Samantha is told that sin (O) = and tan (0)<0, and was asked to determine the value of cos (©).


• She uses the Pythagorean identity and defines it to be sin() + cos2 ( 0 )= 1.


• She substitutes į into the equation for sin (0)


• She then looks at values of sin ( ) and tan () and says that the only quadrant in which sin() is positive and


tan() is negative is the first quadrant.


Samantha determines that the answer is


cos () =


(21)

Answer:

10. A, Increases

11. A, Direct

Step-by-step explanation:

Wavelength and frequency are two such characteristics. The relationship between wavelength and frequency is that the frequency of a wave multiplied by its wavelength gives the speed of the wave

Pls can I have brainliest?

Answer:

10

Step-by-step explanation:

To  find,

HCF of 50 & 70 using Euclid's Division Algorithm.

Solution,

HCF(50 & 70) --  70 = 50 × 1 + 20.

                           50 = 20 × 2 + 10

                           20 = 10 × 2 + 0.

Therefore their HCF is 10.

Answer:

10

Step-by-step explanation:

According to Euclid's Algorithm, c = dq + r ,  0 ≤ r < d  (where r is the remainder)

As 70 > 50, c = 70 and d = 50

Substituting values of c and d:

   70 = (50 x 1) + 20

⇒ 50 = (20 x 2) + 10

⇒ 20 = (10 x 2) + 0

Therefore, the HCF is 10

Answer:

Add 1 unit to the X coordinates and Y coordinates for each new pair.

step-by-step explanation:

X: 10 + 1 = 11 + 1 = 12

Y: 20 + 1 = 21 + 1 = 22

Answer:

w/2 = 7.5/5

3kg

Step-by-step explanation:

Remaining question below:

Which proportion could Maddy use to model this situation?

a. w/2 = 7.5/5

b. w/7.5 = 5/2

Solve the proportion to determine the weight of a 2 liter jug.

_____kg

5 liters jug of sport drink weighs 7.5kg

2 liters jug of sport drink will weigh x kg

Find w

Ratio of weight to volume

7.5kg : 5liters=7.5/5

wkg : 2 liters=w/2

Equates the ratio

7.5 / 5 = w / 2

Cross product

7.5*2=5*w

15=5w

Divide both sides by 5

3=w

w=3kg

Therefore, weight of the 2liters jug of sport drink is 3kg

Answer:

The answer is 3kg!

Step-by-step explanation:

The standard form of the equation of a line perpendicular to the line (3x + 6y = 5) and passing through the point (1, 3) is (2x - y = -1)

To determine the equation of a line perpendicular to the line (3x + 6y = 5) and passing through the point (1, 3), we can follow these steps:

1. Obtain the slope of the provided line.

To do this, we rearrange the equation (3x + 6y = 5) into slope-intercept form (y = mx + b):

6y = -3x + 5

y =\(-\frac{1}{2}x + \frac{5}{6}\)

The slope of the line is the coefficient of x, which is \(\(-\frac{1}{2}\)\).

2. Determine the slope of the line perpendicular to the provided line.

The slope of a line perpendicular to another line is the negative reciprocal of the slope of the provided line.

So, the slope of the perpendicular line is \(\(\frac{2}{1}\)\) or simply 2.

3. Use the slope and the provided point to obtain the equation of the perpendicular line.

We can use the point-slope form of a line to determine the equation:

y - y1 = m(x - x1)

where x1, y1 is the provided point and m is the slope.

Substituting the provided point (1, 3) and the slope 2 into the equation, we have:

y - 3 = 2(x - 1)

4. Convert the equation to standard form.

To convert the equation to standard form, we expand the expression:

y - 3 = 2x - 2

2x - y = -1

Rearranging the equation in the form (Ax + By = C), where A, B, and C are constants, we obtain the standard form:

2x - y = -1

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Let's denote this probability as p, where p represents the probability of a single calculator failing. Therefore, the probability of both calculators failing is given by \(p^2\).

If the failure rate of the second calculator is the same and independent of the first, we can assume that the probability of failure for each calculator remains constant. To determine the probability of both calculators failing, we need to multiply the probabilities of each calculator failing independently. Since the events are independent, we can multiply the individual probabilities together.

Probability of both calculators failing = Probability of first calculator failing * Probability of second calculator failing

= p * p

= \(p^2\)

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Answer:

-168

Step-by-step explanation:

if this is right but hopefully

If we multiply both numerator and denominator of the first ratio by 3, we will get the second ratio, thus, these are equivalent.

For any ratio:

a/b

If we multiply both numerator and denominator by the same real number, we will get an equivalent ratio.

In this case, we can start with the smaller of the two ratios:

1/6.

Now we can multiply both numerator and denominator by 3, then we will get:

(3*1)/(3*6) = 3/18

So yes, the ratios 1/6 and 3/18 are equivalent.

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The mean for grouped data can be calculated when data has been grouped into class intervals in a frequency distribution. (Option A)

When data has been grouped into class intervals, it is not possible to calculate the exact mean of the data. Instead, we use the midpoint of each class interval as a representative value for that interval. Then, we calculate the weighted average of these midpoints to find the mean for grouped data.

Options C and D, the variance and standard deviation, respectively, cannot be directly computed from grouped data. However, we can estimate them using the assumed normal distribution of the data within each class interval and the mean for grouped data.

Therefore, the correct answer is option A: the mean for grouped data can be calculated when data has been grouped into class intervals in a frequency distribution.

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Answer:

LP = 18

Step-by-step explanation:

Given that,

In ΔLPN,

LQ = 6, LM = 11 and MN = 22

We need to find the length of LP.

As QM ║PN, let QP = x

\(\dfrac{LQ}{LP}=\dfrac{LM}{LN}\\\\\dfrac{6}{6+x}=\dfrac{11}{11+22}\\\\\dfrac{6}{6+x}=\dfrac{11}{33}\\\\198=66+11x\\\\198-66=11x\\\\132=11x\\\\x=12\)

LP = 6+x

= 6+ 12

= 18

Hence, the length of LP is 18.

The slope of a line parallel to the graph of -7x+y=-6 is 7. The slope of a line perpendicular to the graph of -7x+y=-6 is -1/7. The slope of a line can be any real number.

The slope-intercept form of a linear equation is given by y = mx + b, where m is the slope of the line.

To determine the slope of a line parallel or perpendicular to a given line, we need to find the slope of the given line.

For the equation -7x + y = -6, we can rearrange it to the slope-intercept form:

The slope of this line is 7.

The slope of a line parallel to this line will be the same, which is 7.

The slope of a line perpendicular to this line is the negative reciprocal of the slope of the given line. The negative reciprocal of 7 is -1/7.

The slope of a line can be any real number, as there are no specific conditions given.

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If Janice walks at the same speed for 110 minutes, she will cover approximately 9.2 miles.

Given that Janice walks 5 miles in 60 minutes, we can calculate her speed using the formula:

Speed = Distance / Time

Substituting the values we know, we have:

Speed = 5 miles / 60 minutes

Now, we can use this speed to determine the distance Janice will walk in 110 minutes. We'll use the same formula, rearranged to solve for distance:

Distance = Speed × Time

Substituting the values we have:

Distance = (5 miles / 60 minutes) × 110 minutes

To simplify this calculation, we can first simplify the fraction:

Distance = (1/12) miles per minute × 110 minutes

Now, we can cancel out the minutes:

Distance = (1/12) miles per minute × 110

The minutes in the numerator and denominator cancel out, leaving us with:

Distance = (1/12) × 110 miles

Calculating this expression:

Distance = 110/12 miles

Rounding this answer to the nearest tenth of a mile, we get:

Distance ≈ 9.2 miles

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Answer:

The first term is -3 and the common difference is 6

Step-by-step explanation:

Recall that the nth term of an arithmetic progression AP is given as

Tn = a + (n - 1)d

where

Tn is the nth term

a is the first term and

d is the common difference while n is the number of terms

Given that the 18th term of Arithmetic progression is 99 and 29th term is 165 then

substituting the given values into the formula

a + 17d = 99

a + 28d = 165

solve both equations simultaneously

11d = 165 - 99

11d = 66

d = 66/11

= 6

recall that a + 17d = 99

a + 17(6) = 99

a + 102 = 99

a = 99 - 102

= -3

hence the first term is -3 and the common difference is 6

Answer:

+_6

Step-by-step explanation:

let the possible values be x.

x÷4=9÷x

from that you will get x^2=36

introduce a square root to both sides and the answer is +_6

Answer:

35.23

Step-by-step explanation:

I'm going to assume this is a right triangle so ill use the Pythagorean thm

Pythagorean Formula: a² + b² = c²

20² + 29² = c²

400 + 841 = c²

1241 = c²

\(\sqrt{1241} =\sqrt{c^2}\)

c = 35.23

Answer:

Step-by-step explanation:

fixed cost = 100

variable cost = 13

soooo....

cost =  (13x + 100)/x

the questions wants to know  when cost  < 22.50

22.5 > (13x+100)/x

look at graph attached ;)

it looks to me like it's at 11

22.5 > (13(11) + 100) / 11

22.5 > 22.09

try 10

22.5 > (13(10) +100)/10

22.5  > 23   not true  so yes.. 11 is when the cost goes below 22.50

Answer:

Y’all the correct answer is 10

3x-y=-9

Step-by-step explanation:

Answer: 3x - y = - 9

Step-by-step explanation:

Re-write the equation in the following form:

3x + 9 = y

Take the y to LHS:

3x + 9 - y = 0

Now, take the 9 to the RHS:

3x - y = -9. This is your answer.

The value of angle x in decimal place is 57.8°.

A decimal number's digits are assigned a place value according to a chart that displays decimal place values. A digit in a number's place value is, as far as we are aware, its numerical value. The correct placement of each digit in a decimal number is therefore determined using decimal place value charts, just like with other place value diagrams. In this chart, the place values of the digits before and after the decimal point are shown.

Draw the altitude of the triangle

We know that

sinθ =  Opposite / Hypotenuse

sin 38° = y/11

y = 11 sin 38°

y = 6.77

sin(x) = y/8

sin(x) = 6.77/8

sin(x) = 0.84625

sin(x) = 57.8°

Thus, the value of angle x in decimal place is 57.8°.

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The unit conversion for the given values are explained below.

Unit conversion is the process of changing a quantity's measurement between different units, frequently using multiplicative conversion factors.

The following measurements: length, weight, capacity, temperature, and speed are all measured in units.

Some basic unit conversions are-

There are two methods to convert the units

The unit conversion for the following factors are-

i) 1 mm = _ m

Here, conversion is from smaller to larger. So, divide by conversion factor.

  1 mm = (1/100)m

ii) _ mm = 1 m

Here, conversion is from larger to smaller. So, multiply with conversion factor.

  1000 mm = 1 m

iii) 1 cm = _ m

Here, conversion is from smaller to larger. So, divide by conversion factor.

   1 cm = (1/100)m

iv) _ cm = 1 m

Here, conversion is from larger to smaller. So, multiply with conversion factor.

  100 cm = 1 m

v) 1 km = _m

Here, conversion is from larger to smaller. So, multiply with conversion factor.

  1 km = 1000 m.

vi) _ km = 1 m

Here, conversion is from smaller to larger. So, divide by conversion factor.

(1/1000) km = 1 m.

vii) 1 cm = _mm

Here, conversion is from larger to smaller. So, multiply with conversion factor.

   1 cm = 10 mm

viii) _cm = 1 mm

Here, conversion is from smaller to larger. So, divide by conversion factor.

   (1/10) cm = 1 mm.

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Answer:

Mr. white started with 45 dollars, he spent 9 dollars on a wallet and was left with 36, he then spent 15 dollars on a tie and was left with 21 dollars.

Step-by-step explanation:

45 * 0.8 = 36
he started with 45 dollars
30 * 0.7 = 21, in the end he was left with 21 dollars

The side lengths of the right triangle are: shorter leg = 7 cm, longer leg = 24 cm, and hypotenuse = 25 cm.

Let's denote the length of the shorter leg as x.

According to the information:

The length of the longer leg is 3 cm more than three times the length of the shorter leg, which can be expressed as 3x + 3.

The length of the hypotenuse is 4 cm more than three times the length of the shorter leg, which can be expressed as 3x + 4.

In a right triangle, the Pythagorean theorem states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. Using this, we can set up the equation:

(x)²+ (3x + 3)² = (3x + 4)²

Expanding and simplifying the equation:

x² + (9x² + 18x + 9) = (9x² + 24x + 16)

Combining like terms:

10x² + 18x + 9 = 9x² + 24x + 16

Moving all terms to one side of the equation:

10x² + 18x + 9 - 9x² - 24x - 16 = 0

Simplifying:

x² - 6x - 7 = 0

Now, we can solve this quadratic equation by factoring or using the quadratic formula. Factoring, we have:

(x - 7)(x + 1) = 0

Setting each factor to zero:

x - 7 = 0   or   x + 1 = 0

Solving for x:

x = 7   or   x = -1

Since lengths cannot be negative, we discard the solution x = -1.

Therefore, the length of the shorter leg is x = 7 cm.

Using this value, we can find the length of the longer leg and the hypotenuse:

Length of the longer leg = 3x + 3 = 3(7) + 3 = 21 + 3 = 24 cm

Length of the hypotenuse = 3x + 4 = 3(7) + 4 = 21 + 4 = 25 cm

So, the side lengths of the triangle are:

Shorter leg = 7 cm

Longer leg = 24 cm

Hypotenuse = 25 cm

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To find the number of countries that have both a population density of fewer than 100 per km^2 and a medium population in North America, we need to use the given frequency of 0.174.

1. Start by multiplying the frequency (0.174) by the total number of countries in North America.
2. Let's assume the total number of countries in North America is "x".
3. Multiply x by 0.174 to find the number of countries with both a population density of fewer than 100 per km^2 and a medium population.
4. The result will give you the number of countries that satisfy the given conditions.

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Answer:

Step-by-step explanation:

Write 1 million first 1 , 000 , 000

Now add the 80                    80

Total                       1,000,080

It's always a good idea to break a problem down into smaller parts. It's easier to handle that way.                              

It will take 19 hours by the 4 hoses to fill the swimming pool with a capacity of 22800-gallon.

Capacity is the maximum volume an object can hold while Volume is the amount of liquid or any substance present in an object.

It is given that:

Each hose is filling at a rate of 300 gallons per hour.

So, 4 hoses will fill with a rate of 300*4 = 1200 gallons per hour

The capacity of the swimming pool = 22800-gallon.

So, the number of hours hoses will take to fill the pool = 22800/1200

The number of hours hoses will take to fill the pool = 19 hours.

Therefore, It will take 19 hours to fill the swimming pool with a capacity of 22800-gallon.

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Question: A 22,800-gallon swimming pool is being filled by four hoses. water flows through each hose at a rate of 300 gallons per hour. How many hours will it take to fill the pool?

Answer: It would take 19 hours to fill the swimming pool.

Explanation: If the total volume is 22,800, with each hose at the rate of 300 gallons per hour, then the total rate of all four hoses would be 1200 gallons per hour (4 x 300 = 1200).

22,800 / 1200 = 19 hours.

For the budget constraint X + Y = 12, there is no optimal bundle that maximizes the utility function U(X, Y).

A) To find the optimal bundle, we need to maximize the utility function U(X, Y) subject to the budget constraint 3X + 5Y = 60.

Let's solve this problem using the Lagrange multiplier method:

1. Set up the Lagrangian function:

L(X, Y, λ) = -(X - 7)^2 - (Y - 7)^2 + λ(3X + 5Y - 60)

2. Find the first-order conditions:

∂L/∂X = -2(X - 7) + 3λ = 0

∂L/∂Y = -2(Y - 7) + 5λ = 0

∂L/∂λ = 3X + 5Y - 60 = 0

3. Solve the system of equations:

-2X + 14 + 3λ = 0    --(1)

-2Y + 14 + 5λ = 0    --(2)

3X + 5Y - 60 = 0     --(3)

From equations (1) and (2), we can solve for X and Y:

X = (14 - 3λ) / 2

Y = (14 - 5λ) / 2

Substituting these expressions into equation (3), we can solve for λ:

3(14 - 3λ) / 2 + 5(14 - 5λ) / 2 - 60 = 0

Simplifying and solving the equation, we find λ = -4.

Substituting λ = -4 back into X and Y expressions:

X = (14 - 3(-4)) / 2 = 13

Y = (14 - 5(-4)) / 2 = 9

Therefore, the optimal bundle is X = 13 and Y = 9.

B) To find the optimal bundle for the budget constraint X + Y = 12, we can rewrite it as Y = 12 - X.

Substituting this into the utility function, we have U(X) = -(X - 7)^2 - (12 - X - 7)^2.

To find the optimal bundle, we need to find the maximum value of U(X) by taking the derivative with respect to X and setting it equal to zero:

dU/dX = -2(X - 7) + 2(12 - X - 7) = 0

Simplifying the equation, we find:

-2X + 14 + 2X - 40 = 0

-26 = 0

Since -26 ≠ 0, there is no value of X that satisfies the first-order condition for optimization.

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