Noel throws a four-sided dice numbered 1, 3, 5 and 7 and a four-sided dice numbered
-1, -2, -3 and -4 at the same time and multiplies the scores.
The sample space diagram below shows all the possible outcomes.
1 3 5 7
-1 -1 -3 -5 -7
-2 -2 -6
-10 -14
-3 -3 -9 -15 -21
-4 -4 -12 -20 -28
Find the probability that Noel gets a number equal to -2.

The surface area of the pyramid can be calculated by adding the area of the base to four times the area of each triangular face.

To calculate the surface area of a square pyramid, we need to consider its base and triangular faces. The base of the pyramid is a square, so its area is determined by multiplying the length of one side (s) by itself (s^2).

The surface area also includes the sum of the areas of the four triangular faces. Each triangular face can be divided into two congruent right triangles. The slant height of the pyramid (l) is the height of these right triangles. Using the formula for the area of a triangle (0.5 × base × height), we can calculate the area of each triangular face as (0.5 × s × l). Therefore, the total surface area of the square pyramid is given by the equation: Surface Area = s^2 + 4 × (0.5 × s × l).

Learn more about pyramid

brainly.com/question/17615619

#SPJ11

Answer:

C

Step-by-step explanation:

Average rate = page/hour

2 hours and 40 minutes into hours is 2.67 hours.

Average rate = 96/2.67

Average rate = 36

Answer:

C. 36

Step-by-step explanation:

\(time \: in \: hours \\ = 2 + \frac{40}{60} \\ \\ = 2 + \frac{2}{3} \\ \\ = \frac{8}{3} \: hrs \\ \\ rate \: of \: reading = \frac{96}{ \frac{8}{3}} \\ \\ = \frac{96 \times 3}{8} \\ \\ = 12 \times 3 \\ \\ = 36 \: pages \: per \: hour\)

Answer:

x=18,y=12

Step-by-step explanation:

Every line equals its other side

Answer:

Chandelier 6ll you multiple 6 x2 you will get 12

Given:

The relation is

\(M = \{ (15k+9, 4), (3\cdot (4k-1), 6) \}\)

To find:

The value of k for which the relation is not a function.

Solution:

A relation is a function if their exist a unique output or y value for each input or x values.

A relation is not a function if it has two y-values for single x value.

So, the given relation is not a function if x-coordinates of both ordered pairs are equal.

\(15k+9=3\cdot (4k-1)\)

\(15k+9=12k-3\)

Isolate variable terms.

\(15k-12k=-9-3\)

\(3k=-12\)

Divide both sides by 3.

\(k=-4\)

Therefore, the given relation is not a function for k=-4.

Answer:

A: Adjacent angles

Answer:

A. adjacent

Step-by-step explanation:

The system of linear equations 6x - 2y = 8 and 12x - ky = 5 does not have a solution if and only if k = 12. This means that when k takes the value of 12, the system of equations becomes inconsistent and there is no set of values for x and y that simultaneously satisfy both equations.

In the given system, the coefficient of y in the second equation is directly related to the condition for a solution. When k is equal to 12, the second equation becomes 12x - 12y = 5, which can be simplified to 6x - 6y = 5/2. Comparing this equation to the first equation 6x - 2y = 8, we can see that the coefficients of x and y are not proportional. As a result, the two lines represented by the equations are parallel and never intersect, leading to no common solution. Therefore, when k is equal to 12, the system does not have a solution. For any other value of k, a unique solution or an infinite number of solutions may exist.

Learn more about Linear equation here : brainly.com/question/32634451

#SPJ11

According to the US Geological Survey (USGS), the total copper contained in world reserves as of 2018 was estimated to be approximately 830 million metric tons.

The USGS gathers and analyzes data on global mineral reserves, including copper. In their 2018 report, they estimated that the total identified copper resources worldwide were approximately 2.2 billion metric tons. However, not all of these resources are economically recoverable. To determine the amount of copper in world reserves, the USGS considers factors such as geology, mining methods, and economic viability.

Based on their analysis, the USGS estimated that around 38% of the identified copper resources were classified as reserves in 2018. Therefore, the calculated amount of copper in world reserves was approximately 830 million metric tons (2.2 billion metric tons x 38%).

In 2018, the USGS estimated that the world's copper reserves contained approximately 830 million metric tons. It is important to note that these estimates are subject to change as new discoveries are made, mining technologies evolve, and economic factors fluctuate. The USGS plays a crucial role in providing reliable and up-to-date information on global mineral resources to aid in resource planning and decision-making.

To know more about global mineral reserves, visit;
https://brainly.com/question/2109497
#SPJ11

1. The x-intercept of a function is the point where the line crosses the x-axis. At this point, the y-coordinate is equal to zero.

You can identify the point from the graph or calculate the coordinates by replacing the equation of the linear function with y=0 and determine the corresponding value of x.

-Looking at the graph, the red line, that corresponds to the equation y=x-3, crosses the x-axis at point (3,0)

-Replacing the equation of the function by y=0:

The x-intercept has coordinates at (3,0)

2. The y-coordinate is the point where the red line crosses the y-axis. At this point, the x-coordinate is equal to zero.

You can identify this point directly from the graph, or calculate it by replacing the equation of the line with x=0 and calculate the corresponding value of y.

-Looking at the graph, the red line crosses the y-axis at the point (0,-3)

-Replace the equation with x=0

The y-intercept is (0,-3)

3. The equation y=4x+2 is represented in the graph by the blue line

As before, you have to identify the point where the line crosses the x-axis.

-From the graph:

-Replace the equation with y=0 and calculate the corresponding value of x:

The x-intercept is (-1/2,0)

4. The y-intercept is the point where the blue line crosses the y-axis.

-You can identify it from the graph:

-Or replace the equation with x=0 and determine the corresponding value of y

The coordinates of the y-intercept are (0,2)

Answer:

2(8x+1)+2(6x-4)

28x - 6

Step-by-step explanation:

2(8x+1)+2(6x-4)

16x +2 + 12x - 8

28x - 6

An equation in the standard coordinates for images that describes an ellipse centered at the origin with a length 4 major cord parallel to the vector images and a length 2 minor axis is (x^2)/4 + (y^2) = 1.

An ellipse centered at the origin with a length 4 major chord parallel to the vector images and a length 2 minor axis can be described by the following equation in standard coordinates:

(x^2)/(a^2) + (y^2)/(b^2) = 1

"a" represents the semi-major axis, and "b" represents the semi-minor axis. Since the major chord has a length of 4, the semi-major axis (a) is half of that, or 2. Similarly, the minor axis has a length of 2, so the semi-minor axis (b) is half of that, or 1.

Substituting these values into the equation, we get:

(x^2)/(2^2) + (y^2)/(1^2) = 1

Simplifying the equation, we have:

(x^2)/4 + (y^2) = 1

Learn more about minor axis here:

https://brainly.com/question/14180045

#SPJ11

Answer:

x = 24

Step-by-step explanation:

The angles of a triangle added together equal 180⁰. Set up a simple equation to solve for x.

90⁰ + 42⁰ + (2x)⁰ = 180⁰

90 + 42 = 132

2x = 180 - 132

2x = 48

x = 24

Answer:

x = 24

Step-by-step explanation:

2x + 42 + 90 = 180

2x + 132 = 180

2x = 48

48/2 = x

x = 24

Have a nice day!

Answer:

the length of the unknown side of the right angle triangle is 1 cm

Step-by-step explanation:

The computation of the length of the unknown side of the right angle triangle is shown below:

= √9^2 - √8^2

= √81 - √64

= 9 - 8

= 1 cm

Hence, the length of the unknown side of the right angle triangle is 1 cm

Suppose a system of equations has 3 equations and 5 variables. additionally, suppose the coefficient matrix for the system has 3 pivot columns. Based on the information provided, it is consistent.

The number of pivot columns in the coefficient matrix of a system of equations determines the rank of the matrix, which is a measure of the number of linearly independent rows or columns. A system of equations is consistent if and only if the rank of the coefficient matrix is equal to the number of unknowns in the system.

In this case, the system has 3 equations and 5 variables, so it is not immediately clear if the rank of the coefficient matrix is equal to the number of unknowns. Additionally, the number of pivot columns alone is not enough to determine the consistency of the system, as there may be additional relationships between the variables that affect the rank.

So,  Based on the information provided, it is consistent.

To learn more about matrix click on,

https://brainly.com/question/28447495

#SPJ4

Answer:

13.5 cm^2

9*3 = 27

27/2=13.5

The null hypothesis would be average of psychology courses= average of biology course.

The null hypothesis is a common statistical theory that contends that there is no statistical relationship or significance between any two sets of observed data and measured phenomena for any given single observed variable.

A scientific hypothesis is a prediction of the results a researcher expects to obtain from their investigation. However, a statistical hypothesis is a prediction of what the statistician does NOT anticipate to find. It is referred to be a NULL hypothesis for this reason.

The null hypothesis in this study is that the average grades in biology and psychology courses are equal. Calculating the difference between the two samples' average grades is the first step: 78.2 - 84.4 = 6.6 The null hypothesis that the average grades in biology and psychology courses are equal is tested using this discrepancy. The p-value for this study is then determined by using a t-test: t(11) = -2.566. This indicates that the average grades in biology courses and psychology courses differ statistically significantly. The alternative hypothesis is that the average grades in psychology courses are different from the average grades in biology courses as a result of the null hypothesis being rejected.

To learn more about null hypothesis visit the link:

https://brainly.com/question/19263925

#SPJ1

The null hypothesis would be average of psychology courses= average of biology course.

What is meant by null hypothesis?

The null hypothesis is a common statistical theory that contends that there is no statistical relationship or significance between any two sets of observed data and measured phenomena for any given single observed variable.

Why is it called null hypothesis?
A scientific hypothesis is a prediction of the results a researcher expects to obtain from their investigation. However, a statistical hypothesis is a prediction of what the statistician does NOT anticipate to find. It is referred to be a NULL hypothesis for this reason.

The null hypothesis in this study is that the average grades in biology and psychology courses are equal. Calculating the difference between the two samples' average grades is the first step: 78.2 - 84.4 = 6.6 The null hypothesis that the average grades in biology and psychology courses are equal is tested using this discrepancy. The p-value for this study is then determined by using a t-test: t(11) = -2.566. This indicates that the average grades in biology courses and psychology courses differ statistically significantly. The alternative hypothesis is that the average grades in psychology courses are different from the average grades in biology courses as a result of the null hypothesis being rejected.

To learn more about null hypothesis visit the link:
https://brainly.com/question/25263462
#SPJ1

Answer:

x + y

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

x + (x - y) + y + (y - x)

Step 2: Simplify

Step-by-step explanation:

\(area \: ofa \: circle = \pi {r}^{2} \)

\(\pi {r}^{2} = \frac{22}{7} \times {r}^{2} \\ 153.86 = \frac{22}{7 } \times {r}^{2} \: \: \: \: \: \: \\ {r}^{2} = \frac{153.86 \times 7}{22} \\ {r}^{2} = \frac{1,077.02}{22}\\ r = \sqrt{48.95} \\ = 6.99\)

So let's take r as 7

\(circumference \: of \: a \: circle = 2\pi r\)

\(2\pi r = 2 \times \frac{22}{7} \)

= 2× 22/7 × 7

= 44

Profitability index is 1.387. Thus, the correct option is (c) 1.387.

The formula for calculating the profitability index is:

P.I = PV of Future Cash Flows / Initial Investment

Where,

P.I is the profitability index

PV is the present value of future cash flows

The initial investment in the project is $30 million. The cash flow at the end of the first year is $2.85 million.

The present value of cash flows can be calculated using the formula:

PV = CF / (1 + r)ⁿ

Where,

PV is the present value of cash flows

CF is the cash flow in the given period

r is the discount rate

n is the number of periods

For the first-year cash flow, n = 1, CF = $2.85 million, and r = 11%.

Substituting the values, we get:

PV = 2.85 / (1 + 0.11)¹ = $2.56 million

To calculate the present value of all future cash flows, we can use the formula:

PV = CF / (r - g)

Where,

PV is the present value of cash flows

CF is the cash flow in the given period

r is the discount rate

g is the constant growth rate

For the subsequent years, CF = $2.85 million, r = 11%, and g = 3.85%.

Substituting the values, we get:

PV = 2.85 / (0.11 - 0.0385) = $39.90 million

The total present value of cash flows is the sum of the present value of the first-year cash flow and the present value of all future cash flows.

PV of future cash flows = $39.90 million + $2.56 million = $42.46 million

Profitability index (P.I) = PV of future cash flows / Initial investment

= 42.46 / 30

= 1.387

Therefore, the correct option is (c) 1.387.

Learn more about Profitability index

https://brainly.com/question/30641835

#SPJ11

The equation of the perpendicular line that passes through the point (- 3, - 1) is y = 2 · x + 5.

In this question we must determine the equation of a line that is perpendicular to another line and pass through a given point. Mathematically speaking, lines are represented by the following equation:

y = m · x + b

Where:

And the slopes of two lines perpendicular to each other satisfy the following relationship:

m · m' = - 1

Where:

First, determine the slope of the perpendicular line by means of the slope relationship:

m = - 1 / 2

m' = - 1 / m

m' = - 1 / (- 1 / 2)

m' = 2

Second, find the intercept of the perpendicular line by the equation of the line:

b = y - m · x

b = - 1 - 2 · (- 3)

b = - 1 + 6

b = 5

Third, write the equation of resulting line:

y = 2 · x + 5

To learn more on the equations of perpendicular lines: https://brainly.com/question/25790244

#SPJ1

Answer:

2x + 13

13

Step-by-step explanation:

Albert and Maxim own

x + (x + 13) = 2x + 13 model airplanes together

Albert owns

(x + 13) - x = 13 less model airplanes than Maxim.

Answer:

They own 2x+13 model airplanes together

Albert owns 13 less model airplanes than Maxim

Step-by-step explanation:

One sec I'll answer this right now

-2 Is the answer!!

Answer:

C(12)=$570.18

C(20)=$57.08

Step-by-step explanation:

Exponential Decay Function

The exponential function is often used to model natural growing or decaying processes, where the change is proportional to the actual quantity.

An exponential decaying function is expressed as:

\(C(t)=C_o\cdot(1-r)^t\)

Where:

C(t) is the actual value of the function at time t

Co is the initial value of C at t=0

r is the decaying rate, expressed in decimal

The depreciation of goods is often modeled as an exponential function. The new car costs $18,000 and its price depreciates at r=25%= 0.25 every year.

The depreciation model is:

\(C(t)=18,000\cdot(1-0.25)^t\)

Operating:

\(C(t)=18,000\cdot 0.75^t\)

At t=12 years, the price will be:

\(C(12)=18,000\cdot 0.75^{12}\)

C(12)=$570.18

At t=20 years, the price will be:

\(C(20)=18,000\cdot 0.75^{20}\)

C(20)=$57.08

The derivative of the given function, 8x² - 9y = 6x + 5, is y' = -4.

To differentiate the function 8x² - 9y = 6x + 5, we need to find the derivative with respect to x, denoted as y'. To do this, we'll differentiate each term separately using the rules of differentiation.

First, let's differentiate the left-hand side of the equation, 8x² - 9y. The derivative of 8x² with respect to x is 16x. To find the derivative of -9y, we need to use the chain rule since y is a function of x. The derivative of -9y with respect to x is -9 * y' (the derivative of y with respect to x). Therefore, the left-hand side becomes 16x - 9y'.

Next, we differentiate the right-hand side of the equation, 6x + 5. The derivative of 6x with respect to x is simply 6. The derivative of a constant (in this case, 5) is zero, as it does not depend on x.

Putting it all together, we have the equation 16x - 9y' = 6. To isolate y', we can rearrange the equation as -9y' = 6 - 16x. Dividing both sides by -9, we get y' = -4x + (2/3).

So, the derivative of the given function is y' = -4.

Learn more about derivative here:

https://brainly.com/question/25324584

#SPJ11

The power of a statistical test generally increases with larger sample sizes.

The power of a statistical test refers to its ability to detect a true effect or difference when it exists. It is influenced by various factors, including the significance level (alpha), effect size, and sample size.

When the sample size is larger, there is a greater likelihood of capturing the true effect, resulting in increased statistical power. This is because larger samples provide more information and reduce the impact of random variability, allowing for more precise estimates and stronger evidence.

On the other hand, a small sample size can lead to decreased statistical power. With smaller samples, there is a higher chance of missing a true effect, as the estimate may be more influenced by random fluctuations and may not accurately represent the population.

It is important to note that there can be exceptions depending on the specific statistical test and the nature of the data. In some cases, smaller sample sizes may be sufficient to detect large and impactful effects, while larger sample sizes may not always guarantee adequate power if the effect size is very small.

In general, the power of a statistical test is positively influenced by larger sample sizes. However, the relationship between sample size and power can be complex and depends on various factors such as the effect size and specific statistical test being used. Researchers should carefully consider the appropriate sample size to achieve adequate power based on the research question and desired level of confidence.

To know more about statistical visit:

https://brainly.com/question/12805356

#SPJ11

Answer:

Step-by-step explanation:

Since it's a right angled triangle we can use trigonometric ratios to find the value of x

To find the value of x we can use either sine or cosine

\( \sin(30) = \frac{5}{x} \\ x \sin(30) = 5 \\ x = \frac{5}{ \sin(30) } \\ x = \frac{5}{0.5} \\ \\ \\ \boxed{x = 10}\)

\( \cos(60) = \frac{5}{x} \\ x \cos(60) = 5 \\ x = \frac{5}{ \cos(60) } \\ x = \frac{5}{0.5} \\ \\ \\ \boxed{x = 10}\)

Hope this helps you

The average time it takes to rent a video tape is 0.141 minutes.

Given data:Customers arrive at a video rental desk at the rate of 12 per minute(Poisson).
Each server can handle 8.15 customers per minute(Poisson). If there are 3 servers, we need to determine the average time it takes to rent a video tape.
Let us assume λ = 12 and μ = 3 × 8.15 = 24.45
Average time it takes to rent a video tape = 1 / (μ - λ/n)
Where, n = number of servers⇒ Average time it takes to rent a video tape = 1 / (24.45 - 12/3)⇒ Average time it takes to rent a video tape = 1 / 8.45⇒ Average time it takes to rent a video tape = 0.1185 minutes = 0.141 rounded to three decimal places.

Thus, the average time it takes to rent a video tape is 0.141 minutes.

To know more about average time, click here

https://brainly.com/question/14521655

#SPJ11

The formula of marginal probability distribution that is P(X) = ΣP(X, Y) and applied on the table. We found that P(0 Bottles) = 0.69 and P(1 Bottle) = 0.31.

Given probability distribution is as follows:Bottles of Liquor Cartons of Cigarettes 0 1 0 0.62 0.16 1 0.07 0.15We have to find the marginal probability distribution of the number of bottles imported. The marginal probability distribution refers to the probability distribution of one or more variables, with the sum of probabilities across the values of each variable equaling 1.

Marginal probability distribution formula is P(X) = ΣP(X, Y). So, the sum of probabilities across the values of each variable equals to 1. In other words, the probability distribution of one variable must add up to one.For example, P(0 Bottles) + P(1 Bottle) = 1. So, we find each of these probabilities separately. We have the following table for the calculation:Bottles of Liquor Cartons of Cigarettes 0 1 Marginal 0 0.62 0.07 0.69 1 0.16 0.15 0.31 Total 0.78 0.22 1So, P(0 Bottles) = 0.69 and P(1 Bottle) = 0.31.We have found the marginal probability distribution of the number of bottles imported. We used the formula of marginal probability distribution that is P(X) = ΣP(X, Y) and applied on the table. We found that P(0 Bottles) = 0.69 and P(1 Bottle) = 0.31.

Learn more about  marginal probability distribution here:

https://brainly.com/question/32243624

#SPJ11

Answer:

To divide powers with the same base and to simplify expressions with negative exponents. 1. Vocabulary Review. Is the expression x5 an exponent or a power

Step-by-step explanation: