4 less than three sevenths as an algebraic expression

Answer:

Answer:

a. 5177 cm³

b. 3,451 cm³

c. 67%

Step-by-step explanation:

Given:

Diameter of each ball (d) = 13 cm

Radius of the ball (r) = radius of the cylinder = ½(13) = 6.5 cm

Height of the cylinder (h) = the sum of the diameters of the 3 balls = 3(13) = 39 cm

a. Volume of cylinder = πr²h

Plug in the values

Volume of cylinder = π*6.5²*39 = 5176.56 ≈ 5177 cm³

b. Total volume of the three balls = 3(volume of 1 ball) = 3(volume of sphere) = 3(⁴/3πr³)

Plug in the value

Total volume of the 3 balls = 3(⁴/3*π*6.5³) = 3(1150.35) = 3,451.05 ≈ 3,451 cm³

c. % of volume of the container occupied by the 3 balls = total volume of the three balls / volume of cylinder × 100

Plug in the values

= 3,451/5177 × 100

= 66.6602279

≈ 67%

Precipitation (inches), 2.08, 1.98, 2.64, 3.29; Snowfall (inches), 17.6, 14.2, 11.7, 3.4; The Ithaca Climate Page.

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Answer:

Rectangle and triangle

Answer: it depends on the number you took

Step-by-step explanation:

Answer:

y=4x-12, y=-0.5x-5, y=7x, y=-4x+10

Step-by-step explanation:

The last value is the y intercept in slope intercept equations. If there is nothing other than mx, then the y intercept is 0

Answer: 1/b^5 (D)

Step-by-step explanation:

Is this a UTHS course I'm seeing?

Answer:

32 is 32% of 100

Step-by-step explanation:

Answer: 100

Step-by-step explanation: 32 is 32% of 100

Answer:

50 rabbits

Step-by-step explanation:

?/2  =    400/100

multiply 2 by 400

2 times 400 = 800

now, divide it by 100

800/100 = 8

every two months = 8 rabits

12 months in a year

12/ 2 equals 6

6 times 8 = 48

+the two begining rabbits

= 50 total rabbits

The best price for her to purchase ice cream is given as follows:

D. $49.60 / five gallon tub.

The best price is obtained applying the proportions in this problem, dividing the price by the volume of the cartoon/tub, in ounces.

For item a, the price per ounce is calculated as follows:

3.99/24 = $0.16625 per ounce.

The ratios for the remaining items are given as follows:

Hence the prices for items b, c and d are given as follows:

Due to the lower cost per ounce, the option D represents the best option for her to purchase ice cream.

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The solution to the equation is

x = b/a ± √(b^2/a^2) / a.

Generally, To solve the equation using the completing the square method, we first move all the terms to one side of the equation by subtracting abx and 2b² from both sides, giving us:

a²x² = abx + 2b²

Which is

a²x² - abx - 2b² = 0

Next, we need to add and subtract a term so that the left side of the equation can be written as a perfect square.

We need to find the square of half of the coefficient of the x term, which is -ab/2a.

So we add and subtract (ab/2a)^2 = (b^2/a^2) on the left side of the equation:

a²x² - abx - 2b² + (b²/a²) - (b²/a²) = 0

This gives us the left side of the equation as

(ax - b/a)² = b²/a².

We can then take the square root of both sides:

ax - b/a = ±√(b²/a²)

Finally, we can add b/a to both sides to get the solution:

x = b/a ± √(b²/a²) / a

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Answer:

the answer is seven units

The option D is correct.Because this equation holds the vertically opposite angle theorem.

Vertically Opposite Angles are holds when two lines intersect each other then the opposite angles formed due to intersection are called vertical angles or vertically opposite angles. A pair of vertically opposite angles are always equal to each other.

Vertical opposite angles that are opposite each other when two lines cross are also known as vertical angles because the two angles share the same corner. Opposite angles are also congruent angles.The equation of a vertical line is given by x = a or x = -a

Now we find

According to vertical opposite angle

x-8=40-2x

x+2x=40+8

3x=48

x=16

We can find value of x by usng vertical opposite angle.

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Answer:

310

Step-by-step explanation:

35 - 5² + (2 * 5)² * 3

Solve inside the parenthesis.

35 - 5² + 10² * 3

Solve the exponents.

35 - 25 + 100 * 3

Solve the multiplication.

35 - 25 + 300

Solve the subtraction.

10 + 300

Add.

310

Answer:

19.5º

Step-by-step explanation:

Every triangle is equal to 180º for all angles. So, you add 33.5 + 127 and subtract the sum by 180.

33.5 + 127= 160.5

180- 160.5 = 19.5

So, the angle F is 19.5º

Hope this helps !!

-Ketifa

Answer:

look at the picture I sent

Answer:

[tex] \frac{9}{10} \times 54 = \frac{9 \times 54}{10} = \frac{486}{10} = 48 \frac{6}{10} = \frac{243}{5} [/tex]

The length of the diagonal of the rectangular tennis court is given as follows:

26.4 meters.

The tennis court is rectangular, meaning that the diagonal is the hypotenuse of a right triangle, in which the sides are the length and the width.

Applying the Pythagorean Theorem, the diagonal length can be obtained as follows:

d² = 24² + 11²

d² = 697

[tex]d = \sqrt{697}[/tex]

d = 26.4 m.

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Answer:

60

Step-by-step explanation:

40%=0.40

0.4x=24

x=24/0.4

x=60

Answer:

The 92.7% confidence interval for the expected amount of garbage per bin for all bins in the city is between 48.135 pounds and 50.685 pounds. The lower limit is 48.135 pounds.

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 46 - 1 = 45

92.7% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 45 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.927}{2} = 0.9635[/tex]. So we have T = 2.1437

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 2.1437\frac{3.99}{\sqrt{45}} = 1.275[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 49.41 - 1.275 = 48.135 pounds

The upper end of the interval is the sample mean added to M. So it is 49.41 + 1.275 = 50.685 pounds.

The 92.7% confidence interval for the expected amount of garbage per bin for all bins in the city is between 48.135 pounds and 50.685 pounds. The lower limit is 48.135 pounds.

The quotient is (6x + 1) and the remainder is (-7x + 1).

We know that if x = a is one of the roots of a given polynomial x - a = 0 is a factor of the given polynomial.

To confirm if x - a = 0 is a factor of a polynomial we replace f(x) with f(a) and if the remainder is zero then it is confirmed that x - a = 0 is a factor.

Given A cubic polynomial 24x³ - 14x² + 20x + 6 divided by 4x² - 3x + 5.

So, (24x³ - 14x² + 20x + 6)/(4x² - 3x + 5).

= (4x² - 3x + 5)(6x + 1) + (-7x + 1)/(4x² - 3x + 5) in rhe form N = DQ + R.

The same applies to the division of polynomials.

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The maximum allowable pipe diameter is given as : 0.501. Option B

From the question the interior diameter of the pipe is said to be 0.49

The pipe is said to have the thickness of 0.005 inches.

The exterior diameter of the pipe would be solved as 0.49 + 2 * 0.005

= 0.49 + 0.01

= 0.5

The questions said the variance in the diameter of this pipe is 0.001

Then the maximum allowable pipe diameter would be solved as: 0.001 + 0.5 = 0.501

The diameter of the pipe that is allowable is 0.501

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x

−

1

x−1?x

)

=

2

x

4

−

3

x

+

3

f(x)=2x

4

−3x+3, then what is the remainder when

f

(

x

)

f(x) is divided by

x

−

1

x−1?

The solution to the equations are

0 ∈ N is False               7/2 ∈ Q is True

√16 ∈ Q' is False          π ∈ Q' is True

3/2 ∈ I is False              -3 ∈  R is True

0 ∈ I is True                  -1 ∈ I⁺ is False

( 1 - 3 ) ∈ N is False       8/2 ∈ I is True

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number be represented as A

Now , the equation will be

a)

Let the number be A = 0

The number 0 is a whole number , rational number and an integer

0 is not a natural number

So , the equation is False

b)

Let the number be A = √16

The value of A = 4

The number 4 is a natural number , whole number , rational number and an integer

4 is not an irrational number

So , the equation is False

c)

Let the number be A = 3/2

The number 3/2 is a rational number

3/2 is not an integer

So , the equation is False

d)

Let the number be A = 0

The number 0 is a whole number , rational number and an integer

0 is an integer

So , the equation is True

e)

Let the number be A =  ( 1 - 3 )

The value of A = -2

The number -2 is a rational number and an integer

-2 is not a natural number

So , the equation is False

f)

Let the number be A = 7/2

The number 7/2 is a rational number

7/2 is a rational number

So , the equation is True

g)

Let the number be A = π

The number π  is an irrational number

π is an irrational number

So , the equation is True

h)

Let the number be A = -3

The number -3 is a real number

7/2 is a real number

So , the equation is True

i)

Let the number be A = -1

The number -1 is an integer and real number

-1 is a negative integer

So , the equation is False

j)

Let the number be A = 8/2

The value of A = 4

The number 4 is a natural , whole , integer and rational number

4 is an integer

So , the equation is True

Hence , the equations are solved

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Answer: 33428.15.

Step-by-step explanation: