in the collection of data, list at least 3 important constants (also known as "controlled variables")?

Answer:

Step-by-step explanation:

The graph of the function y = 30x is plotted and attached.

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.

We have a watch costs $30. The equation y = 30x describes the cost [y] of [x] number of watches.

Refer to the graph of the function representing the direct variation. The graph will be a straight line with slope of 30.

Therefore, the graph of the function y = 30x is plotted and attached.

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Answer:

1

Step-by-step explanation:

Answer:

y= 1x+1

Step-by-step explanation:

Considering concepts of divisibility, the amount of numbers in the set that are divisible by 2 but not by 10 is:

(C) 19.

The data-set has (55 - 10) + 1 = 46 numbers, hence 23 are divisible by 2. 20, 30, 40 and 50 are also divisible by 10, that is, 4 numbers have to be removed, hence the amount is:

23 - 4 = 19.

Which means that option C is correct.

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The value of the identities is sin O = -2/5. Option D

From the information given, we have that;

sec O = 5/3

Then, we have;

Hypotenuse = 5

adjacent = 5

Note that in the fourth quadrant only cosecant and secant identities are positive unlike in the first quadrant were all the identities are positive, then, we have;

cos O = adjacent/hypotenuse

substitute the values, we have

cos O = -3/5

Substitute the values, we get;

For the sine identity

sin O = -2/5

Hence, the ratio is -2/5 for sine identity

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Answer:

1.13 ft

Step-by-step explanation:

use the equation then fill in the missing values. when you have your answer round to the nearest thousandths.

Answer:

Answer on a graph

Answer: 4 miles

Step-by-step explanation:

2.5x+4.7=14.7

        -4.7 -4.7

2.5x=10

2.5x=10

2.5    2.5

x=4

In other words...

Subtract 4.7 from both sides first. Then divide that answer on both sides by 2.5, and WALA!

Answer:

4 miles

Step-by-step explanation:

The value that would complete the table to make the relationship between the two quantity proportional is 4.

When two quantities are proportional, their relationship is constant for all values and as one quantity rises, the other rises as well.

A proportional relationship exists between two quantities if they can be written in the general form y = kx, where k is the proportionality constant. In other words, the ratio between these amounts never changes. In other words, no matter which pair of the two numbers you divide, you always obtain the same number k.

The value that would complete the table to make the relationship between the two quantity proportional is 4.

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The correct answer is Using numerical integration techniques:Approximation using the Trapezoidal Rule (t10) is approximately [2.763211].Approximation using the Midpoint Rule (m10) is approximately [2.079728].Approximation using Simpson's Rule (s10) is approximately [2.094395].

To approximate the values of t10, m10, and s10 for the integral 0 to 8 sin(x) dx, we can use numerical integration techniques, such as the Trapezoidal Rule, Midpoint Rule, and Simpson's Rule.

Trapezoidal Rule (t10):

The Trapezoidal Rule estimates the integral by approximating the area under the curve using trapezoids. The formula for the Trapezoidal Rule is given by:

t10 = (b - a) * [(f(a) + f(b)) / 2 + ∑(f(xi))] / n

where a and b are the limits of integration (0 and 8 in this case), f(x) is the function (sin(x) in this case), xi are the equally spaced points between a and b, and n is the number of intervals.

Using n = 10, we can calculate t10:

t10 ≈ (8 - 0) * [(sin(0) + sin(8)) / 2 + ∑(sin(xi))] / 10

Midpoint Rule (m10):

The Midpoint Rule estimates the integral by approximating the area under the curve using rectangles. The formula for the Midpoint Rule is given by:

m10 = (b - a) * ∑(f(xi + h/2)) / n

where a, b, f(x), xi, and n have the same meanings as in the TrapezoidalRule, and h is the width of each interval (h = (b - a) / n).

Using n = 10, we can calculate m10:

m10 ≈ (8 - 0) * ∑(sin(xi + (8 - 0) / (2 * 10))) / 10

Simpson's Rule (s10):

Simpson's Rule estimates the integral by approximating the area using parabolic arcs. The formula for Simpson's Rule is given by:

s10 = (b - a) * [f(a) + 4 * ∑(f(xi)) + 2 * ∑(f(x2i)) + f(b)] / (3 * n)

where a, b, f(x), xi, and n have the same meanings as in the Trapezoidal Rule, and x2i represents the points with an even index.

Using n = 10, we can calculate s10:

s10 ≈ (8 - 0) * [sin(0) + 4 * ∑(sin(xi)) + 2 * ∑(sin(x2i)) + sin(8)] / (3 * 10)

By evaluating these formulas using numerical methods and rounding the results to six decimal places, you can find the approximations t10, m10, and s10 for the given integral 0 to 8 sin(x) dx.

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Answer:

Factor −5 out of −5m−15n−20.

-5(m+3n+4)

:)

hoped this helped :)

Therefore , the solution of the given problem of arithmetic mean comes out to be a(30) = 265.

When all of the values in a set of data have the same unit of measurement, such as when all of the numbers are heights, miles, hours, etc., this technique is utilized. Take the numbers 4, 7, 9, and 10 as an illustration. The count of numerals is 4, and the sum of the numbers is 30. 30 divided by 4 equals 7.5, which is the numbers' arithmetic mean.

Here,

Given that there is a common difference between each word, this is an arithmetic sequence. In this instance, the following term is obtained by adding 9 to the phrase before it in the sequence.

Alternatively put,

=> an=a1+d(n−1)

.Arithmetic Sequence:

d=9

This is the formula of an arithmetic sequence.

=>an=a1+d(n−1)

Substitute in the values of

=> a1 =4 and

d=9

.=>an=4+9(n−1)

Simplify each term.

Tap for more steps...

an=4+9n−9

Subtract 9 from 4

an=9n−5

Thus 30th term :

=> a(30)=9(30)−5

=> a(30) = 265

Therefore , the solution of the given problem of arithmetic mean comes out to be a(30) = 265.

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Answer:

3.86

Step-by-step explanation:

To solve this problem, we can use sine of the angle 75(which as a reminder, is opposite over hypotenuse):

sin(75)=x/4

x=4*sin(75)

If you plug that into a calculator, you get approximately 3.86.

The picture below shows how to set up the triangle.

The probability that a given voicemail is between 10 and 30 seconds is approximately 15.74%.

To find the probability that a given voicemail is between 10 and 30 seconds, we need to calculate the area under the normal distribution curve between these two values.

First, let's standardize the values using the z-score formula:

z = (x - μ) / σ

where x is the value (in this case, 10 and 30), μ is the mean (40 seconds), and σ is the standard deviation (10 seconds).

For x = 10:

z = (10 - 40) / 10 = -3

For x = 30:

z = (30 - 40) / 10 = -1

Next, we can use the z-table or a calculator to find the area under the standard normal distribution curve between these z-scores.

From the z-table, the area to the left of -3 is approximately 0.0013, and the area to the left of -1 is approximately 0.1587.

To find the area between -3 and -1, we subtract the area to the left of -3 from the area to the left of -1:

0.1587 - 0.0013 = 0.1574

This represents the probability that a given voicemail is between 10 and 30 seconds.

To convert this probability to a percentage, we multiply by 100:

0.1574 * 100 = 15.74%

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Answer:

lol a 6.87$ discount 1$extra for saving the village

Answer:

6.87

Step-by-step explanation:

Answer:

$182.91

Step-by-step explanation:

136.50 times 0.14 (14%) is 19.11

136.50 times 0.2 (20%) is 27.30

13650+19.11+27.30=182.91

The formation's height is 31 meters to the closest meter.

In mathematics, height is defined as the vertical distance between an object's top and bottom. It is also referred to as 'altitude.' The term height in geometry refers to the measurement of an object along the y-axis in coordinate geometry.

Height, altitude, and elevation all refer to the vertical distance between the top and bottom of something or between a base and anything above it. Height is a standard bodily measurement that is commonly measured in feet (ft) + inches (in) in the United States and centimeters (cm) abroad. Because they are length measurements, the SI unit would be meters.

We can use the tangent function to calculate the formation's height, h.

tan ( 36°) = h/43

Here, we have to multiply both sides by 43 we get,

43tan (36°)= h

h=31m

Therefore, the height of the formation to the nearest meter is 31m.

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The correct answer is option B, which is 1/(x+4). To see why, first factor the denominator of the given expression:

x^2 - 16x + 64 = (x - 8)(x - 8) = (x - 8)^2

Now, we can rewrite the original expression as:

(x - 8)^2 / [(x - 8)(x + 4)]

Canceling the common factor (x - 8), we get:

(x - 8) / (x + 4)

This is equivalent to 1/(x+4) since (x - 8) / (x + 4) = (x + 4 - 12) / (x + 4) = 1 - 12 / (x + 4) = 1 - 3 / (x + 4/3). As x approaches infinity, 3/(x+4/3) approaches 0, so 1 - 3 / (x + 4/3) approaches 1. Thus, the expression is equivalent to 1/(x+4) for any value of x except x = -4.

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Answer:

67

Step-by-step explanation:

count by fives 12 times and then add 7

Answer:

3

Step-by-step explanation:

7+12=19

19/5=3 r4

3

I have no more to type but it says I need to type more so here is a sentence.

Answer:

5 days

Step-by-step explanation:

There are 16 quarts in 4 gallons of milk, so if they drink 3 quarts every day just divide 16 by 3 which will give you 5.3 but rounding your answer is 5 days.

I hope this helps!!

The decision rule for rejecting the null hypothesis is:

If the calculated t-value is greater than 1.708, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.

To determine the decision rule for rejecting the null hypothesis, we need to perform a hypothesis test based on the given information. Let's set up the null and alternative hypotheses:

Null Hypothesis (H0): The mean pressure of the valve is 5.8 pounds/square inch.

Alternative Hypothesis (H1): The mean pressure of the valve is greater than 5.8 pounds/square inch (the valve performs above specifications).

We'll conduct a one-sample t-test since we have the sample mean, sample standard deviation, and sample size.

Given:

Sample mean (\(x^-\)) = 6.1 pounds/square inch

Sample standard deviation (s) = 0.9

Sample size (n) = 26

Level of significance (α) = 0.05 (corresponds to a 5% significance level)

To determine the decision rule, we need to find the critical t-value or the critical region for rejection. Since the alternative hypothesis is one-tailed (the mean pressure is expected to be greater than 5.8), we'll find the critical t-value for the upper tail.

Using the t-distribution table or a t-distribution calculator with (n-1) degrees of freedom (df = 26 - 1 = 25) and the significance level α = 0.05, we find the critical t-value.

The critical t-value at a 5% significance level for the upper tail is approximately 1.708.

Therefore, the decision rule for rejecting the null hypothesis is:

If the calculated t-value is greater than 1.708, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.

In summary, the decision rule for rejecting the null hypothesis is: Reject H0 if the calculated t-value is greater than 1.708.

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Answer:

A, B, C, and F is your possible answers

The quotient of means to divide so  it could be any symbol and they could switch places when dividing.

The rule of the function g (x) will be;

⇒ g (x) = - x + 3

What is mean by Translation?

A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.

Given that;

g (x) is the indicated transformation of f (x).

The rule of f (x) is,

f (x) = - x + 5 ; horizontally translation 2 units left.

Now,

The rule of f (x) is,

f (x) = - x + 5 ; horizontally translation 2 units left.

Since, g (x) is the indicated transformation of f (x).

So, g (x) = f (x + 2)

Hence, We get;

g (x) = - (x + 2) + 5

      = - x - 2 + 5

      = - x + 3

Thus, The rule of the function g (x) will be;

⇒ g (x) = - x + 3

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The value of k in the exponential function is -3.

Taking the natural logarithm of both sides of the equation, we have:

ln [ (1 + 65/x)^(3x) ] = ln(e^k)

Using the properties of logarithms, we can simplify the left side of the equation:

3x ln(1 + 65/x) = k

Taking the limit as x approaches infinity, we have:

lim (x → ∞) 3x ln(1 + 65/x)

= lim (x → ∞) [ln(1 + 65/x) / (1/x)] × 3

Using L'Hopital's rule, we can evaluate the limit:

lim (x → ∞) [ln(1 + 65/x) / (1/x)]

= lim (x → ∞) [-65 / (x(1+65/x))]

= -65/65

= -1

Therefore, we have:

lim (x → ∞) 3x ln(1 + 65/x)

= lim (x → ∞) [ln(1 + 65/x) / (1/x)] × 3

= -3

Thus, the exponential equation simplifies to:

-3 = k

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We have the expression:

\(\displaystyle{\lim_{x\to \infty} \left(1+\dfrac{65}{x}\right)^{3x} = e^k} \\\)

As \(\displaystyle{x\to \infty} \\\), the term \(\displaystyle{\dfrac{65}{x}} \\\) approaches 0. Therefore, we can rewrite the expression as:

\(\displaystyle{\lim_{x\to \infty} \left(1+\dfrac{65}{x}\right)^{x \cdot \dfrac{3x}{65}} = e^k} \\\)

Simplifying the exponent, we get:

\(\displaystyle{\lim_{x\to \infty} \left(1+\dfrac{65}{x}\right)^{\dfrac{3x^2}{65}} = e^k} \\\)

Now, as \(\displaystyle{x\to \infty} \\\), the expression \(\displaystyle{\left(1+\dfrac{65}{x}\right)^{\dfrac{3x^2}{65}}} \\\) approaches \(\displaystyle{e^{-3}} \\\).

Therefore, we have:

\(\displaystyle{e^k = e^{-3}} \\\)

Comparing the exponents, we can conclude that:

\(\displaystyle{k = -3} \\\)

Hence, the correct value of k is indeed -3.

Answer:

perimeter-3+6+3+10+6+4=32m

area- 10×6=60m²

Money Birute deposited in a savings account = $500

Rate of simple interest per annum = 1.3%

▪︎We need to find the interest she will earn in 4 years.

We know that :

\(\tt \: \color{hotpink}simple \: interest \color{plum}= \frac{principal \times rate \times time}{100} \)

In this case :

Principal = $500

Rate = 1.3%

Time = 4 years

Which means :

The simple interest she will earn in 4 years :

\( = \tt \frac{500 \times 1.3 \times 4}{100} \)

\( = \tt \frac{2600}{100} \)

\(\color{plum} = \tt\bold{\$26}\)

Thus, the simple interest she will earn in 4 years = $26

Amount = Principal + Interest

Amount she will gain after 4 years :

\( =\tt 500 + 26\)

\(\color{plum} = \tt\bold{\$526}\)

Thus, the amount she will gain after 4 years = $526

Amount change in her account = 526 - 500 = 26

We know that :

\(\tt \: \color{hotpink}percentage \: of \: change\color{plum} = \frac{change}{original \: price} \times 100\)

Which means :

Percentage of change in her savings account :

\( =\tt \frac{26}{500} \times 100 \)

\( =\tt \frac{26 \times 100}{500} \)

\( = \tt\frac{2600}{500} \)

\(\color{plum} = \bold{\tt\bold{5.2\%}}\)

▪︎Simple interest after 4 years = $26

▪︎Money she will earn after 4 years = $526

▪︎Percentage of change in her savings account = 5.2%

The translated triangle is A'B'C', and its vertices are (-3, -1), (-3, -5), and (-1.5, -5). (option b)

To translate the triangle two units to the left, we need to subtract 2 from the x-coordinates of each vertex, while leaving the y-coordinates unchanged. This is because moving the triangle left means we're decreasing its x-values.

So, let's apply this transformation to each point.

The first point, (-1, -1), becomes (-1 - 2, -1), which simplifies to (-3, -1).

The second point, (-1, -5), becomes (-1 - 2, -5), or (-3, -5).

The third point, (0.5, -5), becomes (0.5 - 2, -5), or (-1.5, -5).

These new coordinates give us the vertices of the triangle after it has been translated two units to the left.

Now that we have the new vertices, we can label them A', B', and C' to distinguish them from the original vertices. So, the translated triangle is A'B'C', and its vertices are (-3, -1), (-3, -5), and (-1.5, -5).

This is the second option in the answer choices given.

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The number of additional gifts Jeff can buy with the remaining cost is 1.

Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,

As per the given,

Total cost = $15 + $20 = $35

Total spent = $50

Remaining = $50 - $35 = $15

Since one gift cost $10

Thus, 15/10 = 1.5 since the number of gifts will be the whole number so it will be round to bottom 1 gift.

Hence "With the money still available, Jeff can purchase 1 more present".

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Answer:

------------------------

This is a combination of 4 out of 15.

Use combination formula:

where C - number of combinations, n- total number of objects, r - number of choosing from objects

Substitute 15 for n and 4 for r to get:

Correct choice is B.