Find the difference

-8 - 3

-Let be "p" the number of boxes of pens that Leona ordered and "r" the number of rubber bands she ordered.

According to the information given in the exercise:

- The cost of 1 box of pens is $18 and the cost of 1 box of rubber bands is $6.

- Leona ordered 20 cartons.

- The total cost was $300.

Using this information you can set up the following System of Equations:

In order to solve it, you can apply the Elimination Method:

1. Multiply the second equation by -6.

2. Add the equations.

3. Solve for "p".

Then:

4. Substitute the value of "p" into the second original equation.

5. Solve for "r".

Then:

Therefore, the answer is: Leona ordered 15 boxes of pens and 5 boxes of rubber bands.

Answer:

-Let be "p" the number of boxes of pens that Leona ordered and "r" the number of rubber bands she ordered.

According to the information given in the exercise:

- The cost of 1 box of pens is $18 and the cost of 1 box of rubber bands is $6.

- Leona ordered 20 cartons.

- The total cost was $300.

Answer:

4296 kg

Step-by-step explanation:

40/100 = x/7160

716 times 6 is 4296

Answer:

= 11√2 - 5√7

Step-by-step explanation:

9√2 - 3√7 + √8 - √28

= 9√2 - 3√7 + 2√2 - 2√7

add similar elements

= 11√2 - 3√7 - 2√7

= 11√2 - 5√7

Answer:

11\(\sqrt{2}\) - 5√7

Step-by-step explanation:

= 9\(\sqrt{2}\) - 3\(\sqrt{7}\) + 2√2 - 2\(\sqrt{7}\)

= 11\(\sqrt{2}\) - 3\(\sqrt{7}\) - 2\(\sqrt{7}\)   add similar elements

= 11\(\sqrt{2}\) - 5\(\sqrt{7}\)

Answer:

-1

Step-by-step explanation:

Answer:

m<A = 35

m<B = 55

Step-by-step explanation:

Complementary angles mean the 2 angles add up to 90 so:

y - 16 + y + 4 = 90

2y - 12 = 90

2y = 102

y = 51

m<A:

y - 16

51 - 16

35

m<B:

y + 4

51 + 4

55

The race horse's speed is approximately 256 furlongs per fortnight.

To determine the race horse's speed in furlongs per fortnight, we need to convert both the distance and time units to their respective values.

1 furlong is equal to 180 yards, so the horse's speed in yards per second (7 yards/second) can be converted to furlongs per second:

Speed in furlongs per second = (7 yards/second) / (180 yards/furlong) = 7/180 furlongs/second

Next, we need to convert the time from seconds to fortnights. Since a fortnight is a time period of two weeks, and there are 7 days in a week, a fortnight consists of 14 days:

Time in seconds per fortnight = (14 days/fortnight) * (24 hours/day) * (60 minutes/hour) * (60 seconds/minute) = 1,209,600 seconds/fortnight

Finally, we can calculate the horse's speed in furlongs per fortnight by multiplying the speed in furlongs per second by the time in seconds per fortnight:

Speed in furlongs per fortnight = (7/180 furlongs/second) * (1,209,600 seconds/fortnight) = 46,080/180 furlongs/fortnight ≈ 256 furlongs/fortnight

The race horse's speed is approximately 256 furlongs per fortnight.

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The 10th term of the geometric sequence will be 1,536. Then the correct option is C.

A series of non-zero integers where every term after the first is obtained by increasing the one before it by a constant, non-zero value known as the scale factor.

Let a₁ be the first term and r be the common ratio.

Then the nth term of the geometric sequence is given as,

aₙ = a₁ · (r)ⁿ⁻¹

The given information is a₅ = 48 and a₈ = 384. Then the equations are given below.

a₁ · (r)⁴ = 48           ...1

a₁ · (r)⁷ = 384        ...2

From equations 1 and 2, then we have

r⁷ / r⁴ = 384 / 48

r³ = 8

r = 2

Then the value of the first term is given as,

a₁ · (2)⁴ = 48

a₁ · 16 = 48

a₁ = 3

Then the 10th term of the geometric sequence will be given as,

a₁₀ = 3 · (2)¹⁰⁻¹

a₁₀ = 3 · (2)⁹

a₁₀ = 3 · 512

a₁₀ = 1,536

The 10th term of the geometric sequence will be 1,536. Then the correct option is C.

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By following these steps, you should be able to find the number of counties in Texas with childcare programs offering nighttime care for children.

To answer your question about how many of the 254 counties in Texas have child care programs that state they provide nighttime care for children, we would need to access current data on child care programs in Texas. Unfortunately, I do not have that specific data at the moment. However, I can guide you on how to find this information.
Begin by visiting the Texas Health and Human Services website (https://hhs.texas.gov) as they are responsible for overseeing child care licensing in the state. Look for information on licensed child care facilities that provide nighttime care.
Utilize websites such as Child Care Aware (https://www.childcareaware.org) or Child Care Finder (https://childcarefinder.com), where you can search for child care programs in Texas by county, and filter your search to include only programs offering nighttime care.
You may also want to check with local county websites or contact the County Clerk's office for information on child care programs within their jurisdiction, specifically those offering nighttime care.
Compile the data gathered from the above sources to determine how many of the 254 Texas counties have child care programs providing nighttime care for children.
By following these steps, you should be able to find the number of counties in Texas with child care programs offering nighttime care for children.

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Answer:

Irrational numbers cannot be written as a fraction, or the ratio of two whole numbers.

You would have to find a GCF (greatest common factor) and multiply it out of the radical.

ex.

\(\sqrt{6}\) = 2 x 2 x 2

when you have to multiplier numbers then you can combine two of them to take outside the radical, meaning 2x2x2

2\(\sqrt{2\\}\)

so \(\sqrt{6}\) would be closest to the positive 2 on the number line and 2 notches.

\(\sqrt{11}\)

is an irrational number, so it might fall into 3.3 if turned into a decimal.

Step-by-step explanation:

The corresponding joint probability distribution is:

X\Y 0 1

0 1/12 1/4

1 1/6 1/2

Since X and Y are independent, the joint probability distribution is simply the product of their marginal probability distributions:

f(x,y) = f(x) × f(y)

Therefore, we have:

f(0,0) = f(0) ×f(0) = (1/3) × (1/4) = 1/12

f(0,1) = f(0) × f(1) = (1/3) × (3/4) = 1/4

f(1,0) = f(1) × f(0) = (2/3) × (1/4) = 1/6

f(1,1) = f(1) ×f(1) = (2/3) × (3/4) = 1/2

Therefore, the corresponding joint probability distribution is:

X\Y 0 1

0 1/12 1/4

1 1/6 1/2

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Answer:

I would say about 60%

Step-by-step explanation:

since odd numbers are 3 of the 5 total cards 3/5 gets you 60% likely to pull qn odd number.

Answer:

3.6

Step-by-step explanation:

sorry for the weird looking numbers, I used my mouse to write this

Answer:

The amount that will be in Heidi’s account after 15 years is option A. $164,146.52.What is  Future Value?It can be calculated using the formula for calculating the Future Value (FV) of an Ordinary Annuity as follows:FV = M  (((1 + r)^n - 1) / r)Where;FV = Future value of the amount need to findM = total monthly contribution which is Heidi’s monthly contribution of 11% of her monthly salary + Employer monthly contribution of 6% of Heidi’s monthly salary can be calculated as;= (11% of Heidi’s monthly salary + 6.25% of Heidi’s monthly salary) = (11% of $3,250) + (6.25% x $3,250) = $552.50r = Monthly interest rate= Annual interest rate of 401(k) / 12 = 6.25% / 12 = 0.0625 / 12 r = 0.00520833333333333n = number of months = Number of years x 12 = 15 x 12 n= 180Substituting all the values into equation (1), we have;FV = $552.50  (((1 + 0.00520833333333333)^180 - 1) / 0.00520833333333333)FV = $552.50 x 297.097770863934FV = $164,146.518402324Rounding to the nearest cent, we get;FV = $164,146.52Therefore, the amount that will be in Heidi’s account after 15 years is option A. $164,146.52.

Step-by-step explanation:

.

The coordinate (13, 22) is not on the line since the y-coordinate is 21

The equation of a line in point slope form is expressed as:

y - ya =m(x-xb)

where

m is the slope = 3/2

(xa, ya) is the point. = (1, 3)

Substitute

y - 3 = 3/2(x - 1)

For the coordinate (3, 6). Substitute x = 3and check if the output will be 6

y = 1.5(3 - 1) + 3

y = 1.5(2) + 3

y = 6

Hence the coordinate (3, 6) is on the line since the y-coordinate is 6

For the coordinate (0, 0). Substitute x = 0 and check if the output will be 0

y = 1.5(0 - 1) + 3

y = 1.5(-1) + 3

y = 1.5

Hence the coordinate (0, 0) is not on the line since the y-coordinate is 1.5

For the coordinate (13, 22). Substitute x = 13 and check if the output will be 22

y = 1.5(13 - 1) + 3

y = 1.5(12) + 3

y = 18 + 3 =21

Hence the coordinate (13, 22) is not on the line since the y-coordinate is 21

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Answer:

X=4

Step-by-step explanation:

(2x-5)+(4x-1)=7x-10

2x-5+4x-1=7x-10

6x-6=7x-10

6x=7x-4

x=4

From the given information provided, out of total sodas served, 42% of the sodas served were regular.

To find the percentage of sodas served that were regular, we need to calculate the ratio of the number of regular sodas to the total number of sodas served, and then express this ratio as a percentage.

The total number of sodas served is the sum of regular and diet sodas:

Total sodas served = 21 + 29 = 50

The number of regular sodas served is 21.

To find the percentage of sodas served that were regular, we can use the following formula:

Percentage of regular sodas = (Number of regular sodas / Total number of sodas served) x 100%

Substituting the values, we get:

Percentage of regular sodas = (21 / 50) x 100%

Percentage of regular sodas = 42%

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Answer:

X=-2.5

Step-by-step explanation:

You take -7.5 and distribute to the x and 3 so that would be -7.5x-22.5=3.75 then you take -22.5 and do inverse operation and do 22.5 on both sides which then you will have -7.5x=-18.75 then you divide both side by -7.5 and get -2.5

Answer:

y = 3/2x + 2

Step-by-step explanation:

y = 3/2x + b

-1 = 3/2(-2) + b

-1 = -3 + b

2 = b

y = 3/2x + 2

The another equivalent expression of total liquid is (x+2)/4.

Expressions that perform similarly but differ in appearance are said to be equivalent expressions. When the same value for the variable is entered, two algebraic expressions that are equivalent will have the same result.

x quarts liquid in the container 3/4 part of liquid is removed

Then remaining liquid in container = X - \(\frac{3}{4}X\)

Then remaining liquid in container = x/4quarts

Another 1/2 quart is poured into container

Then total liquid = \(X-\frac{3}{4}X+\frac{1}{2}\) quarts

total liquid = \(\frac{X+2}{4}\) quarts

So, then the another equivalent expression of total liquid is (x+2)/4.

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Answer:

289 miles.

Step-by-step explanation:

4 and 15 mins is 4.25 hours.68 c 4.25 = 289.Hope this helps.

The following is the scatter plot of Price ($) vs Number:

Notice that this scatter plot is congruent with Plot C

Now, a situation that could be modeled by this data could be the following:

A store keeps track of the products sold by transaction and the total cost of such transaction, resulting in the given table and scatter plot of Price vs Number of items.

According to the question The height of the cone that can be created by rolling one of the congruent sectors is approximately 6.32 cm.

To find the height of the cone that can be created by rolling one of the congruent sectors of the circular sheet, we need to calculate the circumference of the base of the cone.

The circumference of the base is equal to the length of the sector's arc, which can be calculated using the formula:

\(\[ \text{Arc Length} = \left(\frac{\text{Central Angle}}{360^\circ}\right) \times \text{Circumference of the Circle} \]\)

Since the sector is one-third of the circle, the central angle of the sector is  \(\( 120^\circ \) (\( \frac{360^\circ}{3} \)).\)

The circumference of the circle is given by the formula:

\(\[ \text{Circumference} = 2 \pi \times \text{radius} \]\)

Substituting the values, we have:

\(\[ \text{Circumference} = 2 \pi \times 6 \, \text{cm} = 12\pi \, \text{cm} \]\)

Now, we can calculate the arc length:

\(\[ \text{Arc Length} = \left(\frac{120^\circ}{360^\circ}\right) \times 12\pi \, \text{cm} = 4\pi \, \text{cm} \]\)

When the sector is rolled to form a cone, the arc length becomes the circumference of the base of the cone.

The circumference of the base of the cone is also equal to \(\( 2\pi \times \text{radius of the cone} \).\)

Therefore, we can equate the two circumferences and solve for the radius of the cone:

\(\[ 2\pi \times \text{radius of the cone} = 4\pi \, \text{cm} \]\)

Dividing both sides by \(\( 2\pi \)\), we find:

\(\[ \text{Radius of the cone} = 2 \, \text{cm} \]\)

Now, the height of the cone can be calculated using the Pythagorean theorem:

\(\[ \text{height}^2 = (\text{radius of the cone})^2 + (\text{radius of the base})^2 \]\)

\(\[ \text{height}^2 = 2^2 + 6^2 = 4 + 36 = 40 \]\)

Taking the square root of both sides, we get:

\(\[ \text{height} \approx \sqrt{40} \approx 6.32 \, \text{cm} \]\)

Therefore, the height of the cone that can be created by rolling one of the congruent sectors is approximately 6.32 cm.

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1. The volume of the prism is 144 cubic units

2. The area of the shaded base is 16units²

A prism is a solid shape that is bound on all its sides by plane faces. A prism can have a rectangular base( rectangular prism) or a triangular base( triangular prism) or a circular base ( cylinder) e.t.c

Generally the volume of a prism is expressed as;

V = base area × height.

base area = l × w

therefore volume = l× w ×h

The base area = l× w

= 8× 2 = 16 square units

therefore the volume of the prism = 16 × 9

= 144 cubic units

Therefore the volume of the prism is 144 cubic units and the shaded base area is 16 units².

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Answers in bold:

S9 = 2

i = 20

R = -2

=====================================================

Explanation:

\(S_0 = 20\) is the initial term because your teacher mentioned \(A_0 = I\) as the initial term.

Then R = -2 is the common difference because we subtract 2 from each term to get the next term. In other words, we add -2 to each term to get the next term.

Here is the scratch work for computing terms S1 through S4.

\(\begin{array}{|l|l|}\cline{1-2}S_{n} = S_{n-1} - 2 & S_{n} = S_{n-1} - 2\\S_{1} = S_{1-1} - 2 & S_{2} = S_{2-1} - 2\\S_{1} = S_{0} - 2 & S_{2} = S_{1} - 2\\S_{1} = 20 - 2 & S_{2} = 18 - 2\\S_{1} = 18 & S_{2} = 16\\\cline{1-2}S_{n} = S_{n-1} - 2 & S_{n} = S_{n-1} - 2\\S_{3} = S_{3-1} - 2 & S_{4} = S_{4-1} - 2\\S_{3} = S_{2} - 2 & S_{4} = S_{3} - 2\\S_{3} = 16 - 2 & S_{4} = 14 - 2\\S_{3} = 14 & S_{4} = 12\\\cline{1-2}\end{array}\)

Then here is S5 though S8

\(\begin{array}{|l|l|}\cline{1-2}S_{n} = S_{n-1} - 2 & S_{n} = S_{n-1} - 2\\S_{5} = S_{5-1} - 2 & S_{6} = S_{6-1} - 2\\S_{5} = S_{4} - 2 & S_{6} = S_{5} - 2\\S_{5} = 12 - 2 & S_{6} = 10 - 2\\S_{5} = 10 & S_{6} = 8\\\cline{1-2}S_{n} = S_{n-1} - 2 & S_{n} = S_{n-1} - 2\\S_{7} = S_{7-1} - 2 & S_{8} = S_{8-1} - 2\\S_{7} = S_{6} - 2 & S_{8} = S_{7} - 2\\S_{7} = 8 - 2 & S_{8} = 6 - 2\\S_{7} = 6 & S_{8} = 4\\\cline{1-2}\end{array}\)

And finally we arrive at S9.

\(S_{n} = S_{n-1} - 2\\\\S_{9} = S_{9-1} - 2\\\\S_{9} = S_{8} - 2\\\\S_{9} = 4 - 2\\\\S_{9} = 2\\\\\)

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

Because we have an arithmetic sequence, there is a shortcut.

\(a_n\) represents the nth term

S9 refers to the 10th term because we started at index 0. So we plug n = 10 into the arithmetic sequence formula below.

\(a_n = a_1 + d(n-1)\\\\a_n = 20 + (-2)(n-1)\\\\a_n = 20 - 2(n-1)\\\\a_{10} = 20 - 2(10-1)\\\\a_{10} = 20 - 2(9)\\\\a_{10} = 20 - 18\\\\a_{10} = 2\\\\\)

In other words, we start with 20 and subtract off 9 copies of 2 to arrive at 20-2*9 = 20-18 = 2, which helps see a faster way why \(S_9 = 2\)

Answer: 3/4

Step-by-step explanation:

9/14 divided by 6/7 is 3/4

Find the reciprocal of the divisor

Reciprocal of 6/7: 7/6

Now, multiply it with the dividend

So, 9/14 divided by 6/7 = 9/14 x 7/6

= 9 x 7 = 63

= 14 x 6 = 84

After reducing the fraction, the answer is 3/4

Hope this helps :)

The division of the fraction 6/7 by 9/15 gives the result 4/3.

To simplify the division of 6/7 divided by 9/14, multiply the first fraction by the reciprocal of the second fraction.

The reciprocal of a fraction is obtained by swapping the numerator and the denominator.

So, the reciprocal of 9/14 is 14/9.

Now, rewrite the division as multiplication:

(6/7) * (14/9)

To multiply fractions, multiply the numerators together and the denominators together:

= (6 * 14) / (7 * 9)

= 84/63

Now, divide the numerator and denominator by their greatest common divisor, which is 21:

= (84/21) / (63/21)

= 4/3

Therefore, 6/7 divided by 9/14 simplifies to 4/3.

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After Louis XVI's failed attempts to sabotage the Assembly and to keep the three estates separate, the Estates-General ceased to exist, becoming the National Assembly. It renamed itself the National Constituent Assembly on July 9 and began to function as a governing body and constitution-drafter.

National assembly

The National Assembly was the first revolutionary government of the French Revolution and existed from June 14th to July 9th in 1789. The National Assembly was created amidst the turmoil of the Estates-General that Louis XVI called in 1789 to deal with the looming economic crisis in France.

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The simplified expression for (f ∘ g)(x) is 2 + x (option d).

To find and simplify (f ∘ g)(x), we need to substitute the expression for g(x) into f(x) and simplify.

Given:

f(x) = log₃(9x)

g(x) = \(3^x\)

Substituting g(x) into f(x):

(f ∘ g)(x) = f(g(x)) = log₃\((9 * 3^x)\)

Now, we simplify the expression:

log₃\((9 * 3^x)\) = log₃(9) + log₃\((3^x)\)

Since logₓ(a * b) = logₓ(a) + logₓ(b), we have:

log₃(9) + log₃\((3^x)\) = log₃\((3^2)\) + x

Using the property logₓ\((x^a)\) = a * logₓ(x), we get:

log₃\((3^2)\) + x = 2 * log₃(3) + x

Since logₓ\((x^a)\) = a, where x is the base, we have:

2 * log₃(3) + x = 2 + x

Therefore, (f ∘ g)(x) simplifies to:

(f ∘ g)(x) = 2 + x

So, the correct answer is (d) 2 + x.

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Complete Question:

Given f(x)=log₃(9x) and g(x)=\(3^x\). Find and simplify (f ∘ g)(x)

(a) 2x

(b) x

(c) \(27^x\)

(d) 2+x

(e) None of these.