a system of equations is shown below. y=2x+1 and y=x+2 what is the solution to the system? A. (0,1) B. (1,2) C. (1,3) D. (2,4)

Answer:

-----------------------------------

The y-intercept is the point where the line crosses the y-axis, which occurs when x = 0.

To find the y-intercept, substitute 0 for x in the equation y = 4x + 2:

The y-intercept is 2 and matching choice is C.

Answer:

2

Step-by-step explanation:

We need to find out the y intercept of the given equation which is y = 4x + 2 .

y intercept is a point where the graph of the equation cuts the y axis. So at y intercept x coordinate will be 0 , so plug in x = 0 , in the given equation as ;

y = 4x + 2

y = 4(0) + 2

y = 0 + 2

y = 2

Therefore the y intercept of the line is 2 . ( option C )

Answer:

w = 28 miles

Step-by-step explanation:

The perimeter is the sum of the lengths of the sides.

The sum of the lengths of the sides is w + 28 + 28.

The perimeter is 84.

w + 28 + 28 must equal 84.

w + 28 + 28 = 84

Now we solve for w.

Add 28 and 28.

w + 56 = 84

Subtract 56 from both sides.

w = 28

Answer: w = 28 miles

Answer: 1000 x 1.05^n

Step-by-step explanation:

1.05 is the increase experienced each year and n is the number of years.

Answer:

The population of bees is increasing by 5% each year since 2010. Let P(n) be the population of bees in the nth year since 2010.

The explicit formula for the bee population can be found using the formula for compound interest:

P(n) = P(0) * (1 + r)^n

where P(0) is the initial population in 2010, r is the annual growth rate, and n is the number of years since 2010.

Substituting the given values, we have:

P(n) = 1000 * (1 + 0.05)^n

Simplifying the expression, we get:

P(n) = 1000 * 1.05^n

Therefore, the explicit formula that models the bee population for n years since 2010 is P(n) = 1000 * 1.05^n.

Answer: 201.06

Step-by-step explanation:

A=πr2=π·8^2≈201.06193

The products written in scientific notation are:

a) [tex]5.88*10^9[/tex]

b) [tex]15*10^{12}\\[/tex]

c) [tex]8.4*10^{-10}[/tex]

d) [tex]42*10^{-7}[/tex]

The first product we need to solve is:

[tex](4.2*10^6)*(1.4*10^3)[/tex]

We can reorder that product into the one below:

[tex](4.2*1.4)*(10^6*10^3)[/tex]

The exponents in the right side are added, so we get:

[tex](4.2*1.4)*(10^6*10^3) = 5.88*10^{3 + 6} = 5.88*10^9[/tex]

Now let's do the same in the others.

b)

[tex](5*10^5)*(3*10^7)\\= 5*3*10^{5 + 7}\\= 15*10^{12}\\[/tex]

Now we need to write the first number between 0 and 10, then we can rewrite this as:

[tex]1.5*10^{13}[/tex]

c) Again doing the same thing.

[tex](4*10^{-3})*(2.1*10^{-7}})\\= 4*2.1*10^{-3 - 7}\\= 8.4*10^{-10}[/tex]

d) Finally, this last product is:

[tex](6*10^{-2})*(7*10^{-5}})\\= 6*7*10^{-2 - 5}\\= 42*10^{-7}[/tex]

Again we need to have a number between 0 and 10, so we can rewrite this as:

[tex]4.2*10^{-8}[/tex]

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Answer:

The second figure.

Step-by-step explanation:

The first figure's perimeter is:

70 in + 42 in + 56 in = 168 inches.

And the second figure's perimeter is:

42 in + 33 in + 33 in + 64 in = 172 inches.

Therefore, Figure 1 < Figure 2.

The expected probability distribution is $4.35

We must multiply each supplied chance by the respective payout value in order to determine the expected value.

As a result, we have the payout probability distribution shown below:

0.35(1) + 2(0.2) + 5(0.1) + 8(0.2) + 10(0.15) (0.15)

= 0.35 + 0.4 + 0.5 + 1.6 + 1.5

= $4.35

When the set of possible outcomes is discrete in nature, the distribution is referred to as a discrete probability distribution. When a dice is rolled, all conceivable results, for instance, are discrete and result in a large number of outcomes. A different name for it is the probability mass function.

statistical distributions that can be used

Uniform discrete distribution The chances of each outcome are equal.

Single-trial distribution with two potential results.

A series of Bernoulli events are called the binomial distribution.

Poisson Distribution: The likelihood that a particular occurrence may or may not occur.

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If the probability an American will die from falling is 0.41%, the probability a American will not die from falling is 100% - 0.41% = 99.59%.

Answer: 99.59%.

Answer:

Proofs attached to answer

Step-by-step explanation:

Proofs attached to answer

Answer:

If a polygon is dilated by a scale factor of k, then its area is multiplied by k².

a. When k = 4, the area of the image is 10 × 4² = 160 square units.

b. When k = 1.5, the area of the image is 10 × 1.5² = 22.5 square units.

c. When k = 1, the area of the image is 10 × 1² = 10 square units. (The image is the same size as the original.)

d. When k = 1/3, the area of the image is 10 × (1/3)² = 10/9 square units.

Step-by-step explanation:

The second segment on the left, which is equal to the price per bag of lemons (X) times the quantity of bags of lemons, represents the cost of the lemons (7).

A way for resolving proportionality issues is the unitary method. Finding the value of one unit and then using that value to determine the value of another unit in relation to the first is what this process entails. If we already know that three pens cost $6, for instance, we can use the unitary technique to get the price of five pens as follows: 1 pen costs $6, 3 pens cost $2. Five pens cost $10, or $5 multiplied by $2.

given

The arrow on the right in the diagram above, which is equal to $29.12, represents the total cost of the cookies and lemons.

The first segment on the left, which is $2.66, represents the price of the cookies.

The second segment on the left, which is equal to the price per bag of lemons (X) times the quantity of bags of lemons, represents the cost of the lemons (7).

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The dilated figure has the following coordinates: A' (-15, 0), B' (-5, 10), C' (10, 10), D' (15, -5), and E' (5, -10).

In this sense, coordinates are the points where a grid system intersects. Latitude and longitude are the traditional ways to express GPS coordinates. Degrees of separation north and south from the equator, which is 0 degrees, are measured by lines of latitude coordinates.

Just multiply the coordinates of each point by 5 to construct a figure about the origin using a scale factor of 5.

A (-3, 0)

B (-1, 2)

C (2, 2)

D (3, -1)

E (1, -2)

The coordinates of each point are multiplied by 5 to enlarge the image by a scale factor of 5:

A' = (-3 * 5, 0 * 5) = (-15, 0)

B' = (-1 * 5, 2 * 5) = (-5, 10)

C' = (2 * 5, 2 * 5) = (10, 10)

D' = (3 * 5, -1 * 5) = (15, -5)

E' = (1 * 5, -2 * 5) = (5, -10)

The coordinates of the dilated figure are:

A' (-15, 0)

B' (-5, 10)

C' (10, 10)

D' (15, -5)

E' (5, -10)

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The height that the T-short lands on the bleachers is x = 0.65.

The quadratic equation may be solved by adding and subtracting the same number within the parenthesis to get a perfect square trinomial, which is how the quadratic formula is obtained. A version of the equation that can be solved using the square root function is the result of this method.

Given that it can be used to solve any quadratic equation regardless of the values of the variables a, b, and c, the quadratic formula is an effective tool for solving quadratic equations.

The equation of the path of T-shirt is y = -18x² + 4x and that of the height of bleachers is 3y=2x−14 or y = 2/3x - 14/3

To find the height of the T-shirt landing we find the intersection of the two equations as follows:

-18x² + 4x = (2x - 14)/3

-54x² + 12x = 2x - 14

54x² - 10x - 14 = 0

27x² - 5x - 7 = 0

Using the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

Substitute the values;

x = (-(-5) ± √((-5)² - 4(27)(-7))) / 2(27)

x = (5 ± √(925)) / 54

x = (5 ± 5√37) / 54

x = (5 + 5√37) / 54 = 0.65 and

x = (5 - 5√37) / 54 = -0.47

Hence, the height that the T-short lands on the bleachers is x = 0.65.

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Normal quantile plot is a graph of points (x,y) where each x-value is from the original set of sample data, and each y-value is the corresponding Z-score that is a quantile value expected from the standard normal distribution.

What is a Normal Quantile Plot?

A normal quantile plot is a graphical tool used to determine whether a data set is normally distributed or not.

It plots sample data versus a theoretical normal distribution.

In general, the points on the plot should form a straight line if the data is normally distributed. If the data is not normally distributed, the points on the plot will not form a straight line.

A normal quantile plot can be used to evaluate the following:

The normal quantile plot of the residuals is the most important diagnostic tool for examining whether the assumptions of a linear regression model have been met.

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Answer:

x = 3

Step-by-step explanation:

Solving systems of linear equations via substitution:

[tex]2x-6y=-6[/tex]

[tex]y=1.5x-2.5[/tex]

We are already given the value of y, so to find the value of x, we need to plug in the y value in the other equation.

[tex]2x-6(1.5x-2.5)=-6[/tex]

Distribute 6

[tex]2x-9x+15=-6[/tex]

Combine our like terms

[tex]-7x+15=-6[/tex]

Subtract 15 to both sides

[tex]-7x=-21\\[/tex]

Divide by -7

[tex]x=3[/tex]

Cindy will take 0.25 hours or 15 minutes to travel a distance of 2 miles at a constant speed of 8 miles per hour.

The formula for time is: time = distance / speed where "distance" is the distance traveled by an object, and "speed" is the rate at which the object is moving.This formula can be used to calculate the time taken by an object to travel a certain distance at a constant speed, or to calculate the speed or distance if the other two variables are known.

The formula for speed is: speed = distance / time where "distance" is the distance traveled by an object and "time" is the duration of travel.This formula can be used to calculate the speed of an object if the distance it has traveled and the time it took to travel that distance are known. It can also be used to calculate the distance traveled by an object if its speed and the time it traveled at that speed are known.

In the given question,

We can use the formula:

time = distance / speed

where "distance" is the distance traveled and "speed" is the speed at which Cindy is riding her bike.

Substituting the given values, we get:

time = 2 miles / 8 miles per hour

Simplifying, we get:time = 0.25 hours.

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Answer:

adjacent = cos(angle) x hypotenuse

Answer: 3/5

hope this helped you. Please brainliest! :D

Step-by-step explanation: If I am wrong tell me :D

Step-by-step explanation:

Since it is equilateral the angle at the top is 60 °

for right triangles   sin (angle ) =  opposite leg / hypotenuse

                                 sin (60) = sqrt 6/ x

                                        x = sqrt 6 / sin (60) = sqrt 6 / sqrt(3)/2 =

                                                2 sqrt 2    = 2.83

Increasing lexicographic order: (0, 0), (0, 1/2), (1/4, 0), (1/4, 1/2)).Thus, the increasing lexicographic order of the critical points of the function f(x,y) = xy(1 - 4x - 2y) are (0, 0), (0, 1/2), (1/4, 0), and (1/4, 1/2).

lexicographic order: (0, 0), (0, 1/2), (1/4, 0), (1/4, 1/2)).Thus, the increasing lexicographic order of the critical points of the function f(x,y) = xy(1 - 4x - 2y) are (0, 0), (0, 1/2), (1/4, 0), and (1/4, 1/2).

Suppose that f(x,y) = xy(1 - 4x - 2y). f(x,y) has 4 critical points.

Let's discuss what are critical points and how we can determine them,A critical point is a point on the graph where the derivative changes its sign.

In other words, the derivative either changes from negative to positive or from positive to negative. A critical point is also known as a stationary point or a turning point

To determine the critical points, we need to find the derivative of the given function and set it equal to zero.The given function is[tex]f(x,y) = xy(1 - 4x - 2y).[/tex]

Let's find the partial derivative of f with respect to [tex]x:f_x(x,y) = y(1 - 4x - 2y) - 4xy = (1-2y)(1-4x)y.[/tex] (1)

Now, find the partial derivative of f with respect to y:f_y(x,y) = x(1 - 4x - 2y) - 2xy = (1-2x)(1-2y)x. (2)

To find the critical points, we need to set both partial derivatives (1) and (2) equal to zero.

(1-2y)(1-4x) = 0 and (1-2x)(1-2y) = 0.

Solving both equations separately, we have the following critical points:(1/4, 1/2), (1/4, 0), (0, 1/2), and (0, 0).

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No, the statements are not equivalent as the statement "a > b" simply means that "a" is greater than "b" and there exists a number "c" such that when added to "b", it equals "a". This does not necessarily mean that "a" is greater than "b".

The statements "a>b" and "there is the number c, so that a=b+c" are not equivalent. The statement "a>b" simply means that "a" is greater than "b," while the statement "there is the number c, so that a=b+c" means that "a" can be expressed as the sum of "b" and another number "c."

These statements are not equivalent because even if "a" is greater than "b," it may not be possible to express "a" as the sum of "b" and another number "c."

Additionally, even if "a" can be expressed as the sum of "b" and another number "c," it may not necessarily be true that "a" is greater than "b."

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To see if there is a significant difference in the costs of airline flights between the west and east coasts to Lincoln, Nebraska, one can use a two-sample t-test. It is okay to perform the inference procedure, but the following assumptions and conditions must be checked.

Assumptions: Independence: The airfares for each coast should be independent of each other. Normality: The populations of airfares for both coasts should be approximately normally distributed .Equal variances: The population variances for both coasts should be equal.

Conditions: Sample sizes: Both samples should be large enough so that the Central Limit Theorem applies. Rule of thumb for t-tests is that the sample size should be at least 30.Random sampling: Both samples should be random .To test if the conditions are met, one can create a boxplot for each coast, check the normal probability plots, perform the F-test to check for equal variances, and check the sample sizes. If the assumptions and conditions are met, a two-sample t-test can be used to determine if there is a significant difference in the costs of airline flights between the west and east coasts to Lincoln, Nebraska.

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The standard deviation of the sampling distribution of pCheck to see if the 10% condition is 0.44.

If a large candy machine has 45% orange candies, and an SRS of 25 candies is taken from it, then the 10% condition can be checked to see if it is met. To do this, it is necessary to calculate the sample proportion p. To calculate p, the number of orange candies in the sample (let's call it x) is divided by the total number of candies in the sample (25). Thus, p = x/25. The 10% condition is met if the value of p is less than or equal to 0.1 (10%).

Since the value of p is unknown, the number of orange candies in the sample must first be determined. To find this number, the proportion of orange candies in the entire candy machine must be used. The proportion of orange candies is 45%, or 0.45.

This means that for every 100 candies in the candy machine, 45 are orange. Since there are 25 candies in the sample, 0.45*25 = 11.25 orange candies are expected in the sample. Since this is a sample proportion, the exact value of x must be rounded to the nearest whole number. This gives a value of 11 orange candies in the sample.

Now that the value of x is known, the value of p can be calculated. This gives p = 11/25 = 0.44.

Since 0.44 is greater than 0.1 (10%), the 10% condition is not met in this case.

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The power of the test to detect an average increase in height of 1 inch could be increased by d. giving the drug to 25 randomly selected students instead of 50.

The power of a test is the probability of correctly rejecting the null hypothesis when it is false. In this case, the null hypothesis is that the drug does not cause people to grow taller, and the alternative hypothesis is that the drug causes an average increase in height of 1 inch.

To increase the power of the test, we want to increase the probability of correctly rejecting the null hypothesis when it is false. One way to do this is to increase the sample size, which will reduce the standard error of the mean and increase the t-statistic, making it more likely to reject the null hypothesis.

However, in this case, we can increase the power of the test by giving the drug to a smaller sample size of 25 instead of 50. This is because the effect size of the drug is not known, and giving the drug to a larger sample size will increase the variance of the data, making it harder to detect a significant difference. By reducing the sample size, we can increase the power of the test while still maintaining a reasonable sample size.

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[tex]\textit{arc's length}\\\\ s = \cfrac{\theta \pi r}{180} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ \theta =42\\ r=2.8 \end{cases}\implies s=\cfrac{(42)\pi (2.8)}{180}\implies s=\cfrac{49\pi }{75}\implies s\approx 2.05 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{ \textit{Perimeter of the sector} }{2.8~~ + ~~2.8~~ + ~~2.05} ~~ \approx ~~ \text{\LARGE 7.65}[/tex]

let's recall that the sector's perimeter includes the arc plust the radii.

Answer:

( 9, 1/7 )

Step-by-step explanation:

I/9x- y=6/7                  equation    (1)

1/18x-2y=3/14              equation    (2)

9x(1)-18x(2)              multiply equation (1 ) by 9 and (2 ) by 18 and subtract  

                                                                                                      them                                                                                                                

we get y=1/7

then put the value of y=1/7 in ( 1 ) or (2)

1/9x-1/7=6/7 ⇒x=9

therefore  the right answer is ( 9, 1/7 )

In this particular question, we are being asked to find the number of normal subgroups of order 7 in a group of order 14. Before we begin, let's try to understand the different types of subgroups.Subgroups can be of two types: Proper Subgroups and Improper SubgroupsProper Subgroups are defined as subgroups which have more than one element and not equal to the entire group. Improper Subgroups are the subgroups which contain every element of the group.To determine the number of normal subgroups of order 7 in a group of order 14,

we need to use the following formula: `n_p = n/H`, where `n` represents the total number of subgroups of the group, `p` is the order of the subgroup we are looking for, and `H` is the normalizer of the subgroup in question.Using this formula, we can find that the order of the group is 14, and since 7 is a prime number, any subgroup of order 7 will be cyclic. Now, let's look at the different subgroups of the group of order 14:As 7 is a prime number and 7 divides 14, there will be one unique subgroup of order 7, and it will be cyclic.Since the group of order 14 is not a cyclic group, there are no other subgroups of order 7 besides the cyclic subgroup. Thus, the number of normal subgroups of order 7 in a group of order 14 is 1.

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The equation m = 12 + 2Y1 gives the slope of the line through the points P1=(-1.5, Y1) and P2=(-2, -6)

To find a point's coordinates in a coordinate system, you perform the opposite. Starting at the point, move vertically up or down until you reach the x-axis. Your x-coordinate is shown there. Afterwards, you'll be able to get a better understanding of how to use it.

It is assumed that the formula you supplied would be used to determine the slope (m) of the line connecting the two specified points, P1 and P2.

We may use the following formula to find the slope (m) of the line passing through the coordinates P1=(X1, Y1) and P2=(X2, Y2):m = (Y2 - Y1) / (X2 - X1) (X2 - X1)

Using the values provided:

P1 = (-1.5, Y1) (-1.5, Y1)

P2 = (-2, -6) (-2, -6)

These values can be used as substitutes in the formula:

m = (-6 - Y1) / (-2 - (-1.5))

Making the denominator simpler:

m = (-6 - Y1) / (-2 + 1.5)

m = (-6 - Y1) / (-0.5)

m = 12 + 2Y1

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Question:

Formula: m=;

X₂-X1

P₁ = (X₁, Y₁) P₂ = (X2, Y₂)

1) P₁=(-1.5) and P₂=(-2,-6)

How to solve this exercise of linear equations of two points.

Therefore, the smallest positive integer with at least 8 odd factors and at least 16 even factors is N = 1800.

In mathematics, combination is a way to count the number of possible selections of k objects from a set of n distinct objects, without regard to the order in which they are selected.

The number of combinations of k objects from a set of n objects is denoted by [tex]nCk[/tex] or [tex]C(n,k),[/tex] and is given by the formula:

[tex]nCk = n! / (k! *(n-k)!)[/tex]

where n! denotes the factorial of n, i.e., the product of all positive integers up to n.

by the question.

Now, let's consider the parity (evenness or oddness) of the factors of N. A factor of N is odd if and only if it has an odd number of factors of each odd prime factor of N. Similarly, a factor of N is even if and only if it has an even number of factors of each odd prime factor of N. Therefore, the condition that N has at least 8 odd factors and at least 16 even factors can be expressed as:

[tex](a_{1} +1) * (a_{2} +1) * ... * (an+1) = 8 * 2^{16}[/tex]

Let's consider the factor 2 separately. Since N has at least 16 even factors, it must have at least 16 factors of 2. Therefore, we have a_i >= 4 for at least one prime factor p_i=2. Let's assume without loss of generality that p[tex]1=2[/tex] and [tex]a1 > =4.[/tex]

Now, let's consider the remaining prime factors of N. Since N has at least 8 odd factors, it must have at least 8 factors that are not divisible by 2. Therefore, the product (a2+1) * ... * (an+1) must be at least 8. Let's assume without loss of generality that n>=2 (i.e., N has at least three distinct prime factors).

Since a_i >= 4 for i=1, we have:

[tex]N > = 2^4 * p2 * p3 > = 2^4 * 3 * 5 = 240[/tex]

Let's now try to find the smallest such N. To minimize N, we want to make the product (a2+1) * ... * (an+1) as small as possible. Since 8 = 2 * 2 * 2, we can try to distribute the factors 2, 2, 2 among the factors (a2+1), (a3+1), (a4+1) in such a way that their product is minimized. The only possibility is:

[tex](a2+1) = 2^2, (a3+1) = 2^1, (a4+1) = 2^1[/tex]

This gives us:

[tex]N = 2^4 * 3^2 * 5^2 = 1800[/tex]

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A particular concentration of a chemical found in polluted water has been found to be lethal to 20% of the fish that are exposed to the concentration for 24 hours. Twenty fish are placed in a tank containing this concentration of chemical in water. Therefore

a) Probability that exactly 14 fish survive, Let x be the number of fish that survive. Using Binomial distribution, we have:[tex]P(X = x) = C(n,x) * p^x * (1-p)^{(n-x)}[/tex] where n is the total number of fish, p is the probability of survival and C(n,x) is the binomial coefficient. We have n = 20, p = 0.8 (since 20% die) and x = 14. [tex]C(20,14) * (0.8)^14 * (0.2)^6 = 38760 * 0.000016777216 * 0.0264241152 = 0.263[/tex] Therefore, the probability that exactly 14 fish survive is 0.263

b) Probability that at least 10 fish survive To find this probability, we can find the probability that 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9 fish die, and subtract this probability from 1. Using the same formula as in (a), we have: [tex]P(X <= 9) = \sum  C(n,x) * p^x * (1-p)^{(n-x)}[/tex] where n = 20, p = 0.8 and x varies from 0 to 9. Using a calculator or software, we find:P(X <= 9) = 0.0169Therefore,P(X >= 10) = 1 - P(X <= 9) = 1 - 0.0169 = 0.983 Therefore, the probability that at least 10 fish survive is 0.983.

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