Evaluate v-w for the given values. v = -14; w = 7

The clοsest οptiοn tο the actual area οf the οbject is D. 64 square inches.

Area is a measure οf the amοunt οf space inside a twο-dimensiοnal shape, such as a square, rectangle, triangle, circle, οr any οther shape that has a length and a width. It is usually measured in square units, such as square inches, square feet, οr square meters.

Tο find the area οf the οbject, we need tο break it dοwn intο smaller shapes and add up their areas.

First, we can see that the οbject can be divided intο a rectangle with dimensiοns 8 inches by 4 inches (UWVZ), a triangle with base 4 inches and height 6 inches (VXY), and a trapezοid with bases 6 inches and 8 inches, and height 4 inches (WXYU).

The area οf the rectangle is:

A_rectangle = length × width = 8 in × 4 in = 32 square inches

The area οf the triangle is:

A_triangle = 1÷2 × base × height = 1÷2 × 4 in × 6 in = 12 square inches

The area οf the trapezοid is:

A_trapezοid = 1÷2 × (base1 + base2) × height = 1÷2 × (6 in + 8 in) × 4 in = 28 square inches

Therefοre, the tοtal area οf the οbject is:

A_οbject = A_rectangle + A_triangle + A_trapezοid

= 32 square inches + 12 square inches + 28 square inches

= 72 square inches

Therefοre, the clοsest οptiοn tο the actual area οf the οbject is D. 64 square inches.

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If the interest were compounding weekly instead of semi-annually, the account would have been worth more. To calculate how much more, we can use the formula:

A = P(1 + r/n)^(nt)
The difference in the final amount is: $17,135.03 - $16,270.90 = $864.13


Hi! To answer your question, let's first calculate the future value of the account for both semi-annual and weekly compounding interest.

1. For semi-annual compounding (interest compounded every 6 months):
Initial deposit: $6,500
Interest rate: 3.3% per year (0.033 per year or 0.0165 per 6 months)
Number of compounding periods: 30 years * 2 = 60

Future Value = Initial deposit * (1 + Interest rate per period)^(Number of periods)
Future Value = $6,500 * (1 + 0.0165)^60 ≈ $16,883.62

2. For weekly compounding (interest compounded every week):
Initial deposit: $6,500
Interest rate: 3.3% per year (0.033 per year or 0.00063462 per week)
Number of compounding periods: 30 years * 52 weeks = 1560

Future Value = Initial deposit * (1 + Interest rate per period)^(Number of periods)
Future Value = $6,500 * (1 + 0.00063462)^1560 ≈ $17,110.79

Now, let's find out how much more the account would be worth if the interest were compounded weekly instead of semi-annually:

Difference = Future Value (weekly compounding) - Future Value (semi-annual compounding)
Difference = $17,110.79 - $16,883.62 ≈ $227.17

If the interest were compounding weekly, the account would be worth approximately $227.17 more.

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Answer:

Diagram a : y = 7, x = 8

Diagram b : y = 16, x = 6

Diagram c : y = 7, x = 5

Step-by-step explanation:

Diagram a :

calculate y:                              calculate x:

4y - 6 = 22                                  2x + 3 = 19

      +6     +6                                       -3      -3

4y = 28                                          2x = 16

/4      /4                                           /2      /2

y = 7                                                x = 8

Diagram b :

calculate y :                               calculate x :

3 (y-4) = 36                                   5 (x +2 ) = 40

3y - 12 = 36                                  5x +10 = 40

     +12    +12                                       -10    -10

3y = 48                                          5x = 30

/3      /3                                           /5       /5

y = 16                                             x = 6

Diagram c :

calculate y:                                  calculate x :

2y + 9 = 4y - 5                              4x + 2 = 3x + 7

-2y          -2y                                 -3x          -3x

9 = 2y - 5                                       x + 2 = 7

+5         +5                                           -2    -2

14 = 2y                                            x = 5

/2     /2

y = 7

Answer:

3 times 2 equal 5

Step-by-step explanation:

did the test and made 100

The given expression is simplified as 6x+3y³. Therefore, option A is the correct answer.

The given expression is \(\frac{18x^{3}y^{2}+9x^{2} y^{5}}{3x^{2} y^{2} }\).

We need to divide and simplify the given expression.

Division of polynomials by monomial means dividing the polynomials which are written as numerators by a monomial which is written as denominators to find their quotient.

Split the denominators to each numerator and cancel out the common terms and simplify.

Now, \(\frac{18x^{3}y^{2}+9x^{2} y^{5}}{3x^{2} y^{2} }=\frac{18x^{3}y^{2}}{3x^{2} y^{2}} +\frac{9x^{2} y^{5}}{3x^{2} y^{2}}\)

=6x+3y³

The given expression is simplified as 6x+3y³. Therefore, option A is the correct answer.

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The probability, using Bayes' Theorem, is calculated as follows:

p(e|f) = 5/9.

Among the probabilities used in this problem, two conditional probabilities are used, which is the reason for the use of Bayes' Theorem in this problem.

The equation to obtain a probability is presented as follows:

\(P(B|A) = \frac{P(B)*P(A|B)}{P(A)}\)

The parameters are described as follows:

Hence the equation to calculate p(e|f) in this problem is given as follows:

p(e|f) = p(e) x p(f|e)/p(f)

Then, replacing the values given in this problem, the probability is of:

p(e|f) = (2/3 x 5/8)/3/4

p(e|f) = 2/3 x 5/8 x 4/3

p(e|f) = 5/9.

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Answer:

2

Step-by-step explanation:

If two shapes are similar, this means the ratio of similar sides to each other are the same.

So, in the green shape, the long side length is 5 mm. In the purple shape, the long side length is 10 mm in length. The ratio is therefore 5 to 10, which can be simplified to 1 to 2 (which is basically saying that the side lengths of the purple shape are double the length of the sides of the green shape).

Using the same 1 to 2 ratio, you know that the short side length on the green shape is 1. The short side length on the purple shape (j) must therefore be double, which is 2.

Answer:

Step-by-step explanation:

A.

Answer:

=1

Step-by-step explanation:

¾÷¾

¾×reciprocal of ¾=1

1

Answer:

=-1

Step-by-step explanation:

-10+2d=8

-10 from 8

2d=-2

divode both sides by 2

d=-1

Answer:

1234minutos de los pobres de los pinzones

The simplified expression of g(x) = x² - 4x² + x + 6 is g(x) = -3x² + x + 6

From the question, we have the following parameters that can be used in our computation:

g(x) = x² - 4x²+x+6

Rewrite properly

So, we have the following representation

g(x) = x² - 4x² + x + 6

Evaluate the like terms

g(x) = -3x² + x + 6

The above expression cannot be further simplified

Hence, the solution is g(x) = -3x² + x + 6

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The rectangular form of complex number is z = 7i.

To convert the given polar representation of a complex number into its rectangular form, we can use Euler's formula, which states:

\(e^{(i\theta)} = cos(\theta) + i sin(\theta)\)

In this case, we have z = 7 (cos(π/2) + i sin(π/2)). Let's apply Euler's formula to find the rectangular form:

z = 7 (cos(π/2) + i sin(π/2))

 = 7\(e^{(\pi i/2)}\)

Using Euler's formula, we can rewrite \(e^{(\pi i /2)}\) as cos(π/2) + i sin(π/2):

z = 7 (cos(π/2) + i sin(π/2))

 = 7\(e^{(\pi i /2)}\)

Now, let's evaluate \(e^{(\pi i /2)}\):

\(e^{(\pi i /2)}\) = cos(π/2) + i sin(π/2) = 0 + i(1) = i

Substituting this result back into the equation, we get:

z = 7 \(e^{(\pi i /2)}\)

 = 7i

Therefore, the rectangular form of the given complex number z = 7 (cos(π/2) + i sin(π/2)) is z = 7i.

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Answer:

m=14

n=32

p=64

Step-by-step explanation:

B=M, so 154=11m

m=154/11

m=14

E=P, so 118=n+86

n=118-86

n=32

A=L, so 116=180-p

p=180-116

p=64

The 95% confidence interval suggests if the nicotine patch is used for 2 months, there is a high likelihood that the proportion of individuals who will report no smoking incidents.

In the following year will fall between 17.4% and 24.8%. This means that the study results are statistically significant and reliable within this range, and it is likely that the nicotine patch can be effective in reducing smoking incidents for a significant proportion of users.
In the study of the nicotine patch, the appropriate interpretation of the 95% confidence interval (17.4%, 24.8%) is that we can be 95% confident that the true proportion of people who reported no smoking incidents in the following year after using the patch for 2 months lies between 17.4% and 24.8%.

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Answer:

(4)^5

Step-by-step explanation:

When multiplying expressions with exponents you add the exponents together so in this equation you would get -4^11/-4^6. However since both exponent have the same base (-4) you can simplify it farther. When dividing expression with exponents you subtract the exponents. So, here, you would get 4^5.

Hope that helps! :)

To determine which option gives a better chance of winning, we need to calculate the expected number of A's and B's in the 1,000 draws and compare it to the conditions for winning in each option.

Let's calculate the expected number of A's and B's:

Number of A's in "ARABIA": 3

Number of B's in "ARABIA": 1

Total number of letters in "ARABIA": 6

Probability of drawing an A: 3/6 = 1/2

Probability of drawing a B: 1/6

Expected number of A's in 1,000 draws: (1/2) * 1,000 = 500

Expected number of B's in 1,000 draws: (1/6) * 1,000 = 166.67

Now let's analyze the conditions for winning in each option:

Option A: You win a dollar if the number of A's among the draws is 10 or more above the expected number (500 + 10 = 510 or more).

Option B: You win a dollar if the number of B's among the draws is 10 or more above the expected number (166.67 + 10 = 176.67 or more).

Comparing the two options:

Option A requires having 510 or more A's out of the 1,000 draws.

Option B requires having 176.67 or more B's out of the 1,000 draws.

Since it is not possible to have a fraction of a letter, the number of B's will always be an integer. Therefore, it is impossible to reach the condition for winning in option B, as there can't be 176.67 B's.

Therefore, the correct answer is:

(i) Option A gives a better chance of winning than option B.

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Answer:

35

Step-by-step explanation:

Add them together and then divide

Answer:

b + b + h + h

Step-by-step explanation:

You are finding the perimeter of the given rectangle. Note that by definition of a rectangle, the opposite parallel sides will have the same measurement. In this case, Terrance gives the expression of 2b + 2h, and so simply just expand the expression:

2b + 2h = b + b + h + h

~

Answer:

Alternate interior angles.

17x + 6 = 18x - 1.

x = 7.

Step-by-step explanation:

According to the diagram below, the angles are alternate interior angles.

Since they are alternate interior angles, they are congruent. So, 17x + 6 = 18x - 1.

17x + 6 = 18x - 1

18x - 1 = 17x + 6

x = 7

Hope this helps!

The value of m is 10cm and the value of n is 24cm

Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“. The sides of this triangle have been named Perpendicular, Base and Hypotenuse.

a² = b² + c²

for the small rectangular face,

m² = 6² +8²

m² = 36 + 64

m² = 100

m = √100

m = 10cm

to find the value of n

n² = 24² + 8²

n² = 576 + 64

n² = 640

n = √ 640

n = 25.3 cm

Therefore the value of m and n is 10cm and 25.3 cm.

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95% of the bottles of this pain reliever can be expected to have between approximately 92 and 108 tablets.

To determine the lower and upper bounds of the number of tablets in the bottle, we need to calculate the values using the given information.

Since the mean number of tablets in a bottle is 100 and the standard deviation is 4, we can use the properties of the normal distribution to calculate the lower and upper bounds.

The lower bound can be calculated using the formula:

Lower bound = Mean - (Z * Standard Deviation)

The upper bound can be calculated using the formula:

Upper bound = Mean + (Z * Standard Deviation)

To find the appropriate value of Z for a 95% confidence interval, we need to refer to the standard normal distribution table or use a calculator.

For a 95% confidence interval, the Z-value is approximately 1.96.

Plugging in the values:

Lower bound = 100 - (1.96 * 4)

Upper bound = 100 + (1.96 * 4)

Lower bound = 100 - 7.84

Upper bound = 100 + 7.84

Lower bound ≈ 92.16

Upper bound ≈ 107.84

Therefore, 95% of the bottles of this pain reliever can be expected to have between approximately 92 and 108 tablets.

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Applying the distributive property, the solutions are given as follows:

1. No solution.

2. r = -2.

3. p = -7.

4. m = 0.

5. a = -7.

6. n = 1.

7. v = 1.

8. x = All real values.

The distributive property is used when the outside term multiplies each of the inside terms, then if necessary, the like terms are used.

For this problem, the property is used to isolate the variables and find the desired result of the expressions.

6x + 1 = -6(1 - x)

6x + 1 = -6 + 6x

0x = -7

No solution. (division by 0).

4(3r + 4) = -8(2r + 5)

12r + 16 = -16r - 40

28r = -56

r = -2.

11 + 2p = p + 4

p = -7.

2(-6m - 3) = 6(5m - 1)

-12m - 6 = 30m - 6

42m = 0

m = 0.

-3 + 5a = 4a - 10

a = -7.

-16 + 3n = -8 - 5n

8n = 8

n = 1.

-22 + 8v = 7(4v - 6)

-22 + 8v = 28v - 42

20v = 20

v = 1.

3(2x - 4) = 2(3x - 6)

6x - 12 = 6x - 12

0 = 0

x = All real values.

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Answer:

<A = 117degrees

Step-by-step explanation:

<A and <B are verticle angles, as given. Hence they will be of equal measures. It is given that <A = 5x -3, and <B = 4x + 21.

Using this, set up an equation;

<A = <B

5x - 3 = 4x + 21

Inverse operations,

5x - 3 = 4x + 21

    +3          +3

5x = 4x + 24

-4x   -4x

x = 24

Now substitute back in, to find the measure of <A,

5x - 3

x = 24

5 ( 24 ) - 3

120 - 3

117

Answer:

Step-by-step explanation:

A bitmap is a digital image format that is made up of a grid of square colored dots called pixels.

Each pixel in the bitmap contains information about its color and position, which allows the computer to display the image on a screen or print it on paper. Bitmaps are commonly used for photographs, illustrations, and other complex images that require a high degree of detail and color accuracy.

However, because bitmaps store information for each individual pixel, they can be memory-intensive and may result in large file sizes. Additionally, resizing a bitmap can lead to a loss of quality, as the computer must either interpolate or discard pixels to adjust the image size.

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Answer: B (4,6) C (-2,4)

Step-by-step explanation:

just look at the graph and check where they are standing and if you need anymore help search up a graph and you will know the where the negative signs are

The product of any two invertible matrices is invertible that is (BC) = A⁻¹

Now, let's consider the product of two invertible matrices, say A and B. Since A and B are invertible, they both have an inverse, denoted by A⁻¹ and B⁻¹, respectively.

To show that the product AB is also invertible, we need to find a matrix that satisfies the definition of an inverse. Let's call this matrix C.

If C is the inverse of AB, then we should have:

(AB)C = C(AB) = I

where I is the identity matrix.

Now, we can use the associativity of matrix multiplication to expand the left-hand side of the equation:

(AB)C = A(BC)

Notice that B and C are both matrices, so their product BC is also a matrix. Thus, we can write:

A(BC) = I

Since A is invertible, we can multiply both sides by A⁻¹ to get:

A⁻¹A(BC) = A⁻¹I

The left-hand side simplifies to:

(BC) = A⁻¹

Now, we have found a matrix C that satisfies the definition of an inverse for AB, which means that AB is invertible.

To summarize, the product of two invertible matrices is invertible, and the proof relies on the fact that the inverse of a matrix is unique and the associativity of matrix multiplication.

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Answer: A'(4,1) B'(-2,-2) C'(0,8)

Explanation: You subtract 1 from X and add 3 to Y