Find an explicit solution for y ′ =ye^ −x2 ,y(0)=1
. It is alright to leave a definite integral in your answer.

It step 3 I got The same question on khan academy

Answer:

y = 1/3 x - 2

Step-by-step explanation:

Start with the slope-intercept form of the equation of a line.

y = mx + b

b is the y-intercept. That is the y-coordinate of the point of intersection of the line and the y-axis. In this case, that point is (0, -2), so b = -2.

Now we have

y = mx - 2

m is the slope. We look at the two points on the line that are given. Start at (0, -2). Slope = m = rise/run. We go from point (0, -2) to point (3, -1). We start by going 1 unit up. That is a rise of 1. rise = 1. Now we go 3 units to the right. That is a run of 3. run = 3.

m = rise/run = 1/3

Now we substitute 1/3 for m in the last equation we have above.

y = 1/3 x - 2

predictive validity assesses the accuracy of a selection tool in predicting future outcomes or performance, providing valuable insights into the tool's effectiveness in making accurate predictions or forecasts.

The term you are looking for is "predictive validity."

Predictive validity refers to the ability of a selection tool or assessment to accurately predict or forecast a specific criterion or outcome. It assesses how well the tool can predict future performance, behavior, or success based on the scores or results obtained from the tool.

To determine the predictive validity of a selection tool, researchers or organizations typically collect data on individuals' scores or performance on the tool and then observe their subsequent performance or behavior in real-life or relevant contexts. By comparing the scores or results from the selection tool to the actual outcomes, the predictive validity of the tool can be evaluated.

For example, in the context of employee selection, a company might use a pre-employment test to assess job applicants' cognitive abilities. To determine the predictive validity, the company would collect data on the test scores of the applicants and then observe their subsequent job performance once they are hired. If the test scores significantly correlate with job performance, indicating that higher test scores tend to be associated with better job performance, the selection tool demonstrates predictive validity.

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Steps to solve:

4x + 1/3y^2 when x = 2 and y = 3

~Substitute

4(2) + 1/3(3)^2

~Simplify

8 + 1/3(9)

~Simplify

8 + 3

~Add

11

Best of Luck!

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Answer: 14

Explanation:

6 x 2 = 12

1 x 2 = 2

12 + 2 = 14

I hope this helped!

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Answer:

14

Step-by-step explanation:

6*3-2(2*1)

=18-4=14

Answer:

a

Step-by-step explanation: codigo binario

The statement "Using the three standard deviation criterion, the last observation (x=43) would be considered an outlier" is true.

Given data:

7, 11, 12, 18, 20, 22, 43.

To find out whether the last observation is an outlier or not, let's use the three standard deviation criterion.

That is, if a data value is more than three standard deviations from the mean, then it is considered an outlier.

The formula to find standard deviation is:

S.D = \sqrt{\frac{\sum_{i=1}^{N}(x_i-\bar{x})^2}{N-1}}

Where, N = sample size,

             x = each value of the data set,

    \bar{x} = mean of the data set

To find the mean of the given data set, add all the numbers and divide the sum by the number of terms:

Mean = $\frac{7+11+12+18+20+22+43}{7}$

          = $\frac{133}{7}$

          = 19

Now, calculate the standard deviation:

$(7-19)^2 + (11-19)^2 + (12-19)^2 + (18-19)^2 + (20-19)^2 + (22-19)^2 + (43-19)^2$= 1442S.D

                                                                                                                               = $\sqrt{\frac{1442}{7-1}}$

                                                                                                                                ≈ 10.31

To determine whether the value of x = 43 is an outlier, we need to compare it with the mean and the standard deviation.

Therefore, compute the z-score for the last observation (x=43).Z-score = $\frac{x-\bar{x}}{S.D}$

                                                                                                                      = $\frac{43-19}{10.31}$

                                                                                                                      = 2.32

Since the absolute value of z-score > 3, the value of x = 43 is considered an outlier.

Therefore, the statement "Using the three standard deviation criterion, the last observation (x=43) would be considered an outlier" is true.

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Answer:

The coordinates seem to be A(-2, -4), B(3, 4) and C (3, -4). The rule (2x, 2y) means that you multiply the coordinates of the points by 2 so you just have to plot the points A'(-4, -8), B'(6, 8), C'(6, -8) and then connect them.

the area of triangle $AMN$ is 8 square cm.

To find the area of triangle $AMN$, we need to determine the lengths of its base and height.

In square $ABCD$ with side length 4 cm, $N$ is the midpoint of side $BC$, so $BN = NC = \frac{1}{2} \cdot 4 = 2$ cm.

Similarly, $M$ is the midpoint of side $CD$, so $CM = MD = \frac{1}{2} \cdot 4 = 2$ cm.

Now, we can see that $AM$ is the height of triangle $AMN$ and has a length of 4 cm, as it is parallel to side $AD$ of the square.

$AN$ is the base of triangle $AMN$ and has a length of $BN + CM = 2 + 2 = 4$ cm.

Therefore, the area of triangle $AMN$ is given by:

$A_{AMN} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 4 \times 4 = 8$ square cm.

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Answer:

4

Step-by-step explanation:

took the test and got it right!

A 10% increase in the price of good Y will result in a 6% increase in the quality demanded of good X.

A number or variable is a quantity. Measuring the percentage change of the quantity demanded for a good to the percentage change in the price of another good is called cross-elasticity of demand.

As per the question,

As the cross-elasticity of the goods is 0.6 i.e. 1% will increase in the price of good Y, increasing the demand for good X by 0.6%. X and Y are the substitute goods because when the price of Y increases sales of X increase.

⇒ When the price of good Y increases by 10%, then that will result in

    increase in quantity demanded of good X   =   0.6 × 10

                                                                              =   6%

⇒ quantity demanded of good X is 10 units, 6% increase means

    quantity demanded of good X   =   ( 1.06 × 10 )

                                                          =   10.6 units

Therefore, A 6% increase in the quantity demanded of good X, when a 10% increase in the price of good Y i.e. option a is correct.

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The complete question is

At the current prices of goods X and Y, the quantity demanded of good X is 10 units, and the quantity demanded of good Y is 5 units. The cross-price elasticity of demand between goods X and Y is 0.6. A 10% increase in the price of good Y will result in which of the following?

a. A 6% increase in the quantity demanded of good X.

b. A 10% increase in the quantity demanded of good X.

Answer: a

Step-by-step explanation:

Tell me if it is correct

Step-by-step explanation:

x+40=60°{ vertically opposite angle r equal}

hope it helps.

stay safe healthy and happy.

Answer:

x = 20

Step-by-step explanation:

Angle 60 will be the same as x+40

60 = x+40

60-40 = x

20 =x

Answer: 20 miles

Step-by-step explanation:

Hi, since the situation forms a right triangle (see attachment) we have to apply the Pythagorean Theorem:

x^2 = a^2 + b^2

Where x is the hypotenuse of the triangle (in this case the distance between Dayton and Belleville) and a and b are the other sides.

Replacing with the values given:

x^2 = 16^2 + 12^2

x^2 = 256+144

x^2 = 400

x = √400

x = 20 miles

Feel free to ask for more if needed or if you did not understand something.

In summary, the relationships between the corresponding sides and angles of similar triangles are: Corresponding sides are proportional and congruent.

When two triangles are similar, the corresponding sides of the triangles are proportional. This means that the ratio of the lengths of corresponding sides in the two triangles is equal. Similarly, the corresponding angles of similar triangles are congruent. This means that the angles in the two triangles that correspond to each other are equal in measure.

When two triangles are similar, it means that they have the same shape but possibly different sizes. The concept of similarity implies that the corresponding sides of the triangles have the same proportional relationship.

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Answer: She will use 6 cans of pinto beans .

She will use 6 cans of kidney beans.

Step-by-step explanation:

As per given,

For bean salad : lima beans : pinto beans : kidney beans

= 3:2:2

Let quantity of lima beans = 3x, pinto beans 2x , kidney beans 2x.

if she use 9 cans of lima beans, then

3x=9

⇒x=9

Now, 2x= 2 x 3 =6

Thus , she will use 6 cans of pinto beans and 6 cans of kidney beans.

Answer:

7 1/7

Step-by-step explanation:

24 hours  = 1 day

7 days = 1 week

⇒ number of hours in 1 week = 24 x 7 = 168

⇒ number of weeks in 1200 hrs = 1200 ÷ 168 = 7 1/7

Answer:

Check it below

Step-by-step explanation:

Hello!

By definition, the intercept of the 3 bisectors, within a triangle is the Incenter. So let's get started, by tracing three bisectors.

In the triangle PQR::

\(\overline {QR},\:\overline{PR}\)

   4.Trace with a ruler, from each intersection point a line. You'll trace three lines then.

    5. Place the compass' needle point in this intersection point, (inside the triangle) with a hinge up to the triangle side, draw the circle inscribed.

Answer:

edg but few yrs later

Step-by-step explanation:

Thus, the equation of the plane determined by the intersecting lines L1 and L2 is: -2x + 14y + 18z - 48 = 0.

To find the plane determined by the intersecting lines L1 and L2, we need to find a normal vector to the plane.

First, we'll find two direction vectors for the lines L1 and L2.

For L1:

x = -1 + t

y = 2 + 4t

z = 1 - 3t

Taking the differences of these equations, we obtain two direction vectors for L1:

v1 = <1, 4, -3>

For L2:

x = 1 - 4s

y = 1 + 2s

z = 2 - 2s

Again, taking the differences of these equations, we obtain two direction vectors for L2:

v2 = <-4, 2, -2>

Since the plane contains both lines, the normal vector to the plane will be perpendicular to both direction vectors, v1 and v2.

To find the normal vector, we can take the cross product of v1 and v2:

n = v1 x v2

n = <1, 4, -3> x <-4, 2, -2>

Using the cross product formula, the components of the normal vector n can be calculated as follows:

n = <(4 * -2) - (-3 * 2), (-3 * -4) - (1 * -2), (1 * 2) - (4 * -4)>

n = <-8 - (-6), 12 - (-2), 2 - (-16)>

n = <-2, 14, 18>

So, the normal vector to the plane determined by the intersecting lines L1 and L2 is n = <-2, 14, 18>.

Now we can write the equation of the plane using the normal vector and a point on the plane (which can be any point on either L1 or L2).

Let's choose the point (-1, 2, 1) on L1.

The equation of the plane can be written as:

-2(x + 1) + 14(y - 2) + 18(z - 1) = 0

Simplifying:

-2x - 2 + 14y - 28 + 18z - 18 = 0

-2x + 14y + 18z - 48 = 0

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The survey methods that will produce a simple random sample of 60 students in a high school is: Number the students in the official school roster. Use a table of random numbers to choose 60 students from this roster for the survey.

Simple random sampling is a type of probability sampling where the researcher randomly chooses a subset of participants from a population. Each part of the population has the same chance of being selected. Then, data is collected from as large a percentage as possible of the random subset.

The American Community Survey is an example of simple random sampling. In order to gather detailed data on the population of the US, the Census Bureau officials randomly choose 3.5 million households a year and use variety of methods to make them sure to fill out the survey.

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Lewis has to pay $260 more to have his electricity and cable turned on because of his bankruptcy.

Bankruptcy is a legal proceeding involving a person or business that is unable to repay its outstanding debts.

Had Lewis not filed bankruptcy, he would have paid = 90+50+65+75

He would have paid (let us say amount A)= $280

After filing for bankruptcy he has to pay = 205+75+150+110

He has to pay (let us say amount B)= $540

Difference between amount A and amount B = $540-$280

Difference between amount A and amount B = $260

Therefore, Lewis has to pay $260 more to have his electricity and cable turned on because of his bankruptcy.

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The expected value per ticket from the standpoint of the charity is $0.27.

The expected value represents the average amount that the charity earns by selling one ticket. In this case, the charity plans to sell 1100 tickets at a cost of $1.00 each, resulting in a total revenue of $1100.00. Since there is only one prize worth $400.00, the charity's net earnings will be $700.00 ($1100.00 - $400.00) if all the tickets are sold.

To calculate the expected value per ticket, we divide the net earnings by the number of tickets sold, which is $0.64 ($700.00 / 1100). Rounded to the nearest cent, the expected value per ticket is $0.27.

The expected value is a useful concept for assessing the potential outcomes of an event. In this context, it helps the charity estimate the average amount they can expect to earn per ticket sold. It is important to note that the expected value is not necessarily the actual amount that will be earned from each ticket, as individual outcomes can vary. However, it provides a baseline estimate based on probabilities and can help the charity make informed decisions about their fundraising efforts.

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The approximation probability that two people in a group of seven have the same birthday is 0.0000007 or 7 in 10 million.

The approximation probability that two people in a group of seven have the same birthday can be determined using a formula.

To calculate the probability that two people in a group of seven have the same birthday, we can use an approximation formula.

The formula is given as:P(n) = 1 - (365!/(365^n *(365-n)!)) * (1/n!)

Where P(n) is the probability that at least two people share the same birthday, n is the number of people in the group, and the exclamation mark (!) is the factorial function.

For a group of seven people, we substitute n=7 in the formula, and we get:

P(7) = 1 - (365!/(365^7 *(365-7)!)) * (1/7!)This simplifies to:P(7) ≈ 1 - 0.9999993 = 0.0000007

Therefore, the approximation probability that two people in a group of seven have the same birthday is 0.0000007 or 7 in 10 million.

The probability is incredibly small, and it implies that it is unlikely for two people in a group of seven to have the same birthday.

This is because there are only 365 possible birthdays in a year, and the sample size of seven is too small to increase the likelihood of a match.

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Answer:

\( \frac{3}{2 } \times \frac{11}{4} \\ \frac{33}{8} \\ 4 \frac{1}{8} \)

The composite function (f - g)(x) is equal to 3x² - 3.

In Mathematics and Geometry, a polynomial function is a mathematical expression which comprises intermediates (variables), constants, and whole number exponents with different numerical value, that are typically combined by using mathematical operations such as the following:

Next, we would subtract the two (2) given polynomials as follows;

(f - g)(x) = f(x) - g(x)

(f - g)(x) = 3x² + x - (x + 3)

(f - g)(x) = 3x² + x - x - 3

(f - g)(x) = 3x² - 3

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Answer:

x=2/9

Step-by-step explanation:

x^3=8/729

Hence,

x= cube root of (8/729)

x=cube root of 8

  cube root of 729

x=2

   9

Answer: decimal form : x=0.10475656

Step-by-step explanation:

Take roots of both sides and solve

A woman 5-feet tall casts an 8-foot shadow. at the same time of day, the shadow of a tree nearby is 120 feet long. in feet, 75 feet  tall is the tree.

Let the tree height = x

From the question, we have

5/8 = x/120

x = (5*120)/8

x = 75 feet

Tree height = 75 feet

Multiplication:

Mathematicians use multiplication to calculate the product of two or more numbers. It is a fundamental operation in mathematics that is frequently utilized in everyday life. When we need to combine groups of similar sizes, we utilize multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.

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In machine learning, the formula for AUC (Area under ROC Curve) is given below:

AUC = (1/2) [(TPR0FPR1) + (TPR1FPR2) + ... + (TPRm-1FPRm)]

Where, AUC = Area under the ROC Curve

FPR = False Positive Rate

TPR = True Positive Rate

The ROC curve is a curve that is plotted by comparing the true positive rate (TPR) with the false positive rate (FPR) at various threshold settings.

The false positive rate (FPR) is calculated by dividing the number of false positives by the sum of the number of false positives and the number of true negatives.

The true positive rate (TPR) is calculated by dividing the number of true positives by the sum of the number of true positives and the number of false negatives.

AUC is a popular measure for evaluating binary classification problems in machine learning. AUC ranges from 0 to 1, with a higher value indicating better performance of the classifier.

AUC is calculated as the area under the ROC curve, which is a plot of the true positive rate (TPR) versus the false positive rate (FPR) for different threshold values.

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It is given that the odd against an event are 5 to 13.

The probability that the event will occur is

Answer:

ST = CHORD

PR = RADIUS

MN = DIAMETER

Step-by-step explanation:

Answer:

ST) Chord/// PR) Radius/// MN) Diameter