Solve the polynomial equation by factoring and then using the zero-product principle.
4x = 864x
Rewrite the equation in factored form.
(Blank)= 0

What is the solution pair?

Answer: I got you!

Step-by-step explanation:

a) Sophie's distance is given by the formula: distance = rate × time. Therefore, her distance yesterday is s × t miles.

b) Rana's time is given by the formula: time = distance ÷ rate. Therefore, her time yesterday is m ÷ r hours.

c) Sophie's time is given by the formula: time = distance ÷ rate. Let's call the time Sophie waits for Rana "w". Then we have two equations:

Sophie's distance: s × (w + t) = 20

Rana's distance: r × (w + t) = 20 - m

We can solve for "w" by substituting the second equation into the first equation:

s × (w + t) = 20 - r × (w + t) + m

(s + r) × (w + t) = 20 + m

w + t = (20 + m) ÷ (s + r)

w = (20 + m) ÷ (s + r) - t

Therefore, Sophie waits for Rana for (20 + m) ÷ (s + r) - t hours.

d) Sophie's distance tomorrow is s × 3 miles, and Rana's distance tomorrow is r × 3 miles. Therefore, the difference in distance is (s - r) × 3 miles.

Rounding down to the nearest whole number, we can conclude that about 12 women in her age group ran faster than Joan.

A whole number is a number that is not a fraction, decimal or negative. Whole numbers include all positive integers (1, 2, 3, ...), as well as zero (0). They are also sometimes referred to as counting numbers, as they are commonly used for counting objects or items.

A standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1. It is a specific type of normal distribution that has been standardized to have these specific parameters, which makes it easier to calculate probabilities and perform statistical analyses.

In the given question,

We can use the standard normal distribution to solve this problem. Since Joan's finishing time was 1.84 standard deviations faster than the mean for her age group, we know that her finishing time is in the top (100% - 1.84% = 98.16%) of the distribution.

To find the number of women who ran faster than Joan, we need to find the area under the standard normal distribution curve to the right of her z-score. Using a standard normal distribution table or calculator, we can find that the area to the right of a z-score of 1.84 is 0.0322.

Therefore, approximately 395 x 0.0322 = 12.729 women in Joan's age group ran faster than her. Rounding down to the nearest whole number, we can conclude that about 12 women in her age group ran faster than Joan.

To know more about standard normal distribution, visit:

https://brainly.com/question/29509087

#SPJ1

Answer:

D. 7/5

Step-by-step explanation:

In right triangle ABC with right angle C,

sinA = 4/5 = cosB

cosA = 3/5 = sinB

sinB + cosB = 3/5 + 4/5 = 7/5

Answer:

Step-by-step explanation:

The theoretical probability of getting the same side every time in a single coin toss is 1/2. Since we have five independent coin tosses, we can calculate the probability of getting the same side every time by multiplying the probability of getting the same side in each toss:

(1/2) * (1/2) * (1/2) * (1/2) * (1/2) = 1/32

Therefore, the theoretical probability of getting the same side every time in five coin tosses is 1/32, which is equivalent to 0.03125. So, the answer is (C) 0.03125.

Answer:

what is the value of x if figure below 80 degree and 50 degree x?

When g be continuous on [1,6], where g(1) = 18 and g(6): = 11. Does a value 1 < c < 6 exist such that g(c) = 12

The intermediate value theorem is a fundamental theorem in calculus that states that if a continuous function f(x) is defined on a closed interval [a, b], and if there exists a number y between f(a) and f(b), then there exists at least one point c in the interval [a, b] such that f(c) = y.

According to the intermediate value theorem,

since g(x) is a continuous function on the closed interval [1, 6]

since g(1) = 18 is greater than 12, and

g(6) = 11 is less than 12,

there must be at least one value c between 1 and 6 where g(c) = 12.

Therefore, we can conclude that a value of c does exist such that g(c) = 12.

Learn more about intermediate value theorem at:

https://brainly.com/question/30557318

#SPJ1

Answer: C

Step-by-step explanation:

For any function, a value plugged in (x) cannot have more than 1 outcome (y). C states that when x = 10, y has 2 values; 30 and 35. This means C is not a function.

Answer:

103%

Step-by-step explanation:

1.03/1 x 100% = 103%

To convert the decimal 1.03 into a percentage, you multiply it by 100 which gives you 103%, so 1.03 is equal to 103%.

To express 1.03 as a percentage, we need to multiply the decimal by 100.

This is because the word percent in terms of mathematics means 'per hundred'. So, 1.03 multiplied by 100 equals 103.

Hence, 1.03 expressed as a percentage is 103%.

Rewrite your decimal as a fraction with a denominator of 100 to change it into a percentage.

For example, 1.03 can be written as 103/100 which translates into 103% in percentage format.

For more such questions on percentage, click on:

https://brainly.com/question/32197511

#SPJ2

Answer:

5/3

Step-by-step explanation:

1×3=3

3+2=5

So answer is 5/3

The value of the unknown in triangle is F = 90 degrees, angle D = 37 degrees, angle E = 53 degrees, f = 18.33 units, d = 11 units, and e = 14.59 units.

Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions. There are several distinctive trigonometric identities that relate a triangle's side length and angle. Only the right-angle triangle is consistent with the trigonometric identities.

Given that, angle F = 90 degrees, angle D = 37 degrees and d = 11 units.

Using the sum of interior angles of triangle we have:

angle F + angle D + angle E = 180

90 + 37 + angle E = 180

angle E = 53 degrees.

Now, using the trigonometric identities we have:

sin (37) = d / f = 11/f

f = 11 / 0.60

f = 18.33

Using tan we have:

tan (37) = d/e = 11 / e

e = 14.59

Hence, the value of the unknown in triangle is F = 90 degrees, angle D = 37 degrees, angle E = 53 degrees, f = 18.33 units, d = 11 units, and e = 14.59 units.

Learn more about trigonometric functions here:

https://brainly.com/question/6904750

#SPJ1

Answer:

The total labor charges for the job are P3,500.

Step-by-step explanation:

To find the total labor charges for a job that takes 2 1/2 hours, we need to look at the labor charges for each hour and a half-hour fraction and add them up.

For the first hour, the charges are P1,200. For the second hour, the charges are P1,400. For the third hour (the half-hour fraction), the charges are P1,800 / 2 = P900.

So, the total labor charges for 2 1/2 hours of work are

P1,200 + P1,400 + P900 = P3,500

Therefore, the total labor charges for the job are P3,500.

To find the experimental probability for each outcome, we divide the number of times the cup lands in that position by the total number of tosses:

What is a outcome?

An outcome refers to a possible result of an experiment or event that is used to calculate the probability of that result occurring.

What is meant by experimental probability?

Experimental probability is the probability of an event based on actual, repeated trials or experiments rather than theoretical or mathematical calculations.

To know more about experimental probability visit:

https://brainly.com/question/30694293?referrer=searchResults

#SPJ1

Graph D of the given function has the smallest value for b.

As per name signifies, exponents are used in exponential functions. But take note that an exponential function does not have a constant as its base and a variable as its exponent. One of the following forms can be used for an exponential function.

f (x) = aˣ

y=f(x) >0

f(x)=abˣ , where a>0

So, f(x)=abˣ

When, b<1 f(x) decreases

When, b>1 f(x) increases and the larger the b the steeper the graph

So, graph of D is increasing and is steepest

So, graph D has the smallest value for b.

To know more about variable, visit

https://brainly.com/question/17344045

#SPJ1

Answer:

11

Step-by-step explanation:

[tex]61 {}^{2} - {60 }^{2} = 121[/tex]

[tex] \sqrt{121} = 11[/tex]

Answer:

1/3

Step-by-step explanation:

using rise over run fron the two dots, we can find 2/6, which simplifies down to 1/3

Using ratios and proportionality, we can find that the length of the missing part is 18 units.

By comparing two amounts of the same unit and establishing the ratio, we can work out how much of one quantity is contained in the other. Two categories of ratios exist.

The part to whole ratio is one, and the part-to-part ratio is another category that exists. The part-to-part ratio illustrates the relationship between two separate entities or groupings.

Here,

Let the missing length be = x.

Given,

The upper segment is 24.

One part of it is 16.

So, the other part is = 24 - 16 = 8

Now as per the ratios,

16/36 = 8/x

⇒ x = 8 × 36/16

⇒ x = 18 units.

To know more about ratios, visit:

https://brainly.com/question/13419413

#SPJ1

The area is multiplied by 1/16 and the correct option is (a) The area is multiplied by 1/16.

When the radius of a circle is multiplied by 1/4, the effect on the area can be calculated using the formula A = πr², where A is the area and r is the radius. The new radius becomes (1/4)r, so the new area can be calculated by substituting (1/4)r for r in the original formula. Simplifying this expression, we get A' = π((1/4)r)² = (1/16)πr². This shows that the area is multiplied by 1/16, so the correct answer is (a) The area is multiplied by 1/16.

Learn more about radius here: brainly.com/question/28946570

#SPJ4

Complete question:

The radius of a circle is multiplied by 1/4. Which of the following describes the effect of this change on the area?

a. The area is multiplied by 1/16.

b. The area is multiplied by 1/4.

c. The area is multiplied by 1/8.

d. The area is multiplied by 4.

Answer:

m = -4

Step-by-step explanation:

Slope = rise/run or (y2 - y1) / (x2 - x1)

Pick 2 Points (4,7) (5,3)

We see the y decrease by 4 and the x increase by 1, so the slope is

m = -4

Answer:

-4

Step-by-step explanation:

because the slope goes down by 4 according to the table, from 7 to 3 to -1 to -5. hope that makes sense.

Answer:

It is a tangent

Step-by-step explanation:

A tangent is a straight line that brushes the circumference of a circle.

The relation between a point and a circle is relative to the location of the point relative to the circumference of the circle, which can be inside, at the circumference, or outside.

The relationship between a point and a circle can be described as follows:

More can be learned about points and circles at https://brainly.com/question/25871159

#SPJ1

The area of the bigger solid is  67.24 cm².

Assume the smaller shape has a length of 2x and a width of 2y. The larger shape would then have 5x length and 5y width.

Because the area of a rectangle is the product of its length and width, the area of the smaller shape is:

Area of smaller shape = 2x * 2y = 4xy

We know that the similar shapes have an area of 78 cm2. As a result, we can write:

4xy + larger area = 78

(larger shape area) / (smaller shape area) = (linear scale factor)²

Substituting the values from the problem yields:

(larger shape area) / (4xy) = (5/2)2 = 25/4

When we multiply both sides by 4xy, we get:

larger shape area = (25/4) * 4xy = 25xy

Now we can plug the expression we discovered for the area of the smaller shape into the equation we found earlier:

4xy + 25xy = 78

29xy = 78

xy = 78/29

Substituting this xy value into the expression we discovered for the area of the larger shape yields:

larger shape area = 25xy = 25 * (78/29) = 67.24 cm2 (rounded to two decimal places)

As a result, the larger shape has an area of approximately 67.24 cm2.

To Know more about   length  visit:-

https://brainly.com/question/30100801

#SPJ1

Sure! The general term of a sequence is a formula which describes the nth term of the sequence. In this case, the pattern is that each term is increased by 3 when compared to the previous term. This pattern can be expressed as a formula - an=a1+(n-1)d, where a1 is the first term, n is the term number and d is the common difference.

For the sequence given -2,1,4,7

a1=-2

n=4

d=3

Substituting these values in the formula will give us the general term of the sequence an = -2 + 3(n-1)

Hence, the general term of the sequence -2,1,4,7 is an = -2 + 3(n-1).

The probability that X takes the value 1 is 1/4 and the probability that X takes the value 2 is 1/12.

The given CDF of a random variable X is F(X)=-*- on the support of X, where the support of X is x = 1,2,3,... The task is to determine P(X = 1) and P(X = 2).

To find P(X = 1), we need to find the probability that X takes the value 1. From the given CDF, we can see that F(1) = 1/4. Therefore, P(X = 1) = F(1) - F(1-) = 1/4 - 0 = 1/4.

To find P(X = 2), we need to find the probability that X takes the value 2. From the given CDF, we can see that F(2) = 7/12. Therefore, P(X = 2) = F(2) - F(2-) = 7/12 - 1/2 = 1/12.

Find out more about  CDF (cumulative distribution function)

at brainly.com/question/16945299

#SPJ4

Question:-

The CDF Of A Random Variable X Is Given The Function F(X)=-*- On The Support Of X, Where The Support Of X Is X = 1,2,3,... Determine P(X = 1) And P(X = 2). 3x + X

The given statement "Star clusters with lots of bright, blue stars of spectral type O and B are generally younger than clusters that don't have any such stars." is True. The reason for this is that O and B stars are short-lived and burn through their fuel quickly.

The reason for this is that O and B stars burn through their fuel quickly, causing them to exhaust their nuclear fuel and end their lives in a relatively short period, typically within a few tens of millions of years.

On the other hand, stars of lower mass and cooler temperatures, like G and K type stars like our sun, have longer lifetimes and take billions of years to exhaust their nuclear fuel.

Therefore, clusters without any bright, blue stars are likely to have evolved for longer periods, allowing these short-lived stars to have already expired.

To know more about Star clusters:

https://brainly.com/question/30899528

#SPJ4

Step-by-step explanation:

x = weeks

Yours    75 + 5x

Friend's 30 + 10x

When are they equal ?

75 + 5x     =     30 + 10x

45 = 5x

x = 9 weeks

Here is the stem and leaf plot:

5  4

6   0, 1, 2, 2

7    1, 2, 4, 6, 8

8    2, 3, 4,  6, 7,

9   0, 2, 5, 5, 9

The range is 45.

A stem-and-leaf plot is a table that is used to display a dataset. A stem-and-leaf plot divides a number into a stem and a leaf. The stem is the tens digit and the leaf is the units digit. For example, in the number 54, 5 is the stem and 4 is the leaf.

Range is used to measure the variation of a dataset by finding the difference between the highest number and the lowest number.

Range = highest value - lowest value

99 - 54 = 45

To learn more about range, please check: https://brainly.com/question/12372689

#SPJ1

Instead of 2.00 as mentioned in the question, the semester GPA is 1.38. Please double-check your calculations or provide more details if you made an error when reporting your grades or computing your GPA.

Students must devote approximately 135 hours (45 x 3) of class, instructional, and independent time to a three credit unit course. Students who enroll in a course for four credit hours must dedicate around 180 (45 x 4) hours to it, split between in-class and out-of-class work.

You must first translate each letter grade using the common 4.0 scale into its equivalent numerical number before you can determine your semester GPA:

A = 4.0

B = 3.0

C = 2.0

D = 1.0

F = 0.0

E = 0.0 (equivalent to F)

Then, you can use the formula:

(Total grade points) / GPA (total credit hours)

Using this formula, we can calculate your semester GPA as follows:

FYE 105: F (0.0) x 3 credit hours = 0.0 grade points

MAT 150: E (0.0) x 3 credit hours = 0.0 grade points

ENG 101: D (1.0) x 3 credit hours = 3.0 grade points

BIO 112: A (4.0) x 3 credit hours = 12.0 grade points

BIO 113: B (3.0) x 1 credit hour = 3.0 grade points

Total grade points = 0.0 + 0.0 + 3.0 + 12.0 + 3.0 = 18.0

Total credits earned is 13 (3 + 3 + 3 + 3 + 1)

GPA = 18.0 / 13 = 1.3846

To know more about semester GPA visit:-

https://brainly.com/question/13871451

#SPJ1

The absolute maximum is 56 and absolute minimum values is 24 of a function f given by f(x) = 2x³−15x² + 36x +1 on the interval [1, 5] .

A function is defined as a relationship between a set of inputs, each having an output. In short, a function is a relationship between inputs where each input relates to exactly one output. Each function has a domain and a password domain or scope. Functions are usually denoted by f(x), where x is the input.

Given that:

f(x) = 2x³ −15x²+ 36x+ 1

f'(x) = 6x² −30x + 36

Putting f'(x) = 0

⇒ 6x² − 30x+ 36 = 0

⇒ x² −5x+6 = 0

⇒ (x−2)(x−3) = 0

⇒ x=2 or 3

We are given interval [1,5]

Hence, calculating f(x) at 2, 3, 1, 5,

f(2) = 29

f(3) = 28

f(1) = 24

f(5) = 56

Hence, absolute maximum value is 56 at x=5.

Absolute minimum value is 24 at x=1.

Complete Question:

Find the absolute maximum and absolute minimum values  of a function f given by f(x)=2x³−15x² + 36x +1 on the interval [1, 5] .

Learn more about Function:

https://brainly.com/question/12431044

#SPJ4