5x-2=3(x+4)
What is the value of X

Answers

Answer 1

Answer:

[tex]\large\boxed{\textsf{x = 7}}[/tex]

Step-by-step explanation:

[tex]\textsf{For this problem, we are asked to find the value of x.}[/tex]

[tex]\textsf{We should simply isolate the x so that it's only on one side.}[/tex]

[tex]\large\underline{\textsf{How?}}[/tex]

[tex]\textsf{Simply use the Distributive Property for the right side of the equation.}[/tex]

[tex]\textsf{Simplify the equation to where x is by itself.}[/tex]

[tex]\large\underline{\textsf{What is the Distributive Property?}}[/tex]

[tex]\textsf{The Distributive Property is a Property that allow us to distribute expressions further.}[/tex]

[tex]\textsf{Commonly, the form is a(b+c); Where b and c are multiplied by a.}[/tex]

[tex]\large\underline{\textsf{Use the Distributive Property;}}[/tex]

[tex]\mathtt{5x-2=3(x+4)}[/tex]

[tex]\mathtt{5x-2=(3 \times x)+(3 \times 4)}[/tex]

[tex]\mathtt{5x-2=3x+12}[/tex]

[tex]\large\underline{\textsf{Add 2 to Both Sides of the Equation;}}[/tex]

[tex]\mathtt{5x-2 \ \underline{+ \ 2}=3x+12 \ \underline{+ \ 2}}[/tex]

[tex]\mathtt{5x=3x+14}[/tex]

[tex]\large\underline{\textsf{Subtract 3x from Both Sides of the Equation;}}[/tex]

[tex]\mathtt{5x-3x=3x-3x+14}[/tex]

[tex]\mathtt{2x=14}[/tex]

[tex]\large\underline{\textsf{Divide the Whole Equation by 2;}}[/tex]

[tex]\mathtt{\frac{2x}{2} = \frac{14}{2} }[/tex]

[tex]\large\boxed{\textsf{x = 7}}[/tex]

Answer 2

Answer:

[tex] \sf \: x = 7[/tex]

Step-by-step explanation:

Now we have to,

→ Find the required value of x.

The equation is,

→ 5x - 2 = 3(x + 4)

Then the value of x will be,

→ 5x - 2 = 3(x + 4)

→ 5x - 2 = 3(x) + 3(4)

→ 5x - 2 = 3x + 12

→ 5x - 3x = 12 + 2

→ 2x = 14

→ x = 14 ÷ 2

→ [ x = 7 ]

Hence, the value of x is 7.


Related Questions

Sophie invested $92,000 in an account paying an interest rate of 6 1/8% compounded

continuously. Damian invested $92,000 in an account paying an interest rate of 6 5/8%

compounded monthly. After 14 years, how much more money would Damian have in

his account than Sophie, to the nearest dollar?

Answers

Answer:

Step-by-step explanation:

To solve this problem, we need to use the formula for compound interest:

A = P*e^(rt)

where A is the final amount, P is the principal (initial investment), e is the base of the natural logarithm (approximately 2.71828), r is the interest rate (expressed as a decimal), and t is the time (in years).

For Sophie's account, we have:

P = $92,000

r = 6 1/8% = 0.06125 (as a decimal)

t = 14 years

A = 92000*e^(0.06125*14)

A = $219,499.70 (rounded to the nearest cent)

For Damian's account, we have:

P = $92,000

r = 6 5/8% = 0.06625/12 = 0.005521 (as a monthly decimal rate)

t = 14*12 = 168 months

A = 92000*(1+0.005521)^168

A = $288,947.46 (rounded to the nearest cent)

Now we can subtract Sophie's final amount from Damian's final amount to find the difference:

Difference = $288,947.46 - $219,499.70

Difference = $69,447.76

Therefore, Damian would have about $69,448 more in his account than Sophie, to the nearest dollar.

parabola a and parabola b both have the x-axis as the directrix. parabola a has its focus at (3,2) and parabola b has its focus at (5,4). select all true statements.
a. parabola A is wider than parabola B
b. parabola B is wider than parabola A
c. the parabolas have the same line of symmetry
d. the line of symmetry of parabola A is to the right of that of parabola B
e. the line of symmetry of parabola B is to the right of that of parabola A

Answers

In the following question, among the given options, Option (b) "Parabola B is wider than Parabola A" and option (d) "The line of symmetry of Parabola A is to the left of that of Parabola B" are the true statements.

The following statements are true about the parabolas: c. the parabolas have the same line of symmetry, and d. the line of symmetry of parabola A is to the right of that of parabola B.

Parabola A and Parabola B have the x-axis as the directrix, with the focus of Parabola A at (3,2) and the focus of Parabola B at (5,4). As the focus of Parabola A is to the left of the focus of Parabola B, the line of symmetry for Parabola A is to the right of the line of symmetry of Parabola B.

Parabola A and Parabola B may have different widths, depending on their equation, but this cannot be determined from the information given.

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c) assume that 25% of the defendants in the state are innocent. in a certain year 200 people put on trial. what is the expected value and variance of the number of cases in which juries got the right decision?

Answers

The expected value of cases in which juries got the right decision is 150, and the variance is 375.

1. Since 25% of defendants in the state are innocent, that means that 75% of the defendants are guilty.
2. This means that in the given year, 150 out of the 200 people put on trial will be guilty.
3. Thus, the expected value of cases in which juries got the right decision is 150.
4. The variance of the number of cases in which juries got the right decision is calculated by taking the expected value and subtracting it from the total number of people put on trial, which is 200.
5. The result of the calculation is 375, which is the variance of cases in which juries got the right decision.

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why can't we use mean when a data set has one or two values that are much higher than all of the others

Answers

The reason we can't use the mean when a data set has one or two values that are much higher than all of the others is that it skews the average, making it not representative of the rest of the data.

What is the mean?

The mean is a numerical measure of the central tendency of a data set. It is calculated by dividing the sum of all the values in a data set by the number of data points.

A data set is a collection of observations or measurements that are analyzed to obtain information. It can be represented graphically, in tabular form, or in any other format. The data set may be a sample or the entire population.

If a data set has one or two extremely high or low values, it can significantly impact the mean. These values are known as outliers. The outliers can cause the mean to be higher or lower than the actual middle value of the data.

Hence, in such cases, the median is a better choice for finding the central tendency of the data. The median is the middle value of the data set, and it is less affected by outliers than the mean. The mode, which is the value that occurs most frequently in the data set, is also a measure of central tendency that is less sensitive to outliers than the mean.

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Given the triangle, find the length of X. Give your answer in simpliest radical form.

Answers

Answer:

x = 4[tex]\sqrt{2}[/tex]

Step-by-step explanation:

using the cosine ratio in the lower right triangle and the exact value

cos45° = [tex]\frac{1}{\sqrt{2} } }[/tex] , then

cos45° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{4}{x}[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex]  ( cross- multiply )

x = 4[tex]\sqrt{2}[/tex]

LMN is a straight angle. Find m LMP and m NMP​

Answers

From the given information provided, the value of angle LMP and angle NMP is 77 and 103 degrees respectively.

Since LMN is a straight angle, it measures 180 degrees.

We are given the measures of LMP and NMP, and we are told that LMP + NMP = LMN. Therefore, we can set up an equation:

LMP + NMP = LMN

(-16x + 13) + (-20x + 23) = 180

Simplifying and solving for x, we get:

-36x + 36 = 180

-36x = 144

x = -4

Now that we have found the value of x, we can substitute it back into the expressions for LMP and NMP to find their measures:

LMP = -16x + 13 = -16(-4) + 13 = 77 degrees

NMP = -20x + 23 = -20(-4) + 23 = 103 degrees

Therefore, the measures of LMP and NMP are 77 degrees and 103 degrees, respectively, and the measure of LMN is 180 degrees.

Question - LMN is a straight angle. LMP = -16x + 13 NMP =  -20x + 23 LMP + NMP = LMN What are the measures?

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Find the first 4 terms of the sequence represented by the expression 3n + 5

Answers

The first 4 terms of the sequence represented by the expression 3n + 5

is 8, 11, 14 and 17.

Sequence:

In mathematics, an array is an enumerated collection of objects in which repetition is allowed and in case order. Like a collection, it contains members (also called elements or items). The number of elements (possibly infinite) is called the length of the array. Unlike sets, the same element can appear multiple times at different positions in the sequence, and unlike sets, order matters. Formally, a sequence can be defined in terms of the natural numbers (positions of elements in the sequence) and the elements at each position. The concept of series can be generalized as a family of indices, defined in terms of any set of indices.

According to the Question:

Given, aₙ = (3n+5).

First four terms can be obtained by putting n=1,2,3,4

a 1=(3×1+5) = 8

a 2 =(3×2+5) = 11

a 3 =(3×3+5) = 14

a 4 =(3×4+5) = 17

First 4 terms in the sequence are 8, 11, 14, 17.

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Isaiah is grounded and has to stay in his room all day. He made up a game where he throws balled-up paper called a "trashball" into his trash can. The diameter of the top of the trash can 1 the diameter of the top of is 12 in. Isaiah wants the "trashball" to have a diameter that is the trash can. > What should the diameter of Isaiah's "trashball" be? d Level G ? in. 12 in.​

Answers

Answer:

Isiah Thomas

Step-by-step explanation:

I amazing fact

Answer:

the correct answer is 4

Step-by-step explanation:

yea sorry i don’t know step-by-step

X is a Poisson RV with parameter 4. Y is a Poisson RV with parameter 5. X and Y are independent. What is the distribution of X+Y? A. X+Y is an exponential RV with parameter 9 B. X+Y is a Poisson RV with parameter 4.5 C. X+Y is a Poisson RV with parameter 9

Answers

The distribution of C) X+Y is a Poisson RV with parameter 9.

This is because the sum of two independent Poisson distributions with parameters λ1 and λ2 is also a Poisson distribution with parameter λ1 + λ2. Therefore, X+Y follows a Poisson distribution with parameter 4+5 = 9.

Option A is incorrect because an exponential distribution cannot arise from the sum of two Poisson distributions. Option B is also incorrect because the parameter of X+Y is not the average of the parameters of X and Y. Option C is the correct answer as explained above.

In summary, the distribution of X+Y is Poisson with parameter 9.

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Find the tangential and normal components of the acceleration vector for the curve → r ( t ) = 〈 − 3 t , − 5 t ^ 2 , − 2 t ^ 4 〉 at the point t = 1

Answers

The tangential component of the acceleration vector at point t = 1 is aT(1) = 233/3 and The normal component of the acceleration vector at point t = 1 is aN(1) = (1/3)√10459

How do we calculate the tangential component?

The acceleration vector can be found from the following formula:

[tex]a(t) = r''(t) = (-3,-10t,-8t3).[/tex]

To find the tangential component of the acceleration vector, we first need the velocity vector v(t).

[tex]v(t) = r'(t) = (-3,-10t,-8t3) .[/tex]

Next, we need to normalize the velocity vector using the following formula:

[tex]T(t) = v(t) / ||v(t)||,[/tex]

Where ||v(t)|| is the magnitude of the velocity vector.

[tex](1) = (-3,-10,-8) / \sqrt{(3^2 + 10^2 + 8^2)} = (-3/3, -10/3, -8/3) = (-1 , -10/3, -8/3) .[/tex]

Then, the tangential component of a(1) is:

[tex]aT(1) = a(1) T(1) = (-3, -10, -8) (-1, -10/3, -8/3) = 3 + 100/3 + 64/3 = 233/3.[/tex]

How do we calculate the normal component?

To find the normal component of a(1), we simply need to find the magnitude of the tangential component and subtract it from the magnitude of the acceleration vector.

[tex]aN(1) = \sqrt{ (a^2 - aT(1)^2)} = \sqrt{(3^2 + (10)^2 + (8)^2 - (233/3)^ 2)}  = \sqrt{(9 + 100 + 64 - 54289/9)} = \sqrt{(10459/9)} = (1/3)\sqrt{10459}[/tex]

Therefore, the tangential and normal components of the acceleration vector at the point t = 1 are:

[tex]aT(1) = 233/3[/tex] and [tex]aN(1) = (1/3)\sqrt{10459}[/tex]

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Levi's investment account accrues interest biannually. The function below represents the amount of money in his account if the account is left untouched for
t years.
f(t) = 2000 (1.03)2t

The amount of money in the account ( increases or decreases )

by (2 , 3 or 103)

% (every six months, each year, or every two years)

Answers

Answer:

The amount of money in the account increases by 3% every six months, or biannually.

To see why, we can break down the function f(t) = 2000(1.03)^(2t):

The base amount in the account is $2000.The term (1.03)^(2t) represents the interest accrued over time.

Since the interest is compounded biannually, the exponent of 2t indicates the number of six-month periods that have elapsed. For example, if t = 1, then 2t = 2, which means two six-month periods have elapsed (i.e., one year).

Each time 2t increases by 2, the base amount is multiplied by (1.03)^2, which represents the interest accrued over the two six-month periods.

Thus, the amount of money in the account increases by 3% every six months, or biannually.

As for the second part of the question, the amount of increase is not 2%, 3%, or 103%.

find the values of a and b such that
x^2- +5=(x-a)^2+b

Answers

The value οf a = 1/2  and b = 19/4 in the equatiοn x² - x + 5 = (x-a)² + b.

What dο yοu mean by algebra?

The part οf mathematics in which letters and οther general symbοls are used tο represent numbers and quantities in fοrmulae and equatiοn is called algebra.

x² - x + 5 = (x-a)² + b

x² - x + 5 = x² + a² - 2xa + b

-x + 5 = -2xa + a² + b

By matching cοrrespοnding terms,

2a = 1          and        a²+ b = 5

a= 1/2          and        a²+ b = 5

Substituting value οf "a"

(1/2)² + b = 5

1/4 + b = 5

b = 5- 1/4

b = 19/4

Thus, a = 1/2  and b = 19/4.

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what is the probability of reaching into the box and randomly drawing a chip number that is smaller than 212 ? express your answer as a simplified fraction or a decimal rounded to four decimal places.

Answers

The probability of reaching into the box and randomly drawing a chip number that is smaller than 212 is 0.9378

First, we should find the total number of chips in the box. The box contains 225 chips numbered from 1 to 225. Therefore, the probability of reaching into the box and randomly drawing a chip number that is smaller than 212 is 211/225.

The probability can be expressed as a simplified fraction or a decimal rounded to four decimal places. The probability is rounded to four decimal places is 0.9378.

The probability of drawing a chip number that is smaller than 212 from the box is 211/225 or 0.9378 (rounded to four decimal places).

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Analyze the proportion below and complete the instructions that follow. Use a model to find the missing value in the proportion. A. 4 B. 5 C. 10 D. 22 Please select the best answer from the choices provided A B C D

Answers

Step-by-step explanation:

The area of a rectangle is 1,872 ft2. The ratio of the length to the width is 9:13. Find the perimeter of the rectangle.

176 ft

You want to make a scale drawing of your bedroom to help arrange your furniture. You decide on a scale of 3 in. = 2 ft. Your bedroom is a 12 ft by 14 ft rectangle. What should the dimensions of your drawing be?

18 in. by 21 in.

If 5/y + 7/x=24 and 12/y + 2/x=24, find the ratio of x to y.

5/7

Simplify the ratio 8ft/12in. Use the conversion 12 in. = 1 ft.

8/1

Analyze the proportion below and complete the instructions that follow.

2x+5/3 = x-5/4

-7

If a+b/2a-b = 5/4 and b/a+9 = 5/9, find the value of b.

30

Analyze the ratio below and complete the instructions that follow.

$30:$6

Simplify the ratio.

5:1

If 14/3 = x/y then 14/x =

3/y

Analyze the diagram below and complete the instructions that follow.

In the diagram, AB:BC is 3:4 and AC = 42. Find BC.

24

Analyze the diagram below and complete the instructions that follow.

If AB:BC is 3:11, solve for x.

9

If a, b, c, and d are four different numbers and the proportion a/b = c/d is true, which of the following is false?

b/a = c/d

Analyze the diagram below and complete the instructions that follow.

Find the ratio of the width to the length of the rectangle, then simplify the ratio. Use the conversion 100 cm = 1 m.

3/4

Simplify the ratio 3 gal./24 qt. Use the conversion 4 qt = 1 gal.

1/2

The area of a rectangle is 4,320 ft2. The ratio of the length to the width is 6:5. Find the length of the rectangle.

72 ft

Analyze the diagram below and complete the instructions that follow.

Given that CB/CA = DE/DF, find BA.

10.5

Analyze the proportion below and complete the instructions that follow.

2/3 = 8/x

3, 8

Analyze the diagram below and complete the instructions that follow.

Are the polygons shown here similar? Justify your answer. The images are not drawn to scale.

Yes, PQR ~TSV with a scale factor of 1:√3

All __________ are similar.

squares

Analyze the diagram below and complete the instructions that follow.

Determine which 2 triangles are similar to each other. The images are not drawn to scale.

GHI ~ JKL

Analyze the diagram below and complete the instructions that follow.

Pentagon PQRST ~ pentagon XYZVW. Find the value of b. The images are not drawn to scale.

3

Analyze the diagram below and complete the instructions that follow.

If ABC ~ XYZ, find XY. The images are not drawn to scale.

24

ABC is a right triangle. The legs of ABC are 9 ft and 12 ft. The shortest side of XYZ is 13.5 ft, and ABC ~ XYZ How long is the hypotenuse of XYZ?

22.5 ft

I need help with answer this question

Answers

Answer:

y = 2x/15 + 6

Step-by-step explanation:

3y/2 = x/5 + 9

3y = (x/5 + 9) (2)    The 2 that was dividing goes on to multiply on the other side.

3y= 2x/5 + 18

y = (2x/5 + 18) / 3   The 3 that was multiplying goes on to divide on the other side.

y = 2x/15 + 6

Two percent of all individuals in a certain population are carriers of a particular disease. A diagnostic test for this disease has a 95% detection rate for carriers and a 3% detection rate for noncarriers. Suppose the test is applied independently to two different blood samples from the same randomly selected individual. A. What is the probability that both tests yield the same result?

Answers

The probability that both tests yield the same result is 7.7%.

Simply put, probability is the likelihood that something will occur. When we don't know how an occurrence will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of occurrences that follow a probability distribution.
It is predicated on the likelihood that something will occur. The justification for probability serves as the primary foundation for theoretical probability. For instance, the theoretical chance of receiving a head when tossing a coin is 12.
Let's break it down:-
90% don't have of those 99%
5% will be positive
1% positive of those 1%
90% positive
10% negative.
Well we need it to be the same, so 99*(.05*.05+.95*.95)+.01*(.9*.9+.1*.1)= 90.4%.
If both tests are positive, we have:-

0.99*0.05*0.05 and 0.01*0.9*0.9 for being positive, so :-

[tex]\frac{carrier}{positive} = \frac{0.01*0.9*0.9}{(0.99*0.05*0.05+0.01*0.9*0.9)} = 7.7[/tex]

hence, the probability of the two tests yield the same result is 7.7%.

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Determine whether the statement is true or false. If it is false, rewrite it as a true statement. A sampling distribution is normal only if the population is normal. Choose the correct answer below. A. The statement is true. B. The statement is false. A sampling distribution is normal only if n≥30. C. The statement is false. A sampling distribution is normal if either n≥30 or the population. D. The statement is false. A sampling distribution is never normal.

Answers

A sampling distribution is normal only if the population is normal. This  statement is false because A sampling distribution is normal only if n≥30.

If the underlying population is normally distributed, the sampling distribution (such as the sample mean distribution, also known as the xbar distribution) is also normally distributed. Even though the population is not normally distributed, the x(bar) distribution is approximately normal if n > 30, due to the central limit theorem. Some textbooks may use values ​​above 30, but after a certain threshold the x(bar) distribution is effectively "normal".

Option B is close, but misses the normal population part. n > 30 is not necessary if we know the population is normal.

A sampling distribution is the probability distribution of a statistic obtained from a large number of samples drawn from a particular population. The sampling distribution for a given population is the frequency distribution of a range of different outcomes that can occur in the population.

In statistics, a population is the entire basin from which a statistical sample is drawn. A population can refer to an entire population of people, objects, events, hospital visits, or measurements. Thus, a population can be said to be a global observation of subjects grouped by common characteristics.

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PLEASE HELP!!! WILL MARK BRANLIEST!!!

Answers

Answer:

The point z = 3+4i is plotted as a blue dot, and the two square roots are plotted as a red dot and a green dot. The magnitudes of z and its square roots are shown by the radii of the circles centered at the origin.

Step-by-step explanation:

qrt(z) = +/- sqrt(r) * [cos(theta/2) + i sin(theta/2)]

where r = |z| = magnitude of z and theta = arg(z) = argument of z.

Calculate the magnitude of z:

|r| = sqrt((3)^2 + (4)^2) = 5

And the argument of z:

theta = arctan(4/3) = 0.93 radians

Now, find the two square roots of z:

sqrt(z) = +/- sqrt(5) * [cos(0.93/2) + i sin(0.93/2)]

= +/- 1.58 * [cos(0.47) + i sin(0.47)]

= +/- 1.58 * [0.89 + i*0.46]

Using a calculator, simplify this expression to:

sqrt(z) = +/- 1.41 + i1.41 or +/- 0.2 + i2.8

Whats 21 square root of 98 divided by 7 square root of 21

Answers

The 21 square root of 98 divided by 7 square root of 21 = 21√98 / 7√21 = 6.4807407

A square root of a number x is a number y such that y2 = x; in other words, a number y who's square and the result of multiplying the number by itself, or y ⋅ y, is x.

Every nonnegative real number x has a unique nonnegative square root, called the principal square root, which is denoted by √where the symbol √ is called the radical sign.

Every positive number x has two square roots: √ which is positive, and -√ which is negative. The two roots can be written more concisely using the ± although the principal square root of a positive number is only one of its two square roots, the designation "the square root" is often used to refer to the principal square root.

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What is the difference between the simple and compound interest if you borrow $3,000 at a 6% interest rate for 2 years?
$180.00
$10.00
$6.00
$80.00

Answers

Answer:

Correct option is C)

Simple interest =

100

3000×6×2

=360

Compound interest =3000(1+

100

6

)

2

−3000=18×20.6=370.8

∴ Difference is Rs.10.8.

you can convert this value to $$

or simply the answer will be 2. $10

(hob-evzw-zjw) come

Answer:

B is your answer.
10.80$ which you just round to 10. 10 is your answer.

Step-by-step explanation:

For simple interest, the formula is:

Simple Interest = Principal × Rate × Time

For compound interest, the formula is:

Compound Interest = Principal × (1 + Rate)^Time - Principal

Let's calculate the values:

Principal = $3,000

Rate = 6% or 0.06

Time = 2 years

Simple Interest = $3,000 × 0.06 × 2 = $360

To calculate compound interest, we need to use the formula:

Compound Interest = $3,000 × (1 + 0.06)^2 - $3,000

= $3,000 × (1.06)^2 - $3,000

= $3,000 × 1.1236 - $3,000

= $3,370.80 - $3,000

= $370.80

The difference between simple and compound interest is:

$370.80 - $360 = $10.80

cosθ(1+tanθ)=cosθ+sinθ​

Answers

Answer:

Starting with the left side of the equation:

cosθ(1+tanθ) = cosθ(1+sinθ/cosθ) (since tanθ = sinθ/cosθ)

= cosθ + sinθ

Therefore, the left side of the equation is equal to the right side of the equation, which means that cosθ(1+tanθ) = cosθ+sinθ is true.

a 3-digit pin number is selected. what it the probability that there are no repeated digits? the probability that no numbers are repeated is

Answers

The probability that no numbers are repeated = [tex]\frac{720}{1000}=0.72[/tex]

The probability that there are no repeated digits in a 3-digit pin number is 0.72.

Formula used:

[tex]P(n,r)=\frac{n!}{(n-r)!}\\ Probability=\frac{Number of favourable outcomes}{Total number of events in the samples pace}[/tex]

There are 10 digits (0,1,2,3,4,5,6,7,8,9) to choose from.

Therefore, the total number of possible 3-digit pin numbers with no repeated digits is

[tex]P(10,3)=\frac{10!}{(10-3)!}\\P(10,3)= \frac{10!}{7!}\\P(10,3)=720[/tex]

The total number of possible 3-digit pin numbers [tex]= 10 * 10 * 10 = 1000[/tex].

Thus, the probability that no numbers are repeated = [tex]\frac{720}{1000}=0.72[/tex]

Therefore, the probability that there are no repeated digits in a 3-digit pin number is 0.72.

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Three softball players discussed their batting averages after a game.


Probability
Player 1 four sevenths
Player 2 five eighths
Player 3 three sixths


By comparing the probabilities and interpreting the likelihood, which statement is true?

Answers

The statement that is true is: Player 2 has the highest likelihood of getting a hit in their at-bats.

How to determine the true statement from the options

By comparing the probabilities, we can interpret the likelihood of each player getting a hit in their at-bats. The highest probability indicates the highest likelihood of getting a hit.

Comparing the probabilities of the three players, we can see that:

Player 2 has the highest probability (5/8), which means they are the most likely to get a hit in their at-bats.

Player 1 has a lower probability (4/7) than Player 2, but a higher probability than Player 3. This means they are less likely to get a hit than Player 2, but more likely to get a hit than Player 3.

Player 3 has the lowest probability (3/6 = 1/2) of getting a hit, which means they are the least likely to get a hit in their at-bats.

Therefore, the statement that is true is: Player 2 has the   of getting a hit in their at-bats.

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To compare the pain control offered by two different analgesics in pediatric patients, the authors selected the Wong-Baker FACES pain rating scale as the primary end point. Before beginning the clinical trial, the authors sought to validate this ordinal scale by showing a correlation with a previously validated visual analog scale. Which one of the following statistical test is most appropriate to assess whether a correlation exists between these two measurements?
A. Pearson correlation
B. Analysis of variance (ANOVA)
C. Spearman rank correlation
D. Regression analysis

Answers

The most appropriate statistical test to assess whether a correlation exists between the Wong-Baker FACES pain rating scale and a previously validated visual analog scale is the (C) Spearman rank correlation.

What is correlation?

Correlation refers to the connection between two variables in which a modification in one variable is linked to a modification in the other variable. Correlation can be positive or negative.

Spearman rank correlation- A non-parametric approach to test the statistical correlation between two variables is Spearman rank correlation, also known as Spearman's rho or Spearman's rank correlation coefficient. This is based on the ranks of the values rather than the values themselves. The results are denoted by the letter "r".

The formula for Spearman's rank correlation coefficient:

Rs = 1 - {6Σd₂}/{n(n₂-1)}

Where, Σd₂ = the sum of the squared differences between ranks.

n = sample size

Thus, the most appropriate statistical test to assess whether a correlation exists between these two measurements is the (C) Spearman rank correlation.

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y=mx+b

Answers

The required equation of straight line is y = 0.03x + 20.

What is an equation?

A mathematical equation states that two quantities or values are identical. Equations are used when more than one factor has to be examined in order to fully understand or explain a situation.

The general form of an equation is y = mx + b, where m is the slope of equation and b is a constant.

From the given graph we get 2 points.

i.e., (0, 20) and (2000, 80)

Slope of the line is

[tex]m=\frac{80-20}{2000-0}\\\ \ = \frac{60}{2000}\\ = \frac{6}{200} \\= \frac{3}{100}[/tex]

Then the equation will be

[tex]y-20=\frac{3}{100}(x-0)\\\Rightarrow y-20=0.03x\\\Rightarrow y-0.03x-20=0\\\Rightarrow y = 0.03x+20[/tex]

Therefore, the required equation is y = 0.03x + 20, calculating with the help of given graph.

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F(x)=-(x+3)(x+10) pls help

Answers

Answer:

Zeros: x = -10 and x = -3

Vertex: [tex](-\frac{13}{2} , \frac{49}{4} )[/tex]

Step-by-step explanation:

Pre-Solving

We are given the following function:
f(x) = -(x+3)(x+10)

We want to find the zeros and the vertex of the parabola.

SolvingZeros

The zeros are the values of the function where f(x) = 0.

So, in order to find the zeros, we can set f(x) = 0.

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

We can divide both sides by -1, to get:

0 = (x+3)(x+10)

To solve this, we will use zero product property.
Split and solve:

x+3 = 0

x = -3


x+10=0

x = -10

Vertex

Now, to find the vertex, we first get the average of the zeros.

Add the values of the zeros together, then divide by two:

[tex]\frac{-3-10}{2}[/tex] = [tex]\frac{-13}{2}[/tex]

Now, we plug this in for x to get the y value (found through f(x)) of the vertex.

[tex]f(-\frac{13}{2}) = -(-\frac{13}{2} + 3) (-\frac{13}{2} + 10)[/tex] = [tex]\frac{49}{9}[/tex]

So, the vertex is [tex](-\frac{13}{2} , \frac{49}{4} )[/tex]

Each angle of a regular polygon is 1680. How
many sides has it? What is the name of this
polygon?

Answers

Answer: 2 solutions

Step-by-step explanation:

To find the angle of a regular polygon, use the formula 180(n-2)/n (where n is the amount of sides.)

Setting them equal, we get (180n-360)/n = 1680.

Multiplying by n on both sides, we get 180n-360 = 1680n.

Solving, we get 1500n = 360.

n = 0.24, which means it is not a shape, as you cannot have a shape with 0.24 sides.

The other way to look at it is to take full revolutions of 360 away from each angle, giving us 240 (the smallest remainder without it going negative). However, all the angles would be concave. If all the angles are concave, then it might connect backwards.

Subtracting 240 from 360 (to get the "exterior" angles, we get 120. Plugging it in to our equation 180(n-2)/n and solving, we get 180n-360 = 120n, and solving gives us 60n = 360, or n=6.

Since the amount of sides came together cleanly, we can classify this polygon as a normal hexagon, which has 6 sides.

A bus arrives every 10 minutes at a bus stop. It is assumed that the waiting time for a particular individual is a random variable with a continuous uniform distribution.
a) What is the probability that the individual waits more than 7 minutes?
b) What is the probability that the individual waits between 2 and 7 minutes?A continuous random variable X distributed uniformly over the interval (a,b) has the following probability density function (PDF):fX(x)=1/0.The cumulative distribution function (CDF) of X is given by:FX(x)=P(X≤x)=00.

Answers

In the following question, among the various parts to solve- a) the probability that the individual waits more than 7 minutes is 0.3. b)the probability that the individual waits between 2 and 7 minutes is 0.5.

a) The probability that an individual will wait more than 7 minutes can be found as follows:

Given that the waiting time of an individual is a continuous uniform distribution and that a bus arrives at the bus stop every 10 minutes.Since the waiting time is a continuous uniform distribution, the probability density function (PDF) can be given as:fX(x) = 1/(b-a)where a = 0 and b = 10.

Hence the PDF of the waiting time can be given as:fX(x) = 1/10The probability that an individual waits more than 7 minutes can be obtained using the complementary probability. This is given by:P(X > 7) = 1 - P(X ≤ 7)The probability that X ≤ 7 can be obtained using the cumulative distribution function (CDF), which is given as:FX(x) = P(X ≤ x) = ∫fX(t) dtwhere x ∈ [a,b].In this case, the CDF of the waiting time is given as:FX(x) = ∫0x fX(t) dt= ∫07 1/10 dt + ∫710 1/10 dt= [t/10]7 + [t/10]10= 7/10Using this, the probability that an individual waits more than 7 minutes is:P(X > 7) = 1 - P(X ≤ 7)= 1 - 7/10= 3/10= 0.3So, the probability that the individual waits more than 7 minutes is 0.3.

b) The probability that the individual waits between 2 and 7 minutes can be calculated as follows:P(2 < X < 7) = P(X < 7) - P(X < 2)Since the waiting time is a continuous uniform distribution, the PDF can be given as:fX(x) = 1/10Using the CDF of X, we can obtain:P(X < 7) = FX(7) = (7 - 0)/10 = 0.7P(X < 2) = FX(2) = (2 - 0)/10 = 0.2Therefore, P(2 < X < 7) = 0.7 - 0.2 = 0.5So, the probability that the individual waits between 2 and 7 minutes is 0.5.

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The dwarf lantern shark is the smallest shark in the world. At birth, it is about 55 millimeters long. As an adult, it is only 3 times as long. How many centimeters long is an adult dwarf lantern shark? centimeters

Answers

Answer: 165

Step-by-step explanation:

55 x 3 = 165

Halla los números desconocidos de estas operaciones
A)872+. +173=2000
B)9180:. =102
C). -99=706
Con los mismos números y las mismas operaciones podemos obtener diferentes resultados,coloca los paréntesis de manera que se obtengan los resultados indicados. A)3+5x7-2=40
B)3+5×7-2=54
C)3+5×7-2=28
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Answers

In equation A the missing number is 955, In equation B the missing number is 90 and In equation C the missing number is 805.

A) To find the missing number in the equation 872 + ? + 173 = 2000, we need to subtract 872 and 173 from 2000, which gives us:

2000 - 872 - 173 = 955

Therefore, the missing number is 955.

B) To find the missing number in the equation 9180 ÷ ? = 102, we need to divide 9180 by 102, which gives us:

9180 ÷ 102 = 90

Therefore, the missing number is 90.

C) To find the missing number in the equation ? - 99 = 706, we need to add 99 to 706, which gives us:

706 + 99 = 805

Therefore, the missing number is 805.

To obtain the indicated results with the same numbers and operations, we need to use parentheses to change the order of operations.

A) 3 + (5x7) - 2 = 40

B) (3 + 5) × 7 - 2 = 54

C) 3 + (5 × (7-2)) = 28

Equations are used extensively in various fields of science, engineering, economics, and finance, to name a few. It is formed by placing an equal sign between the two expressions. Equations are used to solve problems and find unknown values.

An equation can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. The variables in an equation represent unknown values that need to be found, while the constants are known values that are already given. Solving an equation involves manipulating the expressions on both sides of the equal sign using mathematical operations to isolate the variable on one side and constants on the other. The final solution obtained is the value of the variable that satisfies the equation..

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Complete Question: -

Find unknown numbers of these operations

A ) 872 +. + 173 = 2000

B ) 9180:. = 102

C ). -99 = 706

With the same numbers and the same operations we can obtain different results, place the parentheses so that the indicated results are obtained.

A ) 3 + 5 x 7-2 = 40

B ) 3 + 5 × 7-2 = 54

C ) 3 + 5 × 7-2 = 28

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