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mash [69]
3 years ago
11

Donis bought a t-shirt for $15 and jeans for $35.50. If the sales tax rate is 8.25%. What is the sales tax for the t-shirt and j

eans in dollars and cents? *
Mathematics
1 answer:
SOVA2 [1]3 years ago
6 0
<h3>Answer: 4 dollars and 17 cents</h3><h3>This is the same as saying $4.17</h3>

====================================================

Explanation:

15+35.50 = 50.50 dollars is the total before tax is applied.

Take 8.25% of this to get

0.0825*50.50 = 4.16625

and this rounds to 4.17, which is the amount of sales tax charged.

$4.17 = 4 dollars + 17 cents

---------

Extra info:

The grand total will be 50.50+4.17 = 54.67

Another way to get the grand total is to multiply 1.0825 by the previous subtotal (50.50) getting 50.50*1.0825 = 54.66625 and that rounds to 54.67

The multiplier 1.0825 effectively means "increase by 8.25%"

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Triangle m is similar to triangle n. Triangle m has two angles with measures of 32°and 93°. Which two angles measures could be i
inysia [295]
Given that triangle m and n are similar, then the implication is the ratio of the corresponding sides are the same and the corresponding angles are equal. This implies that if the two angles of triangle m measure 32° and 93°, then the possible size for the two angles in triangle n will be 32° and 93°.
6 0
3 years ago
Y=-x^2+2x+10<br> y=x+2<br><br> Substitution <br> Please show your work<br> Need ASAP
erik [133]

Answer:

The solutions of the system of equations are the points

(\frac{1-\sqrt{33}} {2},\frac{5-\sqrt{33}} {2})  

(\frac{1+\sqrt{33}} {2},\frac{5+\sqrt{33}} {2})  

Step-by-step explanation:

we have

y=-x^{2} +2x+10 ----> equation A

y=x+2 ----> equation B

Solve the system by substitution

substitute equation B in equation A

x+2=-x^{2} +2x+10

solve for x

-x^{2} +2x+10-x-2=0

-x^{2} +x+8=0

The formula to solve a quadratic equation of the form

ax^{2} +bx+c=0

is equal to

x=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}

in this problem we have

-x^{2} +x+8=0

so

a=-1\\b=1\\c=8

substitute in the formula

x=\frac{-1\pm\sqrt{1^{2}-4(-1)(8)}} {2(-1)}

x=\frac{-1\pm\sqrt{33}} {-2}

x=\frac{-1+\sqrt{33}} {-2}  -----> x=\frac{1-\sqrt{33}} {2}  

x=\frac{-1-\sqrt{33}} {-2}  -----> x=\frac{1+\sqrt{33}} {2}  

<em>Find the values of y</em>

For x=\frac{1-\sqrt{33}} {2}  

y=x+2

y=\frac{1-\sqrt{33}} {2}+2  ---->y=\frac{5-\sqrt{33}} {2}  

For x=\frac{1+\sqrt{33}} {2}  

y=x+2

y=\frac{1+\sqrt{33}} {2}+2  ---->y=\frac{5+\sqrt{33}} {2}  

therefore

The solutions of the system of equations are the points

(\frac{1-\sqrt{33}} {2},\frac{5-\sqrt{33}} {2})  

(\frac{1+\sqrt{33}} {2},\frac{5+\sqrt{33}} {2})  

5 0
3 years ago
Find the volume of the given solid. Under the surface z = 6xy and above the triangle with vertices (1, 1), (4, 1), and (1, 2)
Leya [2.2K]

he volume of the solid under a surface  

z

=

f

(

x

,

y

)

and above a region D is given by the formula  

∫

∫

D

f

(

x

,

y

)

d

A

.

Here  

f

(

x

,

y

)

=

6

x

y

. The inequalities that define the region D can be found by making a sketch of the triangle that lies in the  

x

y

−

plane. The bounding equations of the triangle are found using the point-slope formula as  

x

=

1

,

y

=

1

and  

y

=

−

x

3

+

7

3

.

Here is a sketch of the triangle:

Intersecting Region

The inequalities that describe D are given by the sketch as:  

1

≤

x

≤

4

and  

1

≤

y

≤

−

x

3

+

7

3

.

Therefore, volume is

V

=

∫

4

1

∫

−

x

3

+

7

3

1

6

x

y

d

y

d

x

=

∫

4

1

6

x

[

y

2

2

]

−

x

3

+

7

3

1

d

x

=

3

∫

4

1

x

[

y

2

]

−

x

3

+

7

3

1

d

x

=

3

∫

4

1

x

[

49

9

−

14

x

9

+

x

2

9

−

1

]

d

x

=

3

∫

4

1

40

x

9

−

14

x

2

9

+

x

3

9

d

x

=

3

[

40

x

2

18

−

14

x

3

27

+

x

4

36

]

4

1

=

3

[

(

640

18

−

896

27

+

256

36

)

−

(

40

18

−

14

27

+

1

36

)

]

=

23.25

.

Volume is  

23.25

.

4 0
3 years ago
A group of friends shared the cost of a printer. If John, Carl and Jason each paid $15, $25, and $112 respectively, then Carl pa
vfiekz [6]

The percent of the cost of the printer Carl paid is 16.45%

<h3>The total cost of printer</h3>

Since John, Carl and Jason each paid $15, $25, and $112 respectively, the total cost of the printer is T = $15 + $25 + $112 = $152

Since Carl paid $25, we need to find the percent of the total amount Carl paid.

<h3>Percent Carl paid</h3>

So, percent Carl paid = amount Carl paid/total cost × 100 %

Since amount Carl paid = $25 and total cost = $152,

Substituting the values of the variables into the equation, we have

percent Carl paid = amount Carl paid/total cost × 100 %

percent Carl paid = $25/$152 × 100 %

percent Carl paid = 0.1645 × 100 %

percent Carl paid = 16.45%

The percent of the cost of the printer Carl paid is 16.45%

Learn more about percent here:

brainly.com/question/24877689

6 0
2 years ago
A rectangle's length, x, is 2 meters greater than its width. If the perimeter of the rectangle is greater than 112 meters, what
kotykmax [81]
Assume widthis x-2
perimeter is 2*(width+length)
so 2*(x+x-1)>112
2*(2x-1)>112
4x-2>112
x>28.5
so any length greater than 28.5 will work
6 0
3 years ago
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