MATHEMATICS HIGH SCHOOL

The price of a pair of shoes is $45.90. The sales-tax rate is 5 percent. How much sales tax do you need to pay?

Answers

Answer 1

Answer:

Answer:

The sales tax that is needed to be paid is $2.295

Step-by-step explanation:

Given : The price of a pair of shoes is $45.90. The sales-tax rate is 5 percent.

We have to find the sales tax that is needed to be paid.

Consider the given price of shoes as $ 45.90

Since, 5% is sales tax.

So, he pays 5% of 45.90

That is $(5)/(100)* 45.90=2.295$

Thus, The sales tax that is needed to be paid is $2.295.

Answer 2

Answer: The sales tax is 2.295, which rounded is $2.30, which is the sale tax

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He number of 90° angles formed by the intersections of and the two parallel lines and is .
Adam tried to compute the average of his 7 test scores. He mistakenly divided the correct sum of all of his test scores by 6, which yielded 84. What is Adam’s correct average test score?
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Trig help (Problems already solved)?The calculation for the problems are already done but I have to list a reason or what is being done in each step. "Each = and newline made" means a place I have to write what is being done in the calculation.

1. (secx + sinx)cotx = cscx + cosx
=(secx + sinx)cotx = cscx + cosx
=(1 / sinx) + cosx
=cscx + cosx

2. cosx + tanx sinx = secx
=cosx + tanx sinx = cosx + (sinx / cosx)sinx
=cosx + (sin^2x / cosx) = (1 / cosx)(cos^2x + sin^2x)
=1 / cosx
=secx

3. cscx - cosx cotx = sinx
=cscx - cosx cotx = (1 / sinx) - cosx(cosx / sinx)
=(1 / sinx) - (cos^2x / sinx)
=(1 - cos^2x) / sinx
=sin^2x / sinx = sinx

4. (cosx / (1 + cosx)) + (cosx / (1 - cosx)) = 2cotx cscx
=(cosx / (1 + cosx)) + (cosx / (1 - cosx)) = ((cosx (1 - cosx) + cosx (1 + cosx))) / (1 + cosx)(1 - cosx)
=(cosx - cos^2x + cosx + cos^2x) / (1 - cos^2x)
=2cosx / sin^2x
=2(cosx / sinx)(1 / sinx) = 2cotx cscx

Thank you to whoever decides to help me with explaining what is happening on each line.

Answers

The first identity uses the definition of the reciprocal functions $\sec x,\csc x,\cot x$ and the distributive property of multiplication.

$(\sec x+\sin x)\cot x=\left(\frac1{\cos x}+\sin x\right)(\cos x)/(\sin x)$
$=(\cos x)/(\cos x\sin x)+(\cos x\sin x)/(\sin x)$
$=\frac1{\sin x}+\cos x$
$=\csc x+\cos x$

The second uses the definition of $\tan x$ and the distributive property. Then a factor of $\frac1{\cos x}$ is pulled out, which allows you to use the identity $\sin^2x+\cos^2x=1$ .

$\cos x+\tan x\sin x=\cos x+(\sin x)/(\cos x)\sin x$
$=\cos x+(\sin^2x)/(\cos x)$
$=(\cos^2x)/(\cos x)+(\sin^2x)/(\cos x)$
$=\frac1{\cos x}\left(\cos^2x+\sin^2x\right)$
$=\frac1{\cos x}*1$
$=\frac1{\cos x}$
$=1$

The third uses the same ideas as the second: rewrite the reciprocal functions, then invoke the Pythagorean identity $\sin^2x+\cos^2x=1$ , which is equivalent to $\sin^2x=1-\cos^2x$ .

$\csc x-\cos x\cot x=\frac1{\sin x}-\cos x(\cos x)/(\sin x)$
$=\frac1{\sin x}-(\cos^2x)/(\sin x)$
$=\frac1{\sin x}\left(1-\cos^2x\right)$
$=\frac1{\sin x}\sin^2x$
$=(\sin^2x)/(\sin x)$
$=\sin x$

In the last one, you combine the fractions by enforcing common denominators. This lets you add the numerators together, and the denominator can be simplified. Once you do that, you rewrite the factors of cos and sin in the numerator and denominator to make up the cot and csc functions, and you're done.

$(\cos x)/(1+\cos x)+(\cos x)/(1-\cos x)=(\cos x(1-\cos x))/((1+\cos x)(1-\cos x))+(\cos x(1+\cos x))/((1-\cos x)(1+\cos x))$
$=(\cos x(1-\cos x)+\cos x(1+\cos x))/((1-\cos x)(1+\cos x))$
$=(\cos x(1-\cos x+1+\cos x))/(1-\cos^2x)$
$=(2\cos x)/(\sin^2x)$
$=2(\cos x)/(\sin x)\frac1{\sin x}$
$=2\cot x\csc x$

Over a two-hour time period, a snail moved 108 inches. How far is this in yards?

Answers

In two-hour time period, a snail moved 3 yards.

Given that, over a two-hour time period, a snail moved 108 inches.

Metric Conversion refers to the conversion of the given units to desired units for any quantity to be measured.

We know that, 1 yard = 36 inches

Here, in yards = 108/36

= 3 yards

Therefore, in two-hour time period, a snail moved 3 yards.

To learn more about the metric conversion visit:

brainly.com/question/21244256.

#SPJ6

the snail moved 108 inches
108/36=3 yards
as 1 yard=36 in

Evaluate the summation of 20 times 0.5 to the n minus 1 power, from n equals 3 to 12.

Answers

Answer:

The sum of the series is 9.99

Step-by-step explanation:

We are given the series $\sum_(n=3)^(12)20(0.5)^(n-1)$ .

So, $a_(n)=20(0.5)^(n-1)$ , where n=3 to 12

Then, we have,

$1.\ a_(3)=20(0.5)^(3-1)\na_(3)=20(0.5)^(2)\na_(3)=5$

$2.\ a_(4)=20(0.5)^(4-1)\na_(4)=20(0.5)^(3)\na_(4)=2.5$

Thus, the common ratio is $r=(2.5)/(5)=0.5$

Since, the sum of first n terms of a series is $S=(a_(1)(1-r^(n)))/(1-r)$ .

As n = 3 to 12, then the number of terms = 10, first term=a₃= 5 and r= 0.5

So, the sum of 10 terms is $S=(5(1-(0.5)^(10)))/(1-0.5)$

i.e. $S=(5(1-0.00098))/(0.5)$

i.e. $S=(5* 0.99902)/(0.5)$

i.e. $S=(4.9951)/(0.5)$

i.e. S = 9.99

Hence, the sum of the series is 9.99

Answer: 9.99

Step-by-step explanation:

I just took the quiz!

PLEASE HELP. What is the equation of the circle in standard form where the center is (-16,-14) and another point on the circle is (-8,-8)

Answers

recall that the radius is the distance from the center of a circle to any point on the circle.

we know the center is at -16,-14, and we know that -8,-8 is a point on the circle, so the distance between both must be the radius.

$\bf ~~~~~~~~~~~~\textit{distance between 2 points}\n\n(\stackrel{x_1}{-16}~,~\stackrel{y_1}{-14})\qquad(\stackrel{x_2}{-8}~,~\stackrel{y_2}{-8})\qquad \qquadd = √(( x_2- x_1)^2 + ( y_2- y_1)^2)\n\n\n\stackrel{radius}{r}=√([-8-(-16)]^2+[-8-(-14)]^2)\n\n\nr=√((-8+16)^2+(-8+14)^2)\implies r=√(8^2+6^2)\n\n\nr=√(100)\implies \boxed{r=10}\n\n[-0.35em]\rule{34em}{0.25pt}$

$\bf \textit{equation of a circle}\n\n(x- h)^2+(y- k)^2= r^2\qquadcenter~~(\stackrel{-16}{ h},\stackrel{-14}{ k})\qquad \qquadradius=\stackrel{10}{ r}\n\n\n\[x-(-16)]^2+[y-(-14)]^2=10^2\implies \blacktriangleright (x+16)^2+(y+14)^2=100 \blacktriangleleft$

Darien could swim 30 laps anhour last year. This year he can
swim 36 laps an hour. Determine the
percent change

Answers

Answer:

Step-by-step explanation:

If the percent change is 30 to 36 you can already see that it is an increase

here is the work

36 - 30

x 100% = 20%

Answer:

20% increase, which corresponds to the light

Step-by-step explanation:

(y - x)/x * 100

(36 - 30)/30 * 100

(6 * 100)/30

600/30

20% increase

What is the output value for the following function if the input value is 1?y = 3x + 1

32
5
4
0

Answers

If you would like to find the output value for the following function if the input value is 1, you can calculate this using the following steps:

input value ... 1
y = 3x + 1 = 3 * 1 + 1 = 3 + 1 = 4

The correct result would be 4.

Other Questions

Please help I don't understand this

find the area of a triangle with the following dimensions: a = 12 yards b=16 yards and c=24 yards round to the nearest square yard

How much will you save per lb, by buying the least expensive? Round to the nearest cent. 2.5 lbs for $8.75 or 3 pounds for $9.75.

Betty sets up a lemonade stand and charges $1 per glass. It cost her $50 to set up the stand. Which function gives the profit, p, she makes by selling g glasses of lemonade? The number of glasses of lemonade, g, that Betty needs to sell to make a profit, p, if the setup cost her $50 is given by the function . f(g) = .