Divide up the number 73 in the ratio 2:3:4

Thanks!

Answer:

6

Step-by-step explanation:

slope is defined as rise over run. The difference of the x coordinates divided by the difference of the y coordinates will provide the slope. You may have seen this as,

\(m = \frac{y2 - y1}{x2 - x1} \)

plugging the values of the coordinates in, we get

\(\frac{8 - ( - 4)}{ - 4 - ( - 6)} = 6\)

I know right now, this stuff may seem super over your head and odd, I was there too. But trust me when I say, it's worth learning the basics now, or you will struggle through highschool and college if you plan on attending.

Answer:

10

Step-by-step explanation:

25 times .60 then take that answer and subtract it from 25 or half of 25 which it 12.5 then take off another 10%

Answer:

The approximate number of gallons consumed by a person in 2010 will be 4.9 gallons

Step-by-step explanation:

Recall that the formula for exponential decrease is given by a function of the form:

\(f(x)=A\.(1-r)^x\)

where A is the initial value, r is the rate of decrease, and x is the time elapsed.

In our case, the initial value of gallons of juice per person (at the starting time = 1981) is 16.5 gallons. So A = 16.5 gallons.

the rate of decrease "r" is the decimal form of: 4.1%, that is r = 0.041

So we have:

\(f(x)=16.5\.(1-0.041)^x\)

Now we can calculate what the average number of gallons would be in the year 2010, knowing that between 1981 and 2010 there is an elapsed time in years of: 2010-1981 = 29 years. Then:

\(f(29)=16.5\,(1-0.041)^{29}=4.9 \,\, gallons\)

The approximate amount consumed per person in 2010 is  4.9 gallons.

The formula that would used to determine the average gallon of juice consumed in 2010 is:  

FV = P (1 - r)^n

FV = Future value  

P = Present value = 16.5 gallons  

R = rate of decrease = 4.1%  

N = number of years = 2010 - 1981 = 29

16.5 x (1 - 0.041)^29  = 4.9 gallons

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This is compound interest problem. The compound interest formula is:

Where

F is the future amount [we want this, after 9 years]

P is the initial amount [$400, in our case]

r is the rate of interest per period [8% per year. Since per quarter compounding, we want interest rate per quarter, so, 8%/4 = 2%. In decimal, 2/100 = 0.02]

t is the time period [number of compoundings in 9 year would be 9*4 = 36]

We now know the given information, we simply substitute it into the formula and solve for F. Shown below:

The account will be worth $815.95 after 9 years!

Answer:

0 and 1.5850

Step-by-step explanation:

Given the expression

2^2x-4^(2^x)+3=0

Let P = 2^x

P² - 4P + 3 = 0

Factorize

P² -3P-P +3 = 0

P(P-3)-1(P-3) = 0

P-1 = 0 and P-3 = 0

P = 1 and 3

If P = 1

2^x = 1

log 2^x = log 1

xlog 2  =0

x = 0/log 2

x = 0

Also if P = 3

2^x = 3

x log 2 = log 3

x = log3/log 2

x = 0.4771/0.3010

x = 1.5850

Hence the positive value of x are 0 and 1.5850

The probability of tossing "heads" on each of your first two tosses is 0.25

Probability = n(E)/n(S)

Where E is the possibility of an event occurring

and S is the sample space i.e., the total number of possible outcomes.

Probability is the measure of how likely an event can happen. The probability of any event lies between 0 and 1 only.

The sample space for when you toss one coin is - H, T

So the probability to get an H is= 1/2

=0.5

Similarly, The sample space for when you toss two coins is HH, TT, HT, TH

So, the probability to get an H on each of your first two tosses is = 1/4

=0.25

Therefore, The probability of tossing "heads" on each of your first two tosses is 0.25

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Answer:

Solution given:

8x+13+12x+7=180°[exterior angle's sum is supplementary]

20x=180°-20

x=160°/20°

x=8° is your answer.

To find the average rate of change of the function f(x) = 1.85x^2 over the interval 10 ≤ x ≤ 20, we need to find the difference in the function values at the endpoints of the interval and divide by the length of the interval.

The function value at x = 10 is:

f(10) = 1.85(10)^2 = 185

The function value at x = 20 is:

f(20) = 1.85(20)^2 = 740

The length of the interval is:

20 - 10 = 10

So the average rate of change of the function over the interval 10 ≤ x ≤ 20 is:

(f(20) - f(10)) / (20 - 10) = (740 - 185) / 10 = 55.5

Rounding to the nearest tenth, the average rate of change of the function over the interval 10 ≤ x ≤ 20 is approximately 55.5.

A common denominator is a shared multiple of the denominators of the fractions involved when adding or subtracting fractions. It enables fraction comparison and addition/subtraction.

Simplification is the process of reducing a fraction to its simplest form by dividing the numerator and denominator by their greatest common divisor. This is done to represent fractions in the simplest terms viable.

Conversion: The process of transferring a fraction from one form to another while retaining its equal value is known as conversion. Finding a common denominator or expressing a fraction in terms of a specified unit or fraction may be required.

Fraction Addition/Subtraction: When adding or subtracting fractions, a common denominator is required. This entails determining a common multiple of

To rewrite the expression 3 + 1/5 + 2/3 using fifteenths as the common denominator, we need to find a common denominator for 5 and 3, which is 15 (since 5 and 3 are both factors of 15).

First, let's convert the fractions 1/5 and 2/3 to fifteenths:

\((\frac{1}{5})(\frac{3}{3}) = \frac{3}{15}\)

\((\frac{2}{3})(\frac{5}{5}) = \frac{10}{15}\)

Now we can rewrite the expression using the common denominator:

\(3 + \frac{3}{15}+\frac{10}{15}\)

Answer:

the answer is d or e i think its d but its one of the 2

Step-by-step explanation:

Benjamin has 340 cents or $3.40.

Proportion in Mathematics is an equation where two or more ratios are made to be equal.

If a : b = c : d, then we can write a/b = c/d

We know that,

1 nickel = 5 cents

8 nickel = x cents

Using ratio and proportion,

1 : 5 = 8 : x

x = 8 × 5 = 40 cents

Similarly,

1 quarter = 25 cents

12 quarters = 12 × 25 = 300 cents

Total cents Benjamin has = 300 + 40 = 340 cents = $3.40

Hence, Benjamin has a total of $3.40.

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Graph A represents the solution set of the equations y = x² + 4x + 3 and y = 2x + 6.

The vertex of the parabola is (-2,-1), which corresponds to Graph A. We can find it we the formula  h = -b/(2a)

a is the coefficient of x² (which is 1 in this case) and b is the coefficient of x (which is 4 in this case).

h = -4/(2×1) = -2.

To find the y-coordinate of the vertex, we substitute x = -2

y = (-2)² + 4(-2) + 3 = -1.

∴ vertex ⇒ (-2,-1), which corresponds to Graph A.

The equation y = 2x + 6 is a linear equation and represents a straight line with a slope of 2 and y-intercept of 6.

The line passes through the points (-3, 0) and (1, 8), which also corresponds to Graph A.

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No,  the slope of a horizontal line y=6 is,  zero not negative.

What is a Slope?

In Mathematics, a slope of a line is the change in y coordinate with respect to the change in x coordinate.

The net change in y-coordinate is represented by Δy and the net change in x-coordinate is represented by Δx.

Hence, the change in y-coordinate with respect to the change in x-coordinate is given by,

m = change in y/change in x = Δy/Δx

Where “m” is the slope of a line.

Generally, the slope of a line gives the measure of its steepness and direction. The slope of a straight line between two points says (x1,y1) and (x2,y2) can be easily determined by finding the difference between the coordinates of the points. The slope is usually represented by the letter ‘m’.

Slope Formula

If P(x1,y1) and Q(x2,y2) are the two points on a straight line, then the slope formula is given by:

Slope, m = Change in y-coordinates/Change in x-coordinates = Δy/Δx

m = (y2 – y1)/(x2 – x1)

In the given equation of line y=6 .

The line crosses the y-axis at 6, as the line is always at that value. As it is a horizontal line, the slope is zero.

The equation y = 6 means for each and every value of x, y will be equal to 6.

This is the definition of a horizontal line.

By definition, the slope of a horizontal line is m = 0

When x = 0 then y = 6

Therefore, the y-intercept is: (0, 6).

Hence , the the slope of a horizontal line , m = 0.

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The solution to the equation sqrt 2-3x / sqrt 4x = 2 is x = -2/3.

To solve the equation, we must first clear the denominators and simplify the equation. We can do this by multiplying both sides by sqrt(4x) and then squaring both sides. This gives us:
sqrt 2-3x = 4sqrt x
2 - 6x + 9x² = 16x
9x² - 22x + 2 = 0
Using the quadratic formula, we can find that x = (-b ± sqrt(b² - 4ac)) / 2a. Plugging in a = 9, b = -22, and c = 2, we get:
x = (-(-22) ± sqrt((-22)² - 4(9)(2))) / 2(9)
x = (22 ± sqrt(352)) / 18
x = (22 ± 4sqrt22) / 18
Simplifying this expression, we get:
x = (11 ± 2sqrt22) / 9
Therefore, the solution to the equation is x = -2/3.
To solve the equation sqrt 2-3x / sqrt 4x = 2, we must clear the denominators and simplify the equation. This involves multiplying both sides by sqrt(4x) and then squaring both sides.

After simplifying, we end up with a quadratic equation. Using the quadratic formula, we can find that the solutions are x = (11 ± 2sqrt22) / 9.

However, we must check that these solutions do not result in a division by zero, as the original equation involves square roots. It turns out that the only valid solution is x = -2/3.

Therefore, this is the solution to the equation.

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The value of e can be calculated by  e = A - f/2.

Usually, simplification involves proceeding with the pending operations in the expression.

For example, 5 + 2 is an expression whose simplified form can be obtained by doing the pending addition, which results in 7 as its simplified form.

Simplification usually involves making the expression simple and easy to use later.

We have been given an expression as;

A =e+f/2

We need to find the solution for 'e'.

So,

A = e+f/2

Subtract from f/2 on each side, we get;

A - f/2 = e

Thus, e = A - f/2

Therefore, the value of e can be calculated by  e = A - f/2.

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Answer:

1. gcf: 6 lcm: 660

2. gcf: 2 lcm: 308

3. gcf: 7 lcm: 56

4. gcf: 2 lcm: 220

5. gcf: 1 lcm: 52

Step-by-step explanation:

Hope this helps :)

First a definition:

A given set is closed under a given operation if, for any given pair of elements of the set under that operation, the outcome also belongs to the set.

With this, we will find that the set of integer numbers is not closed under division.

Now let's be more clear.

The definition particularly means that a set is closed under division only if for any pair of elements of the set, the division of these elements also does belong to the set.

Here we want to see if the set of integers is closed under division. To see that this is false, we just need to find a counterexample.

This is, finding a pair of integer numbers that have a quotient that is not an integer.

A really simple example is:

1 and 2.

2/1 = 2 is integer.

but

1/2 = 0.5 is not integer.

Thus we can conclude that the set of integers is not closed under division.

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Answer:

D, g(x) = 1/4 x^2

Step-by-step explanation:

You can try plugging in the x and y values into each equation. The answer to this would be D, where if you plug in 2 as the x value, you get 1/4 * 4 which equals 1. This also makes sense because 2x would have a narrower curve while 1/2x would have a wider curve.

The balance of Jennifer's account after 15 years is given as follows:

$295,243.41.

The amount of money earned, in compound interest, after t years, is given by:

\(A(t) = P\left(1 + \frac{r}{n}\right)^{nt}\)

In which:

The parameters for this problem are given as follows:

P = 145000, r = 0.0475, n = 12, t = 15.

Hence the balance of the equation after 15 years is given as follows:

\(A(t) = P\left(1 + \frac{r}{n}\right)^{nt}\)

\(A(15) = 145000\left(1 + \frac{0.0475}{12}\right)^{12 \times 15}\)

A(15) = $295,243.41.

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2.7×1012 (i.e.2,732.4) is greater than 1.5×108 (i.e. 162)

Given two numbers

1)2.7×1012

2) 1.5×108

Two numbers can be equal or one is greater than the other or one is less than the other. there will be no other case rather than these three.

1)2.7×1012=2,732.4

2) 1.5×108=162

The value of the 1st number is 2,732.4 and the value of the 2nd number is 162

1st given number is greater than the 2nd number i.e. 2,732.4>162

Therefore,2.7×1012 (i.e.2,732.4) is greater than 1.5×108 (i.e. 162)

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The vertices of the feasible region is (4, 3)

From the question, we have the following parameters that can be used in our computation:

x + y ≤ 7

x - 2y ≤ -2

x ≥ 0

y ≥ 0

Express as equations

So, we have

x + y = 7

x - 2y = -2

Subtract the equations

3y = 9

So, we have

y = 3

Next, we have

x + 3 = 7

This gives

x = 4

Hence, the vertex of the feasible region is (4, 3)

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To describe the temperatures for the week, we can apply the following statistical tools:

a) Find the mean, median, mode, and range.

c) Construct a line graph.

d) Construct a stem and leaf plot.

We can describe temperatures using measures of central tendencies (especially the mean, median, and mode).

The mean temperature is the average, which shows the overall trend in temperature changes.  It is computed by adding up the temperatures for the period and diving by the number of data values.

In addition, the median gives the middle value when the data set is ordered in ascending or descending orders. Similarly, the mode gives the highest temperature occurrence within the period. It may not be useful here.

We can estimate the difference between the highest and lowest temperature for the week with the range.

A line graph (showing connecting lines) and a stem-and-leaf plot (like a bar graph) can graphically describe the temperatures for the week.

Thus, we can use Options A, C, and D to describe the temperature.

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What could you do to describe the following data, showing temperatures for the week? (Check all that apply.)

Mon - 65°

Tues - 67°

Wed - 66°

Thur - 70°

Fri - 72°

Sat - 68°

Sun - 69°

a) Find the mean, median, mode, and range.

b) Survey people about the weather.

c) Construct a line graph.

d) Construct a stem-and-leaf plot.

Answer:

7

Step-by-step explanation:

Answer:

-11,11

Step-by-step explanation:

JUst add 5 to both.

Therefore , the solution of the given problem of area comes out to be

r = 8.

The term "area" describes the amount of space occupied by a 2D form or surface. We use cm2 or m2 as our units for measuring area. A shape's area is determined by dividing its length by its breadth.

Here,

A 90 degree sector occupies 1/4 of a circle, which has 360 degrees. Consequently, the area of the whole circle can be written as

Sector Size/Sector Area = Circle Area/360

16 ft2/90 = n/360

(360) (16 ft2)/90 = n

(4)(16 ft2) = n

The total size of the circle is n = 64 ft2.

Since Area of a Circle equals r2,

∏r2 = 64

r2 = 64/∏

r = √(64/∏)

We multiply by / to get by rationalizing the denominator.

r = √(64∏)/√(∏2) Then using the denominator's square root, we can obtain the solution of

r = √(64∏)/∏

r = 8

Therefore , the solution of the given problem of area comes out to be

r = 8.

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Answer:

Explained below.

Step-by-step explanation:

When drawing line of symmetry on a figure and reflecting, we have to know that pairs of segments in that figure must have the same length while pairs of angles must have the same measurement. This is to ensure that half of that figure must concise with the other half part of it when that figure is folded across a line of symmetry.

Answer:

3:2

Step-by-step explanation:

If you are comparing one data point (A) to another data point (B), your formula would be A/B. This means you are dividing information A by information B. For example, if A is five and B is 10, your ratio will be 5/10.

for this problem we use 0.90 and 0.60, so our ratio is 0.90/0.60

using whole numbers can be converted now by actually dividing these data points and then multiplying to a whole number:

0.9/0.6 = 1.5

1.5 x 2 = 3

this gives 3/2 = 1.5

so we know that the ratio is 3:2 and this is the smallest whole number that it could be

The probability that the mean of a sample of 40 families will be between 17.1 and 18.1 pounds is given as follows:

0.5874 = 58.74%.

The z-score of a measure X of a variable that has mean symbolized by \(\mu\) and standard deviation symbolized by \(\sigma\) is obtained by the rule presented as follows:

\(Z = \frac{X - \mu}{\sigma}\)

The parameters for this problem are given as follows:

\(\mu = 17.2, \sigma = 2.5, n = 40, s = \frac{2.5}{\sqrt{40}} = 0.3953\)

The probability that the mean of a sample of 40 families will be between 17.1 and 18.1 pounds is the p-value of Z when X = 18.1 subtracted by the p-value of Z when X = 17.1, hence:

\(Z = \frac{X - \mu}{\sigma}\)

By the Central Limit Theorem:

\(Z = \frac{X - \mu}{s}\)

Z = (18.1 - 17.2)/0.3953

Z = 2.28

Z = 2.28 has a p-value of 0.9887.

Z = (17.1 - 17.2)/0.3953

Z = -0.25

Z = -0.25 has a p-value of 0.4013.

Hence:

0.9887 - 0.4013 = 0.5874 = 58.74%.

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