If f(x) = x - 4 and g(x) = 3x + 5, find (f + g)(x).

To create a 95% confidence interval for the population proportion of adults who ate fast food at least once in the past month, we need to first calculate the sample proportion.

The sample proportion is calculated by dividing the number of adults who ate fast food at least once in the past month (722) by the total number of adults surveyed (1000). This gives us a sample proportion of 0.722.

To calculate the confidence interval, we can use the following formula:

Plugging in the values, we get:

This gives us a 95% confidence interval of (0.6901, 0.7539). Rounded to four decimal places, the confidence interval is (0.6901, 0.7539).

Note: To calculate the confidence interval using Excel, you can use the following formula:

Where "alpha" is the desired confidence level (e.g., 0.95 for a 95% confidence interval), "standard_dev" is the standard deviation of the sample, and "size" is the sample size. To calculate the standard deviation, you can use the STDEV.P function.

For example, to calculate the lower and upper bounds of the 95% confidence interval, you could use the following formulas:

Where A1:A1000 is a range containing the values "1" for those adults who ate fast food at least once in the past month and "0" for those who did not. This will give you the same result as the manual calculation above.

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The critical value is given as 1.69

The margin of error is 0.00161

We are to find the critical value ta/2  used for finding the margin of error

T∝ / 2 = 1 - 0.10 / 2

1 - 0.05 = 0.95

The critical value at the level if we use the critical value table is 1.69

2. Next we would have to solve for the margin of error

When comparing your results to the actual population value, a margin of error indicates how many percentage points they will deviate.

ME= [tex]z * \frac{s}{\sqrt{n} }[/tex]

z is the critical value = 1.69

s = standard deviation = 0.00573

n = sample size

where z = 1.69

s = 0.00573

n = 36

We would have to put these values in the formula above to get the margin of error

[tex]1.69 * \frac{0.00573}{\sqrt{36} }[/tex]

Margin of error = 0.00161

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The decibel equation is used in many different contexts, including acoustics, audiology, and engineering, to measure and compare the intensity of sounds.

The decibel equation is a measure of sound intensity, which is a way to describe the strength or magnitude of a sound. It is expressed as dB, and it is defined as the ratio of the intensity of a sound to a reference intensity. The reference intensity is usually set at a level that is the minimum intensity that a person can hear, which is approximately 0 dB.

The decibel equation is typically written as:

dB = 10 × log10(I / I0)

where I is the intensity of the sound being measured and I0 is the reference intensity. The log10 part of the equation is used to express the ratio of the two intensities on a logarithmic scale, which allows the decibel value to be more easily interpreted.

The decibel scale is logarithmic, which means that a small change in decibel value corresponds to a much larger change in sound intensity. For example, a sound with a decibel value of 60 dB is much louder than a sound with a decibel value of 50 dB, even though the difference between the two values is only 10 dB.

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At t = 0.6, the instantaneous velocity of the bug is equal to the average velocity of the bug on [0,6], so the bug is neither speeding up nor slowing down.

The instantaneous velocity of a bug at any particular moment in time is the rate at which the bug is changing its position. The average velocity of the bug over a particular interval (in this case, [0,6]) is the average rate at which the bug changes its position over the entire interval. To compare the instantaneous velocity to the average velocity, the two velocities need to be measured at the same time.

At t = 0.6, the instantaneous velocity of the bug is equal to the average velocity of the bug on [0,6]. That means that the bug is neither speeding up nor slowing down.

The Complete the question is :

at what time t is the instaneous velocity equal to the averge equal to the equal to the average velocity of the bug on 0,6 is the bug speeding up or slowing down at t = 0.6

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Answer:

The normal price of a pen is £8

Step-by-step explanation:

let p be the normal price.

The statement : “normal prices are reduced by 15%. The normal price of a pen is reduced by £1.20”

Means

[tex]p \times \frac{15}{100} = 1.20[/tex]

Then

[tex]p = 1.20 \times \frac{100}{15} = \frac{120}{15} = 8[/tex]

Answer:

The normal price of the pen is £8

Step-by-step explanation:

Reduced by 15%

Reduced by £1.20

Meaning that 15% is £1.20

To find the 100% or the normal price of the pen we find the 1% first then the 100%

So, 1% = £1.20/15

100% =£1.20/15 x 100

= 8

Checking..

If normal price was 8 and reduction is 15%

8(1- R/100) {R = %}

8(1 -15/100) = 6.8 (Reduced price)

8 - 6.8 = £1.20 ( Reduction price aka the 15%)

Therefore, the normal price of the pen is £8.

The expression that we can use to substitute into the first equation is

x = - 3y + 12.    

The algebraic approach to solving linear equations is known as the substitution method. This procedure involves substituting a variable's value from one equation into the other. By doing this, a pair of linear equations are combined into a single equation with a single variable, making it simpler to solve.

Here we have

2x + y = 8 ---- (1)

- x - 3y = -12 ----- (2)  

We can isolate x in the second equation  as given below

=> - x - 3y = -12

Add 3y on both sides

=>  - x - 3y + 3y = - 12 + 3y

=>  - x = - 12 + 3y

Multiply by -1 on both sides

=>  -(- x) = - (- 12 + 3y)

=>  x = + 12 - 3y

=>  x = - 3y + 12      

Therefore,

The expression that we can use to substitute into the first equation is

x = - 3y + 12.    

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Using the area of rectangle formula, w = A/l, determine the width of the rectangle first before determining its length.

In conclusion, you must divide a rectangle's area by its known width in order to determine its length.If you have an area A and a width w, you can calculate the length w using the formula h = A/w.

If you know the perimeter P and the width w, you can calculate the length using the formula h = P/2w.

Given a diagonal (d) and a width (w), its length is given by h = (d2w2).The basic formula for volume is length, breadth, and height, as opposed to length, width, and height for the area of a rectangular shape.

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Assume you are buying a bond with a par value of $1,000 which is listed in the Wall Street Journal at a price of 100.50. The bond price is: $1,005.

Using this formula to determine the bond price

Bond price = Bond par value × price/100

Where:

Bond par value = $1,000

Price = 100.50

Let plug in the formula

Bond price = $1,000 × 100.50 /100

Bond price = $100,500 /100

Bond price =$1,005

Therefore the bond price is $1,005.

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Answer: 7/3 or 2.333

Step-by-step explanation:

the formula for slope is y2-y1 over x2-x1

so if you apply the formula here its going to be

4-(-3) over 5-2

which is 7 over 3 therefore your slope will be

7/3

Answer:

[tex]m=\frac{7}{3} =2.33333... = 2.\overline{3}[/tex]

Step-by-step explanation:

Answer:139 is the answer

Step-by-step explanation:

Answer:

y = 3/4 x + 3

Step-by-step explanation:

slope of the line :

(0-3)/(-4-0)

-3/-4

3/4

y = 3/4 x + 3

The solution is A = 4000

The equation after rounding up numbers is A = 10 x 400 = 4000

What is rounding up numbers?

There are basically two rules while rounding up numbers

If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down and if the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.

Non-zero digits are always significant

Zeros between non-zero digits are always significant

Leading zeros are never significant

Trailing zeros are only significant if the number contains a decimal point

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the first number be = p

The value of p = 13

Let the second number be = q

The value of q = 378

Rounding the number p to 1 significant figure , p = 10

Rounding the number q to 1 significant number q = 400

So , the equation is A = p x q

Substituting the values in the equation , we get

A = 10 x 400

The value of A = 4000

Hence , The equation after rounding up numbers is A = 10 x 400 = 4000

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Anya her distance back to camp and the bearing angle from her starting point is 4.78 km North 26.3° West.

Define direction ?

Direction gives the information about the way towards which an object moves or tends.

The angle formed by the 2 km and 3 km is the supplement of the 35 ° angle west of north;

  180°- 35° = 145°

We know that the length of two sides and one angle.

The opposite side know angle is the direct distance between the starting and ending points.

Using the law of cosines.

[tex]a^{2} = b^{2} + c^{2} - 2bc (cosA)[/tex]

[tex]a^{2} = 2^{2} + 3^{2} - 2(2)(3)(cos 145)[/tex]

[tex]a^{2} = 4 + 9 - 12 (-0.8192)[/tex]

[tex]a^{2} = 22.83[/tex]

a = 4.78 km

To determine the bearing from the starting point , we must determine the angle between the first leg and the direct path.

Using the law of sines

[tex]\frac{4.78}{sin(145)} = \frac{3}{sin C}[/tex] sin(145°)

4.78 sin C = 3 sin 145°

sin C = [tex]\frac{3 sin (145^ 0)}{4.78}[/tex]

sin C = 0.4438

C = 26.3°

Therefore, the distance and bearing of the end point from the starting point is 4.78 km North 26.3 ° West.

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Answer:

8

Step-by-step explanation:

x+7=15 so x=15-7 which is x=8

Answer:

8 ft

Step-by-step explanation:

The length of the shape is 15 ft. The length on the bottom is equal to the length on the top.

We are given 2 "sides" or lines on the bottom. One of them is 7 ft. Find the other "side" length.

x + 7 =15

x = 15 - 7

x = 8

Since, U = FY(Y) is uniform distribution (i.e. U(0, 1)).

In the given question, suppose continuous random variable Y has cumulative distribution function FY (y), and density function fY (y) > 0.

Let random variable U = FY (Y ).

We have to find the density function of U, and identify its distribution (name and parameter(s)) if possible.

A random variable Y has cumulative distribution function FY (y).

A random variable Y has density function f(y).

Let U = FY(Y)

Now we have to find the density function of U using cumulative distribution function method

FU(u) = P(U≤u)

FU(u) = P(FY(Y) ≤ u)

FU(u) = P(Y ≤ F (u))

FU(u) = FY(F (u))

FU(u) = u

fU(u) = F'U(u).1

fU(u) = 1

fU(u) = 1,     0<u<1

Here U = FY(Y) is uniform distribution (i.e. U(0, 1)).

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The logic diagram, characteristic table, and equation of the SR flip-flip are shown. (Refer to the images attached below)

A gated set-reset flip-flop is an SR flip-flop.

The flip-flop is controlled by the S and R inputs when the clock pulse changes from LOW to HIGH.

Till the clock pulse is on a rising edge, the flip-flop won't alter.

There is a chance that the outputs will be HIGH or LOW when S and R are both HIGH at the same time.

A global flip flop with two inputs, the JK flip flop has the letters "J" and "K."

While J and K are not the reduced abbreviated letters for Set and Reset in the SR flip flop, S and R are.

SR flip-flop equation: Qn+1 = S + QnR'

(Refer to the images attached below)

Therefore, the logic diagram, characteristic table, and equation of the SR flip-flip are shown. (Refer to the images attached below)

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The percentage of boys in the class is 60% and the percentage of girls in the class is 40%.

The Latin phrase "per centum," which means "by the hundred," is where the English word "percentage" comes from. Percentage segments are those with a numerator of 100. In other words, it is a connection where the whole is always deemed to be valued 100.

As per the given information in the question,

Total number of students in class = 45

Total number of boys in the class = 27

Then, the percentage of boys in the class will be,

Let the percentage of boys be x.

x% Of 45 = 27

x = (27 × 100)/45

x = 2700/45

x = 60%

Then, total number of girls in the class = 45 - 27 = 18

Assume the percentage of girls in the class be y.

y% Of 45 = 18

y = (18 × 100)/45

y = 1800/45

y = 40%

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The statements that apply to the given random sample situation are:

(A) Despite the idea that the sample must be random, we are unsure of this.

(C) It is underreported how many pupils don't drive to school.

(D) n(1p) is not greater than 10.

A simple random sample, also known as an SRS, is a smaller group of individuals (also known as a sample) chosen randomly and with equal probability from a larger population.

This technique involves picking a sample at random.

The probability of being chosen from any subset of k persons in SRS is the same as that of being chosen from any other subset of k people.

A simple random sample is an objective sampling approach.

A basic sampling method that can be used in conjunction with other, more advanced sampling techniques is simple random sampling.

So, statements that apply in the given situation are:

- We don't know if the sample is random, despite the fact that it must be.

- The number of students who don't drive to school is undercounted.

- n(1−^p) does not exceed 10.

Therefore, the statements that apply to the given random sample situation are:

(A) Despite the idea that the sample must be random, we are unsure of this.

(C) It is underreported how many pupils don't drive to school.

(D) n(1p) is not greater than 10.

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Correct question:
The administration at GSU wants to estimate the number of parking spaces they will need next year. They survey 80 students; 75 of the students in the sample drive to campus by themselves each day. Which of the following is a reason the administration should not calculate a confidence interval for the proportion of all students who drive to campus? Check all that apply.

a. The sample needs to be random but we don’t know if it is.

b. The actual count of drivers is too small.

c. The actual count of those who does not drive to campus is too small.

d. n ^ p is not greater than 10. n ( 1 − ^ p ) is not greater than 10.

The probability of observing at least one Type I Error is 16.67%.

Probability is the likelihood of an event occurring, expressed as a number between 0 and 1. It is a measure of how likely it is that something will happen, given the conditions and information available. Probability is the foundation of statistics, which is the science of making decisions when faced with uncertainty. Probability can be used to make predictions about future events and to help us understand how likely various outcomes are.

A Type I Error, also known as a false positive, occurs when an experiment incorrectly rejects a true null hypothesis. This probability can be calculated by multiplying the probability of a Type I Error occurring in each test (0.05) three times, yielding 0.125 (or 12.5%).

We then add 1 minus that probability, which yields 0.167 (or 16.67%). In other words, the probability of observing at least one Type I Error in the three tests is 16.67%.

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Answer:

s² = lw

s = 40      w= 25cm

s² = lh

(40cm)² = (25cm)

1 600 cm² = 25cm L

L = 64 cm

Area of Rectangle = length(width)

Area = 64cm(25cm)

Area = 1 600 cm²

Step-by-step explanation:

Answer:

He has $9.24 left of his gift certificate

Step-by-step explanation:

Given that,

He bought two baseballs for $1.79

Baseball= 1.79+1.79 or 1.79 × 2 (because there are two baseballs.

= $3.58

Baseball Glove = $49.99

Baseball Bat = $12.19

Altogether = $3.58 + $49.99 + $12.19

= $65.76

So you subtract $65.76 from the Original amount in the gift certificate,

=> $75 - $65.76

= $9.24

The original price P will be $72

If we know that the ratio from P to Q is 4:5, we can multiply both sides by y (y = amount multiplied) to get our numbers.

4 × y =?

5 × y =?

We need to input a value in for y.

Let's put 9.

4 × 9 = 36 (P)

5 × 9 = 45 (Q)

Now adding 12 to P, and take away 6 from Q.

36 + 12 = 48

45 - 6 = 39

The numbers aren't the same yet.

Let's use a different value for y.

y = 18

The equations will now look like this:

4 × 18 = 72 (P)

5 × 18 = 90 (Q)

Let's add 12 and 6 to the numbers again.

72 + 12 = 84

90 - 6 = 84

The numbers are now equal

Therefore, the original price of P = $72

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Answer:

0

Step-by-step explanation:

0 divided by any nonzero quantity is zero.

Answer:

  C.  C = $10 +$5h

Step-by-step explanation:

The cost is a $10 admission fee plus $5 per hour for sledding. You want an equation representing the cost C in terms of hours h.

The cost is ...

   cost = admission fee + hourly charge

The hourly charge is the product of the cost per hour ($5) and the number of hours (h).

  C = $10 +$5h

Answer:

1 × ( –6 × – 18 – 8) ÷ 4=[tex]\frac{1}{404}[/tex]

–4 – –20 + –5 ×( –11 – –18)=[tex]18[/tex]

13 – –10 × 16 ÷(14 + –16)=[tex]173[/tex]

1– –9 × 12 × (–19 + 20)=[tex]110[/tex]

By dividing the length of bacteria cell to length of amoeba cell we find option (D) i.e 6.67x102 is the correct answer.

Division is an arithmetic operation that involves dividing one number (the dividend) by another number (the divisor) to find the quotient.

Arithmetic operators are symbols that represent mathematical operations that can be performed on one or more operands. The most common arithmetic operators are:

Addition (+): Adds two operands and produces the sum.

Subtraction (-): Subtracts one operand from another and produces the difference.

Multiplication (*): Multiplies two operands and produces the product.

Division (/): Divides one operand by another and produces the quotient.

Modulo (%) : Divides one operand by another and produces the remainder.

Exponentiation (**): Raises one operand to the power of the other and produces the result.

To compare the sizes of the two cells, we need to divide the length of the bacterial cell by the length of the amoeba cell. The result is 3 x 10^−6 m / 4.5 x 10^−4 m = 0.67 x 10^−2.

So, the bacterial cell is approximately 0.67 x 10^−2 times smaller than the amoeba cell.

The correct answer is therefore (D) 6.67 x 10

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Answer:

Area = 2 10/27 inch²

Step-by-step explanation:

Length: 1 7/9 inches

Width: (3/4)(1 7/9 inches)

Area = Length × Width

Area = (1 7/9 inches) × (3/4)(1 7/9 inches)

Area = 16/9 inches × 16/9 inches × 3/4

Area = 768/324 inch²

Area = 256/108 inch²

Area = 128/54 inch²

Area = 64/27 inch²

Area = 2 10/27 inch²