the gold prospector panned for gold 1000 times and actually found some 53 of those times. what is the probability that he will find the gold the next time he pans for gold?

The factored form of the equation x² + 11x + 24  is  (x + 3)(x + 8).

A quadratic equation is an algebraic equation of the second degree in x. Quadratic equation can be represented in standard form as follows:

ax² + bx + c

where

Factoring a quadratic equation can be defined as the process of breaking the equation into the product of its factors.

Therefore, let's factor the equation x² + 11x + 24 as follows:

x² + 11x + 24

The two numbers we can add to get 11 and multiply to get 24 are 3 and 8.

Therefore,

x² + 3x + 8x + 24

x(x + 3) + 8(x + 3)

Hence, the factored form is (x + 3)(x + 8)

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Answer:y=-1/7x+26/7

Step-by-step explanation: y=mx+b substitute m=-1/7

y=-1/7x+b

The line passes through the point (-2,4)

This means x=-2 and y=4 must be substituted in the above equation

4=-1/7*-2+b

4=2/7+b

Solve for b

To get b on its own we need take 2/7 from both sides

4-2/7=2/7-2/7+b

26/7=b

Need to solve 4/1-2/7

Must make denominators the same

Multiply top and bottom by 7

4*7/1*7-2/7

28/7-2/7=26/7

Answer:

so the(g) semicircle should go up top with

The standard form of (6.31×10⁵ ) + (2.6×10⁴) is 65.7 × 10⁴.

What is a simplification of an expression?

Usually, simplification involves proceeding with the pending operations in the expression.

Simplification usually involves making the expression simple and easy to use later.

As given,

(6.31×10⁵ ) + (2.6×10⁴) = ( 6.31× 10⁴ ×10 ) + (2.6 × 10⁴ )

=  ( 6.31 × 10 + 2.6 )

=  ( 63.1 + 2.6 )

=  ( 65.7 )

= 65.7 × 10⁴

Hence, the standard form of ( 6.31× 10⁵) + (2.6 × 10⁴) = 65.7 × 10⁴.

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Fraction of the sensors on the given satellite which have been upgraded is equal to  option D. 1/7.

As given in the question,

Total number of modular units = 30

Let 'n' be the total number of upgraded sensors available on the entire satellite

Number of non-upgraded sensors available on one unit = ( 1/5)n

                                                                                         = x/5

Number of non-upgraded sensors available on 30 modular unit

= 30n /5

= 6n

Total number of non- upgraded and upgraded sensors makes one unit

⇒n + 6n =  1

⇒7n = 1

Fraction of upgraded sensors are:

⇒ n = 1/7

Therefore, the fraction of the sensors available on the satellite and are upgraded is equal to option D. 1/7.

The above question is incomplete , the complete question is:

A satellite is composed of 30 modular units, each of which is equipped with a set of sensors, some of which have been upgraded. Each unit contains the same number of non-upgraded sensors. If the number of non-upgraded sensors on one unit is 1/5 the total number of upgraded sensors on the entire satellite, what fraction of the sensors on the satellite have been upgraded?

A. 5/6     B. 1/5      C. 1/6     D. 1/7        E. 1/24

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The nth term of the following quadratic sequence -1, 4, 15, 32, 55 is 119.

Any number sequence in which the second difference between any two successive terms is constant is referred to as a quadratic sequence. Think about the example below: 1;2;4;7;11;… We observe that all of the second differences equal one.

When the nth term rule includes a n2, the sequence is said to be quadratic (remember, a term is the word for a number in a sequence). A quadratic sequence's terms do not share a difference, in contrast to a linear sequence. The nth term of an arithmetic series can be calculated using our understanding of finding the nth term to be 2 n 2n 2n.

Let us assume that n=6,

aₙ=(n+1)(3n-1)

a₆=(6+1)(3(6)-1)

a₆=7(17)

a₆=119

Therefore, the nth term of the following quadratic sequence -1, 4, 15, 32, 55 is 119.

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Answer: 3/8

Step-by-step explanation:

The total number is 11 paper clips

We know that three are gold

And the question ask what fraction of the paper clips are gold

So take 3 divided by the total

So the fraction is 3/8

Answer:

Step-by-step explanation:

For number 1, It is $52.4

Divide the cost by the number f days to get your constant

for number 2, It is 2

Just format it to y=mx+b

I do not know the answer to the third one

And the fourth one it is true with a 1/25 fraction

Answer:

195

Step-by-step explanation:

Formula: A=1/2*b*h

6*65=390

390/2=195

So I multiplied those numbers together and decided to divide them by two, just like the formula wanted.

I hope this helps!!!

In Standard Form , [tex]y = -\frac{4x}{3} + 2[/tex] can be written as 4x+3y =6 .

What is Standard Form of a Equation ?

Ax+By=C

The standard form for linear equations in two variables is Ax+By=C. For example, 2x+3y=5 is a linear equation in standard form. When an equation is given in this form, it's pretty easy to find both intercepts (x and y).

The standard form of a linear equation is helpful for determining the x and y-intercepts of a graphed equation. It also helps you understand the concept of least common denominators, which is finding the lowest number to multiply and thus convert two fractions into whole numbers.

Given Equation :[tex]y = -\frac{4x}{3} + 2\\[/tex]

To convert it into Standard form , Multiply both sides with 3

[tex]3y = 3(\frac{-4x}{3} +2)[/tex]

[tex]3y = -4x + 6\\4x + 3y = 6[/tex]

Hence , In Standard Form , [tex]y = -\frac{4x}{3} + 2[/tex] can be written as 4x+3y =6 .

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The area of the triangle with two sides of 8 and 11 units and an angle of 75°

is 85 units².

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

We know in a ΔABC area of the triangle is (a×b×sinC).

The given triangle has two sides 8 units and 11 units and the angle to the unknown side is 75°.

∴ The area of the triangle is (8×11×sin75°) units².

= 88sin75° units².

= 85 units².

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A rectangle is transformed according to the rule R0, 90º.

What does parallelogram mean ?

A quadrilateral with two sets of parallel sides is known as a parallelogram. A parallelogram has opposite sides that are the same length and angles that are the same size.

                 Additionally, the internal angles on the same transverse side are supplementary. 360 degrees is the sum of all interior angles.

We are given that the rotation is

(x,y) --------> (x,y)

This means that the point is rotated back into its original position.

This means that full rotation occurred.

Since the full rotation is 360°,

For the other options:

Rotation 90° gives:

(x,y) ----------> (-y,x)

Rotation 180° gives:

(x,y) ----------> (-x,-y)

Rotation 270° gives:

(x,y) ---------> (y,-x)

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The point that preserves the function is option  A(-3,-8).

What do you mean by function?

A function in mathematics from a set X to a set Y assigns exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

According to the given question,

We have four option for the answer.

Note: if f is a function then each number of the domain has an unique image.

Since (regarding the table) the image of 9 is 6 then the answer D is wrong

The same apply on answers B and C .

Therefore, the right answer is A(-3,-8).

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The group rents 11 person tubes and 4 cooler tubes.

Let the no. of person tubes = x

Let the no. of cooler tubes = y

According to question,

Total no. of tubes = 15

Therefore,    x + y = 15                      ......... (I)

Cost of one person tube = $ 20

    Cost of x person tube = 20x

Cost of one cooler tube = $ 12.50

    Cost of y cooler tube = 12.5y

According to question,

                     Total cost = $ 270

Therefore, 20x + 12.5y = 270           .......... (II)

By solving equation (I) and (II), we get

x = 11

y = 4

Hence, The group rents 11 person tubes and 4 cooler tubes.

Correct Question :

A company that offers tubing trips down a river rents tubes for a person to use and "cooler" tubes to carry food and water. A group spends $270 to rent a total of 15 tubes. Write a system of linear equations that represents this situation. How many of each type of tube does the group rent? Person tube $20 Cooler tube $12.50.

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By using linear inequation it can be calculated that-

One possible solution is Aiden has 8 quarters and 14 dimes

What is linear inequation?

Inequation shows the comparision between two algebraic expressions by connecting the two algebraic expressions by >, <, ≥, ≤

A one degree inequation is known as linear inequation

Aaden has z quarters and y dimes.

He has no more than 22 coins

z + y ≤ 22

z ≤ -y + 22 .... (1)

He has no less than $3.60 combined.

0.25z + 0.1y ≥ 3.60

5z  + 2y ≥ 45

5z ≥ -2y + 45

z ≥ -0.4y + 9 .... (2)

This system of linear inequation is solved graphically

From the graph it is clear that

one solution is z = 8 and y = 14

One possible solution is Aiden has 8 quarters and 14 dimes.

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Answer:

6.50

Step-by-step explanation:

Answer:

To make sure who ever want the job is reliable and suitable for it.

Step-by-step explanation:

The sale price of the 2nd Washing machine is more expensive and profitable than the first Washing machine, So Kareem should choose the 2nd Washing machine to get profit.

The price a buyer pays for a good or service is known as the selling price. When the selling price is greater than the cost price, then we will get a Profit. Marked price, is the amount that a seller actually receives from a customer after negotiating a price or striking a deal.

Here we have

The selling price of washing machines is $520

The first one is marked down by 40%.

The second is marked down by 10% with an additional 30% off.

For the first Washing machine,

Let x be the sale price of the machine

Given that the price is 40% marked down

=> the selling price of Washing machine = x - 40% of x

= [tex]x - \frac{40x}{100}[/tex]

= x - 0.4x = 0.8x

As we know the selling price of the washing machine = $ 520

=> 0.8x = 520

=> x = 520/0.8

=> x = 650

The sale price of the first washing machine = $ 650.

For the 2nd Washing machine,

Let y be the sale price of the machine

Given that the price is 10% marked down

=> the selling price of Washing machine = y - 10% of y

= [tex]y - \frac{10y}{100}[/tex]

= x - 0.1x = 0.9x

And given 30% off

30% off on 0.9x = 30% of 0.9x

The selling price will be = 0.9x - 30% of 0.9x

=> 0.9x - 0.27x = 0.63x

As we know the selling price of a washing machine = $ 520

=> 0.63x = 520

=> x = 520/0.63

=> x = 825.39

The sale price of the 2nd washing machine = $ 825.39.

By the above calculations

The sale price of the 2nd Washing machine is more expensive and profitable than the first Washing machine, So Kareem should choose the 2nd Washing machine to get profit.

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The value of x is 21.

If the ratios of the lengths of the respective sides of two figures are the same and their corresponding angles are congruent, then the figures are said to be similar.

Given that, the corresponding angles of the two trapezoids are equal, therefore, the trapezoids are similar.

Since the trapezoids are similar, the ratio of their corresponding sides are in proportional:

14/18 = x/27

x = 27× (14/18)

x = 21

Hence, the value of x is 21.

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As per the concept of complex number, the equivalent expression to the given complex number is: –16 + 30i.

In math, the term complex number is defined as the following form:

=> a+bi,

where a and b are real numbers.  

where the variables: a is the real part and bi imaginary part.

Here we have given that the complex expression: (3+5i)²

And we need to find the equivalent expression for this one.

Here we know that the same properties used for real numbers can be applied to complex numbers.

According to this rule, we have to solve the operations math with these numbers, it is important to know that i²= -1.

As we know that the algebraic expressions are considered equivalent when they are equal.

Therefore, for solving this question, you should:

We have to apply the power rules and then  select the option that is equal to the result found.

= > (3+5i)²

Now it can be expanded like the following,

=> 9+30i+25i²

Apply the rule,

=> 9+30i+25*(-1)

=> 9+30i-25

=> -16 + 30i

Therefore, option (a) is correct.

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Therefore, the total cost of producing the first 16 units of a certain commodity is 28940.

The mathematical formula for a straight line on a graph is called a linear equation. Y = mx + b, where m is the line's slope  b seems to be the y-intercept, or the place where the line crosses the y-axis, is how it is expressed. Because they simply have one variable and no exponents, linear equations are comparatively easy to solve. They may be used to simulate a variety of real-world events, including population increase and the supply-demand connection in the economy. Generally speaking, linear equations are a fundamental algebraic tool produced and are used to represent and analyse a wide variety of data types.

How to solve?

dc/da = [tex]9x^{2} + 4x + 15x^(1/4) +10[/tex]

Differentiate with respect to x

dc/da = [tex]18x + 4 + 15/4 x^(-3/4)[/tex]

input the value 100 for the value of x,

dc/da = 1800 + 4.75

dc/da = 1808.75

To produce the first 16 units,

1808.75 × 16 = 28940

The cost of producing the first 16 units is 28940

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The probability is: 3/5

What is probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a proposition is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

There are : 41 | 43 | 47 | 53 | 59 (5 primes)  Between 40 and 60.

41 + 12 =53 is a prime

43 + 12 =55 Not a prime

47 + 12 =59 is a prime

53 + 12 =65 Not a prime

59 + 12 =71 is a prime

Therefore, the probability is: 3/5

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Answer:

11 and 13

(11x13)

Last night, the two dinner specials at Dwayne's favorite restaurant were salmon filet and steak. The restaurant served 25 specials in all, 24 percent of which were salmon filets 6 salmon filets did the restaurant serve.

10%, a comparative figure denoting one hundredth of any quantity. One percent (symbolized as 1%), being the hundredth component, is represented as 100 percent, while 200 percent signifies twice the amount specified.

A percentage in mathematics is a figure or ratio that may be stated as a fraction of 100. If we need to determine a percentage of a number, we should divide it by 100 and multiply the result.

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Answer: I Do not know specifically but If we are talking about rates/per hour the answer is 55 Per hour

Step-by-step explanation:

165 miles ÷ 3 hours because It may be talking about rates. Per "HOUR"

The assumptions been met (0.6581,0.7819).

What is American adults?

In 2020, the U.S. Census Bureau counted 331.4 million people living in the United States; more than three-quarters (77.9%) or 258.3 million were adults, 18 years or older — a 10.1% increase from 234.6 million in 2010.

Given that.

[tex]$$\begin{aligned}& p=0.72 .(1-p)=1-0.72=0.28 \\& n=200 .\end{aligned}$$[/tex]

At [tex]$95 \%$[/tex] confidence level x value is 1.96

z=1.96

So r

A 95 % confidence interval bor percent of American adults who beleive in Aliens is,

[tex]$$\begin{gathered}p \pm 2 \sqrt{\frac{p \times q}{n}} \\\therefore 0.72+1.96 \sqrt{\frac{0.72 \times 0.28}{200}} \\\therefore 0.72 \pm 1.96 \sqrt{0.0010} \\0.72 \pm 0.0619 \\\therefore \quad(0.6581,0.7819)\end{gathered}$$[/tex]

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Answer:

x = 7

Step-by-step explanation:

Compare the ratios of the longer side length to the shorter side length:

8 : 10 = (3x - 9) : 15

8*(3/2) : 15 = (3x - 9) : 15

Then, form an equation.

8 * (3/2) = 3x - 9

12 = 3x - 9

21 = 3x

7 = x

Answer:

D.None of the above are correcr

Step-by-step explanation:

if the population of peachwood increases by 5% every year then after 1 year 5 percent of 12,000 would be added to 12,000 and 5 percent of 12,000 is 600 so the answer would be 12,600

Option B is the correct Answer and $12600 people are in the city after 1 year.

Given the population of peachwood=12000

The rate that increases per year is given as 5%

We are given the function that g(f) = 12000 * 1.05x is considered as equation(1)

Here  x in f(x) defines the number of years that passed in the city of Peachwood

so x value is considered as 1

The f(x) is the total population of Peachwood these are two key elements in this function

Now substitute the x value in equation (1)

Therefore after 1 year, the equation would be

f(x)=12000*1.05x

f(1)=12000*1.05(1)

g(f)=$126000

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