Zoe, RJ, and Mia went
to buy smoothies. Zoe's
cost $3.45, RJ's cost
$3.25, and Mia's cost
$2.95. Zoe had a coupon
for $3.50 off the total cost
of their order. Which
equation shows the total
amount of money spent?

For the given arithmetic sequence we have:

We know that we have 20 seats on the front row, and then we add 3 more on each row, so the formula will be:

\(A_n = 20 + (n - 1)*3\)

This gives the number of seats on the n-th row.

B) The last row has 83 seats, then we need to solve:

\(A_n = 20 + (n - 1)*3 = 83\\\\(n - 1)*3 = 83 - 20 = 63\\\\n - 1 = 63/3 = 21\\\\n = 21 + 1 = 22\)

So we conclude that there are 22 rows.

C) The total number of seats will be:

\(\sum_{n = 1\ to\ 22} (20 + (n - 1)*3)\)

D) Instead of using the sum above (we should add 22 terms) we use the general formula for the sum of N terms in an arithmetic sequence:

\(S_N = (N/2)*(2A_1 + (N - 1)*d)\)

In this case, we replace N by 22, and d is the common difference of the sequence, which we know is equal to 3, so we wil have:

\(S_{22} = (22/2)*(2*20+ (22 - 1)*3) = 11*(40 + 21*3) = 1,133\)

There are 1,133 seats in total.

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Answer:

the number represent the opposite of E is 3

Answer:

PT = 17

Step-by-step explanation:

Since T is the midpoint of PQ, then

PT = TQ , substitute values

4x + 5 = 8x - 7 ( subtract 4x from both sides )

5 = 4x - 7 ( add 7 to both sides )

12 = 4x ( divide both sides by 4 )

3 = x

Thus

PT = 4x + 5 = 4(3) + 5 = 12 + 5 = 17

Answer:

17

Step-by-step explanation:

since T is mid point of PQ

PT=TQ

\(4x + 5 = 8x - 7 \\ 5 + 7 = 8x - 4x \\ 12 = 4x \\ x = 12 \div 4 \\ x = 3 \\ \)

so

\(pt = 4x + 5 \\ = 4(3) + 5 \\ = 12 + 5 \\ pt = 17\)

The expression that represents the perimeter of the other shape is 9x + 6y.

Option(b) is the correct one.

Expressions in mathematics are mathematical statements that comprise at least two terms that contain numbers, variables, or both, and are joined by an operator. Addition, subtraction, multiplication, and division are all examples of mathematical operators.

Given:

Expression for the sum of the perimeter of two shapes = 13x + 4y

Expression for the perimeter of one shape = 4x - 2y

Expression for the perimeter of the other shape is,

(13x + 4y) - (4x - 2y)

= 13x - 4x + 4y + 2y (combine the like terms and solve)

= 9x + 6y

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Answer:

The average monthly payment would be most affected by Mark's observation of one significantly lower payment. The reason is that the average is calculated by summing all the payments and dividing by the total number of payments, so any extreme values (such as the significantly lower payment) can have a substantial impact on the average value.

Step-by-step explanation:

"The analysts at the casino try to choose the spread so that there is a 50% chance that the outcome will be below that amount, and a 50% chance that the outcome will be above that amount" is TRUE.

The analysts at the casino do not try to choose the spread so that there is a 50% chance of the outcome being below or above that amount. The spread is chosen based on factors such as the teams playing, their past performances, and other relevant statistics.

The goal of the casino is to balance the amount of money bet on each side, not to ensure a 50/50 chance of winning for either side. The spread is simply a tool used to even out the betting and ensure a profit for the casino.
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The expression (1/4 - 3/5) is equivalent to the following expressions -

Given is the expression as -

(1/4 - 3/5)

The given expression is -

(1/4 - 3/5)

1/4 - 3/5

(5 - 12)/20

-7/20

We can write the fraction : -7/20 in many ways as given below -

-7/20 = (3/20 - 10/20) = (1/4 - 3/5)

-7/20 = (13/20 - 1) = (1/4 - 3/5)

-7/20 = (23/20 - 3/2) = 1/4 - 3/5)

Therefore, the expression (1/4 - 3/5) is equivalent to the following expressions -

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Answer:

It would be -6 degrees Celsius.

Step-by-step explanation:

The identified parameters are:

ta = 6 minutes

tθ = 11 minutes

∂a = 4 minutes

∂θ = 20 minutes

ra = 1/6 minutes^(-1)

rθ = 1/11 minutes^(-1)

ta: Mean time between calls to the center

tθ: Effective response time

∂a: Standard deviation of the time between calls to the center

∂θ: Standard deviation of the effective response time

ra: Rate of calls to the center (inverse of ta, i.e., ra = 1/ta)

rθ: Rate of effective response (inverse of tθ, i.e., rθ = 1/tθ)

Given information:

Mean time between calls to the center (ta) = 6 minutes

Standard deviation of time between calls (∂a) = 4 minutes

Effective response time (tθ) = 11 minutes

Standard deviation of effective response time (∂θ) = 20 minutes

Using this information, we can determine the values of the parameters:

ta = 6 minutes

tθ = 11 minutes

∂a = 4 minutes

∂θ = 20 minutes

ra = 1/ta = 1/6 minutes^(-1)

rθ = 1/tθ = 1/11 minutes^(-1)

So, the identified parameters are:

ta = 6 minutes

tθ = 11 minutes

∂a = 4 minutes

∂θ = 20 minutes

ra = 1/6 minutes^(-1)

rθ = 1/11 minutes^(-1)

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Answer:

-3

Step-by-step explanation:

A number, n, decreased by 5:   n - 5

3 times the number +1 = 3*n + 1 = 3n + 1

3n +1 = n -5

Subtract 1 from both sides

3n = n - 5 - 1

3n = n - 6

Subtract 'n' from both sides

3n - n = -6

      2n = -6        {Divide both sides by 2}

       n = -6/2

      n = -3

The number = - 3

Answer:

There are 1,360 pears.

Step-by-step explanation:

Suppose that there are P pears and A apples.

We know that:

"If 20 apples and 60 pears are sold every hour, there will be 80 pears when all the apples are sold."

Suppose that all of these are sold after N hours, then:

20*N = A

80*N = P - 80

We also know that:

"if 60 apples and 20 pears are sold every hour, there will be 400 pears when all the apples are sold."

60*N = A

20*N = P - 400

Then we have four equations:

20*N = A

80*N = P - 80

60*N = A

20*N = P - 400

From the first one and the second one, we get:

20*N = A = 20*N = P - 400

A = P - 400

Now we have 3 equations:

80*N = P - 80

60*N = A

A = P - 400

Now we can just replace the third equation into the second one, then we get:

60*N = A = P - 400

Now we have two equations:

80*N = P - 80

60*N = P - 400

Now, remember that we want to find the number of pears, so we want to find the value of P.

To do it, we can take the quotient of the two equations, so we get:

(80*N)/(60*N) = (P - 80)/(P - 400)

8/6 = (P - 80)/(P - 400)

Now we can solve this for P

(8/6)*(P - 400) = P - 80

(8/6)*P - (8/6)*400 = P - 80

(8/6)*P - P = (8/6)*400 - 80

(2/6)*P = (8/6)*400 - 80

P = (6/2)*( (8/6)*400 - 80 )

P = 3*( (8/6)*400 - 80 ) = 1,360

There are 1,360 pears.

Answer:

(5,2)

(5,1)

(8,1)

Step-by-step explanation:

Vertices are the vertex's of a triangle. In this triangle A has 3 vertices.

so all you have to do is find the coordinates of the triangle which is

(5,3)

(5,1)

(8,1)

Answer:

6 inches = 152.4 mm

Step-by-step explanation:

Answer:

40%

Step-by-step explanation:

In order to turn a fraction into a decimal or percentage, you need to make the denominator 100. In this case you just need to multiply the numerator and denominator by 20:

2/5 --> 2*20/5*20 --> 40/100

So, it is 40%. Though if you want to turn ANY fraction (specifically fractions with hard to multiply denominators) into a percentage, just follow this rule:

(100n/d)%

The 2/5 is equivalent to 40%.

To calculate what percent is equivalent to 2/5, we can use the formula:

Percent = (Part / Whole) * 100

In this case, the part is 2 and the whole is 5.

Percent = (2 / 5) * 100

Now, perform the division:

Percent = 0.4 * 100

To find the percentage, multiply 0.4 by 100:

Percent = 40%

Therefore, 2/5 is equivalent to 40%. To understand this better, consider that 2 out of 5 parts is 40% of the whole. The percentage represents the proportion of the part (2) in relation to the whole (5) expressed as a fraction of 100. In this scenario, 2/5 is equivalent to 40%, indicating that 40% of the whole is represented by the fraction 2/5.

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Answer:

10 + 2y

Step-by-step explanation:

2(5+y)

Distribute

10 + 2y

Answer:

2y + 10

Step-by-step explanation:

2(5(2) + y(2))

2 x 5 = 10

y x 2 = 2y

2y + 10

Ricky had 176 cookies initially.

Let Ricky has x number of cookies

Cookies left after he ate 1/8 of his cookies and additional 14 cookies:

x - (1/8x + 14)

Cookies left after he ate 3/10 of the remaining cookies and an additional 24 cookies on Saturday:

x - (1/8x + 14) - 3/10(x - (1/8x + 14)) + 24)

Cookies left after he ate 40 more cookies on Sunday

x - (1/8x + 14) - 3/10(x - (1/8x + 14)) + 24) - 40 ------(1)

Cookies left with him at the end = 34

Therefore, equating equation (1) with 34

(7/10)((7x/8) - 14) - 64 = 34

x = 176

Thus Ricky had 176 cookies intially

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complete question:

Ricky has some cookies. he ate 1/8 of his cookies and an additional 14 cookies on friday. he then ate 3/10 of the remaining cookies and an additional 24 cookies on saturday. he ate 40 cookies on sunday and had 34 cookies left. how many cookies did ricky have at first?

When operating under Instrument Flight Rules (IFR) with a Visual Flight Rules (VFR) on-top clearance, the altitude to be maintained depends on the specific clearance and regulations in place.

Generally, when flying VFR-on-top, the pilot is authorized to operate in VFR conditions above a layer of clouds or other obscuring phenomena. In terms of altitude, the pilot is expected to maintain a cruising altitude appropriate for the direction of flight and comply with the relevant airspace regulations. This typically involves flying at the appropriate altitude for the specific airspace class, as defined by the Federal Aviation Regulations (FARs) or the applicable regulatory authority. It's important for pilots to review and understand the specific requirements and altitude restrictions outlined in their VFR-on-top clearance, as well as any additional instructions provided by air traffic control.

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Answer:

See step by Step

Step-by-step explanation:

Both are correct. As long as we undo the operations that was given from the original term to both sides until we get the variable by itself., any way can be applied.

Both, Spencer and Jeremiah are correct. We can verify this by testing their methods.

Spencer's method:

\(6x - 2 = - 4x + 2\)

\(6x - 2 + 4x= - 4x + 2 + 4x\)

\(10x - 2 = 2\)

\(10x = 2 + 2\)

\(10x = 4\)

\(x = \frac{4}{10} \)

\(x = 0.4\)

Jeremiah's method:

\(6x - 2 = - 4x + 2\)

\(6x - 2 - 6x = - 4x + 2 - 6x\)

\( - 2 = - 10x + 2\)

\( - 2 - 2 = - 10x\)

\( - 4 = - 10x\)

\( \frac{ - 4}{ - 10} = x\)

\(0.4 = x\)

As seen, we get the correct answer by using Spencer's and Jeremiah's method. So, we can say that they both are correct.

Part B: The total area of Riley's backyard is 6x² - 14x + 8 Part C: The total area of Riley's garden is x² + 2x - 15 Part D: The area of Riley's backyard not including the garden is 5x² - 16x + 23

What is area?

The word "area" refers to a free space. A shape's length and width are used to compute its area. Unidimensional length is expressed in terms of feet (ft), yards (yd), inches (in), etc. But a shape's area is a two-dimensional measurement. As a result, it is expressed in square measurements like square inches.

To find the total area of Riley's backyard, we need to multiply the length and width:

Total Area = length × width

Total Area = (3x-8) × (2x-1)

Total Area = 6x² - 6x - 8x + 8

Total Area = 6x² - 14x + 8

PART C:

To find the area of Riley's garden, we need to multiply the length and width:

Garden Area = length × width

Garden Area = (x+5) × (x-3)

Garden Area = x² + 2x - 15

PART D:

To find the area of Riley's backyard not including the garden, we need to subtract the garden area from the total area of the backyard:

Backyard Area (without garden) = Total Area - Garden Area

Backyard Area (without garden) = (6x² - 14x + 8) - (x² + 2x - 15)

Backyard Area (without garden) = 6x² - 14x + 8 - x² - 2x + 15

Backyard Area (without garden) = 5x² - 16x + 23

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The difference in the Beatles length is 1 / 10 centimeters.

We have,

The lengths of Beetles are 4/5 cm and 7/10 cm.

So, the difference in the beetles length can be calculated as

difference between the beetles length = 4 / 5 - 7 / 10

                                                                 = 8 - 7 / 10

                                                                  = 1/10 cm

Thus, the difference in beetles length is 1/10 cm.

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The percentage of spiders that weigh less than 10 grams can be calculated using the normal distribution. The answer is approximately 30.85%, which corresponds to option a.

To determine this percentage, we need to calculate the area under the normal curve to the left of the value 10 grams. We can convert this value into a standardized z-score using the formula z = (x - μ) / σ, where x is the value (10 grams), μ is the mean (11 grams), and σ is the standard deviation (2 grams). Substituting the values, we get z = (10 - 11) / 2 = -0.5.

We can then use a standard normal distribution table or a statistical calculator to find the area to the left of the z-score -0.5, which is approximately 0.3085 or 30.85%. This indicates that approximately 30.85% of spiders weigh less than 10 grams, leading to the conclusion of option a.

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Answer:

1)  See attachment.

2a)  Initial Amount = 3600.
      Growth/Decay factor = ³/₂.

2b)  Growth function.

\(\textsf{3)}\;\;\; f(x)=1*2^x\)

4)  69 lions.

Step-by-step explanation:

General form of an exponential function

\(\boxed{y=ab^x}\)

where:

If b > 1 then it is an increasing function.

If 0 < b < 1 then it is a decreasing function.

Given function:

\(f(x)=\left(\dfrac{1}{2}\right)^x\)

Complete the table of ordered pairs by substituting the values of x into the given function:

\(\begin{array}{|c|c|}\cline{1-2}x&y\\\cline{1-2}-3&8\\\cline{1-2}-2&4\\\cline{1-2}-1&2\\\cline{1-2}0&1\\\cline{1-2}1&0.5\\ \cline{1-2}\end{array}\)

Plot the ordered pairs on the given coordinate plane (see attached graph) and draw a curve through them.

This exponential function has a horizonal asymptote at y = 0.  

As the value of x approaches infinity, the function gets closer and closer to y = 0 (x-axis) but doesn't actually touch it.

Given exponential function:

\(f(x)=3600\left(\dfrac{3}{2}\right)^x\)

Part 2a

To find the initial amount "a" and growth/decay factor "b", simply compare the given function with the general exponential function.  

Therefore:

Part 2b

As  b = ³/₂ and ³/₂ > 1, this is a growth function (increasing).

"a" is the initial value (y-intercept) of an exponential function.

The y-intercept of a function is the y-value when x = 0.  

Therefore, from inspection of the given table, the y-intercept of the given function is 1.

Therefore, a = 1.

"b" is the base (growth/decay factor) of an exponential function.

To find the base (growth/decay factor) of the given function, divide a value of y by its preceding value of y:

\(\implies b=\dfrac{4}{2}=\dfrac{2}{1}=\dfrac{1}{\frac{1}{2}}=...=2\)

Therefore, b = 2.

So the exponential function for the given table is:

\(f(x)=\boxed{1}*\boxed{2}\;^x\)

If the population of lions started at 80, then the initial value "a" of the exponential function is 80.

If the population has been decreasing by 3.5% per year, then the population each year is 96.5% of the previous year since:

Therefore, the base "b" of the exponential function is 0.965 (in decimal form).

Substitute the found values of a and b into the exponential function formula to create an exponential function for the given scenario:

\(\boxed{f(t)=80(0.965)^t}\)

where:

To find how many lions will there be in four years, substitute t = 4 into the found exponential equation:

\(\implies f(4)=80(0.965)^4=69.37440005\)

Therefore, there will be 69 lions in four years.

Answer:

what even is that..

Step-by-step explanation:

Answer:

$35 + $50 = $85 per hour

$85 x 3 = $255

So this company would cost $255 for 3 hours.

Answer:

answer A

Step-by-step explanation:

2(x+9) + 7x + 4

2x+18+7x+4

9x+18+4

9x+22

Answer:

27

Step-by-step explanation:

h(-3) = -9(-3) = 27

negative x negative = positive

Answer:

h= 9

Step-by-step explanation:

h(-3)=-9(-3)

h(-3)=27

h=27/3

h=9

Answer:

C. 20

Step-by-step explanation:

Use the Pythagorean theorem which is \(a^{2} +b^{2} =c^{2}\).

\(a^{2}\) and \(b^{2}\) are the sides of the triangle squared, AB and AC. \(c^{2}\) is the hypotenuse (the slanted side of the triangle) or BC.

So, \(12^{2} + 16^{2} =400^{2}\). Then you square root 400 to get your answer.

\(\sqrt{400}\) = 20.

20 is your answer.

Answer:

f(-1) = 3

Step-by-step explanation:

Plug -1 into the equation

-(-1)+2

-14 is the value of the expression b - 3a at a =6 and b = 4.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Given an expression b - 3a

For this expression given,

a = 6 and b = 4

Thus the value of expression at given values

=> b - 3a

=> 4 - 3 * 6

=>4 - 18

=> -14

Therefore, the value of the expression b - 3a at a =6 and b = 4 is -14.

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One glass contains 7,000 milligrams of protein.

One glass contains 7 grams of protein. In order to calculate how many milligrams of protein one glass contain, we have to remember that 1 gram equals 1,000 milligrams.

Thus, we can calculate the number of milligrams of protein in one glass as follows:

7 grams x 1,000 milligrams/1 gram = 7,000 milligrams

Therefore, one glass contains 7,000 milligrams of protein.

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