Question 7:
Given two terms in an arithmetic sequence find the nth term.
a) 18th = 3362 and 38th= 7362

گرم
a​

The volume of a stack of 9 books is 1368.75 cubic inches.

To find the volume of a stack of 9 books, we first need to find the height of the stack. Since each book is 3/4 inch thick, the height of the stack is 9 times 3/4 inch, which is 6 3/4 inches.

Now we need to find the area of the base of the rectangular prism formed by the stack of books. Since each book has an area of 22 1/2 square inches, the total area of the base of the stack is 9 times 22 1/2 square inches, which is 202 1/2 square inches.

Therefore, the volume of the stack of 9 books is:

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The measure of arc BC is 264°

A circle is a special kind of ellipse in which the eccentricity is zero and the two foci are coincident.

Since the triangle is isosceles, this means that angle B = angle C

therefore angle A = 180- ( 24+24)

= 180- 48

= 132°

From the theorem that says that the angle at the circumference is twice the angle at the centre.

therefore arc BC = 2 × 132

arc BC = 264°

therefore the measure of arc BC is 264°

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Answer:

y = 4

Step-by-step explanation:

3 + x = y

given x = 1

plug in x = 1

3 + 1 = y

4 = y

y = 4

Answer:

y = 4

Step-by-step explanation:

3 + x = y

3 + 1 = y

4 = y

Answer:

\(36\)

Step-by-step explanation:

The expression \(_nC_k\) is used to denote the number of ways you can choose \(k\) things from a set of \(n\) things. It is equal to:

\(_nC_k=\binom{n}{k}=\frac{n!}{k!(n-k)!}\)

In this case, \(n=9\) and \(k=2\), so:

\(\implies \frac{9!}{2!(9-2)!}=\frac{9!}{2!7!}=\boxed{36}\)

You can also think of it like this:

\(_9C_2\) is saying 9 choose 2. We are choosing 2 things from a set of 9 things, where order doesn't matter. For the first thing we choose, there are 9 options. Then 8 options, 7, and so on. Since we're only choosing two things, there are \(9\cdot 8=72\) permutations. However, the order of which we choose each thing does not affect what we've chosen overall (e.g. If we're choosing two donut flavors original and strawberry, it doesn't matter which flavor I choose first, because I'm still getting the same two flavors). Therefore, we must divide this by the number of ways we can arrange two distinct values, which is \(2!\). Our answer is thus \(\frac{72}{2!}=\frac{72}{2}=\boxed{36}\)

=========================================================

Explanation:

We have 9*8 = 72 different permutations. This is if we used the nPr formula with n = 9 and r = 2.

Notice the countdown from 9 to 8. This is because we don't reuse the same element twice.

Since order doesn't matter with nCr, we will divide by 2. This is because something like AB is the same as BA. So we go from 72 to 72/2 = 36

The value 36 is found in Pascal's Triangle in the row that has 1,9,... at the start of it. Start at the left hand side and count exactly 3 spaces to the right, and you should land on 36.

The APY corresponding to a nominal rate of 9% compounded quarterly is approximately 9.31%.

The Annual Percentage Yield (APY) represents the total effective annual rate of return on an investment, taking into account compounding. To calculate the APY, we need to consider the nominal rate and the compounding frequency. In this case, the nominal rate is 9% and the compounding is done quarterly.

To find the APY, we use the formula: APY = \((1 + r/n)^ n-1\), where r is the nominal rate and n is the number of compounding periods per year.

Substituting the given values into the formula, we have: APY = \((1 + 0.09/4)^4 - 1.\)

Calculating this expression, we find: APY ≈ 0.0931 or 9.31%.

Therefore, the APY corresponding to a nominal rate of 9% compounded quarterly is approximately 9.31%. This means that if you invest in an account with this APY, your investment will grow by approximately 9.31% over the course of one year, taking into account the effects of compounding.

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James is 24 years old.

Let John's age now is J.

Let james's age now is A.

From the question, we have

John is 3/4 the age of  james.

J=3/4*A

J=3A/4

Three years ago, John was 5/7 the age of james.

J-3=5/7*(A-3)

J-3=(5A-15)/7

J=(5A-15)/7+3

3A/4=(5A-15)/7+3

21A=4(5A-15)+84

21A=20A-60+84

A=24

James is 24 years old.

Multiplication:

Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious. In mathematics, the repeated addition of one number in relation to another is represented by the multiplication of two numbers. These figures can be fractions, integers, whole numbers, natural numbers, etc. When m is multiplied by n, either m is added to itself 'n' times or the other way around.

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A- The specific heat of the sugar syrup can be converted to 2,060 kJ/kg·°C, and

b- the rate of heating, which is the heat energy transferred per unit time, is approximately 156.96054 kJ/s in SI units.

A- To convert the specific heat from Btul⁻¹F⁻¹ to kJkg⁻¹°C⁻¹, we use the conversion factor: 1 Btul⁻¹F⁻¹ = 4.184 kJkg⁻¹°C⁻¹.

Specific heat of the sugar syrup = 0.9 Btul⁻¹F⁻¹.

Converting to kJkg⁻¹°C⁻¹:

Specific heat = 0.9 Btul⁻¹F⁻¹ * 4.184 kJkg⁻¹°C⁻¹/Btul⁻¹F⁻¹

Specific heat ≈ 3.7584 kJkg⁻¹°C⁻¹.

(b) The rate of heating, or the heat energy transferred per unit time, can be calculated using the formula:

Rate of heating = (mass of the syrup) × (specific heat) × (temperature change) / (time)

The mass of the syrup can be calculated using the volume and density:

Mass = (volume) × (density) = 50 ft³ × 66.9 lb/ft³ ≈ 3345 lb ≈ 1516.05 kg.

The temperature change is ΔT = 80°C - 20°C = 60°C.

Plugging these values into the formula, we get:

Rate of heating = (1516.05 kg) × (0.388 kJ/(kg⋅°C)) × (60°C) / (30 min × 60 s/min) ≈ 156.96054 kJ/s.

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Answer:

22/3

Step-by-step explanation:

because it is

Answer:

23

13

13/23

Step-by-step explanation:

Hi!

"The quotient of" means you divide, so the quotient of 20 and x means you divide 20 by x:

20:x

Now, increase by 7:

(20:x)+7 (Answer)

Hope it helps!

Enjoy your day!

Please feel free to ask if you have any doubts :)

❖Sparkles❖ here to help

 \(\dfrac{20}{x} +7\)

Quotient is defined as when divide one number by another, the result is called the quotient.

The quotient of 20 and x, increased by seven

The following are possible interpretations of the given expression.

\(\dfrac{20}{x} +7\)

Here, "quotient" is the answer to a division.

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Answer: y = 2.75x

Step-by-step explanation:

well, truely I made my own graph and divided every number to (4,11) and got 2.75. I hope your going to use this.

The relationship between the x and y-values represented by the equation,

⇒ y = 2.75x

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

Given that;

Jermaine plots the points (0,0) and (4, 11) on a graph to represent a proportional relationship.

Let an equation to represent the proportion relationship between a and y is,

⇒ y = kx

Here, Jermaine plots the points (0,0) and (4, 11) on a graph to represent a proportional relationship.

Hence, The points satisfy the above equation,

Substitute x = 4, y = 11

⇒ y = kx

⇒ 11 = k × 4

⇒ k = 11/4

⇒ k = 2.75

Hence, We get;

The relationship between the x and y-values represented by the equation is,  

⇒ y = 2.75x

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The derivative of the function ƒ(x) = (10²(6x² + 7)³)²(9x⁶ - 4)⁹ can be simplified using logarithmic functions as follows: In f(x) = A(x) + B(x) + C. To simplify the given function using logarithmic functions, we can take the natural logarithm (ln) of both sides:

ln(f(x)) = ln[(10²(6x² + 7)³)²(9x⁶ - 4)⁹]

Using the properties of logarithms, we can split the logarithm of a product into the sum of logarithms:

ln(f(x)) = ln[(10²(6x² + 7)³)²] + ln[(9x⁶ - 4)⁹]

Next, we can bring down the exponents as coefficients in front of the logarithms:

ln(f(x)) = 2ln(10²(6x² + 7)³) + 9ln(9x⁶ - 4)

Further simplification can be achieved by using the properties of logarithms:

ln(f(x)) = 2[ln(10²) + ln((6x² + 7)³)] + 9ln(9x⁶ - 4)

Since ln(10²) is a constant, it can be simplified to:

ln(f(x)) = 2ln(100) + 2ln((6x² + 7)³) + 9ln(9x⁶ - 4)

The expression ln(100) can be further simplified to ln(10²) = 2ln(10) = 2.

Thus, we have:

ln(f(x)) = 2 + 2ln((6x² + 7)³) + 9ln(9x⁶ - 4)

Therefore, the simplified expression for In f(x) is In f(x) = A(x) + B(x) + C, where A(x) = 2, B(x) = 2ln((6x² + 7)³), and C(x) = 9ln(9x⁶ - 4).

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Answer:

black

black

Step-by-step explanation:

The experimental probability that a shoppers  age from 18 to 40 years is, 0.40.

What is experimental probability?

Experimental Probability: what actually happens throughout the experiment. For instance, the likelihood of getting a head when flipping a coin is 1/ 2, since there are only 2 possible outcomes (a head or a tail), and each has an equal likelihood of happening.

In the question it is given that the total number of shoppers in the store are, 4 + 22 + 29 + 0 = 55.

And the number of shoppers in the store whose age is between 18 to 40 years is 22.

So, the probability that a shoppers age is from 18 to 40 years is,

\(P=\frac{22}{55}=\frac{2}{5}=0. 40\)

Hence, the experimental probability is 0.40

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Answer:X=4

Step-by-step explanation: you add 12 to both sides which should get you 2x=68 and then divide both sides by 2 which should get you X=4

Answer:

The value for X is 25

Step-by-step explanation:

I hope this helps you out!

Answer:

32.17

Step-by-step explanation:

\(A= \pi\) × \(r^{2}\)

A= \(\pi\) × \(3.2^{2}\) ≈ \(32.16991\)

A= \(32.17\)

Answer:

C= 70.4

Step-by-step explanation:

The formula of finding the circumference: C=2πr

Therefore, C=2(3.142)(11.2)

C= 6.284*11.2

C= 70.4

answer:

if you rounded it the answer is 15 years old!

step-by-step explanation:

when know that your sister is 9 years old, so lets start off with that. because your sister is 4 older then your brother then that must mean that you brother is 5 years old

9-4

= 5

we also know that you brother is 1/3 your age so divide 5 by 1/3 or .33

5/ .33

= 15.15

but since it looks like we only need the whole number. just round down to 15 since your age is not close enough to round up to 16

( here is a tip i have gotten for rounding )

1-4 stay on the floor

5-9 climb the vine

haha they might sound super du-mb but they have helped me when i was younger!

hope this helps you and if you ever need anymore help/questions just ask me! :)

The amount of time it takes Joshua to iron 8 shirts when he iron one shirt in 4 minutes, is 32 minutes. The correct option is C: 32min

Given that Joshua can iron one shirt in 4 minutes.

Now, let us assume that the time it takes him to iron 8 shirts is s.

Using the equation

(s)/4 = 8 to find the amount of time it takes him to iron 8 shirts.

Now we can solve for s by multiplying both sides by 4

s/4 = 8 × 4s = 32

Thus, the amount of time it takes Joshua to iron 8 shirts is 32 minutes.

Option C: 32min

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The degree measures of each angle in the triangle are 82, 49 and 49

From the question, we have the following parameters that can be used in our computation:

The triangle

Where we have

E = 3x + 43

F = 4x - 3

The sum of angles in a triangle is 180

So, we have

3x + 43 + 4x - 3 + 4x - 3 = 180

Evaluate the like terms

11x = 143

Divide by 11

x = 13

So, we have

E = 3 * 13 + 43 = 82

F = 4 * 13 - 3 = 49

Hence, the degree measures of each angle in the triangle are 82, 49 and 49

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After dilation with the given scale factor, the coordinate of M is (-4/3, 2/3)

Dilation of a figure is a transformation that changes the size of the figure while preserving its shape. In a dilation, the figure is either enlarged or reduced by a scale factor, which is a constant ratio. The scale factor determines how much the figure is stretched or compressed.

During a dilation, each point of the original figure is multiplied by the scale factor to determine the corresponding position of the dilated figure. The center of dilation is a fixed point around which the figure is expanded or contracted.

In he figure given, the point M have coordinate at (-2, 1)

After dilation with a scale factor of 2/3, the coordinate of M changes to;

M(-2, 1) = 2/3(-2, 1) = -4/3, 2/3

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Bruce's principle is $140.

The interest that Bruce earned is $9.80

The interest rate that Bruce savings account is 7%.

Simple interest is the interest that that is earned a certain amount over a period of time given a principal and the number of years.

Simple interest = amount deposited x time x interest rate.

A graph can be described as a pictorial representation of data. A graph has a y-axis and the x-axis. The y-intercept is a point where the graph touches the y-axis. The y-intercept represents the initial amount that is deposited. The principle is $140.

The slope of the graph represents the rate at which the amount invested increases in value.

Interest Bruce earned after 1 year : change in the slope

149.80 - 140 = $9.80

Interest rate = Interest / (principle x time)

9.80 / (140 x 1) = 0.07 = 7%

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(2x - 7) + ( x + 4) = 90°

2x + x - 7 + 4 = 90°

3x - 3 = 90°

3x = 90 + 3

3x = 93

x = 93/3

x = 31°

▪2x - 7

= (2 . 31) - 7

= 62 - 7

= 55°

▪x + 4

= 31 + 4

= 35°

A reasoning which he used in the decision to model the data with a linear equation is: D. the change in y-values is constant for evenly spaced x-values.

A linear equation can be defined as an algebraic equation of the first order that has two (2) variables with each of its term having an exponent of one (1).

Also, the variables in all linear equations share a direct relationship and as such they are directly proportional to one another.

In conclusion, we can deduce that a reasoning which Jordan might have used in the decision to model the data with a linear equation is that the change in y-values is constant for evenly spaced x-values.

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Answer:

d

Step-by-step explanation:

edge 2022

Applying a subtraction operation, it is found that his new ERA was of 3.17.

ERA is a baseball concept, but understanding of baseball is not relevant to this question.

One year, a professional baseball pitcher had a 3.91 ERA. The next year, it was 0.74 points lower, hence it was given by the subtraction of 3.91 and 0.74, that is:

ERA = 3.91 - 0.74 = 3.17.

His new ERA was of 3.17.

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A. The power of the two-tailed hypothesis test with α = .05 is 0.53.

B. The power of the one-tailed hypothesis test with α = .05 is 0.95.

A hypothesis test is used to make decisions about a population based on sample data. It involves specifying a null hypothesis, collecting data, and then assessing the data to either reject or accept the null hypothesis.

A. The power of the two-tailed hypothesis test is calculated using the formula:

Power=

1- β=1- (1-α)\(^{1/2}\)

=1- (1-0.05)\(^{1/2}\)

=0.525

=0.53

This means that the researcher has an 53% chance of correctly rejecting the null hypothesis that there has been no change in the IQ over the past 10 years.

B. The power of the one-tailed hypothesis test is calculated using the formula:

Power=

1- β=1- α

=1- 0.05

= 0.95

This means that the researcher has a 95% chance of correctly rejecting the null hypothesis that there has been no increase in the IQ over the past 10 years.

This is a higher power than the two-tailed test because the one-tailed test focuses on detecting an increase in the IQ, while the two-tailed test can detect both an increase or decrease in the IQ.

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Answer:

10

Step-by-step explanation:

Answer:

Step-by-step explanation:

Step-by-step explanation:

\(\huge{\color{black}{\fbox{\color{pink}{\colorbox{pink}{\color{red}{Answer ✨☑️}}}}}}\)

The number of terms are 8. Step-by-step explanation: Given : The sum n terms of an A.P is 136 the common difference is 4 and last term is 31.

Answer:

Sn=2n{2a+(n−1)d}

a+(n−1)d=31⇒a=31−4(n−1)

∴136=2n{2[31−4(n−1)]+(n−1)d}

n[70−8n+4n−4]=272

n(66−4n)=272

4n2−66n+272=0

2n2−33n+136=0

2n(n−8)−17(n−8)=0

(2n−17)(n−8)=0

∴n=8