Tease your brain

Q1. Subtract six lakh twenty thousand five hundred eight from nine lakh fifty thousand.
Q2. Think of two numbers such that their product is 96.
Q3. What is the difference between the largest and the smallest 5-digit numbers formed by the digits 0,8,6,2,9,7 using each digit only once?
Q4. Among the five boys , Vasant is taller than Manohar, but not as tall as Raju. Jayant is taller than Dutta , but shorter than Manohar . Who is the tallest in the group?
Q5. One brother says of his younger brother " Two years ago, I was three times as old my brother was. In three years time , I will be twice as old my as my brother".How old are they now?
Q6.Old Granny Dadi left half money to her granddaughter and half that amount to her grandson . She left a sixth to her brother, and the remainder, Rs. 1,000 to the dog's home. How much did she leave altogether?
Q7. What single digit appears most frequently between and including the numbers 1 and 1,000?
Q8. Today is Wednesday. What will be the the day after 94 days?

You can use the notation P(A), read “the probability of event B, given event A” to write a conditional probability. The correct answer is C.

Conditional probability refers to the probability of one event occurring given that another event has already occurred. In this case, we are interested in the probability of event B occurring given that event A has already occurred, and we can represent this using the notation P(B|A), where '|' means 'given'.

For example, let's say we are interested in the probability of getting a head on a coin toss (event B), given that the coin was flipped and landed on heads (event A). We could represent this using the notation P(B|A). The value of P(B|A) would be 1, because if the coin already landed on heads, then the probability of getting a head on the next flip is certain.

Conditional probability is an important concept in probability theory and is often used in real-world applications, such as predicting the likelihood of a disease given certain symptoms, or the probability of an event occurring given certain conditions.

The correct answer is C.

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To simplify the expression \(\displaystyle\sf 5x-3(-5y+6x)+4y\), we can follow the order of operations, which involves simplifying the expressions within parentheses, applying the distributive property, and combining like terms.

Using \(\displaystyle\sf \) tags for formatting, the expression becomes:

\(\displaystyle\sf 5x-3(-5y+6x)+4y\)

First, we simplify the expression within the parentheses:

\(\displaystyle\sf 5x-3(-5y+6x)+4y\)

\(\displaystyle\sf 5x+15y-18x+4y\)

Next, we can combine the like terms:

\(\displaystyle\sf 5x-18x+15y+4y\)

\(\displaystyle\sf -13x+19y\)

Therefore, the simplified expression is \(\displaystyle\sf -13x+19y\).

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The distance between the points G and H is D = 8 units

Given data ,

Let the distance between 2 points be represented as D

Now , let the first point be G ( 0 , 8 )

Let the second point be H ( 8 , 8 )

Now , let the distance between G and H be D , where

D = √( ( x₂ – x₁ )² + ( y₂ – y₁ )²)

D = √ ( 0 - 8 )² + ( 8 - 8 )²

D = √64 units

D = 8 units

Hence , the distance is 8 units

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Answer:

The width of the rectangle = 1.15 inches

Step-by-step explanation:

Explanation:-

Given that the length of the rectangle = \(\frac{1}{2} inch\)

The area of the rectangle = \(\frac{2.3}{4}\) inch²

We have to find the width of the rectangle

The area of the rectangle = length × width

                                  \(\frac{2.3}{4} = \frac{1}{2} X width\)

                    ⇒     2 × 2.3 = 4× width

                   ⇒      4.6 = 4 w

                  ⇒      w = 1.15 inches

Final answer:-

The width of the rectangle = 1.15 inches

ok

Area of the triangle = (40 x30)/2

= 1200 / 2

= 600 in^2

Area of the rectangle = 20 x 30 = 600 in^2

Area of the arrow = 600 + 600

= 1200 in^2

Result Area = 1200 in^2

Answer:

Divide both sides by 9.

Step-by-step explanation:

To find the second step of the equation, we actually have to solve parts of the equation until we get to step 2.

Step 1: Add 23 to both sides.

Step 2: Divide both sides by 9.

Therefore, the second step is divide both sides by 9.

Have a lovely rest of your day/night, and good luck with your assignments! ♡

The percentage error in the density of metal will be 3.4%.

The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.

Given that the density of the metal in the handbook is 4.018 g/mL and the measured value of the density is 4.16 g/mL.

The percentage error will be calculated as:-

Percentage = [ ( 4.16 - 4.018 ) / 4.16 ] x 100

Percentage = 0.034x 100

Percentage = 3.4%

Hence, the percentage error will be 3.4% for the densities.

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April bought 16 kilograms of soil in total.

We need to add the amounts of soil she used for her violets and tulips. Since April used kilograms for violets and tulips, we need to convert the 3,000 grams to kilograms before we can add them up.

April bought:

9 kilograms of soil for violets

4 kilograms of soil for tulips

3 kilograms of soil for daisies (since 3,000 grams is 3 kilograms)

Therefore, April bought 16 kilograms of soil in total.

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In relation to the angle L of the right triangle the sides are as follows:

A right angle triangle is a triangle that has one of its angles as 90 degrees.  The sides of a right angle triangle can be named according to the position of the angles in the right angle triangle.

The sides of a right triangle can also be solved by using Pythagoras's theorem or trigonometric ratios.

Let's identify the sides  j,  k, and I in relation to angle L in terms of opposite, adjacent, and hypotenuse.

Therefore,

The hypotenuse side is the longest side of a right triangle.

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(A) The range and IQR for boxplot 1 is 10 and 6 respectively.

(B) The range and IQR for boxplot 2 is 12 and 7 respectively.

The interquartile range defines the difference between the third and the first quartile.

The formula for the interquartile range is given below.

Interquartile range = Upper Quartile – Lower Quartile = Q­3 – Q­1

The range is the difference between the lowest and highest values.

The formula for the interquartile range is given below.

Range = Maximum – Minimum

(A) For boxplot 1, we need to find the range and IQR from the given data set.

So, let 34 be the maximum and 24 be the minimum.

\(\text{Range}=\sf 34-24\)

\(\text{Range}=\sf10\)

Therefore, the range is 10.

Now time to find the IQR.

So, let 33 be Q3 and 27 be Q1.

\(\text{IQR}=\sf 33-27\)

\(\text{IQR}=\sf 6\)

Therefore, the IQR is 6.

(B) Now for boxplot 2, we will do the same thing as from part A.

Let's find the range.

So, let 24 be the maximum and 12 be the minimum.

\(\text{Range}=\sf 24-12\)

\(\text{Range}=\sf12\)

Hence, the range is 12.

Now for the IQR.

So, let 22 be Q3 and 15 be Q1.

\(\text{IQR}=\sf 22-15\)

\(\text{IQR}=\sf 7\)

Hence, the IQR is 7.

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Answer:

-4 +9i

Step-by-step explanation:

complex number in standard form.

(-2+6i)-(2-3i)=

Combine like terms

-2 -2  +6i +3i

Standard form is a+bi

-4 +9i

Answer:

y=x+

-2/3

Step-by-step explanation:

y=x+

2

3

Step 1: Flip the equation.

x+

2

3

=y

Step 2: Add (-2)/3 to both sides.

x+

2

3

+

−2

3

=y+

−2

3

x=y+

−2

3

Answer:

the value of ƒ(5) is 19

Step-by-step explanation:

Answer:

dk

Step-by-step explanation:

The temperature drops by \(31\°C\) from day to night in this city.

To calculate the temperature drop from day to night in \(\°C\), we subtract the average nightly low temperature from the average daily high temperature.

Given:

Average nightly low temperature: \(-40\°C\)

Average daily high temperature: \(-9\°C\)

The temperature drop can be calculated as:

Temperature drop = Average daily high temperature - Average nightly low temperature

Substituting the given values:

Temperature drop = \(-9\°C - (-40\°C)\)

Simplifying the equation:

Temperature drop = \(-9\°C + 40\°C\)

Temperature drop = \(31\°C\)

The concept of temperature drop refers to the difference in temperature between two specific periods or conditions. In this case, we are looking at the temperature drop from day to night in a city in China known for its cold climate.

Therefore, the temperature drops by \(31\°C\) from day to night in this city.

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The lengths of the other two sides of the right triangle are 24m and 25m, respectively.

Let's assume the consecutive integers representing the lengths of the other two sides of the right triangle are x and x + 1, where x is the smaller integer. We are given that the shortest side measures 7m. Now, we can use the Pythagorean theorem to solve for the lengths of the other two sides.

According to the Pythagorean theorem, in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

Using this theorem, we have the equation:

\(7^2 + x^2 = (x + 1)^2\)

Expanding and simplifying this equation, we get:

\(49 + x^2 = x^2 + 2x + 1\)

Now, we can cancel out \(x^2\) from both sides of the equation:

49 = 2x + 1

Next, we can isolate 2x:

2x = 49 - 1

2x = 48

Dividing both sides by 2, we find:

x = 24

Therefore, the smaller integer representing the length of one side is 24, and the consecutive integer representing the length of the other side is 24 + 1 = 25.

Hence, the lengths of the other two sides of the right triangle are 24m and 25m, respectively.

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The sequence is decreasing as n increases and sequence converges to the value 0.

The given sequence is defined as aₙ = 1 / (7n + 3).

To determine if the sequence converges or diverges, we need to analyze its behavior as n approaches infinity.

As n increases, the denominator 7n + 3 also increases which means that the values of aₙ will get smaller and smaller, approaching zero as n becomes larger.

The sequence converges to the value 0.

The sequence is decreasing as n increases.

The sequence converges to the value 0.

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F = cost of the songs.

C = number of songs

F ∝ C

F = KC

K = constant of proportionality.

The constant of proportionality is 0.0048.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example: 2x = 6 is an equation.

We have,

Number of songs      Total cost

1515                              $7.20

1717                               $8.16

2020                            $9.60

Let F = cost of the songs.

C = number of songs

F ∝ C

F = KC

K = constant of proportionality.

We see that,

The total cost of the songs = 0.0048 x the Number of songs.

7.20 = 0.0048 x 1515

8.16 = 0.0048 x 1717

9.60 = 0.0048 x 2020

Thus,

F ∝ C

F = KC

F = cost of the songs.

C = number of songs

K = constant of proportionality.

The constant of proportionality is 0.0048.

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Answer:

50 dimes and 90 quarters

Step-by-step explanation:

This problem you will need 2 equations

1. D + Q = 140 ( shows the total amount of coins)

2. 0.1D + 0.25Q= 27.50 ( shows the total cost)

The best way to do this is by substitution

To get D by itself the first equation would turn into D= 140-Q

Plug 140-Q into the second equation where you see D and solve for Q

Once you solve it you should get Q=90 then to get D it would be 140-90 which gives you D=50.

Answe

G=1.5

Step-by-step explanation:

Answer:

\(\boxed{\sf Yes}\;;\textsf{because $\angle 9$ and $\angle7$ are \boxed{\sf vertical} angles, $m \angle 9=$ \boxed{\sf 90\; degrees}}\;.\)

\(\textsf{Because $\angle6$ and $\angle8$ are \boxed{\sf complementary} angles, $m\angle6+m\angle8=$\;\boxed{\sf 90\;degrees}}\;.\)

\(\textsf{Thus}, \; \boxed{\sf m\angle9 = m\angle6 + m\angle8}\;.\)

Step-by-step explanation:

Vertical Angles Theorem

When two straight lines intersect, the opposite vertical angles are congruent.

Therefore, ∠9  and ∠7 are vertical angles and:

⇒ m∠9 = m∠7 = 90°

Angles on a straight line sum to 180°

⇒ m∠6 + m∠8 + m∠7 = 180°

⇒ m∠6 + m∠8 + 90° = 180°

⇒ m∠6 + m∠8 = 90°

Complementary Angles

Two angles whose measures sum to 90°.

Therefore, ∠6 and ∠8 are complementary angles and:

⇒ m∠6 + m∠8 = 90°

As  m∠9 = 90°  and  m∠6 + m∠8 = 90°  then:

⇒ m∠6 + m∠8 = m∠9

Answer:

X= 24º

Explanation:

A straight line is 180º so, 180º - 151º = 29º - 5º = 24º

The logically equivalent statement to p → q is:

~q → ~p

The conditional statement:

p → q

Assuming p and q are propositions, the conditional statement may be expressed as:

"If p holds true, then q follows suit. "

'

Whenever p is true, q is true as well. This implies that if q is false, then p must also be false.

We can rephrase this statement cleverly using the negative propositions, which include the opposite or contradictory statements.

~p  and ~q

These mean:

Not p and Not q respectively.

Then the statement:

"If q is not true, then p is not true"

Is written as:

~q → ~p

So this is the logically equivalent statement.

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The Complete Question

Given a conditional statement p → q, which statement is logically equivalent?

~p → ~q

~q → ~p

q → p

p → ~q

We are required to find AnU, In words A intersection U

This means we are to find the elements that are common in A and U

The common elements are 3,5,6 and 7. They are both in A and U

Hence,

Answer: x = 3 ± √ 10

Answer:

What is a linear function? A linear function is a function whose graph is a straight line. The rate of change of a linear function is constant. The function shown in the graph below, y = x + 2, is an example of a linear function.

Graph of linear function

Graph of linear function

A linear function has a constant rate of change. The rate of change is the slope of the linear function. In the linear function shown above, the rate of change is 1. For every increase of one in the independent variable, x, there is a corresponding increase of one in the dependent variable, y. This gives a slope of 1/1 = 1.

A linear function is typically given in the form y = mx + b, where m is equal to the slope, or constant rate of change.

Examples of linear functions include:

If a person drives at a constant speed, the relationship between the time spent driving (independent variable) and the distance traveled (dependent variable) will remain constant.

Assuming no change in price, the relationship between the number of pounds of bananas a person buys (independent variable) and the total cost of the bananas (dependent variable) will remain constant.

If a person earns an hourly wage at their job, the relationship between the time spent working (independent variable) and the amount earned (dependent variable) will remain constant.

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Exponential Functions

What is an exponential function? An exponential function is a function that involves exponents and whose graph is a smooth curve. The rate of change in an exponential function is not constant. The functions shown in the graph below, y = 0.5x and y = 2x, are examples of exponential functions.

Graphs of exponential functions

Graphs of exponential functions

An exponential function does not have a constant rate of change. The rate of change in an exponential function is the value of the independent variable, x. As the value of x increases or decreases, the rate of change increases or decreases as well. Rather than a constant change, as in the linear function, there is a percent change.

An exponential function is typically given in the form y = (1 + r)x, where r represents the percent change.

Examples of exponential functions include:

Step-by-step explanation:

A more modern explanation would be, "Parallel lines are two lines within a given plane that never intersect."

Two lines on a sphere are an illustration that defies the notion of parallel lines. Meridians are the name given to longitude lines on spheres like the Earth.

Meridians are lines that run parallel to one another from the North Pole to the South Pole. However, if we take into account two meridian lines, they will cross at the North and South Poles. Two lines that are originally parallel will, therefore, eventually intersect at the poles on a sphere, defying the notion of parallel lines.

We can change the original definition of parallel lines to read, "Parallel lines are two lines that do not intersect within a given plane."

This adjustment accounts for the fact that lines can exist in many geometrical contexts, such as on a sphere or in three-dimensional space, where the idea of parallelism may be different. By including the phrase "within a given plane," we restrict the concept to the typical geometry seen in Euclidean geometry, where parallel lines do not meet.

A newer definition may therefore read, "Parallel lines are two lines within a given plane that never intersect." This updated definition makes clear that parallel lines must be taken into account inside a certain plane in order to maintain their validity, while also acknowledging the limitations of the idea.

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Answer:

3p + 8n,    12p + 2n,    9p+4n,    6p+6n

8 columns bar graph.

Step-by-step explanation:

$2 = pen

$3 = notebook

This could be written as a bar graph in multiples of $6.00 along y axes.

3 pens + 8 notebooks. Then 12 pens + 2 notebooks.

Then 9 pens + 4 notebooks . Then 6 pens + 6 notebooks

3p + 8n,    12p + 2n,    9p+4n,    6p + 6n

3p = $6

8n = $24

12p = $24

2n = $6

9p = $18

4n = $12

6p = $12

6n = $18

and so on...

Answer:

\( - 6x = 3 {x}^{2} + 9 \\ 3 {x}^{2} + 6x + 9 = 0 \\ {x}^{2} + 2x + 3 = 0 \\ so \\ ether \: x = - 2 \\ or \: x = 1 \)

Matt takes 157 seconds to run 1 lap.

Ratio basically compares quantities, that means it shows value of one quantity with respect to other quantity.

If a and b are two values, their ratio will be a:b,

Given that,

Time taken to run 8 laps = 1,256 seconds

To find time taken to run 1 lap, use the ratio property,

8 laps = 1256 seconds

1 lap = 1256/8 seconds

1 lap =  157 seconds

Matt takes 157 seconds to run 1 lap.

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Answer:

  x = 4 5/6

Step-by-step explanation:

The fractions have denominators of 4 and 8. The least common multiple of these is 8, so we can eliminate fractions by multiplying both sides of the equation by 8.

  8(3/4x -3) = 8(5/8)

  6x -24 = 5 . . . . . . . . . eliminate parentheses

  6x = 29 . . . . . . . . add 24

  x = 29/6 = 4 5/6 . . . . divide by 6

The solution is x = 4 5/6.

__

Check

Substituting 26/6 for x, we get ...

  (3/4)(29/6) -3 = 5/8

  29/8 -3 = 5/8

  (29 -24)/8 = 5/8 . . . . . true