The shadow of a tree is 10m longer when the angle of elevation of the sun is 45° than when it is 60°, find the height of the tree.​

The income of the man in discuss as in the task content is; rs 10,200.

Since, it follows that 100 paisas make one rupee. This insinuates that the income tax rate which corresponds to 5 paisa per rupee is; 5%.

Hence, the amount earned by the man in discuss can be evaluated as follows;

(5/100) × Income = 510

Hence, Income = 510/0.05 = rs 10,200.

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Five number summary and IQR of both the data sets are different.

For school A: Minimum=6, Q₁=6.5, Median= 14, Q₃=16, Maximum=17, IQR=9.5

For school B: Minimum=5, Q₁=8, Median= 12, Q₃=15.5, Maximum=19, IQR=7.5

No, the box plots are not symmetric.

Part A:

The given data sets are

School A : 9,14,15,17,17,7,15,6,6

School B : 12,8,13,11,19,15,16,5,8

Arrange the data in ascending order.

School A : 6,6,7,9,14,15,15,17,17

School B : 5,8,8,11,12,13,15,16,19

Divide each data set into four equal parts.

School A : (6,6),(7,9),14,(15,15),(17,17)

School B : (5,8),(8,11),12,(13,15),(16,19)

For school A:

Minimum=6, Q₁=6.5, Median= 14, Q₃=16, Maximum=17

The interquartile range of the data is

For school B:

Minimum=5, Q₁=8, Median= 12, Q₃=15.5, Maximum=19

[tex]IQR=Q_3-Q_1\\ =Q_3-Q_1\\ =16-6.2\\ =9.5[/tex]

The interquartile range of the data is

[tex]IQR=Q_3-Q_1\\ =Q_3-Q_1\\ =15.5-8\\ =7.5[/tex]

Part B:

The box plots are not symmetric because the data values are different. Five number summary and IQR of both the data sets are different.

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Answer:

1/4 + x = (-5)/4

x = -5/4 - 1/4

x = (-5)-1 /4

x = (-6)/4

Answer: [tex]\sum^{24}_{n=1} (4n+5)[/tex]

Step-by-step explanation:

This is an arithmetic series with a common difference of 4, so we can immediately eliminate the two left-hand options.

To determine which of the two options on the right is correct, we can determine the first term of each sum expanded out.

The monthly payment for purchasing the home will be $457.85.

The term loan refers to a sort of credit vehicle in which a sum of money is lent to another party in exchange for the value or principal amount being repaid in the future.

Then the formula of monthly payment (MP) will be

[tex]\rm MP = P \times \dfrac{r(1+r)^n}{(1+r)^n - 1}\\[/tex]

In order to purchase a home, a family borrows $110,000 at 2.9% for 30 years.

We have

P = $110,000

r = 0.029 / 12 = 0.0024

n = 30 × 12 = 360

Then the monthly payment will be

[tex]\rm MP = 110,000\times \dfrac{0.0024(1+0.0024)^{360}}{(1+0.0024)^{360} - 1}\\\\[/tex]

On further solving, we have

MP = 110000 × 0.0024 × 1.723

MP = $ 457.85

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[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\texttt {\:Thomas's age = 44 years } [/tex]

[tex]\texttt {\:Hulian's age = 36 years } [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex] \textsf{Assume Thomas's age be ' x ' } [/tex]

[tex] \textsf{and that of Huilan's age be y } [/tex]

[tex] \texttt{we have two conditions :} [/tex]

[tex]\qquad \tt \rightarrow \:y = x + 8[/tex]

it can be simplified as : -

[tex]\qquad \tt \rightarrow \:y - x= 8 \: \: \: \: \: \: \: \: \: - (1)[/tex]

[tex] \texttt{Next condition } [/tex]

[tex]\qquad \tt \rightarrow \:x + y = 80 \: \: \: \: \: \: \: - (2)[/tex]

`` Add both equations ``

[tex]\qquad \tt \rightarrow \:y - x + x + y = 8 + 80[/tex]

[tex]\qquad \tt \rightarrow \:2y = 88[/tex]

[tex]\qquad \tt \rightarrow \:y = 44[/tex]

[tex] \large \textsf{For x :} [/tex]

[tex]\qquad \tt \rightarrow \:y - x = 8[/tex]

[tex]\qquad \tt \rightarrow \:44 - x = 8[/tex]

[tex]\qquad \tt \rightarrow \:x = 44 - 8[/tex]

[tex]\qquad \tt \rightarrow \:x = 36[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

[tex]\fbox {36 years old}[/tex]

Step-by-step explanation:

Let :

⇒ Age of Huilan = x

⇒ Age of Thomas = x - 8

Then :

⇒ x + x - 8 = 80

⇒ 2x = 88

⇒ x = 44

Thomas's age :

⇒ x - 8

⇒ 44 - 8

⇒ 36 years old

The solution of the given expression is 9. So the correct answer is option B.

The complete question is given below:-

(√16 - √49 )² The solution of the given equation will be

A. 16

B .9

C .49

D. 316

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

The given expression will be calculated as:-

(√16 -√49 )² = (√16)² -2 (√16)(√46) + (√49 )²

                    = ( 16 - 2(4)(7) + 49 )

                    = ( 16 - 56 + 49 )

                    = 9

Therefore the solution of the given expression is 9. So the correct answer is option B.

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C) The probability that you pick at least one purple marble is 98%.

The question is incomplete, since the number of marbles of each color in the bag is missing: 3 blue, 5 green, and 2 purple marbles.

Now, to answer the questions, the following calculations must be done:

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Answer:C) The probability that you pick at least one purple marble is 98%.

Step-by-step explanation:

Answer:

y = 5 and y = 1

Step-by-step explanation:

[tex]\textsc {Subtract 7 from each side :}[/tex]

⇒ (3y - 2)² + 7 - 7 = 43 - 7

⇒ (3y - 2)² = 36

[tex]\textsc {take the square root on each side :}[/tex]

⇒ √(3y - 9)² = √36

⇒ 3y - 9 = ±6

[tex]\textsc {When equal to +6, add 9 on each side :}[/tex]

⇒ 3y - 9 + 9 = 6 + 9

⇒ 3y = 15

[tex]\textsc {Divide by 3 on each side :}[/tex]

⇒ 3y/3 = 15/3

⇒ y = 5

[tex]\textsc {When equal to -6, add 9 on each side :}[/tex]

⇒ 3y - 9 + 9 = -6 + 9

⇒ 3y = 3

[tex]\textsc {Divide by 3 on each side :}[/tex]

⇒ 3y/3 = 3/3

⇒ y = 1

Answer:

Greatest number which divides 6168 is 3084,the greatest number which divides 2447 is1223.5 , and the greatest number which divides 3118 is 1559.

The number of distinguishable ways the letters of the following word can be arranged 'KNICKKNACK' is 37800.

When the order of the arrangements counts, a permutation is a mathematical technique that establishes the total number of alternative arrangements in a collection. Choosing only a few items from a collection of options in a specific sequence is a common task in arithmetic problems.

The number of different permutations of n objects with m₁ repeated items, m₂ repeated items,...,mₙ repeated items can be computed as

m!/(m₁!)(m₂!)...(mₙ!)

Here, the letter 'KNICKKNACK' is a total of 10 letters with 4 K's, 2 N's, 1 I, 2 C's, and 1 A.

So, the number of possible arrangements is

(10!)/(4!*2!*1!*2!*1!) = (10*9*8*7*6*5*4!)/(4!*2*2) = 10*9*7*6*5*2 = 37800

Therefore the number of distinguishable ways the letters of the following word can be arranged 'KNICKKNACK' is 37800.

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Answer:

3x-4=5

Step-by-step explanation:

it is correct

By critically observing the given graphs, we can logically deduce that "graph C" returns greatest integer that is less than or equal (≤) to x.

A greatest integer function can be defined as a type of function which returns the greatest integer that is less than or equal (≤) to the number.

Mathematically, the greatest integer that is less than or equal (≤) to a number (x) is represented as follows:

y = [x].

By critically observing the given graphs, we can logically deduce that y in "graph C" returns greatest integer that is less than or equal (≤) to x.

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Answer:

73,358,400

Step-by-step explanation:

(2465)8 × (465)8

= 19,720 × 3,720

= 73,358,400

The question is incomplete. Below you will find the missing content in the figure.

Prove: m/EIF = m/GIH

Step                                                                    Reason

m∠EIF+m∠FIG = 180°

m∠FIG+m∠GIH= 180°

m∠EIF+m∠FIG= m∠FIG+m∠GIH

m∠EIF = m∠GIH

The figure is shown below.

The correct answer is m∠EIF = m∠GIH

Here lines FH and GE intersect each other at the point I.

we have to prove the angle

m∠EIF = m∠GIH

so,

m∠EIF+m∠FIG = 180° as angels ∠EIF and ∠FIG forming a linear pair summing up to 180°. angels ∠EIF and ∠FIG form straight angels on a line EG.

m∠FIG+m∠GIH= 180° as angels ∠FIG and ∠GIH forming a linear pair summing up to 180°. angels ∠FIG and ∠GIH form straight angels on a line FH.

m∠EIF+m∠FIG= m∠FIG+m∠GIH because of the substitution property of equality. we replace 180° by m∠FIG+m∠GIH.

m∠EIF = m∠GIH because of the subtraction property of equality. We can subtract the same elements from both sides by the subtraction property of equality.

Therefore m∠EIF = m∠GIH.

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replace F with 95:

95 = 9/5C + 32

Subtract 32 from both sides:

63 = 9/5C

Divide both sides by 9/5:

C = 35

answer: 35 Celsius

Using conditional probability, it is found that there is a 0.3349 = 33.49% probability that a student is a 9th grader, given that fishing is their favorite leisure activity.

Conditional probability is the probability of one event happening, considering a previous event. The formula is:

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which:

In this problem, we have that the probabilities are given as follows:

[tex]P(A) = 0.433, P(A \cap B) = 0.29 \times 0.50 = 0.145[/tex]

Hence the conditional probability is:

[tex]P(B|A) = \frac{0.145}{0.433} = 0.3349[/tex]

0.3349 = 33.49% probability that a student is a 9th grader, given that fishing is their favorite leisure activity.

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Answer:

The answer will be A. 6 or fewer.

The probability that during a given 10 minutes the number of smokers passing will be 6 or fewer.

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. For an experiment having 'n' number of outcomes, the number of favorable outcomes can be denoted by x. The formula to calculate the probability of an event is as follows.

Probability(Event) = Favorable Outcomes/Total Outcomes = x/n

Example

Suppose we have to predict about the happening of rain or not. The answer to this question is either "Yes" or "No". There is a likelihood to rain or not rain. Here we can apply probability. Probability is used to predict the outcomes for the tossing of coins, rolling of dice, or drawing a card from a pack of playing cards.

The following terms in probability help in a better understanding of the concepts of probability.

Experiment: A trial or an operation conducted to produce an outcome is called an experiment.

Sample Space: All the possible outcomes of an experiment together constitute a sample space. For example, the sample space of tossing a coin is head and tail.

Favorable Outcome: An event that has produced the desired result or expected event is called a favorable outcome. For example, when we roll two dice, the possible/favorable outcomes of getting the sum of numbers on the two dice as 4 are (1,3), (2,2), and (3,1).

Trial: A trial denotes doing a random experiment.

Given:

There are 5 smokers who passes by in every 10 minutes.

So, the probability that during a given 10 minutes the number of smokers passing will be approx 5 or less.

i.e., 6 or fewer.

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Answer: Wasp has greater kinetic energy of 0.002 Joules

Given for bee:

Given for wasp:

Formula:

Kinetic energy of bee:

Kinetic energy of wasp:

From this, it is determined wasp has greater kinetic energy.

Answer:

it depends on which state your in or in your even in the us usually it is either 6% or 4% some times more or less % so im going to do both

50*0.06=53

50*0.04=52

Hope This Helps!!!

It can be modeled by an exponential function, f(x) is divided by 3 each time x increases by 1.

This means that the base of the exponential function is 1/3, and since the value of f(x) when x=0 is 81, [tex]f(x)=81\left(\frac{1}{3} \right)^{x}[/tex]

D. 9.5 cm

To find the perimeter you need to add all the sides.

2.1 + 2.1 + 1 + 3.3 + 1 = 9.5

Answer:

X=5

Step-by-step explanation:

f(1)= -1^2+4(1)+12=15

f(2)= -2^2+4(2)+12=16

f(3)= -3^2+4(3)+12=15

f(4)= -4^2+4(4)+12=12

f(5)= -5^2+4(5)+12=7

g(1)=1+2=3

g(2)=2+2=4

g(3)=3+2=5

g(4)=4+2=6

g(5)=5+2=7

so g(5)=f(5)= X=5

Answer:

Step-by-step explanation:

You're suppose to plug in the values 1, 2, 3, 4, 5, and 6 into f(x) and g(x) to find where they're equal to find the solution to f(x) = g(x) (when the column values are equal).

So for example

f(1) = -(1)^2 + 4(1) + 12

f(1) = -1 + 4 + 12

f(1) = 15

g(1) = 1 + 2

g(1) = 3

put these two values in the table for f(1) and g(1)

f(2) = -(2)^2 + 4(2) + 12

f(2) = -4 + 8 + 12

f(2) = 16

g(2) = 2 + 2

g(2) = 4

f(3) = -(3)^2 + 4(3) + 12

f(3) = -9 + 12 + 12

f(3) = 15

g(3) = 3 + 2

g(3) = 5

f(4) = -(4)^2 + 4(4) + 12

f(4) = -16 + 16 + 12

f(4) = 12

g(4) = 4 + 2

g(4) = 6

f(5) = -(5)^2 + 4(5) + 12

f(5) = -25 + 20 + 12

f(5) = 7

g(5) = 5 + 2

g(5) = 7

f(5) = g(5) so the solution is when x=5

f(6) = -(6)^2 + 4(6) + 12

f(6) = -36 + 24 + 12

f(6) = 0

g(6) = 6 + 2

g(6) = 8

Answer:

0.125 mm

Step-by-step explanation:

A/L=W

W=0.125

[tex]{\huge \underline{{ \fbox \color{red}{A}}{\fbox \color{green}{n}}{\fbox \color{purple}{s}}{\fbox \color{brown}{w}}{\fbox \color{yellow}{e}}{\fbox \color{gray}{r } }}}[/tex]

Answer :- The result is 5cm

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{\bf \red {c {}^{2} = a {}^{2} + b {}^{2}} }[/tex]

[tex] \: \: \: \: \: \: \boxed{ \bf \green{c {}^{2} = (3cm) {}^{2} + (4cm) {}^{2}}}[/tex]

[tex] \: \: \: \: \: \: \: \: \boxed{ \bf \gray{c {}^{2} = 9cm {}^{2} + 16cm {}^{2} }}[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{ \bf \blue {c {}^{2} = 25cm {}^{2} }}[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{ \bf \green{\not{\sqrt {c {}^{ \not{2} }}} = \sqrt{25cm {}^{2} }}}[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{ \bf \red{c = 5cm}}[/tex]

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \: hypotenuse = 5 \:\:cm [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex] \textsf{Pythagoras Theorem } [/tex]

[tex]\qquad \tt \rightarrow \: h {}^{2} = p {}^{2} + b {}^{2} [/tex]

[ h = hypotenuse, p = perpendicular and b = base ]

[tex]\qquad \tt \rightarrow \: {h}^{2} = {3}^{2} + {4}^{2} [/tex]

[tex]\qquad \tt \rightarrow \: {h}^{2} = 9 + 16[/tex]

[tex]\qquad \tt \rightarrow \: h {}^{2} = 25[/tex]

[tex]\qquad \tt \rightarrow \: h = \sqrt{25} [/tex]

[tex]\qquad \tt \rightarrow \: h = 5 \: \: cm[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

f(x) is a linear function, so both the domain and the range are the set of real numbers.

Answer:

[tex] - \frac{1}{6} [/tex]

Step-by-step explanation:

Using the slope formula:

[tex] \frac{ - 1 - 0}{0 - ( - 6)} = - \frac{1}{6} [/tex]

A straight line passing through the point (-2,1) and having a gradient of -3 yields the equation y = -3x - 5.

We know that a straight line is an infinitely long line with no curves on it. A straight line's equation is

y = mx + c...(1), where m is the gradient of the straight line and c is a constant.

Given that the gradient of the given straight line = m = -3.

Putting this value in (1), we get

y = -3x + c ...(2)

Again, the given straight line passes through the point (-2,1). So, we can put x = -2 and y = 1 to get the value of the constant c.

So, 1 = (-3)(-2) + c

i.e. 6 + c = 1

i.e. c = 1 - 6 = -5

(2) can be written as

y = -3x - 5

Therefore the equation of the given straight line is

y = -3x - 5

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Answer:

([tex]\frac{7}{2}[/tex],[tex]\frac{1}{2}[/tex])

Step-by-step explanation:

For this you use the midpoint formula

[tex](\frac{x_{2} +x_{1} }{2} ,\frac{y_{2} +y_{1} }{2} )[/tex]

the points would be (2,1) and (5,2)

The midpoint would be ([tex]\frac{7}{2}[/tex],[tex]\frac{1}{2}[/tex])