Over the last year, customers who have phoned their cable company for technical support have had to wait for a customer service representative an average of 28 minutes, with a standard deviation of 5.5 minutes. Company records have shown wait times to be normally distributed. What is the likelihood that a person phones the cable company and waits between 10 to 20 minutes for service?

Answers

Answer 1

The probability that a person phones the cable company and waits between 10 to 20 minutes for service is approximately 0.0729, or about 7.29%.

What is the mean and standard deviation?

The standard deviation is a summary measure of the differences of each observation from the mean. If the differences themselves were added up, the positive would exactly balance the negative and so their sum would be zero. Consequently, the squares of the differences are added.

We can start by standardizing the values using the z-score formula:

z = (x - μ) / σ

where:

x = the wait time in minutes

μ = the population mean (average wait time of 28 minutes)

σ = the population standard deviation (5.5 minutes)

For x = 10 minutes:

z = (10 - 28) / 5.5 = -3.27

For x = 20 minutes:

z = (20 - 28) / 5.5 = -1.45

Next, we can use a standard normal distribution table (or a calculator or software) to find the area under the standard normal curve between these two z-scores.

Using a standard normal distribution table, we can find that the area to the left of z = -1.45 is 0.0735, and the area to the left of z = -3.27 is 0.0006. Therefore, the area between z = -3.27 and z = -1.45 is:

0.0735 - 0.0006 = 0.0729

Hence, the probability that a person phones the cable company and waits between 10 to 20 minutes for service is approximately 0.0729, or about 7.29%.

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Related Questions

What is the perimeter of the triangle?

Answers

Answer:

40 units

Step-by-step explanation:

a = 8

b = 15

To find c, we can use the formula: [tex]a^{2} +b^{2} =c^{2}[/tex]

[tex]8^{2} +15^{2} =x^{2}[/tex]

64 + 225 = c^2

289 = c^2

c = 17

a + b + c = perimeter

8 + 15 + 17 = 40

Answer:

  40 units

Step-by-step explanation:

You want the perimeter of the triangle shown in the graph.

Dimensions

You can count the grid squares to find the horizontal and vertical dimensions of the triangle. You find they are 8 units and 15 units, respectively.

The length of the slant side is the hypotenuse of a right triangle with sides 8 and 15. If you don't recognize this {8, 15, 17} Pythagorean triple, you can find the hypotenuse using the Pythagorean theorem:

  c² = a² +b²

  c² = 8² +15² = 64 +225 = 289

  c = √289 = 17

The long side of the triangle is 17 units.

Perimeter

The perimeter of the triangle is the sum of the lengths of its sides:

  P = 8 + 15 + 17 = 40

The perimeter is 40 units.

__

Additional comment

A "Pythagorean triple" is a set of three integer side lengths that form a right triangle. The triple is "primitive" if the numbers have no common factor. There are a few Pythagorean triples that regularly show up in algebra, trig, and geometry problems. Some of them are ...

  {3, 4, 5}, {5, 12, 13}, {7, 24, 25}, {8, 15, 17}, {9, 40, 41}

You will also see multiples of these, for example, 2·{3, 4, 5} = {6, 8, 10}.

The smallest is {3, 4, 5}, and it is the only set that is an arithmetic sequence (has constant differences between lengths). In every case, the sum of the numbers is even. (A right triangle cannot have integer side lengths and an odd perimeter value.)

1. You go to the ice cream shop with your friends and you can choose an ice cream, a topping
and sprinkles. How many different sundaes can you make when you order one flavor of ice
cream, one topping and one color of sprinkles from the chart below? Show all possible
outcomes in a tree diagram.
Ice Cream
Chocolate
Vanilla
Strawberry
Topping
Fudge
Marshmallow
Sprinkles
Chocolate
Rainbow
How many sample spaces are there? HINT: How many possible combinations?
b. P (Chocolate, Fudge, Rainbow)

Answers

Answer:

Step-by-step explanation:

Answer:

You can make 12 possible sundaes with these toppings.

Step-by-step explanation:

Chocolate, Vanilla, and Strawberry all have 4 possible outcomes:

1. Fudge & Chocolate Sprinkles

2. Fudge & Rainbow Sprinkles

3. Marshmallow & Chocolate Sprinkles

4. Marshmallow & Rainbow Sprinkles

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

4 x 3 will equal 12, the total possible sundaes you can make with these toppings and ice cream flavors.

An economy is operating with output $400 billion above its natural level, and fiscal policymakers want to close this expansionary gap. The central bank agrees to adjust the money supply to hold the interest rate constant, so there is no crowding out. The marginal propensity to consume is 3/4, and the price level is completely fixed in the short run.

to close the expansionary gap, the government would need to increase or decrease spending by $ billion.

Answers

Hence, to close the expansionary gap, the government would need to decrease spending by $100 billion.

To close the expansionary gap, the government would need to decrease spending by $100 billion.

The formula to calculate the change in equilibrium output due to a change in government spending is:

∆Y = (∆G / (1 - MPC))

Where:

∆Y = change in equilibrium output

∆G = change in government spending

MPC = marginal propensity to consume

Here, the output is $400 billion above its natural level, and the central bank agrees to adjust the money supply to hold the interest rate constant, so there is no crowding out. Therefore, we can assume that the change in government spending (∆G) would have a one-to-one effect on the equilibrium output (∆Y).

Given that MPC = 3/4, we can plug in the values into the formula:

400 = (∆G / (1 - 3/4))

∆G = (1 - 3/4) * 400

∆G = (1/4) * 400

∆G = 100

Hence, to close the expansionary gap, the government would need to decrease spending by $100 billion.

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^4√p7
in exponential form.

Answers

Answer:1111

Step-by-step explanation:

Problem 7: Find the surface area and round to the nearest tenth.

Answers

Answer:

1629.24m

Step-by-step explanation:

starting with the easy ones

1) Rectangle 1:

Surface area of rectangle=Length x width

SAR= 24x21

= 504m

2) Rectangle 2:

SAR= 19x21

=399

3) Rectangle 3

SAR= 21x8

=168

4) Rectangle 4:

SAR= 21x11

=231

*because the top and bottom are trapeziums the formular for it is

A=1/2(a+b)h

although those trapeziums don't have h(Height)

it needs to be broken down into two triangles and a rectangle. to find the height*

5) side/height of triangle A:

formula: C squared= a squared + b squared

in this case we already have C and A. meaning we have to rearrange the formula to:

x = c^2 - a^2

x = 8^2 - 2.5^2

x = sqrt 57.75

x = 7.61

6) Trapezium

SA= 1/2(a+b)h

SA= 1/2(19+24)7.61

=163.62

7) add all surface area together

which should equal 1629.24m

The sum of 2 vector forces is <5, -3>. What is the magnitude of the resulting force?

Answers

According to the question the magnitude of the resulting force is 5.83.

What is magnitude?

Magnitude is a measure of the size or intensity of a physical quantity. It is an expression of how large or small a quantity is in comparison to a reference value. Magnitude is typically used in physics and astronomy, but it can also be used in other areas such as engineering and seismology. Magnitude is not an absolute measurement; rather, it is a relative measure of how much larger or smaller one quantity is compared to another. For example, the magnitude of a star's brightness is a measure of how much brighter it is compared to other stars.

The magnitude of the resulting force can be calculated using the Pythagorean theorem. The formula for calculating the magnitude of a vector is:
[tex]\sqrt[]{(x2 + y2)}[/tex]
In this case, x = 5 and y = -3, which gives us:
[tex]\sqrt{(52 + (-3)2)}[/tex] = [tex]\sqrt{(25 + 9)}[/tex] = √[tex]\sqrt{(34)}[/tex] = 5.83.
Therefore, the magnitude of the resulting force is 5.83.

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Help Please...
You have 67 coins consisting of half-dollars and quarters. The number of quarters is 7 more than three times the number of half-dollars.
How many quarters do you have?
How many half -dollars do you have?

Answers

There are 52 quarters and 15 half-dollars

To solve this problem

Let's represent the number of half-dollars as "x" and the number of quarters as "y".

From the problem statement, we know that:

x + y = 67 (because there are a total of 67 coins)

y = 3x + 7 (because the number of quarters is 7 more than three times the number of half-dollars)

We can use substitution to solve for x:

x + (3x + 7) = 67

4x + 7 = 67

4x = 60

x = 15

So there are 15 half-dollars. We can use this to find the number of quarters:

y = 3x + 7

y = 3(15) + 7

y = 52

So there are 52 quarters.

Therefore, there are 52 quarters and 15 half-dollars.

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Triangle PQR is rotated 180 degrees clockwise about the origin to produce the image Triangle P’Q’R’. Which of the following statements is TRUE abóyate Triangle P’Q’R’.

Answers

Answer:

Step-by-step explanation:

We get triangle PQR by plotting the point P (1, 4), Q (3, 1), R (2, -1) on the graph paper when rotated through 180° about the origin. The new position of the point is: P (1, 4) → P' (-1, -4) Q (3, 1) → Q' (-3, -1) R (2, -1) → R' (-2, 1) Thus, the new position of ∆PQR is ∆P’Q’R’.

Find an equation of the osculating plane and an equation of the normal
plane of the curve x = sin 2t, y = t, z = cos 2t at the point (0, π, 1).

Answers

The equation of the normal plane is 4y = 4π, or equivalently, y = π.

What is osculating plane?

The word osculate comes from the Latin osculatus, which is a past participle of the verb osculari, which means "to kiss." Thus, an osculating plane is one that "kisses" a submanifold.

To find the osculating plane and normal plane of the curve x = sin 2t, y = t, z = cos 2t at the point (0, π, 1), we need to follow these steps:

Find the first and second derivatives of the curve with respect to t.Evaluate the derivatives at t = π to get the velocity, acceleration, and curvature vectors at the point (0, π, 1).Use the velocity and acceleration vectors to find the normal vector of the osculating plane.Use the normal vector and the point (0, π, 1) to find the equation of the osculating plane.Use the curvature vector to find the normal vector of the normal plane.Use the normal vector and the point (0, π, 1) to find the equation of the normal plane.

Step 1: Find the first and second derivatives of the curve with respect to t.

x' = 2cos2t

y' = 1

z' = -2sin2t

x'' = -4sin2t

y'' = 0

z'' = -4cos2t

Step 2: Evaluate the derivatives at t = π.

x'(π) = 2cos2π = 2

y'(π) = 1

z'(π) = -2sin2π = 0

x''(π) = -4sin2π = 0

y''(π) = 0

z''(π) = -4cos2π = -4

So the velocity vector at the point (0, π, 1) is v = ⟨2, 1, 0⟩, the acceleration vector is a = ⟨0, 0, -4⟩, and the curvature vector is κv = ⟨0, 4, 0⟩.

Step 3: Use the velocity and acceleration vectors to find the normal vector of the osculating plane.

The normal vector of the osculating plane is given by the cross product of the velocity and acceleration vectors:

n = v × a = ⟨2, 1, 0⟩ × ⟨0, 0, -4⟩ = ⟨4, 0, 0⟩

Step 4: Use the normal vector and the point (0, π, 1) to find the equation of the osculating plane.

The equation of the osculating plane is given by:

4(x - 0) + 0(y - π) + 0(z - 1) = 0

Simplifying, we get:

4x - 4 = 0

So the equation of the osculating plane is 4x = 4, or equivalently, x = 1.

Step 5: Use the curvature vector to find the normal vector of the normal plane.

The normal vector of the normal plane is given by the curvature vector:

n' = κv = ⟨0, 4, 0⟩

Step 6: Use the normal vector and the point (0, π, 1) to find the equation of the normal plane.

The equation of the normal plane is given by:

0(x - 0) + 4(y - π) + 0(z - 1) = 0

Simplifying, we get:

4y - 4π = 0

So, the equation of the normal plane is 4y = 4π, or equivalently, y = π.

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4. Assuming that the rectangles have whole number side lengths, why is it possible to draw two different rectangles that have an area of 30 square inches but not possible to draw two rectangles with an area of 7 square inches?​

Answers

Answer:

hm

Step-by-step explanation:

The reason why it is possible to draw two different rectangles that have an area of 30 square inches is that there are multiple pairs of whole numbers that multiply to 30. For example, a rectangle with dimensions 5 inches by 6 inches has an area of 30 square inches, and so does a rectangle with dimensions 2 inches by 15 inches.

However, the number 7 is a prime number, which means it can only be divided evenly by 1 and itself. Therefore, the only way to get an area of 7 square inches for a rectangle is by multiplying 1 and 7, which means the dimensions of the rectangle would be 1 inch by 7 inches. Since there are no other pairs of whole numbers that multiply to 7, it is not possible to draw two different rectangles with an area of 7 square inches.

Which of the numbers 0, 1, 2, 3 or 4 make the equation 8/y2 + 2 true?

Answers

None of the given numbers make the equation 8/y² + 2 true.

What is algebra?

Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas.

To solve this problem, we can substitute each of the given numbers (0, 1, 2, 3, 4) for y in the equation 8/y² + 2 and see if the equation is true.

Substituting y=0 would make the denominator of the fraction zero, which is undefined, so y=0 is not a valid choice.

Substituting y=1 would give us:

8/1² + 2 = 8 + 2 = 10

So, 1 is not the answer.

Substituting y=2 would give us:

8/2² + 2 = 8/4 + 2 = 2 + 2 = 4

So, 2 is not the answer.

Substituting y=3 would give us:

8/3² + 2 = 8/9 + 2 = 0.888 + 2 = 2.888

So, 3 is not the answer.

Substituting y=4 would give us:

8/4² + 2 = 8/16 + 2 = 0.5 + 2 = 2.5

So, 4 is not the answer.

Therefore, none of the given numbers make the equation 8/y² + 2 true.

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whats the answer to 102-38x14 divided by 7+162= help plss

Answers

Answer:

-2.5

Step-by-step explanation:

follow BIMDAS.

like my answer if you find it helpful

What’s the length of side AB?

Answers

tan = 1/√3= perpendicular/ base

1/√3 = AB / AC

AB / 6 = 1/√3

AB = 6/√3

complete the equatiotin 3 over 4 x 6 =
PLEASE HELP

Answers

Answer:

1/8

Step-by-step explanation:

If "over" refers to (4 * 6) as a whole,

[tex]\frac{3}{4*6}\\\\=\frac{3}{24}\\\\=\frac{1}{8}[/tex]

If "over" refers to division,

[tex]3 \div 4 \times 6\\= 0.75 \times 6\\= 4.5[/tex]

I would suppose it's the first one, so, ignore the second one if you haven't learnt BODMAS yet.

Hope this helps and be sure to mark this as brainliest! :)

Suppose that the functions fand g are defined as follows.
f(x)=2x-1
g(x)=√3x-5

Answers

The composite functions (f/g)(x) and (f-g)(x) are (2x-1)/√(3x-5) and (2x-1) -√(3x-5)

Calculating the composite functions (f/g)(x) and (f-g)(x)

To calculate (f/g)(x), we need to divide f(x) by g(x):

(f/g)(x) = f(x)/g(x) = (2x-1)/√(3x-5)

The domain of (f/g)(x) is the set of all x-values for which the denominator √(3x-5) is not equal to zero and non-negative

3x-5 ≥ 0, or x ≥ 5/3

Therefore, the domain of (f/g)(x) is x ≥ 5/3.

To calculate (f-g)(x), we need to subtract g(x) from f(x):

(f-g)(x) = f(x) - g(x) = (2x-1) - √(3x-5)

The domain of (f-g)(x) is the set of all x-values for which the expression inside the square root is non-negative:

3x-5 ≥ 0, or x ≥ 5/3

Therefore, the domain of (f-g)(x) is x ≥ 5/3.

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3√b in exponential form

Answers

3sqrt(b) is 3b^1/2 in exponential form.
When you want to change a square root to exponential form, simply change it to the power of 1/2. And if you want to get rid of a square root, square the whole thing.

3. How many ways can you line up 7 books on a shelf?

Answers

Answer:

There are 5040 different ways to arrange the 7 books on a shelf.

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

Use the formula for permutations:

n! = n × (n - 1) × (n - 2) × ... × 1, where n is the number of objects and ! denotes a factorial.

The number of objects is n = 7 books.

Calculate the factorial:

7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5040

Hurry please combine Leon’s results and Celia’s results to find the experimental probability of spinning a 4

Answers

The experimental probability of spinning a 4 will equals to 0.3.

How to find the experimental probability of spinning a 4?

Outcome   Tally   Frequency

1                   IIII          4

2                  III           3

3                  IIIIIIII       7

4                  IIIIII        6  

                   Total     20

The probability of spinning a 4:

= 6/20

= 3/10

= 0.3

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(a) What is the value of x? Show your work.
(b) What is the measure of angle C? Show your work.

Answers

In triangle ABC

a) The value of x = 29⁰

b) The angle c equal to 93⁰

What is a triangle?

A triangle is a closed plane figure that is formed by connecting three line segments, also known as sides, at their endpoints. The three endpoints, or vertices, where the sides of the triangle meet are not collinear. Triangles are important in mathematics and geometry because they are the simplest polygon that can exist in two-dimensional space.

According to the given information

In a triangle, the sum of all interior angles is always 180 degrees. Therefore, we can use this fact to find the value of x and angle c.

We know that:

angle a = 35⁰

angle b = 52⁰

angle c = 3(x+2)⁰

Using the fact that the sum of all interior angles in a triangle is 180 degrees, we can write:

angle a + angle b + angle c = 180

Substituting the values we know, we get:

35 + 52 + 3(x+2) = 180

Simplifying the equation, we get:

87 + 3x + 6 = 180

3x + 93 = 180

3x = 87

x = 29

Therefore, x = 29⁰

To find angle c, we can substitute the value of x into the equation we were given for angle c:

angle c = 3(x+2)

angle c = 3(29+2)

angle c = 3(31)

angle c = 93

Therefore, angle c is equal to 93⁰.

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Help corrections due in 3 hours! giving 25 points and brainlist

Answers

The value of GH in the right angle triangle, given FH and Angle FHG is 22.46 inches.

How to find the value of GH ?

Since we have the adjacent side (FH) and want to find the hypotenuse (GH), we can use the cosine function.

cos(35°) = adjacent side (FH) / hypotenuse (GH)

We know that FH = 18.4 in. So, we can write the equation as:

cos(35°) = 18.4 / GH

GH = 18.4 / cos(35°)

GH = 18.4 / 0.81915

=  22.46 inches

So, the length of GH, the hypotenuse, is approximately 22.46 inches.

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A hamster runs at a speed of 16 centimeters per second in a wheel of radius 15 centimeters.
a) What is the angular velocity of the wheel? (in radians/sec)
b) How fast will the wheel spin in revolutions per minute?

Answers

a) The angular velocity of the wheel is approximately 1.0667 radians per second. b) The wheel will spin at approximately 10.16 revolutions per minute.

What is angular velocity?

Angular velocity is a measure of how quickly an object rotates or revolves around a fixed point, such as an axis or a center of rotation. It is a vector quantity that describes the rate of change of an object's angular position with respect to time, and is usually expressed in units of radians per second (rad/s) or degrees per second (deg/s).

According to given information:

a) To find the angular velocity of the wheel, we can use the formula:

angular velocity = linear velocity / radius

In this case, the linear velocity of the hamster is 16 centimeters per second, and the radius of the wheel is 15 centimeters. So, we have:

angular velocity = 16 / 15

angular velocity = 1.0667 radians per second

Therefore, the angular velocity of the wheel is approximately 1.0667 radians per second.

b) To find the speed of the wheel in revolutions per minute, we need to convert the angular velocity from radians per second to revolutions per minute. There are 2π radians in one revolution, and 60 seconds in one minute. So, we can use the following formula:

angular velocity (in revolutions per minute) = angular velocity (in radians per second) * 60 / 2π

Plugging in the angular velocity we found in part (a), we get:

angular velocity (in revolutions per minute) = 1.0667 * 60 / 2π

angular velocity (in revolutions per minute) ≈ 10.16 revolutions per minute

Therefore, the wheel will spin at approximately 10.16 revolutions per minute.

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Find the area of a rectangle with length 4.3 cm and breadth 3.9 cm

Answers

Answer:

16.77 cm²

Step-by-step explanation:

Area of rectangle = L x W

L = 4.3 cm

Width = 3.9 cm

Let' solve

4.3 x 3.9 = 16.77 cm²

So, the area of the rectangle is 16.77 cm²

Prove: DC = 6 units
A
6 units
D
Statements
AD || BC
ZDAC ZBCA
C
?
DC BA
DC = BA
given
alternate interior angles theorem
AC AC
reflexive property of congruence
ZDCA ZBAC alternate interior angles theorem
DC = 6 units
Which step is missing?
B
O A. ADAC
OB. ADCA
O C. ADCA
Reasons
?
CPCTC
definition of congruent sides
substitution property of equality
ABCA by SAS
ABCA by ASA
ABCA by SAS

Answers

The missing step in the proof is: D. ADCA

What is the missing step and reason of the proof?

In the statements, we are given that AD || BC and ZDAC = ZBCA (alternate interior angles theorem), so we can conclude that triangle ADCA is similar to triangle BCA (by AA similarity criterion).

Therefore, we have the following proportional sides:

DC/AC = AC/BC

Given that DC = BA (given statement), we can substitute BA for DC in the proportion:

BA/AC = AC/BC

Now, we can cross-multiply to get:

BA * BC = AC²

Using the given statement that AC = AC (reflexive property of congruence), we can substitute AC for AC in the equation:

BA * BC = AC * AC

Use the definition of congruent sides to replace BA with DC:

DC * BC = AC * AC

And finally, use the substitution property of equality to replace BC with 6 units (given statement):

DC * 6 = AC * AC

From this equation, we can see that DC = 6 units, which completes the proof. Therefore, the missing step is statement D. ADCA.

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On the Y axis, we have the profit from the trucking company and on the X axis, we have the miles the truck has traveled. The company decided that they needed to start paying for a driver at a price of 0.25 cents a mile. After this change what will happen to the x and y axis/slope?

A. Y intercept will be less and X will be less
B. Y intercept will be less and X intercept will be greater
C. Y intercept will be greater and X will be greater
D. Y intercept will be greater and X will be less

Answers

Answer:

B.

Step-by-step explanation:

Answer:

B.

Step-by-step explanation:

the description is very confusing and lacks any hint about the behavior of the curve before the change.

but ok, let's assume that the curve (line ?) is in general going up. in other words, if the traveled miles go up, so does the profit.

I also don't know how they could drive the miles without paying the driver, but again, let's assume they did.

now they pay the driver. $0.25 per mile.

this has to come out of their profit.

so, the Y (profit) values all go down by 0.25.

therefore, the y-intercept is going down too.

that eliminates C. and D.

for this to be true they have to have some overhead costs that apply even if there are 0 miles traveled (which is the meaning of the y-intercept : the y-value when x = 0).

so, the line must be in a form

y = ax + b

with "b" <> 0.

and since we assumed the line to go up (positive slope), a "sinking" line means that the x-intercept (the break-even point, where the line goes from below the x-axis and therefore negative (y) profit up into positive profit) will move to the right (become greater).

because now that they have additional costs (paying the driver), it takes longer (more driven miles) to make a positive profit.

and that eliminates A, leaving B. as the right answer.

The sum of a number and three is no more than eight

Answers

Answer:5

Step-by-step explanation: hope this helps

Will mark brainliest if answer is correct

Answers

Answer:

[tex]3( {2}^{2} ) - {2}^{2} + 4 = 12[/tex]

[tex] {2}^{3} + b( {2}^{2} ) + 43(2) - 126 = 4b - 204[/tex]

[tex]4b - 32 = 12[/tex]

[tex]4b = 44[/tex]

[tex]b = 11[/tex]

For this value of b, these graphs will intersect at (2, 12). Please use your graphing calculator to confirm that this is the only point of intersection.

There is a 25% chance that a vowel is drawn from a bag of random letter tiles. what is the probability of drawing a vowel, placing it back in the bag, and then drawing a consonant

Answers

The probability of drawing a vowel, placing it back in the bag, and then drawing a consonant is 0.1875 or 18.75%.


Calculating the probability

The probability of drawing a vowel from the bag of random letter tiles is 25%. Since the tile is replaced after drawing, the probability of drawing a vowel on the second draw is also 25%.

The probability of drawing a vowel and then a consonant can be calculated by multiplying the probabilities of each event:

P(vowel and consonant) = P(vowel) x P(consonant)

= 0.25 x 0.75

= 0.1875

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Given cos A = 3/10 and tan A < 0 , find sin A .

Answers

Answer: Since we know that cos A = 3/10, we can use the Pythagorean identity to find sin A:

sin^2 A + cos^2 A = 1

sin^2 A = 1 - cos^2 A

sin A = sqrt(1 - cos^2 A)

Substituting cos A = 3/10, we get:

sin A = sqrt(1 - (3/10)^2)

sin A = sqrt(1 - 9/100)

sin A = sqrt(91)/10

Since we also know that tan A < 0, we know that the sine and tangent of A have opposite signs, and therefore sin A is negative.

Therefore:

sin A = -sqrt(91)/10

Step-by-step explanation:

Write an Algebraic Equation for each problem (include a let statement) and use it to solve the world problem

On number is eight less than five times another. If the the sum of the two numbers is 28, find the two numbers.

The smaller number is __.
The larger number is __.

Answers

The smaller number is 6 .

The larger number is 22

To solve this problem

Let's let x be the smaller number and y be the larger number.

From the problem, we know that one number is eight less than five times the other, so we can write:

y = 5x - 8

We also know that the sum of the two numbers is 28, so we can write:

x + y = 28

Now we have two equations in two variables. We can solve for one of the variables in terms of the other, and substitute that expression into the other equation to eliminate one variable.

Let's solve the first equation for x

x = (y + 8)/5

Now we can substitute this expression for x into the second equation:

(y + 8)/5 + y = 28

Multiplying both sides by 5 to eliminate the fraction, we get:

y + 8 + 5y = 140

Combining like terms, we get:

6y + 8 = 140

Subtracting 8 from both sides, we get:

6y = 132

Dividing both sides by 6, we get:

y = 22

Now we can use the equation y = 5x - 8 to solve for x:

22 = 5x - 8

Adding 8 to both sides, we get:

30 = 5x

Dividing both sides by 5, we get:

x = 6

Therefore, the smaller number is 6 and the larger number is 22.

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Find the compound interest on Rs. 3,500 for 2 years at the rate of 8% per annum.​

Answers

Answer: The formula for compound interest is:

A = P(1 + R/100)^t

where A is the amount after t years, P is the principal amount, R is the rate of interest per annum, and t is the time period in years.

Here, P = Rs. 3,500, R = 8%, and t = 2 years.

So, the amount after 2 years will be:

A = 3,500(1 + 8/100)^2

= 3,500(1.08)^2

= 3,892.32

Therefore, the compound interest for 2 years will be:

CI = A - P

= 3,892.32 - 3,500

= 392.32

Hence, the compound interest on Rs. 3,500 for 2 years at the rate of 8% per annum is Rs. 392.32.

Step-by-step explanation:

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