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Rob is making for his young son a replica armchair of one he uses. The ratio of the length of the arm of the old chair to that of the new chair is 3:2. The arm of the old chair is 9 inches long. How many inches long will the arm of the new chair be?

Answer:

a=4 st=48

Step-by-step explanation:

28=7a; a= 4;

ST= 12a; ST= 12*4= 48

Answer:

the answer of the equation is ST is =3a

Answer:

Step-by-step explanation:

78 sin

(+0

Answer:

3/2

Step-by-step explanation:

slope = m = change in y/change in x OR y2-y1/x2-x1

change in y: -14 - -2= -12 (or -14 + 2, because two negatives make a positive)

change in x: -15- -7 = -8 (or -15+ 7 due to two negatives making a postive)

slope = -12/-8 = 3/2

12/5 yards is the length she should use to make the string.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

Given that Cassandra is hanging crystal stars from the gym ceiling using string for the homecoming dance

She wants the ends of the strings where the stars will be attached to be 7 feet from the floor.

BD is perpendicular to AC.

∠BDA+∠2+∠3=180

∠2+∠3=90 degrees.

∠1=∠3 (the equivalent substitution)

ΔABD=ΔBCD

AD/BD=BD/DC

(Similar triangles have sides that are proportional)

AD.DC=BD²

PC⊥AC

∠ACP=90 degrees.

∠ACM+∠MAC+∠∠CAM=180

∠ACM=∠APC

Therefore ΔAMC~ΔPCA

CM/CD=AC/AD

CM=12/5 yards

Hence, 12/5 yards is the length she should use to make the string.

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Answer: 18

Step-by-step explanation:

First, find x for x-2. So you would use one of the Geometric Mean Theorems using 5 and a height of 10. For this problem, we will use "y" as a placeholder for finding the whole total of that side.

\(\frac{5}{10} =\frac{10}{y} \\\)    Solve. --> \(5y = 100\\\) --> \(\frac{5y}{5} =\frac{100}{5} \\\) --> y = 20

Then subtract 20 from 2 to find x. You get 18 as an answer.

35% more than 78?

35% of 78;

78 x .35 = 27.3

78 + 27.3 = 105.3

Answer:

Option 1 is correct

5.345345... = 5340/999

Hope this helps!

:)

The critical point (1, -1) represents a relative minimum of f(x, y) with a value of -1/3 and (1, -1) is the only extremum or relative maximum of the function.

To find the relative maximum and minimum values of the function f(x, y) = (\(x^3\))/3 + 2xy +\(y^2\) - 3x + 1, we need to analyze its critical points and classify them using the second partial derivative test.

To find the critical points, we need to compute the partial derivatives of f with respect to x and y and set them equal to zero:

∂f/∂x = \(x^2\) + 2y - 3 = 0

∂f/∂y = 2x + 2y = 0

Solving these equations simultaneously, we find x = 1 and y = -1.

Thus, the critical point is (1, -1).

Next, we need to compute the second partial derivatives and evaluate them at the critical point:

∂²f/∂x² = 2

∂²f/∂y² = 2

∂²f/∂x∂y = 2

Now, we can use the second partial derivative test to classify the critical point.

The discriminant D = (∂²f/∂x²) × (∂²f/∂y²) - \(\left(\frac{{\partial^2 f}}{{\partial x \partial y}}\right)^2\) = (2)(2) - \((2)^2\) = 0.

Since D = 0, the test is inconclusive.

To determine the nature of the critical point, we can examine the function near the critical point.

Evaluating f at the critical point (1, -1), we find f(1, -1) = \((1^3)\)/3 + 2(1)(-1) + \((-1)^2\) - 3(1) + 1 = -1/3.

Hence, the critical point (1, -1) represents a relative minimum of f(x, y) with a value of -1/3.

There are no other critical points to consider, so we can conclude that (1, -1) is the only extremum of the function.

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Using breaking apart technique 4 X 23 = 92

To make the multiplication process simpler, you split up one or more of the numbers. It also explains why you would "carry" a number to the following column.

split apart definitions. verb: break anything down into its component parts. substitute words: separate, dismantle, take apart

According to the given question

4×23 = (20×4)+(3×4)

         =80+12

          =92

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The given series is a complex alternating series. By applying the ratio test, we can show that the series converges. However, it does not have a closed form expression, and therefore we cannot obtain an exact value for the sum of the series.

The given series can be written in sigma notation as:

∑n=0 ∞ 7\((-1)^n(\)2n +1) \(3^(2n +1)\) (2n + 1)!

To test for convergence, we can apply the ratio test, which states that if the limit of the absolute value of the ratio of consecutive terms is less than 1, then the series converges absolutely. Applying the ratio test to this series, we get:

lim|(7*\((-1)^(n+1)\) * 3\(^(2n+3)\) * (2n+3)!)/((2n+3)(2n+2)(3^(2n+1))*(2n+1)!)| = 9/4 < 1

Therefore, the series converges absolutely.

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Answer:

-9

Step-by-step explanation:

If you subtract 10 from 1, you get -9, which is the value of y.

Answer:

0

Step-by-step explanation:

→ State the slope formula

( y₂ - y₁ ) ÷ ( x₂ - x₁ )

→ State each value

x₁ = 3, y₁ = 18, x₂ = 0 and y₂ = 18

→ Substitute in each value into the formula

( 18 - 18 ) ÷ ( 0 - 3 )

→ Simplify

0

Answer:

x=-9

Step-by-step explanation:

\(9^{2x-3}=27^{2x+4}\\(3^2)^{2x-3}=(3^3)^{2x+4}\\3^{2(2x-3)}=3^{3(2x+4)}\\3^{4x-6}=3^{6x+12}\)

As the bases(3) are same,

we can conclude that the powers are equal.

Hence,

\(4x-6=6x+12\\-6-12=6x-4x\\-18=2x\\x=-18/2\\x=-9\)

Answer:

y = 13/3

Step-by-step explanation:

First input 10 as our x into the equation. So our new equation is 2(10) - 3y=7.

Once you simplify your equation would be 20 - 3y = 7. Subtract 20 from both sides. New equation is -3y = -13. Divide each side by -3. Your answer for y is 13/3.

Answer: 12

Step-by-step explanation:

You can say about getting the outcome of precisely 500 tails you should not expect exactly 500 tails in 1000 tosses, but the proportion of tails should approach 0.5 as the number of tosses increases. The correct answer is option B.

You should not expect exactly 500 tails in 1000 tosses, but the proportion of tails should approach 0.5 as the number of tosses increases. The probability of getting a head or a tail while flipping a fair coin is 0.5 or 1/2, respectively. If a fair coin is tossed 1000 times, the probability of getting a head or a tail is 0.5.

Hence, you should expect exactly 500 tails in 1000 tosses.

However, the number of tails tossed is a random quantity, and there is no guarantee that half of the tosses will result in tails. Getting 500 tails is just as likely as getting any other number of tails in 1000 tosses.

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A. The waiter earns $25 an hour

Answer:

\( \dfrac{28}{81} \)

Step-by-step explanation:

\(-\dfrac{4}{9}(-\dfrac{7}{9}) =\)

\( = \dfrac{4 \times 7}{9 \times 9} \)

\( = \dfrac{28}{81} \)

When one outcome is favored over another, we call this favoritism or preference.

When one outcome is favored or chosen over another, it is referred to as favoritism or preference. Favoritism implies a bias towards a particular outcome or individual, while preference suggests a personal inclination or choice.

This concept is commonly encountered in various contexts. For example, in decision-making, individuals may show favoritism towards a specific option based on personal preferences or biases. In voting, people may have a preference for a particular candidate or party. In sports, teams or players may be favored over others due to their past performance or popularity. Similarly, in competitions, judges or audiences may exhibit favoritism towards certain participants.

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When one outcome is favored over another, it signifies a subjective inclination or bias towards a specific result based on personal factors, and this preference can influence decision-making and actions.

When one outcome is preferred or desired over another, we commonly refer to this as a preference or favoritism toward a particular result. It implies that there is a subjective inclination or bias towards a specific outcome due to various factors such as personal beliefs, values, or goals. This preference can arise from a range of contexts, including decision-making, competitions, or evaluations.

The concept of favoring one outcome over another is deeply rooted in human nature and can shape our choices and actions. It is important to recognize that preferences can vary among individuals and may change depending on the circumstances. Furthermore, the criteria for determining which outcome is favored can differ from person to person or situation to situation.

In summary, when one outcome is favored over another, it signifies a subjective inclination or bias towards a specific result based on personal factors, and this preference can influence decision-making and actions.

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The function \(y = xe^{(2x)} + Ce^z\) is the general solution to the differential equation \(y' = 2y + e^{(2x)}\). A particular solution satisfying y(0) = a is\(y = xe^{(2x)} + ae^z\).

To show that\(y = xe^{(2x)} + Ce^z\) is the general solution of the differential equation \(y' = 2y + e^{(2x)}\), we need to substitute y into the differential equation and verify that it satisfies the equation.

First, let's find y' by taking the derivative of y with respect to x:

\(y' = d/dx (xe^{(2x)}) + d/dx (Ce^z)\)

Using the product rule, we have:

\(y' = e^{(2x)} + 2xe^{(2x)} + C * d/dx (e^z)\)

Since the derivative of \(e^z\) with respect to x is zero, we have:

\(y' = e^{(2x)} + 2xe^{(2x)}\)

Now, substitute y and y' into the differential equation:

\(e^{(2x)} + 2xe^{(2x)} = 2(xe^{(2x)} + Ce^z) + e^{(2x)}\)

Simplifying, we find that the left side is equal to the right side, verifying that y is a solution to the differential equation.

To find a particular solution satisfying the initial condition y(0) = a, we substitute x = 0 into y:

\(y(0) = 0e^{(2*0)} + Ce^z = 0 + Ce^z = a\)

This implies that \(Ce^z = a\), and we can solve for C:

\(C = a/e^z\)

Therefore, a particular solution satisfying the initial condition is\(y = xe^{(2x)} + (a/e^z)e^z = xe^{(2x)} + ae^z.\)

In summary, \(y = xe^{(2x)} + Ce^z\) is the general solution, and a particular solution satisfying y(0) = a is \(y = xe^{(2x)} + ae^z\).

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The simplified Boolean functions expressed in the sum of minterms are: option 3-F(A, B, C, D) = BD + CD + ABC

d (A, B, C, D) = BD + CD

What is Boolean function?

A Boolean function is a mathematical function that operates on one or more Boolean variables and returns a Boolean value as its output. Boolean variables can only have two possible values: true (1) or false (0).

To simplify the given Boolean functions, we can use Karnaugh maps, also known as K-maps. K-maps provide a graphical representation of the truth table and help identify simplification patterns.

For the function F(A, B, C, D), we construct a 4-variable K-map with minterms Σ(0, 6, 8, 13, 14). We place 1s in the corresponding cells for these minterms. By observing the patterns in the K-map, we can group adjacent 1s to form larger groups. The resulting simplified expression is BD + CD + ABC.

For the function d(A, B, C, D), we construct another 4-variable K-map with minterms Σ(2, 4, 10) along with the don't care conditions. By grouping adjacent 1s, we obtain the simplified expression BD + CD.

The simplified expressions are derived from the K-maps using the rules of Boolean algebra and the objective of minimizing the number of terms and literals.

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the complete question is:

the following boolean functions defined as the sum of minterms can be made simpler using Karnaugh maps.

F(A, B, C, D) = Σ(0, 6, 8, 13, 14)

d (A, B, C, D) = Σ(2, 4, 10)

What is the appropriate response, where d stands for the don't care condition?

1-BD + CD + ABCD

2-BD + CD + ABCD

3-BD + CD + ABC

4-BD + CD + ABCD

Answer: The sale price is $36.

Step-by-step explanation:

40% ÷ 100 = 0.4

0.4 × $60 = $24

$60 - $24 = $36

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

If there is an off of 40% on an item that cost $60.

The regular price of the item is $48.

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Required percentage value = a

total value = b

Percentage = a/b x 100

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

105 = 10/100 = 1/10

Example:

50% of 40 is 20.

50/100 x 40 = 20

25% of 100 is 25.

25/100 x 100 = 25.

We have,

Regular price = $60

Off = 40%

Sale price:

= 60 - (40% of 60)

= 60 - (40/100 x 60)

= 60 - (2/5 x 60)

= 60 - (2 x 12)

= 60 - 24

= $48

Thus.

If there is an off of 40% on an item that cost $60.

The regular price of the item is $48.

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The slope of the line that passes through point (0,-1) and (-1,-4) is 3.

Slope is simply expressed as change in y over the change in x.

Slope m = ( y₂ - y₁ )/( x₂ - x₁ )

Given the data in the question;

Point 1( 0,-1 )

Point 2( -1,-4 )

To determine the slope of the line, plug the coordinates into the slope formula above.

Slope m = ( y₂ - y₁ )/( x₂ - x₁ )

Slope m = ( -4 - (-1) )/( -1 - 0 )

Slope m = ( -4 + 1 )/( -1 )

Slope m = ( -3 )/( -1 )

Slope m = 3

Therefore, the slope of the line is 3.

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Since, Alice ate 5 cookies and 2 carrots for a total of 590 calories; bob ate 3 cookies and 4 carrots for a total of 410 calories. Therefore, In a cookie there are 110 calories.

A calorie is a unit of energy that food and drink provide. we can usually find out how many calories are listed in foods, and wearables like the best fitness trackers let you monitor how many calories you're burning in different activities. Certain foods, such as processed foods, tend to be high in calories. Other foods, such as fresh fruits and vegetables, tend to be low in calories. there is not. Calories are needed to give you enough energy to move, keep warm, grow, work, think, and play. Our circulation and digestion also need to work well with the energy we get from calories.

Let x = calories in cookies.

     y = calories in carrots.

Now, according to the question:

     5x + 2y = 590                   --------------------------------------- (1)

     3x + 4y = 410                    -------------------------------------- (2)

Multiplying equation(1) by 3 and equation(2) by 5:

         15x + 6y = 1770                       ---------------------------(3)

         15x + 20y = 2050                   ---------------------------(4)

Solving we get:

    y = 280/14

or, y = 20 units.

Putting the value of y = 20 in equation (2)

    3x + 4y = 410

⇒  3x + 4 × 20 = 410

⇒ 3x = 410 - 80

⇒ x = 330/3

⇒ x = 110 Units

Therefore, the calories of cookies is 110 units .

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Answer:

27

Step-by-step explanation:

smallest multiple of 33 that is 3 digits is 132 (33*4), and largest is 990 (33*30)

then all the numbers between 4 and 30 would also be 3 digits

including 4 and 30, that makes 27 number in total

Answer:

Vertical angles

Step-by-step explanation:

I just think that's the answer

have a great rest of ur day though

Answer:

yes they do

Step-by-step explanation:

they share a ray

Answer:

The answer is 29.44 degree Celsius.