7-th grade math question :
The circumference of a circle is 25.12 feet. What is the circle's diameter?
|__|feet

The value of the machine after 4 years can be calculated using the formula:
V = P * (1 - r) ^ n
Where:
V = value after n years
P = initial purchase price
r = annual depreciation rate
n = number of years

In this case, P = 3,000.00, r = 0.10 (10%), and n = 4.
Plugging these values into the formula, we get:
V = 3,000.00 * (1 - 0.10) ^ 4
V = 3,000.00 * 0.90 ^ 4
V = 3,000.00 * 0.6561
V = 1,968.30

Therefore, the value of the machine after 4 years is $1,968.30.

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Answer:

a)

b)

Explanation:

a) Let b represent the number of striped bass one is allowed to catch.

Since we're only allowed to catch at most 3 striped basses, that is, the number of striped basses can be less than or equal to 3 but not more, we can go ahead and write the inequality as seen below;

See below the graph of the above inequality on a number line;

b) Let l represent the length of each striped bass

Since each striped bass must not be less than 18 inches long, that is, each striped bass can

be more than or equal to 18 inches in length but not less, we can go ahead and write the inequality as seen below;

Graphing on a number line, we'll have;

Answer:

Continuous

Step-by-step explanation:

Continuous

hopefully this helps you :)

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In the function model, the cost of the cashews is y = $12.79x which linear and continuous.

Given that,
An airport snack stand sells whole cashews for $12.79 per pound.

Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

A continuous function is defined as a function with the continuous interpretation of the assertion that generates a continuous interpretation of the value of the function. This means that there are no sharp changes in value, comprehended as discontinuities.

Since in the question,
An airport snack stand sells whole cashews for $12.79 per pound.
Let y be the cost per pound and x be the weight of cashews in pounds.
Expression formulated as a
y = 12.79*x

above expression is a linear expression and does not have abrupt changes in it, hence function is continuous.

Thus, in the function model, the cost of the cashews is y = $12.79x which linear and continuous.

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The second-order cross partial derivatives ∂²G/∂x∂z = -4 and ∂²G/∂z∂x = 0.

To find the second-order partial derivatives of the given function G, we need to differentiate it twice with respect to each variable separately. Let's go step by step:

First, let's find the second-order partial derivatives with respect to x:

1. Partial derivative with respect to x:

∂G/∂x = -7 + 85 + 2x + 12x^2 - 17x^2 + 19x^2 + 7(3x^2) - 4z + 120

Simplifying this expression, we get:

∂G/∂x = 63 + 7x^2 - 4z + 120

2. Second-order partial derivative with respect to x:

∂²G/∂x² = d(∂G/∂x)/dx

Taking the derivative of the expression ∂G/∂x with respect to x, we get:

∂²G/∂x² = d(63 + 7x^2 - 4z + 120)/dx

∂²G/∂x² = 14x

So, the second-order partial derivative with respect to x is ∂²G/∂x² = 14x.

Next, let's find the second-order cross partial derivatives:

1. Partial derivative with respect to x and z:

∂²G/∂x∂z = d(∂G/∂x)/dz

Taking the derivative of the expression ∂G/∂x with respect to z, we get:

∂²G/∂x∂z = d(63 + 7x^2 - 4z + 120)/dz

∂²G/∂x∂z = -4

2. Partial derivative with respect to z and x:

∂²G/∂z∂x = d(∂G/∂z)/dx

Taking the derivative of the expression ∂G/∂z with respect to x, we get:

∂²G/∂z∂x = d(-4)/dx

∂²G/∂z∂x = 0

In summary, the second-order direct partial derivative is ∂²G/∂x² = 14x, and the second-order cross partial derivatives are ∂²G/∂x∂z = -4 and ∂²G/∂z∂x = 0.

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Answer:

option B)

Step-by-step explanation:

a1/a2= 6/1

b1/b2 = 2/3

since a1/a2 is not equal to b1/b2,

lines have a unique solution

hence answer is option B)

The equation for the rate of change of concentration is Δc/Δt, and this is equal to the rate of change of concentration over a given interval, -0.0680 m/s.

To calculate the final concentration, we must use the equation Δc = rate × time, where Δc is the change in concentration, and rate and time are the rate of change of concentration and the interval, respectively. Plugging in our values, Δc = -0.0680 m/s × 3.0 s = -0.204 m. This means that the final concentration of c is 2.700 m - 0.204 m, which is equal to 2.496 m.

To summarize, the rate of change of concentration equation is Δc/Δt = rate of change, and the equation to calculate the final concentration is Δc = rate × time. Plugging in the rate of change and interval, we get Δc = -0.0680 m/s × 3.0 s = -0.204 m, which gives us the final concentration of c at the end of the same interval as 2.496 m.

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Answer:

AC = 24

Step-by-step explanation:

If you subtract C - A, you get

16 - (-8) = 16 + 8 = 24

Answer:

AC=24

Step-by-step explanation:

Answer:

the volume of the figure is 480cm cubed

Step-by-step explanation:

Answer:

length = 15

Width = 9

Step-by-step explanation:

In a rectangle opposite sides are equal.

5x - y- 8 =3x +5y + 4

5x - 3x  -y - 5y = 4 + 8

2x - 6y = 12

Divide the entire equation by 2

x  - 3y = 6  --------------(I)

3x + y - 4 = 2x - 6y - 3

3x - 2x + y + 6y = -3 + 4

x + 7y = 1 -------------(II)

Multiply equation (II) by (-1)

(I)            x - 3y = 6

(II)*(-1)    -x - 7y = -1   {Now add. 'x' will be eliminated}

                  -10y= 5

                      y = 5/(-10)

                     y = -0.5

Plugin y = -0.5 in equation (I)

x - 3*(-0.5) = 6

x  + 1.5 = 6

        x = 6 - 1.5

        x = 4.5

Length = 5x - y - 8

           = 5*4.5 - (-0.5) - 8

           = 22.5 + 0.5 - 8

            = 23 - 8

Length = 15

Width = 2x - 6y - 3

         = 2*4.5 - 6*(-0.5) - 3

         =  9 + 3 - 3

Width = 9

The hydrologic cycle, also known as the water cycle, plays a crucial role in the Earth's natural processes. It involves the continuous movement of water between the Earth's surface, atmosphere, and underground reservoirs.

The importance of the hydrologic cycle can be understood by considering its various functions:

Transport: The hydrologic cycle facilitates the transport of water across the Earth's surface, including rivers, lakes, and oceans. This movement of water is vital for the distribution of nutrients, sediments, and organic matter, which are essential for the functioning of ecosystems.

Weathering and Contaminant Transport: Water plays a significant role in weathering processes, such as erosion and dissolution of rocks and minerals. It also acts as a carrier for contaminants, pollutants, and nutrients, influencing their transport through the environment.

Energy Balance: Water has a high heat capacity, which means it can absorb and store large amounts of heat energy. This property helps regulate the Earth's temperature and climate by transporting heat through evaporation, condensation, and precipitation.

Greenhouse Gas: Water vapor is a major greenhouse gas that contributes to the Earth's natural greenhouse effect. It absorbs and re-emits thermal radiation, trapping heat in the atmosphere. Approximately 80% of the atmospheric greenhouse effect is attributed to water vapor.

Life: Water is vital for supporting life on Earth. It provides a habitat for numerous organisms and serves as a medium for various biological processes. Terrestrial life forms, including plants, animals, and humans, rely on water availability for their survival, growth, and reproduction.

It is important to note that while water is critical for most terrestrial life forms, human beings have developed technologies and systems that allow them to inhabit regions with limited water availability. However, water still remains a fundamental resource for human societies, and the hydrologic cycle plays a crucial role in ensuring its availability and sustainability.

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Answer:

:Both Tim and Jasmine calculated the volume properly. Tim gave the exact answer with pi in it, whereas Jasmine multiplied by pi and then rounded

Step-by-step explanation:

Answer:  Both Tim and Jasmine calculated the volume properly. Tim gave the exact answer with pi in it, whereas Jasmine multiplied by pi and then rounded to the nearest hundreth.

Step-by-step explanation:

9514 1404 393

Answer:

  C

Step-by-step explanation:

All of the offered answer choices are dilations. When a figure is dilated about the origin, every individual coordinate is multiplied by the dilation factor.

So, the dilation factor can be found by dividing an image coordinate by the pre-image coordinate.

  I'x/Ix = -3/-2 = 1.5

The dilation is 1.5 about the origin.  . . .  matches C

The values between which the sample t is found are  -1.753 < t < 1.753.

To determine the values between which the sample t is found, we need to consider the degrees of freedom (df) and the critical value for the given level of significance (α). The sample t is within the range determined by these critical values.

In this case, the range is determined by the critical t-values for a two-tailed test with the given degrees of freedom. Since the specific degrees of freedom and significance level (α) are not provided, we cannot calculate the exact values. However, if we assume a common significance level (such as α = 0.05), the critical t-values would be -1.753 and 1.753 for a two-tailed test. Therefore, the sample t should fall between these two values.

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The relationship between the distribution values and the t-distribution as per the question with relation to degrees of freedom, the answer will be as follows:

1. When the sample size is small or the population standard deviation is unknown, the t-distribution is a probability distribution that is utilized in hypothesis testing and confidence interval estimates. The degrees of freedom (df), which is a gauge of sample size, determine the form of the t-distribution.

2. The t-distribution gets increasingly symmetric as df rises and becomes closer to a normal distribution. In other words, the t-distribution becomes more like the regular normal distribution and less dependent on the sample standard deviation as the sample size grows. This is so that the population standard deviation may be estimated with greater accuracy thanks to the increased sample size.

3. Since they have thicker tails than the normal distribution, t-distributions tend to be flatter and more dispersed. This results in a broader distribution since there is a larger likelihood that the sample may contain extreme values.

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The measure of PQT = 142.

We know what ray QS bisects angle PQT. If you draw out angle PQT and ray QS you can see that angle PQS is congruent to angle SQT. Because of the definition of angle bisector. This also means that angle SQT is half of PQT. Because of this we know that we can set the measure of PQT equal to 2 times the measure of SQT.

So we can set up and solve the following equation as such:

2(8x-25) = 9x +34

16x - 50 = 9x +34

7x -50 = 34

7x = 84

x = 12

Again I this doesn't seem to be your final answer. To find the answer the measures of each angle you're going to want to plug 12 in for x for one of the angles. So I'll do it for angle SQT.

8(12) - 25

96 -25

71

So the measure of angle SQT should be 71. Therefore since QS bisects PQR, the measure of angle PQS should also be 71. The measure of PQT should be double that which makes it 142.

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do your work buddy and dont cheat

Step-by-step explanation:

dont cheat and actually study

Answer:

12 packages

one pack will contain 3 soap bars and 2 toothbrush

Step-by-step explanation:

Answer:

3 and 2

Step-by-step explanation:

if your doing this on i ready it will ask you next (There are (3) bars of soap and (2) tooth brushes in each package---- and those are your other answers (3) and (2)

\(\frac{2}{x}\)

\(\frac{x}{2}\)

\(\frac{4x^4}{y^3}\)

a. 2x^-3 • 4x^2

To solve this using only positive exponents, follow these steps:

i. Rewrite the expression in a clearer form

2x⁻³ . 4x²

ii. The position of the term with negative exponent is changed from denominator to numerator or numerator to denominator depending on its initial position. If it is at the numerator, it is moved to the denominator. If otherwise it is at the denominator, it is moved to the numerator. When this is done, the negative exponent is changed to positive.

In our case, the first term has a negative exponent and it is at the numerator. We therefore move it to the denominator and change the negative exponent to  positive as follows;

\(\frac{1}{2x^3} . 4x^2\)

iii. We then solve the result as follows;

\(\frac{1}{2x^3} . 4x^2\) = \(\frac{2}{x}\)

Therefore, 2x⁻³ . 4x² = \(\frac{2}{x}\)

b. 2x^4 • 4x^-3

i. Rewrite as follows;

2x⁴ . 4x⁻³

ii. The second term has a negative exponent, therefore swap its position and change the negative exponent to a positive one.

\(2x^4 . \frac{1}{4x^3}\)

iii. Now solve by cancelling out common terms in the numerator and denominator. So we have;

\(\frac{x}{2}\)

Therefore, 2x⁴ . 4x⁻³ = \(\frac{x}{2}\)

c. 2x^3y^-3 • 2x

i. Rewrite as follows;

2x³y⁻³ . 2x

ii. Change position of terms with negative exponents;

\(2x^3.\frac{1}{y^3} .2x\)

iii. Now solve;

\(\frac{4x^4}{y^3}\)

Therefore, 2x³y⁻³ . 2x = \(\frac{4x^4}{y^3}\)

The relationship between a statistic and a parameter is the same as the relationship between , Option(A) a sample and a population

The Population is defied as an entire group of individuals that we are interested in studying, while a sample is a subset of that population that we actually observe and collect data from.

A Parameter is defined as a numerical characteristic of a population, such as its mean or variance, whereas a statistic is a numerical characteristic of a sample, such as its sample mean or sample standard deviation.

The relationship between a sample and a population is similar to the relationship between a statistic and a parameter because a sample is used to estimate  information about the population, and a statistic is used to estimate  information about a parameter.

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Answer:

The first one is 12

The second one is -12

Just multiply, and remember the negative signs.

Answer:

1st Question- Positive Twelve

Second Question- Negative Twelve

Step-by-step explanation:

The given function is:

To find the inverse set f(x)=y

Now, solve for x:

cube both sides of the equation:

Add 5 to both sides:

Now, switch x and y and reorder terms:

Replace y by f^-1(x):

This is the inverse of the function.

The value of the conversion is;

16, 666. 67 minutes

277.78 hours

Conversion of units is described as the conversion between different units of measurement for the same quantity, using the multiplicative factor.

From the information given, we have;

10⁶ seconds

But, we have to take note of;

60 seconds = 1 min

Then 10⁶ seconds = x min

cross multiply

x = 16, 666. 67 minutes

Also,

60 minutes = 1 hour

Then 16, 666. 67 minutes = x

cross multiply

x = 277.78 hours

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To prove that among 7 randomly chosen integers, there must be 2 whose difference is divisible by 6, we can use the pigeonhole principle.

Consider the remainders when any integer is divided by 6. There are six possible remainders: 0, 1, 2, 3, 4, and 5. Now, if we choose seven integers, we can associate each integer with its remainder when divided by 6.

By the pigeonhole principle, if we have seven integers, there must be at least two integers with the same remainder when divided by 6. Let's consider the following cases:

Case 1: Two integers have a remainder of 0 when divided by 6.

In this case, their difference is divisible by 6 since both integers are multiples of 6.

Case 2: Two integers have a remainder of 1 when divided by 6.

Let's assume these two integers are a and b. We have two possibilities:

 a) a > b: In this case, the difference a - b will have a remainder of 1 when divided by 6.

 b) b > a: In this case, the difference b - a will have a remainder of 5 when divided by 6. However, since the order of subtraction doesn't matter, we can consider this as a - b, where a > b. So the difference a - b will have a remainder of 1 when divided by 6.

Case 3: Two integers have a remainder of 2 when divided by 6.

Similar to Case 2, we can show that the difference between these two integers will have a remainder of 2 when divided by 6.

Case 4: Two integers have a remainder of 3 when divided by 6.

Again, similar to Cases 2 and 3, we can show that the difference between these two integers will have a remainder of 3 when divided by 6.

Case 5: Two integers have a remainder of 4 when divided by 6.

Similarly, we can show that the difference between these two integers will have a remainder of 4 when divided by 6.

Case 6: Two integers have a remainder of 5 when divided by 6.

In this case, their difference is divisible by 6 since both integers are multiples of 6.

In each of the six cases, we can find a pair of integers whose difference is divisible by 6. Therefore, by the pigeonhole principle, among 7 randomly chosen integers, there must be 2 whose difference is divisible by 6.

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Answer:

-6 and -3

Step-by-step explanation:

The probability that they end up with four boys on the left and two girls on the right is 1/15.

To solve this problem, we need to calculate the probability of the desired seating arrangement occurring. Let's break it down step by step:

Step 1: Calculate the total number of ways the 6 friends can be seated in a row with no restrictions.

Since there are 6 seats, the first friend can choose any of the 6 seats, the second friend can choose any of the remaining 5 seats, the third friend can choose any of the remaining 4 seats, and so on. Therefore, the total number of ways they can be seated is:

Total ways = 6 x 5 x 4 x 3 x 2 x 1 = 720

Step 2: Calculate the number of ways the four boys can be seated on the left and two girls on the right.

Since there are 4 boys, the first boy can choose any of the 4 seats on the left, the second boy can choose any of the remaining 3 seats, and so on. Similarly, the first girl can choose any of the 2 seats on the right, and the second girl can choose the remaining seat. Therefore, the total number of ways they can be seated according to the desired arrangement is:

Desired ways = 4 x 3 x 2 x 1 x 2 x 1 = 48

Step 3: Calculate the probability by dividing the desired ways by the total ways.

Probability = Desired ways / Total ways = 48 / 720 = 1 / 15

Therefore, the probability that they end up with four boys on the left and two girls on the right is 1/15.

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Answer:

Step-by-step explanation:

5y+y+3+4y+2=55

10y=55-3-2

10y=50

y=50:10

y=5

QR = y+3

5+3=8

To find two divergent series, summation from n equals 1 to infinity of a_n and summation from n equals 1 to infinity of b_n, such that their product converges, we can consider the following series:

1. Summation from n equals 1 to infinity of a_n = ∑(1/n)
2. Summation from n equals 1 to infinity of b_n = ∑n

Solution:

1. The first series, ∑(1/n), is known as the harmonic series. It is a famous example of a divergent series, meaning that its sum approaches infinity as n approaches infinity.

2. The second series, ∑n, is an arithmetic series where the terms increase linearly. This series is also divergent, as the sum increases without bound as n approaches infinity.

Now, we need to verify that the product of these series converges:

3. Summation from n equals 1 to infinity of (a_n * b_n) = ∑((1/n) * n)

4. Simplifying the expression, we get ∑(1), which is a constant series with all terms equal to 1.

5. The sum of the constant series converges, as it approaches a finite value when n approaches infinity.

In conclusion, the two divergent series summation from n equals 1 to infinity of a_n = ∑(1/n) and

summation from n equals 1 to infinity of b_n = ∑n, have a product that converges, as their product ∑((1/n) * n) simplifies to a constant series ∑(1), which has a finite sum.

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Answer:

1.6

Step-by-step explanation: