Northern Bank has two types of account. Both accounts pay compound interest. Cash savings account Interest 2.5% per annum Shares account Interest 3.5% per annum Ali invests £2000 in the cash savings account. Ben invests £1600 in the shares account. (a) Work out who will get the most interest by the end of 3 years. You must show all your working.

The probability that the schools in Los Angeles will be closed for four days next year is 0.1680.

In order to comprehend separate events that happen at a steady pace over the course of a specified amount of time, Poisson's distributions are frequently utilized.

Formula for Poisson's distribution:

f(x) = ((λ^x)/x!).(e^(-λ))

x = Event to be calculated for

λ = Expected number of occurrences

P(X = x) = ((λ^x)/x!).(e^(-λ))

Here λ = 3 and x = 4

P(X = 4) = (81 / 4!).(e^(-3))

P(X = 4) = (81 * e^(-3))/24

P(X = 4) = (81 * 0.049)/24

P(X = 4) = 0.1680

Hence, the probability that schools in Los Angeles will be closed for four days next year is 0.1680.

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The equivalent expressions indicated are;

1) 1/a^6b^4

2) a^6/b^6

3) a^6/b^5

4) b^6/a^6

5) a^5b^3

We have to note that when we talk about the equivalent expressions, we mean the expressions that we have to get from each other when we carry out a little computational work on the original expression.

Thus, the equivalent expression has shown that the expression that is in the bracket is the same as the original expression by the use of the laws of exponents.

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The distance of the car from the tall building to the nearest meter is 23m.

Given the data in the question;

We use trigonometric ratio since the scenario forms a right angle triangle.

tanθ = opposite / adjacent

tanθ = opposite / adjacent

tan( 35° ) = 16m / x

x = 16m / tan( 35° )

x = 16m / 0.7002

x = 23m

Therefore, the distance of the car from the tall building to the nearest meter is 23m.

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Using relations in a right triangle, it is found that the tree meets the wire at an angle of 56.4º.

The relations in a right triangle are given as follows:

In this problem, we have that:

Hence:

[tex]\sin{\alpha} = \frac{10}{12}[/tex]

[tex]\alpha = \sin^{-1}{\left(\frac{10}{12}\right)}[/tex]

[tex]\alpha = 56.4^\circ[/tex].

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Answer:

1.5, -1.5

Step-by-step explanation:

Using the quadratic formula, you should have a plus, and minus solution. These should be your answers.

Answer: y=-1/5x+ 8/5    (Third one down)

Answer:

60 kilograms

Step-by-step explanation:

Skew lines and parallel lines do not intersect

As a general rule, skew lines are lined that are not on the same plane; they are not parallel to each other and they do not intersect

Using the above definition as a guide, the skew lines in the figure are:

Parallel lines and skew lines are different in the following ways:

Parallel lines and skew lines are alike in the following way:

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The bronze-casting process that depends on a modelled original form is:  lost-wax casting.

Lost-wax casting is a bronze-casting process which is also referred to as the cire-perdue. In this type of metal casting, a wax model is created when a molten metal is usually poured into a mold. The wax model is then melted and drained.

In summary, the name for this bronze-casting process that relies on this wax model is called: lost-wax casting.

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[tex]\huge\underline{\red{A}\green{n}\blue{s}\purple{w}\pink{e}\orange{r} →}[/tex]

Step-by-step explanation:

5x:9 = 7:3

→ 5x/9 = 7/3

→ x = (7 × 9)/(3 × 5)

→ x = 21/5

Answer:

1800(5/6)^t

Step-by-step explanation:

I don't see any answer choices, but this would be another form if it is listed. The negative exponent means that you get the reciprocal of the fraction (in this case 1.2). This turns 1.2 into (1/1.2), which is equivalent to 5/6.

Answer:

Step-by-step explanation:

9,328 and you would divide that by 98 and the answer would be 95.18367347 boxes

the maximum height is 180ft.

The height of the equation is modeled by:

[tex]y = 60t - 5t^2[/tex]

Notice that this is a quadratic equation with a negative leading coefficient, which means that the maximum is at the vertex, then the maximum is at:

[tex]t = -60/(2*-5) = 6[/tex]

To get the maximum height, we need to evaluate the function in t = 6, we will get:

[tex]y = 60*6 - 5*6^2 = 180[/tex]

This means that the maximum height is 180ft.

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The amount invested in the account that has a rate of 14% is $1767

The amount invested in the account that has a rate of 6% is $1425.

0.06a + 0.14b = 342 equation 1

b - a = $950 equation 2

Where:

a = amount invested in the account that has a rate of 6%

b =  = amount invested in the account that has a rate of 14%

Multiply equation 2 by 0.06

0.06b - 0.06a = 57 equation 3

Subtract equation 3 from equation 2

285 = 0.2a

a = 285 / 0.2

a = 1425

Substitute for a in equation 2

b - 1425 = 342

b = 1425 + 342

b = $1767

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The correct answer is 2.930 × [tex]10^{23}[/tex]

What is Avogadro's number?

Avogadro's number, which is equal to 6.02214076 1023, is the quantity of units in one mole of any material (defined as its molecular weight in grams). Depending on the substance and the nature of the reaction, the units may be electrons, atoms, ions, or molecules (if any).

You have two numbers here. While number 2.0550 is stated with five significant figures, Avogadro's number is supplied with four. This implies that you must provide four significant figures with your result.

(6.022 × [tex]10^{23}[/tex]) / 2.0550 = 2.930 × [tex]10^{23}[/tex]

Therefore, the correct answer is 2.930 ×[tex]10^{23}[/tex] .

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Step-by-step explanation:

3 - 11x

x is "a number".

so, the request is to multiply it by 11 and subtract the result from 3.

Answer:

5.46

111

86

367.2

49

467

use labels

Step-by-step explanation:

1. [tex]\frac{39}{2} times . 0.28[/tex]

[tex]\frac{39}{2} times \frac{28}{100} =\frac{1092}{200} \\[/tex]

[tex]\frac{1092}{200} = \frac{273}{50}[/tex]

Answer 273/50 or 5.46 inches

2. [tex]\frac{97}{87} times \frac{100}{1} =\frac{9700}{87}[/tex]

Answer 9700/87= 111%ft

3. [tex]\frac{146}{1} divided \frac{170}{1}[/tex]

[tex]\frac{146}{1}times\frac{1}{170} =\frac{146}{170}[/tex]

Answer=146/170=73/85=

86%tons

4. [tex]\frac{136}{1} times\frac{270}{100} =\frac{36720}{100}[/tex]

Answer=367.2%ft

5 .[tex]\frac{60}{123}[/tex]=49%inches

6.[tex]\frac{56}{1} times\frac{100}{12} =[/tex]467%inches

The sum of a+b+c = 307.

According to the statement

[tex]$\sqrt[3]{\sqrt[3]{54}+\sqrt[3]{250}}$[/tex] is written as [tex]$a\sqrt[b]{c}$[/tex]

now we find the sum of these

in these terms a=54 and b=3 and c=250

Then

a+b+c = 54+3+250

a+b+c = 307

So, The sum of a+b+c = 307.

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Answer:

$1,800

Step-by-step explanation:

If the Smiths agree to the installment plan and pay $150 every month for 12 months, it will add up to $1,800 at the end of the year.

Based on the fact that Jessica and her best friend split the money and were able to get $16.32, the total amount that they found was $32.64

The fact that they split the money evenly means that they split it in half which each person getting the same amount.

This means that the total amount they found was twice the amount that Jessica and her best friend got.

The total amount found is therefore:

= Jessica's share + Best friend's share

= 16.32 + 16.32

= $32.64

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The correct option is (d) Mutually exclusive events.

Let a and b be the events of the fda approving and rejecting a new drug to treat hypertension, respectively. The events a and b are mutually exclusive events.

Two events are mutually exclusive or disjoint in logic and probability theory if they cannot both occur at the same time. The results of a single coin toss, which can result in either heads or tails but not both, provide a clear illustration.

A statistical term used to describe events that cannot occur concurrently is "mutually exclusive." It is frequently used to refer to circumstances in which the occurrence of one event takes precedence over the other. For instance, it is impossible for war and peace to exist together. They are therefore opposed to one another.

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Answer:

2.0

Step-by-step explanation:

The researchers could utilize a probability sample.

Meaning of a Probability Sample

Every member of a population must have an equal chance of being chosen for a study in order for a sample to be considered a probability sample, and the researcher must be aware of this likelihood. The most typical type of sampling used in public opinion research, election polling, and other studies whose findings will be generalized to a larger population is probability sampling in which probability samples are made use of.

Probability Sample as the Representative of Population Sample

Here, a sample that qualifies for a representative of the population the researchers are studying, must consist of members having equal chances to be chosen for the study. Thus, a probability sample is the best representative of their study population.

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The correct option is (2)  [tex]\frac{8}{5}[/tex] and (3)  [tex]\frac{1}{6}[/tex].

The factor of equation  f(x) = 60[tex]x^{4}[/tex] +  86[tex]x^{3}[/tex] – 46[tex]x^{2}[/tex] – 43[tex]x[/tex] + 8 are [tex]\frac{8}{5}[/tex] and [tex]\frac{1}{6}[/tex].

The rational root theorem, also referred to as the rational zero theorem, is a potent mathematical technique used to identify all potential rational roots of polynomial equations of order 3 and above.

For the given polynomial, the roots are given as;

[tex]$$P(x)=a_{n} x^{n}+a_{n-1} x^{n-1}+\cdots+a_{2} x^{2}+a_{1} x+a_{0}$$\\ \\$\pm \frac{\text { factors of } a_{0}}{\text { factors of } a_{n}}$.[/tex]

Factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 and factors of 8 are 1, 2, 4 and 8.

Out of the given options, only   [tex]\frac{8}{5}[/tex] and [tex]\frac{1}{6}[/tex] can be written in the form:  

[tex]\begin{aligned}&\frac{8}{5}=\frac{\text { a factor of } 8}{\text { a factor of } 60} \\&\frac{1}{6}=\frac{\text { a factor of } 8}{\text { a factor of } 60}\end{aligned}[/tex]

Therefore, the rational roots of polynomial f(x) = 60[tex]x^{4}[/tex] +  86[tex]x^{3}[/tex] – 46[tex]x^{2}[/tex] – 43[tex]x[/tex] + 8 are [tex]\frac{8}{5}[/tex] and [tex]\frac{1}{6}[/tex].

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The complete question is-

Which is a factor of f(x) = 60[tex]x^{4}[/tex] +  86[tex]x^{3}[/tex] – 46[tex]x^{2}[/tex] – 43[tex]x[/tex] + 8? use the rational root theorem to help you find your answer.

Answer:

1.

x=-10

x=-6

2.

x=10

x=-3

Step-by-step explanation:

to find the zeros of a function you need to set it equal to zero:

x^2+16x+60=0

then you factor

(x+10)(x+6)=0

then you have to finish factoring/simplifying

x+10=0

  -10

x=-10

x+6=0

 -6

x=-6

and the same thing for number 2

x^2-7x-30=0

(x-10)(x-3)=0

x=10, x=3

Answer:

1.) x = -10, x = - 6

2.) x = 10, x = -3

Step-by-step explanation:

1.) factorize and set the equation to zero by multiplying a and c and finding factors of it that will result in b once added/subtracted

[tex]x^2+16x+60\\(x+10)(x+6)\\(x+10)(x+6)=0\\x=-10, x=-6[/tex]

2.) do the same for number 2:

[tex]x^2-7x-30\\(x-10)(x+3)\\(x-10)(x+3)=0\\x = 10, x = -3[/tex]

i hope this helped!

OPTION A is the correct answer

Answer:

  D.  π/30 + n(π/15)

Step-by-step explanation:

The given equation can be solved by isolating the cosine function and using the inverse function to find the angles.

  30cos(30x) +14 = -16

  30cos(30x) = -30 . . . . . . subtract 14

  cos(30x) = -1

This is an extreme value of the cosine function that first occurs where the argument is π, and repeats every 2π after that:

  30x = π +2nπ

  x = π/30 +n(π/15) . . . . . odd multiples of π/30

__

Additional comment

The answer choices other than D include all multiples of π/30, or only even multiples of π/30. Either way, they are not part of the correct answer.

The equation of the logarithmic function is y = log(x - 1)

The points are given as:

(0,3) and (2,0)

The equation is represented as:

y = A log(x + B)

Substitute (2,0) in y = A log(x + B)

y = A log(x + B)

This means that:

0 = A log(2 + B)

This means that:

A = 0 or log(2 + B) = 0

Take the antilog of both sides of log(2 + B) = 0

2 + B = 1

Solve for B in 2 + B = 1

B = -1

Substitute B = -1 in y = A log(x + B)

y = A log(x - 1)

Substitute (0,3) in y = A log(x - 1)

3 = A log(0 - 1)

So, we have:

3 = A log(-1)

The above equation is undefined.

Hence, the equation of the logarithmic function is y = log(x - 1)

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Complete question

Write an expression, of the type A log(x + B), for the transformed logarithmic function shown below:

(0,3) and (2,0)