W X
Y
Z
List the sample space for the experiment.
Os = {X, Y, Z}
Os = {W, Z, Z}
Os = {W.Y.Y. Z}
Os = {W, X, Y, Z}

Answer:

12 Days

A ratio has two or more numbers that symbolize relation to each other. Ratios are used to compare numbers, and you can compare them using division.

To find the ratio of the problem (days: pages) we can use this equation:

pages read ÷ days it took = pages read each day

Fitting the numbers into the equation:

168 ÷ 7 = 24

So, everyday Kelly reads 24 pages.

To find out how many more days Kelly needs to read, if she reads at the same rate, we can use this equation:

(456 - 168) ÷ 24 = days left

We can use this to check our work:

168 + (24 ×?) = 456

Solving for the first equation:

(456 - 168) ÷ 24 = days left

288 ÷ 24 = 12

Now, we can check our work.

168 + (24 ×?) = 456

Inserting 12 into the equation:

168 + (24 × 12) = 456

168 + 288 = 456

Therefore, to complete the book it will take Kelly 12 more days.

Answer: The total number of members in the club is 140 + 695 + 210 = 1,045.

The number of non-senior members is 140 + 695 = 835.

The probability that the first member selected at random will not be a senior member is 835 / 1,045 = 0.798 or 79.8%.

So, the answer is 0.798 or 79.8%.

Step-by-step explanation:

5 additional trees give maximum yield and 35 trees per acre will give largest crop of apple.

Let's assume that, we are planting x apple trees extra per acre. So, net 10x apple will be less.

Let say, total number of apples = y

Then, y = (30+x)×(400–10x)

For, optimum number of trees, let's do the differentiation of the above equation with respect to x.

d(y)/d(x) = (400–10x)×1 + (30+x)×(-10)

= 400–10x-300–10x

= 100–20x …………..(1)

For mimima or maxima, the above equation must be equal to 0.

So, 0 = 100–20x

=> x=5

Let's do the second differentiation of equation (1) and substitute the the value of x I.e x=5

[tex]d^2(y)/d(x^2) = -20[/tex]

The above equation is negative for all values of x which indicates that at x=5 we will have the maximum value.

So, the number of trees for maximum apple will be (30+x)

So, 30+5 = 35 trees per acre will give the largest crop of apple.

Hence 5 additional trees give maximum yield and 35 trees per acre will give largest crop of apple.

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Answer:31.42 sq.

Step-by-step explanation:

Answer:

Tech 9 rock and no answer

Step-by-step explanation:

The answer is given below:

Binomial distribution is a discrete  probability distribution in which it gives two values that is either success or failure.

A local donut shop began putting an extra donut in some of the boxes.

The shop owner claimed that one in seven boxes had an extra donut.

Nine customers each bought one box of donuts at the shop.

Probability of success fixed is, [tex]p=\frac{1}{7}[/tex]

A value of n fixed, n=9.

We can use binomial distribution to solve this problem,

The probability mass function for the Binomial distribution is given as:

Assume  X is a binomial distribution, [tex]B(n=9,p=\frac{1}{7}=1.143)[/tex].

[tex]P(X)=(nCx)(p)^{x} (1-p)^{n-x}[/tex]

The mean is given by:

[tex]E(X)=np=9*\frac{1}{7}=1.29\\[/tex]

The variance is given by,

[tex]Var(X)=np(1-p)=9*\frac{1}{7}(1-\frac{1}{7} )[/tex]=1.1094

From variance, the standard deviation is given by, [tex]std(X)=\sqrt{1.1094}[/tex]=1.05.

Two of the nine customers buy a box of donuts with an extra donut. Compute P(X ≥ 2) and use the result to justify your answer.

[tex]P(X\ge2)=1-P(X=2)\\1-P(X\le1)=1-[P(X=0)+P(X=1)][/tex]

And if we find the individual probabilities we got,

[tex]P(X=0)=(9C0)(0.143)^{0} (1-0.143)^{9-0}=0.249\\P(X=1)= (9C1)(0.143)^{1} (1-0.143)^{9-1}=0.374[/tex]

[tex]P(X\ge2)=1-P(X=2)\\1-P(X\le1)=1-[P(X=0)+P(X=1)]\\[/tex]

                      = 1-[0.249+0.374]

                       = 0.377

Hence, [tex]P(X\ge2)=[/tex] 0.377.

This case makes sense the claim since the probability is higher or equal than the expected with the claim.

Corrected question:

To increase sales, a local donut shop began putting an extra donut in some of the boxes. Customers are unaware of which boxes had the extra donut and the shop owner claimed that one in seven boxes had an extra donut. Nine customers each bought one box of donuts at the shop. Let X = the number of customers that bought a box containing an extra donut.A. Is X a binomial random variable? Explain.B. What is the mean and standard deviation of X? Provide an interpretation for each value in context.C. Two of the nine customers buy a box of donuts with an extra donut. Is the shop's claim accurate? Compute P(X ≥ 2) and use the result to justify your answer.

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The average rate of change of f(x) over the interval 3≤x≤4 is 15

From the question, we have the following parameters that can be used in our computation:

The table of values

On the table, we have

f(3) = -4

f(4) = 11

The average rate is then calculated as

Average rate = [f(4) - f(3)]/[4 - 3]

Substitute the known values in the above equation, so, we have the following representation

Average rate = (11 + 4)/(4 - 3)

Evaluate

Average rate = 15

Hence, the average rate is 15

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Complete question

Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 3\le x \le 43≤x≤4.

X f(x)

3 -4

4 11

5 8

6 10

7 11

8 14

Using the concept of rates, the machine will complete 9 9/64 inches in 8.67 minutes

To determine how long it will take to turn a particular length of iron, we can calculate the rate at which it works and it must be in a definite proportion.

If the lathe moves 3/128 in one revolution.

And the machine completes 45 revolutions in 1 minutes, we can determine how many inches in moves in that minute.

3/128 in = 1 rev

x in = 45

45 * (3/128) = 45 revolutions = 1 minute

1.054 inches in 1 minute.

We can further use this to determine the time it takes to move 9 9/64 inches

1.054 inches = 1 minute

9 9/64 inches = x minute

cross multiply both sides and solve

x = 8.67 minutes

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Answer:

[tex]-\dfrac{4}{5}[/tex]

Step-by-step explanation:

We have the following expression

[tex]3 \;\dfrac{1}{2} x - 5\;\dfrac{1}{2}x[/tex]

and asked to evaluate this expression at  [tex]\[x = {2\over\displaystyle 5\][/tex]

First convert [tex]3 \; \dfrac{1}{2}[/tex]   and  [tex]5 \; \dfrac{1}{2}[/tex]  to mixed fractions

[tex]3 \; \dfrac{1}{2} = \dfrac{3 \times 2 + 1}{2} = \dfrac{7}{2}\\[/tex]

[tex]5 \; \dfrac{1}{2} = \dfrac{5 \times 2 + 1}{2} = \dfrac{11}{2}[/tex]

Therefore
[tex]3 \;\dfrac{1}{2} x - 5\;\dfrac{1}{2}x\\\\= \dfrac{7}{2}x - \dfrac{11}{2}x\\\\= \dfrac{7 - 11}{2} x\\\\= -\dfrac{4}{2}x \\\\= -2x\\\\[/tex]

[tex]\mathrm{For \;x =\dfrac{2}{5}},\\\\= -2x \\= - 2 \times \dfrac{2}{5}\\\\= -\dfrac{4}{5}[/tex]

Answer:

Step-by-step explanation:

The height of the tree to the nearest foot is 27 feet.

The height of the tree can be found as follows:

The height of the tree can be found using trigonometric ratios. Therefore,

let

tan ∅ = opposite / adjacent

Therefore,

opposite side = adjacent tan ∅

Hence,

height of the tree = 20 + x tan 45° = x tan 75°

20 + x tan 45° = x tan 75°

20 tan 45 + x tan 45° = x tan 75°

20 tan 45 =  x tan 75° -  x tan 45°

20 tan 45 =  x(tan 75 - tan 45)

20 tan 45 = x(3.73205080757 - 1)

2.73205x = 20

x = 20 / 2.73

x  = 7.32600732601

x = 7.34

Therefore,

height of the tree = x tan 75°

height of the tree = 7.34 × tan 75°

height of the tree = 27.3186119114

height of the tree = 27 ft

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Answer:

Step-by-step explanation:

Answer:  Yes, it's wrong.

Step-by-step explanation:

In the equation, it was [tex]A=\pi r^{2}[/tex]3 ft is the circle's diameter, and d is not the r.

r = d/2 = 3/2 = 1.5 ft

[tex]A=\pi r^{2}\\[/tex]

   ≈ 3.14 x 1.5

   = 4.71

Measure of angle B is 36.87°.

Trigonometric functions are defined as the real functions or the periodic functions which relate an angle in a right angled triangle to the ratios of the length of two sides.

Given is a right angled triangle.

We have to find measure of angle B.

Cosine of an angle in a right angled triangle is equal to the ratio of it's adjacent side to the hypotenuse.

Hypotenuse = AB = 5

Adjacent side to B = CB = 4

Cos B = 4/5

∠B = Cos⁻¹ (4/5)

     = 0.6435 radians

     = 36.87°

Hence the measure of the angle B is 36.87°.

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The area of the figure is solved to be

The area of a kite is solved using the formula

= P * q / 2

Where

p = length of long diagonal

q = length of short diagonal

Using the figure the length can be traced to be

p = 3 - -5 = 3 + 5 = 5

q = 6 - 2 = 4

Area of the figure

= 5 * 4 / 2

= 20 / 2

= 10 square units

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The result to the factorization of the polynomial is 3x (x + 10) (x - 10).

Factoring polynomials involves utilizing prime factorization to break the given polynomial down into a product of two or more polynomials. Polynomials can be readily simplified by factoring them.

Writing each term of the longer expression as the product of its elements is the initial step to factorization polynomials.

= 3x³ - 300x

= 3x(x²) - 300x

= 3x(x²) - 3x(100)

= 3x(x² - 100)

= 3x(x² - 10²)

Since both terms are perfect squares, factor using the difference of squares formula, a² − b² = ( a + b ) ( a − b );

where

= 3x (x+10) (x−10)

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get rid of y. that's all you have to do.

The temperature at 3 AM is about 53 degrees Fahrenheit.

The average kinetic energy of the particles in a medium, such as a gas, liquid, or solid, is measured by its temperature. It is a basic physical characteristic that governs the rate and amount of heat transmission between two bodies that are in thermal contact.

A thermometer is commonly used to measure temperature. It does this by detecting changes in a substance's physical characteristics that change with temperature, such as the expansion or contraction of a liquid or the resistance of a wire.

We are aware that a sinusoidal function models temperature, and the following information is crucial:

A high of 80 degrees is reached at 5 PM, or 17:00 in a 24-hour period.

The day's average temperature is 60 degrees.

We're looking for the temperature at three in the morning, or three in 24-hour time.

We can utilize the fact that the temperature moves through one full cycle in a 24-hour day to determine the frequency. As the time frame is 24 hours, the frequency is:

B = 2π/24 = π/12

To find the phase shift, we can use the fact that the high temperature occurs at 5 PM, which is 8 hours after noon (when the temperature starts to rise). So the phase shift is:

C = (8/24) * 2π = (1/3)π

To find the amplitude, we can use the fact that the temperature swings 10 degrees above and below the average. So the amplitude is:

A = 10

Finally, we can use the formula to find the temperature at 3 AM:

f(x) = A sin(B(x - C)) + D

f(3) = 10 sin(π/12(3 - (1/3)π)) + 60

f(3) ≈ 53.4

So the temperature at 3 AM is about 53 degrees Fahrenheit.

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The correct option is C, P - value is 0.0718.

A sample proportion in statistics is a measurement of the proportion or percentage of a sample that demonstrates an important characteristic or quality. It is computed by dividing the sample's overall population by the proportion of participants who exhibit the characteristic.

For instance, if a sample of 100 individuals is chosen to estimate the percentage of people who love chocolate ice cream, and 30 of those individuals state that they do, the sample proportion would be 0.3 or 30%, as 30 out of 100 individuals state that they do.

We must first compute the test statistic in order to determine the P-value for Aurelia's test. The test statistic has a typical normal distribution when the null hypothesis is true.

The sample proportion of heads is:

p' = 43/100 = 0.43

The test statistic is:

[tex]z = \frac{(p' - p)}{ \sqrt{(p(1-p) / n)}}[/tex]

where p is the hypothesized proportion under the null hypothesis, and n is the sample size.

Substituting the given values, we get:

[tex]z = \frac{(0.43 - 0.5)}{/ {sqrt(0.5 \times 0.5 / 100)}} = -1.8[/tex]

Since this is a two-sided test, we need to find the area under the standard normal distribution curve in both tails of the distribution that is more extreme than the observed test statistic.

Using a standard normal distribution table, we find that the area to the left of -1.8 is 0.0359. Therefore, the area in both tails is:

P-value = 2 × 0.0359 = 0.0718

So, the correct answer is:

c) 0.0718

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Answer:C

Step-by-step explanation: Kahn Academy

Answer:

The height of the kite above the ground is; approximately 50.69 feet.

What are trigonometric identities?

Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.

The height of his hands above the ground, h is given by 3 feet

Angle of elevation of the string (above the horizontal), θ = 32°

Length of the string, l is given as 90 feet

The height of the kite above the ground is given by trigonometric ratios as ;

Sin∅ =h /90

Sin 32°= h/90

0.52 =h /90 (Sin32°= 0.52)

so h= 47.69 feet

Then height from ground is (H) = 3 +47.69  

H = 50.69 feet

The height of the kite above the ground ,  ≈ 50.69 feet

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Step-by-step explanation:

Answer:

20

Step-by-step explanation:

snajakskdmcjwiwjcjf

Answer:

20

Step-by-step explanation:

70% is 70/100 = 0.70

20 x 0.70 = 14

Answer:

131,072 Zombies:

the equation: 32 x 4^6 = 131,072

the equation in scientific notation form: 3.2 x 4^7 = 131,072

Step-by-step explanation:

The amount of zombies starts at 32. It quadruples per hour, so we need to multiply the amount by 4 six times(once for every hour).

We can use an exponent to represent this in an equation:

32 x 4^6 = 131,072

Or, if we put it in scientific notation,

3.2 X 4^7 = 131,072.

The equation which represents the number of zombies is;

= [tex]1.31072[/tex]×[tex]10^{5}[/tex]

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign.

Given that

The amount of zombies = 32.

And It quadruples per hour,

Therefore,

Multiply the amount by 4 six times (as it occurs once for every hour).

The the exponent form to represent this equation:

32 x 4^6 = 131,072

Hence, in scientific notation the equation is,

= [tex]1.31072[/tex]×[tex]10^{5}[/tex]

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One box of dog food costs $7, while one can of cat food costs $8.

Equations are statements in mathematics that have two algebraic expressions on either side of the equals (=) sign.

It illustrates that the expressions printed on the left and right sides have an equal relationship.

Some of the components of an equation are coefficients, variables, operators, constants, terms, expressions, and the equal to sign. When expressing an equation, the "=" symbol and terms on both sides are a need.

Given data ,

Let the price of a single box of dog food at  x.

Let's say the price of one can of cat food is y.

The cost of 1 box of dog food and 2 cans of cat food is  = $ 23

One can of cat food and two boxes of dog food cost $22, total.

So , the equation will be

1x + 2y = 23                                 ....... (1)

2x + 1y = 22                                  ....... (2)

Equation (1) is multiplied by 2 to get

2x + 4y = 46                                ....... (3)

When equation (2) is subtracted from equation (3), we obtain

3y = 24

value of y is obtained by dividing both sides by 3,

y = $ 8

Equation (1) can be solved by substituting the value of y.

x + [tex]2*8[/tex] = 23

x + 16 = 23

16 is subtracted from both sides, giving us

x = $ 7

Therefore , the value of x is $ 7 and value of y is $ 8

Thus, one package of dog food costs $7, while one can of cat food costs $8.

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5 to the power of one sixth (5¹/⁶) will be equal to square root of the cube root of 5.

What is the definition of square root?

The square root of a number is a value that, when multiplied by itself, yields the original number. The square root is the opposite of squaring a number. As a result, squares and square roots are ideas that are connected.

If x is the square root of y, it is denoted as x=√y, or the same equation may be expressed as x² = y. √" is the radical symbol used to symbolise the numerical root here. When a positive number is multiplied by itself, it represents the number's square. The square root of a positive number yields the original value.

Now,

Given that square root of the cube root of 5 i.e. √∛5=?

=√5¹÷³

=5¹/²*¹/³

=5¹/⁶

hence,

          5 to the power of one sixth (5¹/⁶) will be equal to square root of the cube root of 5.

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Answer:70% chance they vote yes

Step-by-step explanation:

Answer:

3/10 for red people and 7/10 for blue people.

Step-by-step explanation:

A knitted hat pattern comes in 4 styles with 4 stitch options and 3 sizes, and there are 7 yarns appropriate for the hat. There are 112 different hats that can be made using the knitted hat pattern, disregarding size.

To find the total number of different hats that can be made using the knitted hat pattern, we need to multiply the number of choices for each feature.

There are 4 styles to choose from and 4 stitch options, so there are 4 x 4 = 16 different combinations of style and stitch.

For each of these style and stitch combinations, there are 7 yarns that can be used, so the number of possible yarn choices is 7.

Therefore, the total number of different hats that can be made, disregarding size, is:

16 (style and stitch combinations) x 7 (yarn choices) = 112

This calculation shows how the multiplication principle of counting can be used to find the total number of outcomes in a multi-stage process where the number of choices at each stage is known. In this case, we multiplied the number of style and stitch combinations by the number of yarn choices to find the total number of different hats that can be made.

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Complete question is:

A knitted hat pattern comes in 4 styles with 4 stitch options and 3 sizes, and there are 7 yarns appropriate for the hat. Disregarding size, how many different hats can be made?

The probability of a college student being either female or having financial aid can be expressed as P(A ∪ B) = P(A) + P(B).

What is Probability?

Probability is a mathematical concept used to measure the likelihood of a particular event occurring. It is a way of expressing the chance or possibility of an event happening, ranging from 0 (impossible) to 1 (certain).

In probability theory, an event is a subset of the possible outcomes of an experiment or a random process. Probability can be expressed in terms of fractions, percentages, or decimals.

The symbol for the event that a college student is female is A, as given in the statement. The symbol for the event that a college student has financial aid is B, as given in the statement.

So, A={A student is female} and B={A student has financial aid}.

These events are mutually exclusive because one does not necessarily affect the other. For example, a male student can have financial aid and a female student may not have financial aid. Hence, the occurrence of one event does not influence the occurrence of the other event.

Therefore, the probability of a college student being either female or having financial aid can be represented as the union of the events A and B. It can be denoted as P(A ∪ B) and is calculated as:

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

Where P(A ∩ B) represents the probability of a student having both characteristics, i.e., being female and having financial aid.

However, as these events are mutually exclusive, P(A ∩ B) = 0. So the probability of a college student being either female or having financial aid is simply the sum of their individual probabilities:

P(A ∪ B) = P(A) + P(B) - 0

P(A ∪ B) = P(A) + P(B)

Hence, the probability of a college student being either female or having financial aid can be expressed as P(A ∪ B) = P(A) + P(B).

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4A. The number of whole pie shaded are 2

4B . The number of partial pie shaded is 3

4C.  The mixed number formed is 2 3/5

5A. The whole number part which is 2 is the quotient

5B.  The remainder is 3

In mathematics, a fraction is a number that represents a part of a whole. It consists of two parts: a numerator, which is the part of the fraction that represents the number of parts being considered, and a denominator, which is the number that represents the total number of parts in the whole.

A mixed number is a combination of a whole number and a fraction. It represents a quantity that is greater than the fraction but less than the next whole number.

For example, In the division problem, the dividend is 13 and and the divisor is 5. the division results to mixed number of value 2 3/5.

The mixed number 2 3/5 represents a quantity that is equal to

two whole and three fifths.

converting to improper fractions gives 13/5

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