Evaluate each arithmetic series described (find the sum).
15
(13 – 5n)
=
n=1
Helppppp

The values of tht missing part of the triangle are;

A= 20.9°

a = 13.06

c = 33.6

The sine rule states that if a, b and c are the lengths of the sides of a triangle, and A, B and C are the angles in the triangle; with A opposite a, etc., then a/sinA=b/sinB=c/sinC.

To find side c

sinB/b = sinC/c

sin45.9/26.30 = sin113.2/c

csin 45.9 = 26.30 × sin113.2

0.718c = 23.90

c = 23.90/0.718

c = 33.6

Angle A = 180-(113.2+ 45.9)

angle A = 20.9°

sinA/a = sinB/b

sin20.9/a = 0.718/26.30

0.357 × 26.30 = 0.718a

a = 9.389/0.718

a = 13.06

Therefore A = 20.9°

a = 13.06

c = 33.6

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According to the solution we have come to find that, the total cost of renting a mid-size car for three days and 500 miles would be $125.00.

Linear equations are mathematical equations that describe a straight line. They have the general form of:

y = mx + b

where:

y is the dependent variable or the output of the equation

x is the independent variable or the input of the equation

m is the slope or rate of change of the line

b is the y-intercept, which is the point where the line crosses the y-axis

Based on the rental car agency chart, the cost of renting a mid-size car for three days and 500 miles would be:

The fee per day for a mid-size car is $25.00

The cost per mile for a mid-size car is $0.10

The rental period is three days, so the rental fee would be $25.00 x 3 = $75.00

The total mileage is 500 miles, so the mileage cost would be 500 x $0.10 = $50.00

Adding the rental fee and mileage cost, the total cost would be $75.00 + $50.00 = $125.00

Therefore, the total cost of renting a mid-size car for three days and 500 miles would be $125.00.

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Answer:

11

Step-by-step explanation:

29-20= 91

2+9=11

11+9=

The interval where the product will be at least break even equals to 18 units.

In accounting, the break-even point refers to the production level at which total revenues equal total expenses.

Given data

Cost is given as C = 45x + 450

Revenue is given as: R = 70x

In this case, the point of breakeven will be:

Cost = Revenue

45x + 450 = 70x

We will collect like terms:

70x - 45x = 450

25x = 450

We will divide both side by 25:

25x/25 = 450/25

x = 18

Therefore, the interval where the product will be at least break even equals to 18 units.

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Answer:

<

Step-by-step explanation:

1) Substitute 5 into the question

2) Work out the sides

3) Put it into an inequality

5 < 7

Hope this helps, have a great day!

Answer:

This pandemic has affected millions (maybe billions) of people, who are either sick or are being killed due to the spread of this disease. The most common symptoms of this viral infection are fever, cold, cough, bone pain, and breathing problems, ultimately leading to pneumonia.

Stay safe during these tuff times please mark me -liest

God bless

The Vertex is : (-6, -30)

The X-intercepts are : Approximately (-10.89, 0) and (-1.11, 0)

The Y-intercept is : (0, 6)

The Axis of symmetry is : x = -6

The functions Domain: is All real numbers

The Range is : All real numbers greater than or equal to -30.

To sketch the graph of the quadratic function \(f(x) = x^2 + 12x + 6,\) we can start by identifying the vertex, x-intercepts, y-intercept, axis of symmetry, domain, and range.

To find the vertex, we can use the formula x = -b/2a, where a, b, and c are the coefficients of the quadratic equation in standard form\((ax^2 + bx + c).\)

In this case, a = 1, b = 12, and c = 6.

Applying the formula, we get x = -12/(2 \(\times\) 1) = -6.

To find the y-coordinate of the vertex, we substitute this x-value into the equation:\(f(-6) = (-6)^2 + 12(-6) + 6 = 36 - 72 + 6 = -30.\)

So, the vertex is (-6, -30).

To determine the x-intercepts, we set f(x) = 0 and solve for x. In this case, we need to solve the quadratic equation \(x^2 + 12x + 6 = 0.\)

Using factoring, completing the square, or the quadratic formula, we find that the solutions are not rational.

Let's approximate them using decimal values: x ≈ -10.89 and x ≈ -1.11. Therefore, the x-intercepts are approximately (-10.89, 0) and (-1.11, 0).

The y-intercept is obtained by substituting x = 0 into the equation: \(f(0) = 0^2 + 12(0) + 6 = 6.\)

Thus, the y-intercept is (0, 6).

The axis of symmetry is the vertical line that passes through the vertex. In this case, it is the line x = -6.

The domain of the function is all real numbers since there are no restrictions on the possible input values of x.

To determine the range, we can observe that the coefficient of the \(x^2\) term is positive (1), indicating that the parabola opens upward.

Therefore, the minimum point of the parabola occurs at the vertex, (-6, -30).

As a result, the range of the function is all real numbers greater than or equal to -30.

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The correct expression is  \($(150 \cdot 1.15)^7$\) (Choice A).

The problem states that the painting's value increases by a factor of 1.15 each year. This means that the value at the end of each year is 1.15 times the value at the beginning of the year. Therefore, after one year, the value of the painting is\($150 \cdot 1.15 = 172.50$\).

To find the value after 7 years, we need to multiply the value of the painting each year by 1.15 a total of 7 times. This can be represented mathematically as \($(150 \cdot 1.15)^7$\). This expression is equal to the starting value of the painting, 150, multiplied by 1.15$ raised to the 7th power, which represents the 7 years of appreciation.

If we were to choose expression B, it would give an incorrect result because it uses a value of 1.1 instead of 1.15 to represent the yearly increase in value.

Expressions C and D are also incorrect because they are not taking into account the compounding effect of the yearly increase. Expression C adds the initial value and the total years together, and expression D adds the initial value to the yearly increase multiplied by 7, neither of which correctly reflects the exponential growth of the painting's value.

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Answer:

Add 16.20+ 40+8

Step-by-step explanation: 16+20+40+8= 84

Answer:

3) 194 feet

Step-by-step explanation:

The other house:

"a house that is 33 ft wide and 50 ft long"

area = LW = (33 ft)(50 ft) = 1650 ft²

This house:

LW = A

L × 22 ft = 1650 ft²

L = 75 ft

P = 2(L + W)

P = 2(75 ft + 22 ft)

P = 194 ft

Answer: 3) 194 feet

Answer:

3) P = 194 ft.

Step-by-step explanation:

\(A=wl\)

\((30)(50)=22l\)

\(1650=22l\)

\(l=1650/22=75\)

the dimensions of the house are: (22 × 75)

Perimeter:

\(p=2(22)+2(75)=44+150=194\)

Hope this helps

Answer:

(a)\(A(n)=5500(1.01)^{4n}\)

(b)$5955.71

(c)15.02 years

Step-by-step explanation:

For an initial principal P deposited in an account at an annual interest r compounded for a number of period k, the amount in the account after n years is given by the model:

\(A(n)=P(1+\dfrac{r}{k})^{nk}\)

(a)Aunt Ga Ga gave you $5,500 to save for college.

P=$5,500

Annual Interest, r=4%=0.04

Since interest is compounded quarterly, Number of Periods, k=4

Therefore, an exponential function modeling this situation is:

\(A(n)=5500(1+\dfrac{0.04}{4})^{4n}\\A(n)=5500(1+0.01)^{4n}\\$Simplified\\A(n)=5500(1.01)^{4n}\)

(b)After 2 years, i.e. when n=2

\(A(2)=5500(1.01)^{4*2}\\=\$5955.71\)

(c)When A(n)=$10000, we have:

\(10000=5500(1.01)^{4n}\\$Divide both sides by 5500\\(1.01)^{4n}=\dfrac{10000}{5500} \\$To solve for n, we change to logarithm form\\Log_{1.01}\dfrac{10000}{5500}=4n\\= \dfrac{ Log \dfrac{10000}{5500}}{Log 1.01}=4n\\4n=60.08\\n=60.08 \div 4\\n=15.02\\$Therefore, in 15.02 years, the account would be worth $10,000.\)

y = 6x + 2 is the function which Adam charges a rate of $6 per hour and an additional fee of $2 for the bus fare.

The linear function in the form y = mx + b represents the situation where y represents the cost of the babysitting job

x represents the number of hours, "m" represents the hourly rate, and "b" represents the additional fee (bus fare).

y = 3x + 2 represents an hourly rate of 3 and an additional fee of 2.

y = 3x + 1 represents an hourly rate of 3 and an additional fee of 1.

y = 6x + 2 represents an hourly rate of 6 and an additional fee of 2.

y = -6x + 2 represents a negative hourly rate of -6 and an additional fee of 2.

Hence, y = 6x + 2 is the which Adam charges a rate of $6 per hour and an additional fee of $2 for the bus fare.

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Answer:

3.34.

Step-by-step explanation:

4.2 * 0.2 + 2.5

= 0.84 + 2.5

= 3.34.

Answer:

3.34

Step-by-step explanation:

the product is 4.2×0.2=0.84

add is 2.5 + 0.84=3.34

\(x^2-100\\\\=x^2-10^2\\\\=(x+10)(x-10)\\\\\text{The difference of two squares formula is}~ a^2 -b^2 =(a+b)(a-b),\\\\\text{So, the student did not apply it properly}\)

The fish's total distance traveled is 17 meters in 5 minutes based on multiplication and addition operations.

The total distance the fish traveled can be determined using mathematical operations, especially multiplication and addition.

We know that distance is the product of speed and time, i.e. d = st, where s is speed, t is time, and d is distance.

In this situation, we separately find the distance the fish traveled during its descent and ascent by multiplying time and speed.

The results are added to obtain the total distance the fish traveled for both activities.

The fish's descent speed = 4 meters per minute (MPM)

The total time for the descent = 2

The total distance for the descent = 8 miles (4 x 2)

The fish's ascent speed = 3 meters per minute (MPM)

The total time during ascent = 3 minutes

The total distance for the ascent = 9 miles (3 x 3)

The total distance the fish traveled for descent and ascent = 17 meters (8 + 9)

Thus, we can mathematically conclude that the fish traveled 17 meters.

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Answer:

$13

Step-by-step explanation:

Answer:

2-cup carton of frozen yogurt for $0.80

Step-by-step explanation:

We know

2-cup carton of frozen yogurt for $0.80

1 cup = 0.25 quart

2 cups = 0.50 quart

0.80 / 0.50 = $1.60 per quart

2-quart carton of frozen yogurt of $5.52

5.52 / 2 = $2.76 per quart

So, 2-cup carton of frozen yogurt for $0.80 is better buy.

Answer:

Step-by-step explanation:

To determine which option is a better buy, we need to compare the price per unit (in this case, the price per cup) of the two options.

For the 2-cup carton of frozen yogurt that costs $0.80, the price per cup can be calculated as:

$0.80 / 2 cups = $0.40 per cup

For the 2-quart carton of frozen yogurt that costs $5.52, we first need to convert quarts to cups. There are 4 cups in a quart, so a 2-quart carton contains:

2 quarts x 4 cups per quart = 8 cups

The price per cup can then be calculated as:

$5.52 / 8 cups = $0.69 per cup

Therefore, the 2-cup carton of frozen yogurt for $0.80 is a better buy, as the price per cup is lower at $0.40, compared to $0.69 per cup for the 2-quart carton.

Answer:

110

Step-by-step explanation:

nth term = 3n + 2

3 (36) + 2

108 + 2 = 110

Answer:

The 36th term in the sequence is 104.

Here's how to find it:

- Start with the first number in the sequence: 5.

- Add the common difference, which is 3, to get the second number in the sequence: 8.

- Add the common difference to the second number to get the third number: 11.

- Continue adding the common difference to each subsequent number to find the next term in the sequence.

- The 36th term is three less than 37 times the common difference added to the first term.

- Using that formula, we can calculate the 36th term as: 5 + (36 - 1) * 3 = 5 + 105 = 110.

- Therefore, the 36th term in the sequence is 104.

Answer:

Step-by-step explanation:

the answer is unknown or undefined,  it basically is going to infinity

Answer:

Distance between points = 8.6

Step-by-step explanation:

Formula :

Distance between two points = √(xB−xA)2+(yB−yA)2(xB-xA)2+(yB-yA)2

Solution :

Distance between two points = √(−2−−9)2+(−6−−1)2(-2--9)2+(-6--1)2

= √72+(−5)272+(-5)2

= √49+2549+25

= √7474 = 8.6023

Distance between points (-9, -1) and (-2, -6) is 8.6023

The initial velocity is  0 m/sec

The car speed up to 72km/h which is equivalent to  36m/sec

The acceleration of the car is 2.88 m/sec².

Acceleration is the rate of change of the velocity of an object with respect to time. Vector quantities are accelerations. Acceleration = (Final Velocity - Initial Velocity)/ Time taken

Given that car can accelerate from rest to 72km/h in 12.5 seconds. Therefore, we can write:

Initial Velocity = 0 m/sec

Final Velocity = 72 km/hr = 72×(0.50) m/sec = 36m/sec

Time taken = 12.5 second

Now, the car’s acceleration in m/s can be written as,

Acceleration = (Final Velocity - Initial Velocity)/ Time taken

(36 m/sec - 0 m/sec)/12.5 seconds

= 2.88 m/sec²

Hence, the car’s acceleration in m/s is 2.88 m/sec².

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Answer:

"Type II error" is the right answer.

Step-by-step explanation:

Thus the above is the right answer.

The perimeter of the given shape as represented in the task content is; 29 cm.

It follows from the task content that the perimeter of the given shape on the centimeter grid as required is to be determined.

Since each grid line has 1cm as it's length;

The perimeter of the shape is the sum of all side lengths of the shape;

Perimeter, P = 6+2+3+2+2+1+3+2+2+2+2+1

P = 29 cm

Hence, the perimeter of the shape is; 29 cm.

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The average score of the spelling test is 90.6%

To find the average score of the test, we need to add up all the scores and divide by the total number of students. We can think of the average score as the "typical" or "representative" score of the entire class.

First, let's add up all the scores:

2(100) + 9(95) + 10(90) + 3(80) + 1(70) = 200 + 855 + 900 + 240 + 70 = 2265

Next, we divide by the total number of students:

Average score = (2 + 9 + 10 + 3 + 1) / 25 * 100% = 25 / 25 * 100% = 90.6%

Therefore, the average score of the spelling test is 90.6% when rounded to one decimal place.

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Answer:$39

Step-by-step explanation:

The discounted price is going to be 60% of the original price because 100 - 40 = 60. So we want to find 60% of the original price, or 65. 65 x . 6 = 39, so the pair of rollerskates will be $39 at the discounted price.

Floyd needs 33 matches to make a rectangle with a length of 20 matches.

To find out how many matches Floyd needs to make a rectangle with a length of 20 matches, we can observe a pattern in the given information.

From the given data, we can see that as the length of the rectangle increases by 4 matches, the number of matches used increases by 8. This means that for every additional 4 matches in length, Floyd requires 8 more matches.

Using this pattern, we can calculate the number of matches needed for a rectangle with a length of 20 matches.

First, we need to determine the number of 4-match increments in the length of 20 matches. We can do this by subtracting the starting length of 3 matches from the target length of 20 matches, which gives us 20 - 3 = 17.

Next, we divide the number of 4-match increments by 4 to determine how many times Floyd needs to add 4 matches. In this case, 17 ÷ 4 = 4 with a remainder of 1.

Since Floyd requires 8 matches for each 4-match increment, we multiply the number of increments by 8, which gives us 4 × 8 = 32 matches.

Finally, we add the remaining matches (1 match in this case) to the total, resulting in 32 + 1 = 33 matches needed to reach a length of 20 matches.

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Answer:

y=12

Step-by-step explanation:

12=24-y

step 1

subtract each side by 24

24-24 cancels out

12-24=-12

now we have

-y=-12

we now have to divide by -1

-1/-1=1

-12/-1=12

so we can conclude that y=12

Answer:

y = 12

Step-by-step explanation:

12=24-y

y = 24 - 12

y = 12