Find the value of x.

Answer: Calculate the sphere volume, the volume of a spherical cap or of a hemisphere thanks to this sphere volume calculator.

Answer:

the answer is $26.38

Step-by-step explanation:

I hope this helps!

Answer:

B, C, D

Step-by-step explanation:

He made a mistake in each product.

-2(-8x) = 16x, not 10 x

-2(-4y) = 8y, not -8y

-2(3/4) = -1 1/2, not - 1/14

Answer:

Step-by-step explanation:

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I answered it here.

Using simple interest, we can find the value of interest here to be $162 per month.

Calculating the amount of interest that will be owed on a sum of money at a certain rate and for a specific period of time is possible using simple interest. The principal amount in the case of simple interest does not change, in contrast to compound-interest, where the interest is added to the principal to calculate the principal for the new principal for the following year.

Given in the question,

Principle, P = $18000

Rate of interest, R = 0.45%

= 0.45/100

Time in years, T = 24 months

= 2 years.

I = P R T

= 18000 × 0.45/100 × 2

= $162

Therefore, interest here is $162 per month.

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The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

To find the quotient of z₁ by z₂ in trigonometric form, we'll express both complex numbers in trigonometric form and then divide them.

Let's represent z₁ in trigonometric form as z₁ = r₁(cosθ₁ + isinθ₁), where r₁ is the magnitude of z₁ and θ₁ is the argument of z₁.

We have:

z₁ = 7(cos(577°) + i sin(577°))

Now, let's represent z₂ in trigonometric form as z₂ = r₂(cosθ₂ + isinθ₂), where r₂ is the magnitude of z₂ and θ₂ is the argument of z₂.

From the given information, we have:

z₂ = 21(cos(-7°) + i sin(-77°))

To find the quotient, we divide z₁ by z₂:

z₁ / z₂ = (r₁/r₂) * [cos(θ₁ - θ₂) + i sin(θ₁ - θ₂)]

Substituting the given values, we have:

z₁ / z₂ = (7/21) * [cos(577° - (-7°)) + i sin(577° - (-7°))]

= (7/21) * [cos(584°) + i sin(584°)]

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

Option C, 21(cos(-7°) + i sin(-77°)), is not the correct answer as it does not represent the quotient of z₁ by z₂.

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Answer:

  5/10

Step-by-step explanation:

An equivalent fraction will have the numerator and denominator multiplied by the same value.

The denominator of 2 must be multiplied by 5 to get a denominator of 10. Then the equivalent fraction is ...

  \(\dfrac{1}{2}=\dfrac{1}{2}\cdot\dfrac{5}{5}=\dfrac{1\cdot5}{2\cdot5}=\boxed{\dfrac{5}{10}}\)

There is no stationary point at x = 2. The nature of the curve at x = 2 cannot be determined since there is no stationary point.

To verify that the curve has a stationary point at x = 2, we need to find the derivative of the equation and set it equal to zero.

Given the equation:

y = 2x + 1/(x-1)²

Let's find the derivative dy/dx:

dy/dx = d/dx [2x + 1/(x-1)²]

To find the derivative, we can use the power rule and the chain rule. Let's differentiate each term separately:

For the first term, 2x, the derivative is 2.

For the second term, 1/(x-1)², we can rewrite it as (x-1)^(-2) to apply the power rule. The derivative is then:

d/dx [(x-1)^(-2)] = -2(x-1)^(-3) * d/dx (x-1)

Using the chain rule, d/dx (x-1) = 1, so the derivative becomes:

-2(x-1)^(-3) * 1 = -2/(x-1)^3

Now, let's set dy/dx equal to zero and solve for x:

-2/(x-1)^3 = 0

This equation is satisfied when the numerator is equal to zero:

-2 = 0

However, -2 is not equal to zero, which means there is no x value that makes dy/dx equal to zero.

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Answer:

The value of a₅ is 1875.

Step-by-step explanation:

Given:

a₁ = 3

aₙ = 5aₙ₋₁

To find the value of a₅, we can apply the recursive formula to compute each term successively:

Step 1: Compute a₂

a₂ = 5a₁ = 5(3) = 15

Step 2: Compute a₃

a₃ = 5a₂ = 5(15) = 75

Step 3: Compute a₄

a₄ = 5a₃ = 5(75) = 375

Step 4: Compute a₅

a₅ = 5a₄ = 5(375) = 1875

Answer:25.45

Step-by-step explanation:

52936/1 year x 1 year/52 weeks x 1 week/40hours

Answer:

a = 3

Step-by-step explanation:

Collect like-terms:

\( - 16 = a - 19\)

\(a = - 16 + 19\)

\(a = 3\)

Answer: 3

Step-by-step explanation: you take 19 from 3 giving you -16

The rectangle that will side lengths of 5units and 4 units will have coordinate of A(3, 3), B(3, 7), C(8, 7), D(8, 3) ( option B)

Distance between two points is the length of the line segment that connects the two points in a plane. The formula to find the distance between the two points is usually given by d=√((x2 – x1)² + (y2 – y1)²).

For a rectangle, the opposite sides are equal this means AB = C D and CB = AD

To verify the answer, The distance between AB = √((3– 3)² + (7– 3)²).

line AB = √0+16= 4units

line AD = √((8– 3)² + (3– 3)²).

line AD = √25+0

line AD = 5 units

therefore the sides of the rectangle are 5units and 4 units.

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Answer:

Step-by-step explanation:

Mmmmmmmm.

Answer:

Baseballs is: $10

Bats is: $4

Step-by-step explanation:

Let x represent bats

and y represent baseballs

So we have :

(1) 4x + 7y = 68

(2) x + y = 14 => y = 14 - x

Use substitution.

Substitute equation (2) into equation (1)

4x + 7(14 - x) = 68

Solve for x

4x + 98 -7x = 68

-3x + 98 = 68

-3x = -30

x = 10

Solve for y, replace x = 2 into equation (2)

y = 14 - 10 = 4, so y = 4

Since x represents bats and y represents baseballs, it cost $10 for the bats and $4 for the baseballs.

Answer:

x < -3 or x > 2

Step-by-step explanation:

x² + x - 6 > 0

Convert the inequality to an equation.

x² + x - 6 = 0

Factor using the AC method and get:

(x - 2) (x + 3) = 0

If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.

x - 2 = 0

x = 2

x + 3 = 0

x = -3

So, the solution is x < -3 or x > 2

Answer:

A common factor is a whole number which is a factor of two or more numbers.

\(factors \: of \: 9 = 1 \times 3 \times 3\)

\(factors \: of \: 15 = 1 \times 3 \times 5\)

since both of the numbers have only 1 and 3 in common.

therefore ,

Option A is correct.

______________________________________

______________________________________

Additional information

★ The highest common factor (HCF) is the greatest factor that will divide into two or more numbers.

★ The lowest common multiple (LCM) is the smallest multiple that is common to two or more numbers.

hope helpful :D

Answer:

-5

Step-by-step explanation:

(i^2) = -1 so -1 -1 + 3x = 3x - 2. If x = i^2 = -1, then 3x = -3. -3 - 2 = -5

If we divide 300 into parts using the ratio 2:3:5, we get:

2 parts = 2/10 of the total ratio = 2/10 x 300 = 60

3 parts = 3/10 of the total ratio = 3/10 x 300 = 90

5 parts = 5/10 of the total ratio = 5/10 x 300 = 150

Therefore, 300 divided in the ratio 2:3:5 would result in three parts of 60, 90, and 150.

I hope I helped!

~~~Harsha~~~

Answer:

.052

Step-by-step explanation:

sin(3) = .052

() = sin(3)

() = .052

The angle sum property of a triangle and the angle formed between a tangent and a radius of a circle indicates.

m∠ADC = 58°

A tangent to a circle is a straight line which touches the circumference of a circle at only one point.

The vertical angles theorem indicates that we get;

∠1 ≅ ∠2

Therefore; m∠1 = m∠2

The tangent to a circle indicates that we get;

The angle formed at vertex B and Q are 90 degrees angles and the triangles ABP and AQP are right triangles, which indicates that the acute angles of each of the right triangles are complementary, therefore;

m∠1 + 26° = 90°

m∠1 = 90° - 26° = 64°

Therefore, m∠2 = m∠1 = 64°

m∠2 = m∠CAD = 64°

The segments AC and AD are radial lengths therefore, the triangle ΔACD is an isosceles triangle.

m∠ADC ≅ m∠ACD (Base angles of an isosceles triangle)

The angles ∠ADC and ∠ACD are therefore;

m∠CAD + m∠ADC + m∠ACD = 180° (Angle sum property of a triangle)

m∠CAD + m∠ADC + m∠ADC = 180°

m∠CAD + 2 × m∠ADC = 180°

64° + 2 × m∠ADC = 180°

m∠ADC = (180° - 64°)/2 = 58°

m∠ADC = 58°

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Answer:

idk if this helps but here:

Cutoff points are a crucial piece of calculus and are among the main things that understudies find out about in a calculus class. So, finding the constraint of a capacity implies figuring out what esteem the capacity approaches as it draws nearer and more like a specific point.

Step-by-step explanation:

I don't know if you meant

\(\vec F = (-3\,\vec\imath + 4\,\vec\jmath - 2\,\vec k)\,\mathrm N\)

or

\(\vec F = (-31\,\vec\imath + 43\,\vec\jmath - 2\,\vec k)\,\mathrm N\)

I'll assume the first force is correct.

The object in question undergoes a total displacement of

\(\vec d = (-4\,\vec\imath + 4\,\vec\jmath+4\,\vec k)\,\mathrm m - (4\,\vec\imath + \vec\jmath - 5\,\vec k)\,\mathrm m = (-8\,\vec\imath + 3\,\vec\jmath + 9\,\vec k)\,\mathrm m\)

Then the work W done by \(\vec F\) along this displacement is

\(W = \vec F \cdot \vec d = ((-3)\times(-8)+4\times3+(-2)\times9)=18\,\mathrm{Nm} = \boxed{18\,\mathrm J}\)

Another approach using calculus (it's overkill since \(\vec F\) is constant, but it doesn't hurt to check our answer): parameterize the line segment by

\(\vec r(t) = (1 - t)(4\,\vec\imath+\vec\jmath-5\,\vec k)\,\mathrm m + t(-4\,\vec\imath+4\,\vec\jmath + 4\,\vec k)\,\mathrm m \\\\ \vec r(t) = \left((4-8t)\,\vec\imath+(1+3t)\,\vec\jmath+(-5+9t)\,\vec k\right)\,\mathrm m\)

with 0 ≤ t ≤ 1.

Then the work W done by \(\vec F\) along the given path is equal to the line integral,

\(\displaystyle W = \int_0^1 \vec F(\vec r(t)) \cdot \frac{\mathrm d\vec r(t)}{\mathrm dt}\,\mathrm dt \\\\ W = \int_0^1 \left((-3\,\vec\imath+4\,\vec\jmath-2\,\vec k)\,\mathrm N\right) \cdot \left((-8\,\vec\imath+3\,\vec\jmath+9\,\vec k)\,\mathrm m\right) \,\mathrm dt \\\\ W = \int_0^1((-3)\times(-8)+4\times3+(-2)\times9)\,\mathrm{Nm}\,\mathrm dt \\\\ W = 18\,\mathrm{Nm} \int_0^1\mathrm dt \\\\ W = 18\,\mathrm{Nm} = \boxed{18\,\mathrm J}\)

The point where the line 2x + 3y = 6 intersects the x-axis is (3, 0). This means that when x is equal to 3, y is equal to 0.

To graph the equation 2x + 3y = 6, we can rewrite it in the slope-intercept form, y = mx + b, where m represents the slope and b represents the y-intercept.

Starting with the given equation, we isolate y to one side:

3y = -2x + 6

y = (-2/3)x + 2

Now, we have the equation in slope-intercept form, y = (-2/3)x + 2. The slope is -2/3, and the y-intercept is (0, 2).

To find the point where the graph intersects the x-axis, we need to determine the coordinates where y is equal to zero. This occurs when the line crosses the x-axis.

Setting y = 0 in the equation, we have:

0 = (-2/3)x + 2

(-2/3)x = -2

x = (-2)(-3/2) = 3

Therefore, the point where the line 2x + 3y = 6 intersects the x-axis is (3, 0). This means that when x is equal to 3, y is equal to 0, indicating the point of intersection with the x-axis on the graph.

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Keshawn, this is the solution to part B:

P (blue) = 25% = 1/4

P (brown) = 75% = 3/4

If Ruth performs 10 trials, the theoretical probability would be:

P (blue) = 25% = 2.5/10

P (brown) = 75% = 7.5/10

Upon saying that, the outcome of 1 of having three children with blue eyes isn't a theoretical probability, it is a experimental probability.

Finally, the theoretical probability of having three children with blue eyes is:

P (3 chlildren with blue eyes) = 1/4 * 1/4 * 1/4 = 1/64

The values of the expression following the collection of like terms, rearranging and factoring are presented as follows;

1.1 4·x + 5·a + 3·a + x - 6 = 5·x + 8·a - 6

1.2. 6·a·b + 2·b - 16·a - 2 = 2·(3·a·b + b - 8·a - 1)

1.3. 1024000 : 360000 : 180000 = 256 : 90 : 45

1.4. 150 min : 3 hours = 5 : 6

A mathematical expression comprises of mathematical symbols, numbers and variable, properly arranged to represent a value.

The simplification of the expressions can be presented as follows;

1.1. 4·x + 5·a + 3·a + (x - 6)

The terms in the above expression can be rearranged as follows;

4·x + 5·a + 3·a + (x - 6) = 4·x + x + 5·a + 3·a - 6

4·x + x + 5·a + 3·a - 6 = 5·x + 8·a - 6

Therefore, whereby the expression in the question is; 4·x + 5·a + 3·a + (x - 6), we get;

1.2. Whereby the possible expression in the question is; 6·a·b + 2·b - 16·a + (-2), we get;

The factor common to the terms of the expression 6·a·b + 2·b - 16·a + (-2) is 2. Therefore by factoring the expression, we get;

1.3. 1024000: 360,000 : 180,000

The expression is a ratio of the form a : b : c

Dividing each term in the ratio by 1,000, we get

1024000 ÷ 1000 : 360,000 ÷ 1000 : 180,000 ÷ 1000 = 1024 : 360 : 180

1024000: 360,000 : 180,000 = 1024 : 360 : 180

The common factors of 1024, 360 and 180 are; 1, 2, and 4

Therefore, the GCF of 1024, 360, and 180 is 4

Dividing the terms of the ratio 1024 : 360 : 180 by 4, we get;

1024 ÷ 4 : 360 ÷ 4 : 180 ÷ 4 = 256 : 90 : 45

Therefore;

1.4 150 min : 3 hours

The above ratio can be simplified by rewriting the ratio using unit conversion as follows;

3 hours = 180 minutes, therefore;

150 min : 3 hours = 150 min : 180 min

150 : 180 = 5 : 6

Therefore; 150 min : 180 min = 5 min : 6 min

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Answer:

lol

Step-by-step explanation:

0-2-4-3-5

Where the above conditions are given, the IQR for X is from 156 acres to 192 acres.

To find the interquartile range (IQR), we need to first find the first and third quartiles of the sample.

Given:

Sample size (n) = 38

Sample mean (μ) = 174

Sample standard deviation (σ) = 55

We know that the first quartile (Q1) is the 25th percentile and the third quartile (Q3) is the 75th percentile.

Using the standard normal distribution table, we can find the z-scores for Q1 and Q3:

z-score for Q1 = invNorm(0.25) = -0.6745

z-score for Q3 = invNorm(0.75) = 0.6745

Now, we can use the following formulas to find Q1 and Q3:

Q1 = μ + z-score for Q1 * (σ / sqrt(n))

Q3 = μ + z-score for Q3 * (σ / sqrt(n))

Substituting the given values, we get:

Q1 = 174 - 0.6745 * (55 / sqrt(38)) ≈ 155.52

Q3 = 174 + 0.6745 * (55 / sqrt(38)) ≈ 192.48

Therefore, the IQR for X is from 156 acres to 192 acres.

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The exact solutions of the qudratic equation 3x^2 - 6x + 2 = 0 are:

a. negative 1 plus or minus the square root of 3 divided by

3 (x = (-1 ± √3) / 3) .So, option a is the correct answer.

To find the solutions of the quadratic equation 3x^2 - 6x + 2 = 0, we can use the quadratic formula, which states that for an equation of the form ax^2 + bx + c = 0, the solutions are given by:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 3, b = -6, and c = 2. Substituting these values into the formula, we have:

x = (-(-6) ± √((-6)^2 - 4(3)(2))) / (2(3))

x = (6 ± √(36 - 24)) / 6

x = (6 ± √12) / 6

x = (6 ± 2√3) / 6

x = (3 ± √3) / 3

Therefore, the exact solutions of the equation 3x^2 - 6x + 2 = 0 are:

a. negative 1 plus or minus the square root of 3 divided by 3 (x = (-1 ± √3) / 3)

So, option a is the correct answer.

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The point-slope form of a line is given by:

y - y1 = m(x - x1)

where (x1, y1) is a point on the line, and m is the slope of the line. To find the equation of the line through (3, 5) and (4, 1), we can use either point as (x1, y1) and find the slope between the two points:

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

Using the first point, (3, 5), we have:

m = (1 - 5) / (4 - 3) = -4

So the equation of the line in point-slope form is:

y - 5 = -4(x - 3)

Expanding and simplifying, we get:

y = -4x + 17

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