if kenneth has 11 dimes and nickels in his pocket, and they have a combined value of 80 cents, how many of each coin does he have?

"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 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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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 information about your sample data is summarized and provided by summary statistics.It provides information regarding the values in your data set.This covers the distribution of the mean and the skewness of your data.

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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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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 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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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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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 distance of the reaction as Jerry drives at a rate of 35 mph is 11.73 m.

Distance is the total movement of an object without any regard to direction.

To calculate the approximate reaction distance, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitiute these values into equation 1

Hence, the distance of the reaction is 11.73 m.

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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 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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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:

Answer: 75 minutes to 25 minutes

Step-by-step explanation:

To find the ratio between 1 1/4 hours and 25 minutes, we first need to convert both quantities to the same unit of time. Since 1 hour is equal to 60 minutes, 1 1/4 hours is equal to 1.25 * 60 = 75 minutes. Therefore, the ratio between 1 1/4 hours and 25 minutes is 75 minutes to 25 minutes, or 3 to 1.

583 times the length of jeff's ride was larry's bike ride

Word problem in maths is a maths question written as one sentence or more that requires children to apply their maths knowledge to a ‘real-life’ scenario. a word problem is a mathematical exercise (such as in a textbook, worksheet, or exam) where significant background information on the problem is presented in ordinary language rather than in mathematical notation. As most word problems involve a narrative of some sort, they are sometimes referred to as story problems and may vary in the amount of technical language used.Word problems are usually made up of a few sentences describing a scenario that needs to be solved through maths. These scenarios are usually ‘real-life- ones, situations that people might find themselves in every day. For example, it could be the division of pizza between party members or working out how long a train might take from one place to another.

This means that children must be familiar with the vocabulary associated with the mathematical symbols they are used to, in order to make sense of the word problem.

Given,jeff jogged 4 miles today, and larry biked 2 1/3 miles.

Let x times the length of jeff's ride was larry's bike ride.

4x= 7/3

x=.583 times

So, .583 times the length of jeff's ride was larry's bike ride.

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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: 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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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).

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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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: 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

A logarithmic function is defined by f(x) = [tex]log_a[/tex]x(r) y = [tex]log_a[/tex]x, where a > 0 and y = [tex]log_a[/tex]x. It is the inverse of the exponential function [tex]a^{y}[/tex] = x.

During the 16th century, Scottish mathematician, scientist, and astronomer John Napier discovered logarithms. The technique is widely used in astronomical and scientific calculations involving huge numbers. As an inverse of exponential functions, logarithmic functions are closely related to exponential functions. By transforming [tex]a^{x}[/tex] = N into [tex]log_a[/tex] N = x, the exponential function is transformed into a logarithmic function.

Let's say that y=[tex]10^{\log x}[/tex]

see this, 100=[tex]10^2[/tex],

then [tex]log _{10}[/tex] 100 = 2

therefore, [tex]log _{10}[/tex] y=[tex]\log _{10}[/tex] xy = x

[tex]10^{\log x}[/tex] = x

Hence, proved.

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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 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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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 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:

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

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 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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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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