Karen paid $43.70 for a book. The price of the book was $40. what was the sale tax rate

Answer:

The student made the error at step 2.

Step-by-step explanation:

The correct step will be:

Step 2; 6x − 12 = 14 + 2x

As 3 will be multiplied with 2x and 4 which will give 6x − 12

A left-skewed distribution has a long left tail. This is also called negatively-skewed distributions. That’s for the reason that there is a long tail in the negative direction on the number line. The average is also to the left of the peak.

A right-skewed distribution has a long right tail, or positive-skew distributions. That’s for the reason that there is a long tail in the positive way on the number line. The average is also to the right of the peak.

Answer:

c

Step-by-step explanation:

Answer: [tex]5\sqrt{2}\ in[/tex]

Step-by-step explanation:

Given: In a 45-45-90 triangle, the length of one of the legs= 5 in.

Let H be the hypotenuse of the given right triangle.

Since the two angles are equal (45°) in the given right triangle,also in a triangle the side opposite to the equal angles are equal.

Therefore, the other leg of given right triangle = 5 in.

Now applying Pythagoras theorem, we get

[tex]H^2=5^2+5^2=25+25\\\\\Rightarrow\ H^2=50\\\\\Rightarrow H=\sqrt{50}\\\\\Rightarrow H=5\sqrt{2}\ in[/tex]

Hence, the length of the hypotenuse = [tex]5\sqrt{2}\ in[/tex]

Solution for Q1:

Given is the height of ice-cream cone, h = 6 inches.

Given is the diameter of ice-cream cone, d = 2 inches. Then radius of cone would be half of diameter, r = d/2 = 1 inch.

The ice-cream without scoop would be in the shape of cone only. So we need to find the volume of cone.

We know the formula for volume of cone is given as follows :-

[tex] Volume = \frac{1}{3} \pi r^{2} h \\\\Volume = \frac{1}{3} \pi (1)^{2} (6) \\\\Volume = \frac{6\pi}{3} = 2\pi = 2(3.14) = 6.28 \;cubic \;inches. [/tex]

So the volume is 6.28 ≈ 6 in³.

Hence, option A is correct i.e. 6 cubic inches.

Solution for Q2:

A candy is in shape of sphere with diameter, d = 0.25 inches.

Then radius of sphere, r = d/2 = 0.250/2 = 0.125 inches.

The formula for volume of sphere is given as follows :-

[tex] Volume = \frac{4}{3} \pi r^{3} \\\\Volume = \frac{4}{3} \pi (0.125)^{3} \\\\Volume = 0.00818123 \;cubic \;inches. [/tex]

So, volume of one candy = 0.00818123 cubic inches.

There are total 120 candies in the machine.

Total volume of all 120 candies = 120 x 0.00818123 = 0.981748 cubic inches.

Hence, the total volume of all candies in the machine is about 0.982 in³.

Answer:

This should definitely help for question 1 :)

What is the volume of a ball if its diameter is 6 inches? Leave your answer in terms of π.

A)V = 12 π cubic inches

B)V = 36 π cubic inches

C)V = 288 π cubic inches

D)V = 27.75 π cubic inches

Explanation:The volume of the ball above is V = 36 π cubic inches. Use the formula V = 4/3π 3. Just remember to cut the diameter in half to get the radius.

Step-by-step explanation:

Answer:

26

Step-by-step explanation:

3 x 8 = 24

50-24=26

She will get $26 dollars back

Easy Step by Step explanation

Final answer:

To find out how far the plane is from the closer end of the runway, we use the angles of depression and runway length to calculate the distance using trigonometric ratios. The distance is found to be approximately 26153 meters.

Explanation:

To determine the distance from the plane to the closer end of the runway, we use trigonometric ratios based on the angles of depression given. The angles of depression to the ends of the runway are 14° and 20°. Since the problem involves a horizontal surface (runway) and vertical angles (angles of depression), we can create two right triangles. One triangle has an angle of 14° between the plane's line of sight and the horizontal surface, and the other one has a 20° angle.

Let x be the distance from the plane to the point directly above the closer end of the runway and y be the distance from the plane to the point directly above the far end of the runway. We are looking for x, which can be found using the tangent of the 14° angle.

x = runway length / (tan(20°) - tan(14°))

Given the runway length as 3000 meters, we can calculate:

x = 3000 / (tan(20°) - tan(14°))

Crunching the numbers:

x ≈ 3000 / (0.3640 - 0.2493)

x ≈ 3000 / 0.1147

x ≈ 26153 meters (rounded to the nearest tenth)

Therefore, the distance from the plane to the closer end of the runway is approximately 26153 meters.

Answer:

36 years old

Step-by-step explanation:

Answer:

Option 2. f(x) = 4x² + 9x

Step-by-step explanation:

In this question we have to tell which function grows at the fastest rate for increasing values of x.

1) h(x) = 2x It's a linear function increasing with the value of x.

2). f(x) = 4x²+9x It's a function representing parabola. Moreover the value of the function increases exponentially as the function is in the form of quadratic equation.

3). g(x) = 18x it's again a linear function.

Therefore out of three functions Function 2 will grow at the fastest rate for increasing values of x.

Answer:

360°

Step-by-step explanation:

I just took the test.

The area of the remaining wall after the mural has been painted is 46x^2+73x+15. Hence, he correct answer is [tex]\(\boxed{\text{A. }46x^2+73x+15}\)[/tex]

To find the area of the remaining wall after the mural has been painted, we need to find the area of the entire wall and then subtract the area of the mural.

The area of the rectangular wall is given by the product of its dimensions:

[tex]\[ \text{Area of wall} = (6x+7)(8x+5) \][/tex]

Expanding this expression:

[tex]\[ \text{Area of wall} = 48x^2 + 30x + 56x + 35 \][/tex]

[tex]\[ \text{Area of wall} = 48x^2 + 86x + 35 \][/tex]

Now, the area of the mural is given by the product of its dimensions:

[tex]\[ \text{Area of mural} = (x+4)(2x+5) \][/tex]

Expanding this expression:

[tex]\[ \text{Area of mural} = 2x^2 + 5x + 8x + 20 \][/tex]

[tex]\[ \text{Area of mural} = 2x^2 + 13x + 20 \][/tex]

Now, to find the area of the remaining wall, we subtract the area of the mural from the area of the wall:

[tex]\[ \text{Area of remaining wall} = \text{Area of wall} - \text{Area of mural} \][/tex]

[tex]\[ \text{Area of remaining wall} = (48x^2 + 86x + 35) - (2x^2 + 13x + 20) \][/tex]

[tex]\[ \text{Area of remaining wall} = 48x^2 + 86x + 35 - 2x^2 - 13x - 20 \][/tex]

[tex]\[ \text{Area of remaining wall} = 46x^2 + 73x + 15 \][/tex]

So, the correct answer is [tex]\(\boxed{\text{A. }46x^2+73x+15}\)[/tex].

The complete question is:

A group of art students are painting a mural on a wall. The rectangular wall has dimensions of (6x+7) by (8x+5) and they are planning the mural to be (x+4) by (2x+5). What is the area of the remaining wall after the mural has been painted?

A. 46x^2+73x+15

B. 48x^2+86x+35

C. 2x^2+13x+20

D. 50x^2+99x+55

Answer:

circle 1 is a dilation of circle 2 with a scale factor of 2.5.

Step-by-step explanation:

The radius of circle 1 is 5x and the radius of circle 2 is 2x.

This means the scale factor of the dilation is 5x/2x = 2.5.

Circle 1 is a dilation of circle 2 with a scale factor of 0.4.

Two figures are said to be similar if they have the same shape and the ratio of their corresponding sides are in the same proportion.

Given that circle 1 has radius of 5x and circle 2 has radius of 2x, hence:

Circle 1 scale factor = 2x / 5x = 0.4

Hence:

Circle 1 is a dilation of circle 2 with a scale factor of 0.4.

Find out more on similar figures at: https://brainly.com/question/14285697

The water in the mattress weighs approximately 1,747 pounds.To find the weight of water in the mattress, calculate the volume by multiplying the dimensions and then multiply the volume by the weight of water per cubic foot.

To determine the weight of the water in the mattress, follow these steps:

Calculate the volume of the waterbed mattress by multiplying its dimensions:

Volume = 7 ft * 4 ft * 1 ft = 28 ft³

Next, use the given weight of water per cubic foot to find the total weight:

Weight of Water = Volume * Weight per Cubic Foot

Weight of Water = 28 ft³ * 62.4 lb/ft³

Finally, multiply these values:

Weight of Water = 28 * 62.4 = 1,747.2 lb

To the nearest pound, the weight of the water in the mattress is 1,747 pounds.

Answer:

Option D is correct

Step-by-step explanation:

Given Equations of Circles:

Circle 1 - [tex](x+12)^2+(y+16)^2=(r_1)^2[/tex]

Circle 2 -  [tex](x-30)^2+(y-16)^2=(r_2)^2[/tex]

Both circles passes through origin.

To find: Values of [tex]r_1\:,\:r_2[/tex]

Coordinates of origin = ( 0 , 0 )

Circles passes through origin means x = 0 & y = 0 must satisfy the equation of circles.

So, Substituting x = 0 &  y = 0 in Eqn of Circle 1

we get

[tex](0+12)^2+(0+16)^2=(r_1)^2[/tex]

[tex](r_1)^2=12^2+16^2[/tex]

[tex](r_1)^2=144+256[/tex]

[tex](r_1)^2=400[/tex]

[tex]r_1=\sqrt{400}[/tex]

[tex]r_1=20[/tex]

Now, Substituting x = 0 &  y = 0 in Eqn of Circle 2

we get

[tex](0-30)^2+(0-16)^2=(r_2)^2[/tex]

[tex](r_2)^2=(-30)^2+(-16)^2[/tex]

[tex](r_2)^2=900+256[/tex]

[tex](r_2)^2=1156[/tex]

[tex]r_2=\sqrt{1156}[/tex]

[tex]r_2=34[/tex]

Therefore, Option D is correct .i.e., [tex]r_1=20\:\:,\:\:r_2=34[/tex]

To model the depreciation of a textbook initially worth $120 with a 12% annual decrease, use the function V(t) = 120 x (1 - 0.12)^t. After 9 years, the textbook's value will be approximately $38.24.

The student asks for a function to model the depreciation of a textbook and the value of the textbook after 9 years. The textbook costs $120 initially and depreciates at 12% annually. To model this, we can use an exponential decay function, which is generally of the form V(t) = V_0  imes (1 - r)^t, where V(t) is the value after time t, V_0 is the initial value, r is the rate of decay, and t is time in years.

Plugging in the given values:

V_0 = $120

r = 0.12 (12% as a decimal)

t = 9 years

The function becomes V(t) = 120  imes (1 - 0.12)^t. Now, we find the value of the textbook after 9 years by substituting t with 9:

V(9) = 120 x (1 - 0.12)⁹

Calculate:

V(9) = 120 x (1 - 0.12)⁹
V(9) = 120 x 0.88^9
V(9) =120 x 0.318630...\approx $38.24

Thus, the value of the textbook after 9 years will be approximately $38.24.

Answer:

Answer:

The answers in order are 2,5,1,4,3

Step-by-step explanation:

Correct on edge

Answer: $200.00

Step-by-step explanation:

$6.95+ $3.00= $19.90

$19.90 * 100= $1,990

$1,990 / $9.95 = $200.00

take the orginal cost 6.95 plus the $3 labor which equals 19.90 then you multiply by the number of bulbs 100 which equals 1990 then divide 1990 by the cost of bulbs 9.95 which equals 200!