b) Work out the value of (6.8 x 10²) × (1.3 × 10³)
Give your answer in standard form. Pls help

Answer:

answer is D

Step-by-step explanation:

...........

Yes, this is true.

A normal distribution with a mean of 0 and a standard deviation of 1 is often denoted as N(0, 1) or n(0, 1). This distribution is also known as the standard normal distribution. It is a symmetric bell-shaped distribution where the majority of the data falls within approximately three standard deviations from the mean.

The standard normal distribution, denoted as N(0, 1) or n(0, 1), is a specific type of normal distribution that has a mean of 0 and a standard deviation of 1. It is often used as a benchmark for comparing and standardizing data in statistical analysis.

The shape of the standard normal distribution is symmetric and bell-shaped. It follows the familiar "bell curve" pattern, where the data is concentrated around the mean and gradually tails off towards the extremes. The total area under the curve is equal to 1, representing the entire probability space.

The standard deviation of 1 indicates the spread or variability of the data. In a standard normal distribution, about 68% of the data falls within one standard deviation of the mean, approximately 95% falls within two standard deviations, and roughly 99.7% falls within three standard deviations.

The standard normal distribution is widely used in statistical calculations and hypothesis testing. It serves as a reference distribution for many statistical methods, such as z-tests and z-scores. By converting data from other normal distributions into standard units using z-scores, researchers can compare and analyze data from different distributions on a common scale.

The standard normal distribution also has specific properties that make it mathematically tractable. The cumulative distribution function (CDF) of the standard normal distribution, often denoted as Φ(z), gives the probability that a standard normal random variable is less than or equal to a given value z. This CDF is tabulated in standard statistical tables or can be calculated using mathematical functions.

Overall, the standard normal distribution is a fundamental concept in statistics, providing a reference distribution for comparing and analyzing data and serving as a basis for many statistical techniques and calculations.

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Therefore, visually interpreting histograms can be a powerful tool for data analysis, but it is important to be aware of their strengths and limitations.

Histograms are an effective way to display data graphically. They are used to show how often certain values or ranges of values appear in a data set. Visual interpretation of histograms has many strengths and limitations. Some of the strengths of visually interpreting histograms are that they are easy to read and understand, they provide a clear picture of how the data is distributed, and they can help identify outliers or gaps in the data. However, some of the limitations of visually interpreting histograms are that they can be influenced by the number of bins chosen, the way the data is grouped, and the choice of the scale used. Therefore, it is important to carefully consider these factors when interpreting a histogram. In conclusion, visually interpreting histograms can be a powerful tool for data analysis, but it is important to be aware of their strengths and limitations.

Therefore, visually interpreting histograms can be a powerful tool for data analysis, but it is important to be aware of their strengths and limitations.

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Boys are taller than girls on average, with a larger center of data and larger range in height;

the dot plots are not shown.

Answer:

x = 15

Step-by-step explanation:

Using the Altitude- on- Hypotenuse theorem

(leg of large Δ )² = (part of hypotenuse below it ) × ( whole hypotenuse )

x² = 9 × (9 + 16) = 9 × 25 = 225 ( take square root of both sides )

x = \(\sqrt{225}\) = 15

Answer:

I did this quickly, so please check the logic.

I find x = 15

Step-by-step explanation:

See attached image.  Note that I've defined 3 triangles and their Pythagorean equations.  I also define a third line, RQ, as z.  Rearrange the equations and substitute in a way that allows elimination of all variables except x.

To calculate the investment amount in an account that has a 3.2% interest rate compounded quarterly and that will yield a payment of\($1000\) each quarter for the next five years, we can use the formula for the present value of an annuity.

The formula is as follows: \(PV = PMT * [1 - (1 + r/n)^(-nt)] / (r/n)\)where PV is the present value, PMT is the payment amount, r is the interest rate, n is the number of times the interest is compounded in a year, and t is the number of years. Substituting the values in the formula:\(PV = 1000 * [1 - (1 + 0.032/4)^(-4*5)] / (0.032/4) = $ (39,905.77)\)

Therefore, to receive payments of \($1000\)each quarter for the next five years from an account that earns a 3.2% interest rate compounded quarterly, you should invest \($39,905.77\) in the account.The above answer has less than 100 words.

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Answer:

x = \(\frac{15}{2}\) , x = 1

Step-by-step explanation:

(a)

\(\frac{4x-1}{2}\) = x + 7 ( multiply both sides by 2 to clear the fraction )

4x - 1 = 2x + 14 ( subtract 2x from both sides )

2x - 1 = 14 ( add 1 to both sides )

2x = 15 ( divide both sides by 2 )

x = \(\frac{15}{2}\)

(b)

3x + 2 = \(\frac{2x+13}{3}\) ( multiply both sides by 3 to clear the fraction )

9x + 6 = 2x + 13 ( subtract 2x from both sides )

7x + 6 = 13 ( subtract 6 from both sides )

7x = 7 ( divide both sides by 7 )

x = 1

The balanced equation can be found by ensuring that the number of atoms of each element is the same on both sides of the equation.

To find a balanced chemical equation, you need to ensure that the number of atoms of each element is the same on both sides of the equation.

Here are the steps to follow:

1) Write the unbalanced equation, with the reactants on the left side of the arrow and the products on the right side.

2) Count the number of atoms of each element on both sides of the equation.

3) Balance the equation by adjusting the coefficients (the numbers in front of the chemical formulas) until the number of atoms of each element is the same on both sides of the equation.

4) Check your balanced equation by counting the number of atoms of each element again to make sure they are the same on both sides.

It's important to note that the subscripts in chemical formulas should never be changed to balance an equation. Only the coefficients should be adjusted.

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Answer:

1) Scalene

2) Equilateral

3) Isosceles

4) Right

5)Obtuse

Step-by-step explanation:

The requried correct match for the given triangle and its sides and angle has been shown.

Following the given characteristic the match of the the properties of triangle is given as:
Type of Triangle:            Characteristics

Scalene:                 all side lengths and angles are different sizes

Equilateral:            all side lengths are equal and all angles are 60°

Isosceles:              two sides and their base angles are equal

Right:                     one angle is 90°

Obtuse:                 one angle is greater than 90°

Thus, the required match shown above is the correct match.

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Answer:

Step-by-step explanation:

To solve an algebraic expression in simplest form, you can follow these steps:

1. Use the order of operations (PEMDAS) to simplify any arithmetic in the expression (parentheses, exponents, multiplication and division, addition and subtraction).

2. Combine like terms by adding or subtracting any coefficients in front of similar variables.

3. Divide or multiply both sides of the equation by the same non-zero number to solve for the variable.

4. If possible, factor the expression to make it simpler.

5. If the expression is a fraction, check for a common denominator and then simplify by canceling any common factors in the numerator and denominator.

6. If the expression is a radical, check for a perfect square and simplify by taking the square root of the number inside the radical.

7. Use the properties of exponents and logarithms to simplify the expression.

8. Evaluate the expression by plugging in the values of any known variables.

It's important to keep in mind that there may be multiple ways to simplify an algebraic expression and the solution that is in simplest form may not always be obvious.

There are 4 ice cream flavors :

chocolate (c), vanilla (v), moos tracks (m), and dark chocolate (d).

There are 3 types of sauces :

hot fudge (h), butterscotch (b), and strawberry (s).

There are 2 types of toppings :

whipped cream (w) and fruit (f)

The sample space are the combinations of ice cream flavors, sauces and toppings with one of each kind.

Listing down the sample spaces as {flavors, sauces, toppings}, will give us :

{c,h,w}, {c,h,f}, {c,b,w}, {c,b,f}, {c,s,w}, {c,s,f}

{v,h,w}, {v,h,f}, {v,b,w}, {v,b,f}, {v,s,w}, {v,s,f}

{m,h,w}, {m,h,f}, {m,b,w}, {m,b,f}, {m,s,w}, {m,s,f}

{d,h,w}, {d,h,f}, {d,b,w}, {d,b,f}, {d,s,w}, {d,s,f}

All in all, there are 24 sample spaces, which is also the product of 4 flavors, 3 sauces and 2 toppins (4 x 3 x 2 = 24)

Answer:

c. 15

Step-by-step explanation:

20 - 15 + 5

35 - 15(2)

35 - 30 = 5

We need to isolate x.

2tx-n³= 4f

2tx = 4f + n^3

x = (4f + n^3)/(2t)

Done!

The value of x is x= 2f/t + n³/2t.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

2tx-n³=4f

Now, solving for x

2tx=4f + n³

x= 1/2t (4f + n³)

x= 4f/2t + n³/2t

x= 2f/t + n³/2t

Hence, the value of x is x= 2f/t + n³/2t.

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\(0.000000778\implies \stackrel{ \textit{rounded up} }{0.000000800} ~\hfill 0.00000000155\implies \stackrel{ \textit{rounded up} }{0.00000000200} \\\\[-0.35em] ~\dotfill\\\\ 0.\underset{ 6~zeros }{\underline{000000}}800\implies 8.00\times 10^{-6}\implies \boxed{8\times 10^{-6}} \\\\\\ \underset{ 8~zeros }{0.\underline{00000000}200}\implies 2.00\times 10^{-8}\implies \boxed{2\times 10^{-8}} \\\\[-0.35em] ~\dotfill\)

\(\cfrac{\stackrel{ \textit{dust particle} }{8\times 10^{-6}}}{\underset{ \textit{grain of pollen} }{2\times 10^{-8}}}\implies \cfrac{8}{2}\times\cfrac{10^{-6}}{10^{-8}}\implies 4\times10^{-6}10^{8}\implies 4\times 10^2\implies \boxed{400}\)

Answer:

Step-by-step explanation:

Step one:

For Ryan

Principal= $775

rate= 4.24%

time = 4 years

the simple interest formula

SI= PRT/100

SI=(775*4.24*4)/100

SI=13144/100

SI=$131.44

Step two:

For Brian

Principal= $775

rate= 4.24%

time = 1years

the simple interest formula

SI= PRT/100

SI=(775*4.24*1)/100

SI=3286/100

SI=$32.86

Answer:

1) 160×20/100

=32

2) 27/50×100

=54percent

3) no. of girls 25-7=18

=18/25×100

=72percent

5) 45percent

6) 14/25×100

=56percent

7) 225percent

9) 9:5

Answer:

1) 32

2) 54

3) 72

5) 45%

6)56

7) 225%

9) 9:5

Step-by-step explanation:

Kelly ate approximately 665 cm³ volume of salsa from a jar being 11 cm tall and  radius of 6 cm.

To understand and  solve this problem, we need to calculate the volume of the jar when it was full and then subtract the volume of the jar when it was 6 cm high.

Using the cylindirical volume formula

Volume = πr²h,

where r is the radius of the jar (6 cm) and h is the height of the jar (11 cm).

Volume of full jar = π × 6² × 11 = 1,244 cm³

Volume of jar when 6 cm high = π × 6² × 6 = 678.58 cm³

Now the volume of salsa kelly ate is = 1,244 -  678.58 = 665.42 cm³

Therefore, Kelly ate approximately 665.42  cm³ of salsa, and the answer can be rounded to the nearest whole number, 665 cm³.

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Answer:

-8

Step-by-step explanation:

If you were to do integer operations, then this question algebraically would mean -4-4=-8 because going to the left on a number line is meaning subtraction/negative and going to the right is addition/positve!

Therefore, the answer is -8 :)

We have proved both implications, we can conclude that 4 divides (m^2 * n^2) if and only if m and n are both even.

To prove that 4 divides (m^2 * n^2) if and only if m and n are even, we need to prove two implications:

If 4 divides (m^2 * n^2), then m and n are even.

If m and n are even, then 4 divides (m^2 * n^2).

Let's start with the first implication:

If 4 divides (m^2 * n^2), then m and n are even.

We can prove this by contrapositive. Assume that m and n are not both even, which means that at least one of them is odd. Without loss of generality, let's assume that m is odd. Then m can be written as m = 2k + 1, where k is an integer. Substituting this into the expression for m^2 * n^2, we get:

m^2 * n^2 = (2k + 1)^2 * n^2

= 4k^2 * n^2 + 4kn^2 + n^2

Note that the first two terms in this expression are both divisible by 4, but the last term (n^2) is not necessarily divisible by 4, since n could be odd. Therefore, m^2 * n^2 is not divisible by 4 if m and n are not both even. This proves the contrapositive, and hence the first implication.

Now, let's move on to the second implication:

If m and n are even, then 4 divides (m^2 * n^2).

We can prove this directly. Since m and n are even, we can write them as m = 2k and n = 2j, where k and j are integers. Substituting these into the expression for m^2 * n^2, we get:

m^2 * n^2 = (2k)^2 * (2j)^2

= 4k^2 * 4j^2

= 16(k^2 * j^2)

Since k and j are integers, k^2 * j^2 is also an integer, and hence 16(k^2 * j^2) is divisible by 4. Therefore, m^2 * n^2 is divisible by 4 if m and n are both even. This proves the second implication.

Since we have proved both implications, we can conclude that 4 divides (m^2 * n^2) if and only if m and n are both even.

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Answer:

\(\frac{64}{27} cm^3\)

Step-by-step explanation:

V = L*W*H

V= (4/3)*(4/3)*(4/3)

Volume =  \(\frac{64}{27} cm^3\)

Answer:

Since:

a^2-2ab+b^2 = (a-b)^2

and

a^2+2ab+b^2 = (a+b)^2

We need to find value of * which is 2ab

In your equation = \(\sqrt{6.25} = 2.5 and \sqrt{1/4} = 0.5\\Now 2ab = 2 * 2.5 * 0.5\\ = 2.5\\\\\\* = 2.5ab\)

Answer:

Plato got it correct

Step-by-step explanation:

Its X

The system of equations has infinite solutions, both equations represent the same line.

Here we have the following system of equations:

-3x+6y=12

2y=x+4

And we want to solve this by substitution, first, we can rewrite the first equation as:

-3x + 3*(2y) = 12

Now we can substitute the second equation 2y = x + 4 in the parenthesis, we will get:

-3x + 3*(x + 4) = 12

Now we can solve this for x.

-3x + 3x + 12 = 12

12 = 12

So this is true for any value of x, which means that both equations represent the same line (thus the system has infinite solutions).

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The volume of the sphere is option (d) 904.32 cm³

Volume is a measure of the amount of three-dimensional space occupied by a substance, object, or region of space

The formula for the volume of a sphere is V = (4/3)πr³, where r is the radius of the sphere.

Substituting r = 6 cm and π ≈ 3.14 into the formula, we get:

V = (4/3) × 3.14 × 6³

Find the cube of the number

V = (4/3) × 3.14 × 216

Multiply the numbers

V ≈ 904.32

Rounding the answer to the nearest hundredth, we get approximately 904.32 cm³.

Therefore, the correct option is (d) 904.32 cm³.

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The given question is incomplete, the complete question is:

What is the approximate volume of the sphere when the radius is 6 cm?

Use 3.14 to approximate pi and round the answer to the nearest hundredth if necessary.

a) 48 cm³

b) 150.72 cm³

c) 288.00 cm³

d) 904.32 cm³

Answer:

C

Step-by-step explanation:

Im going to be quick on this since your in a hurry, is AB is 3 and QR = 1  and their similar then BC would be 3 times the amount of RS which is 1.5 so the Answer is 4.5

Answer:

C

Step-by-step explanation:

　　＿＿＿　 AA

*～/■　■　⊂ P

　 |　■　■.（＿）

　 U U￣￣U U

Using trigonometric functions, we can  find a side length of a right triangle with an angle and a side.

Trigonometric ratios are the ratios of a right triangle's sides. The sine (sin), cosine (cos), and tangent (tan) are three often used trigonometric ratios. There are other trigonometric ratios which are reciprocals of these ratios.

Trigonometric ratios can be computed either using the provided acute angle or by calculating the ratios of the right-angled triangle's sides.

You can determine the hypotenuse by dividing the length of the side by sin(θ) if you have an angle and the side opposite to it. Alternatively, to find the length of the side next to the angle, divide the length by tan(θ).

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The main answer for the first argument is that we cannot prove that the band could play rock music based on the given premises and rules of inference.

1. Let's assign the following propositions:

  - P: The band could play rock music.

  - Q: The refreshments were delivered on time.

  - R: The New Year's party was canceled.

  - S: Alicia was angry.

  - T: Refunds were made.

2. The given premises can be expressed as:

  (¬P ∨ ¬Q) → (R ∧ S)

  R → T

3. To prove that the band could play rock music (P), we need to derive it using valid rules of inference.

4. Using the premises, we can apply the rule of modus tollens to the second premise:

  R → T        (Premise)

  Therefore, ¬R.

5. Next, we can use disjunctive syllogism on the first premise:

  (¬P ∨ ¬Q) → (R ∧ S)     (Premise)

  ¬R                    (From step 4)

  Therefore, ¬(¬P ∨ ¬Q).

6. Applying De Morgan's law to step 5, we get:

  ¬(¬P ∨ ¬Q)  ≡  (P ∧ Q)

7. Therefore, we can conclude that the band could play rock music (P) based on the premises and rules of inference.

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Answer: Let x be the cost of one slice of pizza and y be the cost of one soda.

From the problem, we know that:

6x + 4y = 37 ...(1)

4x + 6y = 33 ...(2)

To solve for x and y, we can use the method of elimination. Multiplying equation (1) by 3 and equation (2) by 2, we get:

18x + 12y = 111 ...(3)

8x + 12y = 66 ...(4)

Subtracting equation (4) from equation (3), we get:

10x = 45

Dividing both sides by 10, we get:

x = 4.50

Substituting this value of x into equation (1), we get:

6(4.50) + 4y = 37

Simplifying, we get:

27 + 4y = 37

Subtracting 27 from both sides, we get:

4y = 10

Dividing both sides by 4, we get:

y = 2.50

Therefore, one slice of pizza costs $4.50 and one soda costs $2.50.

Answer:

Yes he will have enough.

Step-by-step explanation:

9 quarts = 2.25 gallons

22 pints = 2.27 gallons

2.25 + 2.27 is 5 gallons : He will have enough to paint the fences w/ 3 leftover gallons