of profit with respect to the number of magazines sold. To find the marginal profit function, we need to calculate the derivative of the profit function.

The profit function is given by P(x) = R(x) - C(x), where R(x) is the revenue function and C(x) is the cost function.

The revenue function R(x) is given by R(x) = p(x) * x, where p(x) is the price function.

Given that p(x) = 4.600.0006x, the revenue function becomes R(x) = 4.600.0006x * x = 4.600.0006x².

The cost function is given by C(x) = 0.0005x² + x + 4000.

Now, we can calculate the profit function:

P(x) = R(x) - C(x) = 4.600.0006x² - (0.0005x² + x + 4000)

      = 4.5995006x² - x - 4000.

Finally, we can find the marginal profit function by taking the derivative of the profit function:

P'(x) = (d/dx)(4.5995006x² - x - 4000)

       = 9.1990012x - 1.

Therefore, the marginal profit function is given by MP(x) = 9.1990012x - 1.

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Answer:

Step-by-step explanation:

b

The justification for Step 1 is the subtraction property of equality. Option B

The justification for Step 1 within the arrangement prepare, which changes the condition 15x − 8 = 14x + 13 into 15x = 14x + 21, is the subtraction property of uniformity.

The subtraction property of equality states that in the event that we subtract the same amount from both sides of an condition, the condition remains genuine. In this case, we are subtracting 14x from both sides of the condition to confine the term with x.

To clarify Step 1 utilizing the subtraction property of correspondence:

The condition 15x − 8 = 14x + 13 is given.

We need to disconnect the x term on one side of the condition. To do this, we got to dispose of the 8 on the cleared out side.

By subtracting 14x from both sides of the condition, we evacuate the 14x term from the correct side:

15x − 14x − 8 = 14x − 14x + 13

Simplifying:

x − 8 = 13

Now, the 14x term is dispensed with from the proper side of the condition.

To advance streamline the condition, we are able include 8 to both sides to dispose of the -8 term on the cleared out side:

x − 8 + 8 = 13 + 8

Simplifying:

x = 21

Now, we have effectively isolated the x term on one side of the condition.

Therefore, the justification for Step 1 is the subtraction property of equality  (B).

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Complete question

What is the justification for step 1 in the solution process?

15x − 8 = 14x + 13

Step 1: 15x = 14x + 21

A.

the addition property of equality

B.

the subtraction property of equality

C.

the division property of equality

D.

the multiplication property of equality

Question

How do you write the equation of a line in point slope form and slope intercept form given point (6, -3) and has a slope of 1/2?

Answer · 0 votes

Point-Slope Form is y+3=12(x−6) Slope-Intercept Form is y=12x−6 Explanation: .

We have to take the GCF (Greatest Common Factor) of 45 and 75 to get our answer.

We prime factorize the numbers. Shown below:

45 = 3 * 3 * 5

and

75 = 3 * 5 * 5

The greatest number of time 3 is common is 1 time

The greatest number o time 5 is common is 1 time

So,

GCF(45, 75) = 3 x 5 = 15 bags

Answer:

To find out how much Laura earns each week, you can set up an equation using the information given. Let's call Laura's weekly pay "W".

You know that Laura has saved 5 times her weekly pay, so you can write this as 5W.

You also know that she spent less than 2 times her weekly pay this week, so you can write this as 2W - X, where X is the amount that she spent less than 2 times her weekly pay.

Finally, you know that she has 156 left after spending some money, so you can write this as 156.

You can now set up the equation:

5W + (2W - X) = 156

Combining like terms, you get:

7W - X = 156

Adding X to both sides, you get:

7W = 156 + X

Dividing both sides by 7, you get:

W = (156 + X) / 7

Thus, Laura's weekly pay is equal to (156 + X) / 7. You know that she spent less than 2 times her weekly pay this week, so X must be less than 2W. However, you don't know the exact value of X, so you can't find the exact value of Laura's weekly pay.

:

If laura has saved her babysitting money for the past two weeks then Laura earns 52 dollars per week.

Two or more expressions with an Equal sign is called as Equation.

Let Laura earns x dollars per week.

According to the problem, after two weeks of saving, she has 5 times her weekly pay, which means she has saved 5x dollars.

This week, she spent less than 2 times her weekly pay, which means she spent less than 2x dollars.

Now, she has 156 dollars left, so we can set up the equation:

5x -  2x = 156

Simplifying this equation, we get:

3x= 156

Divide both sides by 3

x = 52

Hence, Laura earns 52 dollars per week.

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Answer:

6x-3

Step-by-step explanation:

remove breceket

3×2 =6

3×-1= -3

answer is 6x-3

Answer:

C. 39/48 = 81%

Step-by-step explanation:

To determine the percentage of females who only said they like cats using the given two-way table, we need to find the number of females who selected "cats" only and divide it by the total number of females surveyed. We can then multiply the result by 100 to get the percentage.

According to the provided two-way table:

Number of females who only said they like cats = 39

Total number of females surveyed = 48

To calculate the percentage:

Percentage of females who only said they like cats = (Number of females who only like cats / Total number of females surveyed) * 100

Percentage of females who only said they like cats = (39 / 48) * 100 ≈ 81.25%

Therefore, the correct option is:

C. 39/48 = 81%

Answer:

T=7

Step-by-step explanation:

180-90=90

90-49=51

41-6=35

35/5=7

t=7

Answer:

Step-by-step explanation:

49+90 = 139

180 - 139 = 141

141 - 6 = 5t

135 = 5t

135/5 = t

27 = t

We would need to fill the 6.75 L bucket approximately 4,720 times in order to empty the pool of volume 31,860 liters.

To calculate the number of times a 6.75 L bucket has to be filled in order to empty the pool, we first need to find the volume of water in the pool. We can use the formula for the volume of a rectangular prism, which is:

Volume = length x width x height

In this case, the length is 20.0 ft, the width is 12.5 ft, and the height (or depth) is 4.50 ft. Substituting these values into the formula, we get:

Volume = 20.0 ft x 12.5 ft x 4.50 ft

Volume = 1125 cubic feet

However, we need to convert this volume into liters in order to compare it with the volume of the bucket. To do this, we can use the conversion factor that 1 cubic foot is equal to 28.32 liters. Therefore:

Volume = 1125 cubic feet x 28.32 L/cubic foot

Volume = 31,860 liters

Now we can divide this volume by the volume of one bucket:

Number of buckets = Volume ÷ Bucket volume

Number of buckets = 31,860 L ÷ 6.75 L

Number of buckets = <<31860/6.75=4720>>4,720

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Answer:

  (x, y) = (-6, 0)

Step-by-step explanation:

The y-coefficients have opposite signs, so we can eliminate y-terms by multiplying both equations by a positive number and adding the results.

9 times the first equation plus 4 times the second gives ...

  9(5x +4y) +4(3x -9y) = 9(-30) +4(-18)

  45x +36y +12x -36y = -270 -72 . . . . eliminate parentheses

  57x = -342 . . . . . collect terms

  x = -6 . . . . . . . divide by the coefficient of x

__

Substituting into the first equation gives ...

  5(-6) +4y = -30

  4y = 0 . . . . . . . . . add 30

  y = 0

The solution is (x, y) = (-6, 0).

Answer:

21.4, Because x is starts at 11 ending far away down, which means x has to be longer than 11

Step-by-step explanation:

:b

Answer:

girl drop link and I will sc all answers

Answer:

Step-by-step explanation:

slope-intercept form of equation:  y = mx + b

where m is slope and b is y-intercept

If line y=ax+b passes through point (x₀,y₀) that means

that the equation y₀=ax₀+b is true

(2, 5)    ⇒   x=2,   y=5

m = 5

So:

              5 = 5×2 + b

               5 = 10 + b

               b = -5

Therefore equation in  slope-intercept form:

                                                                      y = 5x + (-5)

                                                                      y = 5x - 5                          

The equation of the line in slope-intercept form is y = 5x - 5.

Given that the slope of the line is 5 and it passes through the point (2, 5), we can use the point-slope form of a linear equation to find the equation of the line.

The point-slope form is given by:

y - y1 = m(x - x1),

where (x1, y1) is the given point and m is the slope.

Substituting the values, we have:

y - 5 = 5(x - 2).

Now, let's simplify this equation:

y - 5 = 5x - 10.

Next, let's isolate y:

y = 5x - 10 + 5.

Simplifying further:

y = 5x - 5.

So, the equation of the line in slope-intercept form is y = 5x - 5.

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Answer:

Step-by-step explanation:

3 = 1(1 + x)^4

let q = 1 + x

3 = q^4

ln(3)  = 4  ln(q)

ln(3)/4 = ln(q)

.274 = ln(q)

q = e^.274 = 1.316

x = .316

Future amount = 48(1+.316)^4

Future amount = 143.96

Step-by-step explanation:

we first square both sides to eliminate the square root brackets..

(√(m(y+n)/y)²= p²

m(y+n)/y = p²

(my +mn)/y =p²

so we multiply both sides by y to eliminate the denominator,

(my+mn)/y*y =p²*y

my+mn = p²y

collecting like terms,we have:

mn= p²y-my

so we seperate the y on the right hand side from the rest to have

mn = y(p²-m)

so divided both sides by the value in the bracket on the right hand side we have..

mn/(p²-m)=y(p²-m)/(p²-m)

so we have,

y= mn/(p²-m)

Answer:

y = \(\frac{-mn}{m-p^2}\)

Step-by-step explanation:

Given

\(\sqrt{\frac{m(y+n)}{y} }\) = p ( square both sides )

\(\frac{m(y+n)}{y}\) = p² ( multiply both sides by y )

m(y + n) = p²y ← distribute parenthesis on left side

my + mn = p²y  ( subtract p²y from both sides )

my - p²y + mn = 0 ( subtract mn from both sides )

my - p²y = - mn ← factor out y from each term on the left side

y(m - p²) = - mn ← divide both sides by (m - p²)

y = \(\frac{-mn}{m-p^2}\)

A cyclic quadrilateral is a quadrilateral inscribed in a circle

The measure of angle A is 106

From the question, we have:

<C= 74

Opposite angles of a cyclic quadrilateral add up to 180.

So, we have:

<A + <C = 180

This gives

<A + 74 =180

Subtract 74 from both sides

<A =106

Hence, the measure of angle A is 106

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A sample of 40 provided a sample mean of 26.5. The population standard deviation is 6.

(a) Find the value of the test statistic. (Round your answer to two decimal places.) 1.94

(b) Find the p-value. (Round your answer to four decimal places.) p-value    =  0.0261  

(d) State the critical values for the rejection rule. (Round your answer to two decimal places. If the test is one-tailed, enter NONE for the unused tail.)

test statistics <= 1.645

test statistic >= -∞

To find the value of the test statistic use the formula for the z-test:

z = (sample mean - population mean) / (population standard deviation / √(sample size))

The sample mean is 26.5, the population mean is 25, the population standard deviation is 6, and the sample size is 40.

(a) Value of the test statistic:

z = (26.5 - 25) / (6 / √(40))

z = 1.5 / (6 / √(40))

z ≈ 1.3416 (rounded to two decimal places)

(b) To find the p-value, to calculate the probability of observing a test statistic as extreme as the one obtained (1.3416) under the null hypothesis.

Since the alternative hypothesis is one-tailed (μ > 25), the p-value is the probability of observing a z-value greater than or equal to 1.3416. We can find this probability using a standard normal distribution table or calculator.

Using a standard normal distribution table find that the area to the right of 1.34 is approximately 0.0901.

Therefore, the p-value is approximately 0.0901 (rounded to four decimal places).

(c) The critical values for the rejection rule depend on the chosen significance level assume a significance level of α = 0.05 (5%).

Since the alternative hypothesis is one-tailed and are testing for μ > 25, the critical value is obtained by finding the z-value that corresponds to an area of 0.05 to the right in the standard normal distribution.

Using a standard normal distribution table, find that the critical value is approximately 1.645 (rounded to two decimal places).

Therefore, the critical values for the rejection rule are

test statistic <= NONE

test statistic >= 1.645

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Answer:

\(-\frac{1}{5} t^{15}\)

Step-by-step explanation:

sry if im wrong