How do you do exponents​

The dimension of the wood block in centimeter is  40cm by 20cm by 70cm , the volume is  56000 cubic centimeters .

In the question ,

it is given that ,

the dimension of the block of wood is 0.4m by 0.2m by 0.7m ,

that means

the length of the wood block = 0.4 m

we know that 1 m = 100 cm , So 0.4 m = 40 cm

0.2 m = 20 cm

and

0.7 m = 70 cm

So , the length of the wood block = 40 cm

the width of the wood block = 20 cm

the height of the wood block = 70 cm

The Volume of the wooden block = length × width × height

Substituting the values , we get

Volume = 40 × 20 × 70

= 56000 cm³

Therefore , The dimension of the wood block in centimeter is  40cm by 20cm by 70cm , the volume is  56000 cubic centimeters .

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Answer:

it is because 8 is twice 4 and any number minus twice itself is the numbers opposite and the opposite of 4 which is -4 when multiplied by itself is -4 times -4 which equals 16 or the same as 4 squared

The correct statement is: A. P(E) = 0.3. The probability of event E, denoted as P(E), is equal to 0.3.

To determine the correct answer, let's analyze the given information.

We know that events D and E are independent, which means that the occurrence of one event does not affect the probability of the other event happening.

Given:

P(D) = 0.6

P(D and E) = 0.18

Since events D and E are independent, the probability of both events occurring (P(D and E)) can be calculated as the product of their individual probabilities:

P(D and E) = P(D) * P(E)

Substituting the given values:

0.18 = 0.6 * P(E)

To find the value of P(E), we can rearrange the equation:

P(E) = 0.18 / 0.6

P(E) = 0.3

Therefore, the correct answer is A. P(E) = 0.3.

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Answer: 9

Step-by-step explanation:

The biggest common divisor number is 9.

Answer:

I think it is straight forward, u just have to solve the problem

Step-by-step explanation:

so 35 x 586= 20510

3.5 x 5860=20510

36 x 586=21096

70 x 586=41020

Answer: im not sure but it should be 5 that symbol then 3

Step-by-step explanation: ez dubs and also i love pizza this is for the points XD

Using Pythagorean theorem

\(\\ \sf\longmapsto H^2=P^2+B^2\)

\(\\ \sf\longmapsto H^2=(5√3)^2+5^2\)

\(\\ \sf\longmapsto H^2=75+25\)

\(\\ \sf\longmapsto H^2=100\)

\(\\ \sf\longmapsto H=10\)

Done

Answer:

is A  

Step-by-step explanation:

The answer choice A is correct because it correctly shows both numbers.All of the other answer choices didnt correctly show the answer choices,and they only showed part of the correct answers.So therfore your correct answer is A(hope this helps you if it doesnt tell me)

To ensure that we have at least 2 cards of the same color, we need to remove 11 cards from the box.  The worst-case scenario is when we remove all the cards of one color and one card from each of the other two colors.

In this case, we would have removed a total of 4 red cards, 5 blue cards, and 1 green card, making a total of 10 cards. However, we still wouldn't have 2 cards of the same color.

To guarantee that we have 2 cards of the same color, we need to remove one more card. This could be either a red card or a blue card. Thus, the smallest number of cards we must remove from the box is 11.

By removing 11 cards, we ensure that we have at least 2 cards of the same color, regardless of the specific cards we remove.

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Answer:

150

Step-by-step explanation:

Multiply 5 times 30 because there are 5 days and she pracitced 30 minutes per day.

The name of every month ends in the letter y is the given statement. February is a counterexample to this statement. This is because February does not end with the letter 'y'. So the right  option is (c) February.

What is a counterexample?

In mathematics, a counterexample is an example that opposes or disproves a statement, proposition, or theorem. It is a scenario, an instance, or an example that goes against the given statement.

Therefore, a counterexample demonstrates that the given statement is false or invalid.In this case, the statement is: "The name of every month ends in the letter y." We have to find which of the months listed does not end in "y."February is the only month in the options listed that does not end in the letter "y."

Thus, it is a counterexample to the given statement. Therefore, the correct option is C, February.

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Answer: Diedre collected 24 cans

Step-by-step explanation:

let x be the number of cans Diedre collected

x+36=60

x=60-36

x=24

Answer:

x= 3, y=0, z= 1

Step-by-step explanation:

Let's label the 3 given equations first.

2x +3y +4z= 10 -----(1)

3x +2y -4z= 5 -----(2)

x +4y +2z= 5 -----(3)

(1) +(2):

This is to eliminate the z term.

2x +3y +4z +3x +2y -4z= 10 +5

5x +5y= 15

Divide by 5 on both sides:

x +y= 3 -----(4)

(3) ×2:

2x +8y +4z= 10 -----(5)

(2) +(5):

This is to eliminate z term.

3x +2y -4z + 2x +8y +4z= 5 +10

5x +10y= 15

Divide by 5 throughout.

x +2y= 3 -----(6)

(6) -(4):

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

x +2y -x -y= 0

y= 0

subst. y=0 into (4):

x +0= 3

x= 3

subst. x=3, y=0 into (3):

3 +4(0) +2z= 5

3 +2z= 5

2z= 5 -3

2z= 2

z= 2÷2

z= 1

Answer:

6.25 is the exact number, but you should round it to 6

Step-by-step explanation:

150/24=6.25.

It also equals 6 if you round it.

A 30-year ARM mortgage loan means that the borrower will have a fixed interest rate for the first 30 years of the loan. After that, the interest rate will adjust annually based on the index and margin.

In this case, the start rate is 3.50%. This means that for the first year, the borrower will pay interest at a rate of 3.50%. At the end of the first year, the interest rate will adjust based on the index and margin.
The index used for this mortgage is MTA, which was 3.00% at the start of the loan. At the end of the first year, the MTA was 4.45%, and at the end of the second year, it was 4.50%.
To calculate the new interest rate at the end of each year, we need to add the margin to the current index rate. The margin is 3.00% and remains the same for the duration of the loan.

Let's calculate the new interest rate at the end of the first year:
New Interest Rate = Current Index Rate + Margin
New Interest Rate = 4.45% + 3.00%
New Interest Rate = 7.45%

However, the rate caps limit how much the interest rate can increase or decrease. In this case, the rate caps are 3/2/6, which means that the interest rate can increase by a maximum of 3 percentage points after the first adjustment, 2 percentage points for subsequent adjustments, and 6 percentage points over the life of the loan.

Since the new interest rate calculated above (7.45%) exceeds the rate cap of 3 percentage points for the first adjustment, the interest rate will be capped at the maximum allowed increase. Therefore, the new interest rate at the end of the first year will be 6.50%.

For subsequent adjustments, the interest rate can increase by a maximum of 2 percentage points. Let's calculate the new interest rate at the end of the second year:
New Interest Rate = Current Index Rate + Margin
New Interest Rate = 4.50% + 3.00%
New Interest Rate = 7.50%

Since the new interest rate calculated above (7.50%) exceeds the rate cap of 2 percentage points, the interest rate will be capped at the maximum allowed increase. Therefore, the new interest rate at the end of the second year will be 6.50%.

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Answer:

Step-by-step explanation:

-0.166666666666666667

The value of the definite integral ∫[-6, 8] (2x + 8) dx, as determined by the area under the graph of the integrand, is 140.

To graph the integrand, which is (2x + 8), we can plot the points on a coordinate system and connect them to form a straight line.

Let's choose a range of x-values from -6 to 8 and calculate the corresponding y-values using the equation y = 2x + 8.

When x = -6, y = 2(-6) + 8 = -4.

When x = 0, y = 2(0) + 8 = 8.

When x = 8, y = 2(8) + 8 = 24.

Plotting these points and connecting them, we get a straight line:   |

24 |                     *

  |                   *

  |                 *

  |               *

  |             *

  |           *

  |         *

  |       *

  |     *

  |   *

8 | *

  |

  +-----------------------

    -6  -4  -2  0  2  4  6  8

To evaluate the definite integral ∫[-6, 8] (2x + 8) dx using the area under the graph, we need to calculate the area of the shaded region.

The shaded region is a trapezoid, and the formula to find the area of a trapezoid is:

Area = (base1 + base2) × height / 2

In this case, base1 corresponds to the y-coordinate at x = -6, which is -4.

Base2 corresponds to the y-coordinate at x = 8, which is 24.

The height of the trapezoid is the length of the interval [-6, 8], which is 14.

Plugging in these values, we can calculate the area:

Area = (base1 + base2) × height / 2

= (-4 + 24) × 14 / 2

= 20 × 14 / 2

= 280 / 2

= 140

Therefore, the value of the definite integral ∫[-6, 8] (2x + 8) dx, as determined by the area under the graph of the integrand, is 140.

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No, none of the transformations could be applied to Circle K to make it match Circle B as a blue circle.

In order for Circle K to match Circle B as a blue circle, certain transformations would need to be applied. However, no single transformation can change the color of a circle from one color to another. Transformations such as translation, rotation, and scaling only affect the position, orientation, and size of an object, but they do not alter its color.

Therefore, applying any of these transformations to Circle K would not result in it becoming a blue circle.

To change the color of Circle K to match Circle B, a different approach would be needed. One possible solution could be to change the fill color or stroke color of Circle K directly. This can be achieved through programming or graphic editing software by modifying the color properties of Circle K.

However, this method does not fall under the category of geometric transformations, which are typically limited to altering the shape, position, or size of an object.

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(a) The population after t years is given by:

P = (10/³)t - (22/³)(t³/3) + 48000.

(b) The population after 15 years is approximately 46850 individuals.

a) The population after t years can be found by integrating the instantaneous rate of change function with respect to t.

∫(10/² - 22t²) dt = (10/³)t - (22/³)(t³/3) + C,

where C is the constant of integration. Since we know the initial population is 48000, we can substitute t = 0 and P = 48000 into the equation:

(10/³)(0) - (22/³)(0³/3) + C = 48000,

C = 48000.

Therefore, the population after t years is given by:

P = (10/³)t - (22/³)(t³/3) + 48000.

b) To find the population after 15 years, we substitute t = 15 into the equation:

P = (10/³)(15) - (22/³)((15)³/3) + 48000

P = 50 - 1100 + 48000

P = 46850.

Rounding up the population to the nearest whole number, the population after 15 years is approximately 46850 individuals.

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Answer:

0.259

Step-by-step explanation:

There are some rules in determining what numbers are significant figures.

We can determine how many significant figures the number currently has.

There are currently seven significant figures. In order to round the number to three significant figures, we must round it to the thousandths place, or the 9.

The rounding rules are:

Since 0 is less than 5, the number rounded to 3 significant figures is 0.259.

The probability of three people who share the same birthday is 0.6459.

Let us consider that A₀ be the event that everyone in the room has a distinct birthday. Let Ai be the event that pairs of people share a birthday. Then the probability we are interested in is

P(at lest three people share a birthday) = 1 - P(A₀) - ∑ P(Ai)

where there are n people in the lecture hall.

First we note that P(A₀) is in the book and is

P(A₀) = (365Cn)n!/365^n.

Now we will compute P(Ai).

For i = 1,

P(A₁) = (365) × \(\frac{(nC2)(365-1Cn-2)(n-2)!}{365^{n} }\)

For i = 2,

P(A₂) = \(\frac{(365C2)(nC2)(n-2C2)(365-2Cn-4)(n-4)!}{365^{n} }\)

This generalizes for i pairs of people sharing i distinct birthdays

P(Ai) = (365Ci)πj=1toi(n-2j+2C2)(365-iCn-2i)(n-2i)!/(\(365^{n}\))

Substituting all values into the equation and putting in n = 100, we can compute a value for this probability.

Therefore we get,

P(at least 3 people share a birthday)0.6459.

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Answer:

7/12 is greater

Step-by-step explanation:

You know this because 3/6 is one half or 0.5.

7/12 is 0.58 as a decimal which is greater than 0.5.

Answer:

7/12

Step-by-step explanation:

Because 3/6 = 0.5

while, 7/12 = 0.5833333333

And after approximation it will be

0.6

To determine the maximal velocity from an acceleration vs. time graph, you need to follow these steps:

Identify the time interval during which the acceleration remains constant or nearly constant. This interval can be identified as a straight line on the graph.

Calculate the acceleration value during this interval by finding the slope of the line. The slope is the change in acceleration divided by the change in time.

Use the acceleration value and the time interval to calculate the change in velocity during this interval using the formula:

Δv = aΔt

Where Δv is the change in velocity, a is the acceleration, and Δt is the time interval.

Add the change in velocity to the initial velocity at the start of the time interval to obtain the maximal velocity. If the initial velocity was zero, then the maximal velocity will be equal to the change in velocity.

vmax = vi + Δv

Where vmax is the maximal velocity and vi is the initial velocity.

Note that this method assumes that the acceleration is constant or nearly constant during the time interval of interest. If the acceleration changes significantly during this time interval, you will need to break it down into smaller intervals and repeat the above steps for each interval to determine the maximal velocity.

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Answer:

Try posting another question with an image of the problem attached

Step-by-step explanation:

Answer:

What's the question

Step-by-step explanation:

£270 will be allocated to the first person and £135 will be allocated to the second person.

Ratio is a mathematical expression that is used to compare two or more quantities in relation to each other. It is usually expressed as a fraction or a decimal. Ratios are used to compare values, trends, and proportions. Ratios are essential for understanding the relationship between numbers and for making informed decisions. Ratios are often used in business, finance, economics, and other areas to measure performance and risk.

This is calculated by multiplying the total amount of £405 by the ratio 2:3.
The first person's ratio is 2 out of 5 and the second person's ratio is 3 out of 5.

Therefore, 2/5 of £405 is £270 and 3/5 of £405 is £135.

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Answer: 3/52

Step-by-step explanation:

You want to pick a diamond jack, diamond queen or diamond king

There are only 3 of those so

P(DJ or DQ or DK) = 3/52        There are 3 of those out of 52 total

Answer:

48%

Step-by-step explanation:

Answer:

48%

Step-by-step explanation:

12/25 = x/100

12x100 = 25x

1200/25= x

x = 48%

The countermeasures to avoid potential human errors are   Visual aids & work instructions, education and/or discipline, work standardization and discipline and TPM and skill building etc.

Many major accidents, such as Texas City, Piper Alpha, and Chernobyl, were caused by potential human error. Companies must manage human failure as rigorously as they manage technical and engineering measures to avoid accidents and illness.

There are several countermeasures for amateur or beginner mistakes. Potential human errors can be avoided by some measures including training, skill development, work standardisation, visual aids, and work instructions. Every human being makes mistakes, whether they are professional or not.

Thus, Visual aids and work instructions, education and/or discipline, work standardisation and discipline, TPM and skill building, and other counter measures are used to avoid potential human errors.

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The expressions that represent the number of each coin are

Dimes is 2x, Nickels is 2x + 4, and Pennis is 3x.

To form the equation of a given we need to understand the condition in the given problem. Here we use variable 'x' to represent the unknown values. In the given problem, 'x' represents the number of quarters by taking quarters as 'x' we will express the remaining coins in terms of 'x'.

Here we have

Penelope is collecting money from charity and his collection is

Twice as many dimes as quarters  

4 more nickels than dimes and

three times as many pennies as quarters

Given 'x' represents the number of quarters  

Number of dimes = twice of quarters = 2x

Number of nickels = 4 more than dimes = 2x + 4

Number of Pennis = three times the quarters = 3x

Therefore,

The expressions that represent the number of each coin are

Dimes is 2x, Nickels is 2x + 4, and Pennis is 3x.

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we have proven that either G is abelian or Z(G) = 1.

What is the equivalent expression?

Equivalent expressions are expressions that perform the same function despite their appearance. If two algebraic expressions are equivalent, they have the same value when we use the same variable value.

To prove the statement, we will use the previous problem, which states that if |G| = pq for primes p and q, then either G is cyclic or G has an element of order p and an element of order q.

Let's consider the two cases separately:

Case 1: G is cyclic.

If G is cyclic, then G is abelian since all cyclic groups are abelian.

Case 2: G is not cyclic.

If G is not cyclic, we know from the previous problem that G has an element of order p and an element of order q. Let's denote these elements as a and b, respectively.

Consider the subgroup H generated by a:

H = {e, a, a², ..., \(a^{(p-1)}\)}

Since the order of a is p, H has p elements. Similarly, consider the subgroup K generated by b:

K = {e, b, b², ..., \(b^{(q-1)}\)}

Since the order of b is q, K has q elements.

Now, let's consider the intersection of H and K, denoted as HK:

HK = {h * k | h ∈ H, k ∈ K}

Since G is not cyclic, the intersection HK cannot be equal to G. Therefore, |HK| < |G|.

Now, let's consider the order of the product h * k for arbitrary elements h ∈ H and k ∈ K. By the property of cyclic groups, we know that:

\((h * k)^p = h^p * k^p = e * k^p = k^p\)

Since p is a prime, the order of \(k^p\) can only be 1 or q. If the order is 1, then \(k^p = e\), and thus h * k = h for any h ∈ H. This implies that HK is a subset of H.

Similarly, if the order of \(k^p\) is q, then \(k^p = e\), and thus h * k = k for any h ∈ H. This implies that HK is a subset of K.

In both cases, HK is a proper subset of either H or K. Therefore, |HK| < p or |HK| < q.

Since |HK| is a divisor of |G| = pq, and |HK| < p or |HK| < q, the only possibility is that |HK| = 1.

This implies that the intersection HK contains only the identity element e. Therefore, all elements of H commute with all elements of K.

Now, let's consider an arbitrary element g ∈ G. Since g ∈ H and g ∈ K, g commutes with all elements in H and all elements in K. This means that g commutes with all elements in the subgroup generated by H and all elements in the subgroup generated by K.

Therefore, every element of G commutes with every element in G, and thus G is abelian.

In summary, we have shown that if |G| = pq for primes p and q, then either G is abelian (Case 1) or G is not cyclic, and in this case, the intersection of the subgroups generated by the elements of order p and q is trivial (HK = {e}), implying that Z(G) = 1 (Case 2).

Therefore, we have proven that either G is abelian or Z(G) = 1.

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