If a triangle has 2 side lengths of 17 and 32, can
the length of the third side be 49?

The area to the right of z = 2.01 is 0.0222, which can be found using a standard normal distribution table.

Explanation:

To find the area to the right of z = 2.01, we need to use a standard normal distribution table. A standard normal distribution has a mean of 0 and a standard deviation of 1. The table gives the area under the curve to the left of a given z-score.

Since we want the area to the right of z = 2.01, we need to subtract the area to the left of z = 2.01 from 1. Using the table, we can find that the area to the left of z = 2.01 is 0.9778. Therefore, the area to the right of z = 2.01 is 1 - 0.9778 = 0.0222.

The area to the right of z = 2.01 represents the probability that a standard normal random variable takes on a value greater than 2.01 standard deviations above the mean. This can be used in various applications, such as hypothesis testing or confidence interval estimation, where we want to find the probability of observing a sample mean that is a certain number of standard deviations away from the population mean.

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F(3) is equal to 9, based on the given table and the corresponding values of x and f(x). Option D.

To find the value of F(3) based on the given table, we look at the corresponding x-value of 3 and find its corresponding f(x) value.

From the table, we see that when x = 3, f(x) = 9. Therefore, F(3) = 9.

The table shows the values of x and their corresponding f(x) values. We can see that when x increases by 1, f(x) also increases by 3. This indicates that the function has a constant rate of change, where the change in f(x) is always 3 units for every 1 unit change in x.

Given that F(3) represents the value of the function when x = 3, we look at the x-values in the table and find the corresponding f(x) value. In this case, when x = 3, f(x) = 9.

Therefore, the value of F(3) is 9. Option D is correct.

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Answer:

$8

Step-by-step explanation:

You divide $72 by 9 to get the money for each lawn-mowing job.

72/9 = 8

She charges $8 for each lawn she mows.

When x increases by 1 in the function y=3^x, the value of the function will be multiplied by 3.

Given the function

y = 3^x

An increment in the value of x would make the expression be multiplied by 3

To see why this happens, we can compare the value of the function at x and x+1:

y(x+1) = 3^(x+1)

y(x+1) = 3^x * 3 (by the laws of exponents)

y(x+1) = 3 * 3^x

Therefore, we can see that when x increases by 1, the value of the function is multiplied by 3.

This means that the function grows very quickly as x increases.

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Answer:

sin(2x)=cos(π2−2x)

So:

cos(π2−2x)=cos(3x)

Now we know that cos(x)=cos(±x) because cosine is an even function. So we see that

(π2−2x)=±3x

i)

π2=5x

x=π10

ii)

π2=−x

x=−π2

Similarly, sin(2x)=sin(2x−2π)=cos(π2−2x−2π)

So we see that

(π2−2x−2π)=±3x

iii)

π2−2π=5x

x=−310π

iv)

π2−2π=−x

x=2π−π2=32π

Finally, we note that the solutions must repeat every 2π because the original functions each repeat every 2π. (The sine function has period π so it has completed exactly two periods over an interval of length 2π. The cosine has period 23π so it has completed exactly three periods over an interval of length 2π. Hence, both functions repeat every 2π2π2π so every solution will repeat every 2π.)

So we get ∀n∈N

i) x=π10+2πn

ii) x=−π2+2πn

iii) x=−310π+2πn

(Note that solution (iv) is redundant since 32π+2πn=−π2+2π(n+1).)

So we conclude that there are really three solutions and then the periodic extensions of those three solutions.

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Related Questions (More Answers Below)

The Average Value of f(x) = (sin x)4^(cos x) for the closed interval 0≤ x≤π/2   is (B) 6/(πln(4))   .

The average value of a function over a closed interval can be found by calculating its definite integral over the interval and dividing by the length of the interval.

The function is : f(x) = (sin x)4^(cos x)  ;

Substituting the values :

we get ;

Average Value is = (1/π/2) × \(\int\limits^\frac{\pi }{2} _0\) (sin x)4^(cos x) dx  .

On Simplifying ,

we get ;

Average Value is = [(-2/π)/ln(4) ] (1 - 4)

⇒ 6/(πln(4))

Therefore ,  the average value of the function over the interval 0≤ x≤π/2 is 6/(πln(4)).

What is the average value of f(x) = (sin x)4^(cos x) for the closed interval 0≤ x≤π/2 ?

(A) 3/ln(4)

(B) 6/(πln(4))

(C) 4/ln(4)

D) 8/(πln(4))

(E) 3π/(2ln(4))

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Answer:

0.03, (3 x 1/100) + (3 x 1/1000), 3 tenths

Answer:4/4, 3/4, 1/4 2/4

Step-by-step explanation:

Answer:

I will choose 5 and colour blue

The null hypothesis get rejected comparing the 95% confidence interval to the proportion of the given central valley residents and bay area residents .

As given in the question,

Total number of voters in California = 7525

x₁ = Number of voters of central valley residents approved California legislature

   = 68

n₁ = Total number of voters of central valley residents

   = 200

x₂ = Number of voters of bay area residents approved California legislature

   = 156

n₂= Total number of voters of bay area residents

   = 300

p₁ = proportion of voters of central valley

p₂= proportion of voters of bay area

p₁ = x₁/ n₁

   = 68/200

   = 0.34

p₂ = x₂/n₂

    = 156/300

    = 0.52

Standard error = √p₁(1 -p₁) / n₁ + p₂( 1- p₂)/n₂

                        = √0.34(1-0.34) / 200 + 0.52(1-0.52)/ 300

                        = √0.001122 + 0.000832

                        = 0.044

\(p_{w}\) = (68 + 156 )/ (200 + 300)

   = 0.448

\(q_{w} = 1- p_{w}\)

    = 1 - 0.448

    = 0.552

null hypothesis p₁ - p₂ = 0

z = ( 0.52 - 0.34 ) - 0/ √(0.448)(0.552)( 1/200 + 1/300)

  = 4

Tabular value for confidence interval 95% = 1.96

4 > 1.96

We reject the null hypothesis.

Therefore, the difference of proportion of central valley residents and the bay area residents rejection of null hypothesis as per given 95% confidence interval.

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Answer:

45+61=106

the answer for this question is 106 minutes

Step-by-step explanation:

Answer:

106 minutes/1hour 46 minutes

Step-by-step explanation:

45+ 61 :106

Answer:

(a) The amount of interest you will save on this loan if you make the partial payment and don't purchase the additional serving supplies is $553.80.

(b) The amount you will save by purchasing the discounted serving supplies and not making the partial payment is $2,946.20.

Step-by-step explanation:

Note: This question is note complete. The complete question is therefore presented before answering the question as follows:

You are the owner of four Taco Bell restaurant locations. You have a business loan with Citizens Bank taken out 60 days ago that is due in 90 days. The amount of the loan is $50,000, and the rate is 9.5% using ordinary interest. You currently have some excess cash. You have the choice of sending Citizens $35,000 now as a partial payment on your loan or purchasing an additional $35,000 of serving supplies such as food containers, cups, and plastic dinnerware for your inventory at a special discount price that is "10% off" your normal cost of these items.

(a) How much interest will you save on this loan if you make the partial payment and don't purchase the additional serving supplies?

(b) How much will you save by purchasing the discounted serving supplies and not making the partial payment?

Explanation of the answers is now given as follows:

(a) How much interest will you save on this loan if you make the partial payment and don't purchase the additional serving supplies?

Since an ordinary interest is used, it implies that the total interest amount has to be calculated based on a 360-day year instead of a 365-day year. Therefore, the the interest saved can be calculated as follows:

I_$50K = PRT ........................ (1)

Where,

I_50K = Total Interest on the original $50,000 loan = ?

P = Principal = $50,000

R = interest rate = 9.5%

T = Number of days in the loan period / 360 = (60 + 90) / 360 = 150 / 360 = 0.416666666666667

Substituting the values into equation (1), we have:

I_$50K = $50,000 * 9.5% * 0.416666666666667

I_$50K = $1,979.17

Daily interest on $50,000 loan = I_$50K / Number of days in the loan period = $1,979.17 / 150 = $13.19

Also, we have:

I_PB = PRT ........................ (2)

Where,

I_PB = Innterest on principal balance = ?

P = Principal balance = $50,000 - $35,000 = $15,000

R = interest rate = 9.5%

T = Number of days remaining / 360 = 60 / 360 = 0.166666666666667

Substituting the values into equation (2), we have:

I_PB = $15,000 * 9.5% * 0.166666666666667

I_PB = $237.50

Daily interest on principal balance = I_PB / Number of days remaining the loan period = $237.50 / 60 = $3.96

Daily interest to save = Daily interest on $50,000 loan - Daily interest on principal balance = $13.19 - $3.96 = $9.23

Interest amount to save on the loan = Number of days remaining * Daily interest to save = 60 * $9.23 = $553.80

Therefore, the amount of interest you will save on this loan if you make the partial payment and don't purchase the additional serving supplies is $553.80.

(b) How much will you save by purchasing the discounted serving supplies and not making the partial payment?

This can be calculated as follows:

Discount receivable from purchasing serving supplies = Cost  of serving supplies * Discount rate = $35,000 * 10% = $3,500

Amount to save by purchasing serving supplies = Discount receivable from purchasing serving supplies - Interest payable on loan for the remaining 60 days ................ (2)

Where;

Discount receivable from purchasing serving supplies = $3,500

Interest payable on loan for the remaining 60 days = Interest amount to save on the loan as calculated in part (a) = $553.80

Substituting the values into equation (2), we have:

Amount to save by purchasing serving supplies = $3,500 - $553.80 = $2,946.20

Therefore, the amount you will save by purchasing the discounted serving supplies and not making the partial payment is $2,946.20.

x=-2 is the only solution. This can be solved by simplification.

An extraneous solution in mathematics is a solution that develops during the process of addressing the issue but is not a genuine solution to the problem, such as the answer to an equation. A valid solution to a problem that vanished during the process of addressing it is referred to as a missing solution.

The given equation becomes:

\(\sqrt{x + 6} -4 = x\)

Add 4 to both sides of the equation.

or, \(\sqrt{x + 6} -4 +4= x + 4\)

or, \(\sqrt{x + 6} = x+4\)

Square both sides:

or, \(x + 6 = (x + 4)^2\)

or, \(x + 6 = x^2 + 8x + 16\)

Rewrite in standard form:

or, \(x^2 + 8x - x + 16 - 6 = 0\)

or, \(x^2 + 7x + 10 = 0\)

or, \(x^2 + 2x + 5x + 10 = 0\)

or, \((x + 2) (x + 5) = 0\)

x= -2 or x= -5

Checking for extraneous solution.

When x= -2

\(\sqrt{-2 + 6} - 4 = -2\)

or, \(\sqrt{4} -4 = -2\)

or, - 2 = -2

This statement is true. This implies that: x= -2 is a solution.

When x= -5

\(\sqrt{-5 + 6} - 4 = -5\)

or, -3 = -5

This statement is not true. This implies that: x=-5 is an extraneous solution.

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Answer:

Step-by-step explanation:

55

Answer: 120

Step-by-step explanation: divide 24 by 5 to get 4.8 so its 4.8 minutes for one question

25 x 4.8 = 120

Answer:

-8

Step-by-step explanation:

It would be -2+2(-3)

Which means -2 plus 2 times -3

According to PEMDAS you have to do parenthesis first so 2 times -3 is -6 +-2=-8

So the answer is -8

Answer:

it would be -2 + 2(-3)

Step-by-step explanation:

the numbers given would replace the variables, so x would become -2 since its -x, and y would be (-3) in parenthesis since its to be multiplied (i believe if im remembering correctly) therefore it would become:

-2 + 2(-3)

keeping all the signs and proper places

hope this helped and is what you were looking for!!

The probability that one or more of the backup servers is operational is 1 - P(both servers fail).

To find this probability, first, determine the probability that both servers fail, which is 0.21 * 0.21 = 0.0441. Then, subtract this value from 1: 1 - 0.0441 = 0.9559. Therefore, the probability that one or more servers is operational is 0.9559.

we know that the failure of one server is independent of the other server's failure. The probability that a single server fails is 0.21. To find the probability that both servers fail, we multiply their individual failure probabilities: 0.21 * 0.21 = 0.0441.

However, the question asks for the probability that at least one server is operational, which is the opposite of both servers failing.

So, we subtract the probability of both servers failing from 1 (the total probability of all possible outcomes): 1 - 0.0441 = 0.9559. This means there's a 95.59% chance that at least one server will be operational.

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Answer:

17

Step-by-step explanation:

A standard die has a 1/6 chance of rolling a 6.

Over 100 rolls, a 6 is likely rolled (1/6)*100 times.

100/6=16.66, approximately 17 times

Answer:

.046x

Step-by-step explanation:

Answer:

yea by using a resipe

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

you need eggs, butter, flour, sugar, salt, oil (i prefer olive oil) and baking powder.

fruit if you like them in your sweets.

this makes 12 muffins

2 cups flour

3 tsps baking powder

1/2 tsp salt

3/4 cup sugar

1 egg

1 cup milk

1/4 cup oil

preheat oven. i usually do 350 F, increase the temperature if youd like them to cook faster but keep in mind youll need to check on them often with increased heat.

stir together your dry ingridents and in a seperate bowl beat your egg with a fork. stir in the milk and oil with the egg.

pour into your dry ingriedeints until everything is well mixed.

bake until golden

if you like fruit id suggest blueberries, 1 cup

\(y = 9x + \dfrac 94 \\\\\text{The above equation is in a form of y=mx + b, where b is the y - intercept}\\\\\\\text{Hence the y-intercept is }~ \dfrac 94\)

Answer:

1. (2,1)

2. (6,-1)

3.(-2,3)

Answer:

1. (2,1)

2.  (6,-1)

3. (-2,3)

Step-by-step explanation:

Each of the answer is consistent system because the lines intersect at one point, which is one solution.

Answer:

B. -2 (x+6)/(x+4)(x-4)

Answer:

v=20π ft/s

Step-by-step explanation:

Given:

Distance from the security car to the movie theater, D=25 ft

Distance of the reflection from the car, d=30 ft

Speed of rotation of the strobe lights, 2 rev/s

To find the speed at which the reflection of the security strobe lights is moving along the wall of the movie theater, we need to calculate the linear velocity of the reflection when it is 30 ft from the car.

We can start by finding the angular velocity in radians per second. Since the strobe lights rotate at 2 revolutions per second, we can convert this to radians per second.

ω=2πf

=> ω=2π(2)

=> ω=4π rad/s

The distance between the security car and the reflection on the wall of the theater is...

r=30-25= 5 ft

The speed of reflection is given as (this is the linear velocity)...

v=ωr

Plug our know values into the equation.

v=ωr

=> v=(4π)(5)

∴ v=20π ft/s

Thus, the problem is solved.

The speed of the reflection of the security strobe lights along the wall of the movie theater is 2π ft/s.

To solve this problem, we can use the concept of related rates. Let's consider the following variables:

x: Distance between the security car and the movie theater wall

y: Distance between the reflection of the security strobe lights and the security car

θ: Angle between the line connecting the security car and the movie theater wall and the line connecting the security car and the reflection of the strobe lights

We are given:

x = 25 ft (constant)

y = 30 ft (changing)

θ = 2 revolutions per second (constant)

We need to find the speed at which the reflection of the security strobe lights is moving along the wall (dy/dt) when the reflection is 30 ft from the car.

Since we have a right triangle formed by the security car, the movie theater wall, and the reflection of the strobe lights, we can use the Pythagorean theorem:

x^2 + y^2 = z^2

Differentiating both sides of the equation with respect to time (t), we get:

2x(dx/dt) + 2y(dy/dt) = 2z(dz/dt)

Since x is constant, dx/dt = 0. Also, dz/dt is the rate at which the angle θ is changing, which is given as 2 revolutions per second.

Plugging in the known values, we have:

2(25)(0) + 2(30)(dy/dt) = 2(30)(2π)

Simplifying the equation, we find:

60(dy/dt) = 120π

Dividing both sides by 60, we get:

dy/dt = 2π ft/s

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Answer:

>

Step-by-step explanation:

lets make 52/9 a mixed number, 5 7/9

so >

11> 5 7/9

Answer:

LN and RQ

Step-by-step explanation:

PQR is just an enlargened version of MLN

RQ is just LN but longer

Answer:

-10 vertical and -1 horizontal

Answer:

(9 x 100) + (5 x 10) +  (0 x 1) + (9/10) + (5/100)

hope this helps brainliest <3

Answer:

Step-by-step explanation:

Using a t-distribution table or a calculator, the critical value of t for a 99% confidence level and 24 degrees of freedom (n - 1) is approximately 2.7969 that is option A.

To find the critical value of t for a 99% confidence interval with a sample size of n = 25 and a sample standard deviation of s = 0.05, we need to use the t-distribution table or a statistical calculator.

For a 99% confidence interval, we want to find the critical value that leaves 0.5% of the area in each tail of the t-distribution, since the confidence level is divided equally between the two tails.

Since the sample size is small (n = 25), we use a t-distribution instead of a standard normal distribution.

Using a t-distribution table or a calculator, the critical value of t for a 99% confidence level and 24 degrees of freedom (n - 1) is approximately 2.7969.

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Answer: 20

Step-by-step explanation:

5 boxes with 10, 10, 10, 10, and 10 donuts in each box.

She gives one box away, so that is 50-10=40

Then she gives 2 boxes away, which is 40-20=20, so she has 20 donuts left to share with her classmates.

Answer: 20

Step-by-step explanation:

5 x 10 = 50 Donuts

50 Donuts - 10       for the Bus driver

40 Donuts - 20      for the school principal

=20

She can share 20 Donuts with her classmates.