A man had a square window with sides equal to 1 metre in his house. He decided that it lets in too much light, so he boarded up half of it and still had a square window 1 metre high and 1 metre wide. How did he do that? (6) Total: 40 marks​

\( \frac{14}{35} + \frac{10}{35} - \frac{4}{35} = \frac{4}{7} \)

The solution is, 4/7 is the probability that the child has blonde hair or brown eyes.

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

here, we have,

given that,

in a group of 35 children, 10 have blonde hair, 14 have brown eyes, and 4 have both blonde hair and brown eyes.

let, the event be A,

i.e. A = if a child is selected at random, that child has blonde hair or brown eyes.

now, we have,

total no of sample space = 35

probability of blonde hair = 10/ 35

probability of brown eyes = 14/35

probability of both blonde hair and brown eyes = 4/35

so, we get,

probability of  blonde hair or brown eyes = 14/ 35 + 10/ 35 - 4/35

                                                                    = 20 / 35

                                                                    = 4/7

Hence, The solution is, 4/7 is the probability that the child has blonde hair or brown eyes.

To learn more on probability click:

brainly.com/question/11234923

#SPJ2

If the water snake is initially 30 meters below the ground level and then climbs 20 meters upward, it will be 30 - 20 = 10 meters below the ground level. However, if it then slips down 10 meters, it will be 10 + 10 = 20 meters below the ground level.

The entropy of the outcome of this experiment = 9

A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.

Given that,

A coin having probability p=2/3

Heads is flipped 6 times

If the coin is flipped 6 times

The Total Number of Trial in the Experiment =2/3

It comes up heads 6 times

This Means: Number of Successful Outcome of HEADS =6

In an experimental probability,

Experimental probability of the coin’s coming up heads

=Number of Successful Outcome of HEADS/Total Number of Trials in the Experiment

= 6/(2/3)

= 6*3/2

= 18/2

= 9

Therefore,

The entropy of the outcome of this experiment = 9

To learn more about of Probability visit :

brainly.com/question/29509157

#SPJ4

The simplification of the expressions in the question using the rules of indices are as follows;

1.) 6·e⁰ + (11·f)⁰ - 5/g⁰ = 2

2. (3⁻⁴ + 5⁻³)⁻¹ = \(49\frac{31}{206}\)

3. (3⁻⁴ + 5⁻³)⁻² = \(2415\frac{32685}{42436}\)

4.) \(\dfrac{-5\cdot \left(m^{-4}\cdot n^{-5} \right)^{-3}}{10\cdot c^{-5} \cdot d^6 \cdot e^{-8}}\) = \(\dfrac{c^5\cdot e^8}{2\cdot d^5}\)

5.)  \(\dfrac{-5\cdot \left(m^{-4}\cdot n^{-5}\right)^{-3 }}{7\cdot \left(p^{-6} \cdot q^8\right)^{-4}} =\dfrac{-5\cdot m^{12}\cdot n^{15}\cdot q^{32}}{7\cdot p^{24}}\)

An index or indices is the power by which a number or variable or expression raised.

1.) 6·e⁰ + (11·f)⁰ - 5/g⁰

6·e⁰ + (11·f)⁰ - 5/g⁰ = 6 × 1 + 1 - 5/1

6 × 1 + 1 - 5/1 = 6 + 1 - 5 = 2

Therefore;

6·e⁰ + (11·f)⁰ - 5/g⁰ = 2

2.) (3⁻⁴ + 5⁻³)⁻¹

(3⁻⁴ + 5⁻³)⁻¹ = (1/(3⁴) + 1/(5³))⁻¹ = 1/(1/(3⁴) + 1/(5³))

1/(1/(3⁴) + 1/(5³)) = 1/(1/81 + 1/125) = 1/((125 + 81)/(81×125))

1/((125 + 81)/(81×125)) = (81 × 125)/(125+81) = 10125/209

10125/206 = 49 + 31/206

(3⁻⁴ + 5⁻³)⁻¹ = \(49 \frac{31}{206}\)

3.) (3⁻⁴ + 5⁻³)⁻²

(3⁻⁴ + 5⁻³)⁻² = 1/((1/3⁴ + 1/5³)²)

1/((1/3⁴ + 1/5³)²) = 1/((1/81 + 1/125)²)

1/((1/81 + 1/125)²) = 1/(((125 + 81)/(81 × 125))²)

1/(((125 + 81)/(81 × 125))²) = 1/((206/10125)²)

1/((206/10125)²) = (10125)²/(206)² = 102515625/42436

102515625/42436 = 2415 32685/42436

(3⁻⁴ + 5⁻³)⁻² = \(2415\frac{32685}{42436}\)

4.)  \(\dfrac{5\cdot (2\cdot a^{-1}\cdot b^3)^0}{10\cdot c^{-5}\cdot d^6\cdot e^{-8}}\)

\(\dfrac{5\cdot (2\cdot a^{-1}\cdot b^3)^0}{10\cdot c^{-5}\cdot d^6\cdot e^{-8}} = \dfrac{5\times 1}{10\times \left(\frac{1}{c^5}\times d^6 \times \frac{1}{e^8} \right) }\)

\(\dfrac{5\times 1}{10\times \left(\frac{1}{c^5}\times d^6 \times \frac{1}{e^8} \right) } = \dfrac{5}{10\times \left(\frac{d^6}{c^5\times e^8} \right) }\)

\(\dfrac{5}{10\times \left(\frac{d^6}{c^5\times e^8} \right) } = \dfrac{1}{2\times \left(\frac{d^6}{c^5\times e^8} \right) }\)

\(\dfrac{1}{2\times \left(\frac{d^6}{c^5\times e^8} \right) } = \dfrac{c^5\times e^8}{2\cdot d^6}\)

\(\dfrac{5\cdot (2\cdot a^{-1}\cdot b^3)^0}{10\cdot c^{-5}\cdot d^6\cdot e^{-8}}= \dfrac{c^5\times e^8}{2\cdot d^6}\)

5.) \(\dfrac{-5\cdot \left(m^{-4}\cdot n^{-5} \right)^{-3}}{7\cdot \left(p^{-6}\cdot q^8\rright)^{-4}}\)

\(\dfrac{-5\cdot \left(m^{-4}\cdot n^{-5} \right)^{-3}}{7\cdot \left(p^{-6}\cdot q^8\right)^{-4}} =\dfrac{-5\cdot \dfrac{1}{\left(\frac{1}{m^{4}}\times \frac{1}{n^{5}} \right)^{3}} }{7\cdot \dfrac{1}{\left(\frac{1}{p^{6}}\times q^8\right)^{4}} }\)

\(\dfrac{-5\cdot \dfrac{1}{\left(\frac{1}{m^{4}}\times \frac{1}{n^{5}} \right)^{3}} }{7\cdot \dfrac{1}{\left(\frac{1}{p^{6}}\times q^8\right)^{4}} } = \dfrac{-5\cdot {\left(m^4\times n^5\right)^3} }{7\cdot \left( \dfrac{p^6}{q^8\right)^{4}} }\)

\(\dfrac{-5\cdot {\left(m^4\times n^5\right)^3} }{7\cdot \left( \dfrac{p^6}{q^8\right)^{4}} } = \dfrac{-5\cdot {\left(m^{12}\times n^{15}\right)} }{7} \times \left(\dfrac{q^8}{p^6}\right)^4 }\)

\(\dfrac{-5\cdot {\left(m^{12}\times n^{15}\right)} }{7} \times \left(\dfrac{q^8}{p^6}\right)^4 } = \dfrac{-5\cdot {\left(m^{12}\times n^{15}\right)} }{7} \times \left(\dfrac{q^{32}}{p^{24}}\right) }\)

\(\dfrac{-5\cdot {\left(m^{12}\times n^{15}\right)} }{7} \times \left(\dfrac{q^{32}}{p^{24}}\right) } = \dfrac{-5\times {m^{12}\times n^{15}\times q^{32}} }{7\times p^{24}}\)

\(\dfrac{-5\cdot \left(m^{-4}\cdot n^{-5} \right)^{-3}}{7\cdot \left(p^{-6}\cdot q^8\right)^{-4}} = \dfrac{-5\times {m^{12}\times n^{15}\times q^{32}} }{7\times p^{24}}\)

6.) (3·x⁻⁴·y⁻⁵·z⁻²)⁻²

(3·x⁻⁴·y⁻⁵·z⁻²)⁻² = \(3\cdot \left(\dfrac{1}{\left(\dfrac{1}{x^4} \cdot \dfrac{1}{y^5} \cdot \dfrac{1}{z^2} } \right)^2\right)\)

\(3\cdot \left(\dfrac{1}{\left(\dfrac{1}{x^4} \cdot \dfrac{1}{y^5} \cdot \dfrac{1}{z^2} } \right)^2\right) = 3\cdot \left(x^4\cdot y^5\cdot x^2\right)^2\)

3·(x⁴·y⁵·x²)² = 3·x⁸·y¹⁰·x⁴

Therefore;

(3·x⁻⁴·y⁻⁵·z⁻²)⁻² = 3·x⁸·y¹⁰·x⁴

Learn more about the rules of indices here:

https://brainly.com/question/27150968

#SPJ1

Three or more line segments that only intersect at their ends form closed, two-dimensional shapes known as polygons.

A polygon is a closed, two-dimensional shape with straight sides that is flat or plane. It has straight sides. Polygons are a different category that belongs to the category of two-dimensional figures because two-dimensional (2D) figures are flat because they lack volume.

Polygons are flat 2D shapes that have straight lines and all lines are closed, meaning that they don't have any disconnected lines. Polygons are a subcategory of 2D figures because they carry all traits of 2D figures but also have special ones of their own. Examples of polygons are squares, rectangles, and triangles. Examples of nonpolygons but still are 2D figures are circles, ovals, and any other flat shape.

Learn more about polygon on

https://brainly.com/question/1592456

#SPJ1

Complete question

How can polygons be considered a subcategory of two-dimensional figures?

Answer:

-1/2

Step-by-step explanation:

take the change in y and divide by the change in x: (4 / -2)

Answer: Ig

Step-by-step explanation:

To write a linear expression in standard form, rearrange the terms in alphabetical order.

equations so that the circle is positively oriented in the -plane and starts at  (0, 5, 0)

y = 5 cos(t)

z = 5 sin(t) where t varies from 0 to 2π

The circle of radius 5 in the yz-plane can be described as the set of all points (0, y, z) that are at a distance of 5 from the origin. Using the parametric equation of a circle, we can write:

y = 5 cos(t)

z = 5 sin(t)

where t is a parameter that varies from 0 to 2π. This describes a circle of radius 5 in the yz-plane, centered at the origin, and positively oriented in the counterclockwise direction when viewed from the positive x-axis.

To shift the circle so that it starts at the point (0, 5, 0), we can add 5 to the y-coordinate, giving:

y = 5 + 5 cos(t)

z = 5 sin(t)

So the parametric equations for the circle of radius 5 in the yz-plane, starting at (0, 5, 0) and positively oriented in the counterclockwise direction, are:

x = 0

y = 5 + 5 cos(t)

z = 5 sin(t)

where t varies from 0 to 2π.

To learn more about parametric equation:

https://brainly.com/question/28537985

#SPJ4

\(remainder = 5 \\ please \: see \: the \: attached \: picture \: for \\ full \: solution \\ hope \: it \: helps\)

We see here that new thousand is actually liken to be the result in thousand that is gotten after carrying out an operation.

A thousand is a number that denotes the sum of 1,000 units or ten hundreds.

The word "thousand" is frequently used in daily speech to denote a significant but limited amount, such as a thousand money, a thousand individuals, or a thousand pages. Alternatively, it can be used as a round number to denote an approximation, as in "a thousand times" or "a thousand and one nights."

Learn more about thousand on https://brainly.com/question/29260004

#SPJ1

Answer:

peanut butter cost $0.55

Step-by-step explanation:

j=jelly

p=peanut butter

4p+7j=$6.95

8p+6j=$8.45

solve for p:

8p=8.45-6j

p=(8.45-6j)/8

substitute for p

4(8.45-6j)/8+7j=6.95

reduce

(33.8-24j)/8+7j=6.95

4.225-3j+7j=6.95

4j=6.95-4.225

4j=2.725

j=0.68125

8p+6(0.68125)=8.45

8p+4.0875=8.45

8p=4.3625

p=0.5453

Answer:

the answer for first square is 18

Answer:

The standard deviation of the number of females in the sample is 3.21.

Step-by-step explanation:

For each freshmen, there are only two possible outcomes. Either it is a female, or it is not. Sixty freshmen are randomly selected (without replacement). This means that the hypergeometric distribution is used to solve this question.

Standard deviation of the hypergeometric distribution:

We have that:

N is the population size.

n is the sample size.

s is the number of successes in the sample.

The standard deviation is given by:

\(\sigma = \sqrt{n(\frac{s}{N})(1 - \frac{s}{N})(\frac{N - n}{N-1})}\)

A small liberal arts college in the Northeast has 350freshmen.

This means that \(N = 350\)

One hundred five of the freshmen are female.

This means that \(s = 105\)

Suppose sixty freshmen are randomly selected

This means that \(n = 60\)

Find the standard deviation of the number of females in the sample.

\(\sigma = \sqrt{60(\frac{105}{350})(1 - \frac{105}{350})(\frac{350 - 60}{350 -1})} = 3.21\)

The standard deviation of the number of females in the sample is 3.21.

Answer: 0.0622009569378

Step-by-step explanation:

Step 1: Problem

To determine the equation of a circle with centre (5, -3) and radius 7

Step 2: Substitute the centre value and radius to the equation

Step 3: Simplify the above equation

Hence the equation of the circle is

Answer:

2/3

Step-by-step explanation:

since a is 5 and b is 9.

so, 5+1( according to the expression given)/9

5+1/9 equals 6/9 and taking them down to the lowest terms that makes the answer 2/3

Answer:

JK = 4

KL = 4

JL = 8

Explanation:

Given that K is the midpoint of JL, we have:

See that JK = KL

So,

We then solve for x

Subtract x from both sides

Divide both sides by 3

Therefore

JK = 4x = 4(1) = 4

KL = x + 3 = 1 + 3 = 4

JL = JK + KL = 4 + 4 = 8

Answer:

just divide 18 by 1920 duh

Step-by-step explanation:

The number of catnip toys that Jose can buy will be 3 catnip toys. All the steps are described below.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The table is given below.

       Product                 Cost

Bag of Dog Food          $35

Bag of Cat Food            $18

Chew Toy                      $12

Catnip Toy                      $9

In the event that, your numbers are unique, you should simply supplant the qualities you have with the methodology here, and you ought to find an exact solution.

Presently, Emma has $100 to spend at the store. Along these lines, we really want to ascertain the amount she spends on shopping:

$35 + 2 x $12 = $59

In this way, she burned through $59 in the store, so she has left:

$100 - $59 = $41

She has $41 left to spend on something different. How about we check whether she has sufficient means to purchase multiple times catnip toys as bite toys:

Chew toys: 3 x 12 = $36

Catnip toy: 3 x 9 = $27

Furthermore, Emma has $41 left, so she can either purchase multiple times bite toys or multiple times catnip toys, however not the two of them at that point, on the grounds that the all-out would be 63% dollars, and she will be missing $22.

More about the Algebra link is given below.

https://brainly.com/question/953809

#SPJ1

Answer:

6 hours

Step-by-step explanation:

The swim team trains 4 days every week, with 1/2 hour in the gym and 1 1/4 hours in the pool on Monday, Tuesday and Thursday. On Saturday, there is no gym, but the swim time is doubled, so the total swim time is 2 1/2 hours.

Therefore, the total time spent training each week is 6 hours.

1/2 hour in the gym plus 5 1/2 hours in the pool.

Answer: The swim team trains for 7 hours and 45 minutes a week.

Step-by-step explanation:

Since the swim team trains in the gym and the pool (collectively) on Monday, Tuesday and Thursday, subsequently we will be multiplying GYM TIME + POOL TIME, 3 TIMES to get the time taken for training on the three days i.e. 3 ( ½ + 1 ¼ ) and add twice the time taken in pool for Saturday i.e. 2(1 ¼ )

                                                                   = 3( ½ + 5/4) + 2(5/4)

                                                                   =31/4

                                = 7 ¾

Multiply ¾ with 60 as 1 hour = 60 minutes to get the answer in time format.

Firstly, convert mixed fractions into improper ones and find the final answer. Then, convert the final answer into Time format i.e. hours and minutes.

To try more questions on similar topics on the topic Time,

https://brainly.com/question/1169029

Answer:

2·2·2·2 = 16

Step-by-step explanation:

everytime a number is raised by another, that means you are going to multiply the base number  times itself as many times as the exponents tells you. this is a little but tricky to explain, so let me give you some examples:

2² → in this case the base number is 2 and the exponent is 2 as well, so you will multiply 2 times itself, 2 times:

2² = 2 · 2 = 4

2³ → in this case the base number is 2 and the exponent is 3, so you will multiply 2 times itself, 3 times:

2³ = 2 · 2 · 2 = 8

In the question asked, 2 is being raised by 4, so you will multiply 2 times itself, 4 times:

2^4 = 2·2·2·2 = 16

the same format will be used regardless of the base number and the exponent

i hope this helps! :)

P(x) = 5x² + 5x + 7

"This is a polynomial because it is a 2nd degree trinomial or quadratic".

"Poly: meaning many, and nominal: meaning terms, combine to form the expression: "many terms".

Step-by-step explanation:

By the Right Triangle Altitude Theorem, the two triangles formed by the altitude of a right triangle are similar to the original triangle and to each other.

In this case, triangle ABC is the original right triangle and CE is the altitude. Therefore, the similarity statement that is true is:

△ABC ∼ △AEC

This is because triangles ABC and AEC are both right triangles that share the angle at C, and the altitude CE creates two pairs of congruent angles (the right angles and the angle at A and E) and a pair of proportional sides (CE and AE are corresponding altitudes).

So, we can write the similarity statement as:

△ABC ~ △AEC

Area of sector would be,

⇒ Area of sector = 102.6 feet squared

We have to given that,

Radius of circle = 14 ft

Angle θ = 60°

Now, We know that,

Area of sector = [θ/360]πr²

Where, r is radius of circle.

Hence, We can substitute all the values, we get;

Area of sector = [θ/360]πr²

Area of sector = [60/360](22/7)(14)²

Area of sector = [1/6][22/7][196]

Area of sector = 102.6 feet squared

Thus, Area of sector would be,

⇒ Area of sector = 102.6 feet squared

Learn more about the circle visit:

https://brainly.com/question/24810873

#SPJ1

Answer:

wwwwwwwwwwwwwwwwwww

Answer:

1034

Step-by-step explanation:

Answer:

Z

Step-by-step explanation:

The LCD of 1/(x+2)^2, 3/(x-2)^2, and 4/(x^2-4) is (x+2)^2(x-2)^2(x+2)(x-2) = (x+2)^3(x-2)^3.

To find the lowest common denominator (LCD) of three fractions, we need to identify the factors of each denominator and select those factors that are common to all denominators.The given fractions are: 1/ (x+2)^2, 3/ (x-2)^2, and 4/ (x^2-4).

The first denominator (x+2)^2 can be factored using the formula for the difference of two squares. The denominator of 3/(x-2)^2 can also be factored using the formula for the difference of two squares.

Finally, the denominator of 4/(x^2-4) can be factored using the formula for the difference of two squares and the formula for the sum of two squares.

So, 1/(x+2)^2, 3/(x-2)^2, and 4/(x^2-4) can be rewritten as follows:1/ (x+2)^2 = A/(x+2) + B/(x+2)^2. Multiplying both sides by (x+2)^2 gives:1 = A(x+2) + B ... (1)3/ (x-2)^2 = C/(x-2) + D/(x-2)^2.

Multiplying both sides by (x-2)^2 gives:3 = C(x-2) + D ... (2)4/ (x^2-4) = E/(x-2) + F/(x+2). Multiplying both sides by (x^2-4) gives:4 = E(x-2)(x+2) + F(x+2)(x-2) ... (3)

Now, we need to solve these equations for A, B, C, D, E, and F. First, we will solve equation (1) for A and B by substituting x = -2, which gives A = -1/4. Then we will substitute x = -2 again and solve for B, which gives B = 1/4. Next, we will solve equation (2) for C and D by substituting x = 2, which gives C = 3/4.

Then we will substitute x = 2 again and solve for D, which gives D = -3/4. Finally, we will solve equation (3) for E and F by substituting x = 2 and x = -2, which gives E = 1/2 and F = 1/2.

Now, we have A = -1/4, B = 1/4, C = 3/4, D = -3/4, E = 1/2, and F = 1/2. The LCD is the product of all the factors that appear in the denominators of the fractions, each raised to the highest power that appears.

To learn more about : LCD

https://brainly.com/question/1025735

#SPJ8

Step-by-step explanation:

typically speeds are measured in meters/second, kilometers/hour and such.

I guess, we need to go for "per hour" here.

Logan swam 750 meters in 1/3 hour.

what do we need to do to bring that ratio to a fraction that bases on 1 hour instead of 1/3 hour ?

right, we need to multiply to and bottom by 3.

750×3 / 1×3/3 meters/hour = 2250 / 1 meters/hour =

= 2250 meters/hour = 2.25 km/h

(by using 1000 meters = 1 kilometer).

so, logan's average swimming speed was 2.25 km/h

Mila swam 2/3 × 750 meters in 1/4 hour.

that is

2×750 / 3 meters in 1/4 hour.

1500 / 3 in 1/4 hour = 500 meters in 1/4 hour.

what do we need to do to bring this ratio to a fraction based on 1 hour ?

we need to multiply top and bottom by 4.

500×4 / 1×4/4 meters/hour = 2000 meters/hour = 2 km/h

Mila's average swimming speed was 2 km/h.

Logan was a little bit faster : 2.25 vs. 2 km/h

Answer:

Time taken for both hikers to be at the same elevation = 14 minutes

At that time, they will both be at an elevation of 270 feet

Step-by-step explanation:

Let us represent Jenny's current elevation by x and Julian's current elevation by y

Let T be the time taken when the hikers reach the same elevation

For Jenny

For Julian

Check working
After 14 minutes, Jenny's elevation = 480 - 15 x 14 = 480 = 210 = 270 feet

After 14 minutes, Julian's elevation = 200 + 5 x 14 = 200 + 70 = 270 feet

So it checks out