Can someone help me out with this

The motorcycle needs to travel 40 km, 0.42 gallons of fuel.

Given that,

A motorcycle can travel 60 miles per gallon.

We have to find,

How many gallons of fuel will the motorcycle need to travel 40 km?

According to the question,

The motorcycle travel 60 miles per gallon,

The motorcycle travels 40 km,

To convert it into kilometers 60 miles per gallon.

[tex]\rm 1 \ mile = 1.6\ k.m.\\\\60 \ miles \times 1.6 \ k.m. = 96 \ k.m.[/tex]

Therefore,

The gallons of fuel will the motorcycle need to travel 40 km is,

[tex]= \dfrac{96}{40}\\\\= 0.42[/tex]

Hence, The motorcycle needs to travel 40 km, 0.42 gallons of fuel.

For more details refer to the link given below.

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Answer:

312.5 m

Step-by-step explanation:

let distance be d and velocity be v , then

d = kv² ← k is the constant of variation

To find k use the condition d = 112.5, v= 15

112.5 = k × 15² = 225k ( divide both sides by 225 )

0.5 = k

d = 0.5v² ← equation of variation

When v = 25 , then

d = 0.5 × 25² = 0.5 × 625 = 312.5 m

Answer:

hi

Step-by-step explanation:

Answer:

She reads one page in 1.40

Answer:

No it is not a factor of 56

Answer:

No

Step-by-step explanation:

6,12,18,24,30,36,42,48,54,60

Answer:

Rs. 14560

Hope you could get an idea from here.

Doubt clarification - use comment section.

In rectangle ABCD

[tex]\\ \sf{:}\longrightarrow Area=LB[/tex]

[tex]\\ \sf{:}\longrightarrow Area=50(45)[/tex]

[tex]\\ \sf{:}\longrightarrow Area=2250m^2[/tex]

In rectangle PQRS

[tex]\\ \sf{:}\longrightarrow Area=LB[/tex]

[tex]\\ \sf{:}\longrightarrow Area=48(43)[/tex]

[tex]\\ \sf{:}\longrightarrow Area=2064m^2[/tex]

Now

[tex]\\ \sf{:}\longrightarrow Area_{(Path)}=Area_{(ABCD)}-Area_{(PQRS)}[/tex]

[tex]\\ \sf{:}\longrightarrow Area_{(Path)}=2250-2064=186m^2[/tex]

Cost:-

[tex]\\ \sf{:}\longrightarrow 186(40)[/tex]

[tex]\\ \sf{:}\longrightarrow Rs 7440[/tex]

Answer:

A

Step-by-step explanation:

1.5 c flour = 12 cupcake

0.75 c flour = 6 cupcake

1.5 + 1.5 + 0.75 = 3.75 c flour

Answer:

x=2

y=1

Step-by-step explanation:

9x+0=18

so it's x=2

6=4y=10

so y=1

Answer:

90/360 x 3.14 x [tex]2^{2}[/tex]. (put into calculator)

Step-by-step explanation:

This is a sector of a circle we can see that there is a right angle (90 degrees) so we can say there is 90/360 of a circle.

The formula for the area of a circle is pi times radius squared.

We can use this but also need to use 90/360.

We can say the area of the shape is 90/360 x 3.14 x [tex]2^{2}[/tex].

The given curve crosses the x-axis whenever x is a multiple of π, and it lies above the x-axis between consecutive even and odd multiples of π. So the regions with area S₀, S₁, S₂, ... are the sets

[tex]R_0 = \left\{(x, y) : 0 \le x \le \pi \text{ and } 0 \le y \le e^{-x}\sin(x)\right\}[/tex]

[tex]R_1 = \left\{(x, y) : 2\pi \le x \le 3\pi \text{ and } 0 \le y \le e^{-x}\sin(x)\right\}[/tex]

[tex]R_2 = \left\{(x, y) : 4\pi \le x \le 5\pi \text{ and } 0 \le y \le e^{-x}\sin(x)\right\}[/tex]

and so on, with

[tex]R_k = \left\{(x, y) : 2k\pi \le x \le (2k+1)\pi \text{ and } 0 \le y \le e^{-x}\sin(x)\right\}[/tex]

for natural number k.

The areas themselves are then given by the integral

[tex]S_k = \displaystyle \int_{2k\pi}^{(2k+1)\pi} \int_0^{e^{-x}\sin(x)} dy \, dx = \int_{2k\pi}^{(2k+1)\pi} e^{-x}\sin(x) \, dx[/tex]

Integrate by parts twice. Take

[tex]u = e^{-x} \implies du = -e^{-x} \, dx[/tex]

[tex]dv = \sin(x) \, dx \implies v = -\cos(x)[/tex]

so that

[tex]\displaystyle \int e^{-x}\sin(x) \, dx = -e^{-x}\cos(x) - \int e^{-x}\cos(x) \, dx[/tex]

then

[tex]u = e^{-x} \implies du = -e^{-x} \, dx[/tex]

[tex]dv = \cos(x) \, dx \implies v = \sin(x)[/tex]

so that

[tex]\displaystyle \int e^{-x}\cos(x) \, dx = e^{-x}\sin(x) + \int e^{-x}\sin(x) \, dx[/tex]

Overall, we find

[tex]\displaystyle \int e^{-x}\sin(x) \, dx = -e^{-x}\cos(x) - e^{-x}\sin(x) - \int e^{-x}\sin(x) \, dx[/tex]

or

[tex]\displaystyle \int e^{-x}\sin(x) \, dx = -\frac12 e^{-x} (\cos(x)+\sin(x)) + C[/tex]

Using the antiderivative and the fundamental theorem of calculus, we compute the k-th area to be

[tex]\displaystyle S_k = -\frac12 e^{-(2k+1)\pi} (\cos((2k+1)\pi)+\sin((2k+1)\pi)) + \frac12 e^{-2k\pi} (\cos(2k\pi)+\sin(2k\pi))[/tex]

[tex]\displaystyle S_k = \frac12 e^{-2k\pi} \cos(2k\pi) \left(e^{-\pi} + 1\right)[/tex]

[tex]\displaystyle S_k = \frac{e^{-\pi}+1}2 e^{-2k\pi}[/tex]

Since [tex]\left|e^{-2\pi}\right|<1[/tex], the sum we want is a convergent geometric sum. As n goes to ∞, we have

[tex]\displaystyle \lim_{n\to\infty} \sum_{k=0}^n S_k = \frac{e^{-\pi}+1}2 \cdot \frac1{1 - e^{-2\pi}} = \boxed{\frac{e^\pi+1}{4\sinh(\pi)}}[/tex]

Answer:

x = 1

y = 30°

Step-by-step explanation:

is RS is ⊥ to TU then TS = US so we can use this equation to find 'x':

20x-3 = 5x+12

15x = 15

x = 1

we also know that RS intersecting with TU creates a 90° angle

if 3y = 90 then y = 30

Hey there!

GUIDE

• The word “sum” means add

• The word “difference” means subtract

• The word “product” means multiply

• The word “quotient” means divide

• The word “is” means equal to

• The “unknown number” is a variable that is not known. So people usually label it as a variable until they figure out what the unknown value is.

Now that we have that information out the way we can solve for your given question.

“The [DIFFERENCE] between [a number] & 16 [is] 49

Lets break it down

• DIFFERENCE (between) = subtract☑️

• A NUMBER = UNKNOWN (so we will label it is as “n”]☑️

• 16 will stay the same because NOTHING was done to it!

• IS = is equal to☑️

We have the key terms out of the way so now we met our answer

ANSWER:

“n - 16 = 49”

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Answer:

Square roots are when you multiply the same number by itself like for example, the square root of 5 is 25, because 5*5=25

Step-by-step explanation:

The value of the root of 2√5 is approximately 2.116.

Here, we have,

To find the root of a number, you can use the concept of radicals.

The "root" refers to the inverse operation of raising a number to a power. For example, the square root (√) is the most common root, and it represents finding a number that, when squared, gives the original number.

To find the root of a number, such as the square root (√), you can use the following notation:

√(2 * √(5))

In this case, we have the square root of (2 times the square root of 5).

To simplify this expression further, we can break it down step by step:

Step 1: Simplify the square root of 5:

√(5) = 2.236 (approximately)

Step 2: Substitute the simplified value back into the original expression:

√(2 * 2.236)

Step 3: Simplify the expression:

√(4.472) = 2.116 (approximately)

Therefore, the root of 2√5 is approximately 2.116.

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Answer:

n = 225

Step-by-step explanation:

Multiply 15 by 15

Answer:

we know that

Hillary

swims every 6 days---> Multiples of 6---> 6-12-18-24-30-36-42-48-54

runs every 4 days-----> Multiples of 4----> 4-8-12-16-20-24-28-32-36-40-44-48

cycles every 16 days---> Multiples of 16---> 16-32-48-64

therefore

In 48 days she will do all three on the same day.

the answer is

48 days

Step-by-step explanation:

Answer:

A. 5(y+3) = 5(3+y)

Step-by-step explanation:

Answer:

The answer is 7.5 gallons per hour.

Step-by-step explanation:

16 fluid ounces multiplied by 60 minutes equals 960 fluid ounces

16 * 60 = 960

960 fluid ounces divided by 128 fluid ounces (which is 1 gallon) equals 7.5 gallons.

960 / 128 + 7.5

So the answer is 7.5 gallons per hour.

Hope this helps! :)

The residual of a regression is the difference between the actual value and the predicted value

The true statement about the residual plot is (c) Yes, the points are in a linear pattern

The entries are given as:

x  Given  Predicted    Residual

1    -2.7         -2.84              

2    -0.9         -0.81            

3     1.1            1.22              

4     3.2          3.25              

5     5.4          5.28

The residual of a line of best fit is calculated using:

[tex]Residual = Actual - Predicted[/tex]

Using the entry headings, the formula would be:

[tex]Residual = Given - Predicted[/tex]

So, the residuals of the 5 entries are:

[tex]Residual_1 = -2.7 - -2.84 =0.14[/tex]

[tex]Residual_2 = -0.9 - -0.81 =-0.09[/tex]

[tex]Residual_3 = 1.1 - 1.22 =-0.12[/tex]

[tex]Residual_4 = 3.2 - 3.25 =-0.05[/tex]

[tex]Residual_4 = 5.4 - 5.28 =0.12[/tex]

So, the entries become:

x  Given  Predicted    Residual

1    -2.7         -2.84             0.14

2    -0.9         -0.81            -0.09

3     1.1            1.22             -0.12

4     3.2          3.25           -0.05

5     5.4          5.28            0.12

See attachment for the residual plot.

From the plot, we can see that the points are in a linear pattern.

Hence, the true statement about the residual plot is (c)

Read more about residuals at:

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Hey there!

f(x) = -3|2x - 9| + 4

y = -3|2x - 9| + 4

y = -3|2(-5) - 9| + 4

y = -3|-10 - 9| + 4

y = -3|19| + 4

y = -57 + 4

y = -53

Therefore, your answer should be: f(x) = -53

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Step-by-step explanation:

A1

1 yard = 3 feet

1 foot = 12 inches

therefore,

100 yards = 100×3×12 inches = 3600 inches

A2

again, 1 yard = 3 feet

8 ft = 8/3 = 2.67 yards = 2 2/3 yards

A3

1 gallon = 8 pints

A4

1 liter = 1000 milliliters (remember, "mili" means 1/1000).

therefore,

2.2 liters = 2.2×1000 = 2200 milliliters

A5

again, 1 liter = 1000 milliliters

therefore

1 milliliter = 1/1000 liter

670 milliliters = 670 × 1/1000 liter = 670/1000 liter =

= 0.67 liter

B1

1 kg (kilogram) = 1000 grams ("kilo" means 1000).

we have 3 layers.

each layer weighs (cake plus icing)

1/2 kg + 100 g = 500 g + 100 g = 600 g

3 layers then weigh

3×600 g = 1800 g

the additional candle weighs 250 g.

so, the total is

1800 g + 250 g = 2050 g = 2.05 kg

B2

area is 110 m².

1 m = 100 cm ("centi" means 1/100).

and 1 m² is then 100×100 = 10000 cm².

so, the area in cm² is

110 × 10000 = 1,100,000 cm²

the top area of one brick = 10 × 20 = 200 cm²

so, we need

1,100,000 / 200 = 11,000 / 2 = 5500 bricks

Answer

A

Step-by-step explanation:

The linear function defines the arithmetic sequence is an = -4 + 3(n - 1). The correct option is D.

The sequence in which every next number is the addition of the constant quantity in the series is termed the arithmetic progression.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

The given series is -4, -1, 2, 5, 8. The common difference of the series is  calculated as,

d = -1 - ( -4 )

d = -1 + 4

d = 3

The equation will be written as,

an = a₁ + d(n - 1)

an = -4 + 3(n - 1)

Therefore, the linear function that defines the arithmetic sequence is an = -4 + 3(n - 1). The correct option is D.

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The equation showing the relationship between w and t is [tex]w = 4t[/tex]

From the table, we have the following points:

(0,0) and (1,4)

Start by calculating the slope (m)

[tex]m = \frac{y_2 -y_1}{x_2 -x_1}[/tex]

So, we have:

[tex]m = \frac{4 -0}{1 -0}[/tex]

Simplify the numerator and the denominator

[tex]m = \frac{4}{1}[/tex]

Divide 4 by 1

[tex]m = 4[/tex]

The equation is then calculated as:

[tex]w = m(t - t_1) + w_1[/tex]

This gives

[tex]w = 4(t - 0) + 0[/tex]

Simplify

[tex]w = 4t[/tex]

Hence, the equation is [tex]w = 4t[/tex]

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Answer:  -164

Step-by-step explanation:

Answer:-164

Step-by-step explanation:

−2(−8)

2

+2(−8)−20

Plug into each x-value

−

2

(

64

)

+

2

(

−

8

)

−

20

−2(64)+2(−8)−20

Square first

−

128

−

16

−

20

−128−16−20

Multiply

f

(

−

8

)

=

−

164

f(−8)=−164

Answer:

2055 is the answer.

Step-by-step explanation:

If x represents the number of minutes and y represents the hiker elevation in feet.

y = 8.19x + 663

y = 8.19(170) + 663

y = 1392.3 + 663

y = 2055.3

Hope it helps:)

Answer:

:)

Step-by-step explanation:

Answer:

a)

Slope form y=2x+3

Standard form 2x-y=-3

b)

Slope y=3/5x-6

Standard 3x-5y=30

c)

slope y=-3/2x+9

standard 3x+2y=18

d)

slope y=-3x+0

standard = 3x+y=0

Step-by-step explanation:

a)

Slope form y=2x+3

Standard form 2x-y=-3

b)

Slope y=3/5x-6

Standard 3x-5y=30

c)

slope y=-3/2x+9

standard 3x+2y=18

d)

slope y=-3x+0

standard = 3x+y=0

Answer:

2^2×20

Step-by-step explanation:

2^2×20

because 2×20=40

so, 2^2×20=2^40

The Following are the representation of [tex]2^{40[/tex] as a power in different bases

a) [tex]2^{ 2 * 20}[/tex]

b) [tex]2^{ 5 * 8}[/tex]

c) [tex]2^{ 8 * 5}[/tex]

d) [tex]2^{ 10 * 2}[/tex]

Exponents and powers can be used to represent extremely big or extremely small numbers in a more straightforward fashion.

For example, if we have to show 3 x 3 x 3 x 3 in a simple way, then we can write it as [tex]3^4[/tex], where 4 is the exponent and 3 is the base.

Given:

[tex]2^{40[/tex] as a power

so, writing the above in given bases

a) 2²

= [tex]2^{ 2 * 20}[/tex]

= [tex]2^{40[/tex]

b)[tex]2^5[/tex]

= [tex]2^{ 5 * 8}[/tex]

= [tex]2^{40[/tex]

c) [tex]2^8[/tex]

= [tex]2^{ 8 * 5}[/tex]

= [tex]2^{40[/tex]

d) [tex]2^{10[/tex]

= [tex]2^{ 10 * 2}[/tex]

= [tex]2^{40[/tex]

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Answer:

Step-by-step explanation:

What is the value of the expression Negative 225 divided b (negative 15)?

What is the value of the expression 30 divided by (negative 6)?

I answer for what I understand

-225 : 15 = - 15

30 : (- 6 ) = -5

Create the expression from the data:

The gallon of paint begins as a whole: 8/8

Then he removes 5/8 gallons of paint from the can: - 5/8

Then he adds 5/8 of a different colored paint to the can: + 5/8

Now combine:

8 / 8 - 5 / 8 + 5 / 8 = 8/8

The paint can is full, then he removes an amount from the can. He then pours more paint into the can that is equal to the amount he originally removed. Therefore, the paint can remained full.

Answer:

72

Step-by-step explanation:

50% means ½ of the usual days,

if 50% = 24 days

then the usual day is 48 days

so, 48+24= 72

Answer:8 and 22

Step-by-step explanatio