A project calls for a 50 in. long board to be cut into three pieces. The first piece must be twice the length of the second piece. The third piece is 10 in. shorter than the second piece. How long must each piece be?​

The subset of real numbers √3 belong to is irrational numbers

What is a subset ?

If all of the items in a set A are also in a set B, then the sets A and B are subsets of one another. To put it another way, the set A is contained within the set B. A and B stand for the subset connection.

When all the components of Set A are also present in Set B, Set A is said to be a subset of Set B. Alternatively said, Set B contains Set A. Example: If set A contains X and Y and set B contains X, Y, and Z, then set A is a subset of set B because set B also contains X and Y.

As √3 is irrational number

∴it is a  subset of real numbers √3 belong to is irrational numbers

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The value for which test score is below 95% percent for the given mean and standard deviation on a college placement is equal to 696.

As given in the question,

Given :  95% of the test takers score are below z.

z-score is given  by,

z=(x-μ)/σ

Mean of the score 'μ' = 500

Standard deviation of the score ' σ' = 100

Z = 95%

  = 0.95

P(z<Z) = 1-0.95

           = 0.05

The value of z which corresponds to 0.05 in the table is equal to 1.96.

Substitute all the values we get,

z=(x-μ)/σ

⇒1.96 = ( x - 500 ) / 100

Multiply by 100 both the sides we get,

⇒ 196 = ( x - 500 )

⇒ x = 696

Therefore, the value for which test score is below 95% percent for the given mean and standard deviation is equal to 696.

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For the given inequality 14 - 3f > 2 the option that comes out be correct is

f < 4 i.e option 2.

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way.The majority of the time, size comparisons between two numbers on the number line are made.

Here, "Less than" and "Greater than" have new meanings.

Less-than sign is the symbol for such phrase.

14 - 3f > 2

adding 3f on both sides:

14 - 3f + 3f > 2 + 3f

14 > 2 + 3f

subtracting 2 on both sides:

14 - 2 > 2 + 3f - 2

12 > 3f

dividing 3 on both sides:

(12)/3 > (3f)/3

4 > f

which means f < 4

Therefore, option 2 is correct.

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The gross profit of the Blog Inc would be $22,370.

Gross profit is the profit of a company or an entity after subtracting all the costs that are related to manufacturing and selling its products or services. Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Given that  Sales: $50,000

Returns: $4,680

Cost of goods sold: $22,950

Therefore,

Net Sales: 50,000 - 4,680

= 45,320

We can calculate the Gross Profit;

Gross Profit = (Net Sales – Cost of Goods Sold)

                      = ($45,320- $22,950)

                       = $22,370

Hence, the gross profit would be $22,370.

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The number of yellow marbles based on the given ratio will be 78.

The ratio is the division of the two numbers.

For example, a/b, where a will be the numerator and b will be the denominator.

Proportion is the relation of a variable with another. It could be direct or inverse.

Suppose, the number of yellow marbles is Y while purple marbles are P.

As per the given,

The ratio Y/P = 13/4

Total Y + P = 102

(13/4)P + P = 102

13P + 4P = 408

17P = 408

P = 24

And, Y = 102 - 24 = 78

Hence "The number of yellow marbles based on the given ratio will be 78".

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Answer:

If you divide 32.4 by 6, then you get 5.4 as an answer

Answer:

8

Step-by-step explanation:

x^3/3-y

3^3/3-1

27/3-1

9-1

8

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The formula for 7 to the power of 4 is 74 = 7 7 7 7 = 2401.

The formula for 7 to the power of 4 is 74 = 7 7 7 7 = 2401.

To do this, you must multiply both the ordinates and the powers of ten portions of the two numbers (the mantissas).

In mathematics and algebra, multiplying seven occurrences of a given number by themselves yields the number's seventh power.

Consequently, n7 = n n n n n n.

Let's write 7 to the power of 4.0.2 to the power of 4 is 0.0016 one step at a time.

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The required linear equation that defines the dependent variable, p, in terms of the independent variable, t is p = 3t + 4.

A linear equation is a mathematical condition of the structure y=mx+b. including just a steady and a first-request (straight) term, where m is the slant and b is the y-catch. Sometimes, the above is known as a "straight condition of two factors," where y and x are the factors.

Let linear equation be p = at + b

Where a and b are constant.

On putting the values from the table,

4 = 0×a + b

b = 4

and,

7 = 1×a + b ⇒ a + b = 7

a + 4 = 7

a = 3

Then,

p = 3t + 4

Thus, required equation is  p = 3t + 4.

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Step-by-step explanation:

please see the attachment

Answer:

Step-by-step explanation:

Answer: [tex]\frac{5}{6}z+\frac{1}{2}[/tex]

Step-by-step explanation:

[tex]\frac{5}{6}z+5-\frac{1}{2}-4\\\\\frac{5}{6}z+1-\frac{1}{2}\\\\\frac{5}{6}z+\frac{1}{2}[/tex]

The simplified form of  (2x - 1)/(x² - 2x - 3 + 1)/(x - 3) is

(2x - 1)(x - 3)/(x - 1 - √3)(x - 1 + √3).

A quadratic equation is an algebraic expression in the form of variables and constants.

A quadratic equation has two roots as its degree is two.

Given, (2x - 1)/(x² - 2x - 3 + 1)/(x - 3).

=  (2x - 1)/(x² - 2x - 2)/(x - 3).

=  (2x - 1)/(x - 1 - √3)(x - 1 + √3)/(x - 3).

= (2x - 1)(x - 3)/(x - 1 - √3)(x - 1 + √3).

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Answer:4 tablespoons

Step-by-step explanation:

1 = 16 tablespoons

1/4 = 4 tablespoons

Take 16 divided by 4 = 4

Answer:

its 5

Step-by-step explanation:

Answer:

  No

Step-by-step explanation:

You want to know if there is enough information to claim ∆PQT ≅ ∆SRT by the HL theorem.

The HL theorem tells you right triangles are congruent if they have one leg (L) and the hypotenuse (H) congruent.

Here, the triangles are not indicated as being right triangles, so the HL theorem cannot be applied.

__

Additional comment

There is not enough information here to permit the triangles to be declared congruent.

For congruence by any theorem, we'd need to know that angle T is the largest angle in each triangle, a condition not supported by the evidence.

Though rarely (if ever) seen in congruence discussions, a claim of SSA congruence can only be supported if the angle (A) is opposite the longest side. When the angle is 90°, this is called the HL congruence theorem. When the angle is known to be obtuse, it will always be opposite the longest side.

When the given angle is opposite the shortest of the two given sides, there are two possible triangles that can be constructed. Hence congruence cannot be guaranteed between two triangles with the same SSA dimensions.

Answer:

450x-9000

Step-by-step explanation:

You will be 9,000 dollars in debt, and it costs 300 dollars to make but sells for 750.

750-300 = 450 (profit per desk)

The equation after the transformation is y = -5x - 1

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

Equation: 5x - y = 15

Make y the subject

So, we have

y = 5x + 15

The rule of reflection across the y-axis is

(x, y) = (-x, y)

So, we have the following equation

y = -5x + 15

The rule of translation by (3 -1) is

(x, y) = (x + 3, y - 1)

So, we have the following equation

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

Expand

y = -5x - 15 + 15 - 1

So, we have

y = -5x - 1

Hence, the equation is y = -5x - 1

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To graph a sequence, let a term's position number [tex]n[/tex] in the sequence be [tex]x[/tex]value.

An ordered group of numbers with a shared difference between each succeeding word is known as an arithmetic sequence. For instance, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6. An arithmetic progression is another name for an arithmetic sequence.

Starting with a number and repeatedly adding a fixed constant (d) to it is an easy technique to create a series. An arithmetic sequence is this kind of sequence.

Definition: A sequence of the form a, a + d, a + 2d, a + 3d, a + 4d, etc. is an arithmetic sequence.

The term [tex]a_{n}[/tex] is the corresponding y value

Plot the ordered pairs

Make a table then plot the ordered pairs ([tex]n, a_{n}[/tex])

Position, [tex]n[/tex]                                   Term, [tex]a_{n}[/tex]                                    ([tex]n, a_{n}[/tex])

     1                                                  -15                                        (1, -15)

     2                                                  0                                          (2, 0)

     3                                                  15                                         (3, 15)

     4                                                  30                                        (4, 30)

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Approximately, water does it hold two hours later is = 248.72 liters

Given that,

The holding tank contains 1000 liters of water

Water does it hold two hours later,

Then,

1) Integrate the function, from t =0 to t = 120 minutes to obtain the number of liters pumped out in the entire interval, and

2) Substract the result from the initial content of the tank (1000 liters).

So

We can write,

Let us assume,

Integral of (6 - 6 [tex]e^{-0.13t}[/tex] ) dt  ]from t =0 to t = 120 min

= 6t + 6 [tex]e^{-0.13t}[/tex] / 0.13

= 6t + 46.1538 6 [tex]e^{-0.13t}[/tex] ] from t =0 to t = 120 min

= 6*120 + 46.1538 e^(-0.13*120) - 0 - 46.1538

= 720 + 46.1538 (1.678) - 46.1538  

= 720 + 77.44 - 46.1538 liters

= 751.28 liters

2) If the holding tank contains 1000 liters of water,

1000 liters - 751.28 liters = 248.72 liters

Therefore,

Approximately, water does it hold two hours later is = 248.72 liters

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Answer:

x = 11

Step-by-step explanation:

8(x-3) - 4x = 20

8x - 24 - 4x = 20

4x = 44

x = 11

Answer:

x=11

Step-by-step explanation:

8(x-3)-4x=20

8(x)+8(-3)-4x=20

8x-24-4x=20

4x-24=20

   +24. +24

4x=44

/x.  /x

x=11

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A right circular cylinder with the largest volume that can fit within a sphere with a 10 cm radius will have a maximum radius of 8.165 cm and a maximum height of 11.55 cm. Additionally, the largest volume is 2417.82 cm³.

A cylinder is a three-dimensional solid in mathematics that maintains, at a given distance, two parallel bases connected by a curving surface. These bases often have a circular form (like a circle), and a line segment known as the axis connects the centers of the two bases. The height of the cylinder is "h," while the radius of the cylinder is "r," measuring the distance from the axis to the outside surface.

Here,

radius=10 cm

r²+h²/4=10²

r²=10²-h²/4

volume=πr²h

=π(10²-h²/4).h

V=π(10²h-h³/4)

dV/dh=π(10²-3h²/4)

dV/dh=0

10²=3h²/4

10²*2²/3=h²

20/√3=h

h=11.55 cm

r²=10²-h²/4

=10²-(10²*2²/3)/4

r²=(100-400/12)

r²=100-33.33

r²=66.67

r=√66.67

r=8.165 cm

volume=πr²h

=3.14*8.165*8.165*11.55

volume=2417.82 cm³

The dimensions of a right circular cylinder of maximum volume that can be inscribed in a sphere of radius 10 cm will be 8.165 cm radius and 11.55 cm height. Also the maximum volume is 2417.82 cm³.

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Step-by-step explanation:

When Mr Norman turns 58, he will be two years older than twice the age his daughter will turn in January. How old is Nicole now?

equation: 58 = 2d + 2

58 = 2d + 2

subtract 2 from both sides:

56 = 2d

divide both sides by 2:

d = 28 , so his daughter is 28 years old.

The required transformations would carry reflection over the y-axis of the triangle in the given figure.

A point is transformed when it is moved from where it was originally to a new location. Translation, rotation, reflection, and dilation are examples of different transformations.

The figure is given in the question,

According to the given graph, the required transformations would be as:

In the above illustration, the needed transformations would convey reflection over the y-axis of the triangle.

Thus, the required transformations would carry reflection over the y-axis of the triangle in the given figure.

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The ordered pair that describes the location of M' is (-5, -1)

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

Point M = (5, -1)

This point can be represented as

(x, y) = (5, -1)

Also, from the question, we have the transformation to be:

Point M is reflected over the y axis

Mathematically, this can be expressed as

(x, y) = (-x, y)

So, we have

Point M' = (-5, -1)

Hence, the image is (-5, -1)

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Answer: Foot

Step-by-step explanation:

The point of intersection is called the foot of the perpendicular. I remember learning this in my Math class!

Answer:

  $13.60

Step-by-step explanation:

You want to evaluate the rental cost function C(x) = 12.00 +0.08x for x = 20.

Put the value for x where x is in the cost function and do the arithmetic.

  C(x) = 12.00 +0.08x

  C(20) = 12.00 +0.08·20 = 12.00 +1.60

  C(20) = 13.60

The total rental cost if Josh drives 20 miles is $13.60.

For the given modeled of equation ý = 0.66x + 33.3 the interpretation of the residual is given option  D. 1.3 The regression line underpredicts the students class average.

As given in the question,

Equation to represents the grade of a students based on class attendance is given by :

ý = 0.66x + 33.3

Where ý is the grade of students in form of percentage.

And 'x' is the students attendance

Actual percentage = 94% when x = 90

Predicted percentage is,

ý = 0.66(90) + 33.3

  = 92.7%

Residual = Actual  - Predicted

              = 94% - 92.7%

               = 1.3

Actual > Predicted

Therefore, from the given equation the interpretation of the residual is given by Option D. 1.3 student's class average was underpredicted by the regression line.

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Answer:

DDDDDDDDDD

Step-by-step explanation:

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