[tex]64^{2x+1} =1024[/tex]

Using the information given in the problem to set up two equations and by solving them

25% of the number is 80.

An equation is a mathematical statement that expresses the equality of two expressions. It typically consists of two parts: the left-hand side and the right-hand side, separated by an equal sign (=). The left-hand side and right-hand side can contain variables, numbers, and mathematical operations such as addition, subtraction, multiplication, and division.

Let's call the number we're looking for "x". We can use the information given in the problem to set up two equations:

0.7x = 224 (equation 1)

0.95x = 304 (equation 2)

We want to find 25% of the same number, which can be written as 0.25x. We can solve for x using either equation 1 or equation 2 and then plug that value into 0.25x to find the answer.

Let's solve for x using equation 2:

0.95x = 304

x = 304/0.95

x = 320

Now that we know x is 320, we can find 25% of that number:

0.25x = 0.25(320) = 80

So 25% of the number we were looking for is 80.

To know more about the equation visit:

brainly.com/question/12788590

#SPJ1

Keenan has placed his solar panel at an optimal angle.

The cosine law is a mathematical relationship between the sides and angles of a triangle. The cosine law states that:

cos(C) = (a² + b² - c²) / 2ab

where a, b, and c are the lengths of the sides of the triangle and C is the measure of one of the angles. This law can be used to find unknown side lengths or angle measures in a triangle when given the other values.

Check the attached image for labelling.

The angle we are trying to calculate is labelled C.

cos (C) = (20² + 18² - 19²) / (2*20*18)

cos (C) = 363/720

C = cos⁻¹(363/720)

C = 59.72°

Since the angle obtained is between 58° and 60°. Thus, Keenan has placed his solar panel at an optimal angle.

Learn more about cosine law on:

https://brainly.com/question/8823652

#SPJ1

Complete Question

Check the attached image for complete question

The side lengths on the similar polygons are given as follows:

Similar polygons are polygons that share these two features presented as follows:

Considering the equivalent side lengths, the proportional relationship for the side lengths in this problem is given as follows:

18/16 = 18/EI = ST/24.

Hence the length of EI is given as follows:

EI = 16.

The length of ST is obtained as follows:

18/16 = ST/24

16ST = 18 x 24

ST = 18 x 24/16

ST = 27.

More can be learned about similar polygons at brainly.com/question/14285697

#SPJ1

The probability of choosing a subcommittee of 3 members with no graduate students is 0.2, or 20%.

The number of possible subcommittees that contain only undergraduate students can be calculated by choosing 3 members from the 4 undergraduate students. This can be done in

(4 choose 3) = 4 ways.

The total number of possible subcommittees of three students that can be formed from the 6 members of the committee can be calculated by choosing 3 members from the 6 students. This can be done in

(6 choose 3) = 20 ways.

Therefore, the probability that there will be no graduate students on the subcommittee is:

Number of subcommittees with only undergraduate students / Total number of possible subcommittees

= 4 / 20

= 1/5

= 0.2

So, the probability of choosing a subcommittee of 3 members with no graduate students is 0.2, or 20%.

Learn more about probability :

https://brainly.com/question/30034780

#SPJ4

The probability that the committee has exactly two woman is 0.1758.

Probability determines the likelihood of an event occurring: P(A) = f / N. Odds and probability are related but odds depend on the probability. You first need probability before determining the odds of an event occurring.The ratio of the favorable outcomes to the all possible outcomes.

Given that, 4 women and 5 men are eligible to serve on a committee.

A committee of 3 is randomly selected.

Choosing 2 women out of 3 women is

³[tex]C_{2}[/tex]

= 3

Choosing 1 men out of  5 men is

5C1

= 5

Total number of eligible person is = (4+5)=9

Choosing 3 member out of 9 member is

9C3

=84

The required  probability is

=3*5/84

0.1785

know more about probability click here;

https://brainly.com/question/15584918

#SPJ4

The length of the third side of a triangle with perimeter 9x + 6 and measures of other two sides of the triangle is equal to option a. x + 13.

Perimeter of the triangle is equal to

= 9x + 6

First side of the triangle = 5x

Second side of the triangle = 3x - 7

Let 'n' be the third side of the triangle

perimeter of the triangle = 9x + 6

⇒ 5x + 3x - 7 + n = 9x + 6

⇒ n + 8x - 7 = 9x + 6

⇒ n = 9x -8x + 6 + 7

⇒ n = x + 13

Therefore, the third side of the triangle with given perimeter of the triangle is equal to option a. x + 13.

The above question is incomplete , the complete question is :

A triangle has a perimeter of 9x + 6. the first side of the triangle has a length of 5x, and the second side has a length of 3x − 7. what is the length of the third side of the triangle?

a. x + 13       b. x − 1            c. 8x − 7         d. 17x − 1

Learn more about perimeter here

brainly.com/question/6465134

#SPJ4

Answer: The equation X + y = -5 represents a straight line in a two-dimensional plane. To determine whether a specific point (X, y) is a solution of the equation, you can substitute the values of X and y into the equation and see if it holds true. If the equation is satisfied, then the point (X, y) is a solution. If the equation is not satisfied, then the point (X, y) is not a solution.

For example, if X = 2 and y = -7, then the equation becomes:

2 + (-7) = -5

-5 = -5

Since the equation holds true, the point (2, -7) is a solution of the equation X + y = -5.

Step-by-step explanation:

The solution is 440 ft² because the overall size of the image is 528 sq ft, which in itself is closest approaching 440 square feet.

Parallel forms are defined as having at least two even more parallel lines. If two lines never cross, they are considered to be parallel. There are different parallel shapes, however any parallel sides require an equitable distribution of sides in the shape.

Sum of the measurements of the two main sides divided by height equals the area of a trapezoid.

Let's refer to the longer parallel side's length as "L." The figure's height is 22 feet, while the shorter parallel side's length is 16 feet.

Area = (L + 16) / 2 * 22

We also knows that the distance between a point and the vertical line formed by two studs is 4 feet and the distance between a vertex and the opposing height is 8 feet. The Pythagorean theorem may be used to determine the length of the greater parallel side, L, since these two lengths create a right triangle.

L² = (8 + 4)² = 64

L = 8

We can now calculate the overall area using the formula for a trapezoid's area.

Area = (L + 16) / 2 * 22 = (8 + 16) / 2 * 22 = 24 * 22 = 528

The solution is 440 ft² because the overall size of the figures is 528 sq ft, that is closest towards 440 sq ft.

To know more about Parallel visit:

https://brainly.com/question/1439696

#SPJ1

The probability that there are 30 or fewer successes in 112 trials with a probability of 0.42 of success is  0.874763 rounding to 6 decimaiplaces.

To use the Excel spreadsheet programme to calculate the likelihood that 30 or fewer successes occur in 112 trials with a success probability of 0.42, follow these steps:

In Excel, create a new spreadsheet with the first column labelled "Number of Successes" and the second column labelled "Probability."

Enter "0" in the first row of the "Number of Successes" column.

Enter "1" in the second row of the "Number of Successes" column.

Continue to input numbers in the "Number of Successes" column in ascending order until you reach 30.

Enter the following formula in the field next to the "0" in the "Probability" column: =BINOM.DIST (0,112,0.42,TRUE)

Enter the following formula: =SUM (B1:B31)

The result in the cell where you input the formula in step 8 will be the chance of 30 or fewer successes in 112 trials with a success rate of 0.42.

For more such questions on probability, click on:

brainly.com/question/24756209

#SPJ4

In a magnetometry experiment, It will take 1 more minute for data be collected in order to reduce error the statistical noise by a factor of 10.

To reduce the random error by a factor of 10, we need to reduce the statistical noise to 1/10 picotesla. Since the statistical noise was initially 1 picotesla, this means we need to reduce it by a factor of 10.

We can use the following formula to calculate the time needed to reduce the statistical noise by a certain factor:

t = (log (final noise / initial noise)) / (log (reduction factor))

Here, the final noise is 1/10 picotesla, the initial noise is 1 picotesla, and the reduction factor is 10.

Plugging in these values, we get:

t = (log (1/10 / 1)) / (log (10))

t = (log (1/10)) / (log (10))

t = -1 / 1

t = -1

The negative value of t doesn't make sense in this context, so we need to take the absolute value:

t = |-1|

t = 1

Therefore, it will take 1 more minute to reduce the statistical noise by a factor of 10.

To know more about standard error :

https://brainly.com/question/14615113

#SPJ4

____The given question is incomplete, the complete question is given below:

Reduction of the standard error

In a magnetometry experiment, after a minute of collecting

data the statistical noise was reduced to 1 picotesla.

For how much longer should data be collected in order

to reduce the random error by a factor of 10?

Answer:

all of these equations except 4n = 48

Step-by-step explanation:

your equations are

52 = 8n+4

4(2n+1) = 52

4 = 52-8n

4n = 48

n = 6

let's solve these equations!

52 = 8n + 4

48 = 8n

n = 6

4(2n+1) = 52

8n + 4 = 52

8n = 48

n = 6

4 = 52-8n

-48 = -8n

n=6

4n = 48

n = 12

all of these equations simplify to n = 6 except for 4n = 48, so they're all equivalent

The number of possible requests for free samples is 5^1 = 5. This means that the customer has 5 different requests that they can make for free samples.

The number of possible requests for free samples can be calculated using the combination formula. The combination formula is used to calculate the number of combinations with repetitions of size “n” taken from a set of “r” elements . The formula is: [tex]C(n,r) = n^r[/tex] In this case, n = number of requests (1 request) and r = number of free samples offered (let’s say, 5). Therefore, the number of possible requests for free samples is[tex]5^1 = 5.[/tex]This means that the customer has 5 different requests that they can make for free samples.

Learn more about samples here:

https://brainly.com/question/15659544

#SPJ4

Answer:

Second string, first fret.

Step-by-step explanation:

Answer:

1/4 as fraction

0.25 as decimal

= 0.25

Step-by-step explanation:

Factors of 24 starting at 1 are:
1 x 24 = 24

2 x 12 = 24

3 x  8  = 24

4 x 6 =  24

Then the pattern repeats in decreasing orders of products of numbers . 6 x 4, 8,x 3 etc which are duplicates of the ones shown above

Factors of 24 are:

1, 2, 3, 4, 6, 8, 12, 24

There are 8 factors

Out of the 8 factors, only two  - 12 and 24 are two digit numbers

P(factor is a 2 digit number = # two-digit numbers/Total # factors

= 2/8

= 1/4

= 0.25

Answer:

1/4 as a fraction

0.25 as decimal

0.25

follow me if my answer was helpful to you

Let's call the time it takes to install all the chairs from start to finish "t". The workers install 840 chairs per day, so in "t" days they will have installed 840 * t chairs.

At the end of 5 days, they still have 240 chairs to install, so they have installed 840 * 5 chairs so far. We can use this information to write an equation:

840 * t - 840 * 5 = 240

Expanding and simplifying the equation gives us:

840t - 4200 = 240

Adding 4200 to both sides gives us:

840t = 4440

Finally, dividing both sides by 840 gives us:

t = 5.2857142857...

So it takes approximately 5.29 days to install all the chairs from start to finish.

Answer:

Step-by-step explanation:

The formula used to calculate the surface area of a square pyramid is A = a^2 + 2a[tex]\sqrt{\frac{a^2}{4}+h^2 }[/tex]

The square pyramid is the geometric shape that has a square base and 4 lateral face. The total number of faces will be five. The base shape is square and the side shape will be triangle. Number of edges in the square pyramid is eight

The surface area is the amount space covered by the surface of the object

Here the surface area of the square pyramid is

A = a^2 + 2a[tex]\sqrt{\frac{a^2}{4}+h^2 }[/tex]

Where A is the surface area of the square pyramid

a is the base edge

h is the height of the square pyramid

Therefore, the surface area is A = a^2 + 2a[tex]\sqrt{\frac{a^2}{4}+h^2 }[/tex]

Learn more about square pyramid here

brainly.com/question/28701701

#SPJ4

Answer:

Diatance biked = rate • time

Answer:

240/2, 360/3

Step-by-step explanation:

240/2 and 360/3 both involve division and both of their answers are equal to 120, assuming these count as number sentences.

The solutions to the system of linear equation (x, y) are 1 and 4/3 respectively

A system of linear equations is a collection of two or more linear equations with the same variables. The goal of solving a system of linear equations is to find the values of the variables that simultaneously satisfy all the equations in the system.

From the question given;

-x + 6y = 7 ...eq(i)

6x - 30y = -34 ...eq(ii)

From eq (i)

x = 6y - 7 ..eq (iii)

Put eq (iii) into eq (ii)

6(6y - 7) - 30y = -34

36y - 42 - 30y = -34

6y - 42 = -34

6y = -34 + 42

6y = 8

y = 4/3

Put y = 4/3 into eq (i)

-x + 6(4/3) = 7

-x + 24 / 3 = 7

x = 24/3 - 7

x = 1

Learn more on system of linear equation here;

https://brainly.com/question/13729904

#SPJ1

The most accurate estimated sum of 181 and 204 is 380

The given numbers are 181 and 204

The compatible numbers are defined as the numbers that are easy to do the arithmetic operations. The arithmetic operations are addition, subtraction, division and multiplication etc.

To find the sum of the compatible numbers first we have to round the given numbers to the nearest tens or hundreds and do the the arithmetic operation

Round 181 to the nearest tens = 180

Round 204 to the nearest tens = 200

Then the sum of compatible numbers will be

180 + 200 = 380

Therefore, the most accurate estimation is 380

Learn more about compatible numbers here

brainly.com/question/627054

#SPJ4

The differential equations given correspond to phase lines with slopes that depend on the power of the x term in the equation.

1. y' = x: This differential equation corresponds to a phase line with a slope of 1, since the y' term is equal to the x term.

2. y' = -x: This differential equation corresponds to a phase line with a slope of -1, since the y' term is equal to the negative of the x term.

3. y' = [tex]x^2[/tex]: This differential equation corresponds to a phase line with a slope of 2x, since the y' term is equal to the x squared term.

4. y' = [tex]-x^2[/tex]: This differential equation corresponds to a phase line with a slope of -2x, since the y' term is equal to the negative of the x squared term.

5. y' =[tex]x^3[/tex]: This differential equation corresponds to a phase line with a slope of [tex]3x^2[/tex], since the y' term is equal to the x cubed term.

6. y' = [tex]-x^3[/tex]: This differential equation corresponds to a phase line with a slope of [tex]-3x^2[/tex], since the y' term is equal to the negative of the x cubed term.

7. y' = [tex]x^n[/tex]: This differential equation corresponds to a phase line with a slope of [tex]nx^(n-1)[/tex], since the y' term is equal to the x to the power of n term.

8. y' = -[tex]x^n[/tex]: This differential equation corresponds to a phase line with a slope of [tex]-nx^(n-1),[/tex] since the y' term is equal to the negative of the x to the power of n term.

In summary, the differential equations given correspond to phase lines with slopes that depend on the power of the x term in the equation.

Learn more about differential equations here:

https://brainly.com/question/14620493

#SPJ4

Complete question:

Determine which differential equation corresponds to each phase line. You should be able to state briefly how you know your choices are correct. ?

1.  y' = x

2. y' = -x

3.  y' = [tex]x^2[/tex]

4. y' = [tex]-x^2[/tex]

5.y' =[tex]x^3[/tex]

6.y' = [tex]-x^3[/tex]

7. y' = [tex]x^n[/tex]

8. y' = -[tex]x^n[/tex]

Answer:

To solve the problem, Sarah used the equation:

Left-handed people = (11/100) * Total people

Step 1: Plug in the total number of people (30) into the equation.

Left-handed people = (11/100) * 30

Step 2: Simplify the right side of the equation.

Left-handed people = (11/100) * 30

Left-handed people = 3.3

Step 3: Round the answer to the nearest whole number.

Left-handed people = 3

So, Sarah expects 3 people in a class of 30 to be left-handed. Each step of Sarah's work is justified because she used the percentage formula to find the number of left-handed people in a class and rounded the answer to the nearest whole number.

Answer: 41 degrees

Step-by-step explanation:

121-39=82

82/2=41

Kyle: Rotation about the origin, then reflection across the x axis

Tina: Reflection over the line y = x

In geometry, reflection refers to a transformation that involves flipping a shape or object over a line, often called the "line of reflection".

This transformation preserves the size and shape of the original object, but changes its orientation by reversing the positions of all its points across the line of reflection.

Considering the image, rotation about the origin, then reflection across the x axis when compare with Reflection over the line y = x. will yield similar result.

Learn more about reflection at:

https://brainly.com/question/26494295

#SPJ1

112.8 is the the total sound power, when three drill presses are operating

A relation is a function if it has only One y-value for each x-value.

Given that a function P(n) = 108 + 10 log(n) gives the total sound power in decibels when n drill presses are operating in a factory.

We need to find the total sound power, to the nearest decibel, when three drill presses are operating

We have to consider n as 3

P(3) = 108 + 10 log(3)

=108+10×0.477

=108+4.77

=112.77

Hence, 112.8 is the the total sound power when three drill presses are operating

To learn more on Functions click:

https://brainly.com/question/21145944

#SPJ1