How is multiplying and dividing numbers in scientific notation different from adding and subtracting numbers in scientific notation?

You can _____ numbers written in scientific notation only if their powers of 10 are the same. You can _____ numbers written in scientific notation that have different powers. The laws of exponents are used to combine powers.​

Answer:

Option (2)

Step-by-step explanation:

Given inequality is,

3x + 12 ≤ 24

3x + 12 - 12 ≤ 24 - 12

3x ≤ 12

\(\frac{3x}{3}\leq \frac{12}{3}\)

x ≤ 4

Now we can plot this inequality on a number line.

An arrow starting with a solid point from x = 4 directing towards negative infinity will be the graph on a number line.

Therefore, Option (2) will be the correct option.

The answer choice which could not be modelled by an exponential function among the given answer choices is; A taxi charges a flat fee of $2.00 for pick-up, then an additional fee of 4.75 per mile.

It follows from the task content that the expression which could not be modelled by an exponential expression be identified among the answer choices.

An exponential function is one in which case the change factor is expressed as an exponent of the independent variable.

However, the function described as; A taxi charges a flat fee of $2.00 for pick-up, then an additional fee of 4.75 per mile is termed a linear model in which case;

The rate of change is constant and is equal to; $4.75 per mile.

Hence the required answer choice which cannot be modelled by an exponential function is; A taxi charges a flat fee of $2.00 for pick-up, then an additional fee of 4.75 per mile.

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The balance after 5 years when the interest is compounded quarterly is  $5,593.60

Compound Interest:

Compound interest is the principal plus interest on a loan or deposit, or in other words, principal plus interest. It is the result of reinvesting interest, or adding it to the principal borrowed instead of paying it, or demanding payment from the borrower so that the next installment of interest is principal plus previously accrued interest. Compound interest is the norm in finance and economics.

Lets use the compound interest formula provided to solve this:

P = initial balance

r = interest rate (decimal)

n = number of times compounded annually

t = time

First, change 2.25% into a decimal:

2.25% > 2.25/100 > 0.0225

Since the interest is compounded quarterly, we will use 4 for n. Lets plug in the values now:

      \(A = (1+\frac{0.0225}{4} )4(5)\\\)

Or, A = 5593.60

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Answer:

A

Step-by-step explanation:

hope this helps

Statistical process control technique that permits only 3.4 defects per million opportunities is Six Sigma.

Six Sigma is a statistical technique that emphasizes the necessity of a standardized approach to enhancing and optimizing the efficiency of the production and management processes by reducing the variation and waste within them. It concentrates on controlling a process to ensure that the results of a process are consistent and reliable by using statistical methods. The objective of the Six Sigma process is to produce 3.4 errors or defects per million opportunities. If the process is better than Six Sigma, it is considered more consistent and predictable.
Six Sigma's statistical approach to process control encompasses a range of tools and methods. Six Sigma's primary objective is to increase revenue and profits by developing and delivering high-quality products and services while eliminating defects and reducing waste.
Six Sigma aims to improve quality by detecting and reducing the reasons for variations in production processes. It accomplishes this by developing quality management practices that enable it to assess quality, establish goals, and implement best practices to achieve those goals.
In conclusion, Six Sigma is a process control approach that emphasizes statistical methods for process control and improvement. Six Sigma is used to reduce variability and eliminate waste, and its goal is to achieve 3.4 defects per million opportunities.

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Answer:

A

Step-by-step explanation:

Answer:

l

Step-by-step explanation:

The series ∑3ke − k/28 is a divergent series.

To determine whether the series ∑3ke − k/28 converges or diverges, we can use the ratio test.

The ratio test states that if lim┬(n→∞)⁡|an+1/an|<1, then the series converges absolutely; if lim┬(n→∞)⁡|an+1/an|>1, then the series diverges; and if lim┬(n→∞)⁡|an+1/an|=1, then the test is inconclusive.

Let's apply the ratio test to our series:

|a(n + 1)/a(n)| = |3(n + 1) \(e^(^-^(^n^+^1^)/28) / (3n e^(^-^n^/^2^8^))|\)

= |(n+1)/n| * |\(e^(^-^1^/^2^8^)\)| * |3/3|

= (1 + 1/n) * \(e^(^-^1^/^2^8^)\)

As n approaches infinity, the expression (1 + 1/n) approaches 1, and \(e^(^-^1^/^2^8^)\) is a constant. Therefore, the limit of the ratio is 1.

Since the limit of the ratio test is equal to 1, the test is inconclusive. We need to use another method to determine convergence or divergence.

One possible method is to use the fact that \(e^x > x^2^/^2\) for all x > 0. This implies that \(e^(^-^k^/^2^8^)\) < \((28/k)^2^/^2\) for all k > 0.

Therefore,

|a(k)| = 3k \(e^(^-^k^/^2^8^)\) < 3k\((28/k)^2^/^2\)

= 42k/k²

= 42/k

Since ∑1/k is a divergent series, we can use the comparison test to conclude that ∑|a(k)| diverges.

Therefore, the series ∑3ke − k/28 also diverges.

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Answer:  \(a)\ \text{Vertex}:y=-\dfrac{3}{2}(x+1)^2+6\)

                \(b)\ \text{Standard}:y=-\dfrac{3}{2}x^2-3x=\dfrac{9}{2}\)

              c) Transformations: reflection over the x-axis,

                                               vertical stretch by a factor of 3/2,

                                               horizontal shift 1 unit to the left,

                                               vertical shift 6 units up

Step-by-step explanation:

Intercept form: y = a(x - p)(x - q)

Vertex form: y = a(x - h)² + k

Standard form: y = ax² + bx + c

We can see that the new vertex is (-1, 6). Use the Intercept form to find the vertical stretch: y = a(x - p)(x - q) where p, q are the intercepts.

p = -3, q = 1, (x, y) = (-1, 6)

a(-1 + 3)(-1 -1) = 6

       a (2)(-2) = 6

                a  = -6/4

                 a = -3/2

a) Input a = -3/2 and vertex (h, k) = (-1, 6) into the Vertex form to get:

\(y=-\dfrac{3}{2}(x+1)^2+6\)

b) Input a = -3/2 into the Intercept form and expand to get the Standard form:

\(y=-\dfrac{3}{2}(x+3)(x-1)\\\\\\y=-\dfrac{3}{2}(x^2+2x-3)\\\\\\y=-\dfrac{3}{2}x^2-3x+\dfrac{9}{2}\)

c) Use the Vertex form to identify the transformations:

\(y=-\dfrac{3}{2}(x+1)^2+6\)

Answer:

she is paying back 9112.5 R.O

Interest paid back is 2,403.95

Step-by-step explanation:

To find the amount, we use the compound interest formula.

This is given as;

A = I( 1 + r/n)^nt

where A is the amount we are trying to calculate

I is money borrowed = 6709

r is the interest rate = 12 1/3% = 37/3 = 12.33% which is same as 12.33/100 = 0.1233

n is the number of times interest is compounded. We have 15 2 months in 2 and a half years

t is the number of years = 2.5

Plugging these values, we have;

A = 6709(1 + 0.1233/15)^(15)(2.5)

A = 6709(1.0082)^(37.5)

A = 9112.95 R.O

Interest is amount - principal( money borrowed)

9112.95 - 6709 = 2403.95

The final horse power when the driving a car in Denver that's rated at 300 horsepower is 252.48  , the correct option is (c) .

In the question ,

it is given that ,

the power of the car is rated as = 300 horse power

we know that Rule of thumb states that for every 1000 feet the horsepower reduces by 3 percent .

that means ,

for percent of power loss at 1000 feet = 3%

So , the percent loss of power at 5280 feet is  = (3/1000)×5280

= 0.003 × 5280

= 15.84 % .

So , 15.84% of 300 is = 47.52

So , the power loss is 47.52 .

the final horse power is = 300 - 47.52 = 252.48

Therefore , The final horsepower is 252.48  .

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Answer:

i tried and i got pie something

Step-by-step explanation:

The value of y will be more as the number is repetitive, and both x and y initial three digits after the decimal are the same.

A rational number is one that has the form p/q, where p and q are integers and q is greater than zero. Some rational number examples are 1/3, 2/4, 1/5, 9/3, and so on.

The complete question is, Let x = 0.147 and let y = \(0.\overline{147}\).  Is x a rational number? Is ya rational number? Which is larger, x or y?

Given the value of x is 0.147. As it can be written in the form of a fraction,

\(0.147 = \dfrac{147}{1000}\), we can conclude that x is a rational number.

The value of y = \(0.\overline{147}\) can also be written in the form of a fraction,

\(0.\overline{147} = \dfrac{147}{999}\), therefore, we can conclude that y is also a rational number.

The value of y will be more as the number is repetitive, and both x and y initial three digits after the decimal are the same.

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(a) the probability expected number of flips needed to get three heads in a row is 7.5.

(b) The expected number of flips needed to get k heads in a row is 2k - 1.

A fair coin is one where the probability of obtaining heads is equal to the probability of obtaining tails, that is, P(H) = P(T) = 1/2. When a fair coin is flipped repeatedly, the expected number of flips needed to get three heads in a row is 7.5. This is because the probability of getting three heads in a row is (1/2)^3 = 1/8. This means that on average, 8 flips need to be made for three heads to appear, so the expected number of flips is 7.5.Similarly, the expected number of flips needed to get k heads in a row is 2k - 1. This is because the probability of getting k heads in a row is (1/2)^k. This means that on average, 2k flips must be made for k heads to appear, so the expected number of flips is 2k - 1. For example, the expected number of flips needed to get five heads in a row is 9, since the probability of getting five heads in a row is (1/2)^5 = 1/32, and 32 flips need to be made on average before five heads appear, so the expected number of flips is 9

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Answer:

37.3275

Step-by-step explanation:

I just put it on the calculator :)))))

The probability that the chosen student, a grade 8 student, likes skiing over ice skating is 53.89%.

Given that,

A survey of middle school students asked what is your favorite winter sport so they have given the result in the table we can see.

Below is a summary of the findings. A participant from this study is chosen at random from among these 545 students, who serve as the sample space.

We have to find what is the probability that the chosen student, a grade 8 student, likes skiing over ice skating.

The total 8th grade are 180

The skiing are 171

The ice skating are 163

Probability = 180/(171+163) = 0.5389 = 53.89%

Therefore, the probability that the chosen student, a grade 8 student, likes skiing over ice skating is 53.89%.

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Answer: z 1/2

Step-by-step

:) 100%

Answer to Problem 13 is  34.5  

Answer to Problem 15 is  22.9  

==================================================

Work Shown for Problem 13

sin(x)/17 = sin(91)/30

sin(x) = 17*sin(91)/30

sin(x) = 0.56658036

x = arcsin(0.56658036) or x = 180-arcsin(0.56658036)

x = 34.51210645 or x = 180-34.51210645

x = 34.51210645 or x = 145.48789355

x = 34.5 or x = 145.5

If x = 34.5, then the missing unmarked angle is 180-x-91 = 180-34.5-91 = 54.5 which is a valid angle (since it's between 0 and 180).

If x = 145.5, then the missing unmarked angle is 180-x-91 = 180-145.5-91 = -56.5; but this is NOT valid because the angle needs to be between 0 and 180 (i.e. negative angles aren't allowed)

In short, x = 34.5 is valid while x = 145.5 is not valid.

Therefore, the only possible answer is   34.5  

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

Work Shown for Problem 15

sin(x)/20 = sin(119)/45

sin(x) = 20*sin(119)/45

sin(x) = 0.38871987

x = arcsin(0.38871987) or x = 180-arcsin(0.38871987)

x = 22.87486940 or x = 180-22.87486940

x = 22.87486940 or x = 157.1251306

x = 22.9 or x = 157.1

If x = 22.9, then the missing unmarked angle is 180-x-119=180-22.9-119 = 38.1 which is valid since it's between 0 and 180.

If x = 157.1, then 180-x-119=180-157.1-119 = -96.1 which is NOT a valid angle since it's not between 0 and 180. This allows us to rule out the case that x = 157.1

The only possible answer is therefore   22.9  

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

Side notes:

a) The probability of failing to meet the specification limit of 45-pounds tensile strength 15.87%.

b) The number of parts that would not meet the specification is 7,935.

a) Given that the tensile strength of a metal part is normally distributed with mean 40 pounds and standard deviation 5 pounds.

We have to find the probability of failing to meet the specification limit of 45-pounds tensile strength.

Using the standard normal distribution, we can find the probability of failing to meet the specification limit of 45 pounds as follows:

z = {45 - 40}/{5}

= 1

The probability of failing to meet the specification limit of 45 pounds is the probability that the standardized variable Z is greater than 1, which is given by:

P(Z > 1) = 0.1587

Therefore, the probability of failing to meet the specification limit of 45-pounds tensile strength is 0.1587 or 15.87%.

b) If the probability of failing to meet the specification is 0.1587, the probability of meeting the specification limit is

1 - 0.1587 = 0.8413

.If 50,000 parts are produced, then the expected number of parts that meet the specification limit is:

0.8413* 50,000 =  42,065.

Therefore, the number of parts that would not meet the specification is: 50,000 - 42,065 = 7,935.

Hence, about 7,935 parts would not meet the specification.

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The Laplace transform of the function \(f(t) = 1 is L{f(t)} = 1/s.\)

To find the Laplace transform of the function f(t) = 1, we will use the definition of the Laplace transform:

L{f(t)} = ∫₀^∞ e^(-st)f(t) dt

where s is a complex number.

For the given function, f(t) = 1 for 0 ≤ t < ∞. This means that the function is constant and equal to 1 for all values of t greater than or equal to 0. Therefore, we can write:

L{f(t)} = ∫₀^∞ e^(-st) dt

To evaluate this integral, we can use the formula:

∫₀^∞ e^(-at) dt = 1/a for a > 0

Applying this formula, we get:

L{f(t)} = ∫₀^∞ e^(-st) dt = [1/(-s)] [e^(-st)]0^∞

= [1/(-s)] [(lim{t→∞} e^(-st)) - e^0]

= [1/(-s)] [(0 - 1)]

= 1/s

Therefore, the Laplace transform of the function f(t) = 1 is L{f(t)} = 1/s.

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Answer:

overspeeding,

see if we calculate the speed or average speed,

it would be 159/2 which would be 79.5mph,

so as posted speed was 65mph, but the average speed was 79.5mph(Meaning most of the time she would have been above 65 mph), So,

She would have been charged with overspeeding

HOPE IT HELPS

BYE!

The function f(x) = csc^2(x) can be composed with g(x) = x^7 to create f(g(x)) = csc^2(x^7). This composite function involves taking the csc^2 of the seventh power of x.

Let's break down the composition step by step. Starting with the function g(x) = x^7, we substitute this expression into f(x) = csc^2(x). So, we have f(g(x)) = csc^2(g(x)).

Next, we substitute g(x) = x^7 into the expression above to get f(g(x)) = csc^2(x^7). This means that we are taking the csc^2 of the seventh power of x.

The csc function is the reciprocal of the sine function, so csc(x) = 1/sin(x). Therefore, csc^2(x) = 1/sin^2(x). In our case, we have csc^2(x^7) = 1/sin^2(x^7).

To summarize, the composite function f(g(x)) = csc^2(x^7) involves taking the csc^2 of the seventh power of x. This means we are applying the reciprocal of the sine squared to the value of x raised to the power of seven.

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Answer:

256pie unit³

Step-by-step explanation:

The volume of a cylinder

=pie x r² x h

= pie x 8² x 4

256pie unit³

Answer:

w=-4.5

Step-by-step explanation:

12÷3/8=4.5

-w= 4.5

w= -4.5

To solve the equation -3/8 w = 12 for w, you need to isolate w. You do this by dividing both sides by -3/8 which is equivalent to multiplying by -8/3 (the reciprocal). This gives w = -32.

To solve the given equation -3/8 w = 12 for w, we need to isolate w on one side of the equation. To do this, you can divide both sides of the equation by -3/8. In mathematics, dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of -3/8 is -8/3. So, when you multiply both sides of the equation by -8/3 you get:

w = 12 * (-8/3)

Simplify this further to get: w = -32

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The range of the function g(x) = |x - 12| - 2 is {y | y > -2}, indicating that the function can take any value greater than -2.

To find the range of the function g(x) = |x - 12| - 2, we need to determine the set of all possible values that the function can take.

The absolute value function |x - 12| represents the distance between x and 12 on the number line. Since the absolute value always results in a non-negative value, the expression |x - 12| will always be greater than or equal to 0.

By subtracting 2 from |x - 12|, we shift the entire range downward by 2 units. This means that the minimum value of g(x) will be -2.

Therefore, the range of g(x) can be written as {y | y > -2}, which means that the function can take any value greater than -2. In other words, the range includes all real numbers greater than -2.

Visually, if we were to plot the graph of g(x), it would be a V-shaped graph with the vertex at (12, -2) and the arms extending upward infinitely. The function will never be less than -2 since we are subtracting 2 from the absolute value.

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Answer:

radius = √35 mm or 5.916 mm

Explanation:

Here:

Solve for radius:

\(\rightarrow \sf \pi r^2 = 110\)

\(\rightarrow \sf \dfrac{22}{7} r^2 = 110\)

\(\rightarrow \sf r^2 = \dfrac{110(7)}{22} =35\)

\(\rightarrow \sf r = \sqrt{35}\)

Let's see

The 16% of these students are taller than 66.7 inches and 285 students are between 61.6 and 68.4 inches tall.

It's the probability curve of a continuous distribution that's most likely symmetric around the mean. On the Z curve, at Z=0, the chance is 50-50. A bell-shaped curve is another name for it.

We have:

Mean of 65 inches and a standard deviation of 1.7.

From the graph:

P(X> 66.7) = (13.5 + 2.35 + 0.15)%

P(X> 66.7) = 16%

P(61.6 < X < 68.4) = (13.5 +34 + 34 + 13.5)%  = 95%

= (300×95)/100

= 285 students

Thus, the 16% of these students are taller than 66.7 inches and 285 students are between 61.6 and 68.4 inches tall.

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Answer:

1 - sec (x)

Step-by-step explanation:

Write the problem as a mathematical expression

tan (x) (cot(x)−csc(x)

Apply the distributive property

tan (x) cot(x) +tan (x) (−csc(x)

Rewrite in terms of sines and cosines, then cancel the common factors

1+tan (x) (−csc(x)

Then u get 1 - sec (x)

Answer:

D Sorry if I am wrong mark me brainleist is right

Step-by-step explanation:

When two adjacent angles are formed at a point on a line so that sum of their measures is 180°, angles are called as supplementary to each other.

In the figure attached, ∠7 and ∠8 are supplementary because they are a pair of adjacent angles that form a straight line.

Answer:

a is the answer

Step-by-step explanation:

I know so mark me brainleist