A person is riding a bike at 20 miles per hour and starts to slow down producing a constant deceleration of 5 miles per hr². (a) (3 pts) How much time elapses before the bike stops? (b) (4 pts) What is the distance traveled before the bike comes to a stop?

Answer:

I have two Sisters

Step-by-step explanation:

Answer:

The property of every variable that states that any variable that stands alone is the same as 1 x that variable

Answer:

y-intercept: (0,6)

slope = -2

equation: y = -2x + 6  

Step-by-step explanation:

1) First, identify the y-intercept. The y-intercept is the point at which the line intersects the y-axis. We can see that the line crosses the y-axis at (0,6), so that must be it.

2) Now, find the slope. Pick two points from the line. I chose (0,6) and (3,0). Then, substitute the two points' x and y values into the slope formula \(m = \frac{y_2-y_1}{x_2-x_1}\)and solve:

\(m = \frac{0-6}{3-0}\\m = \frac{-6}{3}\\m = -2\)

So, the slope is -2.

3) With the found information, use the slope-intercept formula \(y = mx + b\) to write the line's equation. Substitute values for the \(m\) and \(b\).

\(m\) represents the slope, so substitute -2 in its place. \(b\) represents the y-intercept, so substitute 6 in its place. This gives the following equation:

\(y = -2x + 6\)

The best method to estimate the size of a population of rabbits living in a large urban park is the Capture a set of rabbits, mark and release them, and then recapture a second set of rabbits, which is option C.

Later, a second sample of rabbits is captured, and the number of marked rabbits in this sample is recorded. The ratio of marked rabbits to the total number of rabbits in the second sample can be used to estimate the total population size.

The CMR method is considered one of the most accurate methods for estimating the size of a population of animals, as it accounts for the potential biases in other methods like counting individual animals within quadrants or along transects.

This method assumes that the marked and unmarked animals have an equal chance of being captured and that there is no migration or mortality between the two sampling periods.

In conclusion, the CMR method is the best option to estimate the size of a rabbit population in a large urban park as it is more accurate than other methods and accounts for potential biases in other methods. Therefore, correct option is C.

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Let the weight (in kg) of a large box be 'x' and the weight of a small box be 'y'.

Given that the weight of 2 large boxes and 3 small boxes is 78 kg,

Also given that the weight of 6 large boxes and 5 small boxes is 180 kg,

Here we will apply the Elimination Method to solve both the equations.

Consider the three times the first equation being subtracted from the second equation,

Simplify the terms,

Substitute this value in the first equation,

Thus, the larger box weighs 18.75 kg while the small box weighs 13.5 kg

The two-sample z-test statistic for evaluating the null hypothesis that the percentage of students who support capital punishment did not change from 1970 to 2005 is -4.08 (rounded to two decimal places).

To calculate the two-sample z-test statistic, we need to compare the proportions of students who support capital punishment in 1970 and 2005. The null hypothesis states that the percentage of students who support capital punishment did not change.

Let p1 be the proportion of students who support capital punishment in 1970, and p2 be the proportion in 2005. We can calculate the sample proportions as p1 = 590/1000 = 0.59 and p2 = 350/1000 = 0.35.

The formula for the two-sample z-test statistic is given by z = (p1 - p2) / sqrt((p(1 - p)(1/n1 + 1/n2))), where p is the pooled proportion and n1 and n2 are the sample sizes.

To calculate p, we compute the pooled proportion as p = (p1n1 + p2n2) / (n1 + n2) = (0.591000 + 0.351000) / (1000 + 1000) = 0.47.

Substituting the values into the formula, we have z = (0.59 - 0.35) / sqrt((0.47*(1 - 0.47)(1/1000 + 1/1000))) = -4.08.

Therefore, the two-sample z-test statistic for evaluating the null hypothesis is -4.08 (rounded to two decimal places).

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The Laplace transform of a bt + ct^2 for some constants a, b, and c can be found using the linearity property of the Laplace transform. The Laplace transform of a linear combination of functions is equal to the linear combination of their Laplace transforms. Therefore, the Laplace transform of a bt + ct^2 is equal to the Laplace transform of at + the Laplace transform of bt^2.

The Laplace transform of at is a/s, and the Laplace transform of bt^2 is 2b/s^3. Therefore, the Laplace transform of a bt + ct^2 is:

a/s + 2b/s^3

This is the direct answer to the problem.

In more detail, the Laplace transform is a mathematical tool that allows us to convert a function of time into a function of complex frequency. It is defined as the integral of the function multiplied by the exponential function e^(-st), where s is the complex frequency parameter. The Laplace transform has many applications in engineering, physics, and mathematics, particularly in the analysis of linear time-invariant systems.

In this problem, we used the linearity property of the Laplace transform to find the Laplace transform of a bt + ct^2. This property states that the Laplace transform of a linear combination of functions is equal to the linear combination of their Laplace transforms. We first found the Laplace transform of at and bt^2 separately using the Laplace transform formulas. Then, we added them together to obtain the Laplace transform of a bt + ct^2.

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The Laplace transform of a bt + ct^2 for some constants a, b, and c can be found using the linearity property of the Laplace transform. The Laplace transform of a linear combination of functions is equal to the linear combination of their Laplace transforms. Therefore, the Laplace transform of a bt + ct^2 is equal to the Laplace transform of at + the Laplace transform of bt^2.

The Laplace transform of at is a/s, and the Laplace transform of bt^2 is 2b/s^3. Therefore, the Laplace transform of a bt + ct^2 is:

a/s + 2b/s^3

This is the direct answer to the problem.

In more detail, the Laplace transform is a mathematical tool that allows us to convert a function of time into a function of complex frequency. It is defined as the integral of the function multiplied by the exponential function e^(-st), where s is the complex frequency parameter. The Laplace transform has many applications in engineering, physics, and mathematics, particularly in the analysis of linear time-invariant systems.

In this problem, we used the linearity property of the Laplace transform to find the Laplace transform of a bt + ct^2. This property states that the Laplace transform of a linear combination of functions is equal to the linear combination of their Laplace transforms. We first found the Laplace transform of at and bt^2 separately using the Laplace transform formulas. Then, we added them together to obtain the Laplace transform of a bt + ct^2.

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Answer:

The answer is A

Step-by-step explanation:

this isnt my answer it is someone named baylee in the comments, i tried it and it was right .

As per the given data, the slope-intercept form of the first equation is y = x - 5, which is represented by option A.

The slope-intercept form of a linear equation is y = mx + b, where m is the slope of the line and b is the y-intercept.

The equation that represents the first equation written in slope-intercept form is:

y = x - 5

To convert the equation 5x - 2y = 10 into slope-intercept form, we need to isolate y on one side of the equation.

Starting with 5x - 2y = 10:

Subtract 5x from both sides: -2y = -5x + 10

Divide both sides by -2: y = (5/2)x - 5

Now, we can simplify the expression (5/2)x - 5 to the form y = mx + b, where m is the slope and b is the y-intercept.

Therefore, the correct option is A.

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Answer:

The last option:  \(3 x^{^{\frac{9}{2}}}y^{^{\frac{3}{2}}}\)

Step-by-step explanation:

Main concepts:

Concept 1. Parts of a Radical

Concept 2. Radicals as exponents

Concept 3. Exponent properties

Concept 4. How to simplify a radical

Concept 1. Parts of a Radical

Radicals have a few parts:

If the index isn't shown, it is the default index of "2".  This default index for a radical represents a square root, which is why people sometimes erroneously call the radical symbol a square root even when the index is not 2.

In this situation, the radical's index is 4, and the radicand is 81 x^18 y^6.

Concept 2. Radicals as exponents

For any radical, the entire radical expression can be rewritten equivalently as the radicand raised to the power of the reciprocal of the index of the radical.  In equation form:

\(\sqrt[n]{x} =x^{^{\frac{1}{n}}}\)

So, the original expression can be rewritten as follows:

\(\sqrt[4]{81x^{18}y^{6}}\)

\((81x^{18}y^{6})^{^{\frac{1}{4}}}\)

Concept 3. Exponent properties

There are a number of properties of exponents:

Continuing with our expression, \((81x^{18}y^{6})^{^{\frac{1}{4}}}\), we can apply the "distributive" property since all of the parts are multiplied to each other...

\((81)^{^{\frac{1}{4}}}(x^{18})^{^{\frac{1}{4}}}(y^{6})^{^{\frac{1}{4}}}\)

Applying the "Bases raised to powers, raised again to another power, multiplies powers" rule for the parts with x and y...

\((81)^{^{\frac{1}{4}}}(x^{^{\frac{18}{4}}})(y^{^{\frac{6}{4}}})\)

Reducing those fractions, (both the numerators and denominators have a factor of 2)...

\((81)^{^{\frac{1}{4}}}(x^{^{\frac{9}{2}}})(y^{^{\frac{3}{2}}})\)

Rewriting the exponent of the "81" back as a radical...

\(\sqrt[4]{81} x^{^{\frac{9}{2}}}y^{^{\frac{3}{2}}}\)

Concept 4. How to simplify a radical

For any radical with index "n", the result is the number (or expression) that when multiplied together "n" times gives the radicand.

In our case, the index is 4.  So, we're looking for a number that when multiplied together four times, gives a result of 81.

One method of simplifying radicals is to completely factor the radicand into prime factors, and forms groups (each containing an "n" number of matching items).

Note that 81 factors into 9*9, which further factors into 3*3*3*3

This is a group of 4 matching items, and since the index of the radical is 4, we have found a group that can be factored out of the radical completely:

\(\sqrt[4]{81} =\sqrt[4]{(3*3*3*3)}=3\)

So, our original expression, simplifies finally to \(3 x^{^{\frac{9}{2}}}y^{^{\frac{3}{2}}}\)

This is the last option for the multiple choice.

The surface area of the triangular prism as per the area formula is as follows:

1104m².

The space that any composite shape occupies is referred to as the area of composite shapes. In order to create the desired shape, a few polygons are connected to create a composite shape. These figures or forms can be constructed using a variety of geometrical elements, including triangles, squares, quadrilaterals, and others.

To determine the area of a composite object, divide it into simple shapes like a square, triangle, rectangle, or hexagon. In essence, a composite shape is a combination of fundamental shapes. It goes by the name's "composite" or "complex" shapes.

In the triangular prism given,

We have 2 triangles and 3 rectangles.

So, to find the surface area of the prism we need to find the area of the individual shapes and add them up.

Length of 1st rectangle = 20m and breadth = 19m.

Area = l × b

= 20 × 19

= 380m².

Length of 2nd rectangle = 19m and breadth = 16m.

Area = l × b

= 19 × 16

= 304m².

Length of the 3rd rectangle = 19m and breadth = 12m.

Area = l × b

= 19 × 12

= 228m².

Now coming to the triangles,

Both the triangles are equal with base = 16m and height = 12m.

Area = 1/2 × b × h

= 1/2 × 16 × 12

= 96m².

We have two triangles so, area of 2 triangles = 2 × 96 = 192m².

Therefore, total area = 380 + 304 + 228 + 192

= 1104m².

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Answer:

5 (4x+3) (4x-3)

Step-by-step explanation:

Both terms are perfect squares, so factor using the difference of squares formula

a^2 - b^2 = (a+b)(a-b)

a will be 4x, and b will be 3

Further solve and you will have your answer

Answer: \(5(4x+3)(4x-3)\)

Step-by-step explanation: Whenever dealing with a factoring problem, always take the GCF which in this case is five. Once in simplest form with the GCF taken out, it will be easy to factor.

Work :

Start by Factoring out the 5 as it is the GCF

\(5(16x^2-9)\)

Use the \(a^2-b^2 = (a+b)(a-b)\) in order to completly factor

\(5(4x+3)(4x-3)\)

That's it!

The standard error of the average sample weight when 15 participants are randomly selected for the sample is 9.05 (rounded to two decimal places).

The standard error of the average sample weight when 15 participants are randomly selected for the sample can be calculated using the formula given below:SE = σ/√nWhere,σ = standard deviation of the populationn = sample sizeSE = standard error of the meansubstituting the given values,SE = 35/√15 = 9.05

Note:When using the given formula, it is important to note that it assumes a normal distribution of sample means. The standard error is used to estimate the true value of the mean from the sample data. The larger the sample size, the smaller the standard error. The smaller the standard error, the more precise the estimate of the true value of the mean.

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Answer:15%

Step-by-step explanation:

Answer: You have a 1/6 chance to roll a 2 when you role a dice since there is 6 sides

Step-by-step explanation:

Answer:

Step-by-step explanation:

Discussion

You haven't given us any choices. Always do that it you have them. Look for the graph that looks like the one below. It has the following characteristics

Answer:

7%

Explanation:

cost of 10 bag is rs 5000.

then cost of one bag is 500.

he sold 7 bag for rs550 each then total =550×7

= 3850

again, he sold rest 3bag at cost price =500 ×3

=1500

then ,. profit percentage; s.p- c.p/5000×100

350/5000×100

= 7%

Answer: Angle 1 is 137, Angle 2 is 43, Angle 3 is 137

Step-by-step explanation:

because angle 2 is a similar angle to 43 measurement

They are both acute

And angle 1 and three I subtracted 180-43= 137

They are both obtuse so they are the same number

hopefully i explained it well

The root of f(x) will be (A) -√7.

To find the root of f(x):

Conjugate pair: A root has two forms one positive and one negative.

Example: a + √b, a - √b

Therefore, the root of f(x) will be (A) -√7.

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The correct question is given below:

If a polynomial function f(x) has roots 3 and a square root of 7 what must also be a root of f(x)?

A. negative square root of 7

B. i square root of seven

C. –3

D. 3i

The decimals of a square root that would be rounded to an approximate value are √3 = 1.732 and √5 = 2.23

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

The decimals are equivalent to a square root.

Example:

√5 = 2.23

This can be rounded to 2.

√3 = 1.732

This can be rounded to 1.7 or 2.

Thus,

The decimals of a square root are √5 = 2.23 and √3 = 1.732.

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Answer:

5^2+12^2= c^2

25+144=c^2

169=c^2

find the square root of 169

the length is = 13 ft

Step-by-step explanation:

Answer:

13

Step-by-step explanation:

In this concept, it forms a right triangle because it is 5 feet high, the base is 12 feet horizontally, and you need to find the hypotenuse (the longest side of the triangle/the slanted side). In this case, you can use the Pythagorean Theorem, which is \(a^{2}+b^{2}=c^{2}\), where a and b are the lengths of the triangle, and c is the hypotenuse.

-We know a and b already, which are 5 and 12. So substitute a and b in the equation:  \(5^{2}+12^{2}=c^{2}\)

-Then, simplify to get:  \(25+144=c^{2}\)

-Add the 25 and 144 to then get:  \(169=c^{2}\)

-Find the square root of both sides to only get c left (the hypotenuse): \(\sqrt{169}=\sqrt{c^{2}}\)

-Then you’ll get: \(\sqrt{169}=c\), which simplifies to \(13=c\)

ANSWER: 13

Hope this helps and answers your question! :)

Answer:

C

Step-by-step explanation:

hope this helps.

Answer: Yes Sofia will have enough money

=======================================================

Explanation:

Refer to the drawing below. I've split the hexagon into two pieces. The bottom is a rectangle and the top is a trapezoid.

The area of the rectangle is 16*7 = 112 square meters.

The trapezoid has 16 as one of the parallel sides. The other side is x meters. We'll use the perimeter 54 to determine what x must be

sum of the exterior sides = perimeter

6+7+16+7+6+x = 54

42+x = 54

x = 54-42

x = 12

The top most side is 12 meters. This is the missing side of the trapezoid. The hexagon has a height of 12.66 meters, so the trapezoid's height must be 12.66-7 = 5.66 meters. Refer to the blue segment I marked in the drawing below.

area of the trapezoid = 0.5*height*(base1+base2)

area = 0.5*5.66*(16+12)

area = 79.24 square meters

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

Recap so far

The total area of the entire hexagon is therefore 112+79.24 = 191.24 square meters.

Let's convert that to square decimeters.

Recall that 1 decimeter = 10 centimeters

Multiply both sides by 10

1 decimeter = 10 centimeters

10*(1 decimeter) = 10*(10 centimeters)

10 decimeters = 100 centimeters

10 decimeters = 1 meter

Then,

\(191.24 \text{ sq m}= 191.24 \text{ sq m} * \frac{10 \text{ dm}}{1 \text{ m}} * \frac{10 \text{ dm}}{1 \text{ m}}\\\\= \frac{191.24*10*10}{1*1} \text{ sq dm}\\\\= 19124 \text{ sq dm}\\\\\)

The entire lawn is 19124 square decimeters.

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

We have one final block of calculations to determine the total price.

x = number of rolls

1 roll covers 90 square decimeters

x rolls cover 90x square decimeters

90x = 19124

x = 19124/90

x = 212.489 approximately

Round up to the nearest integer to get x = 213. It doesn't matter that 212.489 is closer to 212. We round up to clear the hurdle. It means we'll have leftover grass that isn't used (perhaps it could be handy to have some back up grass just in case mistakes are made, and some patches need to be redone).

In short, Sofia needs 213 rolls.

1 roll costs $4.50

213 rolls will cost 213*4.50 = 958.50 dollars.

This is under the $1000 threshold (with 1000-958.50 = 41.50 dollars to spare).

Sofia will have enough money to pay for all of the grass.

Answer:

9800

Step-by-step explanation:

Answer:

9800

Step-by-step explanation:

(100 x 100) - 200

Solving an equation in algebra - mathematics will BOMDAS rule. Multiplication, division, addition, and subtraction are performed before.

However, in order to simplify things, if there are any exponential or logarithmic components, solve them first before applying BOMDAS to reduce them to a single solvable term. This is required by the rules.

So the list goes as

1. Exponents

2. Roots

3. Multiplication

4. Division

5. additional

6. Subtraction

However. Using a regular or scientific calculator will generate a lot of debate. A scientific calculator will adhere to the principles, while a typical calculator will evaluate from left to right or precisely the operator used first.

Using a scientific calculator, 5+2x3=11 instead of the normal one's 5+2x3=21.

Furthermore, the preferred behavior norm for division and multiplication is different.

Thus, people's difficulty with mathematics is not unjustified. The choice of how you want to approach it is ultimately up to you.

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Answer:

7. is not congruent 8. is congruent and 9. is congruent

Step-by-step explanation:

hope this helps

A confounding variable must be associated with both the exposure and the outcome, and it should not be an intermediate step in the causal pathway between the exposure and outcome.

To determine if a variable confounds an association, follow these steps:

1. Identify the exposure, outcome, and potential confounding variable: Determine which variables are your exposure (independent variable), outcome (dependent variable), and the potential confounding variable.

2. Assess the relationship: Evaluate if the potential confounding variable is associated with both the exposure and the outcome. If it is, it could be a confounder.

3. Control for the confounding variable: Adjust your statistical analysis to account for the potential confounding variable, either by stratification or using multivariable regression techniques.

4. Compare the results: Analyze the strength and direction of the association between the exposure and outcome before and after controlling for the confounding variable. If the association changes significantly, it's likely that the variable is a confounder.

Remember that a confounding variable must be associated with both the exposure and the outcome, and it should not be an intermediate step in the causal pathway between the exposure and outcome.

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Answer:

Im pretty sure is B but it might be C.

Step-by-step explanation:

In year one and five, we see that Peer Com and CDX Groul produced the greatest return on investment.

From the graph attached, we see that it represents the year in which the greatest return on investment was made on the x-axis while the y-axis shows the value of 100 shares in dollars.

Now, in year 1, the pair that would give the greatest return on investment are; Peer Com and CDX Groul

Similarly, in year five we see that Peer Com and CDX Groul produce the greatest return on investment.

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Answer:

maybe 95?

Step-by-step explanation:

Answer:

B or A but mainly B

Step-by-step explanation: