The function defined by d = 50+3121-16² gives the height in feet of a cannonball t seconds after the
ball leaves the cannon.
1. What do the terms 50, 312t, and -16? tell us about the cannonball?
2. Use graphing technology to graph the function. Adjust the graphing window to the following
boundaries: 0 n

Answer:

That is a quadratic equation in which

a = 1

b = 6

c = 3

The quadratic formula is:

x = [-b +- sqr root (b^2 -4*a*c)] / 2*a

x = [-6 +- sqr root (36 -4 * 1 * 3)] / 2

x1 = [-6 + sqr root (24)] / 2

x2 = [-6 - sqr root (24)] / 2

Step-by-step explanation:

Answer:

I think

Step-by-step explanation:

#a movement of people from.....

Answer:

having more people living in and around cities than before

Step-by-step explanation:

this was correct for me

The other endpoint of the line segment with the given endpoint and midpoint is (19, 15).

To find the other endpoint of the line segment, we can use the midpoint formula. The midpoint of a line segment is the average of the coordinates of the two endpoints. We can use this information to set up the following system of equations:

x_mid = (x₁ + x₂) / 2

y_mid = (y₁ + y₂) / 2

where (x_mid, y_mid) is the midpoint and (x₁, y₁) and (x₂, y₂) are the two endpoints.

Substituting the given values, we get:

6 = (-7 + x₂) / 2

7 = (-1 + y₂) / 2

Solve for x₂ and y₂.

12 = (-7 + x₂)

x₂ = 19

14 = (-1 + y₂)

y₂ = 15

Therefore, the other endpoint is (x₂, y₂) = (19, 15).

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Answer:

The actual answer is C

Step-by-step explanation:

Answer:

(-1/3; 4)

Step-by-step explanation:

(-2, -1) , (-1, 6 ) and (2, 7).​

x=(-2-1+2)/3= -1/3

y=(-1+6+7)/3=12/3=4

=> (-1/3; 4)

Answer:

The value of 0 is 0 - If you want to round its 37.1

Step-by-step explanation:

The value of 0=0

0\(\neq\)any other # besides zero

if you are wanting to round, you can round to the tenths place and say that 37.06 rounds up to 37.1

Answer:

Answered by Oreo! :)

Step-by-step explanation:

These are the place values of the number 37.0691

3 = tens place

7 = ones place

DECIMAL

0 = tenths place

6 = hundredths place

9 = thousandths place

1 = ten-thousandths place

That is the place value.

At the top u can see that the place value for zero is the tenths place!

Hope this helps! Sorry if anything goes wrong, I’m new to brainly & I can’t wait to learn!

Since u asked for the zero so 0 would equal to zero.

James can conclude about lack of carbon-14 is  ; ( E ) Without carbon-14, James can use relative dating to estimate the age of the fossil.

Relative dating, while it will not give an exact age, can estimate the age of the fossil. James could take a look at the relative order of past events and estimate the age of the fossil that way.

It is important to know that all animals have carbon-14. Carbon 14 is in the air in carbon dioxide molecules, which animals produce through cellular respiration.

James can utilize relative dating, which can be used as a substitute to determine the age of fossils in the absence of Carbon-14, which is essential for Carbon dating, as Carbon-14 is not present in the animal fossils he is studying.

A scientific method of identifying an object's age in relation to another is called relative dating ( i.e. determining the relative order of events ).

We may thus draw the conclusion that James can determine the age of the fossil using relative dating in the absence of carbon-14.

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Complete question:

a) The regular salary per pay period for Fulton is $938.83.

b) The hourly rate of pay is $13.04.

c) The gross pay for a pay period in which Fulton worked 9 hours overtime at time and one half is $645.48.

The gross pay is the total earning for a period before deductions are subtracted.

In this situation, the gross pay results from the addition of the regular pay and the overtime pay, which is computed at one and one half.

Annual salary = $22,532

The regular workweek = 36 hours

The number of pay periods per year = 24 (12 months x 2)

The regular salary per pay period = $938.83 ($22,532 ÷ 24)

The salary per week = $469.42 ($22,532 ÷ 48)

Hourly pay rate = $13.04 ($469.42 ÷ 36)

Gross pay with 9 hours overtime = $645.48 ($13.04 x 36 + $19.56 x 9)

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The probability represents the combination consists only of even numbers as per given condition is equal to 0.020.

Total numbers in combination lock = 38

Numbers from 0 to 37.

To find the probability that the combination consists only of even numbers,

Determine the total number of combinations that can be formed using only even numbers

And divide it by the total number of possible combinations.

Total number of even numbers in the lock

= 19 (since there are 19 even numbers from 0 to 37)

Calculate the total number of combinations using only even numbers,

Use the concept of combinations (nCr).

Since there are 19 even numbers to choose from,

Choose 4 numbers without repetition, the number of combinations is,

Number of combinations

= ¹⁹C₄

= 19! / (4!(19-4)!)

= (19 × 18 × 17 × 16) / (4 × 3 × 2 × 1)

= 3876

Now, calculate the total number of possible combinations without any restrictions.

Since we have 38 numbers to choose from,

and  choose 4 numbers without repetition, the number of combinations is,

Number of total combinations

= ³⁸C₄

= 38! / (4!(38-4)!)

= (38 × 37 × 36 × 35) / (4 × 3 × 2 × 1)

= 194,580

Finally, find the probability by dividing the number of combinations using only even numbers by the total number of combinations,

Probability

= Number of combinations using only even numbers / Total number of combinations

= 3876 / 194580

≈ 0.0199

≈ 0.020 Rounded to three decimal places.

Therefore, the probability that the combination consists only of even numbers is approximately 0.020.

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Answer:

X = -5/2

Step-by-step explanation:

Step-by-step explanation:

\(9x + 4 = 5x - 6\)

Collect like terms and simplify

\(9x - 5x = - 6 - 4 \\ 4x = - 10\)

Divide both sides of the equation by 4

\( \frac{4x}{4} = \frac{ - 10}{4} \)

Simplify

\(x = - \frac{5}{2} \)

The price of the 5th item is $1.64 in his bag.

We have the following information from the question is:

The mean cost for each item in his bag was $3. 24.

He bought a total of 5 items, and the prices of 4 of those items are listed below:

$4. 55, $2. 53, $2. 82, $4. 66

We have to find the price of the 5th item in his bag

Now, According to the question:

Let x be the 5th item of the bag.

Let's calculate the mean value :

Mean value is state that all values added together and divided by the number of values.

=> \(\frac{4.55+2.53+2.82+4.66+x}{5}=3.24\)

Multiply both sides by 5, we get

\({4.55+2.53+2.82+4.66+x}=16.2\)

Calculate the addition :

14.56 + x = 16.2

x = 1.64

Hence, The price of the 5th item is $1.64  

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On a scale drawing of a basketball court, 1 inch equals 8 feet the actual area of the basketball court if the scale drawing is 11. 75 inches by 6. 25 inches will be 4,700 square feet.

Given:

To solve the given question we will assume the court is rectangular in shape so we will solve by using formula of Area of rectangle

\(\rm Area \;of\;rectangle\;= l\times b\)

Where, l=length

            b=breadth

According to the given question,

    \(\rm Area = 94\; feet \times 50\; feet\\\\ = 4,700 \;square\; feet.\\\)

Therefore, Area of the basketball court will be 4,700 square feet.

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Event 9 ("The sum is odd") and Event 10 ("The difference is 1") are not mutually exclusive,

while Event 11 ("The sum is a multiple of x") depends on the specific value of x for its mutual exclusivity to be determined.

9. The events "The sum is odd" and "The sum is less than 5" are not mutually exclusive because there are values of the sum (e.g., 3) that satisfy both conditions simultaneously.

10. The events "The difference is 1" and "The sum is even" are mutually exclusive. The difference between two numbers can only be 1 if their sum is odd, and vice versa. Therefore, the events cannot occur simultaneously.

11. The event "The sum is a multiple of x" depends on the specific value of x. Without knowing the value of x, it cannot be determined whether it is mutually exclusive with other events. For example, if x is 2, then the event "The sum is a multiple of 2" would be mutually exclusive with "The sum is odd" but not with "The sum is less than 5."

Therefore, event 9 is not mutually exclusive, event 10 is mutually exclusive, and the mutual exclusivity of event 11 depends on the specific value of x.

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Complete Question:

Two fair number cubes are rolled. State whether the following events are mutually exclusive. Explain your reasoning. The numbers are equal

9. The sum is odd. The sum is less than 5. ________

10. The difference is 1. The sum is even. ________

11. The sum is a multiple of _______

Answer:

yes

Step-by-step explanation:

Because it is the answr

Answer:

{0.5(7+15),0.5(-3-8)}

Step-by-step explanation:

(0.5(sum of x values),0.5(sum of y values))

As x approaches positive infinity, m(x) approaches positive infinity.

As x approaches negative infinity, m(x) approaches negative infinity.

An expression, rule, or law in mathematics that establishes a connection between one variable (the independent variable) and another variable (the dependent variable).

A graph is considered to be a function if any vertical line formed can cross it at most one point. The graph is not a function if it contains any locations where a vertical line can pass through it twice or more.

If a function produces the same outcome regardless of how the input is represented without changing its value, it is said to be well defined.

A function is a rule that is applied to a number, known as an input, in order to produce a result, known as an output.

when \($x^n$\) ( n is odd number and n > 0), a > 0 and c is any constant,

\($$x \rightarrow \infty, a x^n+c \rightarrow+\infty\)

\($x \rightarrow-\infty, a x^n+c \rightarrow-\infty$\)

The complete question is;

The function f(x) = x^3 has been transformed, resulting in function m.

m(x) = 1\3x^3 + 6

As x approaches positive infinity, m(x) approaches___

As x approaches negative infinity, m(x) approaches___

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Answer:

a

Step-by-step explanation:

Use \(\sec\theta = \dfrac{1}{\cos{\theta}}\)  to get

    \(\sec\theta -\cos{\theta}= \dfrac{1}{\cos{\theta}}-\cos(\theta})\)

Then find a common denominator:

    \(\dfrac{1}{\cos{\theta}}-\cos(\theta}) = \dfrac{1}{\cos{\theta}}-\dfrac{\cos^2\theta}{\cos\theta}\)

But now make that one fraction:

    \(\dfrac{1}{\cos{\theta}}-\dfrac{\cos^2\theta}{\cos\theta} = \dfrac{1 - \cos^2\theta}{\cos{\theta}}\)

But that's just sin^2 on the top

    \(\dfrac{1 - \cos^2\theta}{\cos{\theta}} = \dfrac{sin^2\theta}{\cos{\theta}} = \dfrac{sin\theta\cdot sin\theta}{\cos{\theta}}\)

Split that fraction up:

    \(=\dfrac{ sin\theta}{\cos{\theta}}\cdot sin\theta\)

And tan = sin/cos

    \(=\tan\theta\cdot sin\theta\)

The given integral is ∫(0 / x² √(2² + 490)) dx. To solve this integral, we can make a substitution by letting x = 7tan(θ), where θ is between -π/8 and π/8. Then, dx = 2sec²(θ) dθ. The given integral is ∫(0 / x² √(2² + 490)) dx, and after making the substitution x = 7tan(θ), the integral becomes ∫(0 / 98sec³(θ) √(1 + 122.5tan²(θ))) dθ.

Substituting these expressions in the integral, we have ∫(0 / (7tan(θ))² √(2² + 490))(2sec²(θ)) dθ. Simplifying further, we get ∫(0 / 49tan²(θ) √(4 + 490))(2sec²(θ)) dθ. Rearranging the expression under the square root, we have ∫(0 / 49sec²(θ) √(4(1 + 122.5tan²(θ))))(2sec²(θ)) dθ. This can be simplified to ∫(0 / 98sec³(θ) √(1 + 122.5tan²(θ))) dθ.

In summary, the given integral is ∫(0 / x² √(2² + 490)) dx, and after making the substitution x = 7tan(θ), the integral becomes ∫(0 / 98sec³(θ) √(1 + 122.5tan²(θ))) dθ.

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The given integral is ∫(0 / x² √(2² + 490)) dx. To solve this integral, we can make a substitution by letting x = 7tan(θ), where θ is between -π/8 and π/8. Then, dx = 2sec²(θ) dθ. The given integral is ∫(0 / x² √(2² + 490)) dx, and after making the substitution x = 7tan(θ), the integral becomes ∫(0 / 98sec³(θ) √(1 + 122.5tan²(θ))) dθ.

Substituting these expressions in the integral, we have ∫(0 / (7tan(θ))² √(2² + 490))(2sec²(θ)) dθ. Simplifying further, we get ∫(0 / 49tan²(θ) √(4 + 490))(2sec²(θ)) dθ. Rearranging the expression under the square root, we have ∫(0 / 49sec²(θ) √(4(1 + 122.5tan²(θ))))(2sec²(θ)) dθ. This can be simplified to ∫(0 / 98sec³(θ) √(1 + 122.5tan²(θ))) dθ.

In summary, the given integral is ∫(0 / x² √(2² + 490)) dx, and after making the substitution x = 7tan(θ), the integral becomes ∫(0 / 98sec³(θ) √(1 + 122.5tan²(θ))) dθ.

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Answer:

7898955

Step-by-step explanation:

W212W

Answer:

58

Step-by-step explanation:

━━━━━━━☆☆━━━━━━━

▹ Answer

118784

▹ Step-by-Step Explanation

(26 + 3) * (8⁴)

We are going to follow PEMDAS: Parentheses, Exponents, Division, Addition, Subtraction

First, we will start with parentheses that includes exponents:

(8⁴) = 4,096 (8 * 8 * 8 * 8)

Then, we will work on the other parentheses which involves addition:

(26 + 3) = 29

Therefore,

29 * 4,096 = 118784

Hope this helps!

CloutAnswers ❁

━━━━━━━☆☆━━━━━━━

Answer:

1500 cm^3

Step-by-step explanation:

Volume formula is Length times Width times Height.

50 is the length, 30 is the width and 90 is thr height so we get

\(135000\)

cm^3

length = 50 cm

breadth = 30 cm

height = 90 cm

We will use the formula volume of cuboid = l × b × h

volume of cuboid = l × b × h

V = 50 cm × 30 cm × 90 cm

V = 1500 cm² × 90 cm

V = 135000 cm³

ANSWER =

volume of cuboid is 135000 cm³

Answer:

Step 1: The test statistic is 56.56.

Step 2: Using a chi-square distribution table with 30 degrees of freedom (n - 1), we find that the p-value is less than 0.0001.

Step 3: The rejection region for a left-tailed test with 30 degrees of freedom at the 10% level of significance is any test statistic less than 18.307.

Step 4: The test statistic of 56.56 is greater than the critical value of 18.307.

Step 5:  The 90% confidence interval for the variance of force on the helmets is [1615.46, 4123.82]

In statistics, variance is a measure of the spread or dispersion of a set of data points. It is calculated as the average of the squared differences from the mean.

Step 1: To test whether the standard deviation is significantly less than 40, we can use a chi-square test with the null hypothesis H0: \(σ^{2}\) ≥ 1600 lbs² and the alternative hypothesis H1: σ² < 1600 lb\(s^{2}\). The test statistic is:

chi-square = (n - 1) *\(s^{2}\) / \(σ^{2}\)

where n is the sample size, \(s^{2}\) is the sample variance, and \(σ^{2}\) is the population variance under the null hypothesis.

Substituting the given values, we have:

chi-square = (31 - 1) * 2350 / 1600 = 56.56

Rounding to two decimal places, the test statistic is 56.56.

Step 2: To determine the p-value for a left-tailed test, we need to find the area under the chi-square distribution to the left of the test statistic. Using a chi-square distribution table with 30 degrees of freedom (n - 1), we find that the p-value is less than 0.0001.

Step 3: The rejection region for a left-tailed test with 30 degrees of freedom at the 10% level of significance is any test statistic less than 18.307.

Step 4: Since the test statistic of 56.56 is greater than the critical value of 18.307, we reject the null hypothesis and conclude that there is sufficient evidence to indicate that the standard deviation is significantly less than 40 at the 5% level of significance.

Step 5: To calculate a 90% confidence interval for the variance of force on the helmets, we can use the formula:

[(n - 1) * \(s^{2}\)/ chi-square upper, (n - 1) * \(s^{2}\) / chi-square lower]

where chi-square upper and chi-square lower are the upper and lower critical values, respectively, from the chi-square distribution table for 30 degrees of freedom at the 5% level of significance. Substituting the given values, we have:

chi-square upper = 45.722

chi-square lower = 18.307

[(31 - 1) * 2350 / 45.722, (31 - 1) * 2350 / 18.307] = [1615.46, 4123.82]

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As asked by the question, the value of K for a given equation of a line is equal to the slope of the line.

A line has length but no breadth, making it a one-dimensional figure. A line is made up of a collection of points that may be stretched indefinitely in opposing directions. Two points in a two-dimensional plane determine it.

A line's steepness may be determined by looking at its slope. Slope is computed mathematically as "rise over run" (change in y divided by change in x).

The value of K for a given line is equal to the slope of the line. Since lines are generally expressed in the form of y = mx +b , where m is the slope of the line and b is the y-intercept of the line. Here , the value of K will be equal to the slope m of the line.

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In a 4x3x2x2 factorial experiment, you have 4 independent variables and potentially 4 main effect hypotheses.

The 4 independent variables are represented by the four numbers in the experimental design

(i.e., 4 levels of variable A, 3 levels of variable B, 2 levels of variable C, and 2 levels of variable D).

The potentially 4 main effect hypotheses are one for each independent variable, which states that there is a significant effect of that independent variable on the outcome variable.

A factorial experiment includes multiple factors simultaneously, each consisting of two or more

levels. Many factors simultaneously influence what is studied in a factorial experiment, and

experimenters consider the main effects and interactions between factors.

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Answer:

m=4 is the correct answer

Answer:

73.5 feet

Step-by-step explanation:

The length of a tree =42 feet

Mr. Ash estimates that this tree is 75% as tall now as it will be when fully grown.

We need to find the length of the tree when it is fully grown. It means we need to find the 75% of 42 and adding 42 to it as follows :

\(T=75\%\times 42+42\\\\=\dfrac{75}{100}\times 42+42\\\\=73.5\ ft\)

So, the tree will be 73.5 feet tall when it is fully grown.

Answer:

-19 > k

Step-by-step explanation:

-4 > k + 15

Subtract 15 from each side.

-4-15 > k + 15-15

-19 > k

Any value less than -19 would make this statement true

Answer:

- 19 > k

Step-by-step explanation:

- 4 > k + 15

Subtract 15 from both sides.

- 4 - 15 > k

- 19 > k

The measurement scale that provides information regarding greater than or less than, but not how much greater than or less than, is known as the ordinal scale of measurement.

In the ordinal scale, the data is ranked or ordered based on a certain characteristic or attribute, but the difference between the values or ranks is not measured or quantified. This means that the scale does not have a fixed unit of measurement, and the intervals between the values are not necessarily equal.

For example, in a survey where people are asked to rank their favorite colors, the data can be ordered from most favorite to least favorite, but we cannot infer how much more someone likes their first choice than their second choice.

The ordinal scale is used in various fields such as education, psychology, and marketing, where the data is naturally ordered but does not have a meaningful numerical value. It is often used in surveys or questionnaires where the respondents can indicate their preferences or opinions, but the differences between the options cannot be precisely measured.

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