A box contains 3 plain pencils and 9 pens. A second box contains 9 color pencils and I crayon. One item from each box is chosen at random. What is the
probability that a pen from the first box and a crayon from the second box are selected?
Write your answer as a fraction in simplest form.

Answer:

A. 13

Step-by-step explanation:

What we are given....

If complementary angles add up to equal 90° and ∠A and ∠B are complementary to each other

Then 26 + x + 38 + x = 90

                       ^ ( Note that we just created an equation that we can use to                              solve for x )

Now its just basic algebra

26 + x + 38 + x = 90

step 1 combine like terms

26 + 38 = 64

x + x = 2x

we now have 64 + 2x = 90

step 2 subtract 64 from each side

64 - 64 cancels out

90 - 64 = 26

we now have 26 = 2x

step 3 divide each side by 2

26 / 2 = 13

2x / 2 = x

we're left with x = 13

The value x form the given complementary angles is 13°.

Given that, m∠A = 26° + x and m∠B = 38° + x.

Two angles are said to be complementary angles if they add up to 90 degrees. In other words, when complementary angles are put together, they form a right angle (90 degrees).

Here, m∠A + m∠B =90°

⇒ 26° + x+38° + x =90°

⇒ 2x+64° =90°

⇒ 2x =90°-64°

⇒ 2x =26°

⇒ x = 13°

Therefore, the value x form the given complementary angles is 13°.

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Answer:

(-infinity,+infinity)

Step-by-step explanation:

Any real value of x can be defined with a unique output in this function.

The side of  the initial cube is 42 cm.

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

Rick melted a cube and made a cone with it.

The amount of melted liquid left after making the cone was 49 cm

6/7 of the melted liquid was used in making the cone

We need to find the side of the initial cube.

Cube =a³

Le us the whole liquid be 1.

6/7 of the melted liquid was used in making the cone

1/6/7=7/6 is the left out liquid after making cone.

7/6x=49

x=42 cm

Hence, the side of  the initial cube is 42 cm.

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The expression is factorized to give (x + 7) and (x + 7)

Factorization described a mathematical methods that consists of writing a number or mathematical object as a product of several other factors that are mostly simpler or smaller objects of the same kind.

Given the quadratic equation;

x² + 14x +49

Find the pair factors of 49 that sum up to 14, the numbers are 7 and 7

Now, substitute the numbers in the expression

x² + 7x + 7x + 49

Make into two expressions, we have;

(x² + 7x) + (7x + 49)

factor out the common terms, we get;

x(x + 7)+ 7(x + 7)

Then, we have;

(x + 7)

(x + 7)

Hence, the factorized form is (x + 7) and (x + 7)

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The angle of elevation of the fly's flight path is approximately 57.74 degrees.

In a right triangle, the hypotenuse is the side opposite the right angle. It is always the longest side of the triangle and is the side opposite to the 90 degrees angle. It is also the side that forms the "hypotenuse" of the right triangle.

The Pythagorean theorem is a fundamental result in Euclidean geometry that states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. It can be written as c^2 = a^2 + b^2, where a and b are the legs of the triangle and c is the hypotenuse. This theorem can be used to find the length of the hypotenuse of a right triangle when the lengths of the other two sides are known.

Let's call the angle we're trying to find "theta". The horizontal distance is 30 feet, the vertical distance is 32 feet and the height is 9 feet.

Using pythagorean theorem:

$c^2 = a^2 + b^2$

$c = \sqrt{30^2 + 32^2}$ = $\sqrt{900 + 1024}$ = $\sqrt{1924}$

Now we can use the tangent function:

$\tan(\theta) = \frac{opposite}{adjacent} = \frac{32}{30}$

Now we can find the angle, theta, by using the inverse tangent function:

$\theta = \tan^{-1}(\frac{32}{30})$

The angle of elevation of the fly's flight path is approximately 57.74 degrees.

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Answer:

c=66°

Step-by-step explanation:

a=51°

51+63=114°

180-114°= 66°

Answer:

66

Step-by-step explanation:

a° = 51° (corresponding angles)

a = 51

a° + c° + 63° = 180° (interior angle sum postulate of a triangle)

51° + c° + 63° = 180°

c° + 114° = 180°

c° = 180° - 114°

c° = 66°

c = 66

Answer:

the value of x would end up being 25

Answer: Both Rick and Jenny could be correct because we do not know what "x" is.

Step-by-step explanation:

The purpose of the variable "x" is to substitute it for an unknown number. Since we do not know what "x" is we can not solve the equation. We can only add like terms.

I hope this helps :)

Answer: To solve a quadratic equation of the form ax^2 + bx + c = 0, there are several steps that Inga could use. Here are three options:

She could complete the square to rewrite the equation in the form (x + p)^2 = q.

She could use the quadratic formula: x = (-b +/- √(b^2 - 4ac)) / (2a).

She could factor the equation to rewrite it in the form (x + r)(x + s) = 0.

Option 1: Completing the square

To complete the square, Inga could add and subtract (b/2)^2 to the equation to get:

a(x^2 + bx + (b/2)^2) - (b/2)^2 = 0

Then, she could rewrite the equation in the form:

a(x + (b/2))^2 = (b/2)^2

Option 2: Using the quadratic formula

To use the quadratic formula, Inga could substitute the values of a, b, and c into the formula to get:

x = (-12 +/- √(12^2 - 4 * 2 * -3)) / (2 * 2)

= (-12 +/- √(144 + 24)) / 4

= (-

Step-by-step explanation:

Answer:

3750

I wish you luck in your assignments.

Answer:

a = -10

Step-by-step explanation:

33 - 4a = 73

To get a by itself, you must move 33 to the other side. To this, you must subtract it from both sides, canceling it out on the left side.

You will be left with: -4a = 73-33

Subtract 73 and 33, which will get you 40.

Now the equation is -4a = 40

To get a by itself, divide -4 into both sides. Doing this will isolate a.

The equation you will have after that is a = 40/-4.

Divide 40 by -4, which will get you -10.

Therefore, a = -10.

Therefore , the solution of the given problem of percentage comes out to be 264414 doctors were registered that year.

A% is a number that represents the percentage of 100 that it is, and it can also be stated as a decimal or a fraction. To convert a percentage to a fraction, place 100 in the denominator and the percentage number in the numerator.

Here,

"Female doctors make up 22.2% of all registered doctors," the inquiry states.

Consider the entire number of doctors who are registered as x; 22.2% of those doctors are women.

and 47,200 divided by 22.2% of x

=>22.2/100 * x = 47,200

in math

264414 doctors were registered that year, or

x = 58700* 100/22.2 x.

Therefore , the solution of the given problem of percentage comes out to be 264414 doctors were registered that year.

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Answer:

Mean: 11

Median: 10.5

Mode: 9

These two perpendicular bisectors will meet at (1, 5, 1). These are the coordinates of the triangle's circumcenter.

the triangle's circle's center. It is the point where the "perpendicular bisectors," or lines parallel to the centre of both sides, cross.

The intersection of any two perpendicular bisectors of any two triangle sides is known as the circumcenter of a triangle ABC.

The equation y=1 is the perpendicular bisector of sides B(3,0) and C(3,2). Because AB's midpoint is at 3,1 and its slope is unknown. The perpendicular bisector has zero slope. The equation for such a line is y=y1.

The equation for the perpendicular bisector of A(0,0) and B is also x=1.5 (3,0). The reason is that AB has a midpoint of zero slope and (1.5,0). The perpendicular bisector's slope won't be clearly defined. The equation for such a line is x=x1.

These two perpendicular bisectors will meet at (1, 5, 1). These are the coordinates of the triangle's circumcenter.

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Answer:

350 is 87.5% of 400

350/400 = 87.5%

Answer:

Your answer is 1

Step-by-step explanation:

3² = 9 is the only possible solution.

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{x^2=9}[/tex]

[tex]\large\text{TAKE the SQUARE ROOT}[/tex]

[tex]\mathsf{x =\pm \sqrt{9}}[/tex]

[tex]\large\text{REMEMBER this symbol }\mathsf{\pm}\large\text{ means plus or minus}[/tex]

[tex]\mathsf{ - \sqrt{9} = \boxed{\bf -3}}[/tex]

[tex]\mathsf{\sqrt{9}=\boxed{\bf 3}}[/tex]

[tex]\large\text{OR YOU COULD SAY THIS TO MAKE THIS SIMPLER TO}\\\large\text{SOLVE}\downarrow[/tex]

[tex]\large\text{-3}\mathsf{^2= \boxed{\bf -9}}[/tex]

[tex]\large\text{3}\mathsf{^2}\large\text{= \boxed{\bf 9}}[/tex]

[tex]\boxed{\boxed{\large\textsf{Therefore, your answer: \huge \bf x = -3 or x = 3 }}}\huge\checkmark[/tex]

[tex]\large\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

See attachment for graph

Step-by-step explanation:

Given

[tex](x_1,y_1) = (1,-9)[/tex] -- point

[tex]x = -3[/tex] --- slope

Required

Plot the graph

First, we determine the equatio using:

[tex]y = m(x - x_1) + y_1[/tex]

This gives:

[tex]y = -3*(x - 1) -9[/tex]

Open bracket

[tex]y = -3x + 3 -9[/tex]

[tex]y = -3x -6[/tex]

See attachment for graph

Answer:

31 hecause the èattern is adding 3

Step-by-step explanation:

9514 1404 393

Answer:

  T, F, F, T

Step-by-step explanation:

No irrational numbers are integers.

All whole numbers are irrational numbers.

Some whole numbers are not rational numbers.

Some rational numbers are not whole numbers.

Answer:

Step-by-step explanation:

Volume of a cone:

We have:

Substitute values and solve for h:

None of the choices is correct

The following is the proper response to this problem's inequality. The relationship between negative one fifth and negative two thirds is higher than or equal when y is bigger than or equal to three tenths.

In mathematics, an inequality is a link between two expressions or values that is not equal. Thus, inequality arises as a result of imbalance. An inequality in mathematics describes the connection between two values that are not equal. Many simple inequalities can be eliminated by modifying both sides until just the variables are left. However, a number of things lead to inequality: On both sides, divide or add negative values. Toggle between left and right.

Given

One fifth less is -1/5.

When a negative two thirds is added to a number, the result is -2/3x. Since the value is unknown, we refer to it as x.

The following is the sign for more than or equal inequality:

The inequality is therefore: -1/5 -2/3x.

So that it will be easier for us to isolate x:

2/3x ≥ 1/5

2x ≥ 3/5

x ≥ 3/10.

Since y is more than or equal to three tenths, the right answer for the inequality is: negative one fifth is greater than or equal to negative two thirds y.

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Answer:

1.65

Step-by-step explanation:

you said one pound is $4.40

and that how much is 3/8 of a pound

so 3/8 multiplied by 4.40

Answer:

$1.65

Step-by-step explanation:

1 pound -------------4.40

3/8 pounds------------x

cross multiplication

1x = 4.40 x (3/8) =

x = 1.65

Answer:

B'(-2, -3)

C'(7, -6)

D'(7, -1)

E'(-2, -1)

Step-by-step explanation:

When you move translate a coordinate horizontally, if it is to the left, you subtract the x value with how many units you move, and if its to the right, you add however many units you move to the x-value. and when you move vertically, if you move down, subtract the amount of units you moved from the y-value, and if you move up, add however many units you moved to the y-value.

Answer:x/6

Step-by-step explanation:

Here the value of x is not given and hence the answer to the question is

x/6

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17. The triangles can be proven congruent by the SSS theorem.

18. The triangles cannot be proven congruent by the HL theorem, as it is not known if the triangles are right triangles.

The side-side-side congruence theorem, abbreviated as SSS, means that if two triangles have three equal side lengths, then the triangles are congruent.

In item 17, we have that:

As the three triangles are equal, then the SSS theorem can be used to prove the congruence of the two triangles.

The HL theorem represents the hypotenuse and leg theorem, which means that if two right triangles share a hypotenuse measure along with a leg measure, then they are congruent.

Hence item 18 cannot be proven congruent by the HL theorem, as there is no information regarding whether the triangles are right triangles.

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B and E Thank you for asking I'm good at fractions!!

Answer:

A. 1/18

Step-by-step explanation:

Answer:

Kindly check explanation

Step-by-step explanation:

Sample 1 :

Mean = (79.2 + 78.8 + 80 + 78.4 + 81) / 5 = 79.48

Range = 81 - 78.4 = 2.6

Sample 2 :

Mean = (80.5 + 78.7 + 81 + 80.4 + 80.1) / 5 = 80.14

Range = 81 - 78.7 = 2.3

Sample 3 :

Mean = (79.6 + 79.6 + 80.4 + 80.3 + 80.8) / 5 = 80.14

Range = 80.8 - 79.6 = 1.2

Sample 4 :

Mean =(78.9 + 79.4 + 79.7 + 79.4 + 80.6)/5 = 79.6

Range = 80.6 - 78.9 = 1.7

Sample 5 :

Mean = (80.5 + 79.6 + 80.4 + 80.8 + 78.8)/5 = 80.02

Range = 80.8 - 78.8 = 2

Sample 6 :

Mean =(79.7 + 80.6 + 80.5 + 80 + 81.1)/5 = 80.38

Range = 81.1 - 79.7 = 1.4

Xbar = mean of the means

Xbar = (79.48+80.14+80.14+79.6+80.02+80.38) / 6 = 79.96

Rbar = Mean of the sample ranges

Rbar = (2.6 + 2.3 + 1.2 + 1.7 + 2 + 1.4) / 6 = 1.87

n =5 ;D4 = 2.11 ; D3 = 0

From table, D4 = 2.11 ; D3 = 0

Range chart :

Upper Control limit, UCL = D4 * Rbar ; 2.11*1.87 = 3.9457 = 3.95

Lower Control limit, LCL = D3 * Rbar ; 0*1.87 = 0

Mean chart :

Xbar ± A2 * Rbar

From the table :

n = 5 ; A2 = 0.58

Lower control limit(LCL) = Xbar - A2*Rbar

LCL = 79.96 - (0.58*1.87) = 78.8754 = 78.88

Upper Control Limit (UCL) = Xbar + A2*Rbar

UCL = 79.96 + (0.58*1.87) = 81.0446 = 81.04

(78.88 ; 81.04)

The value of Each sample mean falls within the mean interval, Hence, We can conclude that process is on control.

According to the table, the Range of pools sold during this period is 8.

The range in statistics for a given data set is the difference between the highest and lowest values. For example, if the given data set is {2,5,8,10,3}, then the range will be 10 – 2 = 8.

Thus, the range could also be defined as the difference between the highest observation and lowest observation. The obtained result is called the range of observation. The range in statistics represents the spread of observations.

Range = Highest Value – Lowest Value

Range = 18 – 10

Range = 8

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