12. Susan has 8 eggs in her fridge.
Two of the eggs have passed their sell by date and are "bad".
She selects 3 eggs at random to bake a cake.
(a) Complete the probability tree diagram.

(b) Work out the probability that Susan will select 3 "good" eggs.
(c) Work out the probability that Susan will select at least one "bad" egg.

The equation be 38.67 + 13.6 then we get 52.27.

A different way to represent a fractional value in mathematics is to use decimal notation. It denotes that base-10 fractional representation is being used. It is possible to change fractions into decimals and vice versa.

The same thing applies to decimals: they each represent a portion of a whole number. The distinction is in the notation used to write decimals vs fractions. By using decimal notation, we can graphically express how much of a whole number we are working with.

The decimal point must be moved till it is to the left of the first non-zero number in order to be written in scientific notation. The exponent is the amount of places the decimal point advances since each movement signifies a "power of 10".

Let the equation be 38.67 + 13.6 then we get 52.27.

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Answer:

1.02, 1.1, 1.101

Step-by-step explanation:

use a calculator

Answer:

In this case, the mean is $1400, and the standard deviation is $200.

So, one standard deviation of the mean is 1400+200= $1600 and 1400-200 = $1200.

Therefore, according to the empirical rule, approximately 68% of the farms will have land and building values per acre between $1200 and $1600.

To estimate the number of farms that fall within this range, we can multiply the total number of farms (74) by 0.68.

(74)*(0.68) = 50.32 or about 50 farms

So, according to the empirical rule, approximately 50 farms will have land and building values per acre between $1000 and $1800.

The set of ordered pairs share the same reference angle is (- 1/2, -√3/2 ), (1/2,√3/2 )

The term ordered pair in math is defined as  a composition of the x coordinate  and the y coordinate by having two values written in a fixed order within parentheses.

Here we have know that the reference angle of x is obtained by either 180-x, 180+x. or 360-x depending on the position of terminal whether II quadrant or iv quadrant, or iii quadrant, etc.

So, based on these condition in order to find the reference angles here we must define that cos will remain cos only and sin will remain sin only there may be only changes in sign.

On the other hand all the ordered pairs given, here we find that I, II, and Iv there is a switch over form cos to sine and sin to cos.  

Based on these condition option (3) is correct one.

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Answer:

1/2 = 3/6 and 1/3 = 2/6

Step-by-step explanation:

we need to make the denominators the same to be able to compare

A controlled experiment is a scientific test conducted under controlled conditions. That is, change only one (or a few) factors at a time and keep all others constant.

Control Experiment:

Controls eliminate alternative explanations for experimental results, particularly experimental error and experimenter bias. Many controls, like molecular markers used in SDS-PAGE experiments, are specific to the type of experiment being performed and may simply have the purpose of confirming that the instrument is functioning properly. I have. Choosing and using appropriate controls and ensuring that experimental results are valid (eg, no confounding variables) can be very difficult. Control measurements can also be used for other purposes. For example, measuring the background noise of a microphone in the absence of a signal allows the noise to be subtracted from later signal measurements to produce a higher quality processed signal.

For example, if a researcher fed a laboratory artificial sweetener to 60 laboratory rats and observed that 10 of them subsequently became ill, the underlying cause could be the sweetener itself or could be something else. Other variables that may not be immediately apparent can interfere with experimental design. For example, an artificial sweetener can be mixed with a diluent, and it could be the diluent that causes the effect.To see the effect of the diluent, he does the same test twice. A diluent with artificial sweeteners and a diluent-only version in the same way. Here the experiment is checked for diluent and the experimenter can distinguish between sweetener, diluent and no treatment. Controls are usually required when confounding factors cannot be easily separated from the primary treatment. For example, a tractor may need to be used to spread manure when there is no other practical way to spread it. The simplest solution is for the tractor to drive over the plot without spreading fertilizer and control the effects of tractor traffic.

The simplest types of controls are negative and positive controls, both of which are found in many different types of experiments. If both are successful, these two controls usually have the most latency. sufficient to eliminate significant confounding variables. That is, an experiment produces a negative result when a negative result is expected and a positive result when a positive result is expected.

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So, on solving the provided question we can say that Percent = 140/250 x100 = 56%

A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) x 100%.

A percentage is a ratio of one unit of an event's result to the entire sample multiplied by 100%. It denotes parts per 100. We divide the percentage of the sample that liked the options by the total sample to arrive at the calculation. As a result, we compute:

Percent = 140/250 x100 = 56%

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The direct relantionship model indicates that variable q is equal to 225 / 19 when r is 45.

In this problem we must derive an equation based on following relationship:

Variable q is directly proportional to r.

In other words, we have the following direct relationship model that describes well the situation:

q = k · r

Where:

First, determine the constant of proportionality:

k = q / r

k = 76 / 20

k = 19 / 5

Second, calculate the variable r is:

q = r / k

q = 45 / (19 / 5)

q = 225 / 19

The statement presents several typing mistakes, correct form is introduced below:

q is directly proportional to r is 76 when r is 20.

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The shaded region corresponding to all values of x and y that satisfy these requirements is shown the graph

Suppose the considered function whose graph is to be made is

f(x)

The values of 'x' (also called input variable, or independent variable) are usually plotted on horizontal axis, and the output values

f(x)

are plotted on the vertical axis.

They are together plotted on the point

(x,y) = (x, f(x))

This is why we usually write the functions as:

y = f(x)

Therefore, the graph is given with shaded region

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The number of gallons that are in the water cooler when it is completely full is; 183.49 gallons

The formula for the volume of a cylinder is;

V = πr²h

Where;

V is volume

r is radius

h is height

We are given;

Radius(r) = diameter/2 = 2.5/2 = 1.25 ft

Height(h) = 5 ft

Thus;

V = π * 1.25² * 5

V = 24.53125 ft³

There are approximately 7.48 gallons of water in a cubic foot, therefore;

Number of gallons in 24.53125ft³ = (24.53125 * 7.48)/1

Number of gallons = 183.49 gallons

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Answer: 183.49 gallons (D)

Step-by-step explanation:

Okay you are trying to find how many gallons of water the water cooler can hold.

So start by using the formula for the volume of a cylinder.

V = πr^2h

First find the radius, which is half the diameter.

The diameter is 2.5 so divide that by 2 to find the radius.

2.5/2 = 1.25

Now that you know the radius, times it by itself:

1.25 x 1.25 = 1.5625

Now multiply 1.5625 by the height, which is 5.

1.5625 x 5 = 7.8125

Now multiply 7.8125 by 3.14

7.8125 x 3.14 = 24.53125

And finally, multiply 24.53125 by 7.48

24.53125 x 7.48 = 183.49375 gallons

Now round to the nearest hundredth:

183.49 gallons

I did the same test and got it right and I have picture proof that it is correct.

Answer:

x= 12.714°

Step-by-step explanation:

<AEB + <CED = 90°

4x+1+3x = 90°

7x+1= 90°

7x=89

x= 12.714°

Dan paid for 2 shirts and 2 pairs of trousers will be shs 1300.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The cost of 7 shirts and 3 pairs of trousers is 2950 while that of 5 pairs of trousers and 3 shirts is less by 200.

Let 'x' and 'y' be the cost of a shirt and trousers, respectively. Then the equations are given as,

7x + 3y = 2950                ....1

5y + 3x = 2950 - 200

3x + 5y = 2750               ....2

Multiply equation 1 by 5 and equation 2 by 3, then we have

35x + 15y = 14750       ...3

9x + 15y = 8250          ...4

Subtract equation 4 from equation 3, then we have

35x - 9x = 14750 - 8250

26x = 6500

x = 250

Then the value of 'y' is given as,

3(250) + 5y = 2750

750 + 5y = 2750

5y = 2000

y = 400

Then Dan pay for 2 shirts and 2 pairs of trousers will be given as,

⇒ 2 x 250 + 2 x 400

⇒ 500 + 800

⇒ 1300

Dan paid for 2 shirts and 2 pairs of trousers will be shs 1300.

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Note that after the expression 2x³-5x²-19x+42, has been factorized, we have (x−2)(x+3)(2x−7).

Factorization or factoring in mathematics is the process of expressing a number or any mathematical object as a product of numerous factors, generally smaller or simpler objects of the same sort.

The polynomial 2x³-5x²-19x+42 can be factorized by using the rational root test. To apply this test first we need to find at least one rational zero.

In this case one rational zero is x=2.

This means that we can divide polynomial 2x³-5x²-19x+42 by x−2 (the factor theorem)

That is:

2x³-5x²-19x+42/ x-2

= 2x² - x - 21, this means that

2x³-5x²-19x+42 =  (2x² - x - 21) * (x-2)

From the above, our constants are given as:

a = 2, b = -1 and c = 21

Multiply the constant terms by the leading coefficient.

a *x = -42

Find out two number that multiply to a*c = -42 and add b = -1

Next we identify all pairs of numbers with a product of -42. They are:

Next we find all factor pair that sum up to b = -1. It is given as 6 +-7 which is identical to item 8 above.

Next, replace the middle term -1x with 6x-7x to get:

(2x²  −x−21) * (x-2) =(2x²  +6x−7x−21) * (x-2)

If we thus apply factoring by grouping, and factor 2x out of the first group and -7 out of the second group, we have: (2x-7) (x+3) (x-2).

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Full Question:

Factorise 2x³-5x²-19x+42

Answer:

x (number of games) = 8

Step-by-step explanation:

We want these two to be equal, which means we want:

4.50x + 5 = 4.75x + 3

We will minus 4.50x and 3 from both sides, giving us:

2 = .25x

Then, multiply by 4 to get a whole number of x, which gives us:

x = 8

Now, we will check our answer. We have:

4.50 * 8 + 5 = 4.75 * 8 + 3

36 + 5 = 38 + 3

41 = 41

So this proves x = 8.

So, the amount of games where the price would be the same is 8, x = 8.

Hope this helped!

Note that the very first step in verifying a statement about a product is represented by the acronym C.L.A.I.M. The first letter "C" stands for Claim.  

L - Logic: Examining the logic of the claim to see if it is reasonable and if the evidence offered supports the assertion.

A - Attribution: Identifying the source of the assertion and assessing its reliability.

I - Investigation: Research and evidence collecting to support or reject the allegation.

M - Measurement: Evaluating the quality and quantity of evidence obtained and assessing whether or not it supports the claim being made.

Following the CLAIM technique allows one to assess the correctness and validity of a claim and make an educated judgment about the product or service in issue.

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The correct null hypothesis in the given situation is:

(A) H0: p = 0.27; Ha: p > 0.27

Any variation between the selected attributes that you observe in a collection of data is thought to be the result of chance, according to the null hypothesis.

For instance, any discrepancy between the average profits in the data and zero is caused by chance if the expected earnings for the gambling game are actually equal to zero.

So, the population proportion serves as the parameter.

The American Academy of Periodontology found that 27% of US individuals admit to lying to their dentist about how frequently they floss their teeth.

So, the following is the null hypothesis:

H0: p = 0.27

Dr. Garcia, a periodontist, thinks that the percentage should be higher than 27% since he feels it is too low.

Consequently, the competing theory is:

H0: p > 0.27

Therefore, the correct null hypothesis in the given situation is:

(A) H0: p = 0.27; Ha: p > 0.27

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Complete question:

The American Academy of Periodontology released a survey, revealing that 27% of US adults admit they lie to their dentist about how often they floss their teeth. Periodontist Dr. Garcia believes that the percentage seems low, so he decides to conduct his own hypothesis test to determine the true proportion. What should he write as the null and alternative hypotheses for this situation?

Answer Options:

A: H0: p = 0.27; Ha: p > 0.27

B: H0: p = 0.27; Ha: p < 0.27

C: H0: p = 0.27; Ha: p ≠ 0.27

D: H0: μ = 0.27; Ha: μ > 0.27

E: H0: μ = 0.27; Ha: μ < 0.27

Simplifying √75 the answer is option D. 5√3.

An expression of a number which has a square root is termed surd. Some procedures are required to solve any given question on surd, especially when the given expression involves numbers that do not have a whole root.

To simplify √75 as required in the question, we have to look for a two numbers. One of these numbers must have a whole square root.

So that we can use 3 and 25.

Thus,

√75 = √(3 x 25)

       = √3 * √25

       = √3 * 5

       = 5√3

√75 = 5√3

The answer is option D. 5√3

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A 1:2 ratio example could be 1 cup of flour and 2 cups of sugar. A ratio is a comparison of two or more numbers that shows the relationship between them. A 1:2 ratio means that for every 1 unit, there are 2 units.

A ratio is a comparison between two or more numbers. A 1:2 ratio means that for every 1 unit, there are 2 units. As an example, if you have 1 cup of flour and 2 cups of sugar, the ratio is 1:2 – 1 cup of flour and 2 cups of sugar.

A ratio is a comparison of two or more numbers that shows the relationship between them. A 1:2 ratio means that for every 1 unit, there are 2 units. For example, If you have 1 cup of flour and 2 cups of sugar, the ratio is 1:2. This means that for every 1 cup of flour, there are 2 cups of sugar. Ratios can be used to compare different items, such as ingredients in a recipe, to make sure that the proportions are correct. Ratios are an important tool when measuring and comparing different values.

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The likelihood of selecting a second ball is 2/8 or 1/4 if that ball is now eliminated.

Probability theory, a subfield of mathematics, gauges the likelihood of an event or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty.  Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a comprehensive set of equally likely outcomes that result in a certain occurrence compared to the total number of outcomes.

given

The ratio of the number of balls of that color to all the balls is the likelihood of selecting a ball from a bag.

In the first case, the likelihood of a red ball is therefore 3/9, or 1/3. The likelihood of selecting a second ball is 2/8 or 1/4 if that ball is now eliminated.

Therefore, the chance of getting a white ball is 1/2*1 plus 1/2*49/99, or roughly 3/4.

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Answer:

first get one odd No, again more odd number than even, Lastly two or more odd number

In the graph the letter "J" has a height of 17 units.

What is a graph?

In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The relationships between two or more items are frequently represented by the points on a graph.

According to the graph the distance from A to B is horizontal, so it need not be counted.

From B to C the distance is = 3 units

Again from C to O the distance is horizontal, so it need not be counted.

From O to D the distance is = 10 units

From D to E the distance is = 4 units

From E to F the distance is horizontal, so it need not be counted.

The distance from F to N need not be counted as it will be the repetition of the total height.

So, the total height is = 3 + 10 + 4 = 17 units

Therefore, the total height on the graph is 17 units.

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The answer and prove are AD = RC, <A≅<R, <AMD≅<RMC

the table shows the statement and the reasons for the proves of congruency of the angles and triangles

The table appears as follows

sn                  Statement                               Reason

1                     AD = RE                                 Given

2                   <A ≅<R                                    Given

3                     <AMD ≅<RMC                      Vertically opposite angles

4                     ΔMAD≅ΔMRC                      Congruent by ASA or SSA

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Answer:

565.004, 565.040, 565.4

Step-by-step explanation:

Answer:

See below.

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{4 cm}\underline{Area of a parallelogram}\\\\$A=bh$\\\\where:\\ \phantom{ww}$\bullet$ $b$ is the base. \\ \phantom{ww}$\bullet$ $h$ is the height.\\\end{minipage}}[/tex]

Given:

Substitute the expressions for b and h and the value of A into the formula for area:

[tex]\implies 1=(2x-1)(4x-7)[/tex]

[tex]\implies (2x-1)(4x-7)=1[/tex]

Expand the brackets:

[tex]\implies 8x^2-14x-4x+7=1[/tex]

[tex]\implies 8x^2-18x+7=1[/tex]

Subtract 1 from both sides of the equation:

[tex]\implies 8x^2-18x+7-1=1-1[/tex]

[tex]\implies 8x^2-18x+6=0[/tex]

Factor out 2 from the left side:

[tex]\implies 2(4x^2-9x+3)=0[/tex]

Divide both sides by 2:

[tex]\implies 4x^2-9x+3=0[/tex]

Hence, showing that 4x² - 9x + 3 = 0.

Answer:

In this case the equation is already in vertex form. The vertex of the parabola is the maximum point and the value of h(t) at that point is the maximum height.

Since the equation is h(t) = -16t² + 70.56, the maximum height is 70.56 feet.

Uday Tahlan

The truck is 6.325 feet long.

Percentage is defined as the parts of a number per fraction of 100. We have to divide a number with it's whole and then multiply with 100 to calculate the percentage of any number.

So the percentage actually means a part per 100.

Percentage is usually denoted by the symbol '%'.

Given that,

A car is 5.5 ft long. A truck is 15% longer than the car.

Length of car = 5.5 feet

Length of truck = 5.5 + (15% × 5.5)

                         = 5.5 + [(15/100) × 5.5]

                         = 5.5 + (0.15 × 5.5)

                         = 5.5 + 0.825

                         = 6.325 feet

Hence the length of the truck is 6.325 feet.

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The ratios are 80 : 2/3, 10 : 1/12 and 90 : 3/4 for the equivalent ratio 20 : 1/6.

By dividing both the antecedent and consequent values by a similar fraction, equivalent ratios can be reduced to the same value. In other words, two ratios are deemed equivalent if the bigger one in value can be expressed as a multiple of the other.

Therefore, we only need to multiply the two amounts by the same number to obtain the equivalent ratio of another ratio. Equivalent ratios and equivalent fractions both have similar ideas. Examples of equivalent ratios include 1:2 and 4:8, 3:5 and 12:20, 9:4 and 18:8, etc.

20 : 1/6

Multiply both by 6

120  : 1

Thus, 120 × 2/3  : 1 × 2/3

80 : 2/3

multiply by 3

80 × 3 : 2/3 × 3

240 : 2

120 : 2

When ratio is 120  : 1

divide both by 120

120/120  : 1/120

1 : 1/120

1 × 10 : 1/120 × 10

10 : 1/12

multiply by 12

120 : 1

1 × 90 : 1/120 × 90

90 : 3/4

multiply by 4

90 × 4 : 3/4 × 4

360 : 3

120 : 1

Thus, the ratios are 80 : 2/3, 10 : 1/12 and 90 : 3/4 for the proportion 20 : 1/6.

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​

The volume of the right circular cone hat has a height of 19 feet and base diameter of 178 is calculated as: 1,575.2 ft³.

To find the volume of a right circular cone, we can use the formula:

V = (1/3) * π * r² * h

Where V is the volume, π is approximately 3.14, r is the radius of the base, and h is the height of the cone.

Given that the diameter of the base is 17.8 feet, we can divide it by 2 to find the radius, which is 8.9 feet.

Substituting these values into the formula:

V = (1/3) * π * (8.9²) * 19

V = (1/3) * 3.14 * 78.41 * 19

V = 1,575.2 ft^3

Rounded to the nearest tenth, the volume of the cone is 1,575.2 ft³

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Answer:

.10d + .05n  ≤ 1.00

Step-by-step explanation:

a dine with worth 10 cents and a nickel is worth 5 cents.  Together this amount cannot be over 1 dollar.