Number 1 solve use counting principle

Answer:x^3+x^2-8x-32

Step-by-step explanation:

Faith earned £96 in interest at the end of the 3 years.

Using the  simple interest formula:

I = P x r x t

where

I is the interest earned,

P is the principal or initial amount invested,

r is the interest rate as a decimal, and t is the time period in years.

In this case, Faith invested £800 for 3 years at a simple interest rate of 0.4% per year, or 0.04 as a decimal. Plugging in the values:

I = £800 x 0.04 x 3

= £96

Therefore, Faith earned £96 in interest at the end of the 3 years.

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Answer:

$3.25 per hotdog

Step-by-step explanation:

This question can be written as a system of equations:

x = price of hotdogs

y = price of drinks

First family:

4x + 4y = 18

Second family

5x + 3y = 20

Multiply each equation so that one of the variables can cancel out:

-3(4x + 4y = 18)

4(5x + 3y = 20)

First equation:

-12x - 12y = -54

Second equation

20x + 12y = 80

Add the equations together

-12x - 12y = -54

20x + 12y = 80

8x = 26

Divide

x = $3.25

Insert the x into one of the original equations to find y:

4(3.25) + 4y = 18

13 + 4y = 18

4y = 5

y = $1.25

Answer: A lot

Step-by-step explanation:

Answer:

Step-by-step explanation: Option A is correct.

The number of ways to arrange all the letters if the arrangement must end in a vowel is; 25,200.

The number of arrangement using only five letters is; 6720.

Since there are 5 options for the last letter, and there a 7 letters left to make an arrangement of 7.

Hence, The number of ways can you arrange all of the letters if the arrangement must end in a vowel is; 5 × 7!

= 5 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 25,200.

b). The number of arrangements if one can only use five letters is; ⁸P₅

= 6720.

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The temperature on the surface of the planet, based on the equation for the temperature, is 47 degrees Celsius.

The equation given of y = 47 - 5x, is such that every one kilometer that we go from the surface of the planet, the temperature reduces by 5 degrees Celsius.

What this means is that at the surface of the planet the temperature is 47 degrees Celsius because this is the temperature when we have not gone a single kilometer above the surface.

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The rest of the question is:

Note that a change can be an increase or a decrease.

For an increase, use a positive number. For a decrease, use a negative number.

What is the temperature on the surface of the planet?

The median of the following salary list is 29763.

The median is the average in the centre of a data collection, which means that 50% of the data points have a value less than or equal to the median, and 50% of the data points have a value greater than or equal to the median. For a small data collection, calculate the number of data points (n) and organize them in ascending order.

The middle score in the group is called the median. Begin by sorting all of the data sets from lowest to highest before calculating the median. The median in an odd-numbered set will be the value that falls exactly in the center of the list. You must determine the average of the two middle integers in a set of even numbers.

Arrange in ascending order

21955, 25963, 27507, 32019, 38850, 43715

Take the two mid terms

27507 and 32019

Median = [tex]\dfrac{27507 + 32019}{2}[/tex]

Median = 29763

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The lateral surface area of the mailer is 234 In²

It is important to note that the formula for the lateral area of a triangular prism is expressed as;

A = (a + b+ c) h

Given that the parameters are enumerated as;

Now, substitute the values into the equation, we have;

Lateral area, A = (4 + 4 + 5) 18

Add the values

Lateral area = (13)(18)

Multiply the values

Lateral area = 234 In²

Hence, the value is 234 In²

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Answer:

[tex]\textsf{C.} \quad \sin x[/tex]

Step-by-step explanation:

Given rational expression:

[tex]\dfrac{\sec^2x \csc x}{\sec^2x + \csc^2 x}[/tex]

Rewrite the numerator and denominator of the given rational expression using the following trigonometric identities:

[tex]\boxed{\boxed{\begin{array}{c}\underline{\sf Trigonometric\;Identities}\\\\\boxed{\sec^2 x=\dfrac{1}{\cos^2x}} \qquad \boxed{\csc^2 x=\dfrac{1}{\sin^2 x}}\qquad \boxed{\csc x=\dfrac{1}{\sin x}}\\\\\end{array}}}[/tex]

Therefore:

[tex]=\dfrac{\dfrac{1}{\cos^2x} \cdot \dfrac{1}{\sin x}}{\dfrac{1}{\cos^2x}+\dfrac{1}{\sin^2x}}[/tex]

Multiply the fractions in the numerator, and make the denominators of the fractions in the denominator the same:

[tex]=\dfrac{\dfrac{1}{\sin x\cos^2x}}{\dfrac{\sin^2x}{\sin^2x\cos^2x}+\dfrac{\cos^2x}{\sin^2x\cos^2x}}[/tex]

[tex]=\dfrac{\left(\dfrac{1}{\sin x\cos^2x}\right)}{\left(\dfrac{\sin^2x+\cos^2x}{\sin^2x\cos^2x}\right)}[/tex]

[tex]\textsf{Apply the trigonometric identity}\;\;\boxed{\sin^2x + \cos^2 x = 1}:[/tex]

[tex]=\dfrac{\left(\dfrac{1}{\sin x\cos^2x}\right)}{\left(\dfrac{1}{\sin^2x\cos^2x}\right)}[/tex]

[tex]\textsf{Apply\:the\:fraction\:rule}\;\;\boxed{\dfrac{\frac{a}{b}}{\frac{c}{d}}=\dfrac{ad}{bc}}:[/tex]

[tex]=\dfrac{\sin^2x\cos^2x}{\sin x\cos^2x}[/tex]

Cancel the common factor cos²x:

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

Simplify:

[tex]= \sin x[/tex]

Therefore:

[tex]\large\textsf{$\dfrac{\sec^2x \csc x}{\sec^2x + \csc^2 x}=$}\;\boxed{\boxed{\sin x}}[/tex]

y-coordinates for x=3, 4.2, 2 are y=3.6, 4.8 and 2.6 respectively.

The general equation of a straight line is y=mx+c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.

The given equation is y=x+0.6

Find the y value for x=3, 4.2, 2

When x=3

y=3+0.6=3.6

When x=4.2

y=4.2+0.6=4.8

When x=2

y=2+0.6=2.6

Therefore, y-coordinates for x=3, 4.2, 2 are y=3.6, 4.8 and 2.6 respectively.

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Answer:

D

Step-by-step explanation:

why the panic ? you only need to compare the tiles with the actual terms in the equations and add them up.

x²

-x²

-x -x

x x x x (clearly that means 4x)

-1 -1 -1

1 1

so, we see it is D.

The ratio 8.64 : 37.76 as a fraction will be 27/118.

What precisely is ratio?

Ratios and proportions are typically described using fractions. When a fraction is presented as a:b, a ratio is shown, whereas a percentage suggests that two ratios are equal. In this case, a and b can be any two numbers. The ratio and proportion are two essential notions that serve as a foundation for understanding other concepts in mathematics and science.

In our daily lives, we apply the notion of ratio and proportion, such as in business when dealing with money or in cooking.

As a consequence, when b is greater than zero, the ratio specifies the connection between two variables, such as a:b. The 2:4 ratio, for example, is written as 2:4 = 1:2. 

Now,

Given ratio is  8.64 : 37.76

we can write this as 8.64/37.76

=864/3776

=432/1888

=216/944

=54/236

=27/118

Hence,

             The ratio 8.64 : 37.76, as a fraction will be 27/118.

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Answer:

It will turn on again, just charge it. All phones come with a charger.

The GCF of the polynomials are

1. for 15x²+18 , the GCF is 3

2. for -18y⁴+6y³+24y² ,the GCF is 6y²

The GCF stands for the “greatest common factor”. The GCF is defined as the largest number that is a factor of two or more numbers. For example, the GCF of 24 and 36 is 12, because the largest factor that is shared by 24 and 36 is 12. 24 and 36 have other factors in common, but 12 is the largest.

The GCF is the highest factor that can be used to divide through 2 or more terms

1. For 15x²+18, 3 is a factor of 15 and 18 and it's the greatest factor, therefore the GCF is 3

2. For -18y⁴+6y³+24y², between 18,6 and 24, 6 is the greatest factor Ang between y⁴ ,y³, y², y² is the greatest factor. Therefore the GCF of the expression is 6y².

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The equation of the polynomial is P(x) = -4(x + 1)(x - 1)(x - 2)^2

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

The graph

On the graph, we have the following readings:

A polynomial is represented as

P(x) = a * (x - zero)^multiplicity

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

P(x) = a * (x + 1)(x - 1)(x - 2)^2

The y-intercept is -12

So, we have

a * (0 + 1)(0 - 1)(0 - 2)^2 = -12

This gives

a = -4

Hence, the expression is P(x) = -4(x + 1)(x - 1)(x - 2)^2

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Answer:

0.89

Step-by-step explanation:

As there is 1 green marble out of 9 total marbles, there's a 1 in 9 chance of selecting the green marble. This means that its complement would be the probability of NOT selecting the green marble would be 8/9, or about 0.89

Answer:0.89

Step-by-step explanation:

Answer:

Given that s = 1.5, the expressions that have a value of 13.5 are:

(1) 5s + 8 = 5 × 1.5 + 8 = 13.5

(2) 2s^2 + 9 = 2 × 1.5^2 + 9 = 13.5

Note: The value of any other expression will depend on the specific formula and the value of other variables used in the expression.

The solution is, 12 (long division) 924 = 77.

Division is the process of splitting a number or an amount into equal parts.

Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.

here, we have,

given that,

12 (long division) 924

so, we get,

12 | 924  | 77

     84

----------------

       84

       84

-----------------

       0

Hence, The solution is, 12 (long division) 924 = 77.

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The value of x to the nearest integer is $294.

percentage, a relative value indicating hundredth parts of any quantity.

We can use the formula for the present value of an increasing annuity to solve this problem:

PV = x/(i-g) × (1 - (1+g)/(1+ i)ⁿ)

where PV is the present value,

x is the first payment,

i is the effective annual interest rate,

g is the annual increase rate of the payments, and

n is the total number of payments.

Substituting the given values, we have:

7229.50 = x/(0.07-0.04) (1 - (1+0.04)/(1+0.07)²⁰)

Simplifying and solving for x, we get:

x = 7229.50×0.03 × (1 - 1/1.07^20) / (1.04 × (1 - 1/1.07²⁰))

x= $294

Therefore, the value of x to the nearest integer is $294.

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The Equation x² − 15x + 12 = 0 have two Real solution and 3x² − 6x + 4 = 0 have Imaginary solution.

The discriminant, denoted by the equation b² - 4ac, can be used to ascertain if the solutions are real, repetitive, or complex:

1) If the discriminant is smaller than 0, there are two imaginary roots to the problem (s).

2) The equation has one repeating real solution if the discriminant equals zero (s).

Given:

x² − 15x + 12 = 0

Solving the Quadratic Equation

x² − 15x + 12 = 0

D = b² - 4ac

D = (-15)² - 4(1)(12)

D =  225 - 48

D = 177 >0

So, the Equation will have two Real solution.

b) 3x² − 6x + 4 = 0

Solving the Quadratic Equation

3x² − 6x + 4 = 0

D = b² - 4ac

D = (-6)² - 4(3)(4)

D =  36 - 48

D =  -12 >0

So, the Equation will have Imaginary solution.

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The mixture should contain 12 pounds of cashews and 18 pounds of Brazil nuts.

A physical combination of two or more unrelated substances is referred to as a mixture. For instance, water and salt are two different substances that, when combined, form a combination.

Let's call the amount of cashews used in pounds "x". The amount of Brazil nuts used in pounds can be calculated as 30 - x.

We know that the total cost of the mixture is $6.08 per pound * 30 pounds = $182.40.

The cost of the cashews in the mixture is $7.70 per pound * x pounds =$7.70x.

The cost of the Brazil nuts in the mixture is $5.00 per pound * (30 - x) pounds = $150 - $5.00x.

The total cost of the cashews and Brazil nuts in the mixture must equal $182.40, so we can set up the equation:

$7.70x + ($150 - $5.00x) = $182.40

Expanding and simplifying the equation:

$2.70x = $32.40

Dividing both sides by 2.70:

$x = 12

So, the mixture should contain 12 pounds of cashews and 18 pounds of Brazil nuts.

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The amount after 13 years with a compound interest of 6.9 % is given by the equation A = $ 5,149.69

Compound interest is interest based on the initial principle plus all prior periods' accumulated interest. The power of compound interest is the ability to generate "interest on interest." Interest can be added at any time, from continuously to daily to annually.

The formula for calculating Compound Interest is

A = P ( 1 + r/n )ⁿᵇ

where A = Final Amount

P = Principal

r = rate of interest

n = number of times interest is applied

b = number of time periods elapsed

Given data ,

Let the amount after compound interest be represented as A

Now , the equation will be

The principal amount P = $ 2,100

The rate of interest r = 6.9 %

The number of years b = 13 years

when compounded continuously ,

The compound interest amount A = Pe^rt

Substituting the values in the equation , we get

A = 2,100.00 ( 2.71828 ) ^ ( 0.069 ) ( 13 )

A = 2,100 ( 2.71828 )^( 0.897 )

On further simplification , we get

A = $ 5,149.69

Hence , the amount after 13 years is $ 5,149.69

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Answer:

12 and 5

Step-by-step explanation:

12+5=17

12x5=60

Answer:

Step-by-step explanation:

5 12 step by step

Answer:

(-3,-1)

Step-by-step explanation:

The two lines intersect at that point. -3 is in the x axis and -1 is in the y axis.

Answer:

D

Step-by-step explanation:

ASA = 2 non included angles + 1 included side

by knowing angle c is congruent to angle z we can prove the triangles are congruent by ASA postulate.

The correct statements would need to be congruent to show that

Δ ABC= ΔXYZ by ASA are,

⇒ ∠ B ≅ ∠ Y

⇒ ∠ C ≅ ∠ Z

An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.

Given that;

AC = XZ

∠ A = ∠ X

Now, To prove the triangles are congruent by ASA , we get;

AC = XZ

∠ A = ∠ X

⇒ ∠ Z = ∠ C

or, ∠ B = ∠ Y

Thus, The correct statements would need to be congruent to show that

Δ ABC= ΔXYZ by ASA are,

⇒ ∠ B ≅ ∠ Y

⇒ ∠ C ≅ ∠ Z

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