What is the fraction in decimal form?

21/6

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y = x⁴ +4x³ +4x² +4x +3

The coefficients of the offered quartics (in order) have 1, 1, 1, and 0 sign changes, respectively. Descartes' rule of signs tells you this means the first three choices all have one (1) positive real root, so the negative real roots -1 and -3 are not the only ones.

The only possible polynomial is the last one. Synthetic division of that polynomial by roots -1 and -3 leave the remaining factor as x²+1, which has only complex zeros.

The appropriate choice is ...

... y = x⁴ +4x³ +4x² +4x +3

a)7^-2=1/7^2=1/49

b) (8^4)^2/8^11=8^8/8^11=1/8^3=1/512.

To find the value of an expression without exponents, divide numbers and subtract the exponents for division, and when squaring, multiply the number by itself. Any number raised to the power of 2 is squared, and to the power of 3 is cubed.

To find the value of an expression without any exponents, you might need to use the rule: to divide two exponential numbers, divide the numbers out front and subtract the exponents. Here's an example:

If we have to find the value of 106 ÷ 103, you'll divide 10 by 10 (which is 1) and subtract the exponents (6 - 3), resulting in 103, which equals to 1000 when you remove the exponent.

In the context of squaring exponents, when you square a number like 52, it means 5 x 5, which equals 25. Squaring is also known as raising to the power of 2. Similar to this, any number raised to the power of 3 is said to be cubed.

These concepts are fundamental when calculating extreme values like $rac{4.81x10^4}{2.05x10^2}$, solving quadratics, and handling scientific notations.

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[tex]35.6\times10^{-4}=35.6\times0.0001=0.00356[/tex]

[tex]a^{-n}=\dfrac{1}{a^n}\\\\10^{-4}=\dfrac{1}{10^4}=\dfrac{1}{10000}=0.0001[/tex]

Final answer:

0.00356.

Explanation:

The question requires us to express the product of a decimal number and a power of ten in standard form. To find 35.6 times 10^-4 in standard form, we can use the rule of multiplying a decimal number by a power of ten. Multiplying by 10^-4 means we move the decimal point four places to the left.

So, 35.6 × 10^-4 becomes 0.00356. This is the number 35.6 shifted four decimal places to the left, as the exponent on the ten is negative, indicating division by ten for each unit of the exponent.

Answer: 5/9 of a mile

Step-by-step explanation:

2/6 + 2/9

3/9 + 2/9

5/9

Answer:

So, it is given to us that Jaden has 3 pound of beef in the first pot and 2 table spoons of chili powder.

(16 ounces = 1 pound)

(48 ounces = 3 pounds)

In he second bowl he uses the SAME amount of beef and 3 times as much chili powder.

Which means that he used 3 pounds of beef and 2*3 = 6 table spoons of chili powder in the second cup.

The question is asking you for the ratio between the two quantities in a cryptic manner.

so, it would end up being 3 pounds of beef every 6 table spoons of chili powder, which is nothing but Half (0.5 pounds of beef every tablespoon of chili powder).

1/2 pounds of beef every tablespoon of chili powder.

HOPE THIS HELPS!

Jaden used 0.5 pounds of beef for every tablespoon of chili powder in the second pot of chili when he tripled the amount of chili powder while keeping the amount of beef unchanged.

In the first pot of chili, Jaden effectively used 48 ounces of beef per 2 tablespoons of chili powder. This equates to 24 ounces of beef per tablespoon of chili powder. However, when Jaden tripled the amount of chili powder in the second pot, the ratio of beef to chili powder decreased since more chili powder is being used for the same amount of beef. Therefore, since he used three times as much chili powder in the second pot, this resulted in a ratio of 48 ounces of beef per 6 tablespoons of chili powder. That equates to 8 ounces of beef for every tablespoon of chili powder which are used in the second pot. Furthermore, since 1 pound equals 16 ounces, the number of pounds of beef used per tablespoon of chili powder in the second pot is 8/16, or 0.5 pounds.

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Answer:

A. You have $48 to spend on socks, but you need to save at least $8 to pay for the bus trip home. You plan to spend the rest on socks at $10 each (including tax).

Step-by-step explanation:

cause it's A

Answer:

A. You have $48.00 to spend on socks, but you need to save at least $8.00 to pay for the bus trip home. You plan to spend the rest on socks at $10.00 each (including tax).

Step-by-step explanation:

A. (0,0) is a solution to n=m and to n=4m.

The equations can be solved by any of the usual means. Using substitution, we have ...

... m = n = 4m

... m(4 -1) = 0 . . . . subtract the left side

... m = 0 . . . . . . . . divide by 3

... n = m = 0

The solution is (m, n) = (0, 0).

Answer:

the answer is A, my answer got deleted

Answer:

.325

Step-by-step explanation:

If she had a quiz on 13 of the 40 days , the fraction is 13/40

13/40 = .325

Answer: The fraction of the days on which the quiz has been held expressed as a decimal is 0.325

Step-by-step explanation:

Decimal numbers are not considered as integers. They are rounded off to write an integer.

Fraction is present in the form of [tex]\frac{p}{q}[/tex] where [tex]q\neq 0[/tex]

We are given:

Number of days, the class had quiz = 13

Total number of days = 40

The fraction becomes: [tex]\frac{13}{40}[/tex]

Expression this as a decimal = 0.325

Hence, the fraction of the days on which the quiz has been held expressed as a decimal is 0.325

36.6

The rule for secants is pretty simple. The product of the distance from the external point to the near intersection with the circle and the distance to the far intersection with the circle is a constant.

This means ...

... BC × AC = DC × (DC+x)

... 8 × 26 = 5 × (x +5) . . . . . AC=AB+BC = 18+8 = 26

... 208 = 5x +25 . . . . . . . . . simplify

... 183 = 5x . . . . . . . . . . . . . subtract 25

... 36.6 = x . . . . . . . . . . . . . divide by 5

Answer:

1/500000000000 is the answer

Just simplify and combine like terms to find your answer. You can add the tens to the -5 power, and the 4 and 2 on the top, then divide by the expression on the bottom.

Therefore, the only expression equivalent to this one is B.

Answer:

C)  a = 10√3, b = 5√3, c = 15 , d = 5

Step-by-step explanation:

Here we use the ratio of 30, 60, 90 degree triangle.

The ratio of sides, 1:√3:2

2x = 10

x = 5

d = 5

b = 5√3

c = 5√3√3

c = 5*3 = 15

c = 15

a = 2(5√3)

a = 10√3

Therefore, a = 10√3, b = 5√3, c = 15 and d = 5

Thank you.

Answer:

The correct answer is C.

Step-by-step explanation:

From the [tex]60\degree[/tex] right angle triangle

[tex]\sin(60\degree)=\frac{b}{10}[/tex]

[tex]10\times \sin(60\degree)=b[/tex]

[tex]10\times \frac{\sqrt{3}}{2}=b[/tex]

[tex]5\sqrt{3}=b[/tex]

From the same [tex]60\degree[/tex] right angle triangle,

[tex]\cos(60\degree)=\frac{d}{10}[/tex]

[tex]10\times \cos(60\degree)=d[/tex]

[tex]10\times \frac{1}{2}=d[/tex]

[tex]5=d[/tex]

From the [tex]30\degree[/tex] right angle triangle

[tex]\sin(30\degree)=\frac{b}{a}[/tex]

[tex]\frac{1}{2}=\frac{5\sqrt{3}}{a}[/tex]

[tex]a=2\times 5\sqrt{3}[/tex]

[tex]a=10\sqrt{3}[/tex]

From the same [tex]30\degree[/tex] right angle triangle,

[tex]\cos(30\degree)=\frac{c}{a}[/tex]

[tex]\frac{\sqrt{3}}{2}=\frac{c}{10\sqrt{3}}[/tex]

[tex]10\sqrt{3} \times \frac{\sqrt{3}}{2}=c[/tex]

[tex]5 \times 3=c[/tex]

[tex]c=15[/tex]

The correct answer is C.

Answer:

12

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

The factors of 3 are: 1, 3

The factors of 4 are: 1, 2, 4

Then the greatest common factor is 1.

Answer:

462 mi

Step-by-step explanation:

Gloria gets 420 mi/tank.

10 % of 420 is

420 × 0.10 = 42 mi

She will be able to drive an extra 42 mi.

420 + 42 = 462 mi

With her new tires, a tank of gas will take her 462 mi.

Answer:

462

Step-by-step explanation:

to find 10% of 420 you take

420 x .10 = 42

then add 42 to 420

420+42=462

Answer:

117 girls

Step-by-step explanation:

If 64% are boys, the percentage of girls can be found by subtracting this amount from 100:

100 - 64 = 36

So 36% of 325 are girls.

To find the amount from a percentage use the following formula:

Original amount * [tex]\frac{percentage}{100}[/tex]

Now plug these values in:

[tex]325 * \frac{36}{100}[/tex] = 117

So there are 117 girls in the 325 children.

Answer:

117

Step-by-step explanation:

If 64% are boys, then 36% are girls. 36% of 325 equals 117, so there are 117 girls at the zoo.

Answer:

l = (P -2w)/2

Step-by-step explanation:

When you're working any "solve for ..." problem, first you look to see where the variable of interest is and what is done to it.

If it is only found on one side of the equation, as here, then you're in luck. If it is only found in one term, as here, you have even better luck.

Identify all the terms on the side of the equation where the variable is located that do not contain the variable. Add their opposite to both sides of the equation. The result will be a term containing the variable, equated to a bunch of other stuff.

... P -2w = 2l . . . . . we added -2w to both sides of the equation

Now, we divide the equation by the coefficient of the variable.

... (P -2w)/2 = (2l)/2

... (P -2w)/2 = l . . . . . . simplify. This is the solution you're looking for

If you like, you can distribute the multiplication by (1/2) to get

... l = P/2 - w

Final answer:

To find the height of the arch 50 ft. from the center, we can use the equation of a semi-ellipse. The height of the arch is approximately 31 ft. when rounded to the nearest foot.

Explanation:

To find the height of the arch 50 ft. from the center, we can use the equation of a semi-ellipse. The equation of a semi-ellipse with a length of a and a maximum height of b is given by: ((x^2)/(a^2))+((y^2)/(b^2)) = 1. In this case, the length of the bridge is 400 ft. and the maximum height is 100 ft., so we have: ((x^2)/(200^2))+((y^2)/(100^2)) = 1. To find the height when x = 50 ft., we substitute x = 50 into the equation and solve for y. Plugging in the values, we get: ((50^2)/(200^2))+((y^2)/(100^2)) = 1. Simplifying, we have: (2500/40000)+((y^2)/(100^2)) = 1.

Multiplying both sides by 40000 to get rid of the denominators, we have: 2500 + 400((y^2)/10000) = 40000. Simplifying further, we get: 2500 + 40(y^2) = 40000. Subtracting 2500 from both sides, we have: 40(y^2) = 37500. Dividing both sides by 40, we have: (y^2) = 937.5. Taking the square root of both sides, we have: y = 30.62. So, the height of the arch 50 ft. from the center is approximately 31 ft. when rounded to the nearest foot.

The graph of [tex] f(x) [/tex] is a straight line, so it is a linear function.

The graph of [tex] g(x) [/tex] has the same shape of the graph of [tex] y=e^x [/tex] (for example), so it is an exponential function.

Answer:

f(x) is linear

g(x) is exponential

Step-by-step explanation:

exponential  -> It is a graph of half curve

quadratic  -> it is a graph of a U shaped curve

cubic  -> it is a graph of a full curve that goes top and bottom

linear -> It is a graph of a line

In the give graph f(x) is a line graph , so it is Linear

The graph g(x) is a curve that goes at the top not at the bottom. Its like a half curve. so it is an exponential

Answer:

5

Step-by-step explanation:

1. according to the condition

[tex]\frac{price \ radio1}{price \ radio2} =\frac{x}{y}[/tex]

2. when the both prices are increased the ratio is

[tex]\frac{x+20}{y+20}=\frac{5}{2}[/tex]

3. when the both prices are reduced the ratio is

[tex]\frac{x-25}{y-25} =\frac{5}{1}[/tex]

4. using the equations written in steps 2&3 it is possible to make up the system of the two equations:

[tex]\left \{ {{\frac{x+20}{y+20}=\frac{5}{2}  } \atop {\frac{x-25}{y-25}= \frac{5}{1} }} \right.[/tex]

where x=160; y=52.

5. ration x:y=5.

Get the surd by itself, then square and solve the resulting linear equation.

1. Subtract 2, then square

... √c = 25

... c = 25² = 625

2. √x = 3

... x = 3² = 9

3. √(x-2) = 4

... x -2 = 4²

... x = 16 +2 = 18 . . . . add 2

5. √(2x) = 1

... 2x = 1²

... x = 1/2 . . . . . . . divide by the coefficient of x

First, let's subtract 1 (100%) by 2/6:

1 - 2/6 = 4/6

Knowing that Conner gave his neighbor 1/4 of the remainder, we simply have to multiply 4/6 by 1/4:

4/6 * 1/4 = 4/24 = 1/6

Conner gave 1/6 of his pears to his neighbor.

Answer: it is 117 inches.

Step-by-step explanation:

1 yard= 36 inches

36 times 3= 108

1/4 of 36= 9

36 divided by 4 is 9 so 1/4 of 36 is 9.

108 + 9= 117

Answer:

The answer is 20

Step-by-step explanation:

Given that f(2)=1/5

And f(n+1)=f(n)*10

Let's start from n=2

f(2+1)=f(2)*10

f(3)=(1/5)*10

f(3)=2

Now let's take n=3

f(3+1)=f(3)*10

f(4)=2*10

f(4)=20

Answer:

d = 8t

Step-by-step explanation:

To find a correlation, you need to find what numbers correlate and how.

Lets try multiplying the t value by 8 to get the value ( as one value is 1 and the other is 8 so it would seem suitable)

1 * 8 = 8

2 * 8 = 16

Both values match up which means that to get d, you multiply t by 8.

This means that your answer is d = 8t.

18. x = y = -3

21. y was substituted into the wrong equation. The solution is (x, y) = (2, 1).

18. Adding y to the first equation transforms it to ...

... x = y

Then you can substitute for either variable in the second equation.

... 2y -5y = 9 . . . . . substitute for x

... -3y = 9 . . . . . . . . simplify

... y = -3 . . . . . . . . . divide by the coefficient of y

.. x = -3 . . . . . . . . . x and y have the same value

___

21. The first equation is being used to find an expression for y in terms of x. If you substitute that expression back into the same equation, it will tell you nothing you didn't already know. (Here, it is telling you 5 = 5.) The expression is only useful if you substitute it into a different equation. Here, it needs to be substituted into the second equation:

... Step 2: 3x -2(-2x+5) = 4 ⇒ 7x -10 = 4 . . . . . substitute for y in the second eqn

... Step 3: 7x = 14 . . . . . add 10

... Step 4: x = 2 . . . . . . . divide by 7

... Step 5: y = -2·2 +5 = 1 . . . . . find the value of y from x using the expression from step 1. Now, you know the solution is (x, y) = (2, 1).

_____

The attached graph shows the solution to the problem of 21.

Answer:

Coordinate Plane

Step-by-step explanation:

This is a plane with two axes as a frame of reference. The x-axis is a horizontal line and the y-axis is perpendicular to it (i.e., the y-axis is vertical). The intersection of the two axes is called the origin.

Answer with explanation:

≡This plane is Called→ Two Dimensional Coordinate plane or x y plane.And the given statement is true Statement.

The Plane has two axes as a frame of reference. The x-axis is a horizontal line and the y-axis is perpendicular to it (i.e., the y-axis is vertical). The intersection of the two axes is called the origin.

⇒The value of x lies from (-∞,∞) .x∈[-∞,∞]

And ⇒,the value of y lies from (-∞,∞).y∈[-∞,∞]

And the points in this plane is represented in terms of Ordered pairs that is in the form of , (x,y).

→There are four Quadrants , in this plane and description of points is as follows:

In First Quadrant , both ,x and y positive.

In Second Quadrant  ,x negative, and y positive.

In Third Quadrant  ,x negative and y Negative.

In Fourth Quadrant  ,x positive and y Negative.

Answer:

the Answer would be 17.     Hope it helped ; )

Step-by-step explanation:

Answer:

"Grows by a constant percent."

Step-by-step explanation:

5% of 500 is 25 = 525

5% of 525 is 26.25 = 551.25

5% of 551.25 is 27.56 = 578.81

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Answer:

Step-by-step explanation:

These sorts of calculations are best done with a calculator that knows statistics.

a) The z-value of the limit ofv interest is (45,000 -35,551)/(5100) ≈ 1.8743. The empirical rule tells you between 16 and 2.5% of the distribution will lie above a limit that is between 1 and 2 standard deviations. So, our calculator value of 3% is approximately correct.

b) The standard deviation of the sample mean is reduced by a factor of √75 from that of the parent distribution for a sample size of 75. Then the z-value is ...

... (38,000 - 35,441)/(5100/√75) ≈ 2559/588.90 ≈ 4.345

The probability of exceeding this valus is pretty small, about 6.95×10^-6.

A(x) = x(16 -x)

Area is the product of length and width. If the length is x, then the width will be half of the total perimeter less the two sides of length x, (32-2x)/2 = 16-x.

So, the area is ...

... A = length · width

... A(x) = x(16 -x)

_____

If you like, you can expand this to ...

... A(x) = -x² +16x

The area of a rectangular figure is calculated by multiplying the length and the width of the figure. So, the area as a function of x is: [tex]A(x) = x(16 - x)[/tex]

Given that:

[tex]P = 32[/tex] --- the perimeter of the fence

Represent

[tex]x \to[/tex] length

[tex]y \to[/tex] width

The perimeter of a rectangular fence is calculated as:

[tex]Perimeter = 2 \times (Length + Width)[/tex]

So, we have:

[tex]P= 2 \times (x+ y)[/tex]

[tex]32= 2 \times (x+ y)[/tex]

Divide both sides by 2

[tex]16= x+ y[/tex]

Make y the subject

[tex]y = 16 - x[/tex]

The area (A) of the fence is:

[tex]Area = Length \times Width[/tex]

So, we have:

[tex]A = x \times y[/tex]

Substitute [tex]y = 16 - x[/tex]

[tex]A = x \times (16 - x)[/tex]

[tex]A = x(16 - x)[/tex]

So, the area as a function of x is:

[tex]A(x) = x(16 - x)[/tex]

Read more about area and perimeters at:

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the set of point M, point N, and all the points between point M and point N

We assume you're interested in a description of line segment MN, the portion of the line containing M and N that has endpoints M and N. That description is found in "Answer:" above.

Other choices:

... all collinear points: describes line MN, not segment MN

... point M and point N: describes two points, not a line segment

... points the same distance from each: describes the line that is the perpendicular bisector of segment MN

Answer:

the set of point M, point N, and all the points between point M and point N

Step-by-step explanation: