Every day, people face problems at home, work, school, or in their community that they must solve. Think about your life from the past 2 weeks, when something did not work out the way you intended, such as your car breaking down, you running out of milk, or facing a scheduling conflict. A lot of them need you to use math to help solve the problem.

Share at least 1 problem that you encountered recently, and answer the following questions in your main post:

What was the problem, and why it was difficult for you?
How did you use math in trying to solve the problem, and what was the outcome?
How would you approach in the problem differently next time?

The sample size needed to be 99​% confident that the sample proportion will not differ from the true proportion by more than ​4% is given as follows:

n = 1037.

A confidence interval of proportions has the bounds given by the rule presented as follows:

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which the variables used to calculated these bounds are listed as follows:

The margin of error is given as follows:

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

The confidence level is of 99%, hence the critical value z is the value of Z that has a p-value of \(\frac{1+0.99}{2} = 0.995\), so the critical value is z = 2.575.

As we have no estimate, the parameter is given as follows:

\(\pi = 0.5\)

Then the sample size for M = 0.04 is obtained as follows:

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

\(0.04 = 2.575\sqrt{\frac{0.5(0.5)}{n}}\)

\(0.04\sqrt{n} = 2.575 \times 0.5\)

\(\sqrt{n} = \frac{2.575 \times 0.5}{0.04}\)

\((\sqrt{n})^2 = \left(\frac{2.575 \times 0.5}{0.04}\right)^2\)

n = 1037.

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Answer: To calculate the tip amount, we need to multiply the bill amount by the percentage tip as a decimal:

Tip amount = 0.20 x $76 = $15.20

To find the total amount to pay, we add the bill amount and the tip amount:

Total amount = $76 + $15.20 = $91.20

Rounding this to the nearest dollar gives:

Total amount = $91

Therefore, you need to pay $91 in total if you leave a 20% tip on a $76 bill.

Step-by-step explanation:

Answer:

proof below

Step-by-step explanation:

Remember that a number is even if it is expressed so n = 2k. It is odd if it is in the form 2k + 1 (k is just an integer)

Let's say we have to odd numbers, 2a + 1, and 2b + 1. We are after the sum of their squares, so we have (2a + 1)^2 + (2b + 1)^2. Now let's expand this;

(2a + 1)^2 + (2b + 1)^2 = 4a^2 + 4a + 4b + 4b^2 + 4b + 2

= 2(2a^2 + 2a + 2b^2 + 2b + 1)

Now the sum in the parenthesis, 2a^2 + 2a + 2b^2 + 2b + 1, is just another integer, which we can pose as k. Remember that 2 times any random integer, either odd or even, is always even. Therefore the sum of the squares of any two odd numbers is always even.

Answer:

It's not

Step-by-step explanation:

To know this, you have to put a zero to the right.

So it'd be 34.3210, and as you can see, 34.3211 is greater

Answer:

I don't know the answer

Step-by-step explanation:

c.1

Answer:  The correct answer is y = 10x – 45

Step-by-step explanation:

When graphing a line with a slope of 10 from point (5,5), we find that the y-intercept (where the line crosses the y-axis) is -45

Use the slope-intercept form (y=mx+b), where m=slope (10) and b=the y-intercept (-45)

y = 10x - 45

Answer:

The rates are not equivalent since Maria saves $0.50 more per month than Ralph.

Step-by-step explanation:

We can determine if two rates are equivalent by comparing the rates at which they save per month.

Maria's savings per month:

Both 50 and 4 can be divided by 2, which gives us 25/2.  As a regular number, this becomes 12.5/1 which means Maria saves $12.5 per month.

Ralph's savings per month:

Both 60 and 5 can be divided by 5, which gives us 12.  Thus, Ralph saves $12 per month.

Thus, the rates are not equivalent as Maria saves $0.50 more per month than Ralph.

Answer:

Yes

Step-by-step explanation:

yes because if she keeps her money then,

Answer: The smartest option for Isabel in her case would be to keep the Traditional 401 (k), this is because she ends up with 50 more dollars rather than losing money with the Roth 401 (k). This is only true if her assumptions and calculations are accurate. With her saying that she believes that she will not be in a higher tax bracket, and she wants the most take home money possible then I would recommend she stays with the Traditional 401 (k).

Step-by-step explanation:

With a traditional 401 (k) although you don't have to pay taxes up front, you still need to pay taxes on any capital gains/when you take that money out you will then have to pay some taxes. Although this is the case if you are in a higher tax bracket when you take that money out you will have to be paying at that higher tax bracket. With a Roth 401(k) you pay those taxes up front, but all those capital gains you may recieve over time you end up not having to pay taxes on ANY of it. So if you are in a higher tax bracket and get more of those gains over time from being in that bracket then it would be the smartest option to go with the Roth 401(k). Now this would be smart to go with a Roth 401(k) if you are young and just starting out because you can advance through future opportunies, but in Isabel's case this is different. She says that she believes that her tax bracket won't change and if she wants to have the most take home money possible then in her case it would be the smartest option to go with the traditional 401 (k) because she will be taking home 50 more bucks according to her calculations.

Answer:

Hi

please mark brainliest ❣️

Thanks

Step-by-step explanation:

10 + x / 3 = 12

Cross multiply

10 + x = 12× 3

10 + x = 36

Collect like terms

x= 36 - 10

x = 26

Answer:

DEF = 110

Step-by-step explanation:

Supplementary angles add to 180

3x+5  +2x = 180

Combine like terms

5x +5 = 180

Subtract 5 from each side

5x = 175

Divide each side by 5

5x/5 = 175/5

x =35

DEF = 3x+5

     = 3*35 +5

    = 105+5

   = 110

Answer:

x = 45

Step-by-step explanation:

Note that:

The sum of the interior angles of a quadrilateral is 360°.

Angle: ADC+BAD+ABC+BCD = 360°

Thus, Substitute  ∠ABC = 3x, ∠BAD = (2x-5) , ∠ ADC = (x+15), ∠ BCD = 80 turn into ADC+BAD+ABC+BCD = 360° :

Also known as :

(x+15) +(2x-5) + 3x+80=360

Solving for x

Add the numbers

x + 90+2x+3x=360

Combine like terms

6x + 90=360

subtract 90 from both sides

6x = 270

x = 45

Hence the value of x = 45

Kavinsky

Answer:

C. 45

Step-by-step explanation:

1) Sum of the interior angles of any shape:

(n - 2) x 180, where n is the number of vertices of a shape. In this case, we have 4 vertices.

= (4 - 2) x 180

= 2 x 180

= 360°

2) Add all the given values equating to 360.

2x - 5 + 3x + 80 + x + 15 = 360

6x + 90 = 360

6x = 360 - 90

6x = 270

x = 270/6

x = 45

Answer:

5.44 meters

Step-by-step explanation:

We Know

0.3048 meter = 1 ft

How many ft makes a height of 1.66m?

We Take

1.66 ÷ 0.3048 ≈ 5.44 meters

So, the answer is 5.44 meters.

Answer:

19.99%

Step-by-step explanation:

hope this helps

here you go

The value for the Inequality 13x ≤ 200 is x ≤ 15.384.

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Given:

13 times a number x is less than or equal to 200.

Now, Writing the Inequality Mathematically

13x ≤ 200

x ≤ 200 / 13

x ≤ 15.384

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Answer:

It is most likely that, out of 25 online readers, between 12 and 13 work in the business industry.

Step-by-step explanation:

Answer:

There is about a 0.046 chance that 9 or fewer online readers work in the business industry. This is unusual and is convincing evidence that less than 50% of online readers work in the business industry.

Step-by-step explanation:

I just took the test, The other person is very wrong!!!

Answer:

The amount to be paid for 2 kilograms of oranges is 3.0 TL.

Step-by-step explanation:

The total amount of oranges to be bought is, Q = 2 kilograms.

The cost of 1 kilogram of oranges is, C = 1.5 TL.

Compute the cost of 2 kilograms of oranges as follows:

Total cost = Q × C

                \(=2\times 1.5\ \text{TL}\\\\=3.0\ \text{TL}\)

Thus, the amount to be paid for 2 kilograms of oranges is 3.0 TL.

Answer:

12/20

Step-by-step explanation:

\(\displaystyle \frac{3}{5}=\frac{3}{5}\cdot\frac{4}{4}=\frac{12}{20}\)

The answer is:

In-depth-explanation:

The denominator of 3/5 is 5. To get from 5 to 20, we multiply it by 4.

We need to multiply both the numerator and the denominator by 4, so we do this:

\(\sf{\dfrac{3\times4}{5\times4}}\)

\(\sf{\dfrac{12}{20}}\)

Step-by-step explanation:

I don't want the place but the fishy on me

Got a lot to be but the fishy on me

Got a lot to do, I'll slap your knee

Fishy on me, fishy on me

I don't want the place but the fishy on me

Got a lot to be but I'll slap your knee

Fishy 2B but I don't know he

Fishy on me if the fishy 2B

I don't know what the place but the fishy on me

Fishy on me, fishy on me

I don't know the place but the fishy on me

2HB I'll slap your knee  

I'll slap your knee

Fishy on me, a place to be

I don't know what the place but the fishy on me

Fishy on me, I'll slap your knee. fishhhyyyyyyyyyyyyyyyyyyyyyyyyyyy

The volume of the sphere is approximately 3431.82 cubic miles.

To find the volume of a sphere, we need the radius of the sphere. The length of a great circle is the circumference of the sphere, which is related to the radius by the formula C = 2πr, where C is the circumference and r is the radius.

In this case, we are given that the length of the great circle is 60 miles. We can use this information to find the radius of the sphere.

C = 2πr

60 = 2πr

Divide both sides of the equation by 2π:

r = 60 / (2π)

r = 30 / π

Now that we have the radius, we can use the formula for the volume of a sphere:

V = (4/3)πr³

V = (4/3)π(30/π)³

V = (4/3)π(27000/π³)

V = (4/3)π(27000/π³)

V = (4/3)π(27000/π³)

V = (4/3)(27000/π²)

V = (4/3)(27000/9.87) (approximating π to 3.14)

V ≈ 3431.82 cubic miles

Therefore, the volume of the sphere is approximately 3431.82 cubic miles.

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Question

You are given the great circle of a sphere is a length of 60 miles. What is the volume of the sphere?

Question 1:

(a) The equation representing Elaine's total parking cost is:

C = x * t

(b) So the cost of parking for a full 24 hours would be 24 times the cost per hour.

Question 2:

The given system of equations is inconsistent and has no solution.

(a) To represent Elaine's total parking cost, C, in dollars for t hours, we need to know the cost per hour. Let's assume the cost per hour is $x.

(b) If Elaine wants to park her car for a full 24 hours, we can substitute t = 24 into the equation from part (a):

C = x * 24

Question 2:

To solve the linear system:

-x - 6y = 5

x + y = 10

We can use the elimination method.

Multiply the second equation by -1 to create opposites of the x terms:

-x - 6y = 5

-x - y = -10

Add the two equations together to eliminate the x term:

(-x - 6y) + (-x - y) = 5 + (-10)

-2x - 7y = -5

Now we have a new equation:

-2x - 7y = -5

To check the answer, we can substitute the values of x and y back into the original equations:

From the second equation:

x + y = 10

Substituting y = 3 into the equation:

x + 3 = 10

x = 10 - 3

x = 7

Checking the first equation:

-x - 6y = 5

Substituting x = 7 and y = 3:

-(7) - 6(3) = 5

-7 - 18 = 5

-25 = 5

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Answer:

2.5 km/h

Step-by-step explanation:

Here we have a distance problem where we are given the distance the time time:

Rate = ?

Time = 2hrs

Distance = 5km

The simplest way to do this is to rearrange the formula to suit our need and plug in the numbers:

\(R*T=D\\R*\frac{T}{T}=\frac{D}{T} \\R=\frac{D}{T}\)

Now, plug in the numbers and solve:

\(R=\frac{D}{T}\\R=\frac{5}{2} \\R=2.5\)

Answer:

Yes

Step-by-step explanation:

To know if a table is a function or not, we have to see if 1 input only has 1 output.

Looking at the table each input only has 1 output, so it is a function.

Answer:     A: 0.25,      B: 0.15      C: 0.71       D: 0.7125

Step-by-step explanation:

Answer:

y = -4x + 6

Step-by-step explanation:

The graph for the given equation of a line with the coordinates (0, 6), (1, 2), (2, -2), (3, -6) and so on are plotted.

The equation of a line is 4x+y=6.

Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them. The length of the lines and position of the points do not matter.

Here, y=6-4x

Substitute x=0, 1, 2, 3, 4, 5,..... in the given equation, we get

When x=0

y=6

When x=1

y=2

When x=2

y=-2

When x=3

y=-6

So, the coordinates are (0, 6), (1, 2), (2, -2), (3, -6) and so on.

Therefore, the graph for the given equation of a line with the coordinates (0, 6), (1, 2), (2, -2), (3, -6) and so on are plotted.

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Given statement solution is :- "F(g(x)) g(f(x))": The function F(x) is composed with g(x), and the result is further composed with g(f(x)).

"f(g(x)) g(f(x))": The function g(x) is composed with f(x), and the result is further composed with g(f(x)).

The expressions "F(g(x)) g(f(x))" and "f(g(x)) g(f(x))" are compositions of functions. The answer to the question posed would depend on the specific functions F(x) and g(x), as well as f(x) and g(x) in the second expression.

To provide a brief response:

For the expression "F(g(x)) g(f(x))": The function F(x) is composed with g(x), and the result is further composed with g(f(x)). The order of composition is F(g(x)) first, followed by g(f(x)).

For the expression "f(g(x)) g(f(x))": The function g(x) is composed with f(x), and the result is further composed with g(f(x)). The order of composition is f(g(x)) first, followed by g(f(x)).

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In conclusion  the zeros of the function are: (-4 + ✓10, 0) and (-4 - ✓10, 0) and the zeros of the function are complex conjugate pairs, given by: (-1/2 + (✓5/2)i, 0) and (-1/2 - (✓5/2)i, 0)

How to solve?

To find the zeros of x² + 8x + 7, we need to solve the equation x² + 8x + 7 = 0. We can do this by factoring the quadratic expression or using the quadratic formula.

Using the quadratic formula, we have:

x = (-b ± ✓(b² - 4ac)) / 2a

where a = 1, b = 8, and c = 7. Substituting these values, we get:

x = (-8 ± ✓(8² - 4(1)(7))) / 2(1)

x = (-8 ± ✓(40)) / 2

x = (-8 ± 2✓10) / 2

x = -4 ± ✓10

Therefore, the zeros of the function are:

(-4 + ✓10, 0) and (-4 - ✓10, 0)

To find the zeros of 2x² + 2x + 3, we need to solve the equation 2x² + 2x + 3 = 0. We can use the quadratic formula:

x = (-b ± ✓(b² - 4ac)) / 2a

where a = 2, b = 2, and c = 3. Substituting these values, we get:

x = (-2 ± ✓(2² - 4(2)(3))) / 2(2)

x = (-2 ± ✓(-20)) / 4

x = (-2 ± 2✓5i) / 4

Since we cannot have a negative number under the square root for real numbers, the zeros of the function are complex conjugate pairs, given by:

(-1/2 + (✓5/2)i, 0) and (-1/2 - (✓5/2)i, 0)

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Answer:

∠ BDC = 29°

Step-by-step explanation:

the sides of a rhombus are congruent, so CD = ED and Δ EDC is therefore isosceles with base angles congruent , then

∠ BCD = ∠ BED = 61°

• the diagonals are perpendicular bisectors of each other , then

∠ CBD = 90°

the sum of the 3 angles in Δ BCD = 180°

∠ BDC + ∠ CBD + ∠ BCD = 180°

∠ BDC + 90° + 61° = 180°

∠ BDC + 151° = 180° ( subtract 151° from both sides )

∠ BDC = 29°

Answer:

Step-by-step explanation:

a. tan 30/ sin 30 = (sin 30/cos 30) / sin 30 = 1 / cos 30, no

b. cos 30 = √3/2, yes

c. cos 60 tan 60 = cos 60 (sin 60/cos 60) = sin 60 = cos 30, yes

d. sin 60 = cos (90 - 60) = cos 30, yes

\(\bf{b.}\ \ \it cos30^o=\dfrac{\sqrt3}{2}\ \ (True)\\ \\ \bf{d.}\ \ \it sin60^o=cos(90^o-60^o)=cos30^o\ \ (True) \\ \\ \bf{c.}\ \it cos60^o\cdot tan60^o=cos60^o\cdot\dfrac{sin60^o}{cos60^o}=\dfrac{cos60^o}{cos60^o}\cdot sin60^o=1\cdot sin60^o=cos30^o\ (T)\\ \\ \\ \bf{a.}\ \ \it \dfrac{tan30^o}{sin30^o}=tan30^o\cdot\dfrac{1}{sin30^o}=\dfrac{sin30^o}{cos30^o}\cdot\dfrac{1}{sin30^o}=\dfrac{sin30^o}{sin30^o}\cdot\dfrac{1}{cos30^o}=\\ \\ \\ =1\cdot\dfrac{1}{cos30^o}=\dfrac{1}{cos30^o}\ \ne\ cos30^o\)

The triangles are similar by SSS congruence of triangles.

What is SSS congruence of triangles?

The two triangles are congruent if the three sides of one triangle are the same as the corresponding three sides (SSS) of the other triangle.

We are given two triangle ABC and PQR.

In order to see whether these are similar or not, we will use the SSS congruence of triangles.

The ratio of sides are:

⇒AB : PQ = 8 : 6

⇒AB : PQ = 4 : 3

Similarly,

⇒BC : QR = 12 : 9

⇒BC : QR = 4 : 3

Similarly,

⇒AC : PR = 12 : 9

⇒AC : PR = 4 : 3

Since, the ratio of all the sides is same so, the triangles are similar.

Hence, the triangles are similar by SSS congruence of triangles.

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Since, there are multiple questions so, the question answered above is attached below