form an equivalent division problem for 5 divided by 1/3 by multiplying both the dividend and divisor by 3. then find the quotient

Step-by-step explanation:

Hey there!

Simply work with it.

As it is a Right angled triangle, taking angle 40° as a reference angle. Then,

Length of board = hypotenuse = 15 feet.

To find: height of ladder = perpendicular.

Now,

Taking sin ratio,

\( \sin = \frac{p}{h} \)

\(sin \: 40 = \frac{p}{15} \)

or, as in per the given sin value is 0.6428

so,

\(0.6428 = \frac{p}{15} \)

or, 15 × 0.6428 = p

or, p = height of ladder = 9.642.

Therefore, p = height of ladder = 10 feet. { rounding off we get 10 feet as answer}.

Hope it helps...

Answer:

\(50.27\) \(cm\)

Step-by-step explanation:

\(\pi r^2h \times 1/3\)

\(\pi \times 2^2 \times 12 \times 1/3\)

\(\pi \times 4 \times 12 \times 1/3\)

\(16\pi\)

\(\approx 50.265482\)

Answer:

16π cm^3  or 50.27 cm^3 to the nearest hundredth.

Step-by-step explanation:

V = 1/3 π r^2 h

= 1/3 π 2^2 12

= 16π cm^3.

A check or quadrangle is defined by the intersection of pairs of diagonals of a parallelogram.

A parallelogram is a quadrilateral with two pairs of parallel sides. In a parallelogram, the opposite sides are parallel and have the same length. The opposite angles of a parallelogram are equal. A parallelogram is a unique type of quadrilateral with specific characteristics.

A quadrangle or check is defined as the intersection of pairs of diagonals of a parallelogram. In other words, it is the area inside the parallelogram that is divided into four triangles, each of which shares a common vertex in the center of the parallelogram.

The diagonals of a parallelogram are the line segments that connect the opposite vertices of a parallelogram. When these diagonals intersect, they form four triangles, which are also known as the parallelogram's "sub-triangles." The point where the diagonals intersect is called the center of the parallelogram, and it divides each diagonal into two equal parts.

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Using the formula of surface area to calculate the height and using the formula for volume , The answer is 24.98 \(cm^{3}\) .

A cone is a three-dimensional geometric structure with a smooth transition from a flat base—often but not always circular—to the point at the top, also known as the apex or vertex.

The required formula are :

\(SA = \pi r (r + \sqrt {h^{2} + r ^ {2}})\)  (Surface Area)

\(V = \pi r^{2} \frac {h}{3}\) (Volume)

radius = 3 cm

Area= 66 \(cm^{2}\)

\(SA = \pi r (r + \sqrt {h^{2} + r ^ {2}})\)

h = 2.65 cm

\(V = \pi r^{2} \frac {h}{3} = \pi * 3^{2} * \frac {2.65}{3}\)

=24.98 \(cm^{3}\)

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The roots of the quadratic equation 3x² - 2ax + 3 = 0 will be non-real when the absolute value of "a" is less than 3.

For the roots of the quadratic equation 3x² - 2ax + 3 = 0 to be non-real, the discriminant of the equation must be negative. The discriminant is calculated using the formula: b² - 4ac, where a, b, and c are the coefficients of the quadratic equation.

In this case, we have the equation 3x² - 2ax + 3 = 0. Comparing this equation with the general form of a quadratic equation ax² + bx + c = 0, we can identify that a = 3, b = -2a, and c = 3.

Now, let's calculate the discriminant:

Discriminant = (-2a)² - 4(3)(3)

= 4a² - 36

For the roots to be non-real, the discriminant must be negative, so we have:

4a² - 36 < 0

Now, we can solve this inequality to find the range of values for "a" for which the roots of the quadratic equation are non-real:

4a² - 36 < 0

4a² < 36

a² < 9

|a| < 3

Therefore, the roots of the quadratic equation 3x² - 2ax + 3 = 0 will be non-real when the absolute value of "a" is less than 3. In other words, if the value of "a" lies within the range (-3, 3), the roots will be non-real.

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Answer:

Inferential

Step-by-step explanation:

The process of drawing inferences about a population on the basis of information contained in a sample taken from the population is called Statistical Inferences.

In the given question the inferences have to be drawn from the sample which is representative of the population.

So the best answer is inferential statistics.

Answer:

the answers would be: A, C, and E

Step-by-step explanation:

Answer:

A,C,E Are the answers

Step-by-step explanation:

Its a,c,e because 5.40 divided by 2 gallons is 2.70. Its C because 3.38 divided by 1.25 gallons is 2.70. Its E because 2.03 divided by 0.75 is 2.70.

Answer:

37

Step-by-step explanation:

delta math gave me the answer ;)

Answer:

format messed up

Step-by-step explanation:

Answer:

8/11

Step-by-step explanation:

In the given scenario was cannot calculate P(B) directly. As it depends on what happened first, by itself we don’t know what was drawn first. Thus it becomes a conditional probability question:

P( B | A ) ← reads as the probability of “B” happening “given that” “A” has already happened — in this case the probability that the second marble drawn is a blue marble given that the first was a red marble.

The vertex of the Quadratic function with a y-intercept of (5, 0) and an x-intercept of (0, 80) is located at the point (0, 0).

The vertex of a quadratic function given the y-intercept and x-intercept, we need to determine the axis of symmetry, which is the line that passes through the vertex. The x-coordinate of the vertex will be the midpoint between the x-intercepts, while the y-coordinate will be the same as the y-intercept.

Given that the y-intercept is (5, 0) and the x-intercept is (0, 80), we can determine the x-coordinate of the vertex by finding the midpoint of the x-intercepts. The x-coordinate of the midpoint is simply the average of the x-values:

x-coordinate of vertex = (0 + 0) / 2 = 0 / 2 = 0

Since the y-coordinate of the vertex is the same as the y-intercept, the vertex will have the coordinates (0, 0).

Therefore, the vertex of the quadratic function is (0, 0).

In conclusion, the vertex of the quadratic function with a y-intercept of (5, 0) and an x-intercept of (0, 80) is located at the point (0, 0).

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Answer:

(4x + 3)²

Step-by-step explanation:

Given

16x² + 24x + 9

This is a perfect square of the form

(ax + b)² = a²x² + 2abx + b²

Compare coefficients to 16x² + 24x + 9, that is

a² = 16 ⇒ a = \(\sqrt{16}\) = 4

b² = 9 ⇒ b = \(\sqrt{9}\) = 3

and 2ab = 2 × 4 × 3 = 24

Thus

16x² + 24x + 9 = (4x + 3)²

a) The average slope or rate of change between (0, 1) and (2, 4) is 3/2.

b) The average slope or rate of change between (-2, 1/4) and (-1, 1/2) is 1/4.

c) The slope or rate of change is not constant between these two pairs of points, since the average slopes are different.

d) The function connecting these pairs of points is not a linear function.

The average slope or rate of change between two points (x1, y1) and (x2, y2) on a line is given by

average slope = (y2 - y1) / (x2 - x1)

For the points (0, 1) and (2, 4), the average slope is

average slope = (4 - 1) / (2 - 0) = 3/2

For the points (-2, 1/4) and (-1, 1/2), the average slope is

average slope = (1/2 - 1/4) / (-1 - (-2)) = 1/4

The slope or rate of change is not constant between these two pairs of points, since the average slopes are different. Therefore, the function connecting these pairs of points is not a linear function.

Note that a linear function has a constant slope, so if the slope is changing, then the function cannot be linear.

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The probability of the sets are solved and

a) n(P U Q) = 85%

b) n(P ∩ Q) = 20%

c) n(only P) = 35%

d) n(only Q) = 30%

Given data ,

P and are the subsets of universal set U

And , n (p) = 55% n (Q) = 50% and n(PUO)complement = 15%

Now , we'll use the formula for the union and intersection of sets:

n(P U Q) = n(P) + n(Q) - n(P ∩ Q)

n(P ∩ Q) = n(P) + n(Q) - n(P U Q)

n(only P) = n(P) - n(P ∩ Q)

n(only Q) = n(Q) - n(P ∩ Q)

We're given that:

n(P) = 55%

n(Q) = 50%

n(P U Q)' = 15%

To find n(P U Q), we'll use the complement rule:

n(P U Q) = 100% - n(P U Q)'

n(P U Q) = 100% - 15%

n(P U Q) = 85%

Now we can substitute the values into the formulas above:

(i)

n(P U Q) = n(P) + n(Q) - n(P ∩ Q)

n(P ∩ Q) = n(P) + n(Q) - n(P U Q)

n(P ∩ Q) = 55% + 50% - 85%

n(P ∩ Q) = 20%

(ii)

n(P ∩ Q) = 20%

(iii) n(only P) = n(P) - n(P ∩ Q)

n(only P) = 55% - 20%

n(only P) = 35%

(iv)

n(only Q) = n(Q) - n(P ∩ Q)

n(only Q) = 50% - 20%

n(only Q) = 30%

Hence , the probability is solved

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(a) Rectangular equation: \((x-3)^2/9 + y^2/4 = 1;\) conic section: ellipse centered at (3, 0) with semi-major axis 3 and semi-minor axis 2.

(b) Integral for arclength: \(s = \int [0,\pi /2] \sqrt{(72 + 112 cos 2\theta )} d\theta\).

(c) Equation for vertical tangents: θ = arctan(3/4) or θ = arctan(-4/3) + π, corresponding to points on the ellipse at (3+3cos(arctan(3/4)), 2sin(arctan(3/4))) and (3+3cos(arctan(-4/3)+π), 2sin(arctan(-4/3)+π)).

(a) To convert the polar equation to rectangular coordinates, we use the following relations:

x = r cos θ

y = r sin θ

Substituting r = 6 cos θ + 4 sin θ into these expressions, we get:

\(x = (6 cos \theta + 4 sin \theta) cos \theta = 6 cos^2 \theta + 4 sin \theta cos \theta\)

\(y = (6 cos \theta + 4 sin \theta ) sin \theta = 6 sin \theta cos \theta + 4 sin^2 \theta\)

Expanding these expressions using trigonometric identities, we get:

x = 3 + 3 cos 2θ

y = 2 sin 2θ

Thus, the rectangular equation of the curve is:

\((x - 3)^2/9 + y^2/4 = 1\)

This is the equation of an ellipse centered at (3, 0) with semi-major axis 3 and semi-minor axis 2.

(b) To set up an integral for the arclength of the curve, we use the formula:

\(ds = \sqrt{(dx/d\theta ^2 + dy/d\theta ^2) d\theta }\)

We have:

dx/dθ = -6 sin θ + 4 cos θ

dy/dθ = 6 cos θ + 8 sin θ

So,

\((dx/d\theta )^2 = 36 sin^2 \theta - 48 sin \theta cos \theta + 16 cos^2 \theta\)

\((dy/d\theta )^2 = 36 cos^2 \theta + 96 sin \theta cos \theta + 64 sin^2 \theta\)

Therefore,

\(dx/d\theta^2 = -6 cos \theta - 4 sin \theta\)

\(dy/d\theta^2 = -6 sin \theta + 8 cos \theta\)

And,

\((dx/d\theta^2)^2 = 36 cos^2 \theta + 48 sin \theta cos \theta + 16 sin^2 \theta\)

\((dy/d\theta ^2)^2 = 36 sin^2 \theta - 48 sin \theta cos \theta + 64 cos^2 \theta\)

Adding these expressions together and taking the square root, we get:

\(ds/d\theta = \sqrt{(72 + 112 cos 2\theta) }\)

To find the arclength of the curve, we integrate this expression with respect to θ from 0 to π/2:

\(s = \int [0,\pi /2] \sqrt{(72 + 112 cos 2\theta )} d\theta\)

(c) To find points on the curve with vertical tangents, we need to find values of θ where dy/dx is infinite.

Using the expressions for x and y in terms of θ, we have:

dy/dx = (dy/dθ)/(dx/dθ) = (6 cos θ + 8 sin θ)/(-6 sin θ + 4 cos θ)

Setting this expression equal to infinity, we get:

-6 sin θ + 4 cos θ = 0

Dividing both sides by 2 and taking the arctangent, we get:

θ = arctan(3/4) or θ = arctan(-4/3) + π

Plugging these values into the expressions for x and y, we get the corresponding points with vertical tangents.

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Answer:

The age of the youngest child = x = 6 years

The age of middle child = y = 8 years

The age of the oldest child = z = 12 years

Step-by-step explanation:

Let us represent:

The age of the youngest child = x

The age of middle child = y

The age of the oldest child = z

The sum of the ages of the children is 26.

Hence: x + y + z = 26...... Equation 1

The oldest is 4 years older than the middle

z = 4 + y

The youngest child is 2 years younger than the middle child

x = y - 2

Hence, we substitute 4 + y for z and y - 2 for x in Equation 1

x + y + z = 26...... Equation 1

y - 2 + y + 4 + y = 26

y + y + y -2 +4 = 26

3y + 2 = 26

Subtract 2 from both sides

3y + 2 - 2 = 26 - 2

3y = 26 - 2

3y = 24

y = 24/3

y = 8

Solving for x

x = y - 2

x = 8 - 2

x = 6

Solving for z

z = 4 + y

z = 4 + 8

z = 12

Therefore:

The age of the youngest child = x = 6 years

The age of middle child = y = 8 years

The age of the oldest child = z = 12 years

Answer:  I'm gonna go with letter A.

A. y ≥ –3

C. x ≥ –3

Step-by-step explanation:  It's either letter A or letter C.

A.

y ≥ –1

As a result, option a) is accurate since p (c vertical line a) equals fraction numerator p (a vertical line c)p (a)over denominator p (c)end fraction.

Since there can never be more good outcomes than there are possible outcomes, the chance of an event occurring can range from 0 to 1. Additionally, there cannot be any unfavorable outcomes.

given

P(A) = 0.70

P(C|A) = 0.30

So we are to find

P(C|A) = P(A|C) * P( C) / P(A)

As here as we are to find conditional probability .

As a result, option a) is accurate since p (c vertical line a) equals fraction numerator p (a vertical line c)p (a)over denominator p (c)end fraction.

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Answer:

The right answer is C.

Step-by-step explanation:

The parent function is:

\(f(x)=x^3\)

If something is subtracted from variable \(x\) it means the graph shifted toward right and something is added to \(y\) value then the graph is shifted up.

\(f(x)=(x-8)^3\)

graph shifted toward right by \(8\) units right

\(f(x)=(x-8)^3+3\)

graph shifted toward right by \(3\) units up

Thus the new function is:

\(g(x)=(x-8)^3+3\)

The vertex angle is 90 degrees and the base angle is 45 degrees.

In an isosceles triangle, the vertex angle is twice the base angle. Let the base angle be b in degrees. Remember that the sum of the angles of a triangle is 180 degrees. In order to solve this problem, we need to use the property of angles of an isosceles triangle that tells us that the base angles are equal. Let's call the vertex angle V, and the two base angles B. Since the vertex angle is twice the base angle, we can write an equation: V = 2BWe also know that the sum of the angles of a triangle is 180 degrees.

So we can write another equation: V + B + B = 180 degrees Simplifying this equation, we get: V + 2B = 180 degrees Now we can substitute V = 2B into this equation and solve for B: 2B + 2B = 180 degrees 4B = 180 degrees B = 45 degrees So the base angle is 45 degrees. Using V = 2B, we can find the vertex angle: V = 2(45 degrees)V = 90 degrees Therefore, the vertex angle is 90 degrees and the base angle is 45 degrees.

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SOLUTION

Write out the equation given

To find y-intercept, we replace x with 0, hence

Hence

Y - intercept is ( 0, 8/7 )

Similarly, for x-intercept, we replace y with 0 and find x

Hence

x- intercept is ( - 8/5 , 0 )

The numerical value of a dependent variable is dependent on the value of the independent variable. In other words, the numerical value of the dependent variable changes based on the value of the independent variable. For example, in the equation y = 2x + 3, the numerical value of y (the dependent variable) is dependent on the value of x (the independent variable). If x is 1, then the numerical value of y is 5 (2*1 + 3). If x is 2, then the numerical value of y is 7 (2*2 + 3). So, the numerical value of the dependent variable is dependent on the value of the independent variable.

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Answer:

\(x^{\frac{3}{7} } =\sqrt[7]{x^{3} }\)

Step-by-step explanation:

Hope this helps

Answer:

\(x \frac{3}{7} = \sqrt[7]{x^3}\)

Step-by-step explanation:

That is your answer

Answer:

a. 80.83 ft b. 40.42 ft

Step-by-step explanation:

Let h = height of pole = 70 ft, L = length of cable and x = distance of cable on ground to pole and Ф = angle between cable and ground.

a) How long is the cable?

Since L, h and x form a right-angled triangle with angle Ф and h being the opposite side to Ф and L being the hypotenuse side, by trigonometric ratios,

sinФ = h/L

L = h/sinФ

L = 70 ft/sin60°

L = 70 ft/0.8660

L = 80.83 ft

b) How far from the pole should the cable be attached to the ground?

Since L, h and x form a right-angled triangle with angle Ф and h being the opposite side to Ф and x being the adjacent side, by trigonometric ratios,

tanФ = h/x

x = h/tanФ

x = 70 ft/tan60°

x = 70 ft/1.7321

x = 40.42 ft

The length of the cable is 80.83 ft and the distance from the pole should the cable be attached to the ground is 40.42 ft and this can be determined by using the trigonometric function.

Given :

a) The trigonometric function can be used in order to determine the length of the cable.

\(\rm sin\theta=\dfrac{h }{L}\)

where h is the height of the pole, L is the length of the pole, and \(\theta\) is the angle from the ground.

Substitute the known terms in the above expression.

\(\rm L=\dfrac{h }{sin\theta}\)

\(\rm L = \dfrac{70}{sin60}\)

L = 80.83 ft.

b) The trigonometric function can be used in order to determine the distance from the pole should the cable be attached to the ground.

\(\rm tan \alpha =\dfrac{h}{x}\)

where x is the distance between pole and cable.

Substitute the known terms in the above expression.

\(\rm x = \dfrac{70}{tan 60 }\)

x = 40.42 ft.

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To solve the equation 2n^2 / ln(x) - 31 = ln(36), we can follow these steps: Start by adding 31 to both sides of the equation to isolate the term with the natural logarithm: 2n^2 / ln(x) = ln(36) + 31.

Multiply both sides of the equation by ln(x) to get rid of the denominator:

2n^2 = ln(x) * (ln(36) + 31).

Divide both sides of the equation by 2 to isolate n^2:

n^2 = (ln(x) * (ln(36) + 31)) / 2.

Take the square root of both sides of the equation to solve for n:

n = ±√[(ln(x) * (ln(36) + 31)) / 2].

So, the solution for n is ±√[(ln(x) * (ln(36) + 31)) / 2].

Please note that the solution may be valid only for certain values of x that satisfy the given equation.

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so hmmm let's call the points A(-10 , 5) and B(8 , 2) and the point "C" partitions them, so

\(\textit{internal division of a line segment using ratios} \\\\\\ A(-10,5)\qquad B(8,2)\qquad \qquad \stackrel{\textit{ratio from A to B}}{1:2} \\\\\\ \cfrac{A\underline{C}}{\underline{C} B} = \cfrac{1}{2}\implies \cfrac{A}{B} = \cfrac{1}{2}\implies 2A=1B\implies 2(-10,5)=1(8,2)\)

\((\stackrel{x}{-20}~~,~~ \stackrel{y}{10})=(\stackrel{x}{8}~~,~~ \stackrel{y}{2}) \implies C=\underset{\textit{sum of the ratios}}{\left( \cfrac{\stackrel{\textit{sum of x's}}{-20 +8}}{1+2}~~,~~\cfrac{\stackrel{\textit{sum of y's}}{10 +2}}{1+2} \right)} \\\\\\ C=\left( \cfrac{ -12 }{ 3 }~~,~~\cfrac{ 12}{ 3 } \right)\implies C=(-4~~,~~4)\)

The GDP of the hypothetical country in this case is R363 billion.

To calculate GDP, we use the following formula:

GDP = C + G + I + NX

where:

C = consumer spending

G = government spending

I = business investment

NX = net exports (exports - imports)

Now, let's plug in the given values into the formula and calculate the GDP:

GDP = R220 billion (C) + R50 billion (G) + R100 billion (I) + (R25 billion - R32 billion) (NX)

GDP = R220 billion + R50 billion + R100 billion - R7 billion

GDP = R363 billion

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Answer:

The median increases to 7

Step-by-step explanation:

List the numbers in chronological order,

5, 5.5, 6, 6.5, 6.5, 7, 7.5, 8, 8, 8.5

As of now, the median is 6.75.

When a shoe size of 9 is added, we have

5, 5.5, 6, 6.5, 6.5, 7, 7.5, 8, 8, 8.5, 9

Now, the median is 7.

The percentage increase of Seraphina's speed would be = 12.3%

The speed she travelled in the first hour = 57miles/hr

The speed she travelled in the second hour = 73miles/jr

The increase in speed = 73-57 = 16

Therefore the percentage increase;

= 16/130×100/1

= 1600/130

= 12.3%

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