2 x 6 - 21 divided by 7

Answer:

The answer is -7, or x = -7.

(a) A nonzero vector orthogonal to the plane through the points P, Q, and R is (9, -17, 35). (b) The area of triangle PQR is \(\sqrt\)(811) / 2.

(a) To determine a nonzero vector orthogonal to the plane through the points P, Q, and R, we can first find two vectors in the plane and then take their cross product. Taking vectors PQ and PR, we have:

PQ = Q - P = (5, 1, -2) - (-4, 0, 0) = (9, 1, -2)

PR = R - P = (6, 4, 1) - (-4, 0, 0) = (10, 4, 1)

Taking the cross product of PQ and PR, we have:

n = PQ x PR = (9, 1, -2) x (10, 4, 1)

Evaluating the cross product gives n = (9, -17, 35). Therefore, (9, -17, 35) is a nonzero vector orthogonal to the plane through points P, Q, and R.

(b) To determine the area of triangle PQR, we can use the magnitude of the cross product of vectors PQ and PR divided by 2. The magnitude of the cross product is given by:

|n| = \(\sqrt\)((9)^2 + (-17)^2 + (35)^2)

Evaluating the magnitude gives |n| = \(\sqrt\)(811).

The area of triangle PQR is then:

Area = |n| / 2 = \(\sqrt\)(811) / 2.

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Answer:

84 cm

Step-by-step explanation:

the area of a parallelogram is the how tall is it times it by the how long the base

(H x B)

the answer is 84 cm

To show that the total charge contained in the charge distribution is Q, we integrate the charge density over the entire volume. The charge density is given by:

ρ(r) = ρ₀(1 - r/R) for r ≤ R,

ρ(r) = 0 for r > R,

where ρ₀ = 3Q/πR³.

To find the total charge, we integrate ρ(r) over the volume:

Q = ∫ρ(r) dV,

where dV represents the volume element.

Since the charge density is spherically symmetric, we can express dV as dV = 4πr² dr, where r is the radial distance.

The integral becomes:

Q = ∫₀ᴿ ρ₀(1 - r/R) * 4πr² dr.

Evaluating this integral gives:

Q = ρ₀ * 4π * [r³/3 - r⁴/(4R)] from 0 to R.

Simplifying further, we get:

Q = ρ₀ * 4π * [(R³/3) - (R⁴/4R)].

Simplifying the expression inside the parentheses:

Q = ρ₀ * 4π * [(4R³/12) - (R³/4)].

Simplifying once more:

Q = ρ₀ * π * (R³ - R³/3),

Q = ρ₀ * π * (2R³/3),

Q = (3Q/πR³) * π * (2R³/3),

Q = 2Q.

Therefore, the total charge contained in the charge distribution is Q.

To show that the electric field in the region r > R is identical to that created by a point charge Q at r = 0, we can use Gauss's law. Since the charge distribution is spherically symmetric, the electric field outside the distribution can be obtained by considering a Gaussian surface of radius r > R.

By Gauss's law, the electric field through a closed surface is given by:

∮E · dA = (1/ε₀) * Qenc,

where ε₀ is the permittivity of free space, Qenc is the enclosed charge, and the integral is taken over the closed surface.

Since the charge distribution is spherically symmetric, the enclosed charge within the Gaussian surface of radius r is Qenc = Q.

For the Gaussian surface outside the distribution, the electric field is radially directed, and its magnitude is constant on the surface. Hence, E · dA = E * 4πr².

Plugging these values into Gauss's law:

E * 4πr² = (1/ε₀) * Q,

Simplifying:

E = Q / (4πε₀r²).

This is the same expression as the electric field created by a point charge Q at the origin (r = 0).

To derive an expression for the electric field in the region r ≤ R, we can again use Gauss's law. This time we consider a Gaussian surface inside the charge distribution, such that the entire charge Q is enclosed.

The enclosed charge within the Gaussian surface of radius r ≤ R is Qenc = Q.

By Gauss's law, we have:

∮E · dA = (1/ε₀) * Qenc.

Since the charge distribution is spherically symmetric, the electric field is radially directed, and its magnitude is constant on the Gaussian surface. Hence, E · dA = E * 4πr².

Plugging these values into Gauss's law:

E * 4πr² = (1/ε₀) * Q.

Simplifying:

E = Q / (4πε₀r²).

This expression represents the electric field inside the charge distribution for r ≤ R.

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Answer:

the anwser is a i think im helping you out dont repoty

Answer:

5 × 5 × 5

Step-by-step explanation:

expanded basically means broken down... since the exponent is three, you have to multiply 5 three times

125

Step-by-step explanation:

5×5×5

25×5

125

this is the correct answet

The required answer is the nearest hundredth, this is 83.34 cm^2.

To find the area of the sector  of the circle with a central angle of 195° and radius of 7 cm,, we first need to find the fraction of the circle's total area that the sector covers. Since the central angle of the sector is 195° and there are 360° in a full circle, we can find this fraction by dividing 195 by 360:

195° ÷ 360° = 0.542

So the sector covers about 54.2% of the circle's total area. To find the actual area of the sector, we can multiply this fraction by the area of the whole circle, which is πr^2. Plugging in the given values, we get:

Area of sector = 0.542 × π × 7^2
Area of sector ≈ 83.34 cm^2

Therefore, the area of the sector of the circle with central angle of 195° and radius of 7 cm is approximately 83.34 cm^2. Rounded to the nearest hundredth, this is 83.34 cm^2.

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If the probability that a player makes a free throw is 0.4, the probability that they do not make a free throw is 1 – 0.4 = 0.6.

The probability that a player makes three consecutive free throws is 0.4 × 0.4 × 0.4 = 0.064. If a player attempts three free throws, there are three possible outcomes: make all three, miss one and make two, or miss two and make one.

The probability of making all three is 0.064, the probability of missing one and making two is 0.4 × 0.4 × 0.6 + 0.4 × 0.6 × 0.4 + 0.6 × 0.4 × 0.4 = 0.288, and the probability of missing two and making one is 0.6 × 0.6 × 0.4 + 0.6 × 0.4 × 0.6 + 0.4 × 0.6 × 0.6 = 0.432.

Therefore, the probability of leaving the court in three attempts is 0.064 + 0.288 + 0.432 = 0.784. If a player misses all three attempts, they will have to try three more times, and the probability of leaving the court in six attempts is 0.784 + 0.064 × 0.288 × 0.432 = 0.861.

If a player misses all six attempts, they will have to try three more times, and the probability of leaving the court in nine attempts is 0.861 + 0.064 × 0.288 × 0.432 × 0.064 × 0.288 × 0.432 × 0.064 × 0.288 × 0.432 = 0.926.

If a player misses all nine attempts, they will have to try three more times, and the probability of leaving the court in twelve attempts is 0.926 + 0.064 × 0.288 × 0.432 × 0.064 × 0.288 × 0.432 × 0.064 × 0.288 × 0.432 × 0.064 × 0.288 × 0.432 × 0.064 × 0.288 × 0.432 = 0.974.

Since the probability of leaving the court in twelve attempts is greater than 0.9, the probability of leaving the court in ten or fewer attempts is greater than 0.9. Therefore, the probability that a player can leave the court in 10 or fewer attempts is greater than 0.9.

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Answer:

D

Step-by-step explanation:

u just graph all the points and connect the lines; then see where the two lines meet :P

Answer: -1

Step-by-step explanation:

(2–4)/(-2-4)=6/-6=-1

Using the properties of divisibility, we can prove that for all a ∈ N, if for all b ∈ N, a | (6b + 8), then a must be either 1 or 2.

To prove this statement, let's consider two cases:
Case 1: a is odd.
If a is odd, then a can be written as 2k + 1, where k is a non-negative integer. Substituting this into the given statement, we have:
2k + 1 | (6b + 8)
By the definition of divisibility, this implies that there exists an integer m such that (6b + 8) = (2k + 1)m.
Simplifying, we get:
6b + 8 = 2km + m
Rearranging the equation, we have:
2(3b + 4) = m(2k + 1)
This implies that 2 divides the left side of the equation, but it cannot divide the right side since 2k + 1 is odd. This leads to a contradiction, indicating that there are no solutions when a is odd.
Case 2: a is even.
If a is even, then a can be written as 2k, where k is a non-negative integer. Substituting this into the given statement, we have:
2k | (6b + 8)
By the definition of divisibility, this implies that there exists an integer m such that (6b + 8) = 2km.
Simplifying, we get:
6b + 8 = 2km
Dividing both sides by 2, we have:
3b + 4 = km
This implies that 2 divides the left side of the equation, and it must also divide the right side since km is even. Thus, we conclude that a = 2 is a valid solution.
Combining the results from both cases, we have proven that for all a ∈ N, if for all b ∈ N, a | (6b + 8), then a must be either 1 or 2.

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To yield $26,000 in the future, compounded semiannually at an interest rate of 6%, a lump sum investment needs to be made today. The correct amount to invest can be calculated using the present value formula.

The present value formula can be used to calculate the amount that should be invested today to achieve a specific future value. The formula is given by:

PV = FV / (1 + r/n)^(n*t)

In this case, the future value (FV) is $26,000, the interest rate (r) is 6%, and the compounding is semiannually (n = 2). We need to solve for the present value (PV).

Using the formula and substituting the given values:

PV = 26,000 / \((1 + 0.06/2)^(2*1)\)

PV = 26,000 / \((1.03)^2\)

PV = 26,000 / 1.0609

PV ≈ $24,490.92

Therefore, the correct lump sum to invest today, at 6% compounded semiannually, to yield $26,000 in the future is approximately $24,490.92.

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Relative age dating determines the sequence of events without providing specific ages, while radiometric age dating calculates precise numerical ages using radioactive isotopes. Relative age dating is limited by its inability to assign exact ages, while radiometric age dating is limited by the availability of suitable isotopes and its applicability to specific time ranges.

Relative age dating involves comparing the positions of rocks or fossils in different layers or formations to determine their relative ages. It relies on principles such as superposition, cross-cutting relationships, and fossil succession. It can provide information about the sequence of events and the relative order of geological features. However, it does not provide precise numerical ages and is limited to establishing relative age relationships.

Radiometric age dating, on the other hand, uses the decay of radioactive isotopes in rocks and minerals to determine their absolute ages. By measuring the ratio of parent isotopes to daughter isotopes, scientists can calculate the time elapsed since the rock or mineral formed. Radiometric age dating provides precise numerical ages and is particularly useful for dating ancient rocks and fossils. However, it requires the presence of suitable isotopes, and some isotopes may have long half-lives, limiting their applicability to certain time ranges.

In summary, relative age dating provides information about the sequence of events but not specific ages, while radiometric age dating provides precise numerical ages but relies on the availability of suitable isotopes and has limitations in terms of the time range it can cover.

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the complete question is :

Compare and contrast relative age dating with radiometric dating. What are the strengths and limitations (if any) of each?

Rounding up to the nearest unit, it would take Calvin approximately 27 months to pay off his credit card with a monthly payment of $165.

To determine how long it would take Calvin to pay off his credit card, we need to consider the monthly payment amount and the interest rate. Let's calculate the time it would take for two different monthly payment amounts: $220 and $165.

a. Monthly payment of $220:

Let's assume the initial balance on Calvin's credit card is $3,000, and the annual interest rate is 4 percent. To calculate the monthly interest rate, we divide the annual interest rate by 12 (number of months in a year):

Monthly interest rate = 4% / 12 = 0.3333%

Now, we can calculate the time it would take to pay off the credit card using the monthly payment of $220 and the monthly interest rate. We'll use a formula for the number of months required to pay off a loan with fixed monthly payments:

n = -(log(1 - (r * P) / A) / log(1 + r))

Where:

n = number of months

r = monthly interest rate (as a decimal)

P = initial balance

A = monthly payment

Plugging in the values:

n = -(log(1 - (0.003333 * 3000) / 220) / log(1 + 0.003333))

Using a calculator, we can find:

n ≈ 15.34

Rounding up to the nearest unit, it would take Calvin approximately 16 months to pay off his credit card with a monthly payment of $220.

b. Monthly payment of $165:

We can repeat the same calculation using a monthly payment of $165:

n = -(log(1 - (0.003333 * 3000) / 165) / log(1 + 0.003333))

Using a calculator, we find:

n ≈ 26.39

Please note that these calculations assume that Calvin does not make any additional charges on his credit card during the repayment period. Additionally, the interest rate and the balance are assumed to remain constant. In practice, these factors may vary and could affect the actual time required to pay off the credit card balance.

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Answer:

6 is your answer i jsut did this its right

Step-by-step explanation:

Answer:

-12

Step-by-step explanation:

-15+3=x

-12=x

Hope u liked it

Answer: To solve the quadratic equation, we can start by simplifying the left side of the equation:

9(x^2 −10)−3 = 7

9x^2 - 90 - 3 = 7

9x^2 - 93 = 7

Next, we can isolate the x^2 term by adding 93 to both sides:

9x^2 = 100

Finally, we can solve for x by taking the square root of both sides and considering both the positive and negative square roots:

x = ±√(100/9)

x = ±(10/3)

Therefore, the solutions to the quadratic equation are:

x = 10/3 or x = -10/3.

Step-by-step explanation:

Answer: x=10/3

Step-by-step explanation:

9(x^2-10)-3=7

=>9(x^2-10)=7+3

=>x^2-10=10/9

=>x^2=10/9+10

=>x^2=100/9

=>x=10/3

Answer:

Step-by-step explanation:

here is what I got but I hope it helps :)

The opposite of -1.9 on a number line would be 1.9.

The opposite of the opposite of -1.9 would be -1.9.

That is a super weird trick question... what kinda teacher would give that to you???

Answer: C. 4653

Step-by-step explanation:

Use Bayes theorem. When you put the values in (like below) you get 46.53%

Answer:

The probability that she will not have a heart attack IS 0.4653

Step-by-step explanation:

Option C. for plato users, trust me

The graph of the absolute value function f(x) = |x - 2| is given by the image presented at the end of the answer.

A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.

The four translation rules for functions are defined as follows:

The parent absolute value function is given as follows:

f(x) = |x|.

Which has the format of the V-graph, with vertex at the origin.

f(x) = |x - 2| is a translation right two units of f(x) = |x|, hence the vertex will be at the point (2,0).

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The Equation used to determine the number of bottles produced in terms of the number of hours the plant is producing bottles is b = 1500h

Number of soda produced in 8 hours = 12000

We know

The number of soda produced varies directly with the hours works

Consider the number of bottle produced = b

Number of hours = h

Then the relationship will be b directly proportional to h

b ∝ h

b = k × h

Where k is the constant

Then substitute the values in the equation and find the value of k

12000 = k × 8

k = 12000/8

k = 1500

The equation will be

b = 1500h

Hence, equation used to determine the number of bottles produced in terms of the number of hours the plant is producing bottles is b = 1500h

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The value of m from the quadratic equation is m = -1/5 or m = 1

A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.

The roots of the quadratic equations are

x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )

where ( b² - 4ac ) is the discriminant

when ( b² - 4ac ) is positive, we get two real solutions

when discriminant is zero we get just one real solution (both answers are the same)

when discriminant is negative we get a pair of complex solutions

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

x² + 4mx + 4m² - m - 1 = 0   be equation (1)

Now , sum of the roots of the equation = -b/a

where b = 4m and a = 1

So , so the sum of the roots = -4m

From the Vieta's formula , we get

-4m = ( -1 - 4m² + m ) / 1

On simplifying the equation , we get

5m² - 4m - 1 = 0

On factorizing the equation , we get

5m² - 5m + m - 1 = 0

5m ( m - 1 ) + 1 ( m - 1 ) = 0

Taking the common terms in the equation , we get

( 5m + 1 ) ( m - 1 ) = 0

when ( 5m + 1 ) = 0

Subtracting 1 and dividing by 5 on both sides , we get

m = -1/5

when ( m - 1 ) = 0

Adding 1 on both sides , we get

m = 1

So , the two values of m are

m = -1/5 and m = 1

Hence , the equation is solved

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Answer: 3/7

There are 7 months before August, and out of these seve, only 3 have 30 days.

The area of the convex polygon is 21.5 square units

The vertices are given as:

(0,5), (-1,2), (4,4), (-3,-4) and (2,0)

The area is then calculated as:

A = 0.5 * |x1y2 - x2y1 +x2y3 - x3y2 + ....... |

So, we have:

A = 0.5 * |-1 * 5 - 2 * 0 + 0 * 4 - 5 * 4 + 4 * 0 - 4 * 2 +2 * -4 - 0 * -3 - 3 * 2 + 4 * 1|

Evaluate

A = 0.5 * |-43|

Remove the absolute bracket

A = 0.5 * 43

This gives

A = 21.5

Hence, the area of the convex polygon is 21.5 square units

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There are 6 different ways to select a cone if it matters which flavor is on top, which is in the middle and which is on the bottom by permutation.

Permutation is the arrangement of objects when the order of arrangement matters.

Here the arrangement is done in 3! ways.

The formula used is

nPr= n!/(n-r)!

Here n=3, r=3

Therefore 3P3= 3!/ (3-3)!= 3!/ 0! =3!= 6 ways( since 0!=1 )

Alternatively,

When selecting a cone, there are six distinct possibilities if it matters which flavor is on top, which is in the middle, and which is on the bottom.

There are three options for the flavor that will be on top, followed by two options for the middle flavor, and then the remaining flavor for the bottom cone.

This gives you 3*2*1=6 possible cone arrangements.

Suppose we have three flavors: vanilla, chocolate, and strawberry.

If it is important which flavor is on top, which is in the middle, and which is on the bottom, there are only six distinct options that can be chosen for the cone. The six choices are:

v a n i l l a, c h o c o l a t e, s t r a w b e r r y

v a n i l l a, s t r a w b e r r y, c h o c o l a t e

s t r a w b e r r y, c h o c o l a t e, v a n i l l a

s t r a w b e r r y, v a n i l l a, c h o c o l a t e

v a n i l l a, c h o c o l a t e, s t r a w b e r r y

c h o c o l a t e, s t r a w b e r r y, vanilla

Therefore, there are 6 different ways to select a cone if it matters which flavor is on top, which is in the middle and which is on the bottom.

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Answer: x<-9

Step-by-step explanation:

4x-45<\(x^{2}\)

x^2+4x-45<0

factor

(x+9)(x-5)<0

x<-9,x<5

the negative solution is x<-9

The probability that the coin lands on heads if one of them is flipped and lands on heads with probability 0.6 is 0.6 × 1/2 + 0.3 × 1/2 = 0.45. Therefore, the probability that the coin lands on heads is 0.45.  

a) Let A be the event that the chosen coin is the one that lands on heads with probability 0.6 and B be the event that the coin lands on heads. Then, the required probability is P(A | B) = P(A and B) / P(B) .

Here, P(A and B) = probability that the chosen coin is the one that lands on heads with probability 0.6 and it actually lands on heads.

Since the probability that the coin lands on heads are 0.45 and the probability that the chosen coin is the one that lands on heads with a probability of 0.6 is 1/2, we have P(A and B) = 0.6 × 1/2 = 0.3. The probability that the coin lands on heads is 0.45.

So, P(B) = probability that the coin lands on heads = 0.45.P(A | B) = P(A and B) / P(B) = 0.3 / 0.45 = 2/3.

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