Given that R = 9 x + 8 y Find x when y = 8 and R = 4

Answer:

= 1 2

Step-by-step explanation:

Combine multiplied terms into a single fraction

Multiply by 1

Add the numbers

Subtract  7  from both sides of the equation then Simplify

The slope of the line is -4

The formula that is used for calculating the slope of a line is expressed as;

m = y₂ - y₁/x₂- x₁

Such that the parameters of the formula are expressed as;

From the information given, we have that;

Slope, m = (-4 -(4)/3 -1

expand the bracket, we get;

Slope, m = -4 - 4/2

Add the values, we have

Slope, m = -8/2

Divide the values, we get;

Slope, m = -4

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The probability that the sample proportion is between 0.2 and 0.42 can be calculated using the standard normal distribution.

To calculate the probability, we need to assume that the sample proportion follows a normal distribution. This assumption holds true when the sample size is sufficiently large and the conditions for the central limit theorem are met.

First, we need to calculate the standard error of the sample proportion. The standard error is the standard deviation of the sampling distribution of the sample proportion and is given by the formula sqrt(p(1-p)/n), where p is the estimated proportion and n is the sample size.

Next, we convert the sample proportion range into z-scores using the formula z = (x - p) / SE, where x is the given proportion and SE is the standard error. In this case, we use z-scores of 0.2 and 0.42.

Once we have the z-scores, we can use a standard normal distribution table or a statistical software to find the corresponding probabilities. The probability of the sample proportion falling between 0.2 and 0.42 is equal to the difference between the two calculated probabilities.

Alternatively, we can use the z-table to find the individual probabilities and subtract them. The z-table provides the cumulative probabilities up to a certain z-score. By subtracting the lower probability from the higher probability, we can find the desired probability.

In conclusion, the probability that the sample proportion is between 0.2 and 0.42 can be calculated using the standard normal distribution and z-scores. This probability represents the likelihood of observing a sample proportion within the specified range.

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The midpoint approximation of the area under the curve f(x) = 2x(x - 4)(x - 8) over the interval [0, 4) with 4 subintervals is 0. To approximate the area under the curve using a midpoint approximation, we divide the interval [0, 4) into four subintervals of equal width.

The width of each subinterval is (4 - 0) / 4 = 1.

Now, we need to evaluate the function at the midpoint of each subinterval and multiply it by the width of the subinterval.

The midpoints of the subintervals are: 0.5, 1.5, 2.5, and 3.5.

Evaluating the function at these midpoints, we get:

f(0.5) = 2 * 0.5 * (0.5 - 4) * (0.5 - 8) = 6

f(1.5) = 2 * 1.5 * (1.5 - 4) * (1.5 - 8) = -54

f(2.5) = 2 * 2.5 * (2.5 - 4) * (2.5 - 8) = 54

f(3.5) = 2 * 3.5 * (3.5 - 4) * (3.5 - 8) = -6

Now, we calculate the sum of these values and multiply it by the width of the subinterval:

Area ≈ (6 + (-54) + 54 + (-6)) * 1 = 0.

Therefore, the midpoint approximation of the area under the curve f(x) = 2x(x - 4)(x - 8) over the interval [0, 4) with 4 subintervals is 0.

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Answer:

754 logs

Step-by-step explanation:

If you are starting at 48 logs on the bottom row subtracting one log for each row you go up, then you should have 28 logs in the top row.

This is because 48-20=28

now you need to find the factorial of 48 starting at 28.

Factorial is like 1+2+3+4+5=15. So it is basically just adding every single whole number that are in between 2 whole numbers.

So for this equation you would need to do: 28+29+30+31+32+33+34+35+36+37+38+39+40+41+42+43+44+45+46+47+48= 754.

:) Hope that helped!

Answer:

770

Step-by-step explanation:

1st raw =a = 48

2nd raw = 47

.

.

d= -1 , n = 20

Summation S= n/2 [2a+(n-1)d]

= 20/2 [ 2×48 + (20-1)×-1]

= 770

Answer:

I don't understand that type of math sorry hopefully someone else can help you

Step-by-step explanation:

Answer:

D and E are true

Step-by-step explanation:

The degree of a polynomial is the value of the largest exponent of the variable within the polynomial, that is the term

6\(x^{4}\)

Thus the polynomial is of degree 4 → D

The leading coefficient is the coefficient of the variable with the largest exponent, that is

6\(x^{4}\)

The leading coefficient is 6 → E

The coordinates of G' after the rotation = (6, 5)

In this question we have been given a point G, located at (-5, 6) is rotated 270° counterclockwise.

We need to find the coordinates of G' after the rotation.

a point (-5, 6) is located in the second quadrant.

First 90° counterclockwise rotation gives (-6, -5)  because x & y are interchanged and in Quadrant III both coordinates will be negative.

Second 90° counterclockwise rotation yields (5,-6) because x & y are interchanged and in Quadrant IV the y coordinate will be negative.

Last 90° counterclockwise rotation yields (6, 5) because x & y are interchanged and in Quadrant I both coordinates will be positive.

Therefore, the coordinates of G' after the rotation = (6, 5)

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a) The down payment of $60,000 is 30% for a studio apartment of $200,000 purchase price

b) The  down payment of $90,000 is 45% for a studio apartment of $200,000 purchase price.

Given,

The purchase price for the studio apartment = $200,000

The down payment they paid = $60,000

a) We have to find the percentage of down payment to purchase price.

Here,

Percentage = (down payment x 100) / purchase price

= (60,000 x 100) / 200,000

= 60/2

= 30

That is,

The down payment of $60,000 is 30% for a studio apartment of $200,000 purchase price.

b) We have to find the percentage to purchase price if the down payment is $90,000

Here,

Percentage = (down payment x 100) / purchase price

= (90,000 x 100) / 200,000

= 90/2

= 45

That is,

The  down payment of $90,000 is 45% for a studio apartment of $200,000 purchase price.

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Answer:

The answer is 17

Step-by-step explanation:

Answer:

12 years, the slope is 7/2 so if you apply that then its 12 years

Step-by-step explanation:

The value of a that represents the initial amount of money that he had is given as follows:

a = $125.

To obtain the value of a, we must consider that the amount remaining is given by the subtraction of the initial amount by the amount spent, that is:

Amount remaining = Initial amount - amount spent.

The parameters for this problem are given as follows:

Hence the equation is given as follows:

a - 60 = 65.

Solving for a, the value of a is given as follows:

a = 60 + 65

a = 125.

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Answer:

Combine like terms on the left side of equation first

then solve the equation normally

Step-by-step explanation:

9514 1404 393

Answer:

  f^-1(x) = 4+∛((x-6)/5)

Step-by-step explanation:

To find the inverse function, solve ...

  x = f(y)

then write the answer in functional form.

  \(\displaystyle x=f(y)\\\\x=5(y-4)^3+6\\\\x-6=5(y-4)^3\\\\\frac{x-6}{5}=(y-4)^3\\\\\sqrt[3]{\frac{x-6}{5}}=y-4\\\\y=4+\sqrt[3]{\frac{x-6}{5}}\\\\\boxed{f^{-1}(x)=4+\sqrt[3]{\frac{x-6}{5}}}\)

__

The graph shows the function and its inverse to be reflections of each other in the line y=x, as they should be.

A. The probability that one selected subcomponent is longer than 122 cm can be found by calculating the area under the normal distribution curve to the right of 122 cm. We can use the z-score formula to standardize the value and then look up the corresponding probability in the standard normal distribution table.

z = (122 - μ) / σ = (122 - 100) / 5.6 = 3.93 (approx.)

Looking up the corresponding probability for a z-score of 3.93 in the standard normal distribution table, we find that it is approximately 0.9999. Therefore, the probability that one selected subcomponent is longer than 122 cm is approximately 0.9999 or 99.99%.

B. To find the probability that the mean length of three randomly selected subcomponents exceeds 122 cm, we need to consider the distribution of the sample mean. Since the sample size is 3 and the subcomponent lengths are normally distributed, the distribution of the sample mean will also be normal.

The mean of the sample mean will still be the same as the population mean, which is 100 cm. However, the standard deviation of the sample mean (also known as the standard error) will be the population standard deviation divided by the square root of the sample size.

Standard error = σ / √n = 5.6 / √3 ≈ 3.24 cm

Now we can calculate the z-score for a mean length of 122 cm:

z = (122 - μ) / standard error = (122 - 100) / 3.24 ≈ 6.79 (approx.)

Again, looking up the corresponding probability for a z-score of 6.79 in the standard normal distribution table, we find that it is extremely close to 1. Therefore, the probability that the mean length of three randomly selected subcomponents exceeds 122 cm is very close to 1 or 100%.

C. If we want to find the probability that all three randomly selected subcomponents have lengths exceeding 122 cm, we can use the probability from Part A and raise it to the power of the sample size since we need all three subcomponents to satisfy the condition.

Probability = (0.9999)^3 ≈ 0.9997

Therefore, the probability that if three subcomponents are randomly selected, all three of them have lengths that exceed 122 cm is approximately 0.9997 or 99.97%.

Based on the given information about the normal distribution of subcomponent lengths, we calculated the probabilities for different scenarios. We found that the probability of selecting a subcomponent longer than 122 cm is very high at 99.99%. Similarly, the probability of the mean length of three subcomponents exceeding 122 cm is also very high at 100%. Finally, the probability that all three randomly selected subcomponents have lengths exceeding 122 cm is approximately 99.97%. These probabilities provide insights into the performance of the automatic machine in terms of producing longer subcomponents.

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15 8/9 less than the product of 5 and a number b​:

Answer: D

Step-by-step explanation:

Answer:

Step-by-step explanation:

The probability of a continuous random variable taking any specific value is always zero, so the statement p(x = 15) = 0.05 is false.

Answer:

Volume of the cone given rounded to two decimal places is 1415.65in

Explanation:

Volume of a cone

\( = \pi {r}^{2} \frac{h}{3} \)

\( = (3.14)( {9.9}^{2} )( \frac{14}{3} )\)

\( = 3.14 \: \times \: 98.01 \: \times \: 4.6\)

\( = 1415.65644\)

Answer:

Width x length

Step-by-step explanation:

Find the width or how wide it is

Then find the length or how long it is

multiply those

-7 is a constant term and is considered a polynomial of degree zero, also known as a constant polynomial.

A polynomial is a mathematical expression consisting of variables, coefficients, and exponents, combined using addition, subtraction, multiplication, and non-negative integer exponents.

A constant polynomial is a polynomial of degree zero, which means that it has no variables and is simply a constant value, such as 2, -3, or 0.

According to the given information:

In algebra, a polynomial is an expression consisting of variables, coefficients, and exponents, which are combined using addition, subtraction, multiplication, and division. A constant is also considered as a polynomial, but a special kind of polynomial called a constant polynomial. A constant polynomial is a polynomial of degree zero, which means that it has no variables and has a constant value, such as -7, 3, or 0. Unlike other polynomial expressions, a constant polynomial does not involve any operations, variables, or exponents, and its value does not change regardless of the input. However, it can still be added, subtracted, or multiplied with other polynomials.

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Answer:

You need to know that the measures of angle L and angle R are congruent for SAS

Answer:

c

Step-by-step explanation:

Answer:

I'm not 100% sure, but i think it's C. :)

Step-by-step explanation:

i think

We cannot claim that the newsletter publisher's statement is incorrect. Hence, the conclusion is uncertain.

The newsletter publisher's claim is uncertain after performing a test at the 0.02 level of significance as the testing firm fails to reject the null hypothesis.

In this case, we cannot claim that the publisher's statement is incorrect without additional tests and proof. Here is an explanation of the above statement.

A hypothesis test is conducted to find out whether or not there is sufficient evidence to contradict a hypothesis. In this case, the hypothesis test's null hypothesis claims that the newsletter publisher's statement is correct.

The alternate hypothesis claims that the newsletter publisher's claim is incorrect. As a result, the null hypothesis is represented by \(H_0\):

p = 0.71 (71%) and

the alternate hypothesis is represented by \(H_a\):

p ≠ 0.71 (71%).

Where 'p' denotes the percentage of newsletter readers who own a Rolls Royce.

The test statistic for a sample proportion can be calculated by

z = (p - P) / √(P(1 - P) / n)

Where 'p' denotes the sample proportion,

P denotes the population proportion, and

n denotes the sample size.

A two-tailed test is used because the alternate hypothesis is written as \(H_a\):

p ≠ 0.71 (71%).

At a 0.02 significance level, the test statistic's critical value is ±2.58 (round off) Because the test statistic does not fall in the rejection region, we fail to reject the null hypothesis.

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The value that represents the change in Tyler's account is n -180.

An operation in mathematics is subtraction. It is used to exclude words or objects from the phrase.

Let Tyler have n, in dollars, in the account.

He withdrew $250 from his bank account.

And later in the same week, $100 was deposited in the same account by Tyler.

To buy gas, he withdrew $30 again.

So, the amount of change in the account,

= total amount - (the transaction amounts)

= n -250 + 100 - 30

= n - 280 + 100

= n -180

Therefore, n -180 is the change in his account.

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A decrease in the price of cotton can have positive effects on the affordability and availability of socks in the market, benefiting consumers by potentially offering lower prices and a wider range of choices.

If the price of cotton falls in the market for a bag of socks, it is likely to have an impact on the overall cost and availability of socks. Cotton is a common material used in the production of socks, and its price plays a significant role in determining the cost of manufacturing.

When the price of cotton falls, it reduces the cost of raw materials for sock manufacturers. As a result, manufacturers may experience lower production costs. This can lead to several outcomes:

1. Decrease in sock prices: With lower production costs, manufacturers have the option to reduce the prices of socks to attract customers. This can result in more affordable socks for consumers, making them more accessible.

2. Increase in sock supply: Lower production costs may incentivize manufacturers to increase their sock production. As a result, the supply of socks in the market could rise, leading to a greater availability of socks for consumers.

3. Potential for improved quality or additional features: Manufacturers may choose to invest the cost savings from lower cotton prices into enhancing the quality of socks or adding extra features. This can result in socks with improved durability, comfort, or design, providing more options for consumers.

It's important to note that the impact of falling cotton prices on sock prices and availability may also depend on other factors, such as production and distribution costs, market competition, and consumer demand. Additionally, the extent to which the price reduction in cotton translates into lower sock prices may vary among different brands and retailers.

Overall, a decrease in the price of cotton can have positive effects on the affordability and availability of socks in the market, benefiting consumers by potentially offering lower prices and a wider range of choices.

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Answer:

x=4.4

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

14x+9=10.1

Step 2: Subtract 9 from both sides.

14x+9−9=10.1−9

14x=1.1

Step 3: Multiply both sides by 4.

4*(14x)=(4)*(1.1)

x=4.4