Nick and his family travel by train to New York City.
The clocks show when the train leaves the station and when it arrives in New York City.

How long is the train ride?

[tex]\bold{\huge{\underline{ Solution }}}[/tex]

Here, We have given

We know that,

Area of triangle

[tex]{\sf{=}}{\sf{\dfrac{1}{2}}}{\sf{ {\times} base {\times} height }}[/tex]

Subsitute the required values,

[tex]{\sf{=}}{\sf{\dfrac{1}{2}}}{\sf{ {\times} 3 {\times} 6}}[/tex]

[tex]\sf{ = 3 {\times} 3 }[/tex]

[tex]\bold{ = 9 }[/tex]

Therefore,

Area covered by 4 right angled triangles

[tex]\sf{ = 4 {\times} 9 }[/tex]

[tex]\bold{ = 36}[/tex]

Now,

We have to find the area of the big square

We know that,

Area of square

[tex]\sf{ = Side {\times} Side }[/tex]

Subsitute the required values,

[tex]\sf{ = 9 {\times} 9 }[/tex]

[tex]\bold{ = 81 }[/tex]

Therefore,

The total area of shaded region

= Area of big square - Area covered by 4 right angled triangle

[tex]\sf{ = 81 - 36 }[/tex]

[tex]\bold{ = 45 }[/tex]

Hence, The total area of shaded region is 45 .

Here,

We have to find the area of non shaded region

According to the question

Let the hypotenuse of the given right angled triangle be x

Therefore,

By using Pythagoras theorem,

That is,

[tex]\sf{ (Perpendicular)^{2} + (Base)^{2} = (Hypotenuse)^{2} }[/tex]

Subsitute the required values

[tex]\sf{ (6)^{2} + (3)^{2} = (x)^{2} }[/tex]

[tex]\sf{ 36 + 9 = (x)^{2} }[/tex]

[tex]\sf{ x = \sqrt{45}}[/tex]

[tex]\bold{ x = 6.7 }[/tex]

That means,

We know that ,

Area of square

[tex]\sf{ = Side {\times} Side }[/tex]

Subsitute the required values,

[tex]\sf{ = 6.7 {\times} 6.7 }[/tex]

[tex]\bold{ = 44.89 \:\: or \:\: 44.9 }[/tex]

Therefore ,

Area of non shaded region

= Area of big square - Area of small square

[tex]\sf{ = 81 - 44.9 }[/tex]

[tex]\bold{ = 36.1 }[/tex]

Hence, The total area of non shaded region is 36.1 or 36 (approx) .

Here, we have to

The total area of the figure

= Non shaded region + Shaded region

[tex]\sf{= 36 + 45 }[/tex]

[tex]\bold{= 81}[/tex]

Hence, The total area of the given figure is 81 .

Answer: 4:18

Work:

2:9

2 inch:9 feet

2 · 9 = 18

2 · 2 = 4

4 inch:18 feet

Answer: what grade is this

Step-by-step explanation:

Answer: 97

Step-by-step explanation:

Answer:

[tex]a_n=\frac{1}{8} (2^{n-1})[/tex]

Step-by-step explanation:

This is a geometric sequence.  You start with the first term, 1/8, then multiply it by 2 to get 1/4, then double that to get 1/2, etc.

The number you multiply by is called the common ratio.  In this case, the common ratio is 2.

A formula for the general (nth) term is:  [tex]a_n=a_1 r^{n-1}[/tex].

[tex]a_1=1/8\\r=2[/tex]

So the nth term is [tex]a_n=\frac{1}{8} (2^{n-1})[/tex]

Answer:

a) 17.5%

b) $150,000

c) 27°

Step-by-step explanation:

Angles around a point add up to 360°.

Therefore, to find the percentage of the portion of the pie chart, divide the degree of the portion by 360° and multiply by 100%

Assuming that Real Estate is half of the circle, and Mutual Funds are a quarter of the circle.

a)  Government Bonds = (63° ÷ 360°) x 100% = 17.5%

b) Crypto Currency = 90° - 63° = 27°

Therefore, (27° ÷ 360°) x 100% = 7.5%

7.5% of $2,000,000 = 0.075 x $2,000,000 = $150,000

c) Crypto Currency = 90° - 63° = 27°

#a

Find percentage (whole is 360°)

#2

Angle of crypto=180-(90+63)=180-153=27°

Percentage:-

Total

#c

Found in second part

The rate of change of Julian given the equation y = 37.8x is 37.8

The equation:

y = 37.8x

where,

If x = 3 gallons

y = 37.8x

= 37.8 × 3

y = 113.4 miles

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Answer: B

Step-by-step explanation:

When f(x) turns into f(2x), we need to halve the value of x.

The roots of f(2x) will be equal to ( 1 / 2 ) and -1.

It is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.

Given that the root of function f(x) are 1 and -2. The roots of F(2x) will be calculated as:-

( x - 1 ) ( x + 2 ) =0

( 2x - 1 )( 2x + 2 ) =0

x = 1 / 2

x = -1

Therefore, the roots of f(2x) will be equal to ( 1 / 2 ) and -1.

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Answer:

42cm³

Step-by-step explanation:

7*2*3=42

7*2=14

14*3=42

42

Answer: the opposite of 15

Step-by-step explanation:

Answer:122/600= 0.20333333333

Step-by-step explanation:

[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]

Let's write the equation in standard form ~

[tex]\qquad \sf  \dashrightarrow \: {x}^{2} + {y}^{2} - 2y - 15 = 0[/tex]

[tex]\qquad \sf  \dashrightarrow \:(x ){ }^{2} + {y}^{2} - 2y = 15[/tex]

[tex]\qquad \sf  \dashrightarrow \:(x ){ }^{2} + {y}^{2} - 2y + 1 = 15 + 1[/tex]

[tex]\qquad \sf  \dashrightarrow \:(x ){ }^{2} +( {y}^{} - 1 ) {}^{2} = 16[/tex]

Now, it's the required form of circle ~

The Hypotheses are; Null Hypothesis; H₀: μ = 76.4 and Alternative Hypothesis; Hₐ: μ > 76.4 where μ is the true mean height of all trucks.

We are given;

Population Mean; μ = 76.4 inches

Sample Mean; x' = 77.1 inches

Sample standard deviation; s = 5.2 inches

Sample size; n = 100 trucks

Now we can thus define the hypotheses as;

Null Hypothesis; H₀: μ = 76.4

Alternative Hypothesis; Hₐ: μ > 76.4

where μ is the true mean height of all trucks

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The parameters for computing the area of triangle is first listed out and the expression for the area of triangle was used to find the algebraic method

Parameters for find the area of triangle are

Let the base be x, and let the height be y

We know that the expression for the area of triangle is given as

Area = 1/2 (Bass* Height)

Substituting our parameters we have

Area = 1/2*x*y

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Answer:

2.987

Step-by-step explanation:

The mean is calculated by dividing the sum of the terms by the # of terms.

For this problem, add all of the terms together:

3.245 + 3.678 + 3.3 + 2.499 + 2.9 + 3.206 + 2.081 = 20.909

Now, divide the product by the number of terms there are. There are 7 terms.

20.909 ÷ 7 = 2.987

Answer:

4x + 2

Step-by-step explanation:

x - 1 is adding an x and subtracting a 1 ,so

x + x + x + (x - 1) + 1 + 1 + 1

= x + x + x + x - 1 + 1 + 1 + 1 ← collect like terms

= 4x + 2

Answer:

25a^2b^4c^2

Step-by-step explanation:

step 1:

Remove the bracket by multiplying all the power inside the bracket with the power outside the bracket.

5^2a^2b^2x2c^2=25a^2b^4c^2

Answer:

Step-by-step explanation:

Hailey paid 80% of the regular price.

We have Hailey who paid 40$ for a jacket whose regular price was 50$.

Assume that she paid [x]% of the regular price.

Then, we can write -

40 = x% of 50

40 = (x/100) x 50

x = (4000/50)

x = 80%

Therefore, Hailey paid 80% of the regular price.

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The polynomial that Amir subtracted from 3x² + 8x - 16 to get x² - 4 is: 2x² + 8x - 12.

To subtract polynomials from each other, take like terms together and subtract.

To find out what quantity Amir subtracted from 3x² + 8x - 16 to get x² - 4, do the following:

(3x² + 8x - 16) - (x² - 4)

Open bracket

3x² + 8x - 16 - x² + 4

Combine like terms

2x² + 8x - 12

Therefore, the polynomial that Amir subtracted from 3x² + 8x - 16 to get x² - 4 is: 2x² + 8x - 12.

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The value of x which saisfies the equation sin(x+37)°=cos(2x+8)° is 135 or 15.

We can use the fact that:

[tex]\sin(\theta ^\circ) = \cos(90 - \theta^\circ)[/tex]

to convert the sine to cosine (but the angles won't stay same unless its 45 degrees).

For this case, we're specified the equation sin(x+37)°=cos(2x+8)°.

Converting sine to cosine, we get:

[tex]\cos(90 - x - 37)^\circ = \cos(2x + 8)^\circ\\[/tex]

Since cosine is a periodic function with period of [tex]360^\circ[/tex], thus, we get:
[tex]90 - x - 37= 2x + 8 +360 n[/tex]

where n = an integer (positive, negative, or zero).

or

[tex]90 - 37 - 8= 3x + 360 n\\\\x = \dfrac{45 - 360n}{3} = 15 - 120n[/tex]

This is the general solution of the considered equation.

Assuming that only principal values (from 0 to 360 degrees) angles are allowed, we need:

[tex]0 \leq x + 37 \leq 360\\\\and\\\\0 \leq 2x+8 \leq 360[/tex]

The first inequality gives:

[tex]-37 \leq x \leq 323[/tex]

The second inequality gives:

[tex]-4 \leq x \leq 176[/tex]

We need to satisfy both the inequalities, so the final boundaries on x are:

[tex]-4 \leq x \leq 176[/tex] (the minimum ones for which both inequalities stay true).

n < -2 gives x > 255, and n > 1 gives x < -105

So, values of n for which [tex]-4 \leq x \leq 176[/tex] is true are n = -1, or n = 0

Thus, x = either 135 or 15

sin

Thus, the value of x which saisfies the equation sin(x+37)°=cos(2x+8)° is 135 or 15

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The total amount of interest will Gertrude pay by the time the subsidized Stafford loan is repaid is $2094.80.

Compound interest is the amount charged on the principal amount and the accumulated interest with a fixed rate of interest for a time period.

The formula for the final amount with the compound interest formula can be given as,

[tex]A=P\times\left(1+\dfrac{r}{n\times100}\right)^{nt}\\[/tex]

Here, A is the final amount (principal plus interest amount) on the principal amount P of with the rate r of in the time period of t.

Gertrude will graduate four years after taking out the loan. if the loan has an interest rate of 6.8%, compounded monthly, and Gertrude makes monthly payments.

Put the values in the above formula as,

[tex]5500=P_{mt}\times\left(1-\dfrac{6.8}{12\times100}\right)^{-12\times10}\\P_{mt}=63.29[/tex]

In the 10 years, the refund she gets,

[tex]A_r=63.29\times12\times100\\A_r=7594.8[/tex]

Interest paid by her is,

[tex]I=7594.8-5500\\I=2094.8[/tex]

Thus, the total amount of interest will Gertrude pay by the time the subsidized Stafford loan is repaid is $2094.80.

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Answer: D

Step-by-step explanation:

Answer:

105,000

Step-by-step explanation:

I'd the scale is 1 : 50,000, you would first take the 2.1km and multiply it by your 50,000. This will put your answer to scale coming in at 105,000 km on the map

Answer:

40 degrees

Step-by-step explanation:

(to find coterminal angles to a given angle, we add 360 degrees to the given angle or subject 360 degrees from the given angle any angle any number of time).

-1400 degrees is negative angl, so to get the coterminal angle between 0 degrees and 360 degrees ( the smallest positive coterminal angle), we must add multiples of 360 degrees until we get a possitive coterminal angle:

-1400 degrees+(360 degrees*4)

=-1400 degrees+1440

=40 degrees

so the answer is 40 degrees

Answer:

Step-by-step explanation:

The area of a parralelogram is B*H

Base is 20.2

Hight is 12

20.2*12=242.4

Perimeter is the sum of all sides

20.2*2+12*2=64.4

Answer:

4 Years.

Step-by-step explanation:

Principle ⇒ 2000

Interest ⇒ 400

Rate ⇒ 5%

Time ⇒ _

Simple interest ⇒ p * x * t / 100

⇒ 400 = 2000 * 5 * t / 100

⇒ 400 = 200 * 5 * t / 10

⇒ 400 = 20 * 5 * t

⇒ t = 400 / 20 * 5

⇒ t = 40 / 2 * 5

⇒ t = 20 / 5

⇒ t = 4

Answer:

Umm..... sorry but.....my answer came.......

The probability that the number picked is divisible by 3 or 5 is 0.555.

Probability sampling is defined as a sampling technique in which the researcher chooses samples from a larger population using a method based on the theory of probability.

An integer number is chosen randomly between 1 and 1000.

The number of numbers divisible by 3, which is;

[tex]\rm \dfrac{1000}{3}=3333.3 = 333[/tex]

The number of numbers divisible by 5, which is;

[tex]\rm \dfrac{1000}{5}=200[/tex]

The probability that the number picked is divisible by 3 or 5 is;

[tex]\rm Probability=\dfrac{Number \ divisble \ by \ 3+ Number \ divisble \ by \ 5}{1000}\\\\ Probability =\dfrac{333+200}{1000}\\\\Probability=\dfrac{533}{1000}\\\\Probability=0.533[/tex]

Hence, the probability that the number picked is divisible by 3 or 5 is 0.555.

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Answer:

I am sorry but u didn't really ask any question to be answered so next time give a question to be answered

Hey there!

$10.00 + 0.25¢ + 0.25¢ + 0.25¢ + 0.25¢

= $10.25 + 0.25¢ + 0.25¢ + 0.25¢
= $10.50 + 0.25¢ + 0.25¢

= $10.75 + 0.25¢

= $11.00

OR YOU COULD READ THE EQUATION LIKE:

$10.00 + $1.00

= $11.00

Thus, your answer is: FALSE because $10 + 4 quarters gives you $11 NOT $15

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

False

Step-by-step explanation:

$10+$1=$11 and .25+.25+.25+.25=$1

which would equal $12 so your answer would be falses if thats what your asking