9•10^7 is how many times as large as 3•10^7​

Slope intercept form for he given equation is \(y=3x+17\).

The line with m as the slope, m and c as the y-intercept is the graph of the linear equation \(y = mx + c\). The values of m and c are real in the slope-intercept form of the linear equation.

The slope, m, is a measure of how steep a line is. Sometimes, the gradient of a line is referred to as its slope. A line's y-intercept, c, denotes the y-coordinate of the location where the line's graph crosses the y-axis.

Slope intercept form:\(y = mx + c\)

Point slope form: \(y-y1=m(x-x1)\)

Given point(-3,8) and slope of 3;

⇒\(y-8=3(x+3);\\y=3x+9+8;\\y=3x+17\)

Slope intercept form for he given equation is \(y=3x+17\).

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The linear equation for the area is:

40 = 7*(x + 4)

The solution is x = 1.71 = x

Remember that for a rectangle of length L and width W, the area is:

A = L*W

In this case, we can see that:

W = 7

L = x + 4

A = 70

Replacing that, we can get the linear equation:

40 = 7*(x + 4)

Now we can solve this, we jus need to isolate x.

40/7 = x + 4

40/7 - 4 = x

5.71 - 4 = x

1.71 = x

The solution is x = 1.71 = x

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Answer:

The measure of angle E is 55°

Step-by-step explanation:

In an isosceles triangle, the vertex angle is the angle including between the two equal sides, the base angles are the other angles of the triangle, the base angles are equal in measures

In triangle DEF

∵ DE is congruent to FD

∴ The length of DE = the length of FD

∵ ∠D is the angle including sides DE and FD

∴ ∠D is the vertex angle

∴ ∠F and ∠E are the base angles

∵ The base angles of the isosceles triangle are equal in measures

∴ m∠F = m∠E

∵ m∠F = 55°

∴ m∠E = 55°

∴ The measure of angle E is 55°

Answer:

John=3150 peter=7350

Step-by-step explanation:

Hope this helps

Value of r is different for every series

let

a , b , c , d ..... be geometric series then

r = b/a or d/c and so on

where r is common ratio

The negative sign indicates that the force is acting opposite to the direction of motion of the aircraft. Thus, the average force that must act on the aircraft to bring it to a stop is approximately -474000 N in mks units correct to three significant figures.

The formula to calculate the average force is: average force = change in momentum / time taken

Here, the change in momentum of the aircraft = m × v, where m is the mass of the aircraft and v is the final velocity of the aircraft.

The initial velocity of the aircraft is 52.1 m/s and it comes to a stop. Thus, the final velocity of the aircraft is 0 m/s.

The distance covered by the aircraft is 991 m.

Mass of the aircraft, m = 33,872 kg

Initial velocity, u = 52.1 m/s

Final velocity, v = 0 m/s

Distance covered, s = 991 m

The time taken to stop can be calculated using the formula:v^2 = u^2 + 2as

0 = (52.1 m/s)^2 + 2a(991 m)

Solving for acceleration, a = -14.032 m/s^2

Now, the change in momentum of the aircraft = m × v = 33,872 × (0 - 52.1)

= -1,763,699.2 kg m/s

The time taken to stop can be calculated as follows: u = a × t + v052.1

= (-14.032 m/s^2) × t + 0

t = 52.1 / 14.032

t ≈ 3.719 s

Therefore, the average force on the aircraft is:

average force = change in momentum / time taken

= -1,763,699.2 / 3.719

= -474048.33 N

≈ -474000 N

The negative sign indicates that the force is acting opposite to the direction of motion of the aircraft. Thus, the average force that must act on the aircraft to bring it to a stop is approximately -474000 N in mks units correct to three significant figures.

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Answer:

x=25

y= 5

Step-by-step explanation:

The translation of the graph from y = x² to y = (x - 2)² +1 is describe by - B.   shift of 2 units left and then shift of 1 unit up.

In geometry, a translation is a transfer that occurs either horizontally to a left or right as well as vertically up or down. It may also consist of a mix of the two.

Given data:

Parent function- y = x²

New function -  y = (x - 2)² +1

Thus, the translation of the graph from y = x² to y = (x - 2)² +1 is describe by - B.   shift of 2 units left and then shift of 1 unit up.

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Complete question:

1. Which of the following most accurately describes the translation of the graph from y = x² to y = (x - 2)² +1?

A.  shift of 2 units right and then shift of 1 unit up.

B.   shift of 2 units left and then shift of 1 unit up.

Answer:

0

Step-by-step explanation:

They all seem to be plotted correctly in accordance with the graph

Answer:

the answer is 4

Step-by-step explanation:

hope this helps

Answer:

1. 2:5

2. 5:2

3. 2,5

Step-by-step explanation:

Hope you have a great day

The position of the player B from the goal is 24 ft.

The position of the player A from the goal = 87 ft

The position of the player B from player A = 63 ft

let the position of the player B from the goal = y

Here is a little sketch of the positions of the players.

|<---------------------------------87 ft---------------------------------------------->|

Player A --------------63 ft-------------Player B ----------y------------Goal

The position of the player B from the goal is calculated as follows;

63 ft + y = 87 ft

y = 87 ft - 63 ft

y = 24 ft

Thus, the position of the player B from the goal is 24 ft.

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Answer:

√-48=4i√3

Step-by-step explanation:

because negative number never has a real root so 1st and 2nd option r out . i^2= -1 so root and Square cuts out eachother so i should be out of the root hence option 4th is also cut out. so 3 rd is correct.

To reduce the third-order ordinary differential equation y - y" - 4y + 4y = 0 into a companion system of linear equations, we introduce new variables u and v:

Let u = y,

v = y',

w = y".

Taking the derivatives of u, v, and w with respect to the independent variable (let's denote it as x), we have:

du/dx = y' = v,

dv/dx = y" = w,

dw/dx = y"'.

Now we can rewrite the given differential equation in terms of u, v, and w:

u - w - 4u + 4u = 0.

Simplifying the equation, we get:

-3u - w = 0.

This equation can be expressed as a system of first-order linear differential equations as follows:

du/dx = v,

dv/dx = w,

dw/dx = -3u - w.

Now we have a companion system of linear equations:

du/dx = v,

dv/dx = w,

dw/dx = -3u - w.

To solve this system completely, we need to find the solutions for u, v, and w. By solving the system of differential equations, we can obtain the solutions for u(x), v(x), and w(x), which will correspond to the solutions for y(x), y'(x), and y"(x), respectively.

The exact solutions for this system of differential equations depend on the initial conditions or boundary conditions that are given. By applying appropriate initial conditions, we can determine the specific solution to the system.

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These cycles are known as the eccentricity cycles, and they are one of the factors that contribute to the long-term climate variations on Earth

The aspect of Earth's orbital relationship to the Sun that varies with a periodicity of both 400 Ka and 100 Ka is the eccentricity of Earth's orbit. The eccentricity refers to the shape of Earth's orbit around the Sun, which is not a perfect circle, but an ellipse. The eccentricity of Earth's orbit changes over time due to gravitational interactions with other planets, particularly Jupiter and Saturn. When Earth's orbit is more elliptical, its distance from the Sun varies more throughout the year, leading to variations in climate and the amount of solar radiation received on Earth's surface. The periodicity of 400 Ka corresponds to a cycle of variations in Earth's eccentricity that affects the amount of solar radiation received at different latitudes and the distribution of ice ages. The periodicity of 100 Ka corresponds to a cycle of variations in Earth's eccentricity that affects the intensity of the seasons and the distribution of glacial periods. These cycles are known as the eccentricity cycles, and they are one of the factors that contribute to the long-term climate variations on Earth.

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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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The rotation per revolution when a wheel rotates 1,800º in 5 revolutions is 360°.

Revolution simply means a complete turn. It's slid known as a full rotation.

Here, the wheel rotates 1,800º in 5 revolutions. The rotation per revolution will be:

= Total degree / Number of revolution

= 1800 / 5

= 360°

The complete information is written below.

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A wheel rotates 1,800º in 5 revolutions. What is the rotation per revolution?

Answer:

the answer will be d=130

Step-by-step explanation:

substruct 110 minus 50 we get 60

Hence, there are 725,760 ways to seat the ten people together in a row, taking into account the two individuals who insist on sitting side-by-side.

If two of the ten people insist on sitting side-by-side, we can consider them as a single entity or a pair. So, essentially, we have nine entities (including the pair) to be seated in a row.

The number of ways to arrange these nine entities in a row is 9!, which is the factorial of 9.

However, within the pair, the two individuals can be arranged in 2! = 2 ways.

Therefore, the total number of ways to seat the ten people together, considering the pair as one entity, is 9! * 2!.

Simplifying this expression:

9! * 2! = 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 * 2 = 725,760

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Answer:

−

5

2

=

3

3

1

0

Step-by-step explanation:

:/

Answer:

y = - 85

Step-by-step explanation:

-y = 52 + 33 (52 flys over " = " and changes sign)

-y = 85

-y / - 1 = 85 / - 1 (getting rid of negative sign of y)

y = - 85

If the diagonal of a rhombus id x-4d and x+ 4d then the area of rhombus is (x² - 16d²) / 4 unit²

In a rhombus, the diagonals are perpendicular bisectors of each other, and they divide the rhombus into four congruent right triangles. Let's call the length of one half of the diagonal "a" and the length of the other half of the diagonal "b". So we have:

a = (x - 4d) / 2

b = (x + 4d) / 2

The area of a rhombus can be calculated as half the product of its diagonals, or as half the product of its side lengths:

Area = (1/2) × a × b × 2

Area = a × b

Substituting the expressions for "a" and "b" from above, we get:

Area = [(x - 4d) / 2] × [(x + 4d) / 2]

Area = (x² - 16d²) / 4

Therefore, the area of the rhombus is (x² - 16d²) / 4 square units.

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Three of them possess pairs corresponding to a Shamir secret sharing scheme, enabling any two people to determine the secret.

In this scenario, there are four people in a room. Three of them possess pairs corresponding to a Shamir secret sharing scheme, enabling any two people to determine the secret.

The remaining person is a foreign agent who has chosen a pair randomly. Thus, if any two of the three people with the valid pairs collaborate, they can successfully uncover the secret, as per the properties of the Shamir secret sharing scheme.

The presence of the foreign agent does not affect the security of the scheme unless they collaborate with another person possessing a valid pair.

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Answer:

2

Step-by-step explanation:

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Answer: Choice A

The two angles must be supplementary and adjacent to form a linear pair.

Adjacent angles are angles that touch and share a common line segment, line, or ray. Think of two rooms that share the same wall and how they are considered adjacent rooms.

Supplementary angles form a straight angle. They add to 180 degrees.

At least 5 expected observations in each cell in order to apply the chi-square test of independence, we prefer to have at least 5 expected observations in each cell. The correct answer is c.

The chi-square test of independence is a statistical method used to determine whether two categorical variables are independent or associated with each other.

To apply this test, it is preferred to have at least 5 expected observations in each cell of the contingency table. The expected frequency is calculated based on the assumption of independence between the two variables.

If the expected frequency is less than 5 in any cell, the chi-square test may not be valid and alternative methods, such as Fisher's exact test, should be considered. Having a sufficient sample size can also improve the accuracy and reliability of the test results.

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Answer:

\(\frac{1}{9}\)

Step-by-step explanation:

Data provided in the question

There is a total group of 45 students

Art + biology = 5

8 study biology but not Art

Neither subject studied = 9

Based on the above information, the probability of student that studies

art and biology is

Since there is a group of 45 students out of which 5 study both art and biology

So, the ratio is

4: 5

Now divide both sides by 5

So, now the ratio is

9:1

Therefore it means the probability is \(\frac{1}{9}\)