a) Show that the cosine rule shown below can be
rearranged to give
b) What is the size of angle in the triangle below?
Give your answer to the nearest degree

The probability that a student has a brother given that they have a sister can be found to be 4 / 10 or 2 / 5.

From the table, we see that the number of students who have a brother and a sister would be 4 out of 10 students.

This means that the probability that a student has a brother given that they have a sister would be:

= Number of students who have a brother and sister / Number of students with sisters

= 4 / 10

When taken to the simplest form, this is:

= ( 4 / 2 ) / ( 10 / 2 )

= 2 / 5

Find out more on probability at https://brainly.com/question/30063166

#SPJ1

the required sample size is approximately 178. Answer (c) is correct.To determine the required sample size, we can use the formula:

n = (z * σ / E)^2

where:
- n is the sample size
- z is the z-score for the desired level of confidence (99% corresponds to z = 2.58)
- σ is the standard deviation of the population
- E is the maximum error we want to allow in our estimate of the population mean

Plugging in the values given in the problem, we get:

n = (2.58 * 14 / 4)^2 ≈ 178

Therefore, the required sample size is approximately 178. Answer (c) is correct.

To  learn  more about sample click here:brainly.com/question/12823688

#SPJ11

A box of 30 pieces of chocolate candies contains approximately 424.11 cubic units of chocolate.

The volume of a sphere can be calculated using the formula:

V = (4/3) * π * r^3

where V is the volume, π is pi (approximately 3.14), and r is the radius of the sphere.

Since the diameter of each candy is 3, the radius is half of that, or 1.5. We can plug this value into the formula to find the volume of one piece of candy:

V = (4/3) * π * r^3

V = (4/3) * 3.14 * 1.5^3

V ≈ 14.137

So one piece of candy has a volume of approximately 14.137 cubic units. To find the total amount of chocolate in a box of 30 candies, we can simply multiply the volume of one candy by the number of candies in the box:

Total volume = 14.137 * 30

Total volume = 424.11

Therefore, a box of 30 pieces of chocolate candies contains approximately 424.11 cubic units of chocolate.

Learn more about candies here

https://brainly.com/question/26368371

#SPJ11

The  distance John would have to walk to get from point A to point B without going through the pond is 60.84 meters.

Since, John walks 36 m south and 49 m east which covered the distance equal to the hypotenuse of a right triangle

Using the Pythagorean theorem

c² = a² + b²

c² = 36² + 49²

c² = 1296 + 2401

c² = 3697

c = √3697

c = 60.84 m

Thus, the distance is 60.84 meters.

Learn more about Pythagoras Theorem here:

https://brainly.com/question/21926466

#SPJ1

All three options are relevant questions to consider when effectively using statistics in a speech.


1. "Are my numbers from reliable sources?" - It is crucial to use reliable and accurate data sources to ensure that your speech presents trustworthy information.
2. "Do I use statistics to quantify ideas?" - Using statistics can help support your arguments and make your points more concrete, making your speech more persuasive and engaging.
3. "Do I relate the statistics to the audience?" - Relating statistics to the audience helps make the data more relevant and understandable, allowing listeners to better grasp the importance of the information.

To effectively use statistics in a speech, you should ensure that you use reliable sources, use statistics to quantify your ideas, and relate the statistics to your audience.

To know more about numbers, visit:

https://brainly.com/question/17429689

#SPJ11

The probability that a randomly sampled household has more than $16,000 in credit card debt is approximately 0.4726 or 47.26%.

The question asks us to find the probability that a randomly sampled household has more than $16,000 in credit card debt, given that the distribution of household debt is somewhat right skewed with a mean of $15,355 and a standard deviation of $10,000.

To solve this problem, we can use the standard normal distribution, which allows us to calculate probabilities for any normal distribution by standardizing the variable of interest (in this case, credit card debt) to a standard normal distribution with a mean of 0 and a standard deviation of 1.

To standardize the value of $16,000, we use the formula:

z = (x - μ) / σ

where x is the value we want to standardize, μ is the mean, σ is the standard deviation, and z is the corresponding z-score. Substituting the given values, we get:

z = (16000 - 15355) / 10000 = 0.0655

This means that $16,000 is 0.0655 standard deviations above the mean. To find the probability that a randomly sampled household has more than $16,000 in credit card debt, we need to find the area to the right of this z-score under the standard normal curve. We can use a standard normal table or calculator to find this probability, which is approximately 0.4726.

It's important to note that this probability is based on the assumptions made about the distribution of household debt, and may not accurately reflect the true probability in practice. Additionally, credit card debt is influenced by a variety of factors beyond just household income and spending habits, so it's important to consider the limitations of this analysis when interpreting the results.

Learn more about probability at: brainly.com/question/32004014

#SPJ11

The function represented by set A is linear.

To determine which function is linear, we need to check if there is a constant rate of change between the ordered pairs.

For example, let's consider the following sets of ordered pairs:

A: {(1, 3), (2, 5), (3, 7)}

B: {(1, 2), (3, 8), (5, 14)}

For set A, we can see that the rate of change between any two consecutive ordered pairs is 2. This means that for every increase of 1 in x, the corresponding y-value increases by 2. Therefore, the function represented by set A is linear.

For set B, the rate of change between the first two ordered pairs is 3, but the rate of change between the second and third ordered pairs is 3. This means that the function is not linear, since there is not a constant rate of change.

Therefore, the function represented by set A is linear.

Learn more about linear here

https://brainly.com/question/2408815

#SPJ11

Hi!
You make $15 per day.
60 divided by 4 (The number of days you work per month since you work once weekly.) is 15.

Hope this helps!

The component vector of F parallel to the ramp is approximately 382.2i - 153.2j.



First, we need to find the weight of the boat and trailer that is distributed on each wheel. Since the weight is evenly distributed, we can simply divide the total weight by 2:

440 lb / 2 = 220 lb

Next, we need to find the component vector of the weight parallel to the ramp. To do this, we will use trigonometry and break the weight vector into its x and y components.

Let's start with the y component. The weight vector is acting perpendicular to the ramp, so we need to find the component that is parallel to the ramp. To do this, we can use the sine function:

sin(21°) = y / 220 lb

y = 220 lb * sin(21°) = 75.9 lb

So the y component of the weight vector parallel to the ramp is -75.9 lb (negative because it is acting downwards).

Now, let's find the x component. Again, we need to find the component of the weight vector that is parallel to the ramp, so we can use the cosine function:

cos(21°) = x / 220 lb

x = 220 lb * cos(21°) = 202.9 lb

So the x component of the weight vector parallel to the ramp is 202.9 lb.

Finally, we can put these components together to get the component vector of the weight parallel to the ramp:

Fpar = 202.9i - 75.9j

Rounding to one decimal place, we get:

Fpar = 382.2i - 153.2j

To know more about trigonometry  visit:

brainly.com/question/11016599

#SPJ11

-5° F represents the change in the temperature of the park city.

Given that the temperature of a park city has been decreased or dropped by 5° F,

We need to represent this as an integer,

So, here dropped means decrease in temperature, that mean whatever was the temperature it is decreased by 5° F.

That mean the change is in negative.

Hence -5° F represents the change in the temperature of the park city.

Learn more about integers click;

https://brainly.com/question/15276410

#SPJ1

SSE and SST alone is not sufficient to compute the slope of the regression line, y-intercept, or x-intercept.

The coefficient of determination, also known as R-squared, can be computed if SSE (sum of squared errors) and SST (total sum of squares) are known. R-squared is a measure of the proportion of variation in the dependent variable (y) that can be explained by the independent variable (x). It ranges between 0 and 1, with higher values indicating a better fit of the regression line to the data.

The formula for R-squared is: R-squared = 1 - (SSE / SST)

However, knowing SSE and SST alone is not sufficient to compute the slope of the regression line, y-intercept, or x-intercept. These require additional information such as the mean values of x and y, or the values of individual data points.

For such more questions on Regression Analysis Computation

https://brainly.com/question/30413080

#SPJ11

Answer:

22

Step-by-step explanation:

As we know the basic rule to solve an expression is BODMAS, the full form is Brackets, Orders, Division, Multiplication, Addition, and Subtraction.

So first, we will solve the first bracket, and as we know if we multiply a negative integer with another negative integer then the result is a positive value ( - * - =  + ), and the expression becomes

-4(-8)+(-10) = 32+(-10)

Now we solve another bracket, and as we know positive multiplied by negative results in a negative sign ( + * - = - ), and the expression becomes

32+(-10) = 32 - 10

And now we subtract 10 from 32, so our final answer is

32 - 10 = 22

To learn more about BODMAS,

https://brainly.in/question/1295210

We cannot find the correlation coefficient between x and y for this bivariate distribution.

To find the correlation coefficient between x and y, we need to first calculate the expected value of x, denoted E(x), the expected value of y, denoted E(y), and the expected value of xy, denoted E(xy).

Using the given distribution, we can calculate:

E(x) = ∑x * p(x,y) = ∑x * 0.5(x y) = 0.5(1+2+3+...) = ∞ (diverges)

E(y) = ∑y * p(x,y) = ∑y * 0.5(x y) = 0.5(1+2+3+...) = ∞ (diverges)

E(xy) = ∑x*y * p(x,y) = ∑x*y * 0.5(x y) = 0.5(1*1 + 2*1 + 2*2 + 3*1 + 3*2 + 3*3 + ...) = ∞ (diverges)

Since the expected values of both x and y diverge, we cannot use the formula for the correlation coefficient that involves standard deviations. Instead, we can use the formula:

[tex]\rho = [E(xy) - E(x)E(y)] / [(E(x^2) - E(x)^2) * (E(y^2) - E(y)^2)]^{(1/2)}[/tex]

Since E(x²) and E(y²) also diverge, we cannot use this formula either.

Learn more about correlation coefficient:

https://brainly.com/question/4219149

#SPJ11

The correct options for the parts of the circle are:

A circle is a spherical plane figure whose edge is made up of points spaced equally apart from a fixed point.

The fixed point from which every point on the circle's edge is equally distant is the center of the circle.

The parts of a circle include the following:

Learn more about parts of a circle at: https://brainly.com/question/29788136

#SPJ1

The notations and the terms that correctly defines them is matched below:

1.)GCB = Major arc. Option I.

2.)CE = Chord. Option B.

3.)AB= Radius. Option C.

4.)CB= Minor arc. Option A.

5.)BAD= central angle. Option F.

6.)A = Center. Option J.

7.)DGC = Minor arc. Option A.

8.)CD = Diameter. Option G.

The circle has the following parts with their various properties described below;

Major arc: This is part of the circle that has an angle which measures more that 180°.

Minor arc: This is part of the circle that has an angle which measures less than 180°.

Diameter: This is defined as the distance across a circle which must pass through its central point.

Radius: This is defined as half the diameter of a circle.

Chord:. This is defined as the line that joins two point on the circumference of a circle.

Learn more about diameter here:

https://brainly.com/question/30460318

#SPJ1

The total discount value percentage the customer is getting is A = 32.5 %

Given data ,

Let the cost of the toaster be x

Now , the customer is getting a discount of 25 % by salesperson

So , the price of the toaster = 0.75x

Now , the customer is getting another 10 % off on new price of toaster

So , price of toaster = 0.75x - 0.075x

The final price of toaster = 0.675x

And , the percentage discount the customer is getting is A

A = x - 0.675x

A = 32.5 %

Hence , the discount percentage is 32.5 %

To learn more about percentage click :

https://brainly.com/question/12861068

#SPJ1

To solve the expression -25 x (84/21) + (-3) x (-6), follow these steps:

Step 1: Perform the division inside the parentheses.
(84/21) = 4

Step 2: Replace the terms and rewrite the expression.
-25 x (4) + (-3) x (-6)

Step 3: Perform the multiplications.
-25 x 4 = -100
-3 x -6 = 18

Step 4: Rewrite the expression and perform the addition.
-100 + 18

Step 5: Calculate the final result.
-100 + 18 = -82

Your answer is -82.

To learn more about expression : brainly.com/question/14083225

#SPJ11

The maximum capacity of the container that can measure the water from both tankers is 34 liters.

To find the maximum capacity of a container that can measure the water from both tankers without leaving any water in either tank, we need to find the greatest common divisor (GCD) of the volumes of the two tankers.

The GCD represents the largest quantity that can evenly divide both numbers. In this case, the GCD will represent the maximum capacity of the container.

Using the given volumes of the tankers:

Tanker 1 volume = 578 liters

Tanker 2 volume = 782 liters

We can find the GCD using a method such as the Euclidean algorithm.

578 = 782 * 0 + 578

782 = 578 * 1 + 204

578 = 204 * 2 + 170

204 = 170 * 1 + 34

170 = 34 * 5 + 0

The GCD of 578 and 782 is the remainder at the last step, which is 34 liters.

Know more about maximum capacity here:

https://brainly.com/question/29680137

#SPJ11

To determine whether the linear transformation T is one-to-one, onto, or neither, we need to analyze the rank and nullity of the transformation.

The rank of T is the dimension of the image space, which is the span of the columns of the transformation matrix. To find the matrix, we can write T(X, Y, Z, W) = (V, W, X, Z) as a matrix equation:

|V|   |0 0 1 0||X|
|W| = |0 1 0 0||Y|
|X|   |1 0 0 0||Z|
|Z|   |0 0 0 1||W|

From this matrix, we can see that the columns are linearly independent, so the rank of T is 4.

The nullity of T is the dimension of the kernel, which is the set of all solutions to the equation T(X, Y, Z, W) = (0, 0, 0, 0). We can set up the augmented matrix for this equation:

|0 0 1 0 0|
|0 1 0 0 0|
|1 0 0 0 0|
|0 0 0 1 0|

Row-reducing this matrix gives:

|1 0 0 0 0|
|0 1 0 0 0|
|0 0 1 0 0|
|0 0 0 1 0|

The only solution is the trivial one, so the nullity of T is 0.

Since the rank of T is equal to the dimension of the domain and the codomain, T is onto. And since the nullity of T is 0, T is also one-to-one. Therefore, the correct answer is "one-to-one and onto".
Hi! To determine whether the linear transformation T: R4 → R4, T(X, Y, Z, W) = (V, W, X, Z) is one-to-one, onto, or neither, let's analyze the properties of this transformation.

1. One-to-one: A linear transformation is one-to-one if different input vectors produce different output vectors.

In this case, T(X, Y, Z, W) = (V, W, X, Z). Observe that every input vector (X, Y, Z, W) uniquely determines the output vector (V, W, X, Z). Thus, this transformation is one-to-one.

2. Onto: A linear transformation is onto if every output vector can be produced by some input vector.

For this transformation, T(X, Y, Z, W) = (V, W, X, Z), every output vector (V, W, X, Z) can be produced by the input vector (X, Y, Z, W). So, the transformation is onto as well.

In conclusion, the linear transformation T: R4 → R4, T(X, Y, Z, W) = (V, W, X, Z) is both one-to-one and onto.

To know more about linear transformation visit:

https://brainly.com/question/29642164

#SPJ11

Answer: (4, 3)

Step-by-step explanation:

-4x + 3(2x-5) = -7 // substitute y=2x-5 for y in the first equation

-4x + 6x - 15 = -7 // simplify by distributing the 3

2x = 8 // add 15 to both sides and simplify

x = 4 // divide both sides by 2

Now that we know x=4, we can substitute this value into either equation to find y. Let's use y=2x-5:

y = 2(4) - 5 = 3

the solution to the system of equations is (4, 3).

The 10th term of the given sequence 40, 24, 72/5, ..... is given by 0.403.

We know that the n th term of a geometric sequence with first term 'a' and common ratio 'r' is given by,

[tex]t_n=ar^{n-1}[/tex]

Given that the first three terms of a sequence are given by: 40, 24, 72/5,....

Now we can see that,

24/40 = 3/5

(72/5)/24 = 72/(24*5) = 3/5

So the given sequence is a geometric sequence with common ratio of 3/5.

So, r = 3/5.

and the first term is (a) = 14

So the 10th term of the sequence is given by,

[tex]t_{10}=ar^{10-1}[/tex] = ar⁹ = 40*(3/5)⁹ = 0.403 (Rounding off to the nearest thousandth)

Hence the 10 th term of the sequence is 0.403.

To know more sequence here

https://brainly.com/question/7882626

#SPJ4

Area = s × s

676 cm² = s²

s = √676

s = 26 cm

V. Cube = s × s × s

= 26 × 26 × 26

= 17,576 cm³

Answer:

Set your calculator to degree mode.

tan B = 5/2

B = tan^-1 (5/2) = 68.20°

the depth perception cue based on the observation that parallel lines converge in the distance is that the depth perception cue based on the observation that parallel lines converge in the distance is known as linear perspective. This is a monocular cue, meaning it can be perceived with just one eye.

When looking at a scene, our brain uses the visual information provided by our eyes to determine depth and distance. Linear perspective is a cue that relies on the way that objects appear to shrink in size and converge towards a vanishing point as they move further away from the viewer. This is why parallel lines, such as the sides of a road or railway tracks, appear to meet at a point in the distance.

Linear perspective is a powerful visual cue that allows us to accurately perceive depth and distance in a scene. It is commonly used in art and architecture to create a sense of depth and realism, and is a crucial component of our visual perception.

To know more about distance, visit:

https://brainly.com/question/31713805

#SPJ11

Based on the pattern of increasing numbers in the table, a reasonable value for the missing cell would be option c, 9.

Looking at the table, we can see that each number is increasing by approximately the same amount from left to right and from top to bottom. Specifically, each row and each column increases by a consistent value of 1.2. For example, the first row increases from 4.4 to 5.6 to 6.8, and the second row increases from 5.6 to 6.8 to 8.0.

Using this pattern, we can estimate the value of the missing cell by looking at the corresponding row and column. The missing cell is in the third row, so we can estimate it by adding 1.2 to the previous cell in the row, which is 7.2. This gives us an estimate of 8.4.

However, none of the answer choices include 8.4, so we need to consider which of the given options is closest to this estimate. Option c, 9, is the closest option, and it is also the option that makes the most sense given the pattern of increasing numbers in the table. Therefore, a reasonable value for the missing cell is option c, 9.

Learn more about table here

https://brainly.com/question/30380331

#SPJ11

what is a reasonable value for the missing cell, if each number is increasing?

a. 8 b. 8.8 c. 9 d. 9.1

The main answer to this question is that there could be several reasons why an experiment may not produce significant results even if the research hypothesis is true.

One possible explanation could be that the sample size used in the experiment was too small, which could have resulted in insufficient statistical power to detect the true effect of the independent variable on the dependent variable. Another explanation could be that there were extraneous variables that were not controlled for in the experiment, which could have influenced the results and made it difficult to detect the true effect of the independent variable.

it is important to consider all possible factors that may affect the results of an experiment and to take steps to minimize their impact. This includes ensuring that the sample size is appropriate, controlling for extraneous variables, and using appropriate statistical tests to analyze the data. By doing so, researchers can increase the likelihood of obtaining significant results that accurately reflect the effects of the independent variable on the dependent variable.

To know more about factors, visit:

https://brainly.com/question/14209188

#SPJ11

The number of students enrolled at a college is 16,500 and grows by 4% each year. To determine the growth rate of the number of students over a certain period, the formula for compound interest can be used. This information can be useful for college administrators in terms of planning and budgeting.

The compound interest formula can be used to calculate the growth rate of the number of students at the college. The formula is A = P(1 + r/n)^nt,

where A is the final amount,

P is the initial principal,

r is the interest rate,

n is the number of times the interest is compounded per year, and

t is the number of years.

In this case, P is 16,500, r is 4%, n is 1 (since the interest is compounded annually), and t is the number of years. For example, if we want to find the number of students after 5 years, the formula would be A = 16,500(1 + 0.04/1)^(1*5) = 20,221.

This means that the number of students will have grown by 3,721 over a period of 5 years.

This information can be useful for college administrators in terms of planning and budgeting. They can use this data to project the number of students that will be enrolled in future years and make decisions about staffing, resources, and facilities accordingly.

For example, if they know that the number of students will be increasing, they may need to hire more faculty and staff, or build new classrooms and dormitories. On the other hand, if the number of students is projected to decrease, they may need to make cuts in certain areas to balance the budget. Overall, understanding the growth rate of the number of students at a college is an important factor in effective planning and decision-making.

The number of students enrolled at a college is 16,500 and grows 4% each year. Based on this information we can determine the following

To learn more about compound interest, click here: brainly.com/question/20406888

#SPJ11

The measure of ∠B in order to use the law of cosines to find the length of AC. Once we have the measure of ∠B, we can use the law of cosines and the length of AC as AC^2 = AB^2 + BC^2 - 2ABBC cos(B).

To use the law of cosines to find the length of side AC of a triangle ABC, we would need to know the measure of the angle ∠B. This is because the law of cosines relates the lengths of the sides of a triangle to the cosine of one of its angles. Specifically, the law of cosines states that:

c^2 = a^2 + b^2 - 2ab cos(C)

where c is the length of the side opposite angle C, and a and b are the lengths of the other two sides.

In the case of triangle ABC, side AC is the side opposite angle ∠B. Therefore, we need to know the measure of ∠B in order to use the law of cosines to find the length of AC. Once we have the measure of ∠B, we can use the law of cosines to calculate the length of AC as:

AC^2 = AB^2 + BC^2 - 2ABBC cos(B)

where AB and BC are the lengths of the other two sides of the triangle.

Learn more about law of cosines here

https://brainly.com/question/4372174

#SPJ11

There are 19 test scores recorded on the stem-and-leaf plot for Charlie's tests throughout the year.

The stem-and-leaf plot consists of two parts: the stem and the leaf. The stem represents the digits of the score that are in the tens place, while the leaf represents the digits in the ones place.

To find the total number of test scores recorded on this plot, we need to count the number of leaves.

Looking at the plot, we can see that there are 9 leaves in the 70s stem, 4 leaves in the 80s stem, and 5 leaves in the 90s stem. There is also 1 leaf in the 100s stem.

Therefore, the total number of test scores recorded is:

9 + 4 + 5 + 1 = 19

To know more about stem-leaf-plot here

https://brainly.com/question/12857419

#SPJ1

This limaçon is symmetrical along the y-axis. The horizontal intercepts are (4,0) and (-4,0). The vertical intercepts are (0,-2) and (0,6).

To determine the type of shape, we look at the value of the constant versus the value of the term with the sign.

As 4>2, this is a dimpled limacon.

We have y-intercepts where θ = [tex]\pi/2[/tex] and [tex]3\pi /2[/tex]

Then, our polar equation is r = 4 + 2 sinθ.

r = 4 + 2 sin θ= 6 if θ = [tex]\pi /2[/tex] and

r = 4 + 2 sin θ = 2 if θ = [tex]3\pi /2[/tex]

Therefore, y-intercepts or vertical intercepts are (0,-2) and (0,6)

We have x-intercepts where θ = 0 and [tex]\pi[/tex]

Then

r = 4 + 2sin θ = 4 for θ = 0 and

r = 4 + 2 sin θ = 4

Therefore, x-intercepts or horizontal intercepts are (4,0) and (-4,0)

This is symmetric about the y-axis.

As we already know that sin θ = sin ( [tex]\pi[/tex] - θ) and

cos θ = cos ([tex]\pi[/tex] - θ)

Therefore, we replace θ with [tex]\pi[/tex] - θ, and thus we prove symmetry about the y-axis.

r = 4 + 2sin([tex]\pi[/tex] - θ)= 4 + 2 sin θ

To learn more about limaçon;

https://brainly.com/question/9422589

#SPJ1