Working on Summer Vacation. An Adweek/Harris (July 2011) poll found that 35% of U.S. adults do not work at all while on summer vacation. In a random sample of 10 U.S. adults, let x represent the number who do not work during summer vacation

a. For this experiment, define the event that represents a "success"

b. Explain why x is (approximately) a binomial random variable

c. Give the value of p for this binomial experiment

d. Find P(x = 3)

e. Find the probability that 2 or fewer of the 10 U.S. adults do not work during summer vacation

Answer:

x = 6, solution is not extraneous

Step-by-step explanation:

If you go and plug in 6 then the equation works well and there are no extraneous solutions.

Based on the net present value profile, Project H has a higher NPV than Project E.

To compare the net present value (NPV) of Project E and Project H, we need to calculate the present value of cash flows for each project and determine which one has a higher NPV. The cash flow patterns for the two projects are as follows:

Project E:

Initial investment: -$100,000

Cash flows for Year 1: $40,000

Cash flows for Year 2: $50,000

Cash flows for Year 3: $60,000

Project H:

Initial investment: -$120,000

Cash flows for Year 1: $60,000

Cash flows for Year 2: $50,000

Cash flows for Year 3: $40,000

To calculate the present value of cash flows, we need to discount them using an appropriate discount rate. The discount rate represents the required rate of return or the cost of capital for the company. Let's assume a discount rate of 10%.

Using the formula method, we can calculate the present value (PV) of each cash flow and sum them up to obtain the NPV for each project:

For Project E:

PV = $40,000/(1 + 0.10)^1 + $50,000/(1 + 0.10)^2 + $60,000/(1 + 0.10)^3

PV = $36,363.64 + $41,322.31 + $45,454.55

PV = $123,140.50

For Project H:

PV = $60,000/(1 + 0.10)^1 + $50,000/(1 + 0.10)^2 + $40,000/(1 + 0.10)^3

PV = $54,545.45 + $41,322.31 + $30,251.14

PV = $126,118.90

Using the financial calculator method, we can input the cash flows and the discount rate to calculate the NPV directly. By entering the cash flows for each project and the discount rate of 10%, we find that the NPV for Project E is approximately $123,140.50 and the NPV for Project H is approximately $126,118.90.

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The measure of the angles for the similar triangles are ∠G = 105°; ∠H = 55° and ∠I = 20°

Two triangles are said to be similar if the ration of their corresponding sides are in the same proportion. Also, all their corresponding angles are congruent with each other.

From the diagram shown:

∠X + ∠Y + ∠Z = 180° (sum of angles in a triangle)

20 + 105 + ∠Z = 180

∠Z = 55°

Since triangle XYZ and triangle GHI are similar, hence:

∠X = ∠G = 105°; ∠Z = ∠H = 55° and ∠Y = ∠I = 20°

The measure of the angles are ∠G = 105°; ∠H = 55° and ∠I = 20°

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The domain value that corresponds to a range value of 4 is,

⇒ x = 1/2

Given that;

Function is,

y = 4x + 2

Since, the equation equal to the range value:

4 = 4x + 2

Then, we can solve for "x":

4 - 2 = 4x

2 = 4x

x = 1/2

Now that we have the value of "x", we can find the corresponding value of "y" by substituting it into the given equation:

y = 4x + 2

y = 4(1/2) + 2

y = 4 + 2

y = 6

Therefore, the domain value that corresponds to a range value of 4 is,

⇒  x = 1/2

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Answer:

11.7 in

Step-by-step explanation:

The most appropriate way to model 9485 with the base ten blocks is
9 - thousand, 4 - hundred, 8- ten, and 5 - once.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

Base ten block implies the number of blocks according to the digit representation,
For the given question,
The number represents there are 9485 cubes, which can be represented as 9 - thousand, 4 - hundred, 8- ten, and 5 - once.

Thus, the most appropriate way to model 9485 with the base ten blocks is 9 - thousand, 4 - hundred, 8- ten, and 5 - once.

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The interest that have been earned after two years is $25.

A type of interest known as compound interest is computed using both the original sum and any accrued interest from earlier periods. The interest that is earned on interest is, in other terms, interest.

We know that by the compound interest formula;

A = P(1 + r/n)^nt

A = amount

P = principal

r = rate

n = Number of times compounded

t = time

Thus;

A = 1100(1 + 0.0114/365)^365* 2

A = $ 1125

Thus the interest after two years is;

$ 1125 - $1100

= $25

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Answer

its scale factor is ​4/3 and 0.75

Step-by-step explanation:

Answer:

correct answer is four sixths

Step-by-step explanation:

you can simplify 2/6 to 1/3 and then it would just be 1/3 plus 1/3. This is 2/3 or 4/6! Hope this helps :)

Answer:

3:8 or 3 to 8 depending on how you personally write it

Step-by-step explanation:

In problems like these you just need to put the numbers in the order that the question asks you in. In this case it is asking for drink mix (3) to water (8) making it 3:8.

Answer:

I saw another question like this but it was the other way like "water to drink mix" and it was 8:3 so technically and mathematically it would be 3:8

Step-by-step explanation:

Answer:

1899

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 3234

Standard deviation = 871

Percentage of newborns who weighed between 1492 grams and 4976 grams:

1492 = 3234 - 2*871

So 1492 is two standard deviations below the mean.

4976 = 3234 + 2*871

So 4976 is two standard deviations above the mean.

By the Empirical Rule, 95% of newborns weighed between 1492 grams and 4976 grams.

Out of 1999:

0.95*1999 = 1899

So the answer is 1899

V is a vector space with the operations of addition and scalar multiplication.

Since f(t) and g(t) are real numbers, you're utilizing the fact that the real numbers themselves are commutative in that step, which truly confused me when I first learned about it and after.

Let V denote the set of all differentiable real-valued functions defined on the real line.

You only need to mention that real-number addition is commutative. Since f is not a number until you evaluate, you couldn't do it before you did.

On a different note, you cannot say that

f+g=f(t)+g(t)

but you can say that (f+g)(t)=f(t)+g(t)

So  V is a vector space with the operations of addition and scalar multiplication.

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For the given distribution, the Expectation, E(2X² + 3X) is 28.9

Now here we see that we have the distribution given to us

We need to find

E(2X² + 3X)

Now we know that

E(X) = ∑xp(x)

Hence we get

E(2X² + 3X) = 2[1 X 0.2  +  4 X 0.3  +  9 X 0.2  +  16 X 0.4] + 3[1 X 0.2  +         2 X 0.3  +  3 X 0.2  +  4 X 0.4]

= 2[0.2 + 1.2 + 1.8 + 6.4] + 3[0.2 + 0.6 + 0.6 + 1.6]

= 2 X 9.6  +  3 X 3

= 19.2 + 9

= 28.9

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Complete Question

(image Attached)

Answer:

(1, 1)

Step-by-step explanation:

not 100% sure though, but hope it helps

The area of both the top face and the bottom face of the cuboid is 63 square centimeters (cm²).

To find the area of each face of the cuboid, we'll use the formulas for finding the area of a rectangle (which is the shape of each face of the cuboid).

Given dimensions:

Length (L) = 9 cm

Width (W) = 7 cm

Height (H) = 4 cm

a) Area of the top face of the cuboid:

The top face is a rectangle with dimensions 9 cm (length) and 7 cm (width).

Area = Length × Width

Area = 9 cm × 7 cm

Area = 63 square centimeters (cm²)

b) Area of the bottom face of the cuboid:

The bottom face is also a rectangle with dimensions 9 cm (length) and 7 cm (width).

Area = Length × Width

Area = 9 cm × 7 cm

Area = 63 square centimeters (cm²)

Therefore, the area of both the top face and the bottom face of the cuboid is 63 square centimeters (cm²).

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Answer: The amount you would pay (including tax) for the item is:

$755.37 + $52.88 = $808.25

Step-by-step explanation: irst, we calculate the amount of discount that is applied to the original price:

30% of $1199 = 0.3 x 1199 = $359.70

So, the discounted price is:

$1199 - $359.70 = $839.30

Next, we apply the additional 10% off coupon to this discounted price:

10% of $839.30 = 0.1 x $839.30 = $83.93

The final price after the coupon is applied is:

$839.30 - $83.93 = $755.37

Finally, we calculate the sales tax on this final price:

7% of $755.37 = 0.07 x $755.37 = $52.88

The amount you would pay (including tax) for the item is:

$755.37 + $52.88 = $808.25

Answer:

The greatest four-digit number that is divisible by 6 is 9996

Step-by-step explanation:

9,996 / 6 = 1,666

The amount invested at 3% is $400, the amount invested at 4% is $700, and the amount invested at 5% is $1000.

Let's assume the amount invested at 4% is x dollars.

According to the given information, the amount invested at 5% is $1000 more than the amount invested at 4%.

So, the amount invested at 5% is (x + $1000).

The total amount invested is the sum of the amounts invested at each rate, which is $2100.

Therefore, we can write the equation:

x + (x + $1000) + (amount invested at 3%) = $2100

Now, we can calculate the amount invested at 3%.

We subtract the sum of the amounts invested at 4% and 5% from the total investment:

(amount invested at 3%) = $2100 - (x + x + $1000) = $2100 - (2x + $1000)

Given that Elena receives $95 per year in simple interest from the investments, we can use the formula for simple interest:

Simple Interest = Principal × Interest Rate

The interest earned from the investment at 3% is (amount invested at 3%) × 0.03, the interest earned from the investment at 4% is (amount invested at 4%) × 0.04, and the interest earned from the investment at 5% is (amount invested at 5%) × 0.05.

According to the problem, the total interest earned is $95.

So we can write the equation:

(amount invested at 3%) × 0.03 + (amount invested at 4%) × 0.04 + (amount invested at 5%) × 0.05 = $95

Now we can substitute the expression for (amount invested at 3%) and solve for x.

Once we have the value of x, we can calculate the amounts invested at 3%, 4%, and 5% using the given information.

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The solid figure is a triangular prism over an unfolding square-based pyramid labelled Net 1.

Simple representations of solids in three dimensions—height, breadth, and length—are solid shapes.

Solid forms are also referred to as 3D shapes. These large forms take up space and are present everywhere. We make use of, feel, and perceive them.

In mathematics, we examine many shapes and attempt to apply them to real-world problems.

Now let's talk about the characteristics of each solid shape. Solid shapes are categorized using a variety of categories. The solid figure is a triangular prism over an unfolding square-based pyramid labelled Net 1.

Therefore, the solid figure is represented by a triangular prism perched above an unfolding square-based pyramid labelled Net 1.

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Answer:

6 donuts

Step-by-step explanation:

first divide the cost of the donuts by the amount of donuts per box

6 donuts:

2.10 ÷ 6 = .35 per donut

12 donuts

5.40 ÷ 12 = .45 per donut

18 donuts

7.20 ÷ 18 = .40 per donut

24 donuts

12 ÷ 24 = .50 per donut

Answer:

$0.91

Step-by-step explanation:

Given:

If one pound of Parmesan cheese costs $14.60, to find the cost of a one-ounce portion, simply divide the cost of one pound by 16:

\(\implies \textsf{1 ounce portion}=\dfrac{\$14.60}{16}=\$0.9125=\$0.91\;\sf (nearest \; cent)\)

Therefore, the standard portion cost for a one-ounce portion of Parmesan cheese is $0.91 (nearest cent).

The instantaneous rate of change is -6 words per day,

the number of words Alex remembers after 5 days, option (D).

What is the instantaneous rate of change ?

An instantaneous rate is the rate at some instant in time. An instantaneous rate is a differential rate: -d[reactant]/dt or d[product]/dt. We determine an instantaneous rate at time t: by calculating the negative of the slope of the curve of concentration of a reactant versus time at time t.

Have given,

Alex learned 80 new vocabulary words

and after t days he learned,

W(t) = \(80 (1-0.1t)^{3}\)

differentiate respect of t

W'(t) = \(80 \frac{d}{dt} (1-0.1t)^{3}\)

W'(t) = \(80 * 3(1-0.1t)^{2} \frac{d}{dt}(1-0.1t)\)

W'(t) = \(240(1-0.1*5)^{2} (0.1)\)

W'(t) = 6

That's mean , the instantaneous rate of change is -6 words per day.

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Answer: 10

Step-by-step explanation:

The value of the expression given, using the concept of absolute value, is given as 10.

Absolute value of an integer returns the positive value of that integer. In other words, absolute value returns the distance between the integer and zero. The absolute value of |x| is x, if x is positive integer and -x, if x is negative integer.

Given in the question,

a = -9

the expression is as follows:

\(\frac{2|a|}{3} + |a+5|\)

Putting the value of a in above expression :

\(=\frac{2|-9|}{3} + |-9+5|\\ \\=\frac{2*9}{3} + |-4|\\ \\= 2*3 + 4\\\\=6+4 =10\)

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Answer:

2. d. 0.0008

3. b. 0.07

4. c. thousandths

5. c. 0.005

17 x 9 = 153

Step-by-step explanation:

the answer is 153

The local tide measurement data contradict the satellite data because the number of decreasing local sea level trends is greater than the number of increasing local sea level trends. So correct option is C.

Measuring tides involves observing and recording changes in the water level of oceans, seas, and other bodies of water over time. Tides are caused by the gravitational pull of the moon and sun on the Earth's water, which results in a rhythmic rise and fall of water levels.

Tide measurements are important for a variety of reasons, including understanding ocean circulation, predicting flooding and storm surges, and planning shipping routes. Tidal data is also used in climate research, as changes in sea level can indicate long-term climate trends.

The local tide measurement data contradict the satellite data because the number of decreasing local sea level trends is greater than the number of increasing local sea level trends.

The measurement is done because the land surfaces are dynamic with some locations rising or sinking relative to sea level changes are different across world coasts.

Therefore, the Option C is correct.

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The complete question is:

The ratio of the number of baskets scored by team A to the number of baskets by team B is 2: 5. Then the correct option is B.

In a basketball game, team B scored 5 baskets for every 2 that team A scored.

The utilization of two or more additional numbers that compares is known as the ratio.

Assume that Team A scored two baskets while Team B netted five.

The problem statement states that for every two baskets Team A scored, Team B scored five. This may be expressed as the ratio shown below:

Ratio = 2x : 5x

Ratio = 2: 5

Thus, the correct option is B.

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