To keep in shape, Vincent exercises at a track near his home. ​ ​He requires 40 minutes to do 4 laps running and 7 laps walking. ​In contrast, he requires 18 minutes to do 2 laps running and 3 laps walking. ​ ​Assuming he maintains a consistent pace while running and while walking, how long does Vincent take to complete a lap at each pace?

Answer:

Step-by-step explanation:

B :10/(x+1)  +5

The amount that should be in Nickey's savings account immediately after her last deposit on September 30, 2012, using the future value concept, is R15,282.91.

The future value refers to the compounded value (at an interest rate) of the present value, including the periodic cash investments, over a period.

The future value can be determined using either the future value formula, future value table, or an online finance calculator, as below.

N (# of periods) = 18 months

I/Y (Interest per year) = 15%

PV (Present Value) = R1,000

PMT (Periodic Payment) = R 700

Results

FV = R15,282.91 (R12,600 + R1,000 + R1,682.91)

Sum of all periodic payments = R12,600 (R700 x 18)

Total Interest = R1,682.91

Thus, the amount that should be in Nickey's savings account immediately after her last deposit on September 30, 2012, using the future value concept, is R15,282.91.

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648 is the three-digit positive integers have three different digits

According to the statement

we have given that there are three positive digit number are formed with three distinct digits.

And we have to find that the how many words are formed with distinct numbers.

So, to solve this type of problem the Combination formula is best.

Because it provides the all possibilities that from how many ways numbers are formed.

So, from a combination formula

here we take 9 two times because first time when we let a number then remaining numbers are 9.  and second time remaining numbers are also 9 because we let the distinct number but for third number there will be a probability that choosing number will be same.

So, Three digit positive number become from 9*9*8 =648

So, 648 is the three-digit positive integers have three different digits.

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Answer:

The ladder is 98 inches tall in inches.

Step-by-step explanation:

⇒ 8 (feet)  × 12 (inches)  = 96 inches

⇒ Add the extra 2 inches

⇒ 98 inches tall.

The metallurgist would need 46.875 lb of an alloy containing 30 % copper and 3.125 lb of an alloy containing 62 % copper to produce 50 lb of a third alloy.

In this question we must prepare a third alloy by using correct quantity of two alloys with different copper concentrations. Required weights can be determined by applying concept of weighted average:

(32/100) · (50 lb) = (30/100) · x + (62/100) · (50 - x)

32 · 50 = 30 · x + 62 · (50 - x)

32 · 50 = 30 · x + 62 · 50 - 62 · x

32 · x = 30 · 50

x = 46.875

The metallurgist would need 46.875 lb of an alloy containing 30 % copper and 3.125 lb of an alloy containing 62 % copper to produce 50 lb of a third alloy.

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Answer:

C. (2;9)

Step-by-step explanation:

for more details see the attachment.

Answer:

[tex]f(x) = \frac{1}{2}x + 5[/tex]

Step-by-step explanation:

So you can generally express a linear function use the slope-intercept form as such: [tex]y=mx+b[/tex] where m=slope, and b=y-intercept.

The y-intercept is defined as the value of f(0), since when the line crosses the y-axis, the x-value is 0, and as provided in the table that value is 5, so we have the function rule: [tex]f(x) = mx+5[/tex]

The slope is defined as how much y-changes, as x increases by 1. We can generally use the formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] and this can be found using any two points, since the slope is constant.

We can use the two points (0, 5) and (2, 6) and plug it into the equation, to find the rise/run

[tex]\frac{6-5}{2-0} = \frac{1}{2}[/tex]

So plugging this into the slope-intercept form you get the function

[tex]f(x) = \frac{1}{2}x + 5[/tex]

The simple interest rate is 4.7%

The given parameters are:

Principal = $2100

Interest = $1,559.46

Time = 15.8 years

The simple interest is calculated as:

I = PRT

Make R the subject

R = I/(PT)

So, we have:

R = 1559.46/(2100 * 15.8)

Evaluate

R = 0.047

Express as percentage

R = 4.7%

Hence, the simple interest rate is 4.7%

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Answer:

The Pythagoras theorem states that if a triangle is right-angled (90 degrees), then the square of the hypotenuse is equal to the sum of the squares of the other two sides. Observe the following triangle ABC, in which we have BC2 = AB2 + AC2. Here, AB is the base, AC is the altitude (height), and BC is the hypotenuse. It is to be noted that the hypotenuse is the longest side of a right-angled triangle.

Pythagoras Theorem Equation

The Pythagoras theorem equation is expressed as, c2 = a2 + b2, where 'c' = hypotenuse of the right triangle and 'a' and 'b' are the other two legs. Hence, any triangle with one angle equal to 90 degrees produces a Pythagoras triangle and the Pythagoras equation can be applied in the triangle.

Answer:

In the binomial distribution​ for probability function, [tex]_{n}C_{x}[/tex] represents the number of ways of obtaining x successes in n trials: True

The binomial distribution is a type of probability distribution that expresses the probability that, given a certain set of characteristics or assumptions, a value would take one of two distinct values.

The underlying assumptions of the binomial distribution are that each trial has exactly one possible outcome, that each trial has the same success chance, and that each trial is either independent of or mutually exclusive with every other trial.

As opposed to a continuous distribution, like the normal distribution, the binomial distribution is a frequent discrete distribution used in statistics.

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The Equation in terms of m, m^2+7m+10=0

What is substituting in the equation ?

substituting means changing or replacing the values in the given equation.

Calculation:

Given equation is (x^2+3)^2+7x^2+21=-10

            and m= X^2 + 3.

make the given equation in the form X^2 + 3,

             now,

                     (x^2+3)^2+7x^2+21=-10

                     (x^2+3)^2+7(x^2+3)=-10

             where,

                      X^2 + 3= m

              after putting the value or replacing the values

             we get, m^2+7m=-10

                      m^2+7m+10=0

          the above equation is in the form of "m".

The Equation in terms of m, m^2+7m+10=0

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Answer:

m^2+7m+10=0

Step-by-step explanation:

Give brainly lol

The notation for the translation is (x, y) → (x + 2, y + 2)

The translations are given as:

The above implies that we add 2 to the x coordinate and 2 to the y coordinate.

So, we have:

(x, y) → (x + 2, y + 2)

Hence, the notation for the translation is (x, y) → (x + 2, y + 2)

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The term that has a degree of 8 is -2x³y⁵

The polynomial above is a monomial. A monomial is a polynomial with a single term.

Therefore, the degree of a monomial is the sum of the exponents of all its variables.

In other words, a monomial is a number, a variable or a product of a number and a variable where all exponents are whole numbers.

Hence, the term with degree of 8 is -2x³y⁵

Degree = 0 + 3 + 5 = 8

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Answer:

The answer to your question is 125

Step-by-step explanation:

x = 25 X 5= 125.

The required number is 125.

I hope this helps and have a good day!

Answer: [tex]f^{-1}(x)=\frac{x-3}{3}[/tex]

Step-by-step explanation:

Let [tex]f(y)=x[/tex]

[tex]x=3y+3\\\\x-3=3y\\\\y=\frac{x-3}{3}\\\\\therefore f^{-1}(x)=\frac{x-3}{3}[/tex]

Answer:

$4.50

Step-by-step explanation:

Okay so, first add both.

50+40 is 90, then multiply 90 by the tax percent which is

90x5%=4.5

If expression then,

x=money that they have to pay.

5%(50+40)=x    (the original)

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Answer: Option 1

Step-by-step explanation:

[tex]|x+4|=2\\\\x+4=\pm 2\\\\x=-4\pm 2\\\\x=-6, -2[/tex]

Solve Absolute Value.

| x + 4 | = 2

We know either x + 4 = 2 or x + 4 = −2

x + 4 = 2 (Possibility 1)

x + 4 - 4 = 2 - 4 (Subtract 4 from both sides)

x = -2

x + 4 = −2 (Possibility 2)

x + 4 - 4 = - 2 - 4 (Subtract 4 from both sides)

x = -6

Answer: x = - 2 or x = -6

Therefore we conclude that the solution of the exercise | x + 4 | = 2, is the first number line, since both results are negative.

Answer:

B. 2√3+4

Step-by-step explanation:

3√3+4−√3

=2√3+4 (Decimal: 7.464102)

[tex](2m+1)+(2n+1)=2m+2n+2\\\\=2(m+n+1)[/tex]

The surface area of the cone is 282.6 square centimeters.

For a cone of radius R and height H, the surface area is given by:

[tex]A = pi*R^2 + pi*R*\sqrt{R^2 + H^2}[/tex]

Where pi = 3.14

In this case, we have:

[tex]A = 3.14*(5cm)^2 + 3.14*5cm*\sqrt{(5cm)^2 + (12cm)^2} = 282.6 cm^2[/tex]

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The value of x comes out to be 6 from the algebraic equation.

Solving the Given Algebraic Equation for x:

Given algebraic equation is,

3x + 12 = 8x - 18

⇒ 12 = 8x - 3x -18

8x - 3x - 18 = 12

5x - 18 = 12

5x = 12 + 18

5x = 30

x = 30 / 5

x = 6

What is an algebraic equation?

A mathematical statement in which two expressions are put equal to one another is known as an algebraic equation. One or more variables, coefficients, and constants make up an algebraic equation in most cases. Anything on one side of the equal sign must have the exact same value on the opposite side in order for it to not be considered unequal.

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The sample size required is mathematically given as

n=1454

Generally, the equation for Margin of error is  mathematically given as

[tex]M=Z_{\alpha/2} > \frac{\sigma}{\sqrt{n}}[/tex]

Therefore

[tex]M= 0.11 \leq \frac{ 2.33*1.8}{\sqrt{n}}\\\\\sqrt{n} \leq 38.127[/tex]

n=1453.69.

In conclusion, The sample size required is mathematically given as

n=1454

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The Success rate of (PN) had 82.57% which is greater than traditional method's success rate.

According to the statement

we have given that the percutaneous nephrolithotomy (PN) had a success rate in removing kidney stones of 289 out of 350 patients. And

The traditional method was 78% effective.

we have to show that the success rate for PN is greater than the historical success rate then

we use the percentage formula to find the success rate of the new method. So,

(a) Total patients = 350

Success rate in number of patient = 289

Percentage of success rate = (289/350)*100

Then after calculating

Percentage of success rate = 82.57%

It is clear that the outcome success rate is 82.57% which is greater than traditional method.

(b) we have a 95% confidence that the success rate of new method is higher than the older method from a confidence interval of 2.262 and 3.67

So, The Success rate of (PN) had 82.57% which is greater than traditional method's success rate.

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The ages of Carl and Angela given from the expression is 25 years and 18 years respectively

5(x + 7) + 4x = 197

5x + 35 + 4x = 197

9x = 197 - 35

9x = 162

x = 162/9

x = 18

So,

Angela's age = x

= 18 years

Carl's age = x + 7

= 18 + 7

= 25 years

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The 50 mile distance traveled downstream and back that takes 2 hours and 5 hours respectively gives;

Let v represent the speed of the boat and let u represent the speed of the river current.

Distance the boat travels downstream = 50 miles

Time taken to travel downstream by the boat = 2 hours

Time taken to travel back upstream = 5 hours

[tex]velocity = \frac{distance}{time} [/tex]

Therefore;

Which gives;

[tex]v + u = \frac{50}{2} = 25...(1)[/tex]

[tex]v - u = \frac{50}{5} = 10...(2)[/tex]

Adding equation (1) to equation (2) gives;

(v + u) + (v - u) = 2•v = 25 + 10 = 35

2•v = 35

v = 35 ÷ 2 = 17.5

u = 25 - v

Which gives;

u = 25 - 17.5 = 7.5

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The additional information would you want to know about the survey before you accepted the results of the study will be:

In research of human subjects, a survey is a list of questions aimed for extracting specific data from a particular group of people.

Surveys may be conducted by phone, mail, through the internet or in malls. From the information, a recent survey points to the transformation underway in the automotive retail landscape.

It is important to know the sampling design that was used, the population from which the design was selected and the response rate.

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The solution set of the inequalities y ≤ x² – 3 and y > –x² + 2 is the darker region shown in the graph.

An equation is an expression that shows the relationship between two or more variables and numbers.

Inequality is an expression that shows the non equal comparison of two or more numbers and variables

The solution set of the inequalities y ≤ x² – 3 and y > –x² + 2 is the darker region shown in the graph.

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The graphs of f(x) and g(x) are transformed function from the function y = x^2 and the solution of the set of inequalities is (±1.581, -0.5)

The complete question is in the attached image (the first graph)

From the graph, we have:

f(x) = x^2 - 3 and g(x) = -x^2 + 2

To derive y ≤  x^2 - 3, we simply change the equality sign in the function f(x) to less than or equal to.

To derive y > -x^2 + 2, we simply change the equality sign in the function g(x) to greater than

The inequalities of the graphs become

y ≤ x^2 - 3 and y > -x^2 + 2

From the graph of the above inequalities (see attachment 2), we can see that the curves of the inequalities intersect at (±1.581, -0.5)

Hence, the solution of the set of inequalities is (±1.581, -0.5)

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Answer:

3/2y-5

Step-by-step explanation:

Answer:

35 inches

Step-by-step explanation:

7 x 5 = 35 lol

The number which represents a change in the amount of thread on the spool exists 35 inches.

In mathematics, an operation exists as a process that takes zero or more input values to a well-defined output value.

Given: Length of thread a student cuts = 5 inches

Total number of students that cut thread = 7

Length of thread a student cuts = 5 inches

Length of thread 7 student cuts = 5 [tex]*[/tex] 7 = 35 inches

The negative length that 7 students cut from the spool exists the number that represents a change in the amount of thread.

The number which represents a change in the amount of thread on the spool exists 35 inches.

Therefore, the correct is option b) 35 inches.

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