There are 12 girls and 10 boys in Mrs. Jones’ Kindergarten class. How many ways can she choose a line leader and a caboose each day?

After filling 1,295 bags of 6 ounces each, there will be 1 ounce of cookies left.

To find out how many bags of cookies can be filled, we need to divide the total number of ounces of cookies by the size of each bag:

7,771 ounces ÷ 6 ounces/bag = 1,295.1667 bags

We can't have a fraction of a bag, so we need to round down to the nearest whole number:

1,295 bags

Now we can find out how many ounces of cookies will be left by subtracting the total number of ounces used for the filled bags from the total number of ounces produced:

Total ounces produced - (number of bags filled × size of each bag)

= 7,771 ounces - (1,295 bags × 6 ounces/bag)

= 7,771 ounces - 7,770 ounces

= 1 ounce

Therefore, there will be 1 ounce of cookies left after filling as many 6-ounce bags as possible.

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Answer:

15

Step-by-step explanation:

180-15

Hello!

the sum of the angles in the triangle = 180°

so the 3rd angle = 180° - 165° = 15°

3900000×18% = 702000

702000÷2500 = 280.8 per share dividend

450×280.8 = 126360

A half-life of 9 minutes corresponds to a decay factor k such that

\(\dfrac12=e^{9k}\implies k=-\dfrac19\ln\left(\dfrac12\right)\)

Then the time it takes for the substance to decay from 610 g to 124 g is time t such that

\(124\,\mathrm g=(610\,\mathrm g)e^{kt}\)

Solve for t :

\(\dfrac{62}{305}=e^{kt}\)

\(\ln\left(\dfrac{62}{305}\right)=kt\)

\(t=\dfrac1k\ln\left(\dfrac{62}{305}\right)\approx20.686\)

so it takes about 20.7 min for the 610 g sample to decay down to 124 g.

If we divide 300 into parts using the ratio 2:3:5, we get:

2 parts = 2/10 of the total ratio = 2/10 x 300 = 60

3 parts = 3/10 of the total ratio = 3/10 x 300 = 90

5 parts = 5/10 of the total ratio = 5/10 x 300 = 150

Therefore, 300 divided in the ratio 2:3:5 would result in three parts of 60, 90, and 150.

I hope I helped!

~~~Harsha~~~

Answer:

(- 3, 1.5)

--------------------------

Given system:

The first expression is ready to be substituted as no further operation is required to simplify it.

Find x:

3.5 kilograms is 3500 grams

Answer: 3500

Step-by-step explanation: one kilogram is 1000 gram so multiply 3.5 x 1000

Answer: C

Step-by-step explanation:

The number of minutes for 20 bacteria be left is 439minutes. The decay constant is 0.0081

An exponential function is a mathematical function, which is used in many real-world situations. It is mainly used to find the exponential decay or exponential growth or to compute investments, model populations and so on.

The No of bacteria left at a particular time t is given as N(t)= Noe^-kt

where No= initial number of bacteria

k= decay constant and t = time

after 13 minutes

630= 700e^-13k

divide both sides by 700

630/700= e^-13k

0.9= e^-13k

ln0.9= -13k

k= ln0.9/-13 = -0.1054/-13 = 0.0081

time for 20 bacteria to be left =

20= 700e^-0.0081t

= 20/700=e^-0.0081t

0.0286= e^-0.0081t

ln0.0286= -0.0081t

-3.554= -0.0081t

divide both sides by -0.0081

t= -3.554/-0.0081= 439 minutes ( nearest minutes)

therefore the time for the bacteria to be left is 439minutes

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Answer:

=13/12=1 and 1/12

Step-by-step explanation:

hi

1/2= 6/12

1/4=3/12

1/3=4/12

6/12+3/12+4/12 = 13/12

break a legs!

The solutions to the system of equations are x = 2 and 4

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

f(x) = x - 3

g(x) = 1/(x - 3)

The solution to the system of equations implies that

f(x) = g(x)

So, we have

x - 3 = 1/(x - 3)

Cross multiply the equation

This gives

(x - 3)² = 1

So, we have

x - 3 = ±1

Add 3 to both sides

x = 3 ± 1

So, we have

x = 2 and 4

Hence, the solutions to the system of equations are x = 2 and 4

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Weight of Omar after 4 weeks is 9.4375 pounds.

The same attribute is expressed using a unit conversion, but in a different unit of measurement.

For instance, time can be expressed in minutes rather than hours, and distance can be expressed in kilometres, feet, or any other measurement unit instead of miles.

Given:

Weight of Omar at the time of birth = 8 pound 3 ounces

Weight gained by Omar in 4 weeks = 5 × 4 = 20 ounces

New weight of Omar

= (8 lb 3 ounces) + 20 ounces

= 8 lb + 23 oz

As, we know 16 ounces = 1 pound

23 ounces = 1.4375 pound

Now, total weight of Omar after 4 weeks = 8 lb + 23 oz

                                                                  ≈ 8 lb + (1.4375) lb

                                                                   ≈ 9.4375 pounds

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Answer:

I would say 1,749,600

Step-by-step explanation:

Answer:

Step-by-step explanation:

If the diameter is 4 meters, then the radius has to be 2 because the radius is half of the diameter.

The benefit of obtaining a personal loan is getting large amounts of money to use immediately.

Option D is the correct answer.

A personal loan is a type of loan that individuals can take out from a bank, credit union, or online lender to cover personal expenses such as home improvements, medical bills, or other unexpected expenses.

We have,

The benefit of obtaining a personal loan can vary depending on the specific terms and conditions of the loan, but typically it allows individuals to borrow a larger amount of money upfront with a fixed interest rate and set repayment schedule, which can be beneficial for large expenses such as home renovations, debt consolidation, or major purchases.

However, the interest rates and repayment terms can vary depending on the borrower's credit score, income, and other factors, so it's important to compare options and choose a loan that meets one's specific needs and budget.

Thus,

The benefit of obtaining a personal loan is getting large amounts of money to use immediately.

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Answer:

D. 5

Step-by-step explanation:

From the information given:

The derivatives of functions and functions have a different average rate. The average rate expanded over an interval of two distinct point (a f(a)) and (b f(b)) is represented by the equation:

\(\dfrac{f(b)-f(a)}{b-a}\)

where; the two points are:

(-1 , f( -1) )    &    ( 1,  f(1) )

For f(1); we have:

f(1) = 1 +3(1)³ - 5(1)² + 2(1) - 2

f(1) = 1 + 3 - 5 + 2 -2

f(1) = - 1

For  f( -1); we have:

(-1)⁴ + 3(-1)³ - 5(-1)²+2(-1)-2

= 1 - 3 - 5 -2 - 2

= -11

∴

\(=\dfrac{-1-(-11)}{1 - (-1)}\)

\(=\dfrac{-1+11}{1 +1}\)

\(=\dfrac{10}{2}\)

= 5

3^3 = 27, so 3 is a good value.

(-3)^3 = -27, not it's not -3

9^3 = 729, so 9 is not good.

(-9)^3 = -729, so -9 is not good.

The answer is A) x=3.

Answer:

2x^4−11x^3+7x^2+5x−3

Step-by-step explanation:

The  ^  means exponent

Answer:

The Area of the trapezium is \(60cm^2\)

Step-by-step explanation:

Given,

Height (h)= 8cm

Sum of the parallel sides (a+b)= 15cm

Area of trapezium = \(1/2*h*(a+b)\)

                              =\(1/2*8*15\)

                              =\(4*15\)

Area of trapezium=60cm^2

Answer: Area = 60 cm²

Step-by-step explanation:

To find the area of a trapezium we use the formula

Area of trapezium = 1/2 (sum of parallel sides) × height

∴ Area = 1/2 ×15 cm × 8 cm

           = 60 cm²

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Answer:

$7/lb

Step-by-step explanation:

$70 / 10 lb = $7/lb

Answer:

$7 per pound of letuce

Step-by-step explanation:

We know

10 pounds = $70

1 pounds = ?

We cross multiply and get:

$7 per pound of letuce

So, the answer is $7 per pound of letuce

Answer:

To find the effective annual rate (EAR) of an account that pays interest at the nominal rate of 7% per year, compounded daily, we can use the following formula:

EAR = (1 + r/n)^n - 1

where r is the nominal annual interest rate (expressed as a decimal), and n is the number of times the interest is compounded in a year.

For daily compounding, n = 365 (since there are 365 days in a year), so we have:

EAR = (1 + 0.07/365)^365 - 1 = 0.0725 or 7.25%

To find the effective annual rate for hourly compounding, we need to adjust the value of n to account for the fact that interest is compounded more frequently. There are 365 days * 24 hours = 8,760 hours in a year, so we can use n = 8,760:

EAR = (1 + 0.07/8760)^8760 - 1 ≈ 0.0727 or 7.27%

Therefore, the effective annual rate for hourly compounding is approximately 7.27%.

The Polynomial x⁵ + x³ - 5 is divided by x - 2, the quotient is x⁴ + 3x³ + 6x² + 12x + 24, and the remainder is 48.

The quotient and remainder when the polynomial x⁵ + x³ - 5 is divided by x - 2, we can use polynomial long division. Here's the step-by-step process:

1. Write the dividend (x⁵ + x³ - 5) and the divisor (x - 2).

   x - 2 | x⁵ + x³ + 0x² + 0x - 5

2. Divide the first term of the dividend (x⁵) by the first term of the divisor (x) to get x⁴. Write x⁴ above the line. x⁴

   x - 2 | x⁵ + x³ + 0x² + 0x - 5

3. Multiply the divisor (x - 2) by the quotient term (x⁴) to get x⁵ - 2x⁴. Write this under the dividend and subtract it.  x⁴

  x - 2 | x⁵ + x³ + 0x² + 0x - 5

 - (x⁵ - 2x⁴)

3x⁴ + 0x³ + 0x² + 0x - 5

4. Bring down the next term (-5) from the dividend.

x⁴ + 3x³

x - 2 | x⁵ + x³ + 0x² + 0x - 5

- (x⁵ - 2x⁴)

3x⁴ + 0x³ + 0x² + 0x - 5

5. Divide the first term of the new dividend (3x⁴) by the first term of the divisor (x) to get 3x³. Write 3x³ above the line.

 x⁴ + 3x³

   x - 2 | x⁵ + x³ + 0x² + 0x - 5

 - (x⁵ - 2x⁴)

3x⁴ + 0x³ + 0x² + 0x - 5

6. Multiply the divisor (x - 2) by the new quotient term (3x³) to get 3x⁴ - 6x³. Write this under the new dividend and subtract it.

x⁴ + 3x³

x - 2 | x⁵ + x³ + 0x² + 0x - 5

- (x⁵ - 2x⁴)

3x⁴ + 0x³ + 0x² + 0x - 5

- (3x⁴ - 6x³)

6x³ + 0x² + 0x - 5

7. Repeat steps 4-6 until you have subtracted all terms.

x⁴ + 3x³ + 6x² + 12x + 24

x - 2 | x⁵ + x³ + 0x² + 0x - 5

- (x⁵ - 2x⁴)

3x⁴ + 0x³ + 0x² + 0x - 5

- (3x⁴ - 6x³)

6x³ + 0x² + 0x - 5

- (6x³ - 12x²)

12x² + 0x + 0

 - (12x² - 24x)

 24x + 0

- (24x - 48)

 48

8. The quotient is x⁴ + 3x³ + 6x² + 12x + 24, and the remainder is 48.

Therefore, when the polynomial x⁵ + x³ - 5 is divided by x - 2, the quotient is x⁴ + 3x³ + 6x² + 12x + 24, and the remainder is 48.

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Answer:

angle a is acute and angle b is obtuse

Step-by-step explanation:

a) 004 044 000

040 404 444 8 numbers

400 440

b) None

c) None, because we only have 2 digits, I need to repeat at least 1 number.

Answer:

20:30 goes to 8:12

the rest goes to 6:18

Step-by-step explanation:

i may be wrong

Answer:

7:12 is equivalent to 6:18

20:30 is equivalent to 8:12

5:15 is equivalent to 6:18

Step-by-step explanation:

plz mark brainliest

Simplifying this equation, we get:

8 + 4k + 4k + 6 = 30

8k + 14 = 30

8k = 16

k = 2

Therefore, the value of k is 1.

In mathematics, a polynomial is an expression consisting of variables (usually represented by x), coefficients, and non-negative integer exponents, which are combined using the operations of addition, subtraction, and multiplication. For example,

\(3x^2 + 2x - 1\)

is a polynomial with three terms, or a "trinomial," where the variable x is raised to the powers of 2 and 1, and the coefficients are 3, 2, and -1.

The degree of a polynomial is the highest power of the variable in the expression. For example, the polynomial above has a degree of 2, since the highest power of x is 2.

Polynomials are used in many areas of mathematics, including algebra, calculus, and geometry, and are used to model many real-world phenomena.

We can use the remainder theorem, which states that if a polynomial f(x) is divided by (x - a), then the remainder is equal to f(a). In this case, we know that when the polynomial\(l x^3 + kx^2 + 2kx\) + 6 is divided by (x - 2), the remainder is 30. So, we can set up the following equation:

\(x^3 + kx^2 + 2kx + 6 = (x - 2)q(x) + 30\)

where q(x) is the quotient when. \(x^3 + kx^2 + 2kx + 6\) is divided by (x - 2). We don't need to know what q(x) is, since we're only interested in finding k.

Now, let's substitute x = 2 into the equation above:

\(2^3 + k(2^2) + 2k(2) + 6 = (2 - 2)q(2) + 30\)

Simplifying the left-hand side, we get:

\(8 + 4k + 4k + 6 = 30\)

\(16k = 16\)

\(k = 1\)

OR

8 + 4k + 4k + 6 = 30

8k + 14 = 30

8k = 16

k = 2

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Answer:

a. 5.0 and 2.18, respectively

Step-by-step explanation:

n = numbers of spins = 100 times

p = 0.55 - 0.50 = 0.05

q = 1 - 0.05 = 0.95

Mean = n x p = 100 x 0.05 = 5

Standard Deviation = \(\sqrt{npq}\)

Standard Deviation = \(\sqrt{100 X 0.05 X 0.95}\)

Standard Deviation = \(\sqrt{4.75}\)

Standard Deviation = 2.1794

Standard Deviation = 2.18

The number of tickets which should be sold to $24 and $40 are 4500 and 1500 respectively.

Given, A 6000-seat theater has tickets for sale at $24 and $40.

How many tickets should be sold at each price for a sellout performance to generate a total revenue of $168,000 = ?

first, assign variables:

X = # of $24 tickets,  Y = # or $40 tickets

write equations based on the data presented:

"6000 seat theater..."

   X + Y = 6000 ...equation 1

"total revenue of 168,000"

The revenue from each type of ticket is the cost times the number sold, so:

  24X + 40Y = 168,000 .....equation 2

from equation 1:

   X = 6000 - Y

substitute this into equation 2:   (replace X with 6000-Y)

   24 (6000 - Y) + 40Y = 168,000

expand:

144,000 -24Y + 40Y = 168,000

rearrange and simplify:

    16Y = 168,000 - 144,000

    y = 24000/16

     Y = 1500

from equation 1:

     X = 6000 - 1500

     X = 4500

hence the number of tickets for sale at $24 should be 4500.

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Answer:

Total Weight of all the five boys is 234 kg.

Step-by-step explanation:

Given that there are five boys.

They have weighed themselves in pairs in all possible combinations.

And their weights are: 88 kg, 90 kg, 91 kg, 92 kg, 93 kg, 94 kg, 95 kg, 96 kg, 98 kg and 99 kg

To find: Total weights of the five boys = ?

Solution:

First of all, we need to find the total number of pairs that can be formed from a total of 5 number of boys.

Total number of pairs possible = \(_5C_2 =10\)

If we select one boy, there are 4 other boys with whom pairs can be formed.

So, every boy's weight is repeated 4 number of times in these 10 pairs.

If we add all the 10 measured weights given and then divide them with 4 we will get the total weight of the five boys.

\(\text{Total weight of boys = } \dfrac{88+90+91+92+93+94+95+96+98+99}{4}\\\Rightarrow \text{Total weight of boys = } \dfrac{936}{4}\\\Rightarrow \text{Total weight of boys = } 234\ kg\)

So, Total Weight of all the five boys is 234 kg.