Casey was asked to find XY. What is Casey error?

The system of linear equations that can be solved from the matrices is given as follows:

Considering that the row [3, -6] is common to matrices Ax and Ay, the matrix A is given as follows:

A = [-5 4; -8 1]

Hence the multiplication of matrices representing the system is given as follows:

[-5 4; -8 1][x; y] = [3; -6]

Applying the multiplication of matrices, the system of equations is given as follows:

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Answer:it’s 1/4

Step-by-step explanation:

To factor the expression 4x^2 - 25, we can use the difference of squares formula, which states that a^2 - b^2 can be factored as (a + b)(a - b).

In this case, we have 4x^2 - 25, which can be written as (2x)^2 - 5^2. Comparing it with the difference of squares formula, we can identify that a = 2x and b = 5. Therefore, the correct option is:

b. (2x)^2 - (5)^2

Using the difference of squares formula, we can factor it as follows:

(2x + 5)(2x - 5)

Hence, the correct factorization of 4x^2 - 25 is (2x + 5)(2x - 5), which is equivalent to option b.

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The entropy of the outcome of this experiment = 9

A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.

Given that,

A coin having probability p=2/3

Heads is flipped 6 times

If the coin is flipped 6 times

The Total Number of Trial in the Experiment =2/3

It comes up heads 6 times

This Means: Number of Successful Outcome of HEADS =6

In an experimental probability,

Experimental probability of the coin’s coming up heads

=Number of Successful Outcome of HEADS/Total Number of Trials in the Experiment

= 6/(2/3)

= 6*3/2

= 18/2

= 9

Therefore,

The entropy of the outcome of this experiment = 9

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In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

2/6

equivalent fraction = ?

Step 02:

number line

The equivalent fraction in the number line is 1 /3 .

The answer is:

The equivalent fraction in the number line is 1 /3 .

Answer: d($30)

Explanation: $30 times d which d is the number of days.

\(\boxed{\sf Slope=m=tan\Theta=\dfrac{y_2-y_1}{x_2-x_1}}\)

Looking at options

#A

\(\\ \sf\longmapsto m=\dfrac{3}{-3}=-1\)

#B

\(\\ \sf\longmapsto m=tan\Theta=tan0=0\)

#C

\(\\ \sf\longmapsto m=tan90=\infty\)

#D

\(\\ \sf\longmapsto m=\dfrac{3}{3}=1\)

Hence option D is correct

Answer:

• The first graph.

→ Consinder points (-2, 0) and (-3, -1) from the graph:

\({ \tt{slope = \frac{y _{2} - y _{1} }{x _{2} - x _{1} } }} \\ \\ { \tt{slope = \frac{0 - ( - 1)}{ - 2 - ( - 3)} = \frac{1}{1} }} \\ \\ { \boxed{ \tt{slope = {}^{ + } 1}}}\)

Answer:

observational study

Step-by-step explanation:

Answer:

I am not sure but I would say rectangular prisim

Step-by-step explanation:

The amount after 5 years on $100 using the compound interest is $122.

According to the question,

We have the following information:

Principal = $100

Interest Rate = 4%

Time= 5 years

We know that the following formula is used to find the total amount if there is compound interest:

Compound amount = \(P(1+\frac{r}{100})^{t}\) where P is the principal, r is interest rate and t is the time in years

(Note that there are different formulas for compound interest depending on how it is calculated.)

A = \(100(1+\frac{4}{100})^{5}\)

A = \(100(\frac{104}{100})^{5}\\100(1.04})^{5}\)

A = 100*1.22

A = $122

Hence, the amount after 5 years on $100 using the compound interest is $122.

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a) Either 3 or 4 questions did Mike answer correctly.

b) Either 7 or 8 questions did Sheila answer correctly.

In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

a) Let mike did x correct

then, incorrect will be (10- x)

The equation is:

Now, 5x + (10 - x) (-3) = 0

=> 5x - 30 + 3x = 0

=> 8x = 30

=> x = 30/8

=> x > 3 and x < 4

b) Let Sheila did y correct

then, incorrect = (10 - y)

Now, 5y + (10 - y) (-3) = 32

=> 5y - 30 + 3y = 32

=> 8y = 62

=> y > 7 and y< 8

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The given question is incomplete, complete question is:

In a school test consisting of 10 questions, 5 points are awarded for a correct answer but 3 points are deducted for an incorrect answer.

A blank answer scores (). Mike scored a total of () and he did not leave all of the answers blank. (a) How many questions did Mike answer correctly? _ _ _ _ _ _ _ _ Sheila scored a total of 32. (b) How many questions did Sheila answer correctly?

The rate of the slower car is 77km/hr

Velocity is the rate of change of displacement with time. It is measured in meter per second and it is a vector quantity.

velocity = displacement/time

displacement = velocity × time

represent the faster car by v1 and the slower car by v2

v1 = v2+16

V2 = v1-16

Total displacement = 680km

680 =( v1+V2)t

680 = (v1+V2)4

v1+v2 = 680/4

v2+16+v2 = 170

2v2 = 170-16

2v2 = 154

v2 = 154/2

v2 = 77km/hr

therefore the rate of the slower car is 77km/hr

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Answer:

Step-by-step explanation:

Triangle area formula:

We have:

The area is:

Correct choice is C

Answer:

100-43= 57

Explanation:

So, Frazer did 57% wrong

Answer:

57% incorrect wow he should have studied better lol ;)

Step-by-step explanation:

If he SCORED 43%, than out of 100% the remaining is 57%

Answer:

-7/4x-68

Step-by-step explanation:

If the original triangle has an area equal to 729 small dotty triangles. The original triangle has an area of 8 square units.

Let's first find the pattern of the number of small triangles in each row. The first row has 1 small triangle. The second row has 3 small triangles. The third row has 5 small triangles, and the fourth row has 7 small triangles. We can see that the pattern is that each row has 2 more small triangles than the previous row.

To find how many small triangles are in the third row, we add 2 to the number of small triangles in the second row:

3 + 2 = 5

So there are 5 small triangles in the third row.

To find how many small triangles are in the fourth row, we add 2 to the number of small triangles in the third row:

5 + 2 = 7

So there are 7 small triangles in the fourth row.

To find the total number of rows, we can count the number of rows from the top of the triangle to the bottom. Alternatively, we can use the formula for the sum of an arithmetic series to find the number of terms in the sequence. In this case, the first term is 1, the common difference is 2, and the last term is 7. Using the formula:

n = (last term - first term) / common difference + 1

n = (7 - 1) / 2 + 1

n = 4

So there are 4 rows in the triangle.

Finally, we can use the formula for the sum of an arithmetic series to find the total number of small triangles in the original triangle. In this case, the first term is 1, the common difference is 2, and the number of terms is 4. Using the formula:

sum = (n / 2) * (first term + last term)

sum = (4 / 2) * (1 + 7)

sum = 4 * 4

sum = 16

So there are 16 small triangles in the original triangle. Since each small triangle has an area of 1/2, the total area of the original triangle is:

area = 16 * (1/2)

area = 8

Therefore, the original triangle has an area of 8 square units.

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The description that will show that it is safe to perform inference is that (a) Both dotplots are roughly symmetric. There are no outliers in either dotplot.

In order to use the two-sample t procedure to make inferences, certain conditions need to be met such as the sample being random and independent.

The variances for the groups in the data need to be equal which is why the presence of no outliers in either dotplot would present an safe opportunity to be able to perform inferences on the data.

In conclusion, option A is correct.

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The value of c is 1/17.

It is a branch of mathematics that deals with the occurrence of a random event.

Here it is given that the function f(x) can serve as a probability distribution of the discrete random variable X when f(x) = c(x² + 4), for x = 0, 1 ,2

We have to find the value of c

Since f(x) represents the probability distribution x = 0, 1 ,2

So we have f(0)+f(1)+f(2)=1

c(0²+4)+c(1²+4)+c(2²+4)=1

4c+5c+8c=1

17c=1

Divide both sides by 17

c=1/17

Hence, the value of c is 1/17.

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Determine the value c so that each of the following function can serve as a probability distribution of the discrete random variable X when f(x)=c(x2+4), for x=0, 1,2?

a.

1/3

b.

1/17

c.

1/2

d.

1/13

The value of the experimental probability of tossing heads is,

⇒ 1 / 3

We have to given that;

Coin Toss Results: T, H, T, H, T, H, T, T, T, T, H, T, H, T, T

Where, H stands for heads and T stands for Tails.

Hence, Total outcomes = 15

And, Head outcomes = 5

Thus, The value of the experimental probability of tossing heads is,

⇒ 5 / 15

⇒ 1 / 3

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Answer:

32,64,128

Step-by-step explanation:

previous number × 2

Answer:

let the two number is x and y

x + y = 4 1/2 .....(i)

x - y = 3 1/4 ......(ii)

adding question (i) and (ii)

x + y = 9/2

x - y = 31/4

=> 2x = 31/4

x = 8/31

substituting the value x in equation 1

8/31 + y = 9/ 2

y = 9/2 - 8/31

y =203/62

the value of x = 8/31

y = 203/62

Answer:

(a) The probability that a randomly selected Time interval between irruption is longer than 84 minutes is 0.3264.

(b) The probability that a random sample of 13 time intervals between irruption has a mean longer than 84 minutes is 0.0526.

(c) The probability that a random sample of 20 time intervals between irruption has a mean longer than 84 minutes is 0.0222.

(d) The probability decreases because the variability in the sample mean decreases as we increase the sample size

(e) The population mean may be larger than 75 minutes between irruption.

Step-by-step explanation:

We are given that a geyser has a mean time between irruption of 75 minutes. Also, the interval of time between the eruption is normally distributed with a standard deviation of 20 minutes.

(a) Let X = the interval of time between the eruption

So, X ~ Normal(\(\mu=75, \sigma^{2} =20\))

The z-score probability distribution for the normal distribution is given by;

                            Z  =  \(\frac{X-\mu}{\sigma}\)  ~ N(0,1)

where, \(\mu\) = population mean time between irruption = 75 minutes

           \(\sigma\) = standard deviation = 20 minutes

Now, the probability that a randomly selected Time interval between irruption is longer than 84 minutes is given by = P(X > 84 min)

    P(X > 84 min) = P( \(\frac{X-\mu}{\sigma}\) > \(\frac{84-75}{20}\) ) = P(Z > 0.45) = 1 - P(Z \(\leq\) 0.45)

                                                        = 1 - 0.6736 = 0.3264

The above probability is calculated by looking at the value of x = 0.45 in the z table which has an area of 0.6736.

(b) Let \(\bar X\) = sample time intervals between the eruption

The z-score probability distribution for the sample mean is given by;

                            Z  =  \(\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }\)  ~ N(0,1)

where, \(\mu\) = population mean time between irruption = 75 minutes

           \(\sigma\) = standard deviation = 20 minutes

           n = sample of time intervals = 13

Now, the probability that a random sample of 13 time intervals between irruption has a mean longer than 84 minutes is given by = P(\(\bar X\) > 84 min)

    P(\(\bar X\) > 84 min) = P( \(\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }\) > \(\frac{84-75}{\frac{20}{\sqrt{13} } }\) ) = P(Z > 1.62) = 1 - P(Z \(\leq\) 1.62)

                                                        = 1 - 0.9474 = 0.0526

The above probability is calculated by looking at the value of x = 1.62 in the z table which has an area of 0.9474.

(c) Let \(\bar X\) = sample time intervals between the eruption

The z-score probability distribution for the sample mean is given by;

                            Z  =  \(\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }\)  ~ N(0,1)

where, \(\mu\) = population mean time between irruption = 75 minutes

           \(\sigma\) = standard deviation = 20 minutes

           n = sample of time intervals = 20

Now, the probability that a random sample of 20 time intervals between irruption has a mean longer than 84 minutes is given by = P(\(\bar X\) > 84 min)

    P(\(\bar X\) > 84 min) = P( \(\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }\) > \(\frac{84-75}{\frac{20}{\sqrt{20} } }\) ) = P(Z > 2.01) = 1 - P(Z \(\leq\) 2.01)

                                                        = 1 - 0.9778 = 0.0222

The above probability is calculated by looking at the value of x = 2.01 in the z table which has an area of 0.9778.

(d) When increasing the sample size, the probability decreases because the variability in the sample mean decreases as we increase the sample size which we can clearly see in part (b) and (c) of the question.

(e) Since it is clear that the probability that a random sample of 20 time intervals between irruption has a mean longer than 84 minutes is very slow(less than 5%0 which means that this is an unusual event. So, we can conclude that the population mean may be larger than 75 minutes between irruption.

The purchasing power in five years will be $15,476.

To predict the purchasing power in five years, we can substitute the value of X as 5 into the equation y = 20000(0.95)^X.

Plugging in X = 5, we have:

\(y = 20000(0.95)^5\)

Calculating the expression, we find:

\(y ≈ 20000(0.774)\)

Simplifying further, we get:

\(y ≈ 15480\)

Rounding the result to the nearest dollar, the predicted purchasing power in five years would be approximately $15,480.

Therefore, the closest option to the predicted purchasing power in five years is $15,476.

So the correct answer is:

$15,476.

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Rounding to the nearest dollar, the predicted purchasing power in five years is approximately $15,480.

To predict the purchasing power in five years using the given equation, we substitute the value of x (representing the number of years) as 5 and calculate the result.

The equation provided is: y = 20000(0.95)^x

Substituting x = 5 into the equation, we have:

y = 20000(0.95)⁵

Now, let's calculate the result:

y ≈ 20000(0.95)⁵

≈ 20000(0.774)

y ≈ 20000(0.774)

≈ 15,480

This means that, according to the given equation, the purchasing power of $20,000, with an inflation rate of five percent, would be predicted to be approximately $15,480 after five years.

By changing the value of x (representing the number of years) to 5, we can use the preceding equation to forecast the buying power in five years.

The example equation is: y = 20000(0.95)^x

When x = 5 is substituted into the equation, we get y = 20000(0.95).⁵

Let's now compute the outcome:

y ≈ 20000(0.95)⁵ ≈ 20000(0.774)

y ≈ 20000(0.774) ≈ 15,480

This indicates that based on the equation, after five years, the purchasing power of $20,000 would be estimated to be around $15,480 with a five percent inflation rate.

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The linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

To determine the linear function with the same y-intercept as the graph, we need to find the equation of the line passing through the points (3, 4) and (5, 0).

First, let's find the slope of the line using the formula:

slope (m) = (change in y) / (change in x)

m = (0 - 4) / (5 - 3)

m = -4 / 2

m = -2

Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1)

Using the point (3, 4) as our reference point, we have:

y - 4 = -2(x - 3)

Expanding the equation:

y - 4 = -2x + 6

Simplifying:

y = -2x + 10

Now, let's check the given options to find the linear function with the same y-intercept:

Option 1: The table with x-values (-3, -1, 1, 3) and y-values (-4, 2, 8, 14)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 2: The table with x-values (-4, -2, 2, 4) and y-values (-26, -18, -2, 6)

The y-intercept is not the same as the given line. So, this option is not correct.

Option 3: The table with x-values (-5, -3, 3, 5) and y-values (-15, -11, 1, 5)

The y-intercept is the same as the given line (10). So, this option is correct.

Option 4: The table with x-values (-6, -4, 4, 6) and y-values (-26, -14, 34, 46)

The y-intercept is not the same as the given line. So, this option is not correct.

Therefore, the linear function that has the same y-intercept as the given graph is the equation y = -2x + 10, corresponding to option 3.

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Answer:

its just a rotation. its as simple as rotating it back to its origonal form and matching up the corners

Step-by-step explanation:

Answer:

15 tables with 4 seats and 8 tables with 2 seats.

Step-by-step explanation:

x = 4 seated tables

y = 2 seated tables

x + y = 23

4x + 2y = 76

Multiply first equation by -2 to cancel y's:

-2x - 2y = -46

4x + 2y = 76

2x = 30

x = 30 / 2

x = 15

And we said 23 tables so:

23 - 15 = 8

x = 15

y = 8

The linear function for the given graph is y = x + 20.

What is a linear function?

A straight line on the coordinate plane is represented by a linear function. It has one independent variable and one dependent variable. For slope (m) and y-intercept (b) form, the equation is given by:

y = mx + b

From the graph,

The coordinates of the given graph are (0,20) and (20,40)

Then, slope (m) = (40-20)/(20-0) = 20/20 = 1

and y-intercept (b) = 20

So, the equation will be y = 1x + 20

Hence, the linear function for the given graph is y = x + 20.

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If you're talking about a discrete distribution, then

\(P(X=x)=\begin{cases}\frac1{61}&\text{for }x\in\{10,11,12,\ldots,70\}\\0&\text{otherwise}\end{cases}\)

(1/61 because there are 61 numbers in the range of integers from 10 to 70) so that

\(P(X<25)=\displaystyle\sum_{x=10}^{24}P(X=x)=\boxed{\dfrac{15}{61}}\)

If the distribution is continuous, we would have the same density function, but x can be any real number in the interval [10, 70]. So we have

\(P(X<25)=\displaystyle\int_{-\infty}^{25}P(X=x)\,\mathrm dx=\frac1{60}\int_{10}^{25}\mathrm dx=\dfrac{15}{60}=\boxed{\dfrac14}\)