A bag contains 10 red pens, 15 blue pens, and 20 black pens. Joseph will pull a pen from the bag.
When Joseph pulls a pen from the bag, how many outcomes are possible?

A) 45
B) 10
C) 20
D) 15

AE(X) = $23,333.33  could John expect to collect in yearly leases for the whole building in a given year.

What is  probability ?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a proposition is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

The given table is:

Number of Lease Offices :  0           1         2       3        4         5

Probability                         : 5/18     1/4     1/9    1/18     2/9      1/12

The expected probability is

Expected probability \($=\sum_{i=0}^5 x_i p\left(x_i\right)$\)

Expected probability \($=0 p(0)+1 P(1)+2 P(2)+3 P(3)+4 P(4)+5 P(5)$\)

Expected probability \($=0 \cdot\left(\frac{5}{18}\right)+1 \cdot\left(\frac{1}{4}\right)+2 \cdot\left(\frac{1}{9}\right)+3 \cdot\left(\frac{1}{18}\right)+4 \cdot\left(\frac{2}{9}\right)+5 \cdot\left(\frac{1}{12}\right)=\frac{35}{18}$\)

It is given that the yearly lease \($=\$ 12,000$\).

The yearly leases for the whole building in a given year is

Yearly leases \($=\frac{35}{18} \times 12000=23333.3333333 \approx 23333.33$\)

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Answer:

24

Step-by-step explanation:

use a calculator for these type of problems next time!

the answer to this equation would be 24x

Answer:

16/51

Step-by-step explanation:

simplify -4/7 divided by -3/4

then you will get -16/51 but you have to add the rule so its 16/51

I hope this is the correct answer

The slope of the linear model satisfies which shows that the slope of the linear model is governed by the correlation coefficient and the maximum possible value of g are 5

Correlation coefficient is the  measure of  strength of the linear relationship between two variables. That can be ranged from -1 to +1 . Correlation coefficient with the value -1 denotes the perfect negative . Coefficient with the value 1 shows a perfect positive or the direct relationship and Coefficient with the value 0 shows that there is no relationship.

When the points on a scatterplot do not show any pattern, then there is no relationship

When the points on a scatterplot shows any positive pattern, then there is a direct relationship

When the points on a scatterplot shows any negative pattern, then there is an indirect relationship

So, the slope of the linear model satisfies which shows that the slope of the linear model is governed by the correlation coefficient and the maximum possible value of g are 5

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6 ≤ 1 - 5x can be written as -5x ≤ -5, which can be further simplified to x ≥ 1.

An equation is a mathematical statement that states that two expressions are equal. It is written using an equals sign, ‘=’, to show that the two expressions being compared have the same value. Equations are used in many areas of mathematics, including algebra, calculus and geometry.

2) -6.9 < 8.1 - 1.5x can be written as 1.5x > 14.9, which can be further simplified to x > 9.93.

3) 7/9 × -2/3 > 1/6x + 3 can be written as -2/3x > 15/2, which can be further simplified to x < -10.

4) 3(x + 1) > 5x + 7 can be written as 3x + 3 > 5x + 7, which can be further simplified to x > 4.

5) 4(3 - 0.1x) ≤ 15 - 0.6x can be written as -0.4x ≤ 12, which can be further simplified to x ≥ 30.

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The measure of angle ZCBD is 90°. Therefore, the correct option is J. 90.

To find the measure of angle ZCBD, we need to examine the given information.

From the figure, we know that angle CDE is 155°.

Since the opposite angles of a rectangle are congruent, angle BCD is also 155°.

In a rectangle, the sum of the interior angles at a vertex is always 90°.

Therefore, angle CBD is 90°.

Hence, the measure of angle ZCBD is 90°.

Therefore, the correct option is J. 90.

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Answer: See explanation

Step-by-step explanation:

x=-(2-2*the square root of 6)/5, about 0.58

or

x=-(2+2*the square root of 6)/5, about -1.38

The values of the x from equation  \(5x^2+4x-4=0\) are  x = 0.5798 and -1.38.

Given that:

Equation:  \(5x^2+4x-4=0\)

To find the values of x that satisfy the equation \(5x^2+4x-4=0\), use the quadratic formula:

\(x = \dfrac{ -b \± \sqrt{b^2 - 4ac}}{ 2a}\)

Compare the equation with \(ax^2 + bx + c = 0\).

Here, a = 5, b = 4, and c = -4.

Plugging in the values to get,

\(x = \dfrac{-4 \± \sqrt{4^2 - 4 \times 5 \times (-4)}}{2 \times 5} \\x = \dfrac{-4 \± \sqrt{16 +80}}{10} \\x = \dfrac{-4 \± \sqrt{96}}{10}\\x = \dfrac{-4 \± {4\sqrt6}}{10}\)

So the solutions for x are calculates as:

Taking positive sign,

\(x = \dfrac{-4 + {4\sqrt6}}{10}\\x = \dfrac{-4 + {9.798}}{10}\\\)

x = 5.798/10

x = 0.5798

Taking negative sign,

\(x = \dfrac{-4 - {4\sqrt6}}{10}\\x = \dfrac{-4 - {9.798}}{10}\\\)

x = -13.798/10

x = -1.38

Hence, the exact solutions for the equation  \(5x^2 + 4x - 4 = 0\)  are x = 0.5798 and -1.38.

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a) The explanatory variable is price. This is because the model is predicting sales based on price (b) The response variable is sales. This is because the model is predicting the amount of sales based on the price.

The explanatory variable is the independent variable in a regression model. It is the variable that is hypothesized to cause or influence the dependent variable. In this case, the explanatory variable is price. The model predicts that sales will increase as price decreases.

Response variable

The response variable is the dependent variable in a regression model. It is the variable that is hypothesized to be caused or influenced by the independent variable. In this case, the response variable is sales. The model predicts that sales will decrease as price increases.

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Since the right side is 0, so equate each factor by 0 and find the values of x

Put 3x - 14 = 0 and 8x + 13 = 0

3x - 14 = 0

Add 14 to both sides

3x - 14 + 14 = 0 + 14

3x = 14

Divide both sides by 3

This is the first value of x

Let us do the same with other factor

8x + 13 = 0

Subtract 13 from both sides

8x + 13 - 13 = 0 - 13

8x = - 13

Divide both sides by 8

This is the second value of x

So the two values of x are

Answer:

Step-by-step explanation:

To find the normal plane and osculating plane, we first need to find the required derivatives.

x = 5t, y = t^2, z = t^3

dx/dt = 5, dy/dt = 2t, dz/dt = 3t^2

So, the velocity vector v and acceleration vector a are:

v = <5, 2t, 3t^2>

a = <0, 2, 6t>

Now, let's evaluate them at t = 1 since the point (5, 1, 1) is given.

v(1) = <5, 2, 3>

a(1) = <0, 2, 6>

The normal vector N is the unit vector in the direction of a:

N = a/|a| = <0, 1/√10, 3/√10>

Using the point-normal form of the equation for a plane:

normal plane equation = 0(x-5) + 1/√10(y-1) + 3/√10(z-1) = 0

Simplifying this equation we get:

5x + 2y + 3z = 30

The osculating plane can be found using the formula:

osculating plane equation = r(t) · [(r(t) x r''(t))] = 0

where r(t) is the position vector, and x is the cross product.

At t = 1, the position vector r(1) is <5, 1, 1>, v(1) is <5, 2, 3>, and a(1) is <0, 2, 6>.

r(1) x v(1) = <-1, 22, -5>

r(1) x a(1) = <12, -6, -10>

v(1) x a(1) = <-12, 0, 10>

Substituting these values into the formula, we get:

osculating plane equation = (x-5, y-1, z-1) · <12, -6, -10> = 0

Simplifying this equation we get:

3x - 15y + 5z = 5

Therefore, the equations for the normal plane and osculating plane at (5, 1, 1) are:

(a) 5x + 2y + 3z = 30

(b) 3x - 15y + 5z = 5

Answer:

See Explanation

Step-by-step explanation:

Given

Students = 24

Musical Instrument and Sport = 6

Neither = 3

Sport = 14

Required

Complete the two-way frequency table

-------------------------------------------------------- Plays sport || Does not play sport

Plays a musical instrument ---------------------6--------------------------------------

Does not play a musical instrument -------------------------------------3-----------

Total ---------------------------------------------------- 14 ---------------------------------------

To solve this, we'll make use of the following naming rules

A represent students that plays musical instrument; A = 6

B represent students that do not play musical instrument

C represent students that plays sport

D represent students that do not play sport; D = 3

Considering the first column [Plays a sport] and taking note of the naming rules;

\(A + B = 14\)

Substitute 6 for A

\(6 + B = 14\)

Solve for B

\(B = 14 - 6\)

\(B = 8\)

Also, given that there are 24 students in the class and 14 of them play sport; this implies that 10 do not play sport

Considering the second column [Does not play a sport]

\(C + D = 10\)

Substitute 3 for D

\(C + 3 = 10\)

Solve for C

\(C = 10 - 3\)

\(C = 7\)

Hence, the complete table is:

-------------------------------------------------------- Plays sport || Does not play sport

Plays a musical instrument ---------------------6--------------------------7----------

Does not play a musical instrument ---------8--------------------------3---------

Total ---------------------------------------------------- 14 -----------------------10---------

Answer:

1. 22

2. 8

3. 31

4. 20

5. 38

6. 22

Answer:

x=-5

Step-by-step explanation:

To solve the equation, you have to plug in n(-5) into x

4(-5)-5=-25

\(2 - \sqrt{1} \\ = 2 - 1 \\ = 1\)

Answer:

16/1071

Step-by-step explanation:

The average is the given by summing all the numbers and deciding by how many numbers you have

So, the answer is given by:

(-1/12 + 4/17 - 3/28) / 3 which yields to 16/1071

Given:

defective units = 29.1

total production = 9,700

Hence:

substituting values in the formula:

ANSWER

0.3 percent of the production is defective.

Answer:

We would predict 177 girls

Step-by-step explanation:

We can set up a proportion

\(\frac{Girls}{Boys}\) = \(\frac{Girls}{Boys}\)  Put in the number that I know and solve for the number that I do not know.

\(\frac{3}{4}\) = \(\frac{g}{236}\)  I can cross multiply to solve for x

4g = 3(236)

4g = 708  Divide both sides by 4

g = 177

Answer:D Below the Dashed line

Step-by-step explanation:

Just took the test

Answer:

Below the dashed line so the answer is D

Step-by-step explanation:

just finished taking the quiz with this same answer!!

Answer:

x = 18.0

Step-by-step explanation:

You must memorize the definitions of the trig functions and then these types of problems are easy.

In your problem,  sin of an angle = opposite side/hypotenuse

So,  sin 51 = 14/x

      x sin 51  = 14

            x = 14/sin 51 = 18.0

Answer:

The correct answer is the last one.

Step-by-step explanation:

Variable data is any kind of information gathered that can be made into a chart or graph representing what was collected. In other words, the data collected must vary.

The first, second, and third answers cannot be made into a chart/graph as it would be a singular number, and not provide varying data (which is required to produce a graph/chart).

The last answer would be correct as one can create a chart as the data collected from that question would vary. For example, five family members could be born in July, six in August, and ten in October. The variable that is "varying" would be these months.

Hope this helps!

the answer is D.

here is proof

The length οf οne side οf the square is √17 and the area οf the square is 17 square units.

Cοοrdinate geοmetry is a branch οf mathematics that uses algebraic equatiοns tο describe the relatiοnships between pοints and shapes in a plane. It invοlves using the Cartesian cοοrdinate system tο represent pοints with οrdered pairs οf numbers.

We can start by finding the distance between twο οppοsite vertices οf the square using the distance fοrmula:

d = √[(x2 - x1)² + (y2 - y1)²]

Let's find the distance between the pοints (5, 4) and (1, 5), which are οppοsite vertices οf the square:

d = √[(1 - 5)² + (5 - 4)²] = √[16 + 1] = √17

Sο the length οf οne side οf the square is √17.

Tο find the area οf the square, we can use the fοrmula:

area = side²

Substituting the value οf the side that we fοund abοve, we get:

area = (√17)² = 17

Therefοre, the area οf the square is 17 square units.

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Answer:

C

Step-by-step explanation:

multiply by 2 to be 2x-6

Answer:

x=8//

Step-by-step explanation:

2(x- 3)

or,2x-6

or,X=6+2

hence,X=8//

Answer:

yes

Step-by-step explanation: yes yes yes ye sy ey eys eys yes

A line segment is also a line but a line with finite length and fixed endpoints. The statements which are true from the given statements are A and C.

A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely.

The given statements can be written as,

A.) If a line segment is divided into smaller adjacent segments, the sum of the lengths of the smaller segments is equal to the length of the original segment.

The given statement is true.

B.) Two distinct intersecting lines intersect at a single point.

The given statement is false. This is because the two intersecting lines are distinct therefore, they may be parallel to each other and intersect with a third line.

C.) If an angle is divided into smaller adjacent angles, the sum of the measures of the smaller angles is equal to the measure of the original angle.

The given statement is true.

D.) Two lines can be drawn between any two points.

The given statement is false because there can only be one and only a straight line between any two of the given points.

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Answer:

50 hours

Step-by-step explanation:

if it takes 5 hours for 2 inches to fall, then you multiply 2 by ten to get 20, you do the same thing to the other half of the equation, or five, to get 50 hours.

C: 3 points.(please see the attached image.)

Use the vertical line test, three points are overlapping making it not a function. So if 3 points are removed, it can be a function.

Hence, 3 points need to be removed from this graph.

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(a)The levels of production that will yield a profit of $359,400 are approximately 292.36 and 651.64 units. (b)So, it is possible to make a profit of more than $359,400.

(a) To determine the level(s) of production that will yield a profit of $359,400, substitute P=359400 in the equation.6400x−18x^2−400 = 359400Adding 400 to both sides:6400x − 18x² = 359800

Dividing both sides by -2:9x² − 3200x + 179700 = 0

Applying the quadratic formula:

x = (-(-3200) ± √((-3200)² - 4(9)(179700))))/(2(9))

= (3200 ± √(10240000 - 6464400))/18

= (3200 ± √(3785600))/18

= (3200 ± 1946.55)/18x

= 292.36 or 651.64

Thus, the levels of production that will yield a profit of $359,400 are approximately 292.36 and 651.64 units.

(b) To determine if a profit of more than $359,400 can be made, we need to determine the maximum profit by completing the square, and comparing it to $359,400.P=6400x−18x^2−400

Completing the square: P= -18(x - 88.89)² + 710937.2

Maximum profit is $710,937.20, which is more than $359,400.

So, it is possible to make a profit of more than $359,400.

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The answer that correctly represents the sequence described is:

-15, -9, -3, 3, 9, ...

In mathematics, a sequence is an ordered list of numbers, called terms, that follow a certain pattern or rule. The terms of a sequence are usually indexed by natural numbers, starting from some fixed initial value.

A sequence can be either finite or infinite. A finite sequence has a fixed number of terms, while an infinite sequence goes on indefinitely. Sequences can be defined in many ways, such as explicitly giving the formula for each term or defining a recursive formula that describes how to calculate each term from the previous ones.

The sequence described in the problem can be generated by starting with -15 and repeatedly adding 6 to the previous term. So the first few terms of the sequence are:

-15, -15 + 6 = -9, -9 + 6 = -3, -3 + 6 = 3, 3 + 6 = 9, ...

In general, we can write the nth term of the sequence as:

aₙ = aₙ₋₁ + 6

where a₁ = -15 is the first term.

Using this recursive formula, we can find any term in the sequence by adding 6 to the previous term.

Therefore, the answer that correctly represents the sequence described is:

-15, -9, -3, 3, 9, ...

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The value of a Chi-Square goodness-of-fit test at a 5% significance level is 13.45

We need to perform a Chi-Square goodness-of-fit test at a 5% significance level.

First we need to calculate the expected count

expected value = ∑(x)/n

= (40 + 33 + 35 + 32 + 60)/5

= 200/5

= 40

Now we need tocalculate the test statistic value

Observed  expected  O - E    (O - E)^t/E       %

40                40             0            0                   0

33                40             -7          1.225          9.11

35                40             -5          0.625         4.65

32                40             -8         1.6                11.90

60                40             20        10                 74.35

Chi square test is 13.45

Therefore, the value of test statistics is 13.45.

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Answer:

Median = 116

Quartiles and median can be calculated from histograms.

From the histogram, we have the following frequency table:

\(\left[\begin{array}{ccc}Score&Frequency&Cumulative\\80 - 90&2.6&2.6&90 - 100&3.4&6&100 - 110&5&11&110 - 120& 5 & 16&120 - 130&3&19&130 - 140& 3 &22 &140 - 150&1.4&23.4& 150 - 160& 1.4 &24.8 & 160 - 170 & 1.4 &26.2 & 170 - 180 & 0.6 & 26.8& 180 - 190 & 0.6 & 27.4 &190 - 200&0.6&28\end{array}\right]\)

(a) The median

Calculate the median class as follows

\(\mathbf{Q_2 = \frac{1}{2}(n)}\)

This gives

\(\mathbf{Q_2 = \frac{1}{2}(28)th}\)

\(\mathbf{Q_2 =14th}\)

The 14th element belongs to 110 - 120 class

The median value is then calculated as:

\(\mathbf{Median = L + \frac{(n/2 -cf)}{f} \times h}\)

Where:

\(\mathbf{n/2 = 14}\)

\(\mathbf{L = 110}\) --- lower limit of the median class

\(\mathbf{cf =11}\) ---- cumulative frequency of the class before the cumulative frequency

\(\mathbf{f = 5}\) ---- frequency of the median class

\(\mathbf{h = 10}\) --- the class size

So, we have:

\(\mathbf{Median = 110 + \frac{14 - 11}{5} *10}\)

\(\mathbf{Median = 110 + \frac{3}{5} *10}\)

\(\mathbf{Median = 110 + 0.6 *10}\)

\(\mathbf{Median = 110 + 6}\)

\(\mathbf{Median = 116}\)

Hence, the median is 116

(b) The lower quartile

Calculate the median class as follows

\(\mathbf{Q_1 = \frac{1}{4}(n)}\)

This gives

\(\mathbf{Q_1 = \frac{1}{4}(28)th}\)

\(\mathbf{Q_1 =7th}\)

The 7th element belongs to 100 - 110 class

The median value is then calculated as:

\(\mathbf{Q_1 = L + \frac{(n/4 -cf)}{f} \times h}\)

Where:

\(\mathbf{n/4 = 7}\)

\(\mathbf{L = 100}\) --- lower limit of the lower quartile class

\(\mathbf{cf =6}\) ---- cumulative frequency of the class before the cumulative frequency

\(\mathbf{f = 5}\) ---- frequency of the median class

\(\mathbf{h = 10}\) --- the class size

So, we have:

\(\mathbf{Q_1= 100 + \frac{7 - 6}{5} *10}\)

\(\mathbf{Q_1= 100 + \frac{1}{5} *10}\)

\(\mathbf{Q_1= 100 + 0.2 *10}\)

\(\mathbf{Q_1= 100 + 2}\)

\(\mathbf{Q_1= 102}\)

Hence, the lower quartile is 102

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