Ken can walk 6 dogs in 4 hours. How many dogs can Ken walk in 10 hours?

What you're really doing is finding the slope of the line between two points you need to calculate.  

Because a=3, you're told that one point will always be (3, f(3)).  

The second point will be (3+h, f(3+h)).

For the first point, f(3) = 7/3, so your first point is always (3, 7/3).

For h=1

The x-value of your second point is a+h, or 3+1 = 4 in this case.

f(4) = 7/4.

So the average rate of change, aka the slope of the line between (3, 7/3) and (4, 7/4), is the usual slope formula:

\(m=\dfrac{y_2-y_1}{x_2 - x_1}\)

In this h=1 situation, that becomes:

\(m=\dfrac{~7/4-7/3~}{4 - 3} = \dfrac{~-7/12~}{1} = -7/12\)

You're repeat this process for each new h-value.

A linear equation to find p, Laredo's population for any year after 1990 is 5441t + 123000.

What is a linear equation?

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

Here, we have

Given:

t = the number of years after 1990.

So, for 1990, t = 0. So the coordinate is (0, 123000).

For 2007, t = 17. So the coordinate is (17, 215500).

Slope = (215500 - 123000)/17

Slope = 5441

P = 5441t + b,

b = 123000

P = 5441t + 123000

Hence,  a linear equation to find p, Laredo's population for any year after 1990 is 5441t + 123000.

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Answer:

2

Step-by-step explanation:

The length of the protein molecule, written in scientific notation, is approximately 2.08 × 10⁻⁷ meters.

Given that a hydrogen atom has about 1.04 × 10⁻¹⁰ meters diameter, whereas a protein molecule has an overall length of 2 × 10³ times the diameter of a hydrogen atom.

We need to find the length of the protein molecule, in meters and in scientific notation.

We must multiply the diameter of a hydrogen atom by the specified factor (2 × 10³), in order to determine the length of the protein molecule in meters.

Let's compute the amount:

Length of protein molecule = Diameter of a hydrogen atom × 2 × 10³

Diameter of a hydrogen atom = 1.04 × 10⁻¹⁰ meters

Length of protein molecule = 1.04 × 10⁻¹⁰ meters × 2 × 10³

To multiply numbers in scientific notation, we add the exponents and multiply the coefficients:

Length of protein molecule = 2.08 × 10⁻⁷ meters

So, the length of the protein molecule, written in scientific notation, is approximately 2.08 × 10⁻⁷ meters.

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The length of the protein molecule, in meters and written in scientific notation, is approximately 2.08 × 10^(-7) meters.

To calculate the length of the protein molecule in meters, we'll start with the given diameter of a hydrogen atom and multiply it by the scaling factor of 2000. Let's perform the calculations:

Diameter of a hydrogen atom = 1.04 × 10^(-10) meters

Length of the protein molecule = 2000 × (Diameter of a hydrogen atom)

Multiplying the diameter by the scaling factor:

Length of the protein molecule = 2000 × (1.04 × 10^(-10))

When multiplying numbers written in scientific notation, we can multiply the coefficients and add the exponents:

Length of the protein molecule = 2000 × 1.04 × 10^(-10)

Calculating the coefficient:

2000 × 1.04 = 2080

Calculating the exponent:

10^(-10)

Putting the coefficient and exponent together:

Length of the protein molecule = 2080 × 10^(-10)

Writing it in scientific notation:

Length of the protein molecule = 2.08 × 10^(-7)

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The calculated sum of the infinite series represented as 72 - 36 + 18 - 9 +... is 48

Given that we have the following infinite series

72 - 36 + 18 - 9 +...

In the above series, we have the following parameters

Initial value, a = 72

Common ratio, r = -36/72

When the above are evaluated, we have

Initial value, a = 72

Common ratio, r = -0.5

The sum of the infinite series is then calculated as

Sum = a/(1 - r)

When values are substituted, we have

Sum = 72/(1 + 0.5)

Evaluate

Sum = 48

Hence, the sum is 48

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An examination, a candidate has to score a minimum of 24 marks in order to clear the exam. the maximum that he can score is 40 marks. The valid equivalence values of the student clears the exam is 29, 30, 31.

An examination, a candidate has to score a minimum of 24 marks in order to clear the exam. the maximum that he can score is 40 marks.

The class will be as follows:

Class i: values<24 => invalid class

Class ii: 24 to 40  => valid class

Class iii: values> 40 => invalid class

We need to identify valid equivalence values. Valid equivalence values will be there in a valid equivalence class. All the values should be in class ii.

Therefore, the answer is 29, 30, 31.

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Answer:

(5,1) (4,2) (1,3)

Step-by-step explanation:

since is going a clockwise rotation the -x(5,4,1) all will become positive

Answer:

24:
6 of 4
or

8 of 3

Step-by-step explanation:

6x4=24
8x3=24

To find out how many of the 39 practice trials would be faster than 62 seconds, we need to calculate the proportion of trials that fall within the range of more than 62 seconds.

We can use the z-score formula to standardize the values and then use the standard normal distribution table (also known as the z-table) to find the proportion.

The z-score formula is:

z = (x - μ) / σ

Where:

x = value (62 seconds)

μ = mean (61 seconds)

σ = standard deviation (1.5 seconds)

Calculating the z-score:

z = (62 - 61) / 1.5

z ≈ 0.6667

Now, we need to find the proportion of values greater than 0.6667 in the standard normal distribution table.

Looking up the z-score of 0.6667 in the table, we find the corresponding proportion is approximately 0.7461.

To find the number of trials faster than 62 seconds, we multiply the proportion by the total number of trials:

Number of trials = Proportion * Total number of trials

Number of trials = 0.7461 * 39

Number of trials ≈ 29.08

Rounding to the nearest whole number, approximately 29 of the 39 practice trials would be faster than 62 seconds.

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Answer:

D. A fee paid to a broker for making a trade

Step-by-step explanation:

Commission in stocks is simply a brokerage fee that is charged when one wants to buy or sell stocks.

It is also known as trading fee and could be charged when buying and selling other investments, like exchange traded funds.

Thus, correct answer is option D.

Answer:

d

Step-by-step explanation:

Answer:

Since f(-1) = 0 and f(-2) = 0, we can set up two equations:

(-1)³ + p(-1)² - q(-1) - 4 = 0

(-2)³ + p(-2)² - q(-2) - 4 = 0

Simplifying each equation, we get:

-1 + p - q - 4 = 0

-8 + 4p - 2q - 4 = 0

Simplifying further, we get:

p - q = 5

2p - q = 6

Solving for p and q, we can add the two equations together to eliminate q:

p - q + 2p - q = 5 + 6

3p - 2q = 11

Then, we can substitute the value of q from the first equation into this equation to solve for p:

3p - 2(q + 5) = 11

3p - 2q - 10 = 11

3p - 2q = 21

3p - 2(5 + p) = 21

p - 10 = 7

p = 17

Substituting this value of p into either equation for q, we get:

q = p - 5 = 12

Therefore, the coefficients are p = 17 and q = 12. To factor the expression, we can use synthetic division or long division. Using synthetic division, we get:

-1 | 1 17 -12 -4

|__ -1 -16 28

1 1 12

This gives us the factorization:

f(x) = (x + 1)(x² + x + 12)

To find the solutions, we can use the quadratic formula on the quadratic factor:

x = (-1 ± sqrt(1 - 4(1)(12))) / 2(1)

x = (-1 ± sqrt(1 - 48)) / 2

x = (-1 ± sqrt(-47)) / 2

x1 = (-1 + i(sqrt(47))) / 2

x2 = (-1 - i(sqrt(47))) / 2

Therefore, the solutions are x1 = (-1 + i(sqrt(47))) / 2, x2 = (-1 - i(sqrt(47))) / 2, and x3 = -1.

Step-by-step explanation:

give me thanks for more! your welcome bud!

Answer:

Step-by-step explanation:

yea

Answer:

it is correct

Step-by-step explanation:

I'm sure of it

Answer:

5

Step-by-step explanation:

3(2x+1)=7x-2

6x + 3 = 7x - 2

6x - 7x = -2 - 3

-x = -5 /(-1)

x = 5

Answer:

5

Step-by-step explanation:

3 ( 2x + 1 ) = 7x - 2

Step 1 : Remove the parentheses

6x + 3 = 7x - 2

Step 2 : Move the variable to the left-hand side and move extra number the right-hand side

6x + 3 = 7x - 2

-7x  -3   -7x  -3

6x - 7x = -2 - 3

Step 3 : Combine like terms

-x = -5

Step 4 : Change the sign to make x positive

x = 5

SOLUTION : x = 5

Hope this helps :)

Answer:

6

Step-by-step explanation:

The required quotient of 3/4 divided by 1/8 on the number line is 6.

A number line is defined as the number marked on the line calibrated into an equal number of units. For example -1, 0, 1, and so on.

As mentioned in the question, it is to be determined quotient when a fraction is 3/4 divided by the number 1/8.
When the 3/4 is simply divided by 1/8 we get,
= 3/4 / [1/8]
= 6

On a number line, the given expression shows the addition of the given fraction for the 8 times by itself as,
= 3/4 = 0.75

Now,
on a number line,
= 0.75 + 0.75 + 0.75 + 0.75 + 0.75 + 0.75 + 0.75 + 0.75
= 6

Thus, on the number line, the quotient 3/4 divided by 1/8 is 6.

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Answer:

The hypotenuse is \(8\sqrt{3}\) and the other missing side is 12

Step-by-step explanation:

We use the 60 degree angle and side length 4sqrt(3) to find the hypotenuse using,

H = Hypotenuse

Y = The other side that we need to find

cos(a) = Adjacent/H

H = Adjacent/cos(a)

\(Adjacent = 4\sqrt{3} \\a = 60\\H = 4\sqrt{3} /cos(60)\\H = 8\sqrt{3}\)

Now, finding the other side,

Using

tan(a) = Y/Adjacent

Y = (Adjacent)(tan(a)

\(adjacent = 4\sqrt{3} \\a = 60\\Y = (4\sqrt{3} )(tan(60))\\Y = 12\)

hence the hypotenuse is 8sqrt(3) and the other side is 12

Answer:

\(506 \frac{2}{3} kg\)

Step-by-step explanation:

50 2/3=

50×2+3/3

=152/3 kg

next 152/3 ×10

=1520/3

=506 2/3

The solution of the system of linear equations, is (1.167, 3.667).

Given that the system of linear equations, y = -2x+6 and y = 4x - 1, we need to find the solution for the same,

y = -2x+6............(i)

y = 4x - 1.......(ii)

Equating the equations since the LHS is same,

-2x+6 = 4x-1

6x = 7

x = 1.167

Put x = 1.16 to find the value of y,

y = 4(1.16)-1

y = 4.66-1

y = 3.667

Therefore, the solution of the system of linear equations, is (1.167, 3.667).

You can also find the solution using the graphical method,

Plot the equations in the graph, the point of the intersection of both the lines will be the solution of the system of linear equations, [attached]

Hence, the solution of the system of linear equations, is (1.167, 3.667).

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Answer:

A

Step-by-step explanation:

Just took the test

The difference between 126 1/4 and 78 7/12 is 143/3 or 47 2/3.

To find the difference between the numbers simplify means;

to subtract 78 7/12 from 126 1/4 .

126 1/4 - 78 7/12

First, convert the mixed fractions into improper fractions.

( 126 × 4 + 1 )/4 - ( 78 × 12 + 7) /12

505/4 - 943/12

Multiply first term by 3/3 which is the same as 1.

( 505/4 × 3/3 ) - 943/12

1515/12 - 943/12

( 1515 - 943) / 12

572 / 12

143/3 or 47 2/3.

Therefore, the difference is 143/3 or 47 2/3.

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Answer:

f ( - 2 ) = - 2

Step-by-step explanation:

Step 1:

f ( x ) = 3x + 4        Equation

Step 2:

f ( - 2 ) = 3 ( - 2 ) + 4     Input x value

Step 3:

f ( - 2 ) = - 6 + 4       Combine Like Terms

Answer:

f ( - 2 ) = - 2          Combine Like Terms

Hope This Helps :)

Answer:

31.82% probability that you will receive 2 apples.

Step-by-step explanation:

The fruits are removed from the bag, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x sucesses is given by the following formula:

\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}\)

In which:

x is the number of sucesses.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

\(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

In this question:

5 + 7 = 12 total fruits, which means that \(N = 12\)

7 apples, which means that \(k = 7\)

You receive 2 fruits, which means that \(n = 2\)

What is the probability, in percent, that you will receive 2 apples, assuming she removes them from the bag in random order?

This is, as a proportion, P(X = 2). So

\(P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}\)

\(P(X = 2) = h(2,12,2,7) = \frac{C_{7,2}*C_{5,0}}{C_{12,2}} = 0.3182\)

0.3182*100% = 31.82%

31.82% probability that you will receive 2 apples.

number of favourable outcome to d is 2

number of possible outcome is 3

p(D)=2/3

p(D, D) =p(D)×p(D)

p(D,D) 2/3 ×2/3

p(D,D)=4/9

probability =4/9 (D)

Answer:

The measure of angle 8 is 54 degrees

Step-by-step explanation:

We know that angles 4 and 2 are linear pairs. Linear pairs add up to 180. Write an equation. (10x+6)+(5x-6). Now solve. 15x=180. x=12. With this, we can find the value of angle 8 by using angle 4's measure because 8 and 4 are congruent because they are corresponding angles. So, plug it in. 5(12)-6=60-6= 54. Therefore, angle 8 is 54 degrees

Using error concepts for hypothesis tests, it is found that there is a Type I error.

A Type I error happens when a true null hypothesis is rejected.

A Type II error happens when a false null hypothesis is not-rejected.

In this problem, the null hypothesis is:

\(H_0: \mu = 24\)

The alternative hypothesis is:

\(H_1: \mu > 24\)

He concludes that the mean age is over 24 when it is not, that is, a true null hypothesis is rejected, hence there is a Type I error.

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Answer:

x-10x3

Step-by-step explanation:

Because there are 3 thousands... and 3 times 10 is 30 so the total -30 is the amount that it drops

Answer:

10,000 I think.

Step-by-step explanation:

10 x 1000. Put the 0 at the back. So it has 4 zero and so you put the zero at the back and what is 1 x 1 well it's 1, so it's 10,000. I think.

Answer:

21 & 11

Step-by-step explanation:

Let x = first number and y = second number. We need to find the values of x and y, so we need to set up a system of linear equations. The first equation would be x + y = 32 because x and y add up to 32. Then the second equation would be x - y = 10 to represent that the two numbers have a difference of 10. Solving by elimination, we add and get 2x = 42, so x = 21. Then substitute 21 for x in either one of the equations to get y = 11.

Answer:

sin(y)=24/25

cos(y)=7/25

tan(y)=24/7

Step-by-step explanation:

We know sinФ=Opposite/Hypotenuse, cosФ=Adjacent/Hypotenuse, and tanФ=Opposite/Adjacent. We can remember this with SOH-CAH-TOA.

We know our angle is y. The Adjacent to y is 7. The opposite to y is 24. The hypotenuse is 25.

Now, we can plug the given information into the formulas in order to get the solutions.

sin(y)=24/25

cos(y)=7/25

tan(y)=24/7

Answer:

Step-by-step explanation:

equation

area(base1 + base2)

Answer:

120

Step-by-step explanation:

an easy way of looking at it is

5x8x3