5 x 5,503 estimate the product by rounding

a. The amplitude of the function y = 4 sin [(2π / 365)(x - 79)] + 12 is 4.

b. The period of the function y = 4 sin [(2π / 365)(x - 79)] + 12 is 365 days.

c. There are approximately 16 hours of daylight on the longest day of the year.

d. There are approximately 8 hours of daylight on the shortest day of the year.

e. The graph for the function is obtained.

What is a function?

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

The function is given as y = 4 sin [(2π / 365)(x - 79)] + 12.

a. The amplitude of the function is the coefficient of the sine function, which is 4.

Therefore, the amplitude of the function is 4.

b. The period of the function is given by the formula: period = (2π/b), where b is the coefficient of x in the sine function.

In this case, b = (2π/365), so the period is -

period = (2π / (2π/365)) = 365

Therefore, the period value is 365 days.

c. The longest day of the year occurs on the summer solstice, which is around June 21.

On this day, x = 171 (assuming January 1 is x = 1). Plugging x = 171 into the function gives -

y = 4 sin [(2π/365)(171 - 79)] + 12 = 15.998 hours

Therefore, the number of hours for daylight is 16 hours.

d. The shortest day of the year occurs on the winter solstice, which is around December 21.

On this day, x = 355. Plugging x = 355 into the function gives -

y = 4 sin [(2π/365)(355 - 79)] + 12 = 8.002 hours

Therefore, the number of hours for daylight is 8 hours.

e. To graph the function for one period, we need to find the values of y for x ranging from 1 to 365.

We can use a graphing tool or software to plot the function.

The graph is plotted.

The x-axis represents the number of days after January 1, and the y-axis represents the number of hours of daylight.

The function oscillates between 8 and 16 hours of daylight over the course of one year, with the maximum occurring around day 171 and the minimum occurring around day 355.

The graph shows that the function is periodic, with a period of 365 days, as expected.

Therefore, the function is plotted.

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In Jameson's drawing, the nose cone has an area of 5 square inches. Each of the fins has an area of 3 square inches and the total area of the drawn rocket is 22 square inches.

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

The drawing (see attachment)

The area of the nose cone is

Area = 1/2 * 5 * 2

Area = 5 square inches

For the fin, we have

Fin = 1/2 * 3 * 2

Fin = 3 square inches

Lastly, we have

Total area = (4 + 2 + 1) * 2 + 5 + 3

Total area = 22 square inches

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Answer: 18/25 or 0.72

Step-by-step explanation:

1. Write all numerators above the least common denominator 25

(15 + 3 / 25)

2. Add the numbers

( 18 / 25 )

3. Solution is 18/25 or 0.72

the graph of Andrew's distance from home will look like this: Time (x-axis)  0  1  2  3  4  5  6  7  8  9  10 Distance (y-axis)  0  5  10 10 15 20 20 24 28 32  0

Graph is a data structure which is used to represent relationships between objects or data points. It is composed of nodes and edges, where nodes are the objects and edges are the connections between the objects. Graphs are used to represent mathematical equations, networks, and data structures such as trees. They are also used to represent relationships between data points in large datasets. Graphs can be used to represent both directed and undirected relationships, and are commonly used in many fields including computer science, engineering, mathematics, and data science.

From the given information, we can create a graph that shows Andrew's distance from home as he drives to the store, to the bank, and back again. The x-axis will represent time (in minutes), and the y-axis will represent the number of blocks away from home.

At time zero, Andrew is at his home, so the graph will begin with a point at (0, 0). As he travels to the store, the graph will move up 5 blocks for every minute he drives. Therefore, after 2 minutes, he will be 10 blocks away from home, so the graph will be at (2, 10). After he stops at the store for 2 minutes, he will still be 10 blocks away from home, so the graph will stay at (2, 10).

When he leaves the store and drives to the bank, he will move 5 blocks each minute. After 5 minutes, he will be 25 blocks away from home, so the graph will be at (5, 25). After he stops at the bank for 3 minutes, he will still be 25 blocks away from home, so the graph will remain at (5, 25).

Finally, when he drives home, he will move 4 blocks for each minute he drives. After 5 more minutes, he will be back at his home, so the graph will be at (10, 0).

Therefore, the graph of Andrew's distance from home will look like this:

Time (x-axis)  0  1  2  3  4  5  6  7  8  9  10

Distance (y-axis)  0  5  10 10 15 20 20 24 28 32  0

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Answer:

1.  d   (last option)

2.  a   (first option)

Step-by-step explanation:

Question 1

Rewrite \(b=\pi r^2+c\) to make r the subject.

Subtract c from both sides:

\(\implies b-c=\pi r^2\)

Divide both sides by \(\pi\) :

\(\implies r^2=\dfrac{b-c}{\pi}\)

Square root both sides:

\(\implies r=\pm\sqrt{\dfrac{b-c}{\pi}}\)

Question 2

Rewrite \(d=\sqrt{\dfrac{h}{6.752}}\) to make h the subject.

Square both sides:

\(\implies d^2=\dfrac{h}{6.752}\)

Multiply both sides by 6.752:

\(\implies h=6.752d^2\)

Comparing the relative change in health care spending from 1977 to 2015 to the overall rate of inflation as measured by the consumer price index is 3665%

The Centers for Medicare and Medicaid (CMS) reported that health care costs in the United States rose 5.8% in 2015 to $3.2 trillion, or $9,990 per person. The share of the US economy spent on health care was 17.8% in 2015, down from 17.4% in 2014, as measured by CMS.

The increase is due to the expansion of coverage from 2014 due to the Affordable Care Act.

Consumer price Index:

The Consumer Price Index (CPI) measures monthly changes in prices paid by US consumers. The US Bureau of Labor Statistics (BLS) calculates the CPI as the weighted average price of a basket of goods and services representative of the entire United States expenses.

The CPI is one of the most popular indicators of inflation and deflation. The CPI report uses a different survey methodology, price sample, and index weighting than the Producer Price Index (PPI), which measures changes in prices received by U.S. producers of goods and services.

According to the Question:

=  \(\frac{CPI_2015 - CPI_1977}{CPI_1977}\)

= 3,200,000,000,000−85,000,000,000 ÷ 85,000,000,000

=  3,200−85 ÷ 85

= 36.647

= 3665%

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Answer:

1. ROUNDED 64.85 + 14.27 = 79.12

NOT ROUNDED 64.85 + 14.26 = 79.11

2. 143.50 + 9.32 = 152.82 not rounded

143.50 + 9.33 = 152.83 rounded

Step-by-step explanation:

1.

We need to find 22% of 64.85, and we do that by multiplying

64.85 x 0.22 = 14.267

Now we have 2 choices, if you round, the tip will be 14.27, but if you do not round, it will be 14.26. If you aren't sure, round the answer. 64.85 + 14.27 = 79.12  OR 64.85 + 14.26 = 79.11

2.

We will first solve for the total cost of the tickets before the sales tax

140.00 + 3.50 = 143.50

Then, we will calculate sales tax

143.50 x 0.065 = 9.32 not rounded

143.50 x 0.065 = 9.33 rounded

143.50 + 9.32 = 152.82 not rounded

143.50 + 9.33 = 152.83 rounded

Answer:

x = 10/243

Step-by-step explanation:

3^5x = 10

243x = 10

Divide 243 on both sides

10/243

Since we know the sequence is quadratic, we expect the \(n\)-th term to have the general form

\(x_n = an^2 + bn + c\)

Plug in the first 3 known values of the sequence to form a system of equations.

\(x_1 = 3 = a + b + c\)

\(x_2 = 12 = 4a + 2b + c\)

\(x_3 = 25 = 9a + 3b + c\)

Eliminating \(c\) gives

\((4a + 2b + c) - (a + b + c) = 12 - 3 \implies 3a + b = 9\)

\((9a + 3b + c) - (a + b + c) = 25 - 3 \implies 8a + 2b = 22 \implies 4a + b = 11\)

Eliminating \(b\) gives

\((4a + b) - (3a + b) = 11 - 9 \implies a = 2\)

Solving for \(b,c\), we get

\(4a + b = 11 \implies b = 11-4\cdot2 = 3\)

\(a+b+c=3 \implies c=3-2-3 = -2\)

So, the \(n\)-th term of the sequence is

\(x_n = \boxed{2n^2 + 3n - 2}\)

Answer:

(a) After 9 months, the unpaid balance is $125,874.09.

(b) Over the 9 months, she paid a total of $4,918.56 in interest.

To create the amortization table, we can use the formula for calculating the monthly payment of a loan:

P = (r * A) / (1 - (1 + r)^(-n))

where:

P = monthly payment

r = monthly interest rate

A = loan amount

n = total number of payments

In this case, we have:

A = $128,000.00

n = 25 years * 12 months/year = 300 months

r = 5.3% / 12 = 0.00441666667

Using the formula, we can calculate the monthly payment:

P = (0.00441666667 * $128,000.00) / (1 - (1 + 0.00441666667)^(-300))

P = $770.82

Now, we can create the amortization table:

The required equation of the circle is (x - 3)² + (y + 7)² = 5²  

A circle is a collection of all points on a plane that is uniformly distanced from a fixed point. The fixed point is referred to as the circle's center. The formula for the Equation of a circle with center (h, k) and radius 'r' is given by

Here we have

The diameter of the circle = 10 units          

=> Radius of the circle = 10/2 = 5 units

And coordinate of center = (3, -7)

As we know the Equation of a circle is (x - h)² + (y - k)² = r²      

By the given formula

Required equation of the circle = (x - 3)² + (y - (-7))² = 5²  

=> (x - 3)² + (y + 7)² = 5²  

Therefore,

The required equation of the circle is (x - 3)² + (y + 7)² = 5²  

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The sοlutiοn οf the given prοblem οf unitary methοd cοmes οut tο be 12 cupcakes, 24 cupcakes, and 50 cupcakes will cοst rοughly $2.42, $2.33, and $2.58 per cupcake, respectively.

Tο cοmplete the assignment, use the tried-and-true straightfοrward methοdοlοgy, the real variables, and any pertinent details frοm the preliminary and specialized questiοns. In respοnse, custοmers might be given anοther οppοrtunity tο range sample the prοducts. In the absence οf such changes, majοr advances in οur knοwledge οf prοgrammes will be lοst.

Here,

We must divide the tοtal cοst by the quantity οf cupcakes in οrder tο determine the unit cοst οf each οptiοn:

Twelve cupcakes:

Unit cοst is calculated as Tοtal Cοst / Cupcakes.

=>  Unit cοst: $29 fοr 12 cupcakes.

=>  $2.42 is the unit cοst per cupcake.

Tο make 24 cupcakes:

Unit cοst is calculated as Tοtal Cοst / Cupcakes.

=> 24 cupcakes equals $56 fοr the unit.

=>  $2.33 is the unit cοst per cupcake.

50 cupcakes =

Unit cοst is calculated as Tοtal Cοst / Cupcakes.

=>  $129 fοr a unit οf 50 cupcakes.

=>  Unit cοst: $2.58 fοr each cupcake

As a result, 12 cupcakes, 24 cupcakes, and 50 cupcakes will cοst rοughly $2.42, $2.33, and $2.58 per cupcake, respectively.

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The area of the poster in inches is,

⇒ A = 4 inches²

We have to given that;

A rectangular poster is 50 centimeters long and 25 centimeters wide.

Here, 1 centimeter is approximately 0.4 inches

Hence, Lenght = 50 cm

Lenght = 50 x 0.4

            = 2 inches

Width = 25 cm

          = 25 x 0.4

           = 1 inches

Thus, The area of the poster in inches is,

⇒ A = 1 x 4

⇒ A = 4 inches²

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Answer:

 

Translations

y = f (x) + k up k units

y = f (x) - k down k units

y = f (x + h) left h units

y = f (x - h) right h units

Stretches/Shrinks

y = m·f (x) stretch vertically by a factor of m

y = ·f (x) shrink vertically by a factor of m (stretch by  

y = f (x) stretch horizonally by a factor of n

y = f (nx) shrink horizontally by a factor of n (stretch by )

Reflections

y = - f (x) reflect over x-axis (over line y = 0)

y = f (- x) reflect over y-axis (over line x = 0)

x = f (y) reflect over line y = x

Hope this helps

Step-by-step explanation:

Answer:

2.221992

Step-by-step explanation:

can i have the crown pls ૮ ♡ﻌ♡ა

Answer:

2.221

Step-by-step explanation:

Answer:

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

There are various combinations of coins.

In total there are:

The percentage of drivers who are at least 45 is 62%

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

The table of values

From the table, we have

Age 45 = 62 percentile

When represented properly

So, we have

Age 45 = 62%

This means that the percentage of drivers who are at least 45 is 62%

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Answer:

(x-8)(x-8) are the factors of the following biominals

Answer:

Step-by-step explanation:

a. (f + g) (0) = 0

b. (f/g) (3) = 2/3

This can be solved by function method.

Function is a mathematical phrase, rule, or law that establishes the connection between an independent variable and a dependent variable (the dependent variable). A function is described as a relationship between a group of inputs and one output each. In simple terms, a function is a connection between inputs, with each input corresponding to exactly one output. Every function has its own domain and codomain, as well as a range. f(x), where x is the input, is a common way to refer to a function.

(a) (f + g) (0) = .........

g(0) = 0, f(0) = 0

(f + g) (0) = f(0) + g(0)

(f + g) (0) = 0 + 0

(f + g) (0) = 0

(b)

(f/g) (3) = ............

f(3) = 2, g(1/3) = 1

(f/g) (3) = f(3) × g(1/3)

(f/g) (3) = 2 × (1/3)

(f/g) (3) = 2/3

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The storage can hold approximately 10.94 cubic meters of grain.

Unit conversion is the process of converting a quantity expressed in one set of units to an equivalent quantity expressed in another set of units. For example, converting a length from feet to meters, or converting a temperature from Celsius to Fahrenheit.  

To convert cubic yards to cubic meters, multiply the given volume in cubic yards by this conversion factor to obtain the equivalent volume in cubic meters.  

Here we have

Adam’s family maintains storage that can hold 14.3 yd³ of grain.

Given that 1 yard is approximately equal to 0.9144 meters

To convert cubic yards (yd³) to cubic meters (m³),

Use the conversion factor:

1 yd³ = (0.9144 m)³

So, we can convert 14.3 cubic yards of grain to cubic meters as follows:

14.3 yd³ x (0.9144 m/yd)³ ≈ 10.94 m³

Rounding this answer to the nearest hundredth gives us:

10.94 m³ rounded to the nearest hundredth = 10.94 m³

Therefore,

The storage can hold approximately 10.94 cubic meters of grain.

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Answer:

Free Coins!!!

Quadrant 1 if that's what your talking about

The graph below shows a couple of plotting points, one of them being 0,1.

Scores between 23 & 59 will give Paul a C for the semester (an average between 70 and 79).

The sum of the scores on the first three, hundred point tests

= 82 + 88 + 87 = 257.

The total score required in four 100-point tests to get an average score of 70 = 70X4= 280.

The total score required in four 100-point tests to get an average score of 79 = 79X4= 316.

Therefore, the score on the fourth test should be between (280-257) & (316-57) i.e, 23 & 59 to get an average score of 70 & 79.

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Answer:

- The value of the 2 test statistic is 6.98

- There is no sufficient evidence to reject the claim of the specific distribution

Step-by-step explanation:

Given

Proportion (p)

\(ABC = 29\% = 0.29\\CBS = 28\% = 0.28\\NBC = 25\% = 0.25\\Others = 18\% = 0.18\\\)

Samples

\(ABC = 95\\CBD = 65\\NBC = 87\\Others = 53\\\alpha = 0.05\)

First, we formulate a table for chi square totals:

\(x^2 = \frac{(O - E)^2}{E}\)

Where

O = Observed Frequency and E = Expected Frequency

So, we have:

\(\begin{array}{cccccc}{\ } & {O} & {E = np} & {O - E} & {(O -E)^2} & {x^2 = \frac{(O - E)^2}{E}} \ \\ \\ {0.29} & {95} & {87} & {8} & {64} & {0.736} &{0.28} & {65} & {84} & {-19} & {361} & {4.300} & {0.25} & {87} & {75} & {12} & {144} & {1.920} & {0.18} & {53} & {54} & {-1} & {1} & {0.019}\ \end{array}\)

For ABC

\(E = np = 300 * 0.29= 87\)

\(O-E =95 - 87 = 8\)

\((O-E)^2 = 8^2 = 64\)

\(x^2 = \frac{(O - E)^2}{E} = \frac{64}{87} = 0.736\)

For CBS

\(E =np = 300 * 0.28 = 84\)

\(O -E = 65 - 84 = -19\)

\((O -E)^2 = (-19)^2 = 361\)

\(x^2 = \frac{(O - E)^2}{E} = \frac{361}{84} = 4.300\)

For NBC

\(E =np = 300 * 0.25 = 75\)

\(O -E = 87 - 75 = 12\)

\((O -E)^2 = (12)^2 = 144\)

\(x^2 = \frac{(O - E)^2}{E} = \frac{144}{75} = 1.920\)

For others:

\(E = np = 300 * 0.18 =54\)

\(O - E = 53 - 54 = -1\)

\((O - E)^2 = (-1)^2= 1\)

\(x^2 = \frac{(O - E)^2}{E} = \frac{1}{54} = 0.019\)

\(\sum x^2 = 0.736 + 4.300 + 1.920 + 0.019\)

\(\sum x^2 = 6.975\)

\(\sum x^2 = 6.98\) --- approximated

The value of the 2 test statistic is 6.98

Next, is to determine the p value:

Calculate the degree of freedom

\(df = n - 1\)

\(df = 4 - 1\)

\(df = 3\)

Using the \(x^2\) table in the 3rd row,

\(\sum x^2 = 6.98\) corresponds to:

\(p = 0.072699\)

The value of p is:

\(0.05 < P < 0.10\)

This implies that, we fail to reject H o

The two column proof showing that  ΔWXZ ≅ ΔYXZ is as shown below

From the given triangle, we see that;

Given: WX ≅ XY, XZ bisects WXY

Prove: ΔWXZ ≅ ΔYXZ

The two column proof for the above is as follows;

Statement 1;  WX ≅ XY, XZ bisects 2

Reason 1; Given

Statement 2: ∠WXZ ≅ YXZ

Reason 2; Angle bisector

Statement 3; XZ ≅ XZ

Reason 3: Reflexive property of congruence

Statement 4:  ΔWXZ  ≅ ΔYXZ

Reason 4:  SAS Congruence Postulate

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Answer:

false

Step-by-step explanation:

I think it is backwards to figure a fifteen percent discount, you would make 15% into .15 and then multiply .15 times the original prioce to see the amount off.