In a 5000 m race on a 400 m track, each athlete must run 12 ½ laps. kara runs the race at a constant pace and finishes in 17.5 min, while hannah runs at a faster pace and finishes 15.3 min. in fact, hannah ran fast enough that she passed kara during the race. how many laps had hannah run when she caught and passed kara?

The answer is [tex]z &=-0.14\left[\ln \left(1-24.5 t^2\right)\right]\end{aligned}$$[/tex]

What do you understand by differential equation?

An ordinary derivative or a partial derivative can both be found in a differential equation. The differential equation describes the relationship between the variable that is constantly varying with respect to the change in another quantity, and the derivative represents a rate of change.

Equations with General Differential. Consider the differential equation y′=3x2, which has a derivative and is an illustration of a differential equation. The variables x and y are related because y is an unidentified function of x. The derivative of y is also on the equation's left-hand side.

Given equation:

[tex]$$\begin{aligned}&e^{-7 z} d z=7 t d t \\&:(-1 / 7) e^{-7 z}=3.5 t^2+C\end{aligned}$$[/tex]

[tex]$C=-1 / 7$[/tex]

[tex]$$(-1 / 7) e^{-7 z}=3.5 t^2-1 / 7$$[/tex]

[tex]$$e^{-7 z}=1-24.5 t^2$$[/tex]

[tex]$$\begin{aligned}-7 z &=\ln \left(1-24.5 t^2\right) \\z &=-0.14\left[\ln \left(1-24.5 t^2\right)\right]\end{aligned}$$[/tex]

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Answer:

[-3,∞)

Step-by-step explanation:

Since x is on the left side and is greater than -3, we will use a bracket in front of the -3. Since we do not know when the interval ends, we finish it with a positive infinity because we know that x is GREATER than (or equal) to -3. If it were less than -3, it would be negative infinity. Similarly, we use a rounded bracket because infinity is a positive value greater than -3.

If Ximena pays a flat cost of $44.50 per month and $4 per gigabyte and she wants to keep her bill at $50.10 per month, then she can use 1.4 gigabyte of data while staying within her budget.

Given,

The flat cost of cell phone plan = $44.50 per month

Cost per gigabyte =$4

She wants to keep her bill amount = $50.10

Consider the number of gigabyte used as x

Then the linear inequality will become

44.50+4x≤50.10

4x≤50.10-44.50

4x≤5.6

x≤1.4

Hence, If Ximena pays a flat cost of $44.50 per month and $4 per gigabyte and she wants to keep her bill at $50.10 per month, then she can use 1.4 gigabyte of data while staying within her budget

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The rounded value of 5,672,874,627 is 5,673,000,000

What is a rounded value?

When a number is rounded, its value is kept relatively constant while being made easier. The outcome is simpler to use but less precise. Since 73 is closer to 70 than to 80, it is 70 when rounded to the nearest ten. But 76 increases to 80.

5,672,874,627

2 is in the million column

5,672,874,627

The nearest million could be 5,672,000,000 or 5,673,000,000.

To round to the nearest million, look at the digit in the column to the right, the hundred thousands.

5,672,874,627

The number in the hundred thousands column is 8.

The rule is, if the number is 5 or more, round up

5,673,000,000

Therefore, the rounded value of 5,672,874,627 is 5,673,000,000

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Jarome can make 6 whole pizzas with the leftover cheese.

Given that Jarome uses 2 1/2 cups of cheese for every 2 3/4 pizzas. He has 6 1/4 cups of cheese left in the bag.

We need to determine the number of pizza pies can he make with the leftover cheese.

To find out how many pizza pies Jarome can make with the leftover cheese, we need to determine how many sets of 2 3/4 pizzas can be made using 6 1/4 cups of cheese.

Let's start by finding the number of sets of 2 3/4 pizzas that can be made from 6 1/4 cups of cheese:

Number of sets = Total cheese available / Cheese per set

Number of sets = 6 1/4 cups / 2 1/2 cups per set

To make the calculation easier, let's convert all the mixed numbers to improper fractions:

6 1/4 cups = (4 x 6 + 1) / 4 = 25/4 cups

2 1/2 cups = (2 x 2 + 1) / 2 = 5/2 cups

Number of sets = (25/4) / (5/2)

Now, to divide fractions, we invert the divisor (5/2) and multiply:

Number of sets = (25/4) x (2/5)

= (25 x 2) / (4 x 5)

= 50/20

= 5/2

So, Jarome can make 5/2 sets of 2 3/4 pizzas with 6 1/4 cups of cheese.

Now, let's see how many pizzas he can make with the leftover cheese:

To calculate the number of pizzas in 5/2 sets, we multiply it by the number of pizzas per set (2 3/4 pizzas):

Number of pizzas = (5/2) x (2 3/4)

Again, let's convert all the mixed numbers to improper fractions:

2 3/4 pizzas = (4 x 2 + 3) / 4 = 11/4 pizzas

Number of pizzas = (5/2) x (11/4)

Now, when multiplying fractions, we simply multiply the numerators together and the denominators together:

Number of pizzas = (5 x 11) / (2 x 4) = 55/8

So, Jarome can make 55/8 pizzas with the leftover 6 1/4 cups of cheese.

Now, let's simplify the fraction:

55/8 = 6 7/8

Therefore, Jarome can make 6 7/8 pizzas with the leftover 6 1/4 cups of cheese.

Since we can't make a fraction of a pizza, he can make 6 whole pizzas with some cheese left over.

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Answer:

Kristen can ride the bike for 20 hours

Step-by-step explanation:

20 - 15 = 5

The rate is 0.25 an hour.

0.25 x 4 = 1 - Currently $4

0.25 x 4 = 1 - Currently $3

0.25 x 4 = 1 - Currently $2

0.25 x 4 = 1 - Currently $1

0.25 x 4 = 1 - No more

Add up all the 4's

She can ride the bike for 20 hours.

Answer:

8/11

Step-by-step explanation:

[tex]2\frac{2}{3} = \frac{8}{3}\\3\frac{2}{3} = \frac{11}{3} \\= \frac{8}{3} \div \frac{11}{3}\\=\frac{8\times 3}{3 \times 11} = \frac{24}{33}\\\\LCM: 3\\\\\frac{24 \div 3}{33 \div 3}\\= \frac{8}{11}[/tex]

In roughly 127 hours the prices of the two stocks will be the same.

So, if we count the hours (x) after 9 a.m., the stock prices will be:

The value of x when A = B can be calculated using:

A = B

Therefore, in 127 hours roughly the prices of the two stocks will be the same.

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Option D is the correct answer (We are 95% confident that the proportion of coworkers who went on a vacation last year away from home for at least a week is between 50% and 66%)

Since the confidence interval is calculated for population proportion (parameter) based on sample data.

Because the figure is based on a sample of the population you are investigating; there is always uncertainty when you generate an estimate in statistics, whether it be a summary statistic or a test statistic. The confidence interval is the range of values. If you repeated your experiment or resampled the population in the same manner, you would anticipate your estimate to fall within a specific proportion of the time. The alpha value determines the confidence level, the proportion of times you anticipate being able to recreate an estimate between the top and lower boundaries of the confidence interval.

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The total number of people who can go to the amusement park in the given scenario is 6. This problem is based on the basic mathematical formulae.

Formulae are mathematical statements comprising expressions, numbers, and variables to ease complex calculations.

Given that

The total amount for the expenditure = [tex]\[/tex]327.75.

Cost of parking per person = [tex]\[/tex]13.75,

Cost of tickets per person = [tex]\[/tex]39.25.

Total cost per person = Cost of parking per person + Cost of tickets per person

Total cost per person = [tex]\[/tex]13.75 + [tex]\[/tex]39.25

                                    = [tex]\[/tex]53

So,

Number of persons = [tex]\frac{The total amount for the expenditure}{Total cost per person }[/tex]

                                 = [tex]\frac{327.75}{53}[/tex] = 6.18.

So, 6 people can go to the amusement park.

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The following can be used to rewrite the provided expression:            6(24) = 6(20 + 4).

The distributive Property states in that it is necessary to multiply every one of the two numbers by the factor before performing the addition operation when a factor is multiplied by that of the sum or addition of two terms. The distributive law, which states that in elementary algebra, equality is always true, is generalized by the distributive principle of binary operations.

The following generic form can be used to specify the distribution property:

a(b+c) = ab + bc

the following expression:

6(24)

We can observe the following by contrasting this to the general form:

a = 6

b + c = 24

Consequently, we must identify two integers from the options whose sum is 24.

These numbers, out of the options provided, are 20 and 4.

The following can be used to rewrite the provided expression:            6(24) = 6(20 + 4).

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Answer:-9

Step-by-step explanation:

Answer:

6425

Step-by-step explanation:

12.85x500=6425

The total amount John has to pay in repaying the loan and interest is $18,600

What makes up the total amount John has to pay?

The total amount that John has to pay comprises of the loan principal of $15,000 and the interest on the loan which is computed at the  simple interest rate of 6% for the loan duration of 4 years

I=PRT

I=interest for 4 years=unknown

P=loan principal=$15,000

R=interest rate=6%

T=number of years of loan=4

I=$15,000*6%*4

I=$3,600

A=P+I

A=$15,000+$3,600

A=$18,600

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Answer:

x = -2

Step-by-step explanation:

2(4 - 3x) = 20

8 - 6x = 20

-8          -8

-6x = 12

÷-6    -6

x = -2

I hope this helps!

Answer:1311

Step-by-step explanation:

2 digit long multiplication.
__________________________________________
Long multiplication can seem very intimidating, especially if you're multiplying two numbers that are pretty large. If you take it step by step, though, you'll be able to do long multiplication in no time.

First, muiltiply the 3 by 5 and 7, and muiltiply the 2 by 5 and 7 as well.

[tex]\frac{\begin{matrix}\:\:&\:\:&5&7\\ \:\:&\times \:&2&3\end{matrix}}{\begin{matrix}0&1&7&1\\ 1&1&4&0\end{matrix}}[/tex]

(NOTE: Remember when you muiltiply two digit numbers, when you pass from the first digit to the other on the bottom side, you ALWAYS add a zero to the beginning of the result BEFORE multiplying the following digit)

Secondly, once you've multiplied, you add both results of the multiplication.

[tex]\frac{\begin{matrix}\:\:&\textbf{\:\:}&1&\:\:&\:\:\\ \:\:&\textbf{0}&1&7&1\\ +&\textbf{1}&1&4&0\end{matrix}}{\begin{matrix}\:\:&\textbf{1}&3&1&1\end{matrix}}[/tex]

[tex]=1311[/tex] <- This is your final answer.
___________________________________________
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The drawing that creates a line of reflection that takes the point A to point B is; D: Draw a line parallel to line AB.

A line of reflection is a line that lies in a position between two identical mirror images so that any point on one image is the same distance from the line as the same point on the other flipped image.

Let us look at the given options;

A) Draw the perpendicular bisector of segment AB; A perpendicular bisector will NOT create a line of reflection that takes point A to point B but rather it will divide the line AB in two equal parts

B) Draw a line through B perpendicular to segment AB; A line through B perpendicular to segment AB will NOT Create a line of reflection that takes point A to point B

C) Draw the line passing through A and B;

A line passing through A and B will NOT create a line of reflection that takes point A to point B but rather will create Line A and B again and not its reflection

D) Draw a line parallel to line AB;

A line parallel to line AB will create a line of reflection that takes point A to point B because a parallel line never meet thereby creating the direct imagery of Line AB.

Thus, the drawing that create a line of reflection that takes the point A to point B is; D: Draw a line parallel to line AB.

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The total time taken by machine A and B working together to produce x amount of peanut butter is 7.2 minutes.

What is the concept of time and work?

Time and work defines the way how the particular work is done in the given time. It gives an exact relationship between the work and the number of days required to complete it.

Calculation of the total time taken by the machines A and B working together

Given that Machine A completes the entire job in 12 minutes.

So, machine A completes 1/12 of the job in one minute.

Machine B takes 18 minutes to complete the entire job.

So, machine B completes 1/18 of the job in one minute

When we combine their work, they will complete (1 / 12 + 1 / 18) job in one minute i.e.  (3 + 2) / 36 = 5/36 job in one minute     —---- 1

To find the time taketaken by them to produce x amount of peanut butter, we will reciprocate the result obtained in equation 1

i.e. 36 / 5 minutes to complete the entire job

i.e. 7.2 minutes

Hence, the time taken by machine A and B working together to produce x amount of peanut butter is 7.2 minutes.

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Answer:

15

Step-by-step explanation:

8 x 6 / 2 -9

48 / 2 - 9

24-9

15

The value are-

Now, for the given question.

Let the given angle be 'x'.

Then, the complement of the angle will be: 90 - x.

6 times the complement = 6(90 - x)

6 times the complement is 44 less; 6(90 - x) - 44.

Now, the supplement of the angle is; 180 - x.

Two time the supplement = 2(180 - x)

The equation will form as;

2(180 - x) = 6(90 - x) - 44

360 - 2x = 540 - 360 - 44

Simplifying the equation;

x = 34.

Thus, the original angle is 34°.

complement angle = 90 - x

= 90 - 34

= 56°

Thus, complement angle = 56°

supplement angle = 180 - x

= 180 - 34

= 146

supplement angle = 146°

Thus, the values of the angles are obtained.

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Answer:4 hours

Step-by-step explanation:

You have to figure out what times 5 would equal 20.

5x=20

5(4)=20

because 5*4=20, the answer is 4

Answer:

A, B, C

Step-by-step explanation:

Step-by-step explanation:

Simplifying

-3(x + 5) = -1(3x + 15)

Reorder the terms:

-3(5 + x) = -1(3x + 15)

(5 * -3 + x * -3) = -1(3x + 15)

(-15 + -3x) = -1(3x + 15)

Reorder the terms:

-15 + -3x = -1(15 + 3x)

-15 + -3x = (15 * -1 + 3x * -1)

-15 + -3x = (-15 + -3x)

Add '15' to each side of the equation.

-15 + 15 + -3x = -15 + 15 + -3x

Combine like terms: -15 + 15 = 0

0 + -3x = -15 + 15 + -3x

-3x = -15 + 15 + -3x

Combine like terms: -15 + 15 = 0

-3x = 0 + -3x

-3x = -3x

Add '3x' to each side of the equation.

-3x + 3x = -3x + 3x

Combine like terms: -3x + 3x = 0

0 = -3x + 3x

Combine like terms: -3x + 3x = 0

0 = 0

Solving

0 = 0

Couldn't find a variable to solve for.

This equation is an identity, all real numbers are solutions.

Answer:

Step-by-step explanation:

-3(x+5) = -(3x+15)

-3x - 15 = -3x - 15

the 2 sides are identical so there are

INFINITE solutions.

Answer:

1) 1x² - 9x - 109 = 0

2) 3x² -12x -15 = 0

3) 3x² + 13x - 27 = 0

4) 6x² + 84x + 236 = 0

5) -16x² + 8x + 383 = 0

Step-by-step explanation:

The standard form of the quadratic equation is ax² + bx + c where a, b and c are constants.

So we have to convert each of the equations into a form that resembles the above

(1) 11x² -98  = 11 + 9x

(2) (2x - 1)² = (x + 4) ²

(3) 4x² + 2x − 9 = (x − 2)(x − 9)

(4) 0 = 6(x +7 )² - 58

(5) -1/2 ( x - 1/4 )² + 12 = 0

The area of the lawn is given as  50 . 24 m²

Area = πr² x θ/360

r = 12m

θ = 40 degrees

Area = 3.14 x 12² * 40/360

= 50.24

Hence the area is 50 . 24 m²

2 x 50.26

= 100.52

Area = πr² x θ/360

The value of  θ is not given

When we plug in the figures we would have

100.52 = πr² x θ/360

Then  θ = 100.53 x 360 / 3.14 x 12²

= 80 degrees

c. θ = 40 degrees

100. 53 =  πr² x 40/360

πr²  = 100.53 x 360 / 40

r = 16.97 m

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Answer:

You would want have more stock and less savings

Step-by-step explanation:

The answer of 18 is y = 0.5x + 0

The answer of 22 is y =  -0.4x + 0

Step-by-step explanation:

c is constant, m is gradient

18. m = 1/2

     m = 0.5

     1 = 0.5(2) + c

     1 = 1 + c

     c = 0

     y = 0.5x + 0

22. m = 2/-5

      m = -0.4

      2 = -0.4(-5) + c

      2 = 2 + c

      c = 0

      y = -0.4x + 0

The probability that he gets at least as many heads as tails is half or 50%.

Probability is obtained by dividing the number of chances that it will take to realize a result by the number of total possible chances. To get the right probability for the question asked here, we need to determine:

The number of chances is equal to 4.

The total number of possible chances is given by the equation:

4 × 2 = 8

Two is obtained by recognizing the fact that there are two sides to the coin. So, he could either get a head or a tail when he tosses the nickel.

Therefore;

4/8 = 1/2 or 50%

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