What is; 24x - 5 - 3

Check the picture below.

[tex]\cfrac{24+x}{24}~~ = ~~\cfrac{36+12}{36}\implies \cfrac{24+x}{24}=\cfrac{48}{36}\implies \cfrac{24+x}{24}=\cfrac{4}{3} \\\\\\ 72+3x=96\implies 3x=24\implies x=\cfrac{24}{3}\implies x=8[/tex]

The final value of the investment is £2517.04.

Calculate the total amount earned over 6 months at 0.5% per month

At 0.5% per month, the investment of £2500 will earn £12.50 per month for six months.

Therefore, the total amount earned over 6 months is £12.50 x 6 = £75.

Determine the value of the investment after 6 months

The value of the investment after 6 months will be the initial investment plus the total amount earned over 6 months.

Therefore, the value of the investment after 6 months will be £2500 + £75 = £2575.

Determine the total amount lost over 9 months at 0.25% per month

At 0.25% per month, the investment of £2575 will lose £6.44 per month for nine months.

Therefore, the total amount lost over 9 months is £6.44 x 9 = £57.96.

Calculate the final value of the investment

The final value of the investment will be the value of the investment after 6 months minus the total amount lost over 9 months.

Therefore, the final value of the investment is £2575 - £57.96 = £2517.04.

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The final value of the investment would be £2491.97. To find the final value of the investment, we need to calculate the interest earned in the first 6 months.

When the rate was 0.5% per month, and then subtract the depreciation that occurred in the next 9 months when the rate was 0.25% per month.

First, calculate the interest earned in the first 6 months:

Next, add this interest to the initial investment to get the value after 6 months:

Finally, calculate the depreciation in the next 9 months:

Subtract the depreciation from the value after 6 months to get the final value:

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Answer:

1.  See below.

[tex]\textsf{2.} \quad \log_x256=\dfrac{1}{2}[/tex]

[tex]\textsf{3.} \quad x^6=1000000[/tex]

[tex]\textsf{4.} \quad \log_2\left(\dfrac{1}{64}\right)=x[/tex]

Step-by-step explanation:

Please note that this question is incorrect.  

I assume the question is missing an "x" term, since log₉27 ≠ -3.

Let's assume 27 should be "x":

[tex]\implies \log_9x=-3[/tex]

[tex]\textsf{Apply the log law}: \quad \log_ab=c \iff b=a^c[/tex]

[tex]\implies x=9^{-3}[/tex]

If, however, the 9 is supposed to be "x":

[tex]\implies \log_x27=-3[/tex]

[tex]\implies x^{-3}=27[/tex]

Given exponential equation:

[tex]\sqrt{x}=256[/tex]

[tex]\textsf{Apply exponent rule} \quad \sqrt{a}=a^{\frac{1}{2}}:[/tex]

[tex]\implies x^{\frac{1}{2}}=256[/tex]

[tex]\textsf{Apply the log law}: \quad \log_ab=c \iff a^c=b[/tex]

[tex]\implies \log_x256=\dfrac{1}{2}[/tex]

Given logarithmic equation:

[tex]\log_x1000000=6[/tex]

[tex]\textsf{Apply the log law}: \quad \log_ab=c \iff a^c=b[/tex]

[tex]\implies x^6=1000000[/tex]

Given exponential equation:

[tex]2^x=\dfrac{1}{64}[/tex]

[tex]\textsf{Apply the log law}: \quad \log_ab=c \iff a^c=b[/tex]

[tex]\implies \log_2\left(\dfrac{1}{64}\right)=x[/tex]

Answer:

The equation for babysitting can be written as y = 20x + 5, where y is the total cost and x is the number of hours.

The slope of the equation is 20, which represents the rate of change in the total cost (y) with respect to the number of hours (x).

The slope represents the rate at which the total cost changes for each unit change in the number of hours. In this case, for each hour of babysitting, the total cost increases by $20.

The y-intercept of the equation is 5, which represents the cost when x = 0, i.e. when there is no babysitting time.

The y-intercept represents the starting value of the total cost, in this case, the amount charged for babysitting even when there is no babysitting time.

Step-by-step explanation:

The function that represents the balance after t years is ,

FV = $470( 1.011)^4t

The formula for calculating future value:

FV = P (1 + r)^nm

Where:

FV = Future value

P = Present value

R = interest rate

m = number of compounding

N = number of years

here, we have,

given that,

P = Present value= $470.

R = interest rate = 4.4%/4 =

m = number of compounding =4

N = number of years = t

FV = $470( 1.011)^4t

Hence,  The solution is, a function to represent the balance A in the account after t years is, FV = $470( 1.011)^4t

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Answer: 11 (Or I'm wrong)

Step-by-step explanation: -2 -1 0 1 2 3 4 5 6 7 8 9 10 11

The simplest form of the polynomial is (x²)-3x+1.

A polynomial is a mathematical expression consisting of constants, variables, and exponents. It can be written in the form of a polynomial equation, which is a mathematical equation with one or more variables.

In this example, we have two functions, f(x) and g(x). The polynomial of these two functions can be written in simplest form by combining the functions together.

The polynomial of f(x) and g(x) is written in simplest form as (x²)-3x+1.

This means that for any value of x, the polynomial will evaluate to the value given by the equation.

If x=2, then the polynomial will evaluate to (2(2)²)-3(2)+1=3.

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The diagram that represent the distance and the journeys is added as an attachment

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

Using the above as a guide, we have the following:

Next, we create the diagram (see attachment)

The attached figure represents the required diagram

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Answer:

1.6

Step-by-step explanation:

[tex]\displaystyle \frac{f(b)-f(a)}{b-a}\\\\=\frac{f(9)-f(1)}{9-1}\\ \\=\frac{15.8-3}{8}\\ \\=\frac{12.8}{8}\\ \\=1.6[/tex]

The exact binomial probability that the total number rolled will add up to 3 or less is 1/12.

The exact binomial probability that the total number rolled will add up to 3 or less is calculated as follows;

The total number that can be rolled with 2 dice is 2 to 12, with 7 being the most likely outcome (the sum of two dice has a maximum of 7).

The probability that the total number is 3 or less is the sum of the probabilities of rolling a 2 and a 1;

The probability P = (1/36) + (2/36)

P = 3/36

P = 1/12

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The solution for the inequalities, y≥x+1​ is (0, 1) and (-1, 0).

and, solution for the inequalities, y≤x−3​ is (0, -3) and (3, 0).

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Given:

y≤x−3​.........(1)

y≥x+1​.............(2)

If we solve the inequality using the graphical method we can see that the inequalities gives the parallel line.

Also, the solution for the inequalities, y≥x+1​ is (0, 1) and (-1, 0).

and, the solution for the inequalities, y≤x−3​ is (0, -3) and (3, 0).

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The number of people in a household with 2.5 pounds of waste are = 11

and we calculate this on the basis of question below

Predict the number of people in a household with 2.5 pounds of waste pounds of waste 0.27,1.41,2.19,2.83,2.19,1.81,0.85,3.05. In Home 2 3 3 6 4 2 1 5

pound    0.27  ,1.41,  2.19  ,2.83  ,2.19  ,1.81  ,0.85,  3.05  

people      2          3      3       6        4        2        1       5

so now the question is complete

in pound section we have to take care which value are greater than 2.5

so 2.83 and 3.05 is greater than 2.5 so here  number of people who's home have greater than 2.5 pound of waste are 6+6=11

and rest people who's home has less than 2.5 pound waste are 2+3+3+4+2+1=15

so final ans is 11.

so this question was in complete and this ans is valid for this Question only.

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Factorized form of polynomial is 3(−b²c+bc²−c²a+ca²−a²b+ab²).

This process of finding two or more expressions whose product is the given expression is known as the factorization of algebraic expressions.

Given polynomial

(b - c)³ + (c - a)³ + (a - b)³

Factoring the polynomial

Calculation is attached below.

we get,

3(−b²c+bc²−c²a+ca²−a²b+ab²)

Hence,

3 and (−b²c+bc²−c²a+ca²−a²b+ab²) are factors of given polynomial.

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Answer:

Value Cars

Step-by-step explanation:

A1 Taxis: A 5-mile journey costs £15

15 divided by 5 = £3 per mile

Crazy Cabs: A 4-mile journey costs £13

13 divided by 4 =  £3.25 per mile

Value Cars: A 10-mile journey costs £28

28 divided by 10 = £2.80 per mile

The bearing of the flight from Elgin to Canton is 231.23°. The solution has been obtained by using law of sines.

What is law of sines?

The ratio of the side length to the sine of the opposing angle is how the law of sines is typically defined. That is true for all three triangle sides, regardless of their sides and angles.

Let the angle formed at Canton be C.

The angle formed at Naples =  90 - 44 = 46°

Using law of sines,

⇒sin (46 ) / 720  =  sin C / 500

⇒500 * sin ( 46 ) / 720  =  sin C

⇒arcsin ( 500 * sin (46) / 720 )  = C  

⇒C ≈ 38.77°

The bearing angle (clockwise from north) of the flight from Elgin to Canton is calculated as follows:

⇒270° - 38.77°

⇒231.23°

Hence, the bearing of the flight from Elgin to Canton is 231.23°.

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The figure of the question has been attached below.

Answer:

Step-by-step explanation:

To find the sine of angle M, we can use the sin function, which relates the sides of a right triangle to the sine of one of its angles. In this case, we have a right triangle with sides MO, NM, and ON, so we can use the following formula:

sin(M) = MO / ON

We know that MO = 8 and ON = 15, so we can calculate the sine of angle M as follows:

sin(M) = 8 / 15

So, the ratio that represents the sine of angle M is 8/15.

Using the method of least squares, the faculty group obtained,  the estimated y-intercept of the line is For a 1-point increase in an administrator's rating, we estimate the administrator's raise to increase $14,000.

The relationship between the variables is calculated and represented as an equation in regression analysis. The dependent variable, independent variables, and line equation constants are all included in this equation. Variables may be related in ways that are linear, quadratic, polynomial, etc.

In this instance, the performance is the independent variable and the increase is the dependent variable. Simple linear regression is the name of the equation, which is shown as a straight-line equation.

Regression analysis makes use of the relationship between independent and dependent variables' relationship equation to forecast the values of the dependent variable y given the values of the independent variable x.

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On solving the provided question, we can say that the equation are cost of producing t units is C = 3t2 + 8t, revenue generated from sales is R = 4t2 + t if t>0 then C = 43t and is t>7 then C =D = 32t

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

the equation are

cost of producing t units is C = 3t2 + 8t,

revenue generated from sales is R = 4t2 + t

if t>0

then C = 43t

and is t>7

then C =D = 32t

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Bold = reason (in reasons 3 and 4 the formatting is odd and goes into the next line)

Statement                                                                     Reason

1. line segment ʜᴏ is parallel to line segment EL,             1. Given

line segment HN intersects line segment OE at W,

the measure of HW is equal to the measure of NW*

2. angle HWO is congruent to angle NWE             2. Vertical angle theorem

3. angle OHW is congruent to angle WNE         3. alternate interior angles theorem

*4. line segment HW is congruent to line segment NW  4. definition of congruent

5. triangle HOW is congruent to triangle NEW    5. ASA postulate

*step 4 might not be needed; I don't know whether the "given" is saying that the measure of line segment HW is equal to the measure of line segment NW, or if it's saying that the two line segments are congruent

You might have to change the reasons for the statements, but this is the gist of how to prove it.

When converting 0.000056 into scientific notation, the decimal point will move 5 spaces to the right.

The resulting number in scientific notation would be 5.6 x 10^-5.

During the party, 6 3/4 pizzas were consumed.

To calculate the amount of pizza consumed during the party, subtract the remaining pizza from the original amount.

The original quantity of pizza was 9 3/8 pizzas, and the remaining quantity was 2 5/8 pizzas, resulting in:

6 3/4 pizzas = 9 3/8 - 2 5/8 pizzas

During the party, 6 3/4 pizzas were consumed.

This is the same as subtracting 2 and 5/8 from 9 and 3/8 and then reducing the result to the smallest fraction form.

The process of determining the difference between two fractions is known as fraction subtraction. To subtract two fractions, do the following:

Check that the fractions have a common denominator: If the denominators are not the same, you must find one. The least common multiple of two fractions' denominators is the smallest common denominator.

Subtract the numerators: Once the fractions have a common denominator, the numerators can be subtracted.

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If a ranger in a 120 m high tower on a plain first noted that the angle of depression to a fire was 4°. The fire travelled 31,968 meters.

Distance = d = v * t

Let v represent speed of the fire .

Where :

t = time elapsed in seconds = 20 * 60 = 1200 seconds

Using the tangent function:

d / v = tan(6°) - tan(4°)

Simplify this expression using the identity:

tan(A + B) = (tan(A) + tan(B)) / (1 - tan(A)tan(B))

Applying this to the above equation, we get:

d / v = (tan(6°) - tan(4°)) / (1 + tan(6°)tan(4°))

Using a calculator to evaluate the tangent values

d / v = 26.64 / v

d = 26.64 * v

Substituting the value of t, we get:

d = 26.64 * v

= 26.64 * 1200

= 31,968 meters (rounded to the nearest meter)

Therefore the fire travelled 31,968 meters.

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The complete question is:

A ranger in a 120 m high tower on a plain first noted that the angle of depression to a fire was 4°. Twenty minutes later the angle of depression was 6°. The fire travelled                         m (to nearest metre)

The sine function for a specified range of angles is shown graphically in the sine graph. A trigonometric graph's horizontal axis is the angle, which is typically denoted by the symbol, and the y-axis is the sine function of that angle.

To graph the sine function, we place the sine of each angle on the vertical y-axis and indicate the angles along the horizontal x axis.

The ratio of the perpendicular of a right-angled triangle to the hypotenuse is known as the sine of the angle. The following is the sin formula: hypotenuse/perpendicular = sin. sin(n+2) = sin for each n.

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Answer:

(9,7,10,8,7)

Step-by-step explanation:

range is the value of y.

Answer: 60

A triangle can only be 180 degrees so if one side is 60 so is the other two sides

The probability that Brad gets all five answers correct is 1/128.

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

true of false = 3

Multichoice = 2

So, the probability that Brad gets all five answers correct is (1/4)^2 * (1/2)^3 = 1/128.

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Answer:

Ten thousands

Step-by-step explanation:

20 x 1000 = 20,000 therefore, ten thousands

The probability that a patient who has been diagnosed with cancer truly has the illness 0.406

It is known from prior experience that there is a 0.05 chance of choosing a cancer-positive adult over 40 in a certain area of the nation. What is the likelihood that an adult over the age of 40 will be given a cancer diagnosis if the probability of a doctor correctly diagnosing a person with cancer as having the disease is 0.78 and the probability of a doctor incorrectly diagnosing a person without cancer as having the disease is 0.06.

We wish to compute P(C | D) this time. Bayes rule is used in this process.

[tex]& P(C \mid D)=\frac{P(C n D)}{P(D)} \\\\& =\frac{P(C) P(D \mid C)}{P(C) P(D \mid C)+P\left(C^{\circ}\right) P\left(D \mid C^*\right)} \\\\& =\frac{0.05 * 0.78}{(0.05 * 0.78)+(0.95 * 0.06)} \\\\& =\frac{0.039}{0.039+0.057} \\\\& =\frac{0.039}{0.096} \\\\& =0.406[/tex]

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