1.5 x 10^8 is written as in standard form

Answer:

9 / 100 ; 0.09

Step-by-step explanation:

From the line plot given :

The number of unlabeled ticks marks between any two labeled tick marks can be obtained by :

(Difference between any two successive labeled tick marks / number of tick marks)

Picking the labeled tick marks, 0 and 1/10

(1/10 - 0) / 10

1 / 10 ÷ 10

1/ 10 * 1 / 10 = 1 / 100

To find the marked point : (this is tick mark 9 from 0) ;

Number of ticks * distance between ticks

Location of marked tick = 1 / 100 * 9 = 9 / 100

Decimal equivalent = 9/100 = 0.09

Answer:

The answer is no solutions

Step-by-step explanation:

Let's solve your equation step-by-step.

x−3=x+3

Step 1: Subtract x from both sides.

x−3−x=x+3−x

−3=3

Step 2: Add 3 to both sides.

−3+3=3+3

0=6

Therefore, no solutions :)

Greetings from Brasil...

The expression that allows you to calculate the distance between two points is:

Bringing to our problem:

d(A; B) = √[(9 - 0)² + (14 - 2)²]

d(A; B) = √[9² + 12²]

d(A; B) = √[81 + 144]

d(A; B) = √[225]

Answer:

n= 3

Step-by-step explanation:

3 (4 + n) = n + 18

you take 3x4=12

then 3x3=9 then you add 12 and 9 which would be in the ( )

12+9 = 21

then if you replace n =3 on other side and add it to 18 answer is 21

therefore both sides would equal 21 so n=3

3(4+3)=3+18

21=21

Option C is the real-world situation that can be represented by 2m + 3. The equation 2m + 3 represents the number 3 more than twice a certain number (m).

In option A, the equation that represents the situation would be 3d + 2, where d is the number of downloads. In option B, the equation that represents the situation would be 2i + 3, where i is the number of items purchased.

In option D, the equation that represents the situation would be 2l - 3, where l is the number of laps Dan swims.

Therefore, option C is the correct answer as it is the only option that represents the situation where one person bikes 2 more than 3 times the miles another person bikes.

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4.512 kg

Step-by-step explanation:

The probability of a song being played on a single day is 0.5. We need to find the probability of the song being played on 2 days out of 4 days. This can be solved using the binomial probability formula, which is P(X=k) = (n choose k) * p^k * (1-p)^(n-k), where n is the number of trials, k is the number of successful events, p is the probability of success, and (n choose k) is the binomial coefficient. Substituting the values, we get P(X=2) = (4 choose 2) * 0.5^2 * 0.5^2 = 0.375. Therefore, the probability that this song will be played on 2 days out of 4 days is 0.375.

The problem can be solved using the binomial probability formula because we are interested in finding the probability of a particular event (the song being played) occurring a specific number of times (2 out of 4 days) in a fixed number of trials (4 days).

We use the binomial probability formula P(X=k) = (n choose k) * p^k * (1-p)^(n-k) to calculate the probability of k successful events occurring in n trials with a probability of success p.

In this case, n=4, k=2, p=0.5. Therefore, P(X=2) = (4 choose 2) * 0.5^2 * 0.5^2 = 0.375.

The probability that a particular song will be played on 2 days out of 4 days at radio station wmzh is 0.375 or 37.5%.

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Answer:

d = 3h - 6

Step-by-step explanation:

Given

h = \(\frac{d}{3}\) + 2 ( subtract 2 from both sides )

h - 2 = \(\frac{d}{3}\) ( multiply both sides by 3 )

3(h - 2) = d , that is

d = 3h - 6

Answer:

0.7627

Step-by-step explanation:

This is a binomial probability problem

Given :

Number of trials, n = 5

p = number of correct option / total options = 1/4 = 0.25

q = 1 - p = 1 - 0.25 = 0.75

Using the binomial probability relation :

P(x = x) = nCx * p^x * q^(n-x)

Getting atleast 1 correct :

P(x ≥ 1) = p(x = 1) + p(x = 2) + p(x = 3) + p(x =4) + p(x = 5)

P(x =1) = 5C1 * 0.25^1 * 0.75^4 = 0.3955

P(x =2) = 5C2 * 0.25^2 * 0.75^3 = 0.2637

P(x =3) = 5C3 * 0.25^3 * 0.75^2 = 0.0879

P(x =4) = 5C4 * 0.25^4 * 0.75^5 = 0.0146

P(x =5) = 5C5 * 0.25^5 * 0.75^0 = 0.0009

P(x ≥ 1) = 0.3955 + 0.2637 + 0.0879 + 0.0146 + 0.0009 = 0.7627

P(x ≥ 1) = 0.7627

The correct answer is: III only. Variance investigation is typically based on a cost-benefit analysis.

Statement I is incorrect because the relative size of a variance, in comparison to other variances, can be important in understanding its significance.

Statement II is incorrect because variance investigation does not focus solely on unfavorable variances. Both favorable and unfavorable variances are considered during the investigation.

Statement III is true. Variance investigation is typically based on a cost-benefit analysis, where the potential benefits of investigating and addressing variances are weighed against the associated costs.

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Answer:

Step-by-step explanation:

Given the expression

\(\left(x+5\right)^2-10=0\)

Add 10 to both sides

\(\left(x+5\right)^2-10+10=0+10\)

Simplify

\(\left(x+5\right)^2=10\)

\(\mathrm{For\:}\left(g\left(x\right)\right)^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}g\left(x\right)=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}\)

solve

\(x+5=\sqrt{10}\)

Subtract 5 from both sides

\(x+5-5=\sqrt{10}-5\)

\(x=\sqrt{10}-5\)

\(x=-1.8\)

so

\(x+5=-\sqrt{10}\)

Subtract 5 from both sides

\(x+5-5=-\sqrt{10}-5\)

Simplify

\(x=-\sqrt{10}-5\)

\(\:x=-8.2\)

As -1.84 > -8.16

so

Answer:

y + 2 = \(\frac{2}{3}\)(x - 1)

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

y - 4 = \(\frac{2}{3}\)(x - 3) ← is in point- slope form

with slope m = \(\frac{2}{3}\)

Parallel lines have equal slopes, thus equation of parallel line

with m = \(\frac{2}{3}\) and (a, b) = Q(1, - 2) is

y - (- 2) = \(\frac{2}{3}\)(x - 1) , that is

y + 2 = \(\frac{2}{3}\)(x - 1)

Answer:

• Let's first assign identifications to the equations given:

\({ \rm{8x + 9y = {}^{ - }3 \: - - - \{equation \: (a) \} }} \\ { \rm{6x + 7y = 1 - - - \{equation \: (b) \}}} \\ \)

• There are various methods to solve this system of equation, namely;

1. Graphical method

→ You'll have to draw a graph, demacate it very well following the suitable scale.

→ Get values to plot from both equation (a) and equation (b).

→ Draw respective lines of each equation. The point of intersection of the lines is the answer of the values of x and y.

→ It'll be in coordinate format i.e; (x, y)

2. Substitution method

→ Lemme first consider equation (a)

\({ \rm{8x + 9y = {}^{ - }3 }}\)

• make x the subject of the equation (a):

\({ \rm{8x = - 3 - 9y}} \\ \\ { \rm{x = \frac{ - 3}{8} - \frac{9}{8}y }} \: { \rm{- - - \{equation \: (c)}} \}\)

→ Considering equation (b) next

\({ \rm{6x + 7y = 1}}\)

• substitute x in equation (b) with x in equation (c)

\({ \rm{6( \frac{ - 3}{8} - \frac{9}{8}y ) + 7y = 1 }} \\ \\ { \rm{ - \frac{9}{4} - \frac{27}{4} y + 7y = 1}} \\ \\ { \rm{ \frac{1}{4} y = \frac{13}{4} }} \\ \\ { \underline{ \rm{ \: \: y = 13 \: \: }}}\)

• then find x using equation (c)

\({ \rm{x = \frac{ - 3}{8} - \frac{9}{8} y }} \\ \\ { \rm{x = \frac{ - 3}{8} - \frac{9}{8} (13)}} \\ \\ { \underline{ \rm{ \: \: x = - 15 \: \: }}}\)

3. Elimination method:

→ Here, we have to align the equations so that if we use addition or subtraction operations we remain with one term giving us zero [ eliminated ]

→ Multiply equation (a) by 6 and multiply equation (b) by 8. In order to eliminate x

→ Then we subtract equation (a) with equation (b)

\({ \underline{ \rm{ - \binom{6(8x + 9y = - 3)}{8(6x + 7y = 1)} }}} \\ { \rm{ 0x \: - 2y = - 26 }} \\ \\ { \rm{ - 2y = - 26}} \\ \\ { \underline{ \rm{ \: \: y = 13 \: \: }}}\)

• find x using equation (c)

\({ \rm{x = \frac{ - 3}{8} - \frac{9}{8} y}} \\ \\ { \underline{ \rm{ \: \: x = - 15 \: \: }}}\)

4. Calculator synthetic method:

→ To use this method, you must have a scientific calculator.

→ If you have it, follow the steps below;

Answer: x = -15, y = 13

The vertical asymptotes of the graph of the function \(f(x) = \frac{{x^2 + x - 30}}{{5x^2 - 23x - 10}}\) are \(x = -2\) and \(x = \frac{5}{3}\).

To find the vertical asymptotes of a rational function, we need to determine the values of \(x\) for which the denominator of the function becomes zero. These values will indicate the vertical lines where the function approaches infinity or negative infinity.

1. Set the denominator \(5x^2 - 23x - 10\) equal to zero and solve for \(x\):

  \(5x^2 - 23x - 10 = 0\)

2. Factor the quadratic equation or use the quadratic formula to find the roots:

  \(5x^2 - 23x - 10 = (x - 2)(5x + 1) = 0\)

  This gives us two possible values for \(x\): \(x = 2\) and \(x = -\frac{1}{5}\).

3. Therefore, the vertical asymptotes of the function occur at \(x = 2\) and \(x = -\frac{1}{5}\).

However, we need to check if the numerator has any common factors with the denominator that could cancel out. In this case, the numerator \(x^2 + x - 30\) does not have any common factors with the denominator. Hence, the vertical asymptotes at \(x = -2\) and \(x = \frac{5}{3}\) are valid.

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The probability that the sample proportion will differ from the population proportion by greater than 4% is 0.990.

According to the Central limit theorem, if from an unknown population large samples of sizes n > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.

The mean of this sampling distribution of sample proportion is:

µ = p

The standard deviation of this sampling distribution of sample proportion is:

σ = √p(1-p)/n

The information provided is:

p = 0.14

n = 41

As the sample size is large, i.e n = 411 > 30. the central limit theorem can be used to approximate the sampling distribution of sampling proportion.

Compute the values of P(p^ - p >0.04) as follows:

P(p^ - p < 0.04) = P(p^-p/σ > 0.04/√0.14(1-0.14)/411

= P(Z>2.33)

= 0.990

Thus the probability that the sample proportion will differ from the population proportion by greater than 4% is 0.990

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Answer:

MINIMUM LENGTH= 28.35 centimeters

MAXIMUM LENGTH= 28.65 centimeter

Step-by-step explanation:      

The inequality provides that the length of the machine part must not depart from 28.5 by more than 0.15

\(L-28.5<0.15\)

So, to calculate the minimum and maximum length,

Minimum length = 28.5- 0.15= 28.35 centimeters

Maximum length = 28.5+0.15=28.65 centimeters

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Answer:

Step-by-step explanation:

for 182 miles you need 14 gallons

???????                            8 gallons

8/14=x/182

x=182*8/14

x miles=104 miles

I believe that its easier to understand the multiplication of a radical than that of a polynomial.

In mathematics, a radical is the opposite of an exponent that is represented with a symbol '√' also known as root.

A polynomial is an expression which is composed of variables, constants and exponents, that are combined using the mathematical operations such as addition, subtraction, multiplication and division.

When multiplying radicals with the same index, multiply under the radical, and then multiply in front of the radical. An example is:

= 3✓2 × 4✓2

= 12✓4

= 12 × 2

= 24

The multiplication of a radical is easier.

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Answer:

8

Step-by-step explanation:

Using the Heron's formula we can find that the total area of the triangle is 84 inches.

Then, to find the height of the triangle, you have to multiply the area by 2 since the formula for the area of a triangle is (h*b)/2

Now, when we multiply 84 and 2 we get 168, so you have to divide 168 by 21 to find 8.

Answer:

-2

Step-by-step explanation:

3n+2n+4=9n+12

5n+4=9n+12

5n-9n=-4+12

-4n=8

n=8/-4

n= -2

Answer:

-2

Step-by-step explanation:

I got this right in my assignment.

Answer: the last box for minutes is 16

And the first box for customers is 1

Step-by-step explanation:

Answer:

See below.

Step-by-step explanation:

1st Box(First row)

We can set up a proportion to solve for the number of customers that would enter the store in 4 minutes:

3 customers is to 12 minutes as x customers is to 4 minutes

This can be written as:

3/12 = x/4

To solve for x, we can cross-multiply and simplify:

3/12 = x/4

3(4) = 12x

12 = 12x

x = 1

Therefore, we can expect 1 customer to enter the store in 4 minutes.

We can use the given ratios to find the time for 10 customers.

From the table, we can see that:

3 customers take 12 minutes.

1 customer takes 4 minutes (divide both sides of the ratio by 3).

So, 10 customers will take:

10 customers × 4 minutes per customer = 40 minutes.

Therefore, for 10 customers, the time is 40 minutes.

Answer:

56 is the answer so it's A, C and E.

Step-by-step explanation:

The value of Absolute maximum are (a) 8, (b) -30.36, (c) -10 and the Absolute minimum are (a) -10, (b) -362.39, (c) -362.39.

We are given a function:f(x) = x³ - 12x² - 27x + 8We need to find the absolute maximum and absolute minimum values of the function f(x) over each of the indicated intervals. The intervals are:

a) Interval = [-2, 0]

b) Interval = [1, 10]

c) Interval = [-2, 10]

Let's begin:

(a) Interval = [-2, 0]

To find the absolute max/min, we need to find the critical points in the interval and then plug them in the function to see which one produces the highest or lowest value.

To find the critical points, we need to differentiate the function:f'(x) = 3x² - 24x - 27

Now, we need to solve the equation:f'(x) = 0Using the quadratic formula, we get: x = (-b ± √(b² - 4ac)) / 2a

Substituting the values of a, b, and c, we get:

x = (-(-24) ± √((-24)² - 4(3)(-27))) / 2(3)x = (24 ± √(888)) / 6x = (24 ± 6√37) / 6x = 4 ± √37

We need to check which critical point lies in the interval [-2, 0].

Checking for x = 4 + √37:f(-2) = -10f(0) = 8

Checking for x = 4 - √37:f(-2) = -10f(0) = 8

Therefore, the absolute max is 8 and the absolute min is -10.(b) Interval = [1, 10]

We will follow the same method as above to find the absolute max/min.

We differentiate the function:f'(x) = 3x² - 24x - 27

Now, we need to solve the equation:f'(x) = 0Using the quadratic formula, we get: x = (-b ± √(b² - 4ac)) / 2a

Substituting the values of a, b, and c, we get:

x = (-(-24) ± √((-24)² - 4(3)(-27))) / 2(3)

x = (24 ± √(888)) / 6

x = (24 ± 6√37) / 6

x = 4 ± √37

We need to check which critical point lies in the interval [1, 10].

Checking for x = 4 + √37:f(1) = -30.36f(10) = -362.39

Checking for x = 4 - √37:f(1) = -30.36f(10) = -362.39

Therefore, the absolute max is -30.36 and the absolute min is -362.39.

(c) Interval = [-2, 10]

We will follow the same method as above to find the absolute max/min. We differentiate the function:

f'(x) = 3x² - 24x - 27

Now, we need to solve the equation:

f'(x) = 0

Using the quadratic formula, we get: x = (-b ± √(b² - 4ac)) / 2a

Substituting the values of a, b, and c, we get:

x = (-(-24) ± √((-24)² - 4(3)(-27))) / 2(3)x = (24 ± √(888)) / 6x = (24 ± 6√37) / 6x = 4 ± √37

We need to check which critical point lies in the interval [-2, 10].

Checking for x = 4 + √37:f(-2) = -10f(10) = -362.39

Checking for x = 4 - √37:f(-2) = -10f(10) = -362.39

Therefore, the absolute max is -10 and the absolute min is -362.39.

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The extreme values of f(x, y) = xy occur at the points (2, 1) and (-2, -1) on the ellipse \(3x^{2} +2y^{2} =1\).

To find the extreme values of f(x, y) = xy on the ellipse \(3x^{2} +2y^{2} =1\), we can use the method of Lagrange multipliers.

Define the function g(x, y) = \(3x^{2} +2y^{2} -1\). We need to find points (x, y) where the gradient of f is proportional to the gradient of g:

∇f = λ∇g

The gradient of f is ∇f = (y, x), and the gradient of g is ∇g = (6x, 4y). Therefore, we have the following system of equations:

y = 6λx
x = 4λy

Substitute the second equation into the first:

y = 6λ(4λy)
y = \(24λ^{2y}\)

If y ≠ 0, then 1 = \(24λ^{2}\), and λ = ±1/2. Plugging this value into the second equation gives x = ±2. Thus, we have two potential extreme points: (2, 1) and (-2, -1).

Now consider the case when y = 0. The constraint equation becomes \(3x^{2} =1\), and x = ±1/√3. However, these points correspond to f(x, y) = 0, which is not an extreme value.

Therefore, the extreme values of f(x, y) = xy occur at the points (2, 1) and (-2, -1) on the ellipse \(3x^{2} +2y^{2} =1\).

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Answer: x=17

Step-by-step explanation:

Simplifying

5x = 85

Solving

5x = 85

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Divide each side by '5'.

x = 17

Simplifying

x = 17

The value of x in the equation is 17 .

Given,

5x = 85

Solving

5x = 85

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Divide each side by '5'.

x = 17

Simplifying

x = 17

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The proportion of a normal distribution located between z = .50 and z = -.50 will be 38.2%.

We have,

A normal distribution located between z = 0.50 and z = -0.50,

So,

Now,

From the Z-score table,

We get,

The Probability corresponding to the Z score of -0.50,

i.e.

P(-0.50 < X < 0) = 0.191,

And,

The Probability corresponding to the Z score of -0.50,

i.e.

P(0 < X < 0.50) = 0.191,

Now,

The proportion of a normal distribution,

i.e.

P(Z₁ < X < Z₂) = P(Z₁ < X < 0) + P(0 < X < Z₂)

Now,

Putting values,

i.e.

P(-0.50 < X < 0.50) = P(-0.50 < X < 0) + P(0 < X < 0.50)

Now,

Again putting values,

We get,

P(-0.50 < X < 0.50) = 0.191 + 0.191

On solving we get,

P(-0.50 < X < 0.50) = 0.382

So,

We can write as,

P(-0.50 < X < 0.50) = 38.2%

So,

The proportion of a normal distribution is 38.2%.

Hence we can say that the proportion of a normal distribution located between z = .50 and z = -.50 will be 38.2%.

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Answer:

a=-1/4

Step-by-step explanation:

a+3 1/4 =5 2/9

change to improper fraction

a+13/4 = 47/9

make sure that both fractions have the same denominator

a+(13/4)9=(47/9)4

a+117/36=108/36

make sure that variable is alone on one side

a=108/36-117/36

a=-9/36= -1/4

a=-1/4

Step-by-step explanation:

a+3 1/4 =5 2/9

change to improper fraction

a+13/4 = 47/9

make sure that both fractions have the same denominator

a+(13/4)9=(47/9)4

a+117/36=108/36

make sure that variable is alone on one side

a=108/36-117/36

a=-9/36= -1/4

(a) 60 experimental runs

(b) 10 experimental runs

How to find experimental runs?

(a) To find the total number of experimental runs possible when using one of the three different temperatures, one of the four different pressures, and one of the five different catalysts, you can apply the product rule. The total number of runs will be:
3 (temperatures) * 4 (pressures) * 5 (catalysts) = 60 experimental runs
(b) To find the number of experimental runs that involve the use of the lowest temperature and the two lowest pressures, apply the product rule again:
1 (lowest temperature) * 2 (two lowest pressures) * 5 (catalysts) = 10 experimental runs

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a. The total number of possible experimental runs is 60

b. The number of experimental runs that involve the use of the lowest temperature and two lowest pressures is 10 experimental runs.

a. To calculate the total number of possible experimental runs, we can use the product rule, which states that if there are n1 ways to do one thing, n2 ways to do another thing, and so on, then the total number of ways to do all of those things together is the product of n1, n2, and so on.

So in this case, there are 3 possible temperatures, 4 possible pressures, and 5 possible catalysts, which gives us:

3 x 4 x 5 = 60

Therefore, there are 60 possible experimental runs when considering all possible combinations of the three factors.

b. We need to consider that we are using the lowest temperature and two lowest pressures. This means that there is only one option for the temperature, and two options for the pressure. As for the catalyst, we have five options to choose from. Therefore, the number of experimental runs that involve the use of the lowest temperature and two lowest pressures is:

1 (temperature) x 2 (lowest pressures) x 5 (catalysts) = 10 experimental runs.

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