The scale of a map is 1 in = 11.9 miles. How many inches will be drawn on the map to represent 30.9 miles?​

Answer:

k = 29

Step-by-step explanation:

5k - 3 + 9 + k = 180

6k + 6 = 180

6k = 180 - 6 = 174

k = 174/6 = 29

Based on the frequency table given,

a) The minimum number of dogs that could have a mass of more than 26 kg is of: 5.

b) The maximum number of dogs that could have a mass of more than 26 kg is of: 16.

The frequency table displays the number of times each value, or range of values, appears in the data-set.

where 11 weights are between 20 and 30,  and all of the dogs in the interval 20 × 30 have weights less than 26 kg, the lowest number of dogs that might have a mass more than 26 kg is 5.

This  implies that only the dogs in the period 30 x 40 would have a mass greater than 26 kg.

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Answer:

174 cm

Step-by-step explanation:

1.83 m to cm is 183.

So, 183 cm - 9 cm = 174cm

Hope you understand ^^

Answer:

174 cm

Step-by-step explanation:

1 meter is equal to 100 centimeter so 1.83m times 100 is equal to 183cm. so 183 cm-9cm=174 cm

Answer:

see below

Step-by-step explanation:

5/10 divide ?/?= 1/2

5/10 divide by 5/5 = 1/2

2. 12/15 divide ?/? = 4/5

12/15 divide by 3/3 = 4/5

3. 10/12divide ?/? = 5/6

10/12 divide by 2/2 = 5/6

4. 14/18 divide ?/? = 7/9

14/18 divide by 2/2 = 7/9

The rate at which the volume of the cylinder is changing is 600 mm^3/min, and the rate at which the surface area is changing is 240π mm^2/min.

To find the rate at which the volume and surface area of the cylinder are changing, we can use the given formulas for volume and surface area and differentiate them with respect to time. Let's calculate the rates at the moment when the radius of the base is 10 mm.

Given:

Radius rate of change: dr/dt = 3 mm/min

Height: h = 20 mm

Radius: r = 10 mm

Volume of the cylinder (V) = \(r^2h\)

Differentiating with respect to time (t), we have:

dV/dt = 2rh(dr/dt) + \(r^2\)(dh/dt)

Since the height of the cylinder is constant, dh/dt = 0.

Substituting the given values:

dV/dt = 2(10)(20)(3) + (10^2)(0)

dV/dt = 600 + 0

dV/dt = 600 mm^3/min

Therefore, the rate at which the volume of the cylinder is changing at the given moment is 600 mm^3/min.

Surface area of the cylinder (SA) = 2πrh + 2π\(r^2\)

Differentiating with respect to time (t), we have:

dSA/dt = 2πr(dh/dt) + 2πh(dr/dt) + 4πr(dr/dt)

Again, since the height of the cylinder is constant, dh/dt = 0.

Substituting the given values:

dSA/dt = 2π(10)(0) + 2π(20)(3) + 4π(10)(3)

dSA/dt = 0 + 120π + 120π

dSA/dt = 240π mm^2/min

Therefore, the rate at which the surface area of the cylinder is changing at the given moment is 240π mm^2/min.

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The factorisation of  x² - x -12 is (x-4)(x+3) and the factors are 4, -3.

A number or other mathematical object is factorized or factored when it is written as the product of numerous factors, often smaller or simpler things of the same sort. For instance, factorizing the number 15 as 3*5

A number is swiftly factorized into smaller numbers or factors of the number using the factorization formula. A factor is a number that evenly divides the inputted number.

The subsequent stages aid in the polynomial factoring process. The steps to factorizing a polynomial are listed below.

The expression is x² - x -12

⇒ x² - x -12 = 0

⇒x² - 4x + 3x - 12 = 0

⇒x(x-4) + 3(x-4) = 0

⇒(x-4)(x+3) = 0

or, x-4 = 0 ⇒ x = 4     and,

x+3 = 0 ⇒ x= -3

The factorisation of  x² - x -12 is (x-4)(x+3) and the factors are 4, -3

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Answer:

Q1. Answer: According to the guidelines, the ratio of the rise (height) to the run (length) of a wheelchair ramp should be no greater than 1:12.

Option A: A ramp with a length of 30 feet and a height of 3 feet. The ratio of the rise to the run is 3/30 = 1/10, which is less than 1:12, so this ramp follows the guidelines.

Option B: A ramp with a length of 20 meters and a height of 0.5 meters. The ratio of the rise to the run is 0.5/20 = 1/40, which is less than 1:12, so this ramp follows the guidelines.

Option C: A ramp with a length of 384 inches and a height of 32 inches. The ratio of the rise to the run is 32/384 = 8/96 = 2/24, which is less than 1:12, so this ramp follows the guidelines.

Option D: A ramp with a length of 1 feet and a height of 12 feet. The ratio of the rise to the run is 12/1 = 12, which is not less than 1:12, so this ramp does not follow the guidelines.

Therefore, the ramps that follow the guidelines are options A, B, and C.

Q2. Answer: The guidelines for a wheelchair ramp suggest that the ratio of the rise (height) to the run (length) of the ramp should be no greater than 1:12. In this case, the rise is 2.5 feet and the run is the length of the ramp (x feet). The ratio of the rise to the run is 2.5/x.

To follow the guidelines, the ratio of the rise to the run should be no greater than 1:12, or 1/12. Therefore, the length of the ramp (x) should be greater than or equal to 2.5/1/12 = 30 feet.

Therefore, the correct answer is C: X ≥ 30.

Step-by-step explanation:

Answer:

1/3

Step-by-step explanation:

common ratio is

9÷27=1/3

3÷9=1/3

1÷3=1/3

therefore common ratio is 1/3

Answer: 1/3

Step-by-step explanation:

Let us confirm that this is a geometric sequence. 9/27 = 1/3 and 3/9 = 1/3. Thus, the common ratio is 1/3.

The period of the function f(t) = 2.3cos(0.25t) is 8π. Hence, the correct answer is d) period 8π.

To determine the period of the function f(t) = 2.3cos(0.25t), we need to consider the coefficient of t inside the cosine function.

In this case, the coefficient is 0.25, which represents the frequency of the cosine function. The period of a cosine function is given by the formula T = 2π/frequency.

Using this formula, we can calculate the period of the function f(t) as follows

T = 2π / 0.25

T = 8π

Therefore, the period of the function f(t) = 2.3cos(0.25t) is 8π.

Hence, the correct answer is d) period 8π.

The period of a function represents the length of one complete cycle or the distance between two consecutive identical points on the graph of the function. In this case, the function is a cosine function, and the period determines how long it takes for the function to repeat its values

The coefficient 0.25 in the function f(t) = 2.3cos(0.25t) affects the frequency of the cosine function. A smaller coefficient results in a slower oscillation, while a larger coefficient leads to a faster oscillation. In this case, since the coefficient is 0.25, it means that the function completes one full cycle within 8π units of time.

Understanding the period of a function is crucial for analyzing its behavior, identifying the frequency of oscillation, and studying its repetitive patterns.

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Answer:between 5 and 5 1/2 inches

Step-by-step explanation:

a) To re-express the given differential equation as a first-order differential equation using matrix and vector notation, we can rewrite it in the form:

\(x' = Ax\)

where x is a vector and A is a square matrix.

b) To determine the stability of the system obtained in part (a), we need to analyze the eigenvalues of matrix A.

If all eigenvalues have negative real parts, the system is stable.

If at least one eigenvalue has a zero real part, the system is neutrally stable.

If at least one eigenvalue has a positive real part, the system is unstable.

c) To compute the eigenvalues and eigenvectors of matrix A, we solve the characteristic equation

\(det(A - \lambda I) = 0\),

where λ is the eigenvalue and I is the identity matrix.

By solving this equation, we obtain the eigenvalues.

Substituting each eigenvalue into the equation

\((A - \lambda I)v = 0\),

where v is the eigenvector, we can solve for the eigenvectors.

d) Once we have computed the eigenvalues and eigenvectors of matrix A, we can construct the diagonalization relationship as follows:

\(A = PDP^{(-1)}\)

where P is a matrix whose columns are the eigenvectors of A, and D is a diagonal matrix whose diagonal elements are the eigenvalues of A.

To show that this relationship is valid, we can compute \(PDP^{(-1)}\) and verify that it equals A.

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Step-by-step explanation:

The pattern in the table:  

Tables: 1 2 3 4 5

Chairs: 5 10 15 20 25

For tables, it is adding 1 each time.

For chairs, it is adding 5 each time.

The balance after 7 years is $11726.12

The given parameters are:

The amount is calculated as:

\(A = P(1 + \frac rn)^{nt}\)

So, we have

\(A = 8000 * (1 + \frac {5.5\%}4)^{4 * 7}\)

Evaluate the expression

A = 11726.12

Hence, the balance after 7 years is $11726.12

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Answer:

If a candle shop is offering a 20% off sale, the prices of all candles will be reduced by 20%. This will affect the mean, median, and mode cost per type of candle in the following ways:

Hope this helps!

Answer:

Mean: The mean is calculated by adding up all the prices of the candles and dividing by the total number of candles. When the prices are reduced by 20%, the new mean will also decrease by approximately 20%. This is because each price is being multiplied by 0.8, and then the total is divided by the same number of candles.

Median: The median is the middle value when all the candle prices are listed in order from lowest to highest. When the prices are reduced by 20%, the relative position of each price will remain the same. However, the actual values will decrease by 20%. Therefore, the new median will also decrease by approximately 20%.

Mode: The mode is the most common value in the set of candle prices. When the prices are reduced by 20%, it is possible that the mode will change, depending on the original distribution of prices. For example, if there are originally two or more prices that are tied for the most common value, then the mode may remain the same. However, if there is only one most common value, and this value is reduced by 20%, then a different value may become the new mode.

Step-by-step explanation:

Answer:

\(p {}^{2} - q { }^{2} \)

Step-by-step explanation:

I hope this helps

Answer:

The answer to this is c) 4.

The resulting graph is a circle with center at (-3,-1) and radius 3.

The graph of the equation (x+3)²+(y+1)²=9

is a circle with center at (-3,-1) and radius 3. The equation of a circle with center (a,b) and radius r is given by the equation (x-a)² + (y-b)² = r². By comparing the given equation with the standard equation of a circle, we can easily see that the center of the circle is (-3,-1) and the radius is 3. To graph a circle, we need to first plot the center of the circle, which is (-3,-1) in this case. Next, we need to mark the radius of the circle, which is 3 units. We can do this by measuring 3 units from the center in any direction and marking the point. Since the radius of the circle is the same in all directions, we can repeat this process for other directions to get points on the circumference of the circle. We can use a compass to make this process easier. After plotting a sufficient number of points, we can draw a smooth curve passing through all the points to obtain the graph of the circle.

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Answer:

0.05 pound of chocolate per gift bag or 1/20 pound of chocolate per gift bag

Step-by-step explanation:

1/5 divided by 4

=0.05 pound of chocolate per gift bag or 1/20 pound of chocolate per gift bag

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y=(-11-sqrt(241))/4=-6.631. or

y=(-11+sqrt(241))/4=1.131

Answer: y=-27     y=-15.625

Step-by-step explanation:

\(\displaystyle\\2y^\frac{2}{3} +11y^\frac{1}{3} +15=0\\Let\ y^\frac{1}{3} =u\\Hence,\\2u^2+11u+15=0\\2u^2+6u+5u+15=0\\2u(u+3)+5(u+3)=0\\(u+3)(2u+5)=0\\u+3=0\\u=-3\\Hence,\\y^\frac{1}{3} =-3\\ Take\ both\ parts\ of\ the\ equation \ to \ the\ third\ power:\\(y^\frac{1}{3})^3=(-3)^3 \\y=(-3)(-3)(-3)\\y=-27\\2u+5=0\\2u+5-5=0-5\\2u=-5\\Divide\ both\ parts\ of\ the\ equation\ by\ 2:\\u=-2.5\\Hence,\\y=(-2.5)^3\\y=-15.625\)

Person 3's payment exceeded person 2's payment by $20.

To find out how much more person 3 paid than person 2, we need to calculate the amounts each person paid based on the given ratio and then compare their payments.

The ratio given is 1:2:3, which means that person 1 gets 1 part, person 2 gets 2 parts, and person 3 gets 3 parts of the total amount.

Step 1: Calculate the total number of parts in the ratio.

1 + 2 + 3 = 6

Step 2: Determine the value of one part.

$120 (total amount) divided by 6 (total number of parts) = $20

Step 3: Calculate the payments for each person based on the ratio.

Person 1: 1 part * $20 = $20

Person 2: 2 parts * $20 = $40

Person 3: 3 parts * $20 = $60

Therefore, person 3 paid $60, while person 2 paid $40. To find out how much more person 3 paid than person 2, we subtract the amount person 2 paid from the amount person 3 paid:

$60 - $40 = $20

Hence, person 3 paid $20 more than person 2.

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The probability that either event A or B will occur is 43/60

Using the parameters given

n(A) = 29

n(B) = 14

Total number of events = 29+17+14 = 60

The probability of each event :

P(A) = 29/60

P(B) = 14/60

P(A or B ) = P(A) + P(B)

P(A or B ) = 29/60 + 14/60

P(A or B ) = 43/60

Therefore, the probability of A or B is 43/60

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The range of f as shown in the graph is -6 ≤ f(x) ≤ 5. The correct option is A. -6 ≤ f(x) ≤ 5

Here, we have,

From the question, we are to determine the range of f.

The range of a function is the set of its possible output values.

The graph of the function, f, is shown in the diagram.

From the graph,

The minimum value of f on the x-axis is -6. That is, f(x) ≥ -6

and

The maximum value of f on the x-axis is 5. That is, f(x) ≤ 5

Combining the two expressions, we get

f(x) ≥ -6 and f(x) ≤ 5

That is,

-6 ≤ f(x) and f(x) ≤ 5

∴ -6 ≤ f(x) ≤ 5

Hence, the range of f as shown in the graph is -6 ≤ f(x) ≤ 5. The correct option is A. -6 ≤ f(x) ≤ 5

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The probability of drawing a king from a standard deck of 52 cards is 1/13.

In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.

To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).

The total number of possible outcomes is 52 because there are 52 cards in the deck.

The favorable outcomes, in this case, are the four kings.

Therefore, the probability of drawing a king is given by:

Probability = (Number of favorable outcomes) / (Number of possible outcomes)

= 4 / 52

= 1 / 13

Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.

This means that out of every 13 cards drawn, on average, one of them will be a king.

It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.

Each draw is independent, and the probability of drawing a king is constant.

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If Darryl uses small unit cubes to make a big cube that is 3 units high, he would need 27 small cubes to complete the task.

Darryl is using small unit cubes to make a big cube that is 3 units high. To complete the big cube, Darryl would need to determine the total number of small unit cubes required.

A cube is a three-dimensional figure that has six faces, eight vertices, and twelve edges of equal length. The small cubes are placed one on top of the other, in layers, to create a larger cube.

Therefore, if the big cube is 3 units high, there will be three layers of small cubes in the vertical direction, each with the same dimensions as the base.

The base of the cube would be a square, and each side would have three small cubes lined up next to each other.

So, the base of the cube would have dimensions of 3 units by 3 units. To fill one layer of the cube, Darryl would need 3 x 3 x 1 = 9 small cubes.

Since there are three layers in total, Darryl would need 9 x 3 = 27 small cubes to complete the big cube.

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Answer:

6+4+15 = 25 and since there are 6 red marbles the answer is 6/25

Answer:

6 out of 25 chance/ 24%

Step-by-step explanation:

15 + 4 = 19 + 6 = 25

6/25 = 0.24 = 24%

Answer:

\(10x {}^{2} + 30x\)

The side lengths for the triangle are given as follows:

Suppose that we have two points of the coordinate plane, and the ordered pairs have coordinates \((x_1,y_1)\) and \((x_2,y_2)\).

The shortest distance between them is given by the equation presented as follows, derived from the Pythagorean Theorem:

\(D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Then the length AC is given as follows:

\(AC = \sqrt{(5 - (-7))^2 + (0 - 3)^2}\)

AC = 12.4.

The length AB is given as follows:

\(AB = \sqrt{(-3 - (-7))^2 + (6 - 3)^2}\)

AB = 5.

The length BC is given as follows:

\(BC = \sqrt{(5 - (-3))^2 + (6 - 0)^2}\)

BC = 10.

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The inverse function is \(f^-^1(x) = \frac{Inx}{In10}\) and Domain (0, infinity) and Range is (-infinity , infinity).

Given,

In the question:

The inverse function f(x) = \(10^x\)

To find the inverse function:

Now, According to the question;

f(x) = \(10^x\)

Rewrite the function using y

y = \(10^x\)

Interchange the position of x and y in the function

x = \(10^y\)

Isolate the dependent variable

y = \(\frac{Inx}{In10}\)

Find the inverse function

\(f^-^1(x) = \frac{Inx}{In10}\)

Hence, The inverse function is \(f^-^1(x) = \frac{Inx}{In10}\) and Domain (0, infinity) and Range is (-infinity , infinity).

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