10.
A
group of friends went to lunch. The bill,/before)
sales tax and tip, was $37.50. A sales tax of 8%
was added. The group then tipped 18% on the
amount after the sales tax was added.
What was
the amount, in dollars, of the sales tax?
What was the total amount the group paid,
including tax and tip?

The volume of a cuboid toy chest is equal to their product of the length,

width, and height.

Reasons:

The dimensions of the toy chest are;

Toy chest A;

Length = 5 feet

Width = 4 feet

Height = 2 feet

Toy chest B;

Length = 4 feet

Width = 2 feet

Height = 4 feet

Volume of Toy chest A = 5 ft. × 4 ft. × 2 ft. = 40 ft.³

Volume of Toy chest B = 4 ft. × 2 ft. × 4 ft. = 32 ft.³

The volume of the toy chest Mrs. Smith needs = 35 ft.³

The toy chest Mrs. Smith should purchase is Toy chest A, that has a volume of 40 ft.³, which can store items that with a volume of 35 ft.³

The correct option is; Only toy chest A will provide the necessary storage space

Possible question options obtained from a similar question found online are;

Either toy chest have the storage space needed

Neither has the storage space needed

Only toy chest A

Only toy chest B

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Answer:

Ask you might know 63×32 is 2,016 so 630×32 is 2,016 just with a 0 added and so far on so 630×32 would be 20,160 and 6300×32 would be 201,600

Answer:

The slope of the tangent line to the curve at the given point is -11/7.

Step-by-step explanation:

Differentiation is an algebraic process that finds the gradient (slope) of a curve.  At a point, the gradient of a curve is the same as the gradient of the tangent line to the curve at that point.

Given function:

\(4x^2+5xy+y^4=370\)

To differentiate an equation that contains a mixture of x and y terms, use implicit differentiation.

Begin by placing d/dx in front of each term of the equation:

\(\dfrac{\text{d}}{\text{d}x}4x^2+\dfrac{\text{d}}{\text{d}x}5xy+\dfrac{\text{d}}{\text{d}x}y^4=\dfrac{\text{d}}{\text{d}x}370\)

Differentiate the terms in x only (and constant terms):

\(\implies 8x+\dfrac{\text{d}}{\text{d}x}5xy+\dfrac{\text{d}}{\text{d}x}y^4=0\)

Use the chain rule to differentiate terms in y only. In practice, this means differentiate with respect to y, and place dy/dx at the end:

\(\implies 8x+\dfrac{\text{d}}{\text{d}x}5xy+4y^3\dfrac{\text{d}y}{\text{d}x}=0\)

Use the product rule to differentiate terms in both x and y.

\(\boxed{\dfrac{\text{d}}{\text{d}x}u(x)v(y)=u(x)\dfrac{\text{d}}{\text{d}x}v(y)+v(y)\dfrac{\text{d}}{\text{d}x}u(x)}\)

\(\implies 8x+\left(5x\dfrac{\text{d}}{\text{d}x}y+y\dfrac{\text{d}}{\text{d}x}5x\right)+4y^3\dfrac{\text{d}y}{\text{d}x}=0\)

\(\implies 8x+5x\dfrac{\text{d}y}{\text{d}x}+5y+4y^3\dfrac{\text{d}y}{\text{d}x}=0\)

Rearrange the resulting equation in x, y and dy/dx to make dy/dx the subject:

\(\implies 5x\dfrac{\text{d}y}{\text{d}x}+4y^3\dfrac{\text{d}y}{\text{d}x}=-8x-5y\)

\(\implies \dfrac{\text{d}y}{\text{d}x}(5x+4y^3)=-8x-5y\)

\(\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{-8x-5y}{5x+4y^3}\)

To find the slope of the tangent line at the point (-9, -1), substitute x = -9 and y = -1 into the differentiated equation:

\(\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{-8(-9)-5(-1)}{5(-9)+4(-1)^3}\)

\(\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{72+5}{-45-4}\)

\(\implies \dfrac{\text{d}y}{\text{d}x}=-\dfrac{77}{49}\)

\(\implies \dfrac{\text{d}y}{\text{d}x}=-\dfrac{11}{7}\)

Therefore, slope of the tangent line to the curve at the given point is -11/7.

Answer:

D. Starla and Lewis will have the same balance in their accounts after 7 months.

Answer:

It would be B because that is the only answer that contains a inequality symbol.

Step-by-step explanation:

Answer:

Option A is a Linear Pair

Step-by-step explanation:

A linear equation is an equation of a straight line, which means that the degree of a linear equation must be 0 or 1 for each of its variables. In this case, the degree of variable x is 1.

The two pairs of conjugates are (\(\sqrt{2}-i\)) and (\(\sqrt{2}+i\)).

In mathematics, a pair of binomials with identical phrases that part opposite arithmetic operators in the midst of these similar terms are referred to as conjugates. Below are a few more instances of conjugate pairs: p + q, p - q. 3 + 1, 3 - 1. 4 - 3i, 4 + 3i.

Let the two pair of conjugates is

(\(\sqrt{2}-i\)) and (\(\sqrt{2}+i\))

Use the formula,

(a+b) and (a-b) = \(a^{2}-b^{2}\)

Then,

(\(\sqrt{2}-i\)) and (\(\sqrt{2}+i\)) = \(\sqrt{2} ^{2}-i^{2}\)

We know that,

\(i^{2}=-1\)

(\(\sqrt{2}-i\)) and (\(\sqrt{2}+i\)) = 2-(-1)

 (\(\sqrt{2}-i\)) and (\(\sqrt{2}+i\)) =  3

Hence, The two pairs of conjugates are (\(\sqrt{2}-i\)) and (\(\sqrt{2}+i\)) with a product 3 .

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According to the solving the  two pairs of conjugates with a product of 3:

(√2 - i ) & (√2 + i ).

When two binomials are identical except for the signs separating the terms, they are said to be conjugates. You only need to rephrase a binomial and alter the sign of the second term to create its conjugate.

given number = 3.

lets the two pair of conjugates is:

(√2 - i ) & (√2 + i )

Use the formula:

a² - b² = (a + b) and  (a - b)

So,

(√2 - i ) & (√2 + i ) = (√2)² -( i )²

We know that,

i² = -1

So,

(√2 - i ) & (√2 + i ) = 2 - (-1)

(√2 - i ) & (√2 + i ) = 3

According to the solving the  two pairs of conjugates with a product of 3:

(√2 - i ) & (√2 + i ).

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Answer:

the value of a - b is 4.

Step-by-step explanation:

We have been given the following two equations:

a + b = 10 ------------(1)

a² - b² = 40 -------(2)

We can factor the left-hand side of equation (2) using the difference of squares identity:

(a + b)(a - b) = 40

Substituting equation (1) into this equation, we get:

10(a - b) = 40

Dividing both sides by 10, we get:

a - b = 4

Therefore, the value of a - b is 4.

Step-by-step explanation:

if I understand this correctly :

a + b = 10

a² - b² = 40

(a² - b²) = (a + b)(a - b) = 40

10(a - b) = 40

(a - b) = 4

Answer:

Solution:

We know that:

Solution:

Hence, 4 cans are required to paint the apartment.

Answer:

4 cans, 10 times 100= 1000, 1000 divided by 250 would be 4.

Step-by-step explanation:

Lexie would need 4 cans!

Answer:

9(p-2)(p-4)

Step-by-step explanation:

Answer:

-18

Step-by-step explanation:

A matrix such that T(x) =Ax is \(Ax = \left[\begin{array}{ccc}-3&7\\5&-2\end{array}\right]\).

What is a matrix?

A matrix is a rectangular array or table with numbers or other objects arranged in rows and columns. Matrices is the plural version of matrix. The number of columns and rows is unlimited. Matrix operations include addition, scalar multiplication, multiplication, transposition, and many others.

The matrix is \(x = \left[\begin{array}{ccc}x_1\\x_2\end{array}\right]\), \(v_1= \left[\begin{array}{ccc}-3\\5\end{array}\right]\) and \(v_2 = \left[\begin{array}{ccc}7\\-2\end{array}\right]\).

The linear transformation is R² → R².

T is defined by the vector equation -

T(x) = x1v1 + x2v2

Substitute the values in the equation -

T(x) = \(x_1 \left[\begin{array}{ccc}-3\\5\end{array}\right] + x_2 \left[\begin{array}{ccc}7\\-2\end{array}\right]\)

A vector equation like this can be rewritten as a matrix equation Ax where the columns of A are just v1 and v2 -

\(Ax = \left[\begin{array}{ccc}v_1&v_2\end{array}\right]\)

Substitute the values in the matrix -

\(Ax = \left[\begin{array}{ccc}-3&7\\5&-2\end{array}\right]\)

Therefore, the matrix obtained is \(Ax = \left[\begin{array}{ccc}-3&7\\5&-2\end{array}\right]\).

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Answer:

8.92 - 2.06 = 6.86

Step-by-step explanation:

The value of R and θ is 6.18 and 53.13 degrees, under the condition that a circle C has center at the origin and radius 5 .

In order to  evaluate the equation of the circle K. The diameter of K has endpoints at the origin and (0,15). Then, the center of K is at (0,7.5) and its radius is 7.5. Therefore, the evaluated equation of K is
x² + (y-7.5)² = 56.25.
The equation of circle C is x² + y² = 25.
The two circles intersect at two points. Now we have to evaluate the coordinates of these points.
Staging y = 5 - x² in the equation of K,
we get
x² + (5-x²-7.5)² = 56.25.
Applying simplification on this equation
x⁴ - 10x² + 31.25 = 0.
Calculating this quadratic equation gives us
x² = 5 ± √(10)/2.
If P lies in the first quadrant,
we choose x² = 5 + √(10)/2 and y = √(25-x²) to get P in Cartesian coordinates.
Converting P to polar coordinates gives us
r = √(x²+y²) and θ = arctan(y/x).
Staging x = √(5+√(10)/2) and y = √(25-x²) in these equations gives us
r ≈ 6.18 and θ ≈ 0.93 radians.
Using this formula to convert into degree
Rad × 180/π
= 0.93 × 180/π
≈ 53.13 degrees
Therefore, r ≈ 6.18 and θ ≈ 53.13 degrees.
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============================================================

Explanation:

Refer to the table below (attached image). I've copied your table and added a third row at the bottom. This new row is the result of multiplying each payout value with the corresponding probability.

Example: for the first entry of this row, have 2*0.45 = 0.9

Once that third row is filled out, you add up everything in that row. That will lead to the expected value.

The expected value is: 0.9+1.2+0.6+0.8+0.5 = 4

Interpretation: You expect, on average, to win $4 each time you play the game. This assumes that the cost to play the game is 0 dollars. If the cost is something else, then it will affect the expected value.

Because the expected value is not 0, this game is not mathematically fair (the bias is leaning in favor of the player).

The total volume of the air space of spherical ball is A = 12.265625 inches³

Given data ,

Since each tennis ball has a diameter of 2.5 inches, the radius of each ball is 1.25 inches.

The air space around the balls can be thought of as a cylinder with a height equal to the diameter of one ball and a radius equal to the radius of one ball.

The height of the cylinder is 2.5 inches, and the radius is 1.25 inches.

The formula for the volume of a cylinder is:

V = πr²h

V = ( 3.14 ) ( 1.25 )² ( 7.5 )

V = 36.796875 inches³

where V is the volume, r is the radius, and h is the height.

So, the volume of the one ball is:

V₁ = ( 4/3 )π(1.25)³

V₁ = 8.177083 inches³

The total volume of three balls is = volume of 3 spherical balls

V₂ = 3V₁ = 3(8.177083) ≈ 24.53125 cubic inches

Therefore, the total volume of the air space around the three tennis balls is approximately A = 36.796875 inches³ - 24.53125 inches³

A = 12.265625 inches³

Hence , the volume of air space is A = 12.265625 inches³

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Answer: $1.50

Step-by-step explanation: 1. subtract the 3.25 from 4.50 to get a difference that is the price of the added hotdog 2. now that you know each hot dog cost $1.25 you can do 3.25 - 2(1.25) to get 0.75 which is the price of one soda. 3. You can no multiply $0.75 by two (the amount of sodas) to get the answer $1.50.

The temperature at the bottom of the mountain is 50.9 °C.

Let's work through the given information step by step to find the temperature at the bottom of the mountain.

The temperature in the hotel is 21 °C.

The temperature in the hotel is 26.7 °C warmer than at the top of the mountain.

Let's denote the temperature at the top of the mountain as T_top.

So, the temperature in the hotel can be expressed as T_top + 26.7 °C.

The temperature at the top of the mountain is 3.2 °C colder than at the bottom of the mountain.

Let's denote the temperature at the bottom of the mountain as T_bottom.

So, the temperature at the top of the mountain can be expressed as T_bottom - 3.2 °C.

Now, let's combine the information we have:

T_top + 26.7 °C = T_bottom - 3.2 °C

To find the temperature at the bottom of the mountain (T_bottom), we need to isolate it on one side of the equation. Let's do the calculations:

T_bottom = T_top + 26.7 °C + 3.2 °C

T_bottom = T_top + 29.9 °C

Since we know that the temperature in the hotel is 21 °C, we can substitute T_top with 21 °C:

T_bottom = 21 °C + 29.9 °C

T_bottom = 50.9 °C

Therefore, the temperature at the bottom of the mountain is 50.9 °C.

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Answer:

$1050

Step-by-step explanation:

I = PRT / 100

I = 21

P = ?

R = 4%

T = 6 months = 0.5 yr

P = 100I / RT

P = (100 * 21) / (4 * 0.5)

P = $1050

Answer:

3 hours and 45 minutes

Step-by-step explanation:

mark me a brainliest answer

Answers:

Domain:  \(x \ge -5\)

Range:  \(y \ge -2\)

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

Explanation:

The domain is the set of all allowed x values of a function. The point on the very left shows that x = -5 is the smallest value possible. So this means the domain consists of x values such that x = -5 or x > -5. We shorten that to \(x \ge -5\)

------------------

The range is the set of possible y outputs. The lowest point is when y = -2 meaning that \(y \ge -2\) is the range (so y can be -2 or larger).

Answer:

Step-by-step explanation:

2 × 3 + 1 72 ÷ ( 8 − 2 ) × 3 + 1 72 ÷ ( 8 − 2 ) × ( 3 + 1 ) 72 ÷ 8 − 2 × ( 3 + 1 )

Answer:

(72 divided by 8) second one, 72 divided by (8 - 2),third one,  72 divided by (8 - 2) x (3 + 1). last one. then the leftover number is the first one.

Step-by-step explanation:

The total interest is $107,270

What is monthly payment formula?

The formula for monthly payment is:

\(M = \frac{P(\frac{r}{12})( 1+\frac{r}{12})}{( 1+\frac{r}{12})^n-1}\)

We can find total interest as shown below:

Value of property = $475,000

Money available as a deposit = $80,000

P = 475,000-80,000

= 395000

t = 25 year

r = 2% = 0.02

n = 25*12 = 300

\(M = \frac{P(\frac{r}{12})( 1+\frac{r}{12})}{( 1+\frac{r}{12})^n-1}\)

Putting the value of P, t, r, and n in the above formula

\(=\frac{395000(\frac{0.02}{12} )(1+\frac{0.02}{12}) }{(1+\frac{0.02}{12})^{300}-1}\)

after solving the above expression

M = $1674.22

Interest = M*n-P

Putting the value of P, n and M

= 1674.22*300-395000

= 502266-395000

= 107,266

Rounding to nearest ten dollar

= $107,270

Hence, the total interest is $107,270.

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Answer:

Step-by-step explanation:

Answer: D

Over the interval [4,7], the local minimum is -7

The solutions to the nearest tenth are x = -0.1 and x = 1.3

From the question, we have the following parameters that can be used in our computation:

5x² - 2x - 1 = 4x

Evaluate the like terms

So, we have

5x² - 6x - 1 = 0

Next, we solve using a graph

The graph of 5x² - 6x - 1 = 0 is added as an attachment

From the attached graph, we can see that the curve intersects with the x-axis at x = -0.1 and x = 1.3

This means that the solutions are x = -0.1 and x = 1.3

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Answer:

The solutions to the equation 5x^2-2x-1=4x to the nearest tenth are x ≈ 1.3 or x ≈ -0.4.

Step-by-step explanation:

To solve the equation 5x^2-2x-1=4x to the nearest tenth, we can start by moving all the terms to one side of the equation.

5x^2-2x-1=4x

5x^2-6x-1=0

Next, we can use the quadratic formula to solve for x:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 5, b = -6, and c = -1.

Plugging these values into the formula gives:

x = (-(-6) ± sqrt((-6)^2 - 4(5)(-1))) / 2(5)

x = (6 ± sqrt(56)) / 10

The height of the rectangular prism is 21 cm.

A rectangle is a quadrilateral with four right angles (90 degree angles) and two pairs of opposite sides that are equal in length. It is a special case of a parallelogram where all angles are right angles.

The volume of a rectangular prism is given by the formula V = lwh, where l, w, and h are the length, width, and height of the prism, respectively. We are given that the volume is 1,680 cm^3, but we don't have enough information to determine the height directly without knowing the other dimensions.

If we are given the dimensions of the rectangular prism or any relationship between them, we can use algebraic methods to solve for the height. For example, if we are given that the length is twice the width and the height is three times the width, we can write:

l = 2w

h = 3w

Substituting these expressions into the volume formula, we get:

\(V = lwh\\\\1680 = (2w)(w)(3w)\\\\1680 = 6w^3\)

\(w^3 = 280\)

\(w = 7 cm\)

Now that we know the width is 7 cm, we can use one of the expressions for the height to find its value:

h = 3w = 3(7) = 21 cm

Therefore, the height of the rectangular prism is 21 cm.

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Complete question:

Answer:

No

Step-by-step explanation:

the reason why i said nonis cause 96+123+106+72=397 which means he still needs 13 more

The side lengths from least to greatest as follows:

IK < KL < IJ < IL < LJ

To order the side lengths IK, KL, IJ, IL, and LJ from least to greatest, we can analyze the given figure.

Since the figure is not drawn to scale, we cannot determine the exact lengths of the sides. However, we can make some observations based on the given angles.

Let's analyze the angles:

Angle L: Since angle L is marked as 47°, we know that side KL is the shortest side, as it is opposite to the smallest angle in a triangle.

Angle I: Since angle I is marked as 20°, we can infer that side IJ is longer than side IK, as it is opposite to a larger angle.

Angle LJ: Since angle LJ is marked as 89°, we can conclude that side LJ is the longest side, as it is opposite to the largest angle in the triangle.

Based on these observations, we can order the side lengths from least to greatest as follows:

IK < KL < IJ < IL < LJ

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Answer:

\((x-8)^2+(y-10)^2=36\)

Step-by-step explanation:

Hi there!

Equation of a circle:

\((x-h)^2+(y-k)^2=r^2\) where \((h,k)\) is the center of the circle and \(r\) is the radius

Plug in the center (8,10) and the radius 6:

\((x-8)^2+(y-10)^2=6^2\\(x-8)^2+(y-10)^2=36\)

I hope this helps!