Ellen walks dogs on weekends. She gets paid $8.50 per hour. Each day she works five hours and 45 minutes. How much does Ellen get paid per weekend?

Answer:

[tex]\frac{22\text{ AUD }\cdot 1\text{ USD}}{1.20\text {AUD}}[/tex]

Step-by-step explanation:

We are told that 1.2 Australian dollars equals to 1 US dollar. We are supposed to write an expression that can be used to convert 22 Australian dollars to US dollars.

To find the amount of US dollars in 22 Australian dollars we will divide 22 by amount of Australian dollars that is equal to 1 US dollar (1.2 AUD).

[tex]22\text{ AUD}=\frac{22\text{ AUD }\cdot 1\text{ USD}}{1.20\text{ AUD}}[/tex]

Australian dollars will cancel out with Australian dollars from unit parts and our unit will be in American dollars.

[tex]22\text{ AUD}=\frac{22\cdot 1\text{ USD}}{1.20}[/tex]

Therefore, our desired expression that can convert 22 Australian dollars to US dollars will be  [tex]\frac{22\text{ AUD }\cdot 1\text{ USD}}{1.20\text { AUD}}[/tex].

The value of the  numerator of the calculation of the variance= 258

and Variance= 51.6

We know that in order to calculate the variance we need to follow following steps:

The data points are:

   90, 75, 72, 88, 85

The mean of these data points are:

[tex]Mean=\dfrac{90+75+72+88+85}{5}\\\\\\Mean=\dfrac{410}{5}\\\\\\Mean=82[/tex]

Now on finding the difference terms i.e.

90-82=8

75-82= -7

72-82= -10

88-82=6

and  85-82=3

The square of these difference term is:

8²=64

(-7)²=49

(-10)²=100

6²=36

and  3²=9

Hence, the mean of these squared quantity i.e. Variance is:

[tex]Variance=\dfrac{64+49+100+36+9}{5}\\\\\\Variance=\dfrac{258}{5}\\\\\\Variance=51.6[/tex]

5000 x (1-0.10)^2

5000 x 0.90^2

5000 * 0.81

it is valued at 4,050 after 2 years

Final answer:

After applying a 10% yearly depreciation to the initial value of £5000, the car's value after 2 years will be £3150.

Explanation:

When a car decreases in value by 10% a year, its value after 2 years can be calculated using exponential decay. To compute the value of the car after two years, we start with the initial value of £5000 and apply a 10% decrease for each year. The formula for the value of the car after a certain number of years is given by:

Future Value = Present Value × (1 - rate of depreciation)^number of years

For the first year:

Future Value = £5000 × (1 - 0.10)¹

Future Value = £5000 × 0.90

Future Value = £4500

For the second year, we use the value at the end of the first year:

Future Value = £4500 × (1 - 0.10)¹

Future Value = £4500 × 0.90

Future Value = £3150

Therefore, after 2 years, the car will be worth £3150.

Answer:

The answer is C. x÷30 = (x + 300)÷55

Step-by-step explanation:

The equation that could be used to find the number of miles the trains will travel is C. x÷30 = (x + 300)÷55.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

A freight train travels at 30 mph. If the freight train is 300 miles ahead of an express train traveling at 55 mph.

The equation will be

Total speed = Total distance / time taken

x ÷ 30 = (x + 300) ÷ 55

The equation that could be used to find the number of miles the trains will travel is C. x÷30 = (x + 300)÷55.

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7 +0.30x = 4 +0.40x

subtract 4 from each side

3+0.30x = 0.40x

subtract 0.3x from each side

3 = 0.10x

divide both sides by 0.10

3 /0.10 = 30

30 checks would make both accounts equal

so he would need to write 31 checks for the first one to be better.

Answer:30

Step-by-step explanation:

it’s right

The total cost of the ski jacket and matching ski pants is $250.

Given that, a ski jacket costing $160 is $20 less than twice the cost of the matching ski pants.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Let the cost of matching ski pants be x.

Now, 2x-20=160

⇒ 2x=180

⇒ x=90

So, the cost of the matching ski pants is $90.

Total cost = 160+90 = $250

Therefore, the total cost of the ski jacket and matching ski pants is $250.

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To find the percent of 85 that is 10, divide 10 by 85 and multiply by 100. The answer is 11.76%.

To find the percent of 85 that is 10, we divide 10 by 85 and multiply by 100.

10 / 85 = 0.1176

0.1176 * 100 = 11.76%

Roundin the answer to the nearest hundredth of a percent, we get 11.76%.

The consecutive even integers such that the smaller added to four times the larger gives a sum of 48 are; 8 and 10

The consecutive numbers are those numbers that follow each other continuously in the order from smallest to largest numbers.

WE have to determine the two consecutive even integers such that the smaller added to four times the larger gives a sum of 48.

Let the two consecutive even integers are; x and (x+2)

Therefore,

X+4(x+2) = 48

X+4x+8=48

5x=40

X=8

Hence The consecutive even integers are; 8 and 10

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The sequence provided (1, 5, 30, 210, 2680) does not match typical simple arithmetic or geometric patterns, suggesting it may involve a more complex rule like factorial growth, though a specific pattern cannot be determined with the provided information.

The question is about finding the pattern in the sequence 1, 5, 30, 210, 2680. To solve this, observe how each term relates to its predecessor. The sequence does not directly follow an arithmetic or geometric pattern; instead, it seems to involve a factorial or multiplicative pattern with increasing multipliers.

However, the information provided does not directly match the given sequence, suggesting that there might have been a typo in the sequence or additional rules that were not stated. Generally, patterns can be identified through arithmetic (addition/subtraction), geometric (multiplication/division), or more complex operations (such as factorial or combinations), but without the correct sequence or a clear rule, it's challenging to provide a decisive pattern.

For sequences that escalate rapidly like this one, factorial operations or exponential growth with additional manipulations (addition, subtraction) are common, but the specific pattern here is unclear without further clarification or the correct sequence.

Answer:

[tex](x, y) \rightarrow (-x, -y)[/tex]

Step-by-step explanation:

Rotation of any point in the form of (x, y) about the origin O through 180 degree in anticlockwise or counterclockwise direction, it will takes the new position (-x, -y)

i.e,

The rule of rotation about the origin through 180 degree is given by:

[tex](x, y) \rightarrow (-x, -y)[/tex]

For example:

Let the point A(-4, 6) rotate by the rule [tex]R_{0, 180^{\circ}}[/tex]

then;

[tex]A(-4, 6) \rightarrow (4, -6)[/tex]

⇒the coordinate of  image of the point A is, (4, -6)

Therefore, the rule represents [tex]R_{0, 180^{\circ}}[/tex]  is, [tex](x, y) \rightarrow (-x, -y)[/tex]

Answer:

B

Step-by-step explanation:

Answer:

the answer is A. 15h>750+3.5h

Im 100% sure.  Good luck!

Answer:

Step-by-step explanation:

I forgot

Answer:

33

Step-by-step explanation:

We need to find 6% of 550.

We can calculate with a direct rule of 3. If the 100% is 550, how much is the 6%?

[tex]100 -\!\!\!-\!\!\!- 550\\ 6 -\!\!\!-\!\!\!- x[/tex]

We use the formula of the direct rule of 3:

[tex]x = \frac {6 * 550}{100} \\ \\ x = \frac {3300}{100}\\ \\ x = 33[/tex]

33 toys will be defective.

If a toy manufacturer produces 550 toys in one day, then the number of toys that would be defective is 33 toys.

Given the following data:

To find the number of toys that would be defective from a production:

[tex]D = \frac{6}{100}[/tex] × [tex]T[/tex]

Substituting the given parameters into the formula, we have;

[tex]D = \frac{6}{100}[/tex] × [tex]550[/tex]

[tex]D = 0.06(550)[/tex]

Defective toys, D = 33 toys.

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When measuring the volume of a swimming pool, larger units of capacity like liters and gallons are used. For an Olympic-sized pool, the volume is often measured in megaliters or cubic meters.

When measuring the volume of a swimming pool, we are dealing with a very large capacity, therefore using small capacity units like milliliters would not be practical due to the large numbers it would involve. In cases such as filling a pool, larger units of capacity are more appropriate. Common units of measure for such large volumes are liters and gallons. For very large swimming pools, like Olympic-sized ones, volume is often expressed in megaliters (ML) because one megaliter equals one million liters. For instance, an Olympic-sized swimming pool holds about 2,500,000 liters, which can also be expressed as 2.5 megaliters (ML).

Additionally, when working with the volume of a pool, it would also be possible to measure in cubic meters (m³). This is particularly common in scientific contexts or in regions where the metric system is standard for all measurements.

Answer:

C. He should have found 8 as the exponent, not –8.

Step-by-step explanation:

We have been given an expression [tex](2^{-4})^{-2}[/tex]. We are asked to find the Pablo's error in simplifying the expression.

Let us check steps done by Pablo.

In first  step Pablo has simplified [tex](2^{-4})^{-2}[/tex] to [tex](2)^{(-2*-4)}[/tex] using power rule property of exponents which states that to raise a power to a power we have to multiply the exponents. Therefore, his first step is correct.  

Now let us check Pablo's second step. We can see that Pablo multiplied -2 by -4 and simplified to [tex]2^{-8}[/tex].  

Since we know that multiplying a negative number with another negative number gives a positive result, therefore, Pablo made mistake in second step. He should have found 8 instead of -8 as the exponent.    

The correct steps for simplifying the given expression will be [tex](2^{-4})^{-2}=2^{(-2*-4)}=2^{8}[/tex].  

Upon looking at our given option we can see that option C is the correct statement about Pablo's error.  

Answer: -1.5i

Step-by-step explanation: This was correct

Answer:

junko enishima

Step-by-step explanation:

multiply 3.5 x 3 = 10.5

 add -5 +-10 = -15

 so you have 10.5 x 10^15

 then you need to move the decimal point 1 place to the left to get 1.05

 since you move the decimal point 1 place to the left you add 1 to the -15 to get -14

 so answer = 1.05 x 10^-14

Option: D is the correct answer.

D = a group of events whose later outcomes are affected by previous outcomes.

We know that two events Event A and event B are said to be dependent if the occurrence of one outcome affects the occurrence of the other outcome.

For example--

If we have a bag containing 5 blue marbles, 2 red marbles and 3 green marbles then if we draw first marble and then draw second without replacement.

Then the event of drawing a blue marble first and then a green marble are dependent events.