MATHEMATICS HIGH SCHOOL

6. John took Ms. Wisth out for sushi and is NOT a cheapskate. Their total sushi bill was $75.68. Johnwanted to leave a 27% tip. How much money did John tip the waiter?

Answers

Answer 1

Answer: I think the answer would be $9.46 left as a tip for the waiter.

Answer 2

Answer:

Answer:

$20.43 is how much tip was

Step-by-step explanation:

27% >>> .27

.27 * 75.68 = 20.43 tip

Bonus: $96.11 is the all out total

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What is one of the solutions to the following equations? y2+x2=53 Y-x=5
It takes 12 hours to clean the windows of a certain office building. During the first day of cleaning, the workers were able to clean for 9 hours. If the variable t stands for the amount of time the workers have left to clean the windows, which of the following choices is the most reasonable value for t?A. 3 hours B. 1 hour C. 30 hours D. 20 hours
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The sum of the measures of the interior angles of a triangle is equal to _____.

Answers

180 degrees I mean I do not know how to really explain it its based on the amount of sides a shape has and the sum of all 3 interior angles is 180

The base of a cube is parallel to the horizon. A plane cuts through the cube creating a pentagon-shaped cross section. Which kind of plane could it be? A. a vertical plane cutting two adjacent edges of the base B. a vertical plane cutting two opposite edges of the base
C. a slanting plane cutting two adjacent edges of the base
D. a slanting plane containing exactly one edge of the cube

Answers

I think the answer is C. a slanting plane cutting two adjacent edges of the base. I thought of the Pentagon building in Washington where it also has a pentagon-shaped cross section.

Answer:

C. a slanting plane cutting two adjacent edges of the base

Step-by-step explanation:

The base of a cube is parallel to the horizon. A plane cuts through the cube creating a pentagon-shaped cross section. The plane could be - a slanting plane cutting two adjacent edges of the base.

The equation of a circle is (x - 3)2 + (y + 2)2 = 25. The point (8, -2) is on the circle.What is the equation of the line that is tangent to the circle at (8, -2)?

Answers

Answer:

The equation of the line that is tangent to the circle at (8, -2) is:

$x=8$

Step-by-step explanation:

We know that the line which is tangent at a point on a circle is perpendicular to the line joining the center of the circle and that point.

Here we are given the equation of a circle as:

$(x-3)^2+(y+2)^2=25$

The center of the circle is at: (3,-2)

( Since, the standard form of a circle with center at (h,k) and radius r is given by:

$(x-h)^2+(y-k)^2=r^2$ )

Also, the equation of a line joining (3.-2) and (8,-2) is given by:

$y-(-2)=(-2-(-2))/(8-3)* (x-3)\n\ni.e.\n\ny+2=(-2+2)/(5)* (x-3)\n\ni.e.\n\ny+2=(0)/(5)* (x-3)\n\ni.e.\ y+2=0\n\ni.e.\ y=-2$

Also, we know that the slope of this line is zero.

Also, we know that if two lines are perpendicular with slope m and m' respectively then,

$m\cdot m'=-1\n\ni.e.\n\nm'=(-1)/(m)$

Hence, we get that the slope of the tangent line is:

$(-1)/(0)$

Also, we know that:

The equation of a line with given slope m' and a passing through point (a,b) is given by:

$y-b=m'(x-a)$

Here (a,b)=(8,-2)

and $m'=(-1)/(0)$

i.e. the equation of the tangent line is:

$y-(-2)=(-1)/(0)(x-8)\n\ni.e.\n\ny+2* 0=-1(x-8)\n\ni.e.\n\n-1* (x-8)=0\n\ni.e.\n\n(x-8)=0\n\ni.e.\n\nx=8$

Hello,

O=(3,-2) is the center of the circle and 5 its radius.

P=(8,-2)
The line OP is parallele to ox axis so then tangent is parallele to oy axis
Its equation is x=8.

If the population of a country increases at a rate of 1.5% annually, and its current population is 430,000, how many years will it take for the population to triple?

Answers

Answer:

Hence, it will take about 73 years for the population to triple.

Step-by-step explanation:

For this case we have an exponential function P(t) which represents the population at time 't' ; which is given as:

i.e. the equation is represented of the form:

$P(t)=Ab^t$

Where,

A: initial amount ( Here we have A=430000)

b: growth rate (Here we have b=1.015)

t: time in years.

As the population has to triple over the time.

Hence, Substituting values we have:

$3* 430000=430000* (1.015)^t$

⇒ $3=(1.015)^t$

Taking logarithmic function on both side we have:

$\log3=t\log1.015$

( Since $\log m^n=n \log m$ )

⇒ $t=(\log 3)/(\log 1.015)\n\nt=73.78876233$

Hence, It will take for the population to triple about:

t = 73 years

3p=p(1+0.015)^n
3=(1.015)^n
n=Log(3)/log(1.015)
n=??

Over the weekend, the All Smiles Run had 16,478 participants for the Half Marathon. The All Smiles 10K had 6,924 participants, and the 5-Mile Walk had 3,067 participants. How many more people participated in the Half Marathon than in the 10K race and the 5-Mile Walk combined?
a. 6,487
b. 6,587
c. 9,991
d. 12,621

Answers

6924
+3067
=9991

16478
- 9991
= 6587

The answer is b.

tony is putting 42 oranges into 4 boxes. Each box holds 12 oranges . How many more oranges are needed to fill all the boxes?

Answers

4 × 12 = 48 needed to fill all boxes so he needs 6 more oranges.

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