Find the exact perimeter of quadrilateral ABCD.

Answer:

Sum of G.P. series is given by,

Sum=

r−1

a(r

n

−1)

when r>1

Where a= first term, n=n

th

term and r is common ratio.

Here, a=1,n=10,r=

3

S

10

=

(

3

−1)

1×{(

3

)

10

−1}

=

(

3

−1)

(3

5

−1)

×

(

3

+1)

(

3

+1)

=

(3−1)

242(

3

+1)

=121(

3

+1).

Answer:

x = 6 units

Step-by-step explanation:

We know that, By pythagoras theorem,

Hypotenuse2 = base2 + perpendicular2

Given, Hypotenuse = 6.5

perpendicular = 2.5

base = x

So, by putting the values,

6.52 = 2.52 + x2

42.25 = 6.25 + x2

36 = x2  

Hence, x = 6 units

The solution of the system of equation 2x + 4y = 16, 2x - 4y = 0 is (4, 2). The correct option is A.

System of equations can be solved using different method such as substitution method, elimination method and graphical method. The system of equation can be solved with the elimination method as follows:

2x + 4y = 162x - 4y = 0

add equation(ii) to equation(i)

2x + 2x  = 16 + 04x = 16

divide both sides by 4x = 16

x = 4

Let's find y

2x - 4y = 0-4

y = -2x-4y = -2(4)

-4y = -8

divide both sides by -4y = -8 / -4y = 2

Therefore, the solution is (4, 2)

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Its molecules' monatomic fraction is 0.444.

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a correct fraction is smaller than the denominator.

The fact that

The formula gamma monatomic

Determines the specific heat ratio of monoatomic gas.

5/3=1.67

Calculates the specific heat ratio of a diatomic gas.

Gamma monatomic =7/5=1.4

We have a monoatomic and diatomic gas mixer with a gamma mixer specific heat ratio of 1.52.

Calculating the monoatomic gas fraction is as follows:

Let's assume that "x" is the percentage of monoatomic

1.67* x+1.4* (1-x)=1.52

1.67* x+1.4-1.4* x=1.52

0.27* x=0.12

x = 0.12/0.27

x= 0.444

Its molecules' monatomic fraction is 0.444.

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The value of x = 50

Exterior angle:

In geometry, an angle of a polygon is formed by two sides of the polygon that share an endpoint. For a simple (non-self-intersecting) polygon, regardless of whether it is convex or non-convex, this angle is called an interior angle (or internal angle) if a point within the angle is in the interior of the polygon. A polygon has exactly one internal angle per vertex.

If every internal angle of a simple polygon is less than π radians (180°), then the polygon is called convex.

In contrast, an exterior angle (also called an external angle or turning angle) is an angle formed by one side of a simple polygon and a line extended from an adjacent side.

given that

m∠6 = x

m∠7 = x-20

m∠11 = 80

we solve this by using exterior angles

sum of 2 interior angles is equal to one  exterior angle

m∠6 + m ∠7 = m∠11

x + x - 20 = 80

2x = 80 + 20

2x = 100

x = 100/2

the value of x = 50

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The function g(x) = √x + 4 is the result of a vertical translation 4 units up of the function f(x) = √x. (Right choice: B)

In this problem we find the definition of a function f(x) and its image g(x). Both f(x) and g(x) are radical functions and we need to determine the transformation rule to obtain the latter function. By direct inspection, g(x) is the result of applying a vertical translation, whose definition is shown below:

g(x) = f(x) + k

Where:

Please notice that k indicates a translation in the +y direction. k > 0 indicantes a vertical shift k units up.

Then, g(x) is the result of a vertical translation (4 units up) on f(x).

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The function that correctly shows the value of k and h is g(x) = 12(x - 5)² - 7

From the question, we have the following parameters that can be used in our computation:

f(x) = 12(x + 6)² - 3

The transformation is given as

11 units to the right and 4 units down

This is represented as

(x - 11, y - 4)

So, we have the following representation

g(x) = 12(x + 6 - 11)² - 3 - 4

Evaluate

g(x) = 12(x - 5)² - 7

Hence, the function is g(x) = 12(x - 5)² - 7

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Answer:

C. 80%

Step-by-step explanation:

To find the percentage of cupcakes that were sold, you can divide the number of cupcakes sold by the total number of cupcakes and multiply the result by 100%. In this case, the percentage of cupcakes sold is:

280 cupcakes / 350 cupcakes * 100% = 80%

Therefore, the correct answer is C: 80%.

Answer:

The correct answers are D and E

Step-by-step explanation:

D is correct because according to exponent rules, you add them when you multiply.

E is correct because the expression will equal 64 when calculated.

The value of c, if In triangle LMN, m ∠ L = (6c + 35)°. If the exterior angle to ∠ L measures 79° is 11, so option D is correct.

Simple polygons with three sides and three internal angles make up triangles. One of the fundamental geometric shapes, it is represented by the symbol and consists of three connected vertices.

Given:

In triangle LMN, m ∠ L = (6c + 35)°

∠ L = 79°

Calculate the angle as shown below,

m ∠ L = 180 - 79

m ∠ L = 101

101 = 6c + 35

6c = 101 - 35

c = 66 / 6

c = 11

Therefore, the value of c, if In triangle LMN, m ∠ L = (6c + 35)°. If the exterior angle to ∠ L measures 79° is 11.

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The probability that more than 90 pizzas will be devoured in a random sample of 10 people is 85.31%.

For the stated question-

Estimate the probability for the consumed pizzas.

P(x > 90/10) = P(x = 9)

P(x = 9) = P[x - μ/ σ/√n > z > (9 - 10) / (3/√10)]

P(x = 9) = P(z > -1.05)

P(x = 9) = 1 - P(z > -1.05)

P(x = 9) = 1 - 0.1469

P(x = 9) = 0.8531

Thus, the probability that more than 90 pizzas will be devoured in a random sample of 10 people is 85.31%.

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The complete question is-

The number of pizzas consumed per month by university students is normally distributed with a mean of 10 and a standard deviation of 3.

what is the probability that in a random sample of size 10, a total of more than 90 pizzas are consumed? (hint: what is the mean number of pizzas consumed by the sample of 10 students?)

Answer: n = 4

9 = x

y = 2

Step-by-step explanation:

2 ( x + 5 ) = 3x + 1

2x +10 = 3x + 1

10 = 1x + 1

- 1       -1

9 = 1x

9 = x

3y - 4 = 6 - 2y

5y -4 =6

5y = 10

y = 2

3 (n + 2) = 9 ( 6-n)

3n + 6 = 54 -9n

3n +9n = 54 - 6

12n =54 -6

12n =48

n = 4

An experiment involves selecting a random sample of 256 middle managers for study. one item of interest is their annual incomes. the sample mean is computed to be $35,420.00. if the population standard deviation is $2,050.00, the standard error of the mean is $128.125

The population mean's likelihood to differ from a sample mean is indicated by the standard error of the mean, or simply standard error. It reveals how much the sample mean would change if a study were to be repeated with fresh samples drawn from a single population.

By dividing the standard deviation by the square root of the sample size, the standard error is determined. By taking into account the sample-to-sample variability of the sample means, it provides the precision of a sample mean.

Standard error of the mean = 2050/sqrt {256} = $128.125

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The given pair of equations has no solution.

Two equations can be solved through three different methods:

Let's use the elimination method in this question

                         20x - 4y = 11      .....(I)

                          10x - 2y = 6      .....(II)

Multiply (II) by 2

                          20x - 4y = 11      .....(I)

                          20x - 4y = 6      .....(II)

Now, subtracting equations (I) and (II) we will get no solution.

It is possible for the two lines to be parallel and not intersect. In this situation, we cannot identify a shared point between the two, and as a result, the system of the two equations representing the two lines cannot provide a solution!

This question is incomplete. The correct question is

Consider the two equations and solve for x and y.

                          20x - 4y = 11    

                          10x - 2y = 6  

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The area of the resulting square is 3600 in²

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.

Given that, a square has area 1600 in² whose length has been increased by 20 in each side.

Area of the square = side²

Let the original side length be x, then,

x² = 1600

x = 40 (neglecting -40, because length of anything can not be negative)

After 20 in increase, the side is (40+20) = 60 in

Area of new square = 60x60 = 3600 in²

Hence, The area of the resulting square is 3600 in²

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"2 more than a number" is equivalent to the mathematical expression X+2.

"2 more than a number" denotes addition because of the word "more." Since we aren't given a definite number, we use a variable in its place (such as x). So, x+2 can be used to represent "2 greater than a number."

An arithmetic value used to indicate an amount is called a number. A number is a mathematical concept that is used for counting, measuring, and labeling. Thus, mathematics is built on numbers. You can think of a number as a count, like when we yell, "3, 2, 1, GO!" during a race, or as a measurement, like John Cena's weight of 275 lbs. There are also decimals like 3.14 and fractions like 22/7.

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Answer: In ΔABF & ΔACE

AB/FB = AC/EC   (As both the triangles are similar)

as B is the midpoint of AC = 48

AB = 24

So,

24/23 = 48 / EC

EC = 46

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The value of EC is equal to 69 units

Triangle Midpoint Theorem: The line segment connecting the midpoints of two sides of a triangle is parallel to the third side and is congruent to one half of the third side.

Given here, AX=24 And FB=23

Now applying the triangle midpoint theorem we get the value of

AC =3×23

      = 69 units

Hence, The value of EC is equal to 69 units

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The given measurement in scientific notation as [tex]6\times10^9[/tex]. Therefore, option D is the correct answer.

Scientific notation is a method for expressing a given quantity as a number having significant digits necessary for a specified degree of accuracy, multiplied by 10 to the appropriate power such as [tex]1.56\times10^7[/tex].

The given distance is 6,000,000,000 miles.

There are 9 zeros in the given number

So, scientific notation is [tex]6\times10^9[/tex]

Therefore, the number in scientific notation is [tex]6\times10^9[/tex].

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The distance between John's friend and the building is 14.9 metres.

From an angle of depression of 50 degrees, John watches his friend approach his building while standing on his rooftop. The rooftop is 16 m from the ground and John's eyelevel is about 1.8m above the rooftop.

Therefore, the distance of John's friend from the building can be calculated as follows:

This situation forms a right angle triangle.

Hence, using trigonometric ratios,

tan 50 = opposite / adjacent

tan 50 = 16 + 1.8 / x

tan 50° = 17.8 / x

cross multiply

x tan 50° = 17.8

x = 17.8 / tan 50

x = 17.8 / 1.19175359259

x = 14.9359734675

x = 14.9 metres

Therefore,

distance of John's friend to the building  = 14.9m

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The limit of 1/n does not diverge.The difference of limit of 1/n is explained below.

It converges to 0 as n approaches infinity. The difference between a series and a limit is that a series is the sum of the terms in a sequence, while a limit is a value that a sequence approaches as its terms become increasingly large. In other words, the limit of a sequence is the "endpoint" of the sequence, while the series is the sum of all the terms in the sequence. In the case of 1/n, the series does not converge because the terms gradually increase with no endpoint. However, the limit of 1/n does converge because the terms become progressively smaller and approach 0 as n approaches infinity. Therefore, the limit of 1/n does converge, while the series of 1/n does not.

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The total maximum area enclosed by both the shapes square and a circle using given wire is equal to 2.27 square feet.

As given in the question,

Let 'x' be the side length of the square

And 'r' be the radius of the circle.

Length of the wire = 4 feet

Maximum side length of the square is:

4x = 4

⇒ x = 1feet

Maximum area of the square = x²

                                                = 1²

                                                = 1

Maximum radius of the circle is:

2πr = 4

⇒ r = 2 / π

Maximum area of the circle = πr²

                                              = π × (2/π)²

                                              = 4 / π

Total maximum area enclosed by square and a circle

= 1 + (4/π)

= 1 + 1.27

= 2.27 square feet.

Therefore, the total maximum area enclosed by square and a circle from the given wire is equal to 2.27 square feet.

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Answer:  He needs 9 days to complete all his overdue assignments and if this is happening to you sry I feel your pain. Just vibing to k-pop while having a mental breakdown doesn't sound bad until you feel it :(

Step-by-step explanation:

Well, he has 36 overdue assignments, and if he completes 4 overdue assignments each day you need 9 days to complete all his overdue assignments.

36 divide 4 = 9 days

The number on round off to each place will be 45,621.

The decimal number is rounded to any place by the following concept -

We look at the number to the right of concerned digit. If that number is more than five or exactly five, then we add 1 to our number. However, if it is less than five, then the number remains same.

For instance, if we round 45.621 to nearest tenth, we will get 45.6. This is because on right to it, the number 2 is less than 5. Now, in the mentioned digit which is 45,621, we see there is no decimal and number after that. So, as the digits are 0 which is less than 5, the number will remain as it is.

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Answer:

D

Step-by-step explanation:

To find the solutions, let's calculate the determinant:

Δ = (-1)²-4(-2)(-1) = 1-8 = -7

the solution is: (1 ±√-7)/(-4)

√-7 indicates there are two complex solutions

The interest that will the customer earn in 10 years is $385.

What is simple interest?

Simple interest is a method for figuring out how much interest was paid on a sum of money during a specific time period at a specific rate.

Simple interest has a constant principal amount. Simple interest is a straightforward and easy technique for calculating interest in money. Interest is always applied to the initial principal amount under the simple interest method, and the rate of interest is the same for each time cycle. When we deposit money in a bank, the bank pays us interest on our investment. Banks charge various sorts of interest, one of which is simple interest.

The customer deposit $3500 when he opens the account.

The interest rate of the bank is 1.1% = 0.011.

He deposits the amount for 10 years.

The formula of simple interest is I = PRT.

I = 3500 × 0.011 × 10

I = 385

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Answer:

(-5, -7) and (-2, -1)

Step-by-step explanation:

The graph of y = h(x) is a line segment joining the points (−7, −5) and (-1, -2).  (Blue line on the attached graph).

The graph of the inverse function is a reflection in the line y = x.

Therefore, the endpoints of the inverse function are:

The graph of the inverse function y = h⁻¹(x) is shown in green on the attached graph.

Answer:

(-5, -7) and (-2, -1)

Step-by-step explanation:The graph of y = h(x) is a line segment joining the points (−7, −5) and (-1, -2).  (Blue line on the attached graph).The graph of the inverse function is a reflection in the line y = x.Therefore, the endpoints of the inverse function are:(-5, -7) and (-2, -1)The graph of the inverse function y = h⁻¹(x) is shown in green on the attached graph.

Step-by-step explanation:

The value of x is 1

Given that,

AB=DE

AC=DF

∠CAB=∠FDE

So by the triangle property of SAS, ΔABC and the ΔDEF are equal means ΔABC≅ΔDEF.

And we know that if two triangles are equal then by their properties their respective sides and angles will also be equal to each other.

So we can write that,

⇒13x-12=7x-6

⇒13x-7x=12-6

⇒6x=6

⇒x=1

Therefore the value of x is 1.

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Answer:

22/55 = 40% = 0.4

Step-by-step explanation:

22/55

Reduce the fraction by dividing the numerator and denominator by 11.

22/55 = 2/5

Now use a calculator, or long division, to divide 2 by 5.

22/55 = 2/5 = 0.4

To change a decimal to a percent, multiply the decimal by 100%.

0.4 × 100% = 40%

Answer: 22/55 = 40% = 0.4

The proportions in this problem are given as follows:

1. a = 40.

2. t = 1.

3. q = 29.25.

4. g = 3.

5. m = 9.8.

6. v = 12.9.

7. w = 1.3.

8. n = 2.28.

9. n = 0.84.

10. k = 1.2.

11. t = 0.57.

12. z = 63.4.

The proportions are solved using these two steps presented as follows:

Then, for item a, the proportion is given as follows:

3/8 = 15/a

Applying cross multiplication, we have that:

3a = 15 x 8

Then, the variable a is isolating applying the division operation, as follows:

a = 15 x 8/3

a = 5 x 8 (as 15/3 = 5)

a = 40.

Then the second proportion is solved as follows:

t/2 = 6/12

12t = 12

t = 1.

And the same procedure is then applied to obtain any of the remaining 10 proportions. Some include operations with decimals, hence calculator used is recommended.

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For the standard normal distribution , the probability will be 0.0401 which means option a is the correct choice.

A standard deviation (or σ) is a degree of ways dispersed the records is when it comes to the mean. Low general deviation approach records are clustered across the mean, and excessive general deviation suggests records are extra unfold out.

Using a standard normal table the area to the right of z = 1.75 is given by

P(z > 1.75) = .0401

Therefore, the correct option is a.

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