Find the sum of all positive integers from 5 to 1555 inclusive, that are divisible by 5.

Answer: 23 - 10

Step-by-step explanation:

The length FE in the circle is 6 units

The arc AE has a measure of 64 degrees

From the question, we have the following parameters that can be used in our computation:

The circle

Given that the lengths from the center to either chords are equal

This means that

FE = 6 units

For the other circle, we have

BC = 58 degrees

AB = ED

The arc AE is calculated as

AE = 180 - BC - ED

Where

AB = ED = BC = 58 degrees

So, we have

AE = 180 - 58 - 58

Evaluate

AE = 64

Hence, the arc AE is 64 degrees

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The method is: Find the increase and find the ratio of the increase and the old price.

The percentage increase is 20%

A percentage is defined as the ratio that can be expressed as a fraction of 100.

The method below shows how you would calculate the % increase.

First step: Find the increase:

increase = 480 - 400 = $80

Second step: Find the ratio of the increase and the old price and multiply by 100 to express in percentage:

80/400 * 100 = 20%

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The amount invested in the account that pays 1.5% interest is $584,285.71.

The amount invested in the account that pays 8.5% interest is $155,714.29.

The system of equations that represent the information in the question is:

x + y = 740,000 equation 1

0.015x + 0.085y = 22,000 equation 2

Where:

In order to determine the values, the elimination method would be used.

Multiply equation 1 by 0.015

0.015x + 0.015y = 11,100 equation 3

Subtract equation 3 from equation 2

0.070y = 10,900

Divide both sides of the equation by 0.070

y = 10,900 / 0.07

y = 155,714.29

Subtract 155,714.29  from $740,000

x = 740,000 - 155,714.29

x = 584,285.71

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Answer:

rotation about Point a and  reflection across line M

Step-by-step explanation:

  got it right on edgentuinty dont know how to spell it lol

Answer:

The first transformation was a : rotated about point A

The second transformation was a : reflection across line M

Step-by-step explanation:

hope this helped <3

Answer:

\((p - q)(x) = (x -1) (x - 4)\)

Step-by-step explanation:

Given

\(p(x) = x^2 - 1\)

\(q(x) = 5(x - 1)\)

Required

(p - q)(x)

This is represented as:

\((p - q)(x) = p(x) - q(x)\)

\((p - q)(x) = x^2 - 1 - 5(x - 1)\)

\((p - q)(x) = x^2 - 1 - 5x + 5\)

Collec like terms

\((p - q)(x) = x^2 - 5x + 5 - 1\)

\((p - q)(x) = x^2 - 5x + 4\)

Expand

\((p - q)(x) = x^2 -4x - x + 4\)

Factorize

\((p - q)(x) = x(x -4) - 1(x - 4)\)

\((p - q)(x) = (x -1) (x - 4)\)

Answer:

4080

Step-by-step explanation:

Answer:$182

Step-by-step explanation:

52/3 = 17.3333333333

so 17.3333333333 * 10.5 = 182

Answer:

3 71/99.

Step-by-step explanation:

0.71.. * 100 =  71.71..

0,71.. * 1    =    00.71..      Subtract:

0.71 * 99 =      71

So 3.71..  = 3 71/99.

Answer:

$535.25

Step-by-step explanation:

539.50 - 39.50 = 504.00

504.00 - 23.75 = 480.25

480.25 + 55.00 = 535.25

Using compound interest formula, her balance after retirement is $430797.77

To calculate the balance of Marissa's retirement account after 30 years, we need to determine how much her savings account and index fund will be worth after 30 years, taking into account the interest earned and her monthly contributions.

First, we'll calculate the balance of her savings account:

Initial deposit: $2000

Interest rate: 1.5%

Monthly contribution: $150

Number of months: 30 years * 12 months/year = 360 months

Using the compound interest formula, the balance of her savings account after 30 years will be:

2000*(1+0.015/12)^360 + 150*(((1+0.015/12)^360-1)/(0.015/12))

A = $71280.33

Next, we'll calculate the balance of her index fund:

Initial deposit: $1000

Interest rate: 6.8%

Monthly contribution: $300

Number of months: 30 years * 12 months/year = 360 months

Using the compound interest formula, the balance of her index fund after 30 years will be:

A = 1000*(1+0.068/12)^360 + 300*(((1+0.068/12)^360-1)/(0.068/12))

A = $359517.44

Then we can add the balance of both the savings account and the stock market to get the total balance of Marissa's retirement account.

Her balance = $71280.33 + $359517.44 = $430797.77

Please note that the above answer is an estimation, in reality there are other factors such as taxes, inflation, fees, and market conditions that should be considered in a real-world scenario.

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Answer:

6 pizzas

Step-by-step explanation:

At least 10 and fewer than 20 makes it 10-19

So,

10-19 => 6 pizzas

6 pizzas have at least 10 pieces of pepperoni but fewer than 20 pieces of pepperoni.

The system of equations as an augmented matrix is \(\left[\begin{array}{ccc|c}1&0&0&100\\0&-5&-7&350\\0&-5&-9&200\end{array}\right]\)

From the question, we have the following parameters that can be used in our computation:

x                  = 100

   -5m  - 7c  = 350

   -5m  - 9c  = 200

The above means that the variables in the system of equations are

x, m and c

So, we have the following representation

x    m     c        

1    0      0        100

0   -5    -7        350

0   -5    -9        200

When represented as an augmented matrix, we have

\(\left[\begin{array}{ccc|c}1&0&0&100\\0&-5&-7&350\\0&-5&-9&200\end{array}\right]\)

Hence, the augmented matrix is \(\left[\begin{array}{ccc|c}1&0&0&100\\0&-5&-7&350\\0&-5&-9&200\end{array}\right]\)

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Answer:

\(\frac{1}{7}\)

Step-by-step explanation:

We know, that probability of an event E, is \(\textrm{P}(\textrm{E})=\frac{\textrm{Number of favorable outcomes}}{\textrm{Total number of outcomes}}\).

Here, there are \(7\) days in a week.

So, total number of outcomes \(=7\).

And only one day, that is, Friday is selected.

So, number of favorable outcomes \(=1\).

Therefore, probability \(=\frac{1}{7}\).

Hence, the probability that a randomly selected day of the week will be a Friday \(=\frac{1}{7}\).

Answer:

D

5 sq.rt. 3

Step-by-step explanation:

use the pythagorean theorem: a^2 + b^2 =c^2

5^2 + x^2 = 10^2

25+ x^2 =100

x^2 = 100 - 25

x^2 =75

x = \(\sqrt{75}\)

x = 5 \(\sqrt{3}\)

Answer:

juan

Step-by-step explanation:

juan won causs he got to 4 meters in 13 mins whereas Antonio did it in 15 mins

for the second part just describe how the differences between the line such as Antonio starts off really fast but slows down

juan starts off at a slow pace behind Antonio but gradually catches up and overtakes him as Antonio stops for a rest for 2 mins

Answer:

25 extra litres

Step-by-step explanation:

Ratio 2:3

2+3=5 so 35/5 =7

7x2 means she used 14 litres of fruit juice

7x3 means she used 21 litres of lemonade

if she has 10 litres of fruit juice left then she can use 10/2=5 5x3=15 15 litres of lemonade

10+15=25 so she can make 25 extra litres

24/35.................

Answer: x = 8

BC = 13

AB = 13

AD = 10

Step-by-step explanation:

The figure shows that AB = BC so:

x+5 = 2x-3

2x-x = 5+3

x = 8

Hence we have:

BC = 2(8)-3 = 13

AB = 8+5 = 13

AD = 8+2 = 10

The next term in the sequence is 98. None of the given options (60, 81, 90, 101) match the expected next term. None of the option is correct.

To find the pattern in the sequence 1, 1, 3, 8, 19, 41, we can examine the differences between consecutive terms:

1 1 3 8 19 41

0 2 5 11 22

Looking at the differences, we can observe that each subsequent difference is obtained by adding consecutive odd numbers: 2, 3, 4, 5, etc. This suggests that the original sequence may be related to square numbers.

Let's check if the differences between consecutive terms are square numbers:

2 = 1²

5 = 2² + 1²

11 = 3² + 2²

22 = 4² + 3²

Based on this pattern, we can make a reasonable assumption that the next difference should be 5² + 4² = 41 + 16 = 57. Adding this difference to the last term of the sequence (41), we get the next term:

41 + 57 = 98

Therefore, the next term in the sequence is 98. None of the given options (60, 81, 90, 101) match the expected next term.

Hence, none of the given options accurately continue the pattern of the sequence. It's important to note that patterns in sequences can sometimes have multiple possible interpretations, and it's always essential to consider alternative patterns or extend the sequence further to confirm the pattern.

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Therefore, the equation of the line passing through the point (1,5) with a slope of 7 is y = 7x - 2.

The equation of a line in the point-slope form is given by the following equation:

y-y_1 = m(x-x_1)

where m is the slope of the line and (x1, y1) is any point on the line.

Therefore, we can write the equation of the line passing through the point (1,5) with a slope of 7 as follows:

y-5 = 7(x-1)

Expanding the right-hand side of the equation gives:

y-5 = 7x-7

Adding 5 to both sides of the equation gives:

y = 7x-2

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Answer: B. Take on a risky loan just to get your credit started.

Step-by-step explanation: Taking on a risky loan, such as a high-interest loan or one with unfavorable terms, can have significant negative impacts on your financial well-being.  It's crucial to exercise caution and choose loans that are manageable for your financial situation.

Financial strain: Risky loans often come with high-interest rates, meaning you'll end up paying more in interest over time.  This can lead to financial strain as a substantial portion of your income may be allocated towards loan repayments.  It's important to consider the monthly payment amount and ensure it fits within your budget.

Difficulties in repayment: Risky loans can make it difficult to meet your repayment obligations.  If you struggle to make timely payments, you may face penalties, late fees, and damage to your credit score.  This can have long-term consequences, making it harder for you to secure future loans or rent an apartment.

To avoid these risks and maintain good credit:

Loan selection: Carefully evaluate the terms and conditions of any loan before accepting it.  Look for options with reasonable interest rates, favorable repayment plans, and borrower protections. Federal student loans, scholarships, grants, and work-study programs should be prioritized before resorting to private loans, which often have higher interest rates and fewer benefits.

Responsible credit behavior: Building and maintaining good credit is crucial for your financial future.  Paying your bills on time and managing credit card balances wisely are key components of responsible credit behavior.  This demonstrates to lenders that you are reliable and trustworthy, increasing your chances of obtaining favorable loan terms in the future.

By being cautious in loan selection and practicing responsible credit behavior, you can avoid the negative consequences of risky loans, protect your financial well-being, and establish a solid credit foundation. Remember to prioritize loans within your means and always be mindful of your financial situation.

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Answer:

b = 5/4

Step-by-step explanation:

We need to find the solution of the following equation :

\(2b+\dfrac{1}{2}=3\)

Subtracting 1/2 both sides we get :

\(2b+\dfrac{1}{2}-\dfrac{1}{2}=3-\dfrac{1}{2}\\\\2b=\dfrac{5}{2}\)

Dividing both sides by 2 we get :

\(b=\dfrac{5}{4}\)

so, the value of b is 5/4.

\(1\frac{3}{4}\) feet as a multiplication expression using the unit, 1 foot, as a factor is \(1\frac{3}{4}\)×1.

The given fraction is \(1\frac{3}{4}\).

\(1\frac{3}{4}\) feet can be written as a multiplication expression as follows: 1 foot × 1 3/4. This is because \(1\frac{3}{4}\) is the same as 1 + 3/4.

Furthermore, 3/4 can be written as 0.75, which is the same as 0.75 × 1 foot.

Therefore, the multiplication expression is 1 foot × \(1\frac{3}{4}\) = 1 foot × (1 + 0.75) = 1 foot × 1 + 1 foot × 0.75 = 1 foot + 1.75 feet.

Therefore, \(1\frac{3}{4}\) feet as a multiplication expression using the unit, 1 foot, as a factor is \(1\frac{3}{4}\)×1.

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Step-by-step explanation:

1ft=12in

1¾ft=x

x=12×7/4=21in

1¾ft=1¾×1 ft

The given cylindrical wind chime of dimensions 16 inches long will not fit inside the box in the shape of rectangular-prism having dimensions 10 inches x 8 inches x 6 inches.

1)shorter than

2) shorter than

3)will not fit.

What is a rectangular-prism?

Rectangular prism also called as cuboid, is a closed three dimensional solid having six faces. This prism has eight vertices or corners and 12 edges. The perimeter of this shape is the total length of 12 edges. The area of this shape is the sum of area of for or six surfaces depending on the given situation.

Given dimensions of cuboid/rectangular prism:

Length=10 inches, height= 6 inches & Width=8 inches

Dimensions of cylindrical wind chime: Length of cylinder = 16 inches

Case I: comparision of diagonal of base of the box & length of wind chime.

Diagonal of base can be found using pythagorean theorem:

Diagonal=\(\sqrt{L^{2} +W^{2} }\)

              =\(\sqrt{(10)^{2} +(8)^{2} }\)

              =\(\sqrt{100+64\\}\)

               =\(\sqrt{164}\)

               =12.8 inches ≠ 16 inches

Diagonal of rectangular prism base shorter than length of wind chime.

Case II:comparision of interior diagonal of the box & length of wind chime.

Interior diagonal of box=\(\sqrt{L^{2} +W^{2} +H^{2} }\)

                                       =\(\sqrt{(10)^{2} + (8)^{2} +(6)^{2} }\)

                                       =\(\sqrt{100+64+36}\)

                                        =\(\sqrt{200}\)

                                        =14.14 inches ≠ 16 inches

Interior Diagonal of rectangular prism is shorter than length of wind chime.

As the wind chime is greater than both the diagonals of cuboid, the chime will not fit into the prism.

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Refer to the complete question attached below.

Answer:27,375

Step-by-step explanation:

75 x 365

Answer:

456.25

or 27375 minutes

Step-by-step explanation:

because if u times 75 and 365(days in a year) u will get 27375 minutes a year which i simplifyed but divideding that number by one hour aka 60 minutes so 27375/60 gets u 456 hours and 25 minutes