what is a acute angle

The value of y in simplest form for the point P = (1/2, y) lying on the unit circle is y = ± √(3)/2.

To find the value of y in simplest form for the point P = (1/2, y) lying on the unit circle, we can use the equation of the unit circle, which states that for any point (x, y) on the unit circle, the following equation holds: x^2 + y^2 = 1.

Plugging in the coordinates of the point P = (1/2, y), we get:

(1/2)^2 + y^2 = 1

1/4 + y^2 = 1

y^2 = 1 - 1/4

y^2 = 3/4.

To simplify y^2 = 3/4, we take the square root of both sides:y = ± √(3/4).

Now, we need to simplify √(3/4). Since 3 and 4 share a common factor of 1, we can simplify further: y = ± √(3/4) = ± √(3)/√(4) = ± √(3)/2.

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Answer:

a) 6.00

b) 3.00

c) 1.50

Step-by-step explanation:

Sample error of the mean is expressed mathematically using the formula;

SE = σ /√n where;

σ  is the standard deviation and n is the sample size.

a) Given σ = 18, n = 9

Standard error of the mean = σ /√n

Standard error of the mean = 18/√9

Standard error of the mean = 18/3

Standard error of the mean = 6.00

b) Given σ = 18, n = 36

Standard error of the mean = σ /√n

Standard error of the mean = 18/√36

Standard error of the mean = 18/6

Standard error of the mean = 3.00

c) Given σ = 18, n = 144

Standard error of the mean = σ /√n

Standard error of the mean = 18/√144

Standard error of the mean = 18/12

Standard error of the mean = 3/2

Standard error of the mean = 1.50

Step-by-step explanation:

a =45°

b=45°

c=30°

d=30°

e=30°

f=30°

total of the angle

90×4=360

The value x in the secant line using the Intersecting theorem is 4.

Intersecting secants theorem states that " If two secant line segments are drawn to a circle from an exterior point, then the product of the measures of one of secant line segment and its external secant line segment is the same or equal to the product of the measures of the other secant line segment and its external line secant segment.

From the figure:

First sectant line segment = ( x - 1 ) + 5

External line segment of the first secant line = 5

Second sectant line segment = ( x + 2 ) + 4

External line segment of the second secant line = 4

Using the Intersecting secants theorem:

5( ( x - 1 ) + 5 ) = 4( ( x + 2 ) + 4 )

Solve for x:

5( x - 1 + 5 ) = 4( x + 2 + 4 )

5( x + 4 ) = 4( x + 6 )

5x + 20 = 4x + 24

5x - 4x = 24 - 20

x = 4

Therefore, the value of x is 4.

Option C) 4 is the correct answer.

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Answer:

100 grams

Step-by-step explanation:

1/2 * 1/2 = (1/2)² = 1/4

1/4 * 400 = 100

Answer: 516 out of 100 would be 516%

After 4 half-lives, only 1/16th (or 0.0625) of the initial amount of the radioactive isotope will remain.

The amount of a radioactive isotope remaining after a certain number of half-lives can be calculated using the formula:

Amount remaining = Initial amount × (1/2)^(number of half-lives)

In this case, we are given the initial amount as "grams" and we want to find out the amount remaining after 4 half-lives.

So, the equation becomes:

Amount remaining = Initial amount × (1/2)^4

Since each half-life reduces the quantity to half, (1/2)^4 represents the fraction of the initial amount that will remain after 4 half-lives.

Simplifying the equation:

Amount remaining = Initial amount × (1/16)

Therefore, after 4 half-lives, only 1/16th (or 0.0625) of the initial amount of the radioactive isotope will remain.

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Answer:

Step-by-step explanation:

1) Reflection over \(\overline{BC}\)

2) The triangles are congruent by SAS, so when \(\triangle GBC\) is mapped onto \(\triangle ABC\), because points \(G\) and \(A\) are corresponding, \(G'\) will correspond with \(A\).

3) Yes, because \(\overline{BG} \cong \overline{AB}, \overline{GC} \cong \overline{AC}, \angle BAC \cong \angle BGC\), so the triangles are congruent by SAS.

Given statement solution is :- It takes 4 months to pay off the card, and the total amount paid, including interest, is $1600.

To determine the number of months it takes to pay off the credit card and the total amount paid, including interest, we can follow these steps:

Step 1: Calculate the monthly interest rate.

The APR (Annual Percentage Rate) is given as 9.5%. To find the monthly interest rate, we divide this by 12 (the number of months in a year):

Monthly interest rate = 9.5% / 12 = 0.0079167

Step 2: Determine the monthly payment.

The monthly payment is given as $400.

Step 3: Calculate the interest and principal paid each month.

The interest paid each month can be calculated by multiplying the monthly interest rate by the current balance.

Principal paid = Monthly payment - Interest paid

Step 4: Track the remaining balance each month.

Starting with the initial balance of $1,367.90, subtract the principal paid each month to determine the new balance.

Step 5: Repeat Steps 3 and 4 until the balance reaches zero.

Continue calculating the interest and principal paid each month, updating the balance, until the remaining balance becomes zero.

Step 6: Determine the total number of months and the total amount paid.

Count the number of months it takes to reach a balance of zero. Multiply the number of months by the monthly payment ($400) to find the total amount paid.

Let's calculate the number of months and the total amount paid, including interest:

Month 1:

Interest paid = 0.0079167 * $1,367.90 = $10.84

Principal paid = $400 - $10.84 = $389.16

New balance = $1,367.90 - $389.16 = $978.74

Month 2:

Interest paid = 0.0079167 * $978.74 = $7.75

Principal paid = $400 - $7.75 = $392.25

New balance = $978.74 - $392.25 = $586.49

Month 3:

Interest paid = 0.0079167 * $586.49 = $4.64

Principal paid = $400 - $4.64 = $395.36

New balance = $586.49 - $395.36 = $191.13

Month 4:

Interest paid = 0.0079167 * $191.13 = $1.51

Principal paid = $400 - $1.51 = $398.49

New balance = $191.13 - $398.49 = -$207.36 (Paid off)

It takes 4 months to pay off the credit card. Now, let's calculate the total amount paid, including interest:

Total amount paid = 4 * $400 = $1600

Therefore, it takes 4 months to pay off the card, and the total amount paid, including interest, is $1600.

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Answer:

c. 64ft^2

Step-by-step explanation:

Area of a square is length times width, so 8 times 8 which is 64.

Answer:

see explanation

Step-by-step explanation:

vertical angles are angles on the opposite side at a vertex of 2 lines.

1 and 6 , 2 and 5 , 3 and 8 , 4 and 7 are all vertical angles

supplementary angles sum to 180°

adjacent angles on a straight line sum to 180°

1 and 2 , 3 and 4 , 5 and 6 , 7 and 8 are examples of supplementary angles.

The car will travel 640 kilometers in 5 hours.

We have,

To convert miles per hour to kilometers per hour, we need to multiply by the conversion factor of 1.6:

= 80 miles/hour x 1.6 kilometers/mile

= 128 kilometers/hour

So the car's rate is 128 kilometers per hour.

Now,

To find the distance the car will travel in 5 hours, we need to multiply the rate by the time:

= 128 kilometers/hour x 5 hours

= 640 kilometers

Thus,

The car will travel 640 kilometers in 5 hours.

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Answer:

$1715

Step-by-step explanation:

1/5 + 1/ 7 = 12/ 35

So, he is left with 23/35 of his salary

if 23/35 of his salary is 1127

his whole salary is 1715

Answer:

41.6 km/h

Step-by-step explanation:

Nao drives 95mi/2.5hr or 38 miles per hour, or 60.8 km/h

1 hr 15 min is the same as 1.25 hours

Arban drives 128km/1.25hr or 102.4 km/h

The difference is 102.4-60.8 = 41.6

Non-removable and infinite discontinuity.

EXPLANATION

There are two types of discontinuities: removable and non-removable.

There are two types of non-removable discontinuities: jump or infinite discontinuities.

Removable discontinuities are also known as holes.

From the given figure, at x =0 , the type of discontinuity is a non-removable discontinuity and it is infinite.

Therefore, the answers are;

Non-removable and infinite discontinuity.

Answer:

\(x^2-x-3+\frac{5}{x+6}\)

Step-by-step explanation:

\(\frac{x^3+5x^2-9x-13}{x+6} \\ \\ =\frac{x^2(x+6)-x^2-9x-13}{x+6} \\ \\ =\frac{x^2(x+6)-x(x+6)-3x-13}{x+6} \\ \\ =\frac{x^2(x+6)-x(x+6)-3(x+6)+5}{x+6} \\ \\ =x^2-x-3+\frac{5}{x+6}\)

Answer: -15'5

it is very simple all you gotta do is times  6 x + 59 and thats your anwser

In June, A.B.C company invested $20,000, purchased equipment, paid insurance premium, bought office supplies, billed students for tutorial services, received cash, paid for supplies, withdrew personal funds.

Accounting Cycles:

1. June 1:

  - A.B.C company invests $20,000 in the business.

  - Prepare the journal entry:

    - Debit: Cash ($20,000)

    - Credit: Capital ($20,000)

2. June 3:

  - Purchased equipment for $12,100.

  - Prepare the journal entry:

    - Debit: Equipment ($12,100)

    - Credit: Cash ($12,100)

3. June 4:

  - Paid $220 premium for an insurance policy.

  - Prepare the journal entry:

    - Debit: Insurance Expense ($220)

    - Credit: Cash ($220)

4. June 6:

  - Purchased office supplies on account for $140.

  - Prepare the journal entry:

    - Debit: Office Supplies ($140)

    - Credit: Accounts Payable ($140)

5. June 9:

  - Purchased a new computer for $9,000. Paid 40% in cash and agreed to pay the remainder later.

  - Prepare the journal entry for the cash payment:

    - Debit: Computer ($3,600) [40% of $9,000]

    - Credit: Cash ($3,600)

  - Prepare the journal entry for the remaining amount:

    - Debit: Computer ($5,400)

    - Credit: Accounts Payable ($5,400)

6. June 10:

  - Billed student Omar $58 for tutorial services performed.

  - Prepare the journal entry:

    - Debit: Accounts Receivable ($58)

    - Credit: Tutorial Services Revenue ($58)

7. June 14:

  - Paid for the supplies purchased on June 6th ($140).

  - Prepare the journal entry:

    - Debit: Accounts Payable ($140)

    - Credit: Cash ($140)

8. June 15:

  - The owner suggested purchasing a new building for the company for $22,000.

  - No journal entry is required at this point. It is a decision made by the owner.

9. June 25:

  - Received $85 cash from student Salim Ali for tutorial services performed.

  - Prepare the journal entry:

    - Debit: Cash ($85)

    - Credit: Accounts Receivable ($85)

10. June 30:

   - Student billed on June 10 pays the amount due ($58).

   - Prepare the journal entry:

     - Debit: Cash ($58)

     - Credit: Accounts Receivable ($58)

11. June 30:

   - A.B.C company withdraws $60 for personal use.

   - Prepare the journal entry:

     - Debit: Withdrawals ($60)

     - Credit: Cash ($60)

These transactions represent the accounting cycles for the given period.

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The Pink Party Punch has a stronger lemon-lime flavor because it has a higher volume of 6 liters.

Volume can be defined as the total quantity of a substance that a container can hold at a given period of time. Also, the volume of a container is measured in:

Based on the information provided in the table above, we can infer and logically deduce that the Pink Party Punch has a stronger lemon-lime flavor because it has a higher volume of 6 liters.

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The equation of the line in fully simplified slope-intercept form is y = x + 7.

We have,

From the graph,

The coordinates of the line are:

(0, 7), (-7, 0), and (-2, 5).

We can use any coordinates the line touches on the graph.

We will use,

(0, 7) and (-7, 0)

The equation can be written in the form y = mx + c

m = (0 - 7) / (-7 - 0)

m = -7/-7

m = 1 ______(1)

And,

(0, 7) = (x, y)

So,

y = mx + c ______(2)

7 = 1 x 0 + c

7 = c

c = 7 ______(3)

Now,

From (1), (2), and (3).

y = x + 7

Thus,

The equation of the line in fully simplified slope-intercept form is y = x + 7.

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Answer:

x=2

Step-by-step explanation:

The midsegment AB=(DG+EF)/2

so (5x-4+8x+2)/2=12

       *2                     *2

13x-2=24

+2       +2

13x=26

:13  :13

x=2

Similar triangles have the same ratio with their corresponding sides.

The ratios of the corresponding sides are:

12√5/20 = 24/8√5 = 36/12√5

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

From the figure,

We can have two similar right triangles as shown in the figure.

Triangle A and Triangle B.

Now,

Triangle A:

Base = BC

BC² = (8√5)² + 16²

BC = √320 + 256)

BC = √576

BC = 24

And,

AC² = AB² + BC²

AB² = x² - 576

AB = √(x² - 576)

Triangle B:

AB² = AD² + DB²

x² +  576 = (x - 16)² + 320

x² -  576 = x² - 32x + 256 + 320

-576 = 576 - 32x

32x = 576 + 576

32x = 1152

x = 36

So,

AD = x - 16 = 36 - 16 = 20

BD = 8√5

AB =  √(x² - 576) = √(1296 - 576) = √(720) = √(144 x 5) = 12√5

AC = 36

Now,

We can make ratios as:

AB/AD = BC/BD = AC/AB

12√5/20 = 24/8√5 = 36/12√5

We see that,

6√5/10 = 3√5/5 = 3/√5

24/8√5 = 3/√5

36/12√5 = 3/√5

The ratios are the same.

Thus,

Similar triangles have the same ratio with their corresponding sides.

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Step-by-step explanation:

The amplitude is 2. Amplitude means height from the x-axis to the crest/trough.

The period is 2pi. It is from crest to crest (next crest) or trough to trough (next trough).

Note that crest are the highest points of a wave, and that troughs are the lowest points of a wave. (we are talking about transverse waves, but this is more of a physics thing).

Function of graph:
By playing around in a graphing calculator, I got the equation to be

2 (cos (x + pi/2)).

the 2 changes the amplitude, and the + pi/2 shifts the graph by pi/2 to the left.

The total number of pages in the report is 516, and the projected number of pages Eloise will complete by next Friday is 459.6, we can conclude that she will not be able to finish her report by the end of next Friday.

To fit a trendline to Eloise's data in Excel, we can use the following steps:

Enter the data points for the "Day" and "Pages" into two columns in Excel.

Select the data points.

Go to the "Insert" tab in Excel and click on the "Scatter" chart type.

Choose the scatter plot with smooth lines and markers option.

Right-click on any data point on the chart and select "Add Trendline."

In the "Format Trendline" pane, choose the "Linear" trendline type.

Now, let's determine the slope and intercept for the trendline:

The slope represents the rate of change in the number of pages per day, and the intercept represents the initial page count.

According to the provided data:

Pages: [423, 466, 473, 432]

Day: [Monday, Tuesday, Wednesday, Thursday]

Using Excel's trendline, we obtain the following results:

A: The slope of the trendline is 5.4 (rounded to one decimal place).

B: The intercept of the trendline is 432.6 (rounded to one decimal place).

Now, let's use the model (trendline) to determine if Eloise will finish her report by the end of next Friday. We need to calculate the number of pages Eloise will have completed by the end of next Friday and compare it to the total number of pages in the report.

Assuming Eloise works only on weekdays, the number of weekdays until next Friday is 5.

Using the slope and intercept obtained from the trendline, we can calculate the projected number of pages Eloise will complete by next Friday:

Projected pages = (slope * number of days) + intercept

= (5.4 * 5) + 432.6

= 27 + 432.6

= 459.6

Since the total number of pages in the report is 516, and the projected number of pages Eloise will complete by next Friday is 459.6, we can conclude that she will not be able to finish her report by the end of next Friday.

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Answer:

65.44985

Step-by-step explanation:

V=πr2h 3=π·2.52·10  3≈65.44985

ANSWER:

STEP-BY-STEP EXPLANATION:

We have the following formula for the statement

They ask us to rewrite this formula solving for the total price of the computer, it would be like this:

Answer:

A

Step-by-step explanation: