find the sum of first 100 even numbers.​

Answer:

A rectangle

because it has to opposite and two congruent sides

The object fell from a height of approximately 7.057 meters above the ground.


We can solve this problem using the equations of motion for a freely falling object. The equation we’ll use is:
H = (1/2) * g * t^2
Where h is the initial height, g is the acceleration due to gravity (approximately 9.8 m/s^2), and t is the time taken to travel the last distance. Rearranging the equation, we get:

H = (24.0 m) + (1/2) * (9.8 m/s^2) * (1.20 s)^2
Calculating this expression, we find that h is approximately 7.057 meters. Therefore, the object fell from a height of approximately 7.057 meters above the ground.

Learn more about Acceleration here: brainly.com/question/29761692
#SPJ11

Answer:

first one is proportional, second is not. (not sure how to answer the number thing lol)

Step-by-step explanation:

The surface area of the solid cuboid 7m 6m and 3m. total surface area of cuboid is 162 \(m^{2}\).

A cuboid is a six-sided solid known as a hexahedron in the geometry. Quadrilaterals make up its faces. Cuboid implies "like a cube," in the sense that a cuboid can be converted into a cube by varying the length of its edges or the angles between its faces. A cuboid is a convex polyhedron with the same polyhedral graph as a cube in mathematics.

A cube with six square faces, a rectangular prism, rectangular cuboid, or a rectangular box with six rectangle faces are special situations. In both circumstances, the faces of the cube and the rectangular prism come together at a right angle.

total surface area of cuboid

= 2(lb+bl+lh)

=2(7×6+6×3+3×7)

=2(81)

=162 \(m^{2}\)

To know more about cuboid visit: https://brainly.com/question/19754639

#SPJ9

Answer:40

Step-by-step explanation:

Answer:

the answer is 40cm^2

Step-by-step explanation:

i multiply them

4.83 x 8.18 = 39.5094

the estimate is 40

Answer:

Binomial

Step-by-step explanation:

The last term does not exist because it has a coefficient of zero and therefore equals zero.

Answer:

51

Step-by-step explanation:

5x+6=9x-30

5x=9x-36

4x=36

x= 9

5×9+6=51

Answer:

y = 3x - 2

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 3x + 2 ← is in slope- intercept form

with slope m = 3

Parallel lines have equal slopes, then

y = 3x + c ← is the partial equation

To find c substitute (1, 1) into the partial equation

1 = 3 + c ⇒ c = 1 - 3 = - 2

y = 3x - 2 ← equation of line

The probability of selecting a card that shows a lion or an odd number from the given deck is approximately 0.65 or 65%.

To determine the probability of selecting a card that shows a lion or an odd number, we need to calculate the number of favorable outcomes and divide it by the total number of possible outcomes.

Out of the 20 cards in the deck, we can identify the following favorable outcomes:

Cards showing a lion: There are 4 lion cards in the deck.

Cards showing an odd number: There are 10 cards in the deck with odd numbers (1, 3, 5, 7, 9).

The total number of favorable outcomes, we need to consider the cards that meet either of the conditions (lion or odd number) without counting any duplicates. In this case, there is one card (with a lion) that also has an odd number. So, we have a total of 13 favorable outcomes.

The total number of possible outcomes is 20 since there are 20 cards in the deck.

Now, we can calculate the probability of selecting a card that shows a lion or an odd number by dividing the number of favorable outcomes by the total number of possible outcomes:

Probability = Number of favorable outcomes / Total number of possible outcomes

Probability = 13 / 20

Probability ≈ 0.65

To know more about probability refer here

https://brainly.com/question/31828911#

#SPJ11

The quadratic equation with the least integral coefficients is 2x² + 17x + 21 = 0.

The roots of the quadratic equation are given by the formula:

x = (-b ± √(b² - 4ac)) / (2a)

where a, b, and c are the coefficients of the quadratic equation:

ax² + bx + c = 0

Knowing that the roots of the quadratic equation are -1.5 and -7, then you can write the equation in the form:

(x + 1.5)(x + 7) = 0

This expands to:

x² + 8.5x + 10.5 = 0

Multiply the whole equation by 2 to obtain integral coefficients.

2(x² + 8.5x + 10.5 = 0)

2x² + 17x + 21 = 0

Hence, the quadratic equation with the least integral coefficients that has -1.5 and -7 as roots is:

2x² + 17x + 21 = 0

Learn more about quadratic equation here: https://brainly.com/question/1214333

#SPJ4

Answer:

5

Step-by-step explanation:

2(4+1)-5

2(5)-5

10-5

5

Answer:

60

good luck!

Answer:

909.09

Step-by-step explanation:

400 divided by 44% is about 909.09.

The conclusion that is appropriate at a 5% level of significance is this:C. There are statistically significant differences in the mean time to recurrence of depression symptoms for patients in the three treatment groups. this suggests that there is a treatment effect.

The correct conclusion is that the result obtained from the analysis is statistically significant, so the null hypothesis can be rejected. This also means that there are 1 in 20 chances of obtaining an error.

So, for a study checking the relationship between the mean time to recurrence of depression symptoms, the 5% level of significance would demonstrate a relationship.

Learn more about the 5% level of significance here:

https://brainly.com/question/28027137

#SPJ1

The two statements about the dilated quadrilateral a'b'c'd' are false.

bc and bc' are on the same line ( False)

The length of the cd and c'd' are the same. (False)

The complete question is attached with the answer below.

Dilation is the process of increasing the size of an object while maintaining its shape. Depending on the scale factor, the object's size can be increased or decreased.

Here the quadrilateral abcd is dilated by the scale factor 5 / 2.So the new quadrilateral is a'b'c'd'.

The given two statements are false:-

bc and bc' are on the same line ( False)

The length of the cd and c'd' are the same. (False)

To know more about dilation follow

https://brainly.com/question/3457976

#SPJ1

Answer:

a = 61

Step-by-step explanation:

The three angles form a straight line which is 180 degrees.

a + 90 + 29 = 180

a + 119 = 180

a = 180-119

a = 61

Given : Find the measure of the missing angle.

Solution : According to the question, here we are provided with a variable α. An angle which is 90° and another angle which is 29° are to be added and the result is 180°. So, subtracting from 180° we will get the required answer

Henceforth, the missing angle is 61°

Answer:

\(y = \frac{1}{8}(x + 4)^2 + 4\)

Step-by-step explanation:

Given:

Focus of parabola: (-4, 6)

Directrix: y = 2

Required:

Equation for the parabola

Using the formula, \( y = \frac{1}{2(b - k)}(x - a)^2 + \frac{1}{2}(b + k) \) , the equation for the parabola can be derived.

Where,

a = -4

b = 6

k = 2

Plug these values into the equation formula

\( y = \frac{1}{2(6 - 2)}(x - (-4))^2 + \frac{1}{2}(6 + 2) \)

\(y = \frac{1}{2(4)}(x + 4)^2 + \frac{1}{2}(8)\)

\(y = \frac{1}{8}(x + 4)^2 + \frac{8}{2}\)

\(y = \frac{1}{8}(x + 4)^2 + 4\)

Pairs of numbers that have the same greatest common factor are: (12, 18) and (12, 30) and (18, 30) with a greatest common factor of 6.

The largest positive integer that divides two or more numbers without producing a remainder is known as the greatest common factor (GCF).

To find the greatest common factor (GCF) of two numbers, we need to find the largest number that divides both of them.

Let's start by listing the factors of each number:

12: 1, 2, 3, 4, 6, 12

18: 1, 2, 3, 6, 9, 18

20: 1, 2, 4, 5, 10, 20

30: 1,  2,  3,  5,  6,  10,  15,  30

Now we can compare the pairs of numbers and see which ones have the same GCF:

GCF(12, 18) = 6

GCF(12, 20) = 4

GCF(12, 30) = 6

GCF(18, 20) = 2

GCF(18, 30) = 6

GCF(20, 30) = 10

So the pairs that have the same GCF are:

12 and 18, with a GCF of 6

12 and 30, with a GCF of 6

18 and 30, with a GCF of 6

Therefore, Pairs of numbers that have the same greatest common factor are: (12, 18) and (12, 30) and (18, 30) with a GCF of 6.

To know more about greatest common factor, visit:

https://brainly.com/question/219464

#SPJ1

Answer:

true

Step-by-step explanation:

Another way to solve a direct variation equation is by setting up a proportion.

Answer:

  0.508 cm

Step-by-step explanation:

Your problem statement tells you that you can find the number of centimeters by multiplying 1/5 inch by 2.54 cm/in:

  1/5 × 2.54 = 0.508

1/5 inch is 0.508 centimeters

The minimum number of graduates to be hired to guarantee that at least ten are from the same school is 30, based on the Pigeonhole Principle .To guarantee that at least ten graduates are hired from the same school, the minimum number of graduates to be hired would be 29.

Assuming that each school has an equal number of graduates being interviewed, we can divide x by 3 to get the number of graduates that we need from each school to guarantee that at least ten are from the same school
x/3 + x/3 + x/3 >= 10
x >= 30

if we hire 30 graduates, we are guaranteed to have at least ten graduates from one school, even if the remaining 20 graduates are evenly distributed among the other two schools. The minimum number of graduates to be hired to guarantee that at least ten are from the same school is 30.


To know more about number visit :-

https://brainly.com/question/28210925

#SPJ11

The area bounded by the two curves is 42 square units.

To find the area bounded by the graphs of the given equations, we need to find the intersection points of the two graphs and then integrate the difference between the two functions over the given interval.

First, we find the intersection points by equating the two functions:

x^2 - 2x - 1 = x + 3

Simplifying, we get:

x^2 - 3x - 4 = 0

Factorizing, we get:

(x - 4)(x + 1) = 0

So the intersection points are x = 4 and x = -1.

Now, we integrate the difference between the two functions over the given interval:

∫[-1, 4] (x + 3 - (x^2 - 2x - 1)) dx

Simplifying, we get:

∫[-1, 4] (-x^2 + 4x + 4) dx

Integrating, we get:

[-(1/3)x^3 + 2x^2 + 4x] [-1, 4]

Substituting the limits of integration, we get:

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

Simplifying, we get:

(-64/3 + 32 + 16) - (1/3 - 2 - 4)

Which simplifies further to:

126/3

And finally, to the improper fraction: 42

Therefore, the area bounded by the two curves is 42 square units.

To know more about calculus refer here:

https://brainly.com/question/30690744?#

SPJ11

Answer:

c = 152

Step-by-step explanation:

c/8+5 = 24

Subtract 5 from each side

c/8+5-5 = 24-5

c/8 = 19

Multiply each side by 8

c/8*8 = 19*8

c =152

Answer:

D. 152

Step-by-step explanation:

First, subtract 5 from both sides:

c/8 + 5 = 24

c/8 = 19

Multiply both sides by 8:

c = 152

So, the correct answer is D, 152

f(n) = ϴ(g(n)) is not true in cases B(sqrt(n)log(n), C(\(3^n 5^n\)), and D(sin(n)+3 cos(n)+1).

A) \(log(n^200) log(n^2)\)

Here, f(n) = \(log(n^200)\) and g(n) = \(log(n^2)\). Now, if we take the limit of f(n) / g(n) as n approaches infinity, then:

f(n) / g(n) = \([log(n^200) / log(n^2)]\) = 100

This means that as n approaches infinity, the ratio f(n) / g(n) is constant, and so we can say that f(n) = ϴ(g(n)). Therefore, f(n) = ϴ(g(n)) is true in this case.

B) sqrt(n) log(n) Here, f(n) = sqrt(n) and g(n) = log(n). Now, if we take the limit of f(n) / g(n) as n approaches infinity, then:

f(n) / g(n) = [sqrt(n) / log(n)]

As log(n) grows much slower than sqrt(n) as n approaches infinity, this limit approaches infinity. Therefore, we cannot say that f(n) = ϴ(g(n)) is true in this case.

C) 3^n 5^n

Here, f(n) = \(3^n\) and g(n) = \(5^n\) . Now, if we take the limit of f(n) / g(n) as n approaches infinity, then:

f(n) / g(n) = \([3^n / 5^n]\)

As \(3^n\) grows much slower than \(5^n\) as n approaches infinity, this limit approaches zero. Therefore, we cannot say that f(n) = ϴ(g(n)) is true in this case.

D) sin(n) + 3 cos(n) + 1

Here, f(n) = sin(n) + 3 and g(n) = cos(n) + 1. Now, if we take the limit of f(n) / g(n) as n approaches infinity, then:

f(n) / g(n) = [sin(n) + 3] / [cos(n) + 1]

As this limit oscillates between positive and negative infinity as n approaches infinity, we cannot say that f(n) = ϴ(g(n)) is true in this case.

Therefore, f(n) = ϴ(g(n)) is not true in cases B, C, and D.

To know more about log refer here:

https://brainly.com/question/32621120

#SPJ11

Answer:

\(\huge\boxed{\sf \$ \ 8.79\ per\ hour}\)

Step-by-step explanation:

Work hours = 2:00 pm - 11:00 pm

So,

9 hours = $79.11

Using unitary method

9 hours = $79.11

Divide both sides by 9

1 hour = $79.11/9

1 hour = $8.79

So, Kenya is being paid $8.79 per hour.

\(\rule[225]{225}{2}\)

For ΔDOG to become ΔD'O'G', it is rotated 180° about the origin and then translated 5 units left.

What is translation?

A translation in mathematics does not turn a shape; instead, it moves it left, right, up, or down. They are congruent if the translated shapes (or the image) seem to be the same size as the original shapes. They have only changed their direction or directions.

The coordinate points for the ΔDOG is -

D(-7,-7) , O(-8,2), and G(2,1)

The coordinate points for the ΔD'O'G' is -

D'(2,7) , O'(3,-2), and G'(-7,-1)

First the Δ DOG is rotated 180° about the origin.

When the triangle is rotated 180° about the origin, the formula becomes (x,y) → (-x,-y)

The new coordinate points are -

D(-7,-7) → [-(-7),-(-7)] → d(7,7)

O(-8,2) → [-(-8),-(2)] → o(8,-2)

G(2,1) → [-(2),-(1)] → g(-2,-1)

Now, the new Δdog is translated 5 units left.

When the triangle is translated 5 units left, the formula becomes (x,y) → (-x - 5,y)

d(7,7) → [(7 - 5),(7)] → D'(2,7)

o(8,-2) → [(8 - 5),(-2)] → O'(3,-2)

g(-2,-1) → [(-2 - 5),(-1)] → G'(-7,-1)

Therefore, the original triangle is first rotated and then translated.

To learn more about translation from the given link

https://brainly.com/question/12861087

#SPJ1

Answer: The cat is 4 years old, and the dog is 6 years old.

Step-by-step explanation:

We know that Buddy is 2 years old than Fluffy.

And 3 years ago, Buddy was 3 times older than Fluffy.

Let's define the variables:

B = age of Buddy

F = age of Fluffy.

The first statement can be written as:

B = F + 2

The second statement can be written as:

B - 3 = 3*(F - 3)

To solve this, we can replace the first equation into the second one, and solve that for F

B - 3 = 3*(F - 3)

(F + 2) - 3 = 3*F - 9

F - 1 = 3*F - 9

-1 + 9 = 3*F - F

8 = 2*F

8/2 = 4 = F

Fluffy is 4 years old, and with the first equation we can find the age of Buddy.

B = F + 2 = 4 + 2 = 6

Buddy is 6 years old

The required age of the dog buddy is 6 years old and the age of cat fluffy is 4 years old.

Given ,

James's dog buddy is 2 years older than Fluffy,

And the neighbor's cat Three Years ago, Buddy was three times older than fluffy.

Let ,

The age of buddy = B

The age of fluffy is = F

According to the question ,

Buddy, is 2 years older than Fluffy= Age of Buddy = Age of fluffy + 2 years older.

B = F +2

Again According to the question,

Three years ago age of Buddy = B - 3

Three years ago age of Fluffy = F - 3

Three years ago Buddy was three times older than fluffy = Three years ago age of Buddy = 3 × Three years ago Age of fluffy

B - 3 = 3 ( F - 3 )

Solving the equations,

B - 3 = 3 ( F - 3 )

Put the value of B from equation 1

F + 2 - 3 = 3 ( F -3 )

F - 1 = 3F - 9

F - 3F = - 9 +1

-2F = -8

2F = 8

\(F = \frac{8}{2}\)

F = 4

The age of fluffy is 4 years old.

Then ,

The age of buddy

B = F + 2

B = 4 + 2

B = 6

The age of buddy is 6 years old.

The required age of the dog buddy is 6 years old and the age of cat fluffy is 4 years old.

For more information about system of equation click the link given below.

https://brainly.in/question/27545639

Because the graph always has a consistent slope of +2, the table x|y-2| 4|0| 6|2| is an illustration of a linear function table.

In order for a table to represent a linear function, there must be a constant rate of change (slope) between any two points on the graph. In other words, the relationship between the x-values and y-values should follow a consistent pattern.

The correct table that represents a linear function is: x|y-2| 4|0| 6|2|This is because there is a constant rate of change of +2 between any two points on the graph. For example, when x goes from 2 to 4, y increases from -2 to 0. When x goes from 4 to 6, y increases from 0 to 2.

This constant rate of change indicates that the relationship between x and y is linear.

In summary, a table represents a linear function when there is a constant rate of change between any two points on the graph. The table x|y-2| 4|0| 6|2| is an example of a linear function table because there is a consistent slope of +2 between any two points on the graph.

For more questions on graph

https://brainly.com/question/29538026

#SPJ8

Answer:

Step-by-step explanation:

\(x^{3}-2x^{2}-x+2\\ =x(x^{2}-2x-1)+2\\\)

We can clearly see here that x = 1 is one of the solution where this expression becomes zero

= x( (x-1)^2-2 ) + 2