3) 5m - 40
what's da answer ?

Answer:

y= 8x + 55

After 25 minutes the tank will have 255 gallons

Step-by-step explanation:

The value of $\sin 2a$ is $\frac{35}{39}$. To find $\sin 2a$, we first need to determine the measure of angle $a$.

Since we are given that the area of the right triangle $abc$ is $4$ and the hypotenuse $\overline{ab}$ is $12$, we can use the formula for the area of a right triangle to find the lengths of the two legs.

The formula for the area of a right triangle is $\frac{1}{2} \times \text{base} \times \text{height}$. Given that the area is $4$, we have $\frac{1}{2} \times \text{base} \times \text{height} = 4$. Since it's a right triangle, the base and height are the two legs of the triangle. Let's call the base $b$ and the height $h$.

We can rewrite the equation as $\frac{1}{2} \times b \times h = 4$.

Since the hypotenuse is $12$, we can use the Pythagorean theorem to relate $b$, $h$, and $12$. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

So we have $b^2 + h^2 = 12^2 = 144$.

Now we have two equations:

$\frac{1}{2} \times b \times h = 4$

$b^2 + h^2 = 144$

From the first equation, we can express $h$ in terms of $b$ as $h = \frac{8}{b}$.

Substituting this expression into the second equation, we get $b^2 + \left(\frac{8}{b}\right)^2 = 144$.

Simplifying the equation, we have $b^4 - 144b^2 + 64 = 0$.

Solving this quadratic equation, we find two values for $b$: $b = 4$ or $b = 8$.

Considering the triangle, we discard the value $b = 8$ since it would make the hypotenuse longer than $12$, which is not possible.

So, we conclude that $b = 4$.

Now, we can find the value of $h$ using $h = \frac{8}{b} = \frac{8}{4} = 2$.

Therefore, the legs of the triangle are $4$ and $2$, and we can calculate the sine of angle $a$ as $\sin a = \frac{2}{12} = \frac{1}{6}$.

To find $\sin 2a$, we can use the double-angle formula for sine: $\sin 2a = 2 \sin a \cos a$.

Since we have the value of $\sin a$, we need to find the value of $\cos a$. Using the Pythagorean identity $\sin^2 a + \cos^2 a = 1$, we have $\cos a = \sqrt{1 - \sin^2 a} = \sqrt{1 - \left(\frac{1}{6}\right)^2} = \frac{\sqrt{35}}{6}$.

Finally, we can calculate $\sin 2a = 2 \sin a \cos a = 2 \cdot \frac{1}{6} \cdot \frac{\sqrt{35}}{6} = \frac{35}{39}$.

Therefore, $\sin 2

a = \frac{35}{39}$.

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We can argue that the volume of square prism is greater than the volume of the cylinder.

To find the volume of a prism, we need to multiply the of area of base by the height. Since the height is the same for both the square prism and the cylinder, we can focus on comparing the areas of their respective cross-sections.

The area of the cross-section of the square prism is given as 157 square units. Since the cross-section is a square, we can find the side length by taking the square root of the area. So, the side length of the square is √157 units.

The area of the cross-section of the cylinder is given as 50π square units. Since the cross-section is a circle, we can find the radius by taking the square root of the area divided by π. So, the radius of the cylinder is √(50π/π) = √50 units.

Now, to compare the volumes, we need to calculate the volume of each shape. The volume of the square prism is equal to the area of the base multiplied by the height, which is (√157)^2 * height. The volume of the cylinder is equal to the area of the base (π * (√50)^2) multiplied by the height. Since the heights are the same, we can compare the volumes by comparing the areas of the bases.

Since (√157)^2 is greater than (√50)^2, we can conclude that the area of the base of the square prism is greater than the area of the base of the cylinder. Therefore, the volume of the square prism is greater than the volume of the cylinder.

In summary, based on the given information, we can argue that the volume of the square prism is greater than the volume of the cylinder.

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Answer:

14 and 10

Step-by-step explanation:

14x5=70

10x3=30

100=70+30

A set of reflections that would carry hexagon ABCDEF onto itself would be "x-axis, y=x, x-axis" or "y=x, x-axis, y-axis".

What is a combination of reflections?

Combination of Two Reflections. A point or object once reflected can further be reflected to form a new image. The axes of these reflections may be parallel to each other or they intersect each other at a point.

Given the coordinates of hexagon ABCDEF, it can be determined that a set of reflections that would carry the hexagon onto itself would be a combination of reflections over the x-axis and y-axis.

One possibility would be to reflect over the x-axis, then reflect over the y=x line, and finally reflect over the x-axis again.

This would take the hexagon from its original position to itself.

Another possibility would be to reflect over the y = x line, then reflect over the x-axis, and finally reflect over the y-axis.

This would also take the hexagon from its original position to itself.

Hence, a set of reflections that would carry hexagon ABCDEF onto itself would be "x-axis, y=x, x-axis" or "y=x, x-axis, y-axis".

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Answer:

1. 1 1/12

2. 1/10

Answer:

1. or 1 or 1.083

2. or 0.1

Step-by-step explanation:

The probability that the mean time for the sample of 150 returns for this year is greater than 92 is 0.95907

Given,

Mean, \(\overline x\) = 90 minutes

standard deviation, \(\sigma\) = 14 minutes

to find probability that mean for sample 150 returns is greater than 92, \(P(\overline x > 92)\)

This means we need to find probability the related z-value of expected mean

where, \(z=\frac{\overline x-\mu_x}{\sigma_x}\)

Here,

\(\mu_x\)= expected mean =92

\(\sigma_x\)=standard deviation for new sample i.e. 150

\(\sigma_x\) can be calculated by formula,

\(\sigma_x=\frac{\sigma}{\sqrt{n}}\\\\\sigma_x=\frac{14}{\sqrt{150}}\\\\\sigma_x=1.143\)

Now,

\(z=\frac{90-92}{1.143}\\\\z=-1.749\)

Now,

\(P(\overline x > 92)\\\\=P(z > -1.749)\\\\=1-P(z < -1.749)\\\\=1-0.04093\\\\=0.95907\)

In above calculation, the z-value is  determined from the z-table.

Thus, the probability that mean is greater than 92 is 0.95907

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Your question is incomplete, please complete the question.

Answer:

Option (A)

Step-by-step explanation:

Graph of function 'f' represents,

x - intercept of the function 'f' → (1, 0)

y - intercept of the function → (0, 6)

As x-approaches ∞, value of the function approaches (-2)

Points in the given table is for the another function 'g'

x - intercept of the function 'g' → (1, 0) [For x - intercept, y = 0]

y - intercept of the function 'g' → (0, 3) [For y - intercept, x = 0]

As x approaches ∞, value of function 'g' approaches (-1).

Therefore, x - intercepts of both the functions are same but end behavior are different when x → ∞.

Option (A) will be the answer.

A triangle shape is formed by the cross-section of a triangular pyramid sliced by a plane that is perpendicular to its base

A triangular pyramid is a geometric solid having a triangle for a base and three triangles with the same vertex on each side.  That is, the triangular pyramid is made up of four triangles. Pyramids made of triangles might be straight or inclined. It resembles a pyramid with four triangular faces that meet at one vertex and a triangular base.

Let's first draw the triangular pyramid. Now, mark the base. Then, denote the plane passing perpendicular to the base. From the diagram we can tell, the plane cuts this pyramid to form a triangle cross-section.

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Answer: 12,620,256

Step-by-step explanation:

Given: The camera shop socks eight different types of batteries and there re at least 31 batteries of each type.

Here we want to select r= 31 batteries from n= 8 kinds of batteries, then formula we use to find number of ways is \(^{n+r-1}C_r=\ ^{31+8-1}C_{31}\)

\(=^{38}C_{31}=\dfrac{38!}{31!(38-31)!}\\\\=\dfrac{38!}{31!7!}\\\\=\dfrac{38\times37\times36\times35\times34\times33\times32\times31!}{31!\times5040}\\\\=12620256\)

Hence, the number of ways can a total inventory of 31 batteries be distributed among the eight different types = 12,620,256

After 12 days, 4.2 grams of curium-243 remains will be left in a sample with 5.6 grams after 12 days.

Given that,

The half-life of curium-243 is 28.5 days.

We have to find how many grams of curium-243 will be left in a sample with 5.6 grams after 12 days.

We know that,

The formula is

A(t) = A₀(1/2\()^{t/h}\)

Here,

t= 12 days, half life,

h =28.5 days .

And the initial value, A(0)=5.6 grams

So we will get

A(t) = 5.6(1/2\()^{12/28.5}\)

A(t) = 5.6×0.747 = 4.2 grams

Therefore, After 12 days, 4.2 grams of curium-243 remains will be left in a sample with 5.6 grams after 12 days.

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To find the differentials of the given functions, we use the rules of differentiation.

(a) y = xe^(-4x)

To find the differential dy, we use the product rule of differentiation:

dy = (e^(-4x) * dx) + (x * d(e^(-4x)))

(b) y = (1 + 2u)/(1 + 3v)

To find the differential dy, we use the quotient rule of differentiation:

dy = [(d(1 + 2u) * (1 + 3v)) - ((1 + 2u) * d(1 + 3v))] / (1 + 3v)^2

(c) y = tan(Vt)

To find the differential dy, we use the chain rule of differentiation:

dy = sec^2(Vt) * d(Vt)

(d) y = ln(sin(o))

To find the differential dy, we use the chain rule of differentiation:

dy = (1/sin(o)) * d(sin(o))

The differential of a function represents the change in the function's value due to a small change in its independent variable.  Let's calculate the differentials for each function:

(a) y = xe^(-4x)

To find the differential dy, we use the product rule of differentiation:

dy = (e^(-4x) * dx) + (x * d(e^(-4x)))

Using the chain rule, we differentiate the exponential term:

dy = e^(-4x) * dx - 4xe^(-4x) * dx

Simplifying the expression, we get:

dy = (1 - 4x)e^(-4x) * dx

(b) y = (1 + 2u)/(1 + 3v)

To find the differential dy, we use the quotient rule of differentiation:

dy = [(d(1 + 2u) * (1 + 3v)) - ((1 + 2u) * d(1 + 3v))] / (1 + 3v)^2

Expanding and simplifying the expression, we get:

dy = (2du - 3(1 + 2u)dv) / (1 + 3v)^2

(c) y = tan(Vt)

To find the differential dy, we use the chain rule of differentiation:

dy = sec^2(Vt) * d(Vt)

Simplifying the expression, we get:

dy = sec^2(Vt) * Vdt

(d) y = ln(sin(o))

To find the differential dy, we use the chain rule of differentiation:

dy = (1/sin(o)) * d(sin(o))

Simplifying the expression using the derivative of sin(o), we get:

dy = (1/sin(o)) * cos(o) * do

These are the differentials of the given functions.

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Answer:

426 balloons

Step-by-step explanation:

274 + 152 = 426

Please give brainliest!

The statement that best describes Lucia's claim is at option (b), that is " Lucia's claim is incorrect since not all the rotations that are multiples of 45° carry a square onto itself".

It is given that, Lucia draws a square and plots the center of the square.

Lucia claims that " any rotation about the center of the square that is a multiple of 45° will carry the square onto itself".

To verify this claim, we need to construct a square (ABCD) as shown in the figure.

When the square ABCD is rotated about 45° where we can it is 1 × 45°, the square formed is A'B'C'D' is not the same as the actual one. So, they are not in symmetry after the rotation n this case.

If we rotate again, that is for the second multiple of 45° (2 × 45°), we get a square A''B''C''D''. But, now the square is similar to the actual one. So, they are in symmetry.

This means we can say that, not for all the multiples of 45° rotation, the square does not carry onto itself.

Therefore, we can conclude that "Lucia's claim is incorrect since not all rotations that are multiples of 45' carry a square onto itself".

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-6

Step-by-step explanation:

First we see 3 is greater than the subject so 3<x 3-9 = -6

The solution is Option A.

The translation of the center of circle is given by ( x , y ) ⟶ ( x - 15 , y + 1 )

A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The circumference of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle.

Given data ,

Let the equation for the circle A be represented as

( x - 7 )² + ( y - 1 )² = 16

Now , the equation is of the form ( x - h )² + ( y - k )² = r²

So , the radius of the circle is 4 and the center of the circle is ( 7 , 1 )

Let the equation for the circle A be represented as

( x + 8 )² + ( y - 2 )² = 16

Now , the equation is of the form ( x - h )² + ( y - k )² = r²

So , the radius of the circle is 4 and the center of the circle is ( -8 , 2 )

So , the translation of circle A to B is given by

( 7 , 1 ) to ( -8 , 2 )

So , the x coordinate is translated by 15 units to left and the y coordinate is translated by 1 unit up

Hence , the translation is given by ( x , y ) ⟶ ( x - 15 , y + 1 )

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There are a total of 12 chocolate chip + 10 sugar + 18 peanut butter = 40 cookies in the sack. The probability of selecting a cookie that is not a peanut butter cookie is (12 chocolate chip + 10 sugar) / 40 = 22/40 or 0.55. So, there is a 55% chance that the selected cookie will not be a peanut butter cookie.

The difference in area between the two packages is -10 square inches. However, since area cannot be negative, we can conclude that the rectangular package has a greater area than the trapezoid-shaped package.

To find the difference in area between the trapezoid-shaped package and the rectangular package, we need to calculate the areas of both shapes and then find the difference.

For the trapezoid-shaped package:

Base = 12 inches

Top side length = 10 inches

Height = 10 inches

Area of a trapezoid = (1/2) × (base + top side length) × height

Area of trapezoid = (1/2) × (12 inches + 10 inches) × 10 inches

Area of trapezoid = (1/2) × 22 inches × 10 inches

Area of trapezoid = 110 square inches

For the rectangular package:

Base = 12 inches

Height = 10 inches

Area of a rectangle = Base × Height

Area of rectangle = 12 inches × 10 inches

Area of rectangle = 120 square inches

Now, let's find the difference in area:

Difference in area = Area of trapezoid - Area of rectangle

Difference in area = 110 square inches - 120 square inches

Difference in area = -10 square inches

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Answer:

0

Step-by-step explanation:

\(\frac{2}{6(x-\frac{9}{10}) } =-2\frac{3}{4}\)

1. The first step is to distribute the 6 to the \((x-\frac{9}{10})\):

\(\frac{2}{6x-7\frac{2}{10}} =-2\frac{3}{4}\)

2. The second step is to get 6x-7 2/10 out of the denominator, so you have to multiply that on both sides which looks like this:

\(2 =-2\frac{3}{4}(6x-7\frac{2}{10})\)

3. The third step is to distribute the -2 3/4 to the (6x-7 2/10):

\(\frac{-5}{4} * \frac{6x}{1}=\frac{-30x}{4}\)

\(\frac{-5}{4} * \frac{72}{10}=\frac{-360}{40}\)

\(\frac{-30x}{4}-\frac{-360}{40}=1\frac{x}{2}\)

\(1\frac{x}{2} =2\)

4. The fourth step is to get x by itself so you are going to change the mixed number into an improper fraction:

\(2+x=2\)

5. All you do is subtract 2 from both sides of the equation and x=0

Answer:

68 + 70 = 138

66 + 72 = 138

The probability that the jackpot prize will be won in each of four consecutive draws is (1/60)⁴.

The number of consecutive draws needed will be, n = 233

Probability is the likelihood or chance of an event happening or not.

From the given question, the probability of the jackpot being won in any draw is 1/60.

The probability that the jackpot prize will be won in each of four consecutive draws will be:

1/60 * 1/60 * 1/60 * 1/60 = (1/60)⁴

b. The number of consecutive draws that needs to be made for there to be a greater than 98% chance that at least one jackpot prize will have been won is calculated as follows:

There is a 100% - 98% chance that that none has been won = 2% that none has been won.

Also, the probability of the jackpot not being won in a draw is = 1 1/60 = 59/60

The number of consecutive draws needed will be (59/60)ⁿ ≤ 0.02

Solving for n by taking logarithms of both sides:

n = 233

In conclusion, probability measures chances of an event occurring or not.

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Sara owed $200 with terms of 2/10, n/60. She made a payment of $80 within ten days. The answer is: Sara paid $80 within ten days.

The terms "2/10, n/60" refer to a discount and a credit period. The first number, 2, represents the discount percentage that Sara can take if she pays within 10 days. The second number, 10, indicates the number of days within which she can take the discount. The letter "n" represents the net amount, which is the total amount owed without any discount. The last number, 60, represents the credit period, which is the maximum number of days Sara has to make the payment without incurring any penalty.

Since Sara paid $80 within ten days, she was eligible for the discount. To calculate the discount, we multiply the discount percentage (2%) by the net amount ($200), which gives us $4. Therefore, the discount Sara received is $4. Subtracting the discount from the net amount, Sara's remaining balance is $200 - $4 = $196.

In conclusion, Sara made a payment of $80 within ten days, received a discount of $4, and still has a remaining balance of $196.

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The probability that the life span of the monitor will be more than 17,340 hours is approximately 0.0359, rounded to four decimal places.

We can use the standard normal distribution to solve this problem by standardizing the value of 17,340 hours to a z-score:

z = (17340 - 15000) / 1300 = 1.8

Using a standard normal distribution table or calculator, we find that the probability of getting a value greater than 1.8 is 0.0359.

Therefore, the probability that the life span of the monitor will be more than 17,340 hours is approximately 0.0359, rounded to four decimal places.

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Answer:

a.

\(f(t) = 21000( {.918}^{t} )\)

b.

\(f(4) = 21000( {.918}^{4}) = 14913.86\)

For the defined function  f(t)=e^rt and g(t)=e^st where r is not equal to s it was proved that the f and g are linearly independent function in F(r,r).

For the defined function f and g we have,

f(t)=e^rt

g(t)=e^st

Where r is not equal to s.

To prove f and g are linearly independent function we need,

f( t) ± g(t) = 0

Substitute the value of f(t) and g(t) we get,

⇒ e^rt ± e^st  = 0

⇒ e^rt ( 1 ± e^( s - r )t = 0

This implies ,

e^rt = 0 or ( 1 ± e^( s - r )t = 0

But e^rt is always greater than zero for all the values of r and t.

e^rt = 0 is not possible.

If ( 1 ± e^( s - r )t = 0

This is possible if and only if r = s .

Which is against the given condition.

Therefore, f(t) and g(t) are linearly independent function in f( r , r).

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The above question is incomplete, the complete question is:

Let f, g, element F(r,r) be the function defined by f(t)=e^rt and g(t)=e^st, where r cannot equal s. prove that f and g are linearly independent in F(r,r).

Answer:

First expression

Degree 3

Number of terms: 3

Second expression

Degree 5

Number of terms: 6

Third expression

Degree 4

Number of terms: 2

Answer:

F

Step-by-step explanation: ITS F

Answer: 10

Step-by-step explanation:

You use the distance formula to find the distance.

Find the difference between the two x variables (8), and the distance between the two y variables (6). Square both differences, (64 and 36), add them (100) and find the square root of the sum, 100.