How many times smaller is 1.9 × 103 than 4.085 × 105?

0.46
2.15
46
215

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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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:

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%.

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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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 common ratio of the sequence which have first term, = 3 and third term  = 192 is calculated to be 6

The common ratio of the sequence is calculated by comparing the preceding terms as done below

first term = a = 3

second term = a * r = 3r

third term = second term * r

= a * r * r

= 3r * r

= 3r²

The given data shows that, third term = 192

3r² = 192

divide through by 3

3r² / 3 = 192 / 3

r² = 64

r = √64

r = 8

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Answer:

55.8,117

Step-by-step explanation:

62 times 0.9 is 55.8

130 times 0.9 is 117

I hope this helps!

"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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The evaluation of 12P7 through permutation is 3991680.

This is a question of permutations . The capital letter P is a symbol for permutations. A permutation is a word that describes the number of ways things can be ordered or arranged. In other words , a permutation is a mathematical technique that determines the number of possible arrangements in a set when the order of the arrangements matters.

The formula for permutation is P(n,r)=n! (n−r)!

Hence , 12P7 = 12!/(12-7)!

⇒ 12!/5!

⇒ 12×11×10×9×8×7×6×5!/5!

Now , cancelling 5! from both denominator and numerator, we get
⇒ 12×11×10×9×8×7×6

⇒ 3991680

Therefore , the answer is 3991680.

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Total number of students is 70.

What do you mean by ratio?

A ratio is a comparison of two quantities. The ratio of a to b can also be expressed as:  a:b

A ratio is the equality of two ratios. Write ratios to help you find equivalent ratios and solve for unknown quantities.

Two common types of relationships are part-to-part and part-to-whole.

In a library, the ratio of students with younger siblings to those without younger siblings was 4:3

There were 42 students without younger siblings.

As the given ratio is 4:3

So, let the number of students with younger siblings  = 4x

let the number of students without younger siblings = 3x

There were 42 students without younger siblings.

3x = 42

x = 42/3

x = 14

Let y be the number of students with younger siblings

y = 4x = 4(14) = 56

Total students = students with younger siblings + students without younger siblings

= 14 + 56

= 70

Therefore, total number of students is 70.

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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 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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G= K (given)

J= M. (given)

HJ= LM (given)

So proved that the GHJ = KLM...

Both the triangle are congruent by AAS(Angle Angle Side) rule...

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

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 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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Luianne earns $4340 weekly by working as waitress at a local emerald Monday restaurant.

As per the known fact, one week comprises of seven days. Concerning this, the formula to be used for calculation is -

Regular weekly pay = Numbers of hours of work × number of days in a week × pay per hour

Keep the values in formula to find the regular weekly pay

Regular weekly pay = 40 × 7 × 15.50

Performing multiplication on Right Hand Side of the equation

Regular weekly pay = 4340

Hence, she earns $4340 weekly.

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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 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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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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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 value of x in the triangle is 22.

The angles in the triangle are 22, 29 and 127.

A triangle is a three-sided polygon with three edges and three vertices. the sum of angles in a triangle is 180 degrees. A scalene triangle is a triangle that has three different angles.

x + (x + 7) + 127 = 180

In order to determine the value of x, take the following steps:

2x + 134 = 180

2x = 180 - 134

2x = 44

x = 44/2

x = 22

x + 7 = 22 + 7 = 29

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Step-by-step explanation:

3x+4x+5x=4(x+2)

12x=4x+8

12x-4x=8

8x=8

8/8=x

1=x

x=1

now the length of one side of the square,

3x 5x 4x x+2 x+2

3x1=3 5x1=5 4x1=4 1+2=3 1+2=3

3+5+4+3+3=18

the length of one side of the square is 18 cm.

In Japan, the average cost is $17.61 and in Switzerland, the average cost is $13.55.

An equation is a relationship between two or more variables expressed in equal to form. The equation of two variables look like ax + by=c. It is solved to find the value of variables.

According to the question, the equation are as under:

3x+2y=79.93----------------1

2x+3y=75.87 ----------------2

Multiply equation 1 by 2 and equation 2 by 3 and subtract the result from equation 2 from the result coming from equation 1.

6x+4y=159.86

6x+9y=227.61

Subtracting

6x+4y-6x-9y=159.86-227.61

-5y=-67.75

y=13.55

Put the value of y=13.55 in 3x+2y=79.93

3x+2(13.55)=79.93

3x+27.10=79.93

3x=79.93-27.10

3x=52.83

x=52.83/3

x=17.61

Hence the average cost in Japan is $17.61 and the average cost in Switzerland is $13.55.

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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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Answer:

# of adult tickets = 10

# of child tickets = 4

Step-by-step explanation:

a = # of adult tickets

c = # of child tickets

a + c = 14

a = 14-c

9a + 5c = 110

9(14-c) + 5c =110

126 - 9c + 5c = 110

-4c = 110-126 = -16

c = -16/-4 = 4

a = 14-4 = 10

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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Answer:

Sandwich = 2

Cookie = 1

Step-by-step explanation:

Let

This would mean :

3x + 2y = 8  and 7x + 2y = 16

Because we have two similar terms in the equations, (2y) we can subtract the two equations from each other cancelling out the terms resulting in us having one term that we can solve for. This is known as the elimination method

  7x + 2y = 16

-  3x + 2y  = 8

-----------------------

4x   +   0y   = 8

==> 4x = 8

==> x = 2

We can now plug in the value of x into one of the equations and solve for y

==> 7x + 2y = 16

==> 7(2) + 2y = 16

==> 14 + 2y = 16

==> 2y = 2

==> y = 1

We can conclude that the cost of a sandwich is 2 and the cost of a cookie is 1

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 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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