earned a weekly wage of $1250. He paid 6% of this into a superannuation fund.
his weekly superannuation payment = $

Answer:

the answer is (C) √(2x² + x). None of the answer options match this expression, but we can simplify it to show that it is equivalent.  option (C) √(2x² + x) is equivalent to the original expression √(2x) * √(x+3) when x > 0.

Step-by-step explanation:

To simplify the expression √(2x) * √(x+3), we can use the property of radicals that says:

√(a) * √(b) = √(a * b)

So, we have:

√(2x) * √(x+3) = √(2x * (x+3))

Multiplying out the terms inside the radical, we get:

√(2x * (x+3)) = √(2x² + 6x)

Therefore, the expression √(2x) * √(x+3) is equivalent to the radical expression √(2x² + 6x) when x > 0.

So, the answer is (C) √(2x² + x). None of the answer options match this expression, but we can simplify it to show that it is equivalent:

√(2x² + 6x) = √(2x² + x + 5x) = √(x * (2x + 5)) = √x * √(2x + 5)

[tex]A-x=\cfrac{xr}{t}\implies At-xt=xr\implies At=xt+xr \\\\\\ At=x(t+r)\implies \cfrac{At}{t+r}=x[/tex]

make x the subject means write all terms in terms of x

look at attachment.

1. A table in a book showed binomial probabilities with a tiny value for n (let's say 20, for example). The binomial formula had to be used, which might be very challenging, to compute the probability for big values of n. The technique was made simpler by using the binomial distribution's normal approximation.

2. In a table in a book, binomial probabilities with a low value for n (let's say, 20) were shown. The binomial formula had to be used, which might be very challenging, to compute the probability for big values of n. The technique was made simpler by using the binomial distribution's normal approximation. Take a basic random sample from the population to calculate the normal approximation to the binomial distribution.

There are n independent trials, where n is a number.

Any trial has two possible outcomes: success or failure.

The likelihood of each trial being successful is p.

3. It is necessary for the normal distribution's shape and the binomial distribution to be identical. The values np and nq must both be greater than five in order to guarantee this (np>5 and nq>5; the approximation is better if they are both greater than or equal to 10).

Just utilising a line to approximate the value of the function at a given position is what is meant by a function's linear approximation. We recall the idea of the tangent line as soon as we come across a curve (of a function) and a point on it. The value of the function at any point that is extremely close to the provided point can be estimated using the equation of the tangent line if we are able to identify the equation of the tangent line at the given point. Because it uses the tangent line, this idea is sometimes referred to as the tangent line approximation. It is also known as the linear approximation.

A table in a book showed binomial probabilities with a tiny value for n (let's say 20, for example). The binomial formula had to be used, which might be very challenging, to compute the probability for big values of n. The technique was made simpler by using the binomial distribution's normal approximation.

In a table in a book, binomial probabilities with a low value for n (let's say, 20) were shown. The binomial formula had to be used, which might be very challenging, to compute the probability for big values of n. The technique was made simpler by using the binomial distribution's normal approximation. Take a basic random sample from the population to calculate the normal approximation to the binomial distribution.

There are n independent trials, where n is a number.

Any trial has two possible outcomes: success or failure.

The likelihood of each trial being successful is p.

It is necessary for the normal distribution's shape and the binomial distribution to be identical. The values np and nq must both be greater than five in order to guarantee this (np>5 and nq>5; the approximation is better if they are both greater than or equal to 10).

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Therefore, the perimeter P of the nonagon is 19.5 units.

Perimeter refers to the total length of the boundary or the outer edge of a closed figure or shape. It is the sum of the lengths of all the sides or edges that enclose the shape.

Here,

Since O is the center of the regular nonagon, all the sides of the nonagon are equal in length. Let the length of one side of the nonagon be s. Then, the perimeter P of the nonagon is given by:

P = 9s

To find s, we can use the fact that the sum of the interior angles of a nonagon is given by (9-2)×180° = 1260°. Since the nonagon is regular, each angle is equal to 1260°/9 = 140°.

Consider the triangle OAB, where A and B are two adjacent vertices of the nonagon. Since O is the center of the nonagon, angle AOB is equal to 360°/9 = 40°. Also, angle OAB and angle OBA are equal to half of (180° - 140°) = 20°.

Therefore, angle AOB is isosceles, and we can use the cosine rule to find s:

cos(20°) = (s/2) / s

cos(20°) = 1/2

s = 2 / cos(20°)

Using a calculator, we get s ≈ 2.165. Therefore, the perimeter P of the nonagon is:

P = 9s

≈ 19.5 (rounded to the nearest tenth)

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Answer:

Bathtub currently has 45 gallons of water.

It drains 7 gallons every three minutes.

How much gallons will it have after 5 minutes.

First, find how much it drains in one minute and multiply it by 5.

7 gallons per 3 minutes.

So 7/3 = 2.3333 or roughly 2 gallons per minute.

How many gallons will it have after 5 minutes of draining.

2*5 = 10 litres will have been drained.

So, 45 - 10 = 35 gallons of water would remain after 5 minutes of draining.

Answer: 28/5

Step-by-step explanation:

each toy had a mass of 4/5 kilograms .there are 7 toys.so the total mass is

7 times 4/5=28/5 kilograms

hope it helps

Answer:

Step-by-step explanation:

P(international | on time)< P(delayed | domestic) <P(on time and domestic)

correct in plato

Cameron would pay $11 for 5.5 pounds of cherries at the same rate.

The interest on a loan or principal sum can be easily calculated using simple interest. Simple interest is a notion that is employed across a wide range of industries, including banking, finance, automobiles, and more.

We can start by finding the cost of cherries per pound:

2 3/5 pounds = (2 × 5 + 3) / 5 = 13/5 pounds

Cost of 13/5 pounds of cherries = $5.25

Cost of 1 pound of cherries = $5.25 ÷ (13/5) = $2

Now we can find the cost of 5.5 pounds of cherries:

Cost of 5.5 pounds of cherries = $2 × 5.5 = $11

Therefore, Cameron would pay $11 for 5.5 pounds of cherries at the same rate.

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[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{15\% of 32}}{\left( \cfrac{15}{100} \right)32}\implies 4.8\hspace{5em}\underset{ \textit{meal \& tip} }{\stackrel{ 32~~ + ~~4.8 }{\text{\LARGE 36.8}}}[/tex]

Answer:

c) The Diameter is Half of the radius

Step-by-step explanation:

A) A diameter ALWAYS passes through the center of the circle, so EVERY diameter WILL pass through the Center of the circle, making this statement valid.

b) A center of a circle will ALWAYS lie in the interior of the circle. it is an Axiom

c) False, the RADIUS is half of the Diameter of a circle.

d) The Longest Chord IS the Diameter, which passes through the circle, so this statement is valid.

So the false option is (C)

Step-by-step explanation:

The first two are not equations, there is no ' = ' sign. Tey are expressions.

C) -3 + (5-4) = ) (-3+5) -4

     -3 +1   = 2 -4

         -2    = -2       True

D)  -5 -4 = -5 +( -4)

        -9    =   -9      True

I will assume the + sign is supposed to =   ( same key)

A)   -3 (5-4)  = -3(5) - 4

       -3  = -19     FALSE

B)  -5 + (-4) =  -4 + (-5)

        -9       =   -9    True

Rounding to the nearest whole number, the number of bacteria still present in the culture after 7 hours is approximately 3481.

How many whole numbers are there?

All natural numbers are added together to form whole numbers. both a fraction and neither a decimal. Integer 0 through 11: 2, 3, 5, 6, 7, 8, 9, & 10. 0 is a counting number or the opposite.

To determine the number of bacteria inside the culture at t hours, use the formula Pt = Po 2(t/d), in which Po is simply the initial population and d is the doubling time.

The values of Po are 870, d, and t are respectively 3 and 7. When we use the formula with these numbers, we get:

[tex]Pt = 870 * 2^{(7/3)}[/tex]

Pt ≈ 3480.5

Hence, the number of bacteria still present in the culture after 7 hours is approximately 3481.

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Therefore , the solution of the given problem of percentage comes out to be  the account's yearly percentage yield (APY) is 2.24%.

The abbreviation "a%" is used to indicate a value or number in statistics that is expressed as a percentage of 100. Versions with "pct," "pct," or "pc" as the initials are also rare. However, the most popular method to do this is to use the percentage symbol ("%"). Additionally, both hints nor a constant ratio of every element to the overall amount exist. Since numbers commonly add up to 100, they are essentially integers.

Here,

The following equation can be used to determine the worth of an account after t years, compounded quarterly:

=>  A = P * (1 + r/4)⁴ⁿ

When we enter the numbers, we obtain:

=>  A = 240 * (1 + 0.022/4⁴ⁿ

By condensing the solution, we obtain:

=>  A = 240 * 1.0055⁴ⁿ

Consequently, the following is the function displaying the account's worth after t years:

=>  f(t) = 240 * 1.0055⁴ⁿ

We can use the following formula to determine the yearly percentage yield (APY):

=> APY = (1 + r/n)ⁿ - 1

where r equals the 2.2% yearly interest rate.

n is the quantity of times interest is added annually. (4, since interest is compounded quarterly)

When we enter the numbers, we obtain:

=> APY = (1 + 0.022/4)⁴ - 1

APY = 0.02237 or 2.24% (rounded to the nearest hundredth of a percent)

As a result, the account's yearly percentage yield (APY) is 2.24%.

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Step-by-step explanation:

For RIGHT triangles such as this one:

sin (60) = opposite LEG/ hypotenuse =  sqrt(3) / 2  / CB       solve for CB

tan (60°) =  opposite LEG / adjacent LEG = sqrt(3)/2  / AC    solve for AC

Answer:

Step-by-step explanation:

35 is the answer because where it says frequency you have to add it all together.

Answer:

The answer is -5. To do this you first draw your number line and label it from +7 to -10. You then count from from seven till the 11th number which in this case it's -5

Using the prοbability cοncept, it is fοund that there is a 0.0887 = 8.87% prοbability all three marbles are the same cοlοr.

A prοbability is the number οf desired οutcοmes divided by the number οf tοtal οutcοmes.

The οrder in which the marbles are chοsen is nοt impοrtant, and they are alsο chοsen withοut replacement, which means that the cοmbinatiοn fοrmula is used tο find the number οf οutcοmes.

Tο find the prοbability that all three marbles selected are the same cοlοr, we need tο cοnsider three cases: selecting three red marbles, selecting three white marbles, οr selecting three blue marbles.

Let's first calculate the tοtal number οf ways tο select three marbles frοm the urn. This can be dοne using the cοmbinatiοn fοrmula:

C(19, 3) = 19! / (3! * 16!) = 969

Sο there are 969 pοssible ways tο select three marbles frοm the urn.

Nοw let's calculate the number οf ways tο select three marbles οf the same cοlοr:

Sο the tοtal number οf ways tο select three marbles οf the same cοlοr is:

20 + 10 + 56 = 86

Therefοre, the prοbability οf selecting three marbles οf the same cοlοr is:

86 / 969 = 0.0887 (rοunded tο fοur decimal places)

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Answer:

To simplify the expression p/ab+2q/ac, we need to find a common denominator for the two fractions in the denominator. The common denominator is abc.

Thus,

p/ab + 2q/ac

= p*c/abc + 2q*b/abc (multiplying the first fraction by c/c and the second fraction by b/b)

= pc/abc + 2qb/abc

= (pc + 2qb) / abc

Therefore, the simplified expression is (pc + 2qb) / abc.

The conditional probability that a randomly selected contestant played an acoustic guitar is 2/5.

What is conditional probability?

The possibility of an event or outcome happening contingent on the occurrence of a prior event or outcome is known as conditional probability. The probability of the prior event is multiplied by the current likelihood of the subsequent, or conditional, occurrence to determine the conditional probability.

Here, we have

Given: Riley was a spectator at his town's air guitar competition. Contestants were allowed to play either the acoustic or electric air guitar, but not both. Riley recorded which type of guitar each contestant played.

Let A be the event of a contestant playing acoustic guitar.

Let B be the event of a contestant wearing leather pants

The conditional probability of a contestant playing acoustic guitar given he wears leather pants, P(A|B) is-

P(A|B) = P(A∩B)|P(B)

Where,

P(A∩B) =  is the probability of simultaneous occurrence of events A and B.

P(A∩B) = 6

P(B) = no. of contestants wearing leather pants

P(B) = 15

P(A|B) = 6/15 = 2/5

Hence, the conditional probability that a randomly selected contestant played an acoustic guitar is 2/5.

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The fractions equivalent to 2/5 are 4/10, 6/15, 8/20. The correct option is B.

When writing equivalent fractions, the numerator and denominator should be multiplied or divided by the same number. This is the reason why when these fractions are simplified, they are reduced to the same value.

Hence, the equivalent fractions for 2/5 are:

(2/5) × (2/2) = (2 × 2) / (5 × 2) = 4/10

(2/5) × (3/3) = (2 × 3) / (5× 3) = 6/15

(2/5) × (4/4) = (2 × 4) / (5 × 4) = 8/20

The fractions equivalent to 2/5 are 4/10, 6/15, 8/20,.

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Which of the lists below includes all of the above expressions that are equivalent to 2/5?

I, 2/6

II,  4/10

III, 6/15

IV. 10/20

V. 4 / 12

VI 8/20

A. I, III, V, VI

B. III, VI

C. II, III, VI

D. II, III, IV, VI

The value of x in right angle whose hypotenuse is given 74 m  one angle is 90° and other angle given is 30° to the nearest tenth is approximately 37 meters.

The branch of mathematics that deals with the relationships between the sides and angles of triangles, particularly right triangles is known as Trigonometry. It involves studying the properties of trigonometric functions, which are mathematical functions that relate the angles of a triangle to the ratios of its sides.

In this triangle, the height is opposite the 30° angle and the hypotenuse is the longest side of the triangle. We can use the trigonometric function sine to relate the height and the hypotenuse:

sin(30°) = x / 74

To solve for x, we can multiply both sides by 74 and simplify:

x = 74 sin(30°)

x ≈ 37 (to the nearest tenth)

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Answer:

Step-by-step explanation:

50+40+15+40+85

=230

The probability that the subject tested negative or did not use marijuana is approximately 0.57.

Probability is a branch of mathematics that deals with the study of random events and their likelihood of occurrence. It is a way of quantifying the uncertainty or randomness associated with an event or an experiment.

In the given question,

To solve this problem, we can construct a table that summarizes the given information:

We are given the following information:

There are 143 subjects with positive test results, of which 20 are false positives.

There are 153 subjects with negative test results, of which 4 are false negatives.

Using this information, we can fill in the table as follows:

The numbers in parentheses are the counts of subjects in each category.

To find the probability that the subject tested negative or did not use marijuana, we need to add the probabilities of the two mutually exclusive events:

Tested negative and did not use marijuana (True Negative): P(True Negative) = 149/296

Tested positive but did not use marijuana (False Positive): P(False Positive) = 20/296

Therefore, the probability that the subject tested negative or did not use marijuana is:

P(Tested Negative or Did not use marijuana) = P(True Negative) + P(False Positive)

= 149/296 + 20/296

= 169/296

≈ 0.57

So, the probability that the subject tested negative or did not use marijuana is approximately 0.57.

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Step-by-step explanation:

blue box is x^2

orange box is 5x

yellow box is 3x

green box is 15

Town B will have a larger population than Town A in the year 2019.

To solve this problem, we can use a year-by-year approach to see when the population of town B surpasses that of town A.

Let's start with year 0 (2015):

Town A population: 9,000

Town B population: 8,000

In year 1 (2016):

Town A population: 9,500 (9,000 + 500)

Town B population: 8,720 (8,000 x 1.09)

In year 2 (2017):

Town A population: 10,000 (9,500 + 500)

Town B population: 9,504.8 (8,720 x 1.09)

In year 3 (2018):

Town A population: 10,500 (10,000 + 500)

Town B population: 10,360.232 (9,508.8 x 1.09)

In year 4 (2019):

Town A population: 11,000 (10,500 + 500)

Town B population: 11,292.653 (10,394.912 x 1.09)

From this calculation, we can see that in the year 2019, the population of Town B will be larger than that of Town A. Therefore, the answer is:

Town B will have a larger population than Town A in the year 2019.

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The straight sections each have a length of 100. So, the total distance around the inner lane of the track is 200 + 40pi units

The area of one of the blue half circles can be found using the formula:

Area = pi x radius squared.

The diameter of the circle is given as 40, so the radius is half of that, which is 20.

Therefore, the area of one blue half circle is:
Area = pi x [tex]\frac{20^{2} }{2}[/tex]

Area = 200pi square units
To cover the entire circle, we need both blue half circles. So the total area needed to be covered with grass is:
Total area = 2 x 200pi = 400pi square units
The distance around one of the semicircles at either end of the soccer field can be found using the formula: Circumference = pi x diameter.

Since the diameter is given as 40.

The circumference is:
Circumference = pi x [tex]\frac{40}{2}[/tex]

Circumference = 20pi units

To find the distance around the inner lane of the track, we need to add the lengths of the straight distances (which are 100 each) to the circumference of the two blue half circles.

The circumference of one blue half circle is 20pi, so the total distance around the inner lane of the track is:
Distance = 2 x 100 + 2 x 20pi

Distance = 200 + 40pi units

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1) The permutation that is the next one in lexicographic order after (4, 6, 2, 7, 3, 1, 5) is (4, 6, 2, 7, 3, 5, 1). Therefore answer is a. (4, 6, 2, 7, 3, 5, 1).

2) The 5-subset from {1, 2, 3, 4, 5, 6, 7, 8, 9} that is the next one in lexicographic order after {2, 3, 7, 8, 9} is {2, 4, 7, 8, 9}. Therefore the answer is d. {2, 4, 7, 8, 9}.

The next permutation in lexicographic order is the one that comes immediately after the given permutation when the permutations are listed in numerical order. To find the next permutation, we need to find the rightmost pair of elements that are in decreasing order. In this case, that pair is (5, 1). We then need to find the smallest element to the right of 1 that is larger than 1, which is 3. We swap 1 and 3 to get (4, 6, 2, 7, 3, 5, 1).

To find the next 5-subset in lexicographic order, we need to find the rightmost element that can be increased. In this case, that element is 9. We then replace 9 with the smallest element to its right that is larger than 9, which is 4. We then need to rearrange the remaining elements in increasing order to get {2, 4, 7, 8, 9}.

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Answer:

approximately 3.84 degrees.

Step-by-step explanation:

The angle of depression is the angle between a horizontal line and the line of sight when looking downwards. We can use trigonometry to calculate this angle.

Let's draw a diagram to represent the situation:

A

/|

/ |

18.5/ | 280

/ |

/θ |

/_____|

B

Here, point A represents the top of the sledding run, point B represents the bottom of the run, and θ is the angle of depression we want to find.

We can see that AB is the hypotenuse of a right triangle, and the vertical drop of 18.5 yards is the opposite side. We can use the tangent function to relate the opposite side to the adjacent side, which is the horizontal distance of the run:

tan θ = opposite/adjacent

tan θ = 18.5/280

Now we can use a calculator to find the value of the tangent:

θ = tan^(-1) (18.5/280)

θ ≈ 3.84 degrees

Therefore, the angle of depression of the run is approximately 3.84 degrees.

The probability that the student was NOT a female that got a “A” is given as follows:

p = 10/19.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The outcomes for this problem are given as follows:

Hence the probability that the student was NOT a female that got a “A” is obtained as follows:

p = 20/38

p = 10/19.

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Answer:

Step-by-step explanation:

To add numbers in base 5, we need to follow the same process as adding numbers in base 10. We will start by aligning the digits based on their place value and then add them up, carrying any remainders as necessary.

4023 base 5

3102 base 5

11325 base 5

Therefore, the sum of 4023 base 5 and 3102 in base 5 is 11325 base 5.