. A sheet of card is 20 centimetres by 30 centimetres. What is
the maximum number of circular name badges, of diameter
60 millimetres, that can be cut from this piece of card?

Answer:

2/3 + 1/3 = 3/4

Step-by-step explanation:

you have 3/4 you can minus the 3/4 by 1/4 to get 2/4 then you can check by adding 2/4 and 1/4 together to get 3/4.

The speed of the plane is equal to 120 mph.

In Mathematics and Geometry, speed is the distance covered by a physical object per unit of time. This ultimately implies that, speed can be measured by using miles per hour (mph).

Mathematically, the speed of any a physical object can be calculated by using this formula;

Speed = distance/time

Time = distance/speed

Let the variable s represent the speed of the plane in miles per hour. Therefore, an equation that models the situation can be written as follows;

240/s = 80/s - 80

80s = 240s - 19200

19200 = 160s

s = 19200/160

s = 120 mph.

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Answer:

675

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Step-by-step explanation:

Step 1: Define

(5t - 3) · (3t + 7)

t = 6

Step 2: Evaluate

Answer:

(5t -3)(3t+7) (im multiplying them together, if that's not what the questions asking lmk. but anyway, put them next to eachother and then plug in 6 for t)

(5(6) -3)(3(6)+7) (multiply where possible)

(30 -3)(18+7) (use the distributive property/foil to multiply the two)

540 +210 -54 -21 (add the positive numbers and subtract the negative )

750 - 75 (subtract)

675 (the answer)

Step-by-step explanation:

I hope this helps :)

Step-by-step explanation:

please mark me as brainlest

Answer:

x=61

Step-by-step explanation:

55(x+3)+x=180

combine like terms

58+x+x=180

58+2x=180

subtract 58 from both sides

2x=122

divide both sides by 2

x=61

Answer:

4 days and 18 hours.

Step-by-step explanation:

1440 Watt hours = 1 day

6840 Watt hours = x

Cross multiply.

1440*x = 6840*1

1440x = 6840

Divide both sides by 1440.

1440x/1440 = 6840/1440

x = 4.75 days

4.75 days is 4 days and 3/4 of a day; because 3/4 = 0.75

We have to find 3/4 of 1 day.

1 day is 24 hours.

3/4* 24

Divide 24 by 4.

3*6 = 18

So, 18 hours.

Therefore a light bulb consumes 6840 Watt hours in 4 days and 18 hours.

I hope this helps. please give brainliest, thank and rate 5 stars.

The required time that is required to consume 6840 watt-hours is 4.75 days.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
a light bulb consumes 1440 Watt-hours per day.. how long it takes to consume 6840 watt-hours​ is to be determined.

In 1 day electricity used = 1440 Watt-hours
Number of days to use 6840 watt- hours = 6840 / 1440 = 4.75 days

Thus, the required time that is required to consume 6840 watt-hours is 4.75 days.

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Answer: They are not parallel, they are coincident

Step-by-step explanation:

If two lines have the same slope but a different y-intercept, the lines are parallel. If two lines have the same slope and the same y-intercept, the lines are coincident.

We can rewrite 5x−y=−5 adding -5x to both sides and multiplying by -1:

5x - y =-5

5x - y -5x = -5 - 5x (adding -5x to both sides)

-y = -5 - 5x

Multiplying by -1

y = 5x + 5

Both equations look the same so they are coincident. They have the same intercept y=5 and the same slope m=5.

Answer:

that's confusing.. is there a picture?

c=2πr

119.32=2πr

119.32=2*3.14r

119.32/(2*3.14)=r

r=19

d=2r

d=2*19

ANSWER: d=38cm

Answer:

We can use the formula for compound interest to find the future value (FV) of Natalie's investment:

FV = P * (1 + r/n)^(n*t)

Where:

P is the principal amount (the initial investment), which is $2,000 in this case

r is the annual interest rate as a decimal, which is 11% or 0.11

n is the number of times the interest is compounded per year, which is 12 since interest is compounded monthly

t is the number of years, which is 20

Substituting the values into the formula, we get:

FV =

2

,

000

∗

(

1

+

0.11

/

12

)

(

12

∗

20

)

�

�

=

2,000 * (1.00917)^240

FV = $18,255.74

Therefore, after 20 years of compounded monthly interest at a rate of 11%, Natalie's investment of 2,000 will be worth approximately 18,256.

Answer:

$17,870

Step-by-step explanation:

You must use the formula for compound interest.

A = P(1 + r/n)^nt

I suggest you look it up at some point so that you can do these more easily in the future!

Answer:

all two digit whole number which are divisible by 11 are

22+33+44+55+66+77+88+99=484

Answer: 495

Step-by-step explanation:

11+22+33+44+55+66+77+88+99 =495

a) The null hypothesis is: \(H_0: p \leq 0\)

b) The alternative hypothesis is: \(H_1: p > 0\)

c) The test statistic is: z = 9.71.

d) The correct option is of: A. Yes.

e) The confidence interval is of: 0.0819 < p < 0.1336.

At the null hypothesis, it is tested if there is not enough evidence that the proportion for men is greater, that is, the subtraction is not greater than 0:

\(H_0: p \leq 0\)

At the alternative hypothesis, it is tested if there is evidence that the proportion for men is greater, that is, if the subtraction is greater than 0, hence:

\(H_1: p > 0\)

We have a right-tailed test, as we are testing if the mean is greater than a value, with a significance level of 0.01, hence the critical value is of:

z = 2.327.

Thus the decision rule regarding the test statistic is given as follows:

For each sample, the mean and the standard error are given as follows:

Hence, for the distribution of differences, the mean and the standard error are given as follows:

The test statistic is given by the division of the mean by the standard error of the sampling distribution of the difference of sample proportions, hence:

z = 0.1078/0.0111 = 9.71.

z > 2.327 -> enough evidence that the proportion is greater.

The confidence interval is obtained as the mean plus/minus the multiplication of the standard error and of the critical value.

Then the bounds of the interval are:

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Answer:

3

Step-by-step explanation:

since 4 is made of four 1s 3 of them is 3

Answer:

1 in 12 chance of landing on 3

1 in 12 chance of landing on 4

1 in 6 chance of landing on either 3 or 4

Step-by-step explanation:

12 equal sections means probability is 1 in 12 of landing on any one numbered section.

2 in 12 or 1 in 6 chance of landing on either of two numbered sections in one attempt.

\(6\left[\cos\left( \frac{11\pi }{6} \right) +i\sin\left( \frac{11\pi }{6} \right) \right] \\\\\\ 6\left[\cfrac{\sqrt{3}}{2}~~,~-\cfrac{1}{2}i \right]\implies (3\sqrt{3}~~,~-3i) ~~ \approx ~~ \stackrel{ \textit{\LARGE S} }{(5.2~~,~-3i)}\)

The cost of the ticket based on the values that we have here would be = $9.50

A straight-line link between two variables is referred to statistically as a linear relationship (or linear association).

We have the linear relationship as y = mx + c

This is given as

y2 - y1 = x2 - x1

wher we have the value of y2 = 62.50 dollars

y1 = 43.50 dollars

x 2 = 5

x 1 = 3

When we put these values in the equation, what we would have would be:

62.50 - 43.50 / 5 - 3

= 19 / 2

= 9.5

Hence the cost that one of the tickets would have would be 9.5 dollars. Option D is the correct answer to the question that we have here.

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Considering the definition of percent of error, the Stephanie’s percent of error in this case is 5.042%.

Percent of error is a measure of how inaccurate a measurement is, standardized based on the size of the measurement.

In other words, the percent of error allows knowing the differences between the estimated value and the real value. The error may be due to the measurement method (tool or human error) or due to approximations used in the calculation (for example, rounding errors).

To calculate the percent of error you must:

Therefore, the expression for calculating the percent of error is

percent of error= [|real value - estimated value|÷ real value]×100

In this case, you know:

Replacing in the definition of percent of error:

percent of error= [|8.33 pounds - 8.75 pounds|÷ 8.33 pounds]×100

Solving;

percent of error= [|-0.42 pounds|÷ 8.33 pounds]×100

percent of error= [0.42 pounds÷ 8.33 pounds]×100

percent of error= 0.05042×100

percent of error= 5.042%

Finally, the percent of error in this case is 5.042%.

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Answer:

Step-by-step explanation:

Step-by-step explanation:

31 + 6x + x + 16 = 180

7x + 47 = 180

7x = 180 - 47

x = 133/7

x = 19

Answer:

The speed of the plane in the still air is 420 miles/hour

The speed of the wind 60 miles/hour

Step-by-step explanation:

Let the speed of the plane with the wind be v

Let the speed of the plane against the wind be u

Now, speed = distance/time

With the wind,

v = (1440 miles)/(3 hours) = 480 miles/hour

v = 480 miles/hour

Against the wind,

u = (1440 miles)/(4 hours) = 360 miles/hour

u = 360 miles/hour

Now, let the speed of plane be p, and speed of wind be w,

Now, with the wind, the speed is 480 mph,

so,

speed of plane + speed of wind = 480 mph

p + w = 480  (i)

and against the wind, the speed is 360 mph,

so,

speed of plane - speed of wind = 360mph

p-w = 360 (ii)

adding equations (i) and (ii), we get,

p+w + p-w = 480 + 360

2p = 840

p = 840/2

p = 420 miles/hour

Then, the speed of the wind will be,

p + w = 480,

420 + w = 480

w = 480 - 420

w = 60 miles/hour

The speed of the plane in still air is calculated to be 420 mph, and the speed of the wind is calculated to be 60 mph by solving the two simultaneous equations obtained from the time, rate, and distance relationship.

This problem is about the rate, time, and distance relationships. The rate at which the airplane travels in still air is r (unaffected by wind), and the speed of the wind is w. When the plane flies with the wind, it is 'assisted' and therefore travels faster - at a speed of (r + w); against the wind, it travels slower - at a speed of (r - w).

From the problem, we know that:

By solving these two equations, we get the following:

Adding these two gives 2r = 840 => r = 420 mph (the speed of the plane in still air), and subtracting gives 2w = 120 => w = 60 mph (the speed of the wind).

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Answer:

\(F^{-1} (x) = 2x + 12\)

Step-by-step explanation:

Let's assume F(x) = y, then

\(y = \frac{1}{2} x - 6\)

Let us solve the equation for x.

\(y + 6 = \frac{1}{2} x\)

\(2y + 12 = x\)

Next, replace y with x and also replace x with F⁻¹(x)

Answer: \(F^{-1} (x) = 2x + 12\)

Total water bill for the month is $62.37.

It seems that you may have accidentally left out the total amount of your water bill.

The total amount by simply adding the amounts of the individual bills together:

Total water bill =\($36.34 + $26.03\)

= \($62.37\)

You have not provided enough information to determine your total water bill.

You have only given the amounts of your individual bills from Metro Water Services and Madison Suburban Utility District.

To find your total water bill, you simply need to add the two bills together.

So, the total amount you owe for water this month would be:

Total water bill = \($36.34 + $26.03\)

= \($62.37\)

It appears that you may have forgotten to include the full amount of your water bill by accident.

Simple addition of the separate bill amounts yields the following sum:

Water bill total = \($36.34 + $26.03\)

= \($62.37\)

Your total water bill cannot be calculated because not enough information has been given.

Only the amounts of your individual Metro Water Services and Madison Suburban Utility District bills have been provided.

You just need to combine the two invoices together to get your total water bill.

As a result, this month's total water bill for you would be:

Water bill total =  \($36.34 + $26.03\)

= \($62.37\)

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Answer:

A)

Step-by-step explanation:

Trust

Answer:

Let us assume that √2 is a rational number.

So it can be expressed in the form p/q where p, q are co-prime integers and q≠0

√2 = p/q

Here p and q are coprime numbers and q ≠ 0

Step-by-step explanation:

√2 = p/q

On squaring both the sides we get,

=>2 = (p/q)2

=> 2q2 = p2……………………………..(1)

p2/2 = q2

So 2 divides p and p is a multiple of 2.

⇒ p = 2m

⇒ p² = 4m² ………………………………..(2)

From equations (1) and (2), we get,

2q² = 4m²

⇒ q² = 2m²

⇒ q² is a multiple of 2

⇒ q is a multiple of 2

Hence, p, q have a common factor 2. This contradicts our assumption that they are co-primes. Therefore, p/q is not a rational number

√2 is an irrational number.

Alex spend $1507.92 in total to buy this stock at 3% charges on each shares.

Shares represent equity ownership in a corporation or financial asset, owned by investors who exchange capital in return for these units.

Alex buys 30 shares of Walmart at the close price of $48.80.

His broker charges him 3% of each share.

Purchasing of 30 shares =48.80 *30

                                         =$1464

Now we have to find the 3% of total purchasing of shares.

So,

Broker's fees =\(\frac{3}{100}*1464\)

                      = 0.03 * 1464

                      = 43.92

So, total cost of stock= 1464+43.92

                                   = 1507.92

Hence, Alex spend $1507.92 in total to buy this stock.

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You have the following PQRS points:

P(2,2) Q(5,2) R(5,6) S(2,6)

which are transformed to the following P'Q'R'S' points:

P(-6,2)Q(-3,2)R(-3,6)S(-6,6)

You can notice that the y coordinate does not change in the transformation.

Furthermore, for the x coordinate, you can notice that each number is decreased in 8 units.

For example, for x coordintate of point P:

2 - 8 = - 6 (which is the coordinate of thenew point P')

Hence, the answer is:

A. Translation of 8 units down

Answer:

2a + b

Step-by-step explanation:

volume = 8a³ + b³ + 12a²b + 6ab² = (2a + b)³

volume = ( Side of the cube )³

( Side of the cube )³ = (2a + b)³

Side of the cube = 2a + b

Answer:

A = $2130.49

Step-by-step explanation:

Given the following data;

Time, t = 5 years

Interest rate, r = 8%

Principal = $1450

To find the future value, we would use the compound interest formula;

\( A = P(1 + \frac{r}{100})^{t}\)

Where;

A is the future value.

P is the principal or starting amount.

r is annual interest rate.

t is the number of years for the compound interest.

Substituting into the equation, we have;

\( A = 1450(1 + \frac{8}{100})^{5}\)

\( A = 1450(1 + 0.08)^{5}\)

\( A = 1450(1.08)^{5}\)

\( A = 1450 * 1.4693 \)

A = $2130.49

Answer:

answer

A) 11.7²+X.6²

B) 7²+10² 0²

Paul pays 1/10 of the holiday cost, while Billy pays 1/2 and Joe pays 2/5.

To determine the fraction of the holiday cost that Paul pays, we need to find the remaining portion after Billy and Joe have paid their shares.

Let's start by calculating the sum of the fractions Billy and Joe have paid:

Billy's share = 1/2

Joe's share = 2/5

To find the combined share of Billy and Joe, we add their fractions:

1/2 + 2/5

To add these fractions, we need a common denominator. The least common multiple of 2 and 5 is 10. So, we can convert the fractions to have a common denominator of 10:

1/2 = 5/10

2/5 = 4/10

Now, we can add the fractions:

5/10 + 4/10 = 9/10

Billy and Joe have paid a combined fraction of 9/10 of the holiday cost. To find the fraction that Paul pays, we need to determine the remaining portion, which can be calculated by subtracting the combined fraction from 1 (since 1 represents the whole).

Remaining fraction = 1 - 9/10

= 10/10 - 9/10

= 1/10

Therefore, Paul pays 1/10 of the holiday cost.

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