Please help me with this!

Energía cinética = 1 / 2mv²

Donde m es la masa y v es la velocidad

De la pregunta

la masa es de 16 libras

la velocidad es de 30 m / s

16 libras es equivalente a 7.257 kg

Entonces la energía cinética es

1/2(7.257)(30)²

Espero que esto te ayude

Answer:

AB = 20 tan55°

Step-by-step explanation:

Using the tangent ratio in the right triangle

tan55° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{AB}{BC}[/tex] = [tex]\frac{AB}{20}[/tex] ( multiply both sides by 20 )

20 tan55° = AB

Answer:  K = ¹/₃, V = 32in³

Step-by-step explanation:

Volume of s cylinder (V) = πr²h where πr² is the base area.

Now from the question,

V ∞ πr²h

V = kπr²h where k is the constant of proportionality which is also the variation constant.

40 = 6 x 20 x k

40 = 120k and

k   = ⁴⁰/₁₂₀

     = ¹/₃.

Now to find the volume when base area is 8in² and h is 12,

V = 8 x 12 x ¹/₃

V = 32in³

Answer:

The beryllium atom; 1.99 times larger.

Step-by-step explanation:

The beryllium atom is 0.000000000112 meters, while the nitrogen atom is 0.000000000056 meters. So, the beryllium atom is larger than the other.

(1.12 * 10^-10) / (5.6 * 10^-11)

= (1.112 / 5.6) * (10^-10 + 11)

= 0.1985714286 * 10

= 1.985714286 * 10^0

So, the beryllium atom is about 1.99 times larger than the other.

Hope this helps!

Answer

B. 27

firist divide 9÷2=4.5

the formula

=1/2×4.5×6

=13.5

cause there are 2 triangles. let's multiply 13.5 with 2

13.5×2= 27²

Answer:

A). 55

Step-by-step explanation:

Number of Variegated Fritillaries for each year is

2009 = 7

2010= 95

2011= 63

The sum total of the samples= 7+95+63

The sum total of the samples= 165

Number of years= 3

The average= total/number of years

The average= 165/3

The average= 55

Answer: A

Step-by-step explanation: I have a massive brain (•-*•)

Answer:

(Y-3)= -1/3(x-7)

Or

(Y-4)= -1/3(x-4)

Steb by step explanation:

The condition for the line is (7,3) and (4,4).

Point slope form of equation is in this format below.

(Y-y1)= m(x-x1)

We have the given parameters in the above format except the m

M = gradient

Gradient= (y2-y1)/(x2-x1)

Gradient=(4-3)/(4-7)

Gradient= 1/-3

Gradient= -1/3

So

(Y-y1)= m(x-x1)

(Y-3)= -1/3(x-7)

Or

(Y-4)= -1/3(x-4)

Answer:

45

Step-by-step explanation:

The n th term of a GP is

[tex]a_{n}[/tex] = a[tex]r^{n-1}[/tex]

where a is the first term and r the common ratio

Given a₂ = 6 and a₅ = 48, then

ar = 6 → (1)

a[tex]r^{4}[/tex] = 48 → (2)

Divide (2) by (1)

[tex]\frac{ar^4}{ar}[/tex] = [tex]\frac{48}{6}[/tex] , that is

r³ = 8 ( take the cube root of both sides )

r = [tex]\sqrt[3]{8}[/tex] = 2

Substitute r = 2 into (1)

2a = 6 ( divide both sides by 2 )

a = 3

Thus

3, 6, 12, 24 ← are the first 4 terms

3 + 6 + 12 + 24 = 45 ← sum of first 4 terms

Answer:

a) y = 25495 - 2707x

b) y = 25495 - 2707(4) = 14,667

c) $2,707 per year

Step-by-step explanation:

Value now: $25,495

Value in 2 years: $20,081

Loss of value in 2 years: $25,495 - $20,081 = $5,414

Loss of value per year: $5,414/2 = $2,707

a) y = 25495 - 2707x

b) y = 25495 - 2707(4) = 14,667

c) $2,707 per year

Answer:

interior angle (2)= 70

interior angle (3)= 60

Step-by-step explanation:

Given:

exterior angle=120°

interior angle (1)=50°

Required:

interior angle (2)=?

interior angle (3)=?

Formula:

exterior angle=interior angle (1) + interior angle (2)

Solution:

exterior angle=interior angle (1)+ interior angle (2)

120°=50°+interior angle (2)

120°+50°=interior angle (2)

70°=interior angle (2)

interior angle (3)= 180°-interior angle (1)- interior angle (2)

interior angle (3)=180°-50°+70°

interior angle (3)=180°-120°

interior angle (3)= 60°

Theorem:

Theorem 1.16

The measure of an exterior angle of a triangle is greater than either of the measures of the remote interior angles.

Hope this helps ;) ❤❤❤

Answer:

3 pairs

Step-by-step explanation:

Top and Bottom

Front and Back

Side and Side.

Cereal Boxes have 6 sides

Answer: E(X) = 4

              V(X) = [tex]\frac{16}{3}[/tex]

Step-by-step explanation: An uniform distribution is a random variable X restricted to a finite interval [a,b] and has a constant function f(x) over this interval, i.e., the function is of form:

f(x) = [tex]\left \{ {{\frac{1}{b-a} } \atop {0}} \right.[/tex]  

The mean or expectation of an unifrom distribution is:

E(X) = [tex]\int\limits^b_a {x.f(x)} \, dx[/tex]

For the density function in interval [0,8], expectation value is:

E(X) = [tex]\int\limits^8_0 {x.(\frac{1}{8-0} )} \, dx[/tex]

E(X) = [tex]\int\limits^8_0 {\frac{x}{8} } \, dx[/tex]

E(X) = [tex]\frac{1}{8}. \int\limits^8_0 {x} \, dx[/tex]

E(X) = [tex]\frac{1}{8}.(\frac{x^{2}}{2} )[/tex]

E(X) = [tex]\frac{1}{8} (\frac{8^{2}}{2} )[/tex]

E(X) = 4

Variance of a probability distribution can be written as:

V(X) = [tex]E(X^{2}) - [E(X)]^{2}[/tex]

For uniform distribution in interval [0,8]:

V(X) = [tex]\int\limits^b_a {x^{2}.\frac{1}{8-0} } \, dx - (\frac{8+0}{2})^{2}[/tex]

V(X) = [tex]\frac{1}{8} \int\limits^8_0 {x^{2}} \, dx - 4^{2}[/tex]

V(X) = [tex]\frac{1}{8} (\frac{x^{3}}{3} ) - 16[/tex]

V(X) = [tex]\frac{1}{8} (\frac{8^{3}}{3} ) - 16[/tex]

V(X) = [tex]\frac{64}{3}[/tex] - 16

V(X) = [tex]\frac{16}{3}[/tex]

The mean and variance are 4 and 16/3, respectively

Answer:

Point of faulty equipment car = 0.2614 (Approx)

Step-by-step explanation:

Given:

Total number of car = 700

Faulty equipment car = 183

Find:

Point of faulty equipment car

Computation:

Point of faulty equipment car = Faulty equipment car / Total number of car

Point of faulty equipment car = 183 / 700

Point of faulty equipment car = 0.261428571

Point of faulty equipment car = 0.2614 (Approx)

Answer:

A. a straight line passing

Step-by-step explanation:

Answer:

a straight line passing

Step-by-step explanation:

Answer:

x² + x - 72 = 0 can be factored into (x - 8)(x + 9) = 0 to find your answer.

Step-by-step explanation:

Step 1: Distribute x

x² + x = 72

Step 2: Move 72 over

x² + x - 72 = 0

Step 3: Factor

(x - 8)(x + 9) = 0

Step 4: Find roots

x - 8 = 0

x = 8

x + 9 = 0

x = -9

Answer:

x² + x - 72 = 0 ⇒ (x - 8)(x + 9) = 0

Step-by-step explanation:

Let the first consecutive integer be x.

Let the second consecutive integer be x+1.

The product of the two consecutive integers is 72.

x(x + 1) = 72

x² + x = 72

Subtracting 72 from both sides.

x² + x - 72 = 0

Factor left side of the equation.

(x - 8)(x + 9) = 0

Set factors equal to 0.

x - 8 = 0

x = 8

x + 9 = 0

x = -9

8 and -9 are not consecutive integers.

Try 8 and 9 to check.

x = 8

x + 1 = 9

x(x+1) = 72

8(9) = 72

72 = 72

True!

The two consecutive integers are 8 and 9.

Answer:

1. Y= 7t^5 +C

2. Y= 35/12x^(12/7)+C

Step-by-step explanation:

The general solution will be determined by integrating the equations as the integration is a simple integration.

For dy/dt = 35t^4

The general solution y

= integral (35t^4)dt

The general solution y

=( 35/(4+1))*t^(4+1)

= 35/5t^5

= 7t^5 +C

To prove by differentiating the above.

Y= 7t^5 +C

Dy/Dt= (5*7)t^(5-1) +0

Dy/Dt= 35t^4

For dy/dx = 5x^(5/7)

Y=integral 5x^(5/7)Dx

Y= 5/(5/7 +1)*x^(5/7+1)

Y= 5/(12/7) *x^(12/7)

Y= 35/12x^(12/7)+C

To prove by differentiating

Y= 35/12x^(12/7)+C

Dy/Dx= (35/12)*(12/7) x^(12/7-1) +0

Dy/Dx=(35/7)x^(5/7)

Dy/Dx= 5x^(5/7)

Answer:

y = x + 0.5

Step-by-step explanation:

This is a very trivial exercise, follow the steps below:

Step 1: Perform the implicit differentiation of the given equation

[tex]x^2 + y^2 = (4x^2 + 2y^2 - x)^2[/tex]

[tex]2x + 2y \frac{dy}{dx} = 2(4x^2 + 2y^2 - x) ( 8x + 4y\frac{dy}{dx} - 1)\\\\[/tex]

Step 2: Make dy/dx the subject of the formula, this will be the slope of the curve:

[tex]x + y \frac{dy}{dx} = (4x^2 + 2y^2 - x) ( 8x + 4y\frac{dy}{dx} - 1)\\\\x + y \frac{dy}{dx} = 32x^3 + 16x^2y \frac{dy}{dx} - 4x^2 + 16xy^2 + 8y^3\frac{dy}{dx} - 2y^2 - 8x^2 - 4xy\frac{dy}{dx} + x \\\\\frac{dy}{dx}(y + 4xy - 8y^3) = 32x^3 - 12x^2 + 16xy^2 - 2y^2\\\\\frac{dy}{dx} = \frac{32x^3 - 12x^2 + 16xy^2 - 2y^2}{y + 4xy - 8y^3}[/tex]

Step 3: Find dy/dx at the point (0, 0.5)

[tex]\frac{dy}{dx}|(0,0.5) = \frac{32(0)^3 - 12(0)^2 + 16(0)(0.5)^2 - 2(0.5)^2}{(0.5) + 4(0)(0.5) - 8(0.5)^3}\\\\\frac{dy}{dx}|(0,0.5) =\frac{-0.5}{-0.5} \\\\\frac{dy}{dx}|(0,0.5) =1\\\\m = \frac{dy}{dx}|(0,0.5) =1[/tex]

Step 4: The equation of the tangent line to a curve at a given point is given by the equation:

[tex]y - y_1 = m(x-x_1)\\\\y - 0.5 = 1(x - 0)\\\\y = x + 0.5[/tex]

Answer:

See Image Below.

Step-by-step explanation:

The Shaded region is the area of numbers that this equation satisfies.

Answer:

Please see attached image

Step-by-step explanation:

In order to graph the inequality, start from plotting the boundary line defined by the equality;

y = 3 x

You just need two points to accomplish such. so let's use two simple values for x and find what the y-values are:

for x = 0 then y = 3 (0) = 0

for x = 1 then y = 3 (1) = 3

Then use the points (0, 0) and (1, 3) to plot the boundary line.

After this, grab any point on the plane either clearly above the boundary line, or clearly below it and check if the inequality satisfies. For example, you can pick the point (3, 0) which is on the x line, 3 units to the right of the origin, and clearly below the boundary line we just plot.

When you use it in the inequality, you get:

(0)  [tex]\leq[/tex] 3 (3)

0   [tex]\leq[/tex] 9

which is a true statement, therefore, the points below the boundary lie are also solutions of the inequality.

Then the solution consists of all the points in the boundary line we just plotted (and indicated by drawing a solid line), plus all the points below the line, as depicted in the attached image.

Answer:

41.1 miles

Step-by-step explanation:

84 - 42.9 = 41.1

Answer:

100yd²

Step-by-step explanation:

length=4x

width=x

perimeter=2(l+w)

50=2(4x+x)

50=2(5x)=10x

50=10x

x=5yd

width=5yd

length=20yd

area=length×width

=20×5

=100yd²

Answer:

[tex]\boxed{\red{100 \: \: {yd} ^{2}}} [/tex]

Step-by-step explanation:

width = x

length = 4x

so,

perimeter of a rectangle

[tex] p= 2(l + w) \\ 50yd = 2(4x + x) \\ 50yd= 2(5x) \\ 50yd= 10x \\ \frac{50yd}{10} = \frac{10x}{10} \\ x = 5 \: \: yd[/tex]

So, in this rectangle,

width = 5 yd

length = 4x

= 4*5

= 20yd

Now, let's find the area of this rectangle

[tex]area = l \times w \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 20 \times 5 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 100 {yd}^{2} [/tex]

Answer:

59 accidents were investigated.

Step-by-step explanation:

The question above is a probability question that involves 2 elements: causes of accidents.

Let

A = Alcohol

E = Excessive speed

In the question, we are given the following information:

18 accidents involved Alcohol and Excessive speed =P(A ∩ E)

26 involved Alcohol = P(A)

12 accidents involved excessive speed but not alcohol = P( E ) Only

21 accidents involved neither alcohol nor excessive speed = neither A U B

We were given P(A) in the question. P(A Only) = P(A) - P(A ∩ E)

P(A Only) = 26 - 18

= 8

So, only 8 accident involved Alcohol but not excessive speed.

The Total number of Accidents investigated = P(A Only) + P( E only) + P(A ∩ E) + P( neither A U B)

= 8 + 12 + 18 + 21

= 59

Therefore, 59 accidents were investigated.

Answer:

Step-by-step explanation:

Hello!

You have to estimate the mean length of 4000 b.c. human skulls trough a 95% confidence interval.

You know that

n= 6 human skulls

[tex]\frac{}{X}[/tex]= 94.2mm

S= 4.9

Assuming that the variable X: length of a 4000b.c. human skull (mm) has a normal distribution, to construct the interval you have to use the t statistic:

[[tex]\frac{}{X}[/tex] ± [tex]t_{n_1;1-\alpha /2} * \frac{S}{\sqrt{n} }[/tex]]

[tex]t_{n-1;1-\alpha /2}= t_{5; 0.975}= 2.571[/tex]

[94.2 ± 2.571 * [tex]\frac{4.9}{\sqrt{6} }[/tex]]

[89.06; 99.34]mm

With a 95% confidence level you'd expect the interval [89.06; 99.34]mm to contain the value for the average skull length for humans 4000 b.c.

I hope this helps!

Answer:

A sample size of 2080 is needed.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

The margin of error is:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

98% confidence level

So [tex]\alpha = 0.02[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.02}{2} = 0.99[/tex], so [tex]Z = 2.327[/tex].

Based on previous evidence, you believe the population proportion is approximately 60%.

This means that [tex]\pi = 0.6[/tex]

How large of a sample size is required?

We need a sample of n.

n is found when [tex]M = 0.025[/tex]. So

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.025 = 2.327\sqrt{\frac{0.6*0.4}{n}}[/tex]

[tex]0.025\sqrt{n} = 2.327\sqrt{0.6*0.4}[/tex]

[tex]\sqrt{n} = \frac{2.327\sqrt{0.6*0.4}}{0.025}[/tex]

[tex](\sqrt{n})^{2} = (\frac{2.327\sqrt{0.6*0.4}}{0.025})^{2}[/tex]

[tex]n = 2079.3[/tex]

Rounding up

A sample size of 2080 is needed.

Answer:

P = 0.0714

Step-by-step explanation:

If two faces of the larger cube that share and edge are painted blue, it means that 28 of the 64 unit cubes are painted in at least one side and 36 cubes have no painting faces.

Additionally, from the 28 cubes painted only 4 have exactly two painted faces.

Then, to calculate the number of ways in which we can select x elements from a group of n, we can use the following equation:

[tex]nCx=\frac{n!}{x!(n-x)!}[/tex]

So, the probability that one of two selected unit cubes will have exactly two painted faces while the other unit cube has no painted faces is:

[tex]P=\frac{4C1*36C1}{64C2}=0.0714[/tex]

Because there are 64C2 ways to select 2 cubes from the 64, and from that, there are 4C1*36C1 ways to select one cube with exactly two painted faces and one cube with no painted faces.

Answer:

Step-by-step explanation:

1. Preferred Share dividends.

There are 300,000 preference shares and each of them got $2.85. Total dividends are;

= 300,000 * 2.85

= $855,000‬

2. Total dividends = $3,500,000

Dividends left for Common Shareholders (preference gets paid first)

= 3,500,000 - 855,000

= $2,645,000

Common shares number 2,500,000

Dividend per share of common stock = [tex]\frac{2,645,000}{2,500,000}[/tex]

= $1.06

Answer:

Step-by-step explanation:

cos^-1(6/13)=62.5136°

sin(2*62.5136°)=0.8189

cos(2*62.5136°)=-0.5740

Answer:

366

Step-by-step explanation:

2×3+4×100-50+10​

PEMDAS says multiply and divide from left to right

6 + 400 - 50 +10

Then add and subtract

406-50+10

356+10

366

Answer:

[tex]\boxed{366}[/tex]

Step-by-step explanation:

[tex]2 \times 3+4 \times 100-50+10[/tex]

Multiplication is first.

[tex]6+400-50+10[/tex]

Add or subtract the numbers.

[tex]350+10+6[/tex]

[tex]366[/tex]

Answer:

0

Step-by-step explanation:

Hope this helps

Answer:

x>3

Step-by-step explanation:

Answer:

45

Step-by-step explanation:

Let's call the missing side x

This is a right triangle and in right triangles the square length of hypotenuse is equal to sum of square length of base and side lengths

53^2 = 28^2 + x^2

x = 45