A marketing research company desires to know the mean consumption of milk per week among people over age 30 . They believe that the milk consumption has a mean of 3.5 liters, and want to construct a 85% confidence interval with a maximum error of 0.07 liters. Assuming a standard deviation of 1.4 liters, what is the minimum number of people over age 30 they must include in their sample? Round your answer up to the next integer.

The student's argument that y=x/9 does not represent a proportional relationship between x and y is false because there is constant factor which shows the proportional relationship.

A proportional relationship exists between two variables if they are related by a constant factor, meaning that multiplying one variable by a constant results in the other variable. However, this constant can also be obtained by dividing one variable by the other, as in the case of y=x/9.

To see why, we can rearrange the equation to x=9y, which shows that x is proportional to y with a constant factor of 9. Multiplying y by 9 results in x, just as dividing x by 9 results in y. Therefore, the relationship between x and y is still proportional, regardless of whether we multiply or divide to obtain the constant factor.

In general, we can say that a relationship between two variables is proportional if it can be written in the form y=kx, where k is a constant. It does not matter whether we use multiplication or division to express this constant, as long as it is the same for all values of x and y.

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Answer:

78.8888888889 or just round to 79

Step-by-step explanation:

Your welcome. Can you please mark me brainliest please? :)

Answer:

78.8888888889

Step-by-step explanation:

The slope of the line and its meaning in terms of the real-world scenario is; C. The slope of the line is −4, which means that the swimmer will complete 4 laps every minute.

In Mathematics and Geometry, the gradient, rate of change, or slope of any straight line can be determined by using the following mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

By substituting the given data points into the formula for the slope of a line, we have the following;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (0 - 24)/(6 - 0)

Slope (m) = -24/6

Slope (m) = -4.

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The cost per ounce of the premium walnut is $0. 23

To determine the value of the cost, we need to note that proportion is simply described as the comparison of numbers such  that they are made equal to another.

From the information given, we have that;

54 ounces of premium walnuts costs $12.95

This is represented as;

54 ounces = $12. 95

Then 1 = x

cross multiply the values, we get;

x = $12.95/54

Divide the values, we get;

x = $0. 23

Hence, the value is $0. 23 per premium walnut

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The first semi-annual interest payment with a credit to in the amount of $109.556.15

Given that, a company issues $50,000 of 8%, 10-year bonds dated January 1 that pay interest semiannually on June 30 and December 31 each year.

We need to find the amount,

[tex]A = P(1+r/2)^{2t}[/tex]

[tex]A = 50,000(1+0.08/2)^{2(10)[/tex]

[tex]A = 50,000(1.04)^{20[/tex]

[tex]A = 109,556.15[/tex]

Hence, the first semi-annual interest payment with a credit to in the amount of $109.556.15

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The graph is a function: yes.

The domain of this function is: all real numbers.

The range of this function: all real numbers.

In Mathematics and Geometry, a range can be defined as the set of all real numbers that connects with the elements of a domain.

Furthermore, the horizontal extent of any graph of a function represents all domain values and they are always read and written from smaller to larger numerical values, and from the left-hand side of the graph to the right-hand side.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:

Domain = {-∞, ∞}, x|x ∈ R, or all real numbers.

Range = {-∞, ∞}, y|y ∈ R, or all real numbers.

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The value of angle 1 given the value of angle 4 as 47° will be 133°

Parallel lines are two lines on a two-dimensional plane that, no matter how far they are extended, never collide. They always keep the same gap between them.

Parallel lines have the same slope, which means they have the same angle of inclination or steepness. In other words, they rise and fall at the same pace along their length.

The value will be:

= 180° - 47°

= 133°

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The point of intersection between a Inverse Functions and its inverse occurs at (2, 2).

The point of intersection between a function and its inverse occurs when the input and output values are the same for both functions.

To find the point of intersection, we need to find the value of x where f(x) = f-1(x).

In this particular case, we can see from the graph that the point of intersection occurs at (2, 2).

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The critical value from the given data is 2.776.

Hypothesis Testing:

Step 1: State the null and alternative hypotheses.

Null Hypothesis (H0): The average number of units taken by students in PSY 190 is equal to the average number of units taken by Rio Hondo students.

Alternative Hypothesis (H1): The average number of units taken by students in PSY 190 is greater than the average number of units taken by Rio Hondo students.

Step 2: Calculate a test statistic.

To calculate a test statistic, we will use a one-sample t-test. The t-test will allow us to compare the average of the PSY 190 students to the average of all Rio Hondo students. The test statistic will be calculated as follows:

t = (x - μ) / (s/√n)

Where x is the sample mean, μ is the population mean, s is the sample standard deviation, and n is the sample size.

In this case, x = 10.6, μ = 9.1, s = 5.1, and n = 5.

Plugging these values into the equation, we get:

t = (10.6 - 9.1) / (5.1/√5) = 1.78

Step 3: Determine the critical value.

To determine the critical value, we need to determine the degrees of freedom, which is equal to n-1 = 4. We can then look up the critical value in a t-table with α = 0.05 and 4 degrees of freedom. The critical value is 2.776.

Step 4: Compare the test statistic to the critical value.

Since the test statistic (1.78) is less than the critical value (2.776), we fail to reject the null hypothesis.

Therefore, the critical value from the given data is 2.776.

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Answer:

If you called at 11:45 pm and were on the phone for 1 hour 24 minutes, the call would have ended at 1:09 am.

Answer: There are 40 questions on Ethan's test.

Step-by-step explanation: To find what 32 is 80% of, you must first convert 80% to a decimal (.8).

Next, divide 32 by .8.

[tex]32/.8 = 40[/tex]

By calculating the median of the data, the meteorologist can claim that Portland tends to receive more rainfall than Seattle.

The median of a data-set is the middle value of a data-set, the value of which 50% of the measures are less than and 50% of the measures are greater than. Hence, the median also represents the 50th percentile of a data-set.

The ordered data-sets for each city are given as follows:

The median is the middle element for each data-set, hence it is given as follows:

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A. The domains and ranges of both functions are not restricted.

For f(x) = 5/8x + 1, any real number can be plugged in for x, so the domain is (-∞, ∞). Similarly, any real number can be obtained by evaluating the function, so the range is also (-∞, ∞).

For g(x) = 2/3x^3, any real number can be plugged in for x, so the domain is (-∞, ∞). As x is cubed, the range can be negative or positive infinity, or any real number in between, so the range is also (-∞, ∞).

Therefore, both functions have unrestricted domains and ranges.

The correct answer is A.

Answer:

2,600.

Step-by-step explanation:

Rounding 2,561 to the nearest hundred means rounding it to the nearest multiple of 100.

To do this, we need to look at the digit in the tens place, which is 6. Since 6 is greater than or equal to 5, we round up the digit in the hundreds place, which is 25, by 1.

Therefore, rounding 2,561 to the nearest hundred gives us 2,600.

The change of base formula log 55 / log 3. The base we use to solve via change of base formula is Base 10. The value of x = 55.

The logarithmic expression given is

log₃ 55 = x

To solve for x using the change of base formula, we can use the formula

logₐ b = log c / log a

where a, b, and c are positive real numbers and a ≠ 1.

Using this formula, we can rewrite the given expression as

log x / log 3 = log 55 / log 3

We can simplify this expression by canceling out log 3 on both sides

log x = log 55

Now, we can use the definition of logarithms, which states that if log a b = c, then [tex]a^c[/tex] = b. Using this definition, we get

x = 55

Therefore, the solution is x = 55, rounded to the nearest hundredth of a decimal.

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Since g(x) = x² - 6x - 16, a statement which is true include the following: C. The zeros are -2 and 8, because the factors of g are (x+2) and (x-

8).

In Mathematics and Geometry, the general form of a quadratic function can be modeled and represented by using the following quadratic equation;

y = ax² + bx + c

Where:

Next, we would solve the quadratic function by using the factorization method as follows;

g(x) = x² - 6x - 16

0 = x² - 6x - 16

0 = x² - 8x + 2x - 16

0 = x(x - 8) + 2(x - 8)

(x - 8)(x + 2)

x = 8 or x = -2.

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Answer:

Step-by-step explanation:

ask ur teacher

Answer:

I believe the answer is 30%

The area of the composite figure is 13 ft².

The figure is a composite figure. The are of the composite figure is the sum of the individual areas.

The composite figure can be divided into two shapes namely rectangle and triangle.

Therefore,

area of the composite figure = area of the rectangle + area of the triangle

Hence,

area of the rectangle = 4.5 × 2

area of the rectangle = 9 ft²

area of the triangle = 1 / 2 bh

where

Therefore,

area of the triangle = 1 / 2 × 4 × 2

area of the triangle = 8 / 2

area of the triangle = 4 ft²

Therefore,

area of the composite figure = 9 + 4

area of the composite figure = 13 ft²

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Answer:16x-4-2x+8=14x+4

Step-by-step explanation:

In order to solve this question you first want to multiply everything inside the bracket by the number outside.

4(4x-1)

so 4 times 4x which is 16x and 4 times -1 which is -4 so the first bracket is

(16x-4)

then do the same for the second bracket

-2(x-4)

so -2 times x would be -2x and -2 times -4 would be 8

for the final step collect the like terms and solve

so your answer would be

16x-2x which would be 14x and -4+8 which would be 4

so in conclusion the answer is

14x+4

Answer: 1085

Step-by-step explanation:

The polynomial can be written as a product of polynomials as (3xy³ - 5x²y⁴)(3xy³ + 5x²y⁴)

option C.

To rewrite the polynomial as the product of its form, we will factor the polynomial as shown below;

9x²y⁶ − 25x⁴y⁸ = x²y⁶(9 − 25x²y²)

The function (9 − 25x²y²), can factored using difference of two squares;

(9 − 25x²y²) = 3² − (5xy)²

3² − (5xy)² = (3 - 5xy)(3 + 5xy)

The final equation as the product of its factors is calculated as;

9x²y⁶ − 25x⁴y⁸ =  x²y⁶(3 - 5xy)(3 + 5xy)

= (3xy³ - 5x²y⁴)(3xy³ + 5x²y⁴)

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0.034141137 o sobre 17/500

[tex](2x^3)^2\cdot (3x)^4\implies (2^2 x^{3\cdot 2})\cdot (3^4x^4)\implies 4x^6\cdot 81x^4 \\\\\\ (4)(81)x^{6+4}\implies 324x^{10}[/tex]

Answer:

A: 6 as a fraction of 30 = 6/30 = 1/5

B: 30 centimetres as a fraction of 2 metres = 30/200 = 3/20

C: 16 pence as a fraction of £1 = 16/100 = 4/25

To compare these fractions, we need to express them with a common denominator. The smallest common multiple of 5, 20, and 25 is 100. So we can convert each fraction to have a denominator of 100:

A: 1/5 = 20/100

B: 3/20 = 15/100

C: 4/25 = 16/100

Now we can see that the largest fraction is C: 16 pence as a fraction of £1, which is 16/100 or 16%.

Step-by-step explanation:

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Answer: the price of the item 8 years from today is approximately $1475.

Step-by-step explanation:

The given exponential function to model the future price of the item is:

P(t) = P(0) * (1.026)^t

Here, P(t) represents the price of the item t years from today, and P(0) is the current price of the item.

1. To find the current price, we need to find P(0):

P(0) = 1200 * (1.026)^0

Since any number raised to the power of 0 is 1:

P(0) = 1200 * 1

P(0) = $1200

So, the current price of the item is $1200.

2. To find the price 8 years from today, we need to find P(8):

P(8) = 1200 * (1.026)^8

Using a calculator:

P(8) ≈ 1200 * 1.229057

P(8) ≈ $1474.87

Rounded to the nearest dollar:

P(8) ≈ $1475

So, the price of the item 8 years from today is approximately $1475.

Differentiating y = x^3 ln 2x/e^x Sin x is: y' = x^2 [(3 ln 2x/e^x Sin x + 3/x) - 2 ln 2x/e^x Sin x cos x + cos x].

Differentiate y can be find using the product and chain rule.

Using the chain rule

v'(x) = [1/(2x/e^x)] * (2e^x - e^x*2x) / (2x/e^x)^2

v'(x) = [e^x(2-e^x)] / (2x)^2

Using the product rule

y' = 3x^2 ln(2x/e^x) sin(x) + x^3 [e^x(2-e^x)] / (2x)^2 sin(x) + x^3 ln(2x/e^x) cos(x)

Simplifying

y' = 3x^2 ln(2x/e^x) sin(x) + (x/2) [2-e^x] sin(x) + x^3 ln(2x/e^x) cos(x)

So,

derivative of y is:

y' = 3x^2 ln(2x/e^x) sin(x) + (x/2) [2-e^x] sin(x) + x^3 ln(2x/e^x) cos(x)

Therefore the differentiate of y is 3x^2 ln(2x/e^x) sin(x) + (x/2) [2-e^x] sin(x) + x^3 ln(2x/e^x) cos(x).

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Answer:

415.67 = (1/3)(13.4)(11.7)h

415.67 = 52.26h

h = about 7.95 feet

The volume of the small cylinder is 36π

Similar figures are two figures having the same shape. The two cylinders are similar but of different radius and height.

The height of the big cylinder is calculated as

V = πr²h

h = V/ πr²

h = 144π/π36

h = 144/36

h = 4 cm

Therefore the scale factor = 4/2

area factor =( 4/2)² = 16/4

therefore the volume of the cylinder is;

16/4 = 144π/ x

16x = 144π × 4

16x = 576

dividing both sides by 16

x = 576/16

x = 36π

therefore the volume of the small cylinder is 36π.

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