Write a cosine function that has an amplitude of 2, a midline of y=4 and a period of 1/7

The equation that could be used to find q is q = 110-0.15(110) where q equal the price of a quarter-page ad after the markdown.

According to the question,

We have the following information:

Cost of a quarter-page ad cost = $110

Mark down in the price = 15%

Now, q represents the price of a quarter-page ad after the markdown.

(Note that when we remove the sign of % means that the number has to be divided by 100.)

So, the equation will be the difference of the markdown price from the original price:

q = 110-(15/100)110

q = 110-0.15*110

q = 110-0.15(110)

Hence, the correct option is the third one.

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The probability that you win the jackpot is 0.00083.

What is probability?

The probability of an event or several events occurring is known as probability. A straightforward formula can be used to compute probability, which is the likelihood of obtaining a specific result.

The possibility of an event occurring divided by the number of anticipated outcomes of the event is another way to define probability. When there are several events, probability is calculated by dividing each likelihood into individual, single computations, multiplying each result, and then adding the results to produce the one potential outcome.

Number of white balls = 10

Number of white balls drawn = 3

Number of red balls = 10

Number of red balls drawn = 1

Probability that first ball drawn is white = \(\frac{3}{10}\)

Probability that second ball drawn is white (without replacement) = \(\frac{2}{9}\)

Probability that third ball drawn is white (without replacement) = \(\frac{1}{8}\)

Probability of drawing red ball = \(\frac{1}{10}\)

Probability that you win jackpot = \(\frac{3}{10}*\frac{2}{9}*\frac{1}{8}*\frac{1}{10}\)

                                                     = 0.00083

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The probability that fewer than five of the 11 randomly selected adult smartphone users will use their phones during meetings or classes is 0.6747

When adults with smartphones are randomly selected, 53% use them during meetings or classes. You need to find the probability that fewer than five of the 11 selected adults use their smartphones during meetings or classes. Here's how to calculate the probability that fewer than five of the 11 randomly selected adult smartphone users will use their phones during meetings or classes:

\(P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)\)

Where X represents the number of smartphone users in the selected group who use their phones in meetings or classes. Using the binomial probability formula, you can calculate each of these probabilities separately.

\(P(X = 0) = (11C0)(0.53)^0(1 - 0.53)^11 = 0.0026\\P(X = 1) = (11C1)( 0.53)^1(1 - 0.53)^10 = 0.0247\\P(X = 2) = (11C2)(0.53)^2(1 - 0.53)^9 = 0.1012\\P(X = 3) = (11C3)(0.53) ^3(1 - 0.53)^8 = 0.2346\\P(X = 4) = (11C4)(0.53)^4(1 - 0.53)^7 = 0.3116\\\)

Therefore, the probability that fewer than five of the 11 randomly selected adult smartphone users will use their phones during meetings or classes is:

\(P(X < 5) = 0.0026 + 0.0247 + 0.1012 + 0.2346 + 0.3116 = 0.6747\)

Therefore, the probability is 0.6747.

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The linear equation perpendicular to 5x-4y=4 is:

y = (-4/5)*x + 42/5

We want to find a line perpendicular to:

5x - 4y = 4

Solving this for y, we get:

y = 4 - 5x

y = (4 - 5x)/-4 = -1 + (5/4)*x

We can see that the slope of this line is 5/4, the slope of a perpendicular line will be the inverse of the opposite, so we get:

slope = -4/5.

Then the line is something like:

y = (-4/5)*x + b

To find the value of b, we use the fact that the line passes through (-8, 2)

2 = (-4/5)*-8 + b

2 = (-32/5) + b

2 + 32/5 = b

10/5 + 32/5 = b

42/5 = b

The linear equation is:

y = (-4/5)*x + 42/5

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Answer:

I hoped this helped :))

Answer:

your answer is c

Step-by-step explanation:

(6^-4 x 8^-7)^-9 =8.0930867e+84

6^36 x 8^63= 8.0930867e+84

so c is your answer

Answer:

all 3 options are true : A, B, C

Step-by-step explanation:

warning : it has come to my attention that some testing systems have an incorrect answer stored as right answer for this problem.

they say that A and C are correct.

but I am going to show you that if A and C are correct, then also B must be correct.

therefore, my given answer above is the actual correct answer (no matter what the test systems say).

originally the information about the alignment of the point F in relation to point E was missing.

therefore, I considered both options :

1. F is on the same vertical line as E.

2. F is not on the same vertical line as E.

because of optical reasons (and the - incomplete - expected correct answers of A and C confirm that) I used the 1. assumption for the provided answer :

the vertical line of EF is like a mirror between the left and the right half of the picture.

A is mirrored across the vertical line resulting in B. and vice versa.

the same for C and D.

this leads to the effect that all 3 given congruence relationships are true.

if we consider assumption 2, none of the 3 answer options could be true.

but if the assumptions are true, then all 3 options have to be true.

now, for the "why" :

remember what congruence means :

both shapes, after turning and rotating, can be laid on top of each other, and nothing "sticks out", they are covering each other perfectly.

for that to be possible, both shapes must have the same basic structure (like number of sides and vertices), both shapes must have the same side lengths and also equally sized angles.

so, when EF is a mirror, then each side is an exact copy of the other, just left/right being turned.

therefore, yes absolutely, CAD is congruent with CBD. and ACB is congruent to ADB.

but do you notice something ?

both mentioned triangles on the left side contain the side AC, and both triangles in the right side contain the side BD.

now, if the triangles are congruent, that means that each of the 3 sides must have an equally long corresponding side in the other triangle.

therefore, AC must be equal to BD.

and that means that AC is congruent to BD.

because lines have no other congruent criteria - only the lengths must be identical.

A pharmaceutical company uses an acceptance sampling plan that tests 30 tablets and accepts the entire shipment if at most one tablet doesn't meet the required specifications. If a shipment of thousands of ibuprofen tablets has a 6% defect rate, we need to find the probability of accepting the whole shipment.

Let p be the proportion of ibuprofen tablets in a batch that do not meet the required specifications, which is given as 6% or 0.06. We can use the binomial distribution to find the probability that out of the 30 tablets tested, at most one tablet does not meet the specifications. The probability of accepting the shipment is the probability that at most one of the 30 tested tablets is defective.

Using the binomial distribution, we get:

P(X ≤ 1) = P(X = 0) + P(X = 1) = C(30, 0) * 0.06^0 * (1 - 0.06)^30 + C(30, 1) * 0.06^1 * (1 - 0.06)^29

Where X is the number of defective tablets in the sample, and C(30, 0) and C(30, 1) are the binomial coefficients

Solving the equation, we get:

P(X ≤ 1) = 0.9984

Therefore, the probability of accepting the whole shipment is 0.9984 or approximately 99.84%.

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Sorry, what is the question? OwO

f(x) = x is a simple linear function with a slope of 1, f(x) = 3 5 6 is a constant function, f(x) = 3-x is a linear function with a negative slope of -1,  f(x) = 1 is a constant function, f(x) = 2 is a constant function

A constant function is a mathematical function whose output value is the same for every input value

From the given parameters, f(x) = x is a simple linear function with a slope of 1, this implies  that for every unit increase in x, the value of y increases by 1.

Also,  f(x) = 3 5 6 is a constant function, where the value of y is always 3 5 6, regardless of the value of x.

In the same way,  f(x) = 3-x is a linear function with a negative slope of -1, which means that for every unit increase in x, the value of y decreases by 1. The fourth function f(x) = 1 is a constant function, where the value of y is always 1, regardless of the value of x.

The domain of the fifth function is 3 0, which means that x can take any value between 3 and 0.

The sixth function f(x) = 2 is a constant function, where the value of y is always 2, regardless of the value of x.

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The Taylor series has convergence within the disk centered at z₀ = 0 with a radius of 1.

The convergence properties of a Taylor series depend on the function being approximated and the point around which the series is being expanded.

The Taylor series for the function 1/(1 + z) around z₀ = 0 is as follows:

1/(1 + z) = 1 - z + z² - z³ + z⁴ - ...

The series converges if the absolute value of the ratio of successive terms is less than 1, i.e.

|(-1)ⁿ zⁿ⁺¹ / (-1)ⁿ⁺¹ zⁿ| < 1

|z| < 1

So, the Taylor series converges in the disk of radius 1 centered at z₀ = 0.

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Answer:

x=19

Step-by-step explanation:

9x = 171

divide both sides by 9 to isolate x

9x/9=171/9

x= 19

A residual plot alone does not provide a definitive answer about the appropriateness of the line of best fit. It should be used in conjunction with other diagnostic tools, such as examining the regression coefficients, goodness-of-fit measures (e.g., R-squared), and conducting hypothesis tests.

The residual plot is a graphical tool used to assess the appropriateness of the line of best fit or the regression model for the data. It helps to examine the distribution and patterns of the residuals, which are the differences between the observed data points and the predicted values from the regression model.

In a residual plot, the horizontal axis typically represents the independent variable or the predicted values, while the vertical axis represents the residuals. The residuals are plotted as points or dots, and their pattern can provide insights into the line of best fit.

To determine if the line of best fit is appropriate, you would generally look for the following characteristics in the residual plot:

Randomness: The residuals should appear randomly scattered around the horizontal axis. If there is a clear pattern or structure in the residuals, it suggests that the line of best fit is not capturing all the important information in the data.

Constant variance: The spread of the residuals should remain relatively constant across the range of predicted values. If the spread of the residuals systematically increases or decreases as the predicted values change, it indicates heteroscedasticity, which means the variability of the errors is not constant. This suggests that the line of best fit may not be appropriate for the data.

Zero mean: The residuals should have a mean value close to zero. If the residuals consistently deviate above or below zero, it suggests a systematic bias in the line of best fit.

It's important to note that a residual plot alone does not provide a definitive answer about the appropriateness of the line of best fit. It should be used in conjunction with other diagnostic tools, such as examining the regression coefficients, goodness-of-fit measures (e.g., R-squared), and conducting hypothesis tests.

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The speed of train A and train B will be 50 miles per hour and 25 miles per hour. Train A traveled 50 miles less than train B. And graph B is steeper than the graph of train A.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

From the graph, train A travels 150 miles in 3 hours and train B travels 100 miles in 4 hours.

The speed of train A is given as,

S = 150 / 3

S = 50 miles per hour

The speed of train B is given as,

S = (125 - 25) / 4

S = 25 miles per hour

The speed of train A and train B will be 50 miles per hour and 25 miles per hour.

Train A traveled 50 miles less than train B. And graph B is steeper than the graph of train A.

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Answer:

193 mg

Step-by-step explanation:

Exponential decay formula:

Our known variables are:

Let's solve for the decay constant of this sample.

Using our new variables, we can now solve for Aₜ at t = 7 years, since we go from 2004 to 2011.

Our new initial mass is A₀ = 270 mg. We solved for the decay constant, r = 0.04794701.

The expected mass of the sample in the year 2011 would be 193 mg.

Given the points (2, k) and (0, -6), and the distance is √5

The distance between two points is calculated by the formula:

Hence,

Therefore, the values of k would be -5 or -7 [option A is correct]

Answer:

the first one

Step-by-step explanation:

-.8x + 4.8y + 16

hope this helps

Answer:

6 13/14

Step-by-step explanation:

Add the whole numbers first.

6 + 2/7 + 9/14

Find the Least Common Denominator (LCD) of 2/7, 9/14. In other words, find the Least Common Multiple (LCM) of 7,14.

LCD: 14

Make the denominators the same as the LCD.

6 + 2 × 2/7 × 2 + 9/14

Simplify. Denominators are now the same.

6 + 4/14 + 9/14

Join the denominators.

6 + 4 + 9/14

Simplify

6 13/14

May I please have Brainliest!!??

- ElizabethKate

The solution is 97/14 of the given exprsseion.

Expressions is the defined as mathematical statements that have a minimum of two terms containing variables or numbers.

Arithmetic operations can also be specified by the subtract, divide, and multiply built-in functions.

The operator that perform arithmetic operation are called arithmetic operators .

Operators which let do basic mathematical calculation

+ Addition operation : Adds values on either side of the operator.

For example 4 + 2 = 6

- Subtraction operation : Subtracts right hand operand from left hand operand.

for example 4 -2 = 2

* Multiplication operation : Multiplies values on either side of the operator

For example 4*2 = 8

/ Division operation : Divides left hand operand by right hand operand

For example 4/2 = 2

Given expression as :

⇒ \(4\dfrac{2}{7} + 2\dfrac{9}{14}\)

⇒ (28 + 2)/7 + (28 + 9)/14

⇒ 30/7 + 37/14

⇒ (60 + 37)/14

⇒ 97/14

Hence, the solution is 97/14 of the given expression.

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Answer:

this is answer$10,000$1o,5oo ok

Answer:

(motorboat speed is 40 km/h)

(current speed) = 10 km/h

Step-by-step explanation:

Ok, let the speed of the water current be x and the speed of the motorboat be y. Then, the speed of the motorboat upstream

against the current is (x - y)

Putting it into the equation, we get,

5h (x - y) = 150 km or

(x - y) = 30 km/h -  1

Now, downstream speed is (x + y).

Again, forming it into equation, we get,

3(x + y) = 150

x + y = 50 km/h  -   2

Adding both equations, we get,

2x = 80 km/h

x (motorboat speed is 40 km/h)

40 - y = 30 km/h

y(current speed) = 10 km/h

Answer:

still water (s): 40 mph

current rate (c): 10 mph

Step-by-step explanation:

We are given two things:

1) 5 hours to travel 150 mi upstream

2) return trip 3 hours downstream

Note that when the boat goes upstream, it must push against the current, versus when it goes downstream, the current helps the boat to move. Also keep in mind the trip is always 150 mi both ways.

With that said, lets set up the problem. First, let s be the rate of the boat in still water, and let c be the rate of the current. We must keep in mind that when the boat goes upstream, it impedes its overall speed. So our equation for that looks like:

5(s-c)=150 (use for upstream)

And downstream would look like:

3(s+c)=150 (use for downstream)

Now that we have both equations, the next step is to expand them. You should get the two following equations:

5s-5c=150 AND 3s+3c=150.

Essentially, we are going to need to solve a system of equations here. You must add them to solve. First, multiply the first equation above by 3 and get 15s-15c=450 and multiply the second one by 5 and get 15s+15c=750.

When we add them we will get the following equation as a result: 30s=1200. Now divide both sides by 30 revelaing s to be 40. Now substiute in:

3(40)+3c=150

120+3c=150

-120      -120

3c=30

c=10

The system of equations is now solved revelaing the speed of the boat in still water to be 40 and the current speed to be 10.

Answer:

the answers for those are number 4 is 150 and 5 is 16%

Step-by-step explanation:

number 4     500 x 30= 15,000

15,000 ÷ 100= 150

number 5   80 x 100=8,000

8,000÷ 500= 16 so 16%

Answer:

150 and 120

Step-by-step explanation:

30% of 500 is 150

80% of 150 is 120

Answer:

Step-by-step explanation:

The ratio as per diagram:

Equivalent ratio from the options is:

There are no matches for 9, 7, 20, 17

Answer:

Equivlent ratio is 8:16

Step-by-step explanation:

8:16 can be further simplified into 2:4 but 8:16 is correct choice.

The simplified version of (sec a - cosec a) / (sec a + cosec a)  is cosec 2a(cosec 2a - 2) / (sec²a - cosec²a).

The study of correlations between triangles' side lengths and angles is known as trigonometry. The field was created in the Hellenistic era in the third century BC as a result of the use of geometry in astronomical research.

Given:

(sec a - cosec a) / (sec a + cosec a)

Multiply the numerator and denominator by (sec a - cosec a)

(sec a - cosec a) / (sec a + cosec a)  × (sec a - cosec a)

(sec²a + cosec²a -2sec a cosec a) / (sec²a - cosec²a)

As we know,

\(sec^2a + cosec^2a = sec^2a \ cosec^2a\)

sec² a cosec² a - 2sec a cosec a /  (sec²a - cosec²a)

sec a cosec a (sec a cosec a - 2) / (sec²a - cosec²a)

cosec 2a(cosec 2a - 2) / (sec²a - cosec²a)

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Answer:

An apple and a pear weigh less than an orange and a peach together, and a pear and an orange weigh less than an apple and a peach together. Which of the pieces of fruit is the heaviest? Step 1: Weigh an apple, a pear, and an orange. Step 2: The apple weighs more than the pear and the orange

Thus, the correct answer is A. 72.85 m².

To find the area of a right spherical triangle, we can use the formula:

Area = r²(A + B + C - π),

where r is the radius of the sphere and A, B, C are the angles of the triangle.

Given that C = 90°, we have:

A = 72°27' = 72 + (27/60) ≈ 72.45°

B = 61°49' = 61 + (49/60) ≈ 61.82°

Substituting these values into the formula, along with C = 90° and the radius r = 10 m, we get:

Area = (10)²(72.45° + 61.82° + 90° - π)

≈ (100)(224.27° - π)

Now, we need to convert the result from degrees to radians since the formula expects angles in radians. There are π radians in 180°, so we divide by 180 to convert degrees to radians:

Area ≈ (100)(224.27° - π) * (π/180)

≈ (100)(224.27 - π) * (π/180)

Calculating the approximate value:

Area ≈ 72.85 m²

Therefore, the area of the spherical triangle is approximately 72.85 m².

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Answer:

parallelograms

Step-by-step explanation:

It's all about diagonals

Answer:

The answer is down below

Step-by-step explanation:

90

Answer:

76

Step-by-step explanation:

Use PEMDAS

Parenthesis first then add

The solution of the equation, (x + 5)² = 9  is x = -2 or x - 8.

The equation (x + 5)² = 9 can be solved as follows:

Therefore, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Therefore, let's solve for the variable x in the equation. A variable is a number represented by a letter in an equation.

Hence,

(x + 5)² = 9

(x + 5)(x + 5) = 9

x² + 5x + 5x + 25 = 9

x² + 10x + 25 = 9

x² + 10x + 25 - 9 = 0

x² + 10x + 16 = 0

x² + 2x + 8x + 16 = 0

x(x + 2) + 8(x + 2) = 0

(x + 2)(x + 8) = 0

Therefore,

x = - 2 or x  = -8

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Using the fact that the triangles are similar, we will see that:

x = 5.626

On the image we can see two triangles, such that one is inscribed on the other.

Just because of that, it is obvious that the two triangles are similar.

And because the triangles are similar, the quotients between correspondent sides must be equal, that allows us to write the equation:

3/x = 8/15

The quotient is "left side over the bottom side"

We can solve that equation for x:

3/x = 8/15

3 = (8/15)*x

(15/8)*3 = x

45/8 = x

5.625 = x

That is the value of x.

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The cumulative distribution function for N when a coin is flipped 3 times with  P[H]=0. 3 is given by ,

F(N≤ 0) = 0.343 , F(N≤1) = 0.784 , F(N≤2) = 0.973 , F(N≤3) = 1.000.

Cumulative distribution function (CDF) of N,

Probability of getting n or fewer heads in three coin flips,

(All values of n from 0 to 3)

Probability of getting exactly n heads in three flips.

Apply binomial distribution,

P(N = n) = ³Cₙ ×(0.3)ⁿ × (0.7)³⁻ⁿ

For cumulative distribution function, add up the probabilities of getting 0, 1, 2, or 3 heads in three flips,

F(N≤ 0)

=P(N=0)

=³C₀ × (0.3)⁰ × (0.7)³

= 1 × 1 × 0.343

= 0.343

For F(N≤1) is equal to,

⇒F(N≤1)

= P(N=0) + P(N=1)

 =  ³C₀ × (0.3)⁰ × (0.7)³ + ³C₁ × (0.3)¹ × (0.7)²

= 0.343 + 0.441

= 0.784

F(N ≤ 2)

= P(N=0) + P(N=1) + P(N=2)

= ³C₀ × (0.3)⁰ × (0.7)³

+ ³C₁ × (0.3)¹ × (0.7)²

+³C₂ × (0.3)² × (0.7)¹

= 0.343 + 0.441 + 0.189

= 0.973

This implies CDF for N is equal to,

F(N ≤n) = \(\sum_{0}^{x}\)³Cₓ × (0.3)ˣ × (0.7)³⁻ˣ

And F(N≤3) is equal to,

⇒F(N≤3)

= P(N=0) + P(N=1) + P(N=2) + P(N=3)

=  ³C₀ × (0.3)⁰ × (0.7)³

+ ³C₁ × (0.3)¹ × (0.7)²

+ ³C₂ × (0.3)² × (0.7)¹

+ ³C₃× (0.3)³ × (0.7)⁰

= 0.343 + 0.441 + 0.189 + 0.027

= 1.000

Therefore, the cumulative distribution function for N is equal to,

F(N≤ 0) = 0.343

F(N≤1) = 0.784

F(N≤2) = 0.973

F(N≤3) = 1.000

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the solution to the initial value problem is y = -2e3t + 7te3t - 2t + 1e-2t - 1. Given y′′ − y′ − 6y = 10te3t − 3e3t + 12t − 10 with initial values y(0) = 6 and y′(0) = −1.

A. Write the characteristic equation for the associated homogeneous equation. (Use r for your variable.)

For the associated homogeneous equation y′′ − y′ − 6y = 0, the characteristic equation is r² - r - 6 = 0.

B. Write the fundamental solutions for the associated homogeneous equation.

y1 =y 2 =The roots of the characteristic equation r² - r - 6 = 0 are r = 3 and r = -2.

The fundamental solutions for the associated homogeneous equation are:

y1 = e3t and y2 = e-2t.

C. Write the form of the particular solution and its derivatives. (Use A, B, C, etc. for undetermined coefficients)

Let the particular solution be of the form Y = Atet + Bte3t + Ct + D (Undetermined coefficients method).

Differentiating, Y′ = A(t + 1)et + 3Bte3t + Aet + C and Y′′ = A(t + 2)et + 6Bte3t + 2Aet.

The derivatives are, Y = Atet + Bte3t + Ct + D Y′ = A(t + 1)et + 3Bte3t + Aet + C Y′′ = A(t + 2)et + 6Bte3t + 2Aet.

D. Write the general solution. (Use c1 and c2 for c1 and c2).

y = c1e3t + c2e-2t + Atet + Bte3t + Ct + D.

E. Plug in the initial values and solve for c1 and c2 to find the solution to the initial value problem.

y(0) = c1 + c2 + D = 6, y′(0) = 3A + A + C - B + 1 = -1

Plug in A = -2, B = 7, C = 0 and D = 1 to get:

y = -2e3t + 7te3t - 2t + 1e-2t - 1

Therefore, the solution to the initial value problem is y = -2e3t + 7te3t - 2t + 1e-2t - 1.

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