12. List Sine, Cosine, targent cosecent secont
and contangent radies shor
Theta=4/3
No decimals
Reduce and Rationalize all
Fractions,

Answer:

465

Step-by-step explanation:

Of means multiply

310% * 150

Change to decimal form

3.10 * 150

465

Answer:

465

Step-by-step explanation:

1 percent of 150 is 1.5.

Multiply 1.5 by 310 to 465

Alicia's estimate of the surface area of the rectangular prism is not reasonable based on her miscalculation of the volume.

To determine whether Alicia's estimate of the surface area of the rectangular prism is reasonable, we first need to check if her calculation of the volume of the rectangular prism is correct.

The formula for calculating the volume of a rectangular prism is:

Volume = length x width x height

Substituting the given values in the formula, we get:

Volume = 11 meters x 5.6 meters x 7.2 meters

Volume = 449.28 cubic meters

As we can see, Alicia's estimate of 334 cubic meters is significantly lower than the actual volume of the rectangular prism, which is 449.28 cubic meters. Therefore, her estimate of the surface area is likely to be incorrect as well.

It is also important to note that the problem statement asks about the estimate of the surface area, not the volume. However, since the formula for calculating the surface area of a rectangular prism also involves the dimensions of length, width, and height, it is highly likely that Alicia's estimate of the surface area would also be incorrect given her miscalculation of the volume.

In conclusion, Alicia's estimate of the surface area of the rectangular prism is not reasonable based on her miscalculation of the volume.

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Answer:

The coordinates of the gas station are (5, 9)

Step-by-step explanation:

As given,

George begins at (2,3), ends at (9,17), and  stops at the gas station at (x,y). If the part to part ratio is 3:4

 A                   P                     B

(2, 3)             (x, y)                (9, 17)

           3         :             4

we use the Interval Division formula :

If P(x,y) lies on the interval A(x1,y1), B(x2,y2) such that AP:PB=a:b, with a and b positive, then

x= \(\frac{bx1 + ax2}{a + b}\)

y=\(\frac{by1 + ay2}{a + b}\)

Here , (x1, y1) = (2, 3)

          (x2, y2) = (9, 17)

           a : b = 3 : 4

⇒ x= \(\frac{bx1 + ax2}{a + b}\) = \(\frac{4(2) + 3(9)}{3 + 4} = \frac{8 + 27}{7} = \frac{35}{7} = 5\)

   y=\(\frac{by1 + ay2}{a + b}\) = \(\frac{4(3) + 3(17)}{3 + 4} = \frac{12 + 51}{7} = \frac{63}{7} = 9\)

∴ The coordinates of the gas station are (5, 9)

Answer:

Step-by-step explanation:

In the first triangle, using Pythagorean's theorem, x^2+3^2=5^2, x = 4

In the second triangle, using Pythagorean's theorem, x^2+7^2=24^2, x = 25

In the third triangle, using Pythagorean's theorem, 8^2+15^2=x^2, x = 17

In the fourth triangle, using Pythagorean's theorem, x^2+8^2=10^2, x = 6

In the fifth triangle, using Pythagorean's theorem, 5^2+12^2=x^2, x = 13

They form supplementary angles when they are added together.

Reason for Being Called Supplementary Angles

It is given that the angle made by the wall in one room is 36° and the angle formed by the same wall in the other room is 144°.

This implies that,

∠1 = 36°

∠2 = 144°

∠1 and ∠2 are adjacent angles and,

∠1 + ∠2 = 36° + 144°

⇒ ∠1 + ∠2 = 180°

Hence, these two adjacent angles make a straight-line angle. Hence, they are supplementary angles.

What are supplementary angles?

Two angles that form a straight line angle, that is, angle equal to 180°, when they are added together are said to be a pair of supplementary angles.

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If p > 2 is prime, then the value of 2p - 2 mod p is 2 - 2/p.

Prime number: A prime number is a positive integer greater than 1 that has no positive integer divisors other than 1 and itself. The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29, with many others following them. Prime numbers are of interest because of their special properties in arithmetic, particularly in number theory. A prime number is an odd number greater than 2 because if it is even, it is divisible by 2, which contradicts the assumption that it is prime.

Using the given formula, we can solve the problem as follows:

2p - 2 mod p

= 2 - 2/p= 2 - 2/(p-1) * (p-1)/p

= (2p - 2)/(p(p-1)/p)

= (2p - 2)/1

= 2 - 2/p

Therefore, the value of 2p - 2 mod p is 2 - 2/p.

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The probability that the sample proportion is between 0.2 and 0.42 can be calculated using the standard normal distribution.

To calculate the probability, we need to assume that the sample proportion follows a normal distribution. This assumption holds true when the sample size is sufficiently large and the conditions for the central limit theorem are met.

First, we need to calculate the standard error of the sample proportion. The standard error is the standard deviation of the sampling distribution of the sample proportion and is given by the formula sqrt(p(1-p)/n), where p is the estimated proportion and n is the sample size.

Next, we convert the sample proportion range into z-scores using the formula z = (x - p) / SE, where x is the given proportion and SE is the standard error. In this case, we use z-scores of 0.2 and 0.42.

Once we have the z-scores, we can use a standard normal distribution table or a statistical software to find the corresponding probabilities. The probability of the sample proportion falling between 0.2 and 0.42 is equal to the difference between the two calculated probabilities.

Alternatively, we can use the z-table to find the individual probabilities and subtract them. The z-table provides the cumulative probabilities up to a certain z-score. By subtracting the lower probability from the higher probability, we can find the desired probability.

In conclusion, the probability that the sample proportion is between 0.2 and 0.42 can be calculated using the standard normal distribution and z-scores. This probability represents the likelihood of observing a sample proportion within the specified range.

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Answer:

No

Step-by-step explanation:

11-(-5)=16

-5+(11)=6

Answer:

z=5/138

Step-by-step explanation:

15 1/3z=5

46/3z=5

3z=5/46

z=5/138

Answer:

here's the answer to your question

Answer: \(y = \frac{3}{4} x +1\)

Step-by-step explanation:

A perpendicular line has slopes that are the opposite reciprocals of each other.

Step 1: Turn the given equation into slope-intercept form.

Given: 4x + 3y = 6 → Slope-Intercept Form: y = mx + b

                                         \(4x + 3y = 6\)

                                          \(-4x\)        \(-4x\)

                                           \(\frac{3}{3}\)\(y\) = \(\frac{4}{3} x\) + \(\frac{6}{3}\)

                                          \(y =\) \(-\frac{4}{3}x + 2\)

Step 2: Find the opposite reciprocal of the given slope.

                                           \(-\frac{4}{3}\) → \(\frac{3}{4}\)

Step 3: Take the slope of the new line and the given point and solve for "b" or y-intercept.

y = mx + b → (-8, -5)

-5 = \(\frac{3}{4}\) (-8) + b

-5 = -6 + b

+6   +6

1 = b

Step 4: Take the slope and the value for b and plug them into the slope-intercept equation.

\(y = \frac{3}{4} x +1\)

Answer:

y = 3x/4 - 1

Step-by-step explanation:

First, we need to find the slope of the given equation 4x + 3y = 6

Subtract 4x from both sides

4x + 3y = 6

- 4x        - 4x

3y = -4x + 6

Divide both sides by 3

3y/3 = (-4x + 6)/3

y = -4x/3 + 2

The slope of the given equation is -4/3

The slope of the perpindicular equation will have to be 3/4

Using slope intercept formula, we now have this

y = 3x/4 + b

Now plug in the given coordinate

-5 = 3(-8)/4 + b

-5 = -24/4 + b

-5 = -6 + b

Add 6 from both sides

-5 = -6 + b

+ 6  + 6

b = -1

Now we have y = 3x/4 - 1

Answer:

umm sorry but i think you can do it im sure your smart go for it!

Step-by-step explanation:

To show that w is in the subspace of R4 spanned by V1, V2, and V3, we need to find constants c1, c2, and c3 such that:

w = c1V1 + c2V2 + c3V3

We can write this as a matrix equation:

| 1 -4 -9 -4 | | c1 | | -2 |

| 6 3 5 1 | x | c2 | = | -1 |

| 2 4 11 -8 | | c3 | | -1 |

| -15 7 22 -14 | | -2 |

We can solve this system of equations using row reduction:

| 1 -4 -9 -4 | | c1 | | -2 |

| 6 3 5 1 | x | c2 | = | -1 |

| 2 4 11 -8 | | c3 | | -1 |

| -15 7 22 -14 | | -2 |

R2 = R2 - 6R1

R3 = R3 - 2R1

R4 = R4 + 15R1

| 1 -4 -9 -4 | | c1 | | -2 |

| 0 27 59 25 | x | c2 | = | 11 |

| 0 12 29 -16 | | c3 | | 3 |

| 0 -23 67 -59 | | -32 |

R4 = R4 + 23R2

| 1 -4 -9 -4 | | c1 | | -2 |

| 0 27 59 25 | x | c2 | = | 11 |

| 0 12 29 -16 | | c3 | | 3 |

| 0 0 174 -294 | | 225 |

R3 = R3 - (12/27)R2

R4 = (1/174)R4

| 1 -4 -9 -4 | | c1 | | -2 |

| 0 27 59 25 | x | c2 | = | 11 |

| 0 0 -1 22/3 | | c3 | | -13/3 |

| 0 0 1 -98/87 | | 25/58 |

R1 = R1 + 4R3

R2 = R2 - 59R3

R4 = R4 + (98/87)R3

| 1 0 -13 -10/3 | | c1 | | 21/29 |

| 0 27 0 -2119/87 | x | c2 | = | 2238/87 |

| 0 0 1 -98/87 | | c3 | | 25/58 |

| 0 0 0 1390/2391 | | 1009/2391 |

R1 = R1 + (13/1390)R4

R2 = (1/27)R2

R3 = R3 + (98/1390)R4

| 1

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The number of ski lift rides at which both companies charge the same amount for a day of skiing is 24 lift rides.

Let's represent the total cost for a day of skiing at the first ski lodge as C1 and the total cost at the second ski lodge as C2. The total cost at the first ski lodge can be calculated as $26 (pass) + $1.50 (ski lift rides), and the total cost at the second ski lodge is $32 (pass) + $1.25 (ski lift rides). To find the number of ski lift rides where both companies charge the same amount, we need to set C1 equal to C2 and solve for the variable. By equating the two expressions, we get:

26 + 1.50x = 32 + 1.25x,

where x represents the number of ski lift rides. Simplifying the equation, we have:

0.25x = 6,

x = 24.

Therefore, the number of ski lift rides at which both companies charge the same amount for a day of skiing is 24 lift rides. The correct option is (d).

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Answer:

Option (D). 110°

Step-by-step explanation:

Since EB and AD are diameter,

\(m(\widehat{ECB})\) = \(m(\widehat{ACD})\) = 180°

\(m(\widehat{ECB})=m(\widehat{EDC})+m(\widehat{BC})\) = 180° -------(1)

And \(m(\widehat{ACD})=m(\widehat{AB})+m(\widehat{BCD})\)

180° = 40° + \(m(\widehat{BCD})\)

\(m(\widehat{BCD})\) = 140°

Since, \(m(\widehat{BCD})=m(\widehat{BC})+m(\widehat{CD})\)

\(2m(\widehat{BC})\) = 140° [Given \(m(\widehat{BC})=m(\widehat{CD})\)]

\(m(\widehat{BC})\) = 70°

From equation (1),

\(m(\widehat{EDC}})\) = 180° - \(m(\widehat{BC})\)

\(m(\widehat{EDC}})\) = 180°- 70°

Therefore, measure of arc(EDC) = 110°

Option (D) will be the answer.

Answer:

m = slope

(x_1, y_1) = coordinates of first point in the line

(x_2, y_2) = coordinates of second point in the line

Slope describes the steepness of a line. The slope of any line remains constant along the line. The slope can also tell you information about the direction of the line on the coordinate plane. Slope can be calculated either by looking at the graph of a line or by using the coordinates of any two points on a line

Answer:

Step-by-step explanation:

Let's plug in x = 2.

f(x) = x^2

f(2) = 2^2 ... replace every x with 2

f(2) = 4

----------

Now plug in x = 3.

f(x) = x^2

f(3) = 3^2 ... replace every x with 3

f(3) = 9

-----------

And x = 5 as well.

f(x) = x^2

f(5) = 5^2 .... replace every x with 5

f(5) = 25

-----------

We see that

f(2)+f(3) = 4+9 = 13

which is not equal to f(5) = 25.

So f(2)+f(3) = f(5) is false.

------------

Another way to phrase why it doesn't work is because (2,3,5) isn't a pythagorean triple. The equation 2^2+3^2 = 5^2 is false.

If it said f(3)+f(4) = f(5), then it would be correct because 3^2+4^2 = 5^2 is a true equation.

In this instance, the three trigonometric ratios are:

Sinx = 15/17

Cosx =  8/17

Tanx = 15/8

Mathematical trigonometric functions connect the angle of a right-angled triangle to the ratios of its two side lengths.

In all areas of study that involve geometry, such as geodesy, solid mechanics, celestial mechanics, and many others, they are widely used.

Review the trigonometric ratios for sine, cosine, tangent, cotangent, secant, and cosecant.

So, the 3 trigonometric ratios in the given situation would be:

Sinx = O/H = 15/17

Cosx = A/H = 8/17

Tanx = O/A = 15/8

Therefore, in this instance, the three trigonometric ratios are:

Sinx = 15/17

Cosx =  8/17

Tanx = 15/8

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Step-by-step explanation:

So what type of maths help do you want

Answer:

Step-by-step explanation:

You meant x^2, right?

We get the graph of g(x) through two transformations of the graph of f(x):  

1.  Reflect the graph of f(x) about the x-axis.

2. Translate the graph obtained in (1) 2 units down.

The probability of drawing a seven and then a four when randomly drawing two cards without replacement is 0.0045 or approximately 0.45%.

The probability of drawing a seven and then a four when randomly drawing two cards without replacement can be calculated using the following steps:

First, we need to determine the total number of possible outcomes when drawing two cards from a standard deck of 52 cards without replacement. This can be found using the combination formula:

C(52,2) = 52! / (2! * (52-2)!) = 1,326

Next, we need to determine the number of favorable outcomes where we draw a seven and then a four.

There are four sevens and four fours in a deck of 52 cards, so the probability of drawing a seven on the first draw is 4/52. Since we are not replacing the card, there are now 51 cards left in the deck, and three of them are fours. Therefore, the probability of drawing a four on the second draw is 3/51.

The probability of drawing a seven and then a four is the product of the probabilities of drawing a seven on the first draw and a four on the second draw:

P(seven and then four) = (4/52) * (3/51) = 0.0045 or approximately 0.45%.

Therefore, the probability of drawing a seven and then a four when without replacement is 0.0045 or approximately 0.45%.

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The ordered pair that is on the function y=f(2x+1)+3 is (-3/2, 6)

Here we know that for the function:

y = f(x)

And we know that the point (-2, 3) belongs to the function, this means that:

f(-2)= 3

Now we want to find a point on the function:

f(2x + 1) + 3

If we find x such that:

2x + 1 = -2

2x = -3

x = -3/2

Now we can evaluate the function in that value of x to get:

y = f(2*-3/2 + 1) + 3

y = f(-2) + 3

y = 3 + 3

y = 6

Then we have the point (-3/2, 6) on the function.

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Answer:

h = \(\frac{2A}{b}\)

Step-by-step explanation:

A = \(\frac{1}{2}\) bh ( multiply both sides by 2 to clear the fraction )

2A = bh ( isolate h by dividing both sides by b )

\(\frac{2A}{b}\) = h

The total amount of water supplied per hour inside a circle of radius 14 is approximately79.90 ft^3 per hour, and the total amount of water that goes through the sprinkler per hour is approximately  2π ft^3 per hour. As R approaches infinity, the total amount of water supplied per hour approaches  2 ft^3 per hour.

To find the total amount of water supplied per hour inside of a circle of radius 14, we need to integrate the function e^(-r) over the region of the circle total amount of water = ∫∫ e^(-r) dA

where the integration is over the circular region of radius 14, and dA is the differential area element.

Using polar coordinates, we can write dA = r dr dθ, and the limits of integration are 0 ≤ r ≤ 14 and 0 ≤ θ ≤ 2π. Substituting these values, we get:

total amount of water = ∫(0 to 2π) ∫(0 to 14) e^(-r) r dr dθ

Integrating with respect to r first, we get:

total amount of water = ∫(0 to 2π) [-e^(-r)](0 to 14) dθ

total amount of water = ∫(0 to 2π) (1 - e^(-14)) dθ

total amount of water = (1 - e^(-14)) ∫(0 to 2π) dθ

total amount of water = 2π(1 - e^(-14))

Thus, the total amount of water supplied per hour inside of a circle of radius 14 is approximately 79.90 ft^3 per hour.

To find the total amount of water that goes through the sprinkler per hour, we need to integrate the function e^(-r) over the entire plane:

total amount of water = ∫∫ e^(-r) dA

where the integration is over the entire plane, and dA is the differential area element.

Using polar coordinates, we can write dA = r dr dθ, and the limits of integration are 0 ≤ r ≤ ∞ and 0 ≤ θ ≤ 2π. Substituting these values, we get:

total amount of water = ∫(0 to 2π) ∫(0 to ∞) e^(-r) r dr dθ

Integrating with respect to r first, we get:

total amount of water = ∫(0 to 2π) [-e^(-r)](0 to ∞) dθ

total amount of water = ∫(0 to 2π) (1) dθ

total amount of water = 2π

Thus, the total amount of water that goes through the sprinkler per hour is exactly 2π ft^3 per hour.

To calculate the total amount of water supplied per hour inside a circle of radius R, then let R → ∞, we can use the result from part B and multiply it by the ratio of the areas of the two circles:

total amount of water = (total amount of water inside circle of radius R) × (area of circle of radius R)/(area of entire plane)

total amount of water = (2πR^2(1-e^(-R))) / (πR^2)

total amount of water = 2(1-e^(-R))

Now we can let R → ∞:

total amount of water = 2

Thus, the total amount of water supplied per hour inside a circle of infinite radius is exactly 2 ft^3 per hour.

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--The given question is incomplete, the complete question is given

"A sprinkler distributes water in a circular pattern, supplying water to a depth of e^-r feet per hour at a distance of r feet from the sprinkler. A. What is the total amount of water supplied per hour inside of a circle of radius 14? ft^3 per hour B. What is the total amount of water that goes through the sprinkler per hour? ft^3 per hour Calculate the total amount of water supplied per hour inside a circle of radius R, then let R rightarrow infinity."--

Answer:

1. 3.9

2. 0.7

3. 2.2

4. 9.8

5. 4.5

6. 8.1

7. 7.7

8. 4.4

9. 4.3

10. 1.2

Step-by-step explanation:

Hope it helps

Answer:

A, B, F

Step-by-step explanation:

Divide both sides of -4x<20 by 4, and we have A

Multiply both sides of -4x<20 by -1, since -1 is a negative number, we reverse the inequality, and we have B

Multiply both sides of -x<5 (A) by -1, since -1 is a negative number, we reverse the inequality, and we have F

The probability that one random student participated in swimming is 1/90.

What is probability ?

The area of mathematics known as probability explores potential outcomes of events, along with the likelihoods and distributions of those occurrences. Simply put, probability is the likelihood that something will occur.

                         We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics describes the examination of events subject to probability.

Probability = Number of favorable outcomes / Number of total outcomes.

Number of favorable outcomes = 1

Number of total outcomes = 90

So,

Probability = 1/90

Hence, the probability that one random student participated in swimming is 1/90.

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Answer:

19 pounds of apple was shared and 3 pounds of apple were left to be shared for the students

A

Answer:

D. 22

Step-by-step explanation:

We're looking for the sum of 19 pounds and 3 pounds. The teacher gave out 19 pounds of apples. After giving them out, they had 3 pounds left of the total. To find the total, we need to add those amounts:

19 + 3 = 22

We can check our answer by doing this:

22 - 19 = 3

As you can see, if you had 22 pounds of apples and gave out 19 pounds, you are left with 3 pounds. This is the amount left, as mentioned in the problem. The answer is D.