Bennet orders 103 teapots to sell. He charges $32.99 per teapot. How much are all of his teapots worth?

Therefore , the solution of the given problem of inequality  comes out to be z < -9 or z ≥ -2 .

In algebra, a disparity can be represented by an association or collection of numbers, even without the equal symbol. Equity always comes after equilibrium. When standards are still incompatible, inequality results. Fairness and disparity are not the same. Because parts are variable  frequently not similar in any way or close to one another, we selected the most common symbol ().

Here,

We will first answer each inequality independently, then combine the results to graph the solution to this inequality.

=> 2z + 9 < -9

=>  2z < -18

=>  z < -9

and

=>  2z - 3 ≥ -7

=>  2z ≥ -4

=>  z ≥ -2

The system's answer is as follows:

z < -9 or z ≥ -2

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The correct option is: D. Between the years of 2007 and 2010, the money in the savings account grew at the higher rate.

Simple interest is a predetermined proportion of the principle amount borrowed or lent that is given or paid over a set period of time.

Principal P = $5,000

Time t = x years

rate of interest r = 1.4%.

Then,

Simple interest = PRT/100

Simple interest = 5,000*1.4*x/100

Simple interest = 70x

And in continuous compounding in high-yield savings account:

A = P[tex]e^{rt}[/tex]

A = 5,000*[tex]2.72^{0.014x}[/tex]

A = 5070 * [tex]e^{x}[/tex]

CI = A - P

CI = 5070 * [tex]e^{x}[/tex] - 5000

Thus, the between the years of 2007 and 2010, the money in the savings account grew at the higher rate.

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Answer: 2x^2+3x

Step-by-step explanation:

2x^2+3x

ez problem

ddddddddddd

This figure is composed of two semicircles and a rectangle. This figure's perimeter is 423.52 meters.

The perimeter of a shape is the space surrounding its edge. The perimeter of various forms can be calculated by summing the lengths of their sides. A perimeter is a closed line that encircles, defines, or surrounds a length in one dimension or a shape in two dimensions. The perimeter of a circle or an ellipse is its circumference. Perimeter calculations have many practical applications. The perimeter of a shape in geometry refers to its whole boundaries. The lengths of a shape's sides and edges are added up to determine its perimeter. Linear measurements like centimeters, meters, inches, and feet are used to express its dimensions. The perimeter of a shape is the space surrounding its edge. A shape's perimeter is always determined by adding up the lengths of its sides.

Perimeter

d=68, a=105

Perimeter [tex]= 2*1/2*3.14*68+2*105\\=423.52m[/tex]

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The angle of elevation from the students feet is 25.64°

The angle between the horizontal line and the line of sight, which is above the horizontal line, is known as the angle of elevation. It develops when a person stares upward. Imagine that you are on a building's terrace, gazing up at the b, the sun, or the moon. The angle of elevation is the angle created as a result of your height above ground level and the produced line of sight.

Now, if the distance has to be taken from students feet then the distance is said to be,

51-0=51ft

Now, lets assume that the angle of elevation is x

tan x=[tex]\frac{51}{105}[/tex]

x=[tex]tan^{-1}\frac{51}{105}[/tex]

x=25.64°

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The drawing of the quadrilateral P(-3, 0), N(6, 0), O(3, -6), and M(3, 9) and the drawing of the image, of the quadrilateral with vertices, P'(-1, 0), N'(2, 0), O'(1, -2), and M'(1, 3), following a dilation by a scale factor of 1/3, created with MS Excel.

The coordinates of the vertices of the quadrilateral are;

P(-3, 0), N(6, 0), O(3, -6), M(3, 9)

The coordinates of the image of a point (x, y) following a dilation by a scale factor of c are; (x·c, y·c)

The coordinates of the image following a dilation by a scale factor of 1/3 therefore, are;

P(-3, 0) dilation by a scale factor of 1/3 → P'(-3/3, 0/3) = P'(-1, 0)

N(6, 0) dilation by a scale factor of 1/3 → N'(6/3, 0/3) = N'(2, 0)

O(3, -6) dilation by a scale factor of 1/3 → O'(3/3, -6/3) = O'(1, -2)

M(3, 9) dilation by a scale factor of 1/3 → M'(3/3, 9/3) = M'(1, 3)

The coordinates of the quadrilateral following the dilation transformation are; P'(-1, 0), N'(2, 0), O'(-2, 0), M'(1, 3)

Please find attached the drawing of the image of the quadrilateral MNOP, following the dilation of a scale factor of 1/3

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Answer: dy/dt = 37.42 fps

Step-by-step explanation:

First, let's define a few variables.

t = time

x = Distance the player is from third base = 20 feet

dx/dt = Velocity the player is running towards third base = -30 fps (since he is running towards third base, the x value will decrease with time, hence the negative value)

y = Distance between the player and home plate (We will find this value below)

dy/dt = Rate of change between the player's distance from home plate (This is the answer to our problem)

Now, let's use the Pythagorean theorem to relate the x and y terms.

y2 = x2 + 902

Use x = 20 feet to find y in this instant.

y2 = 202 + 902

y = 92.2 feet

Now, let's use implicit differentiation to take the derivative of this expression.

2y*dy/dt = 2x*dx/dt + 902

And let's plug in x, y, and dx/dt to solve for dy/dt.

2(92.2)*dy/dt = 2*20*-30 + 902

dy/dt = 37.42 fps

Answer: 0.66666666666

Answer:

exact form: 2/3

Decimal form: 0.6

Answer:

40

Step-by-step explanation:

because 20 can be true and the other 20 can be false so add 20 + 20 you get 40

We can use the Pythagorean theorem to find the length of the zip line.

Let's represent the length of the zip line as "L". According to the problem, the height of the platform is 40 meters and the horizontal distance from the base of the platform to the anchor point is 198 meters. We can use these values to form a right-angled triangle, where the hypotenuse represents the length of the zip line.

Using the Pythagorean theorem, we have:

L^2 = 40^2 + 198^2

L^2 = 1600 + 39204

L^2 = 40804

L = √40804

L ≈ 202.0

Therefore, the length of the zip line is approximately 202.0 meters.

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Answer:

202

Step-by-step explanation:

Khan Academy

Answer:  (without rounding) 4.64, 9.96, 9.96, 4.64, 5.12, 23.58

Step-by-step explanation:

Using calculator type in 11, then tangent, sine , or cosine, then 25 or 65 with parenthesis, and thats the answer

After answering the presented question, we can conclude that As a equation result, Layla's concoction has a total volume of 0.34 L.

An equation is a mathematical statement that proves the equality of two expressions connected by the equal symbol '='. 2x - 5 Equals 13, for example. Expressions include 2x-5 and 13. The character '=' joins the two expressions. A mathematical formula with two algebraic expressions on either side of an equal sign (=) is known as an equation. It demonstrates the relationship of equivalence between the left and right formulas. In every formula, LHS = RHS (left side = right side).

Add the volumes of the blue and green liquids to get the total volume of Layla's mixture:

Overall volume Equals blue liquid volume + green liquid volume

0.155 L + 0.185 L Equals total volume

0.34 L total volume

As a result, Layla's concoction has a total volume of 0.34 L.

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The correct question is -

In science, layla mixed 0.155 L of a blue liquid and 0.185 L of a green liquid. What is the total volume of Layla's mixture?

show your work

a) The perimeter is 330 inches, b) 22 posts are needed, and c) The cost to enclose the garden is $46.75.

a) To solve these problems, we need to use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of squaring the other two sides.

Let's call the length of one leg of the triangle "a" and the length of the other leg "b". Then we have:

a = 88 in

c = 137 in

[tex]c^2 = a^2 + b^2[/tex]

[tex]137^2 = 88^2 + b^2[/tex]

[tex]b^2 = 137^2 - 88^2[/tex]

[tex]b^2 = 18769 - 7744[/tex]

[tex]b^2 = 11025[/tex]

b = [tex]\sqrt{11025[/tex]

b ≈ 105 in

Now we can find the perimeter of the garden:

Perimeter = a + b + c

Perimeter = 88 + 105 + 137

Perimeter ≈ 330 in

b) To find the number of posts we need, we just divide the perimeter by the spacing between each post:

Number of posts = Perimeter / Spacing

Number of posts = 330 / 15

Number of posts ≈ 22

Round up to the nearest whole number to get the answer: 22 posts.

c) To calculate the cost of enclosing the garden, we need to find the total cost of the posts and the fencing. The total length of fencing we need is equal to the perimeter of the garden, which we found to be 377.9 in. we divide by 12, to make this in feet:

Total length of fencing = 330 / 12

Total length of fencing ≈ 27.5 ft

The cost of the posts is $1.25 per post, so for 22 posts, the cost is:

Post cost = 22 * $1.25

Post cost = $27.50

The cost of the fencing is $.70 per foot, so for 27.5 feet, the cost is:

Fencing cost = 27.5 * $.70

Fencing cost = $19.25

Therefore, the total cost to enclose the garden is:

Total cost = Post cost + Fencing cost

Total cost = $27.50 + $19.25

Total cost ≈ $46.75

So it will cost approximately $46.75 to enclose the garden with posts and fencing

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By answering the presented question, we may conclude that As a result, equation Mary takes 10 minutes and Leo takes 15 minutes to wash the automobile by himself.

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=).

1/6=1/M+1/(M +5)

1/6= (2M+5)/(M(M+5))

M(M+5)/6=2M+5 M² + 5M 12M + 30

=M² 7M-30=0

(M-10) (M+3)=0

As a result, M can be either 10 or -3. We reject the answer M = -3 because time cannot be negative. As a result, Mary's time to wash the automobile by herself is 10 minutes.

We can use this to identify Leo's time to wash the car alone: Leo's time equals Mary's time multiplied by 5 = 10 + 5 = 15 minutes.

As a result, Mary takes 10 minutes and Leo takes 15 minutes to wash the automobile by himself.

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Answer:

Step-by-step explanation:

x=-3

The probability of all possible outcomes are:

Probability of Staffs winning is = 6/10

Probability of managers winning = 3/10

Probability of admin winning is = 1/10

Probability also refers to the likelihood that an event will occur. In real life, we frequently have to make predictions about the future.

We might or might not be aware of how an event will turn out. When this occurs, we proclaim that there is a possibility that the event will occur.

Now in the question,

Total employees= 10

Staff = 6

Managers = 3

Admin = 1

There are 2 prizes to be given.

Now as per the question,

Probability of Staffs winning is = 6/10

Probability of managers winning = 3/10

Probability of admin winning is = 1/10

Now, at least one of the winners is a manager,

P = 3/10

Probability that both winners are staff is:

P = 6/10

= 3/5

Probability that admin wins one prize = 1/10

Now probability that admin does not win any prize = 1-1/10

= 9/10

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When they study for 4 hours then their test score is 87, we determined this using the data given in question.

A collection of facts and figures, whether numerical or not, can be called data in mathematics. The data that can be calculated is known as numerical data, and it is always gathered in numerical form. Examples of numerical data include student test scores, employee salaries, player heights on football teams, etc.

Let choose two data (2,71) and (2.5,75) ,

So, 2m + b = 71           ........(1)

and, 2.5m + b = 75     ........(2)

By Subtracting Equation(2) from Equation(1), we get

⇒ 0.5m = 4

⇒ m = 8

So, after putting m=8 in equation (1), we get

⇒ 2 * 8 + b = 71

⇒ b = 71 -16

⇒ b = 55

Thus, our equation is y = 8x + 55.

From the Above equation if they study for 4 hours, then

when, x = 4 , y = 8 * 4 + 55

⇒ y = 32 + 55

⇒ y = 87.

So, when they study for 4 hours then their test score is 87.

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1. The graph for the given data is attached below:

2. When they study for 4 hours then their test score is 87, we determined this using the data given in question.

A collection of facts and figures, whether numerical or not, can be called data in mathematics. The data that can be calculated is known as numerical data, and it is always gathered in numerical form. Examples of numerical data include student test scores, employee salaries, player heights on football teams, etc.

Let choose two data (2,71) and (2.5,75) ,

So, 2m + b = 71           ........(1)

and, 2.5m + b = 75     ........(2)

By Subtracting Equation(2) from Equation(1), we get

⇒ 0.5m = 4

⇒ m = 8

So, after putting m=8 in equation (1), we get

⇒ 2 * 8 + b = 71

⇒ b = 71 -16

⇒ b = 55

Thus, our equation is y = 8x + 55.

From the Above equation if they study for 4 hours, then

when, x = 4 , y = 8 * 4 + 55

⇒ y = 32 + 55

⇒ y = 87.

So, when they study for 4 hours then their test score is 87.

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Jenny should expect to see a total of $25.14 on her bank statement.This total is the amount Jenny should expect to see on her bank statement when she checks online.

This calculation is made by adding the $16.20 order cost, $4.50 delivery charge, and the 18% tip. The 18% tip can be calculated by multiplying the order cost and the delivery charge by 0.18. This would give us a total of $(16.20 * 0.18) + (4.50 * 0.18) = $3.84. To get the total amount we add the order cost, delivery charge, and tip together: $16.20 + $4.50 + $3.84 = $24.54. We then round up to the nearest cent, giving us a total of $25.14. This total is the amount Jenny should expect to see on her bank statement when she checks online.

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The measure οf the supplementary angle οf x = 61.33° is fοund tο be 118.67°.

An angle is a figure in plane geοmetry that is created by twο rays οr lines that have a shared endpοint. The twο rays are termed the sides οf an angle, and the cοmmοn terminatiοn is called the vertex. Angles are typically expressed as degrees. A "prοtractοr" is a crucial geοmetrical instrument that aids in measuring angles in degrees. Twο sets οf numbers οn a prοtractοr are οriented in οppοsitiοn tο οne anοther. On the οutside rim, οne set gοes frοm 0 tο 180 degrees, while οn the inner rim, the οther set gοes frοm 180 tο 0 degrees.

Let the angle be x.

Twο angles are cοmplementary when their sum is 90°.

Tοw angles are supplementary when their sum is 180°

If x is οne angle, then its cοmplementary angle is (90-x)°

Given x is 4 mοre than twice its cοmplement.

We can write the equatiοn as:

x = 4 + 2*(90-x)

Sοlving,

x = 4 + 180 - 2x

3x = 184

x = 61.33°

Nοw we are asked tο find the supplementary angle οf x.

Supplementary angle = 180 - x = 180 - 61.33 = 118.67°

Therefοre the measure οf the supplementary angle οf x = 61.33° is fοund tο be 118.67°.

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Constants, positive exponents, and at least one variable are all commonly present in polynomial expressions. [tex]-4x^2(2x^2 + 1)[/tex] Thus, option D is correct.

A polynomial expression is any expression made up of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division.

Depending on how many terms are included in the expression, polynomial expressions can be categorized as monomials, binomials, or trinomials.

To find the quotient of [tex]-40x^6 - 20x^4 / 5x^2[/tex] , by dividing the numerator by the denominator, which provide us:

[tex]-40x^6 - 20x^4 / 5x^2[/tex]  [tex]= -8x^4 - 4x^2[/tex]

We can factor out  [tex]-4x^2[/tex] from this expression, which gives us:

[tex]-8x^4 - 4x^2 = -4x^2(2x^2 + 1)[/tex]

Therefore, the only expression that shows the quotient of [tex]-40x^6 - 20x^4 / 5x^2[/tex] As a product of two polynomials, is [tex]-4x^2(2x^2 + 1)[/tex]

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Answer: C. 4 meters

Step-by-step explanation: So we know that 720/3 is equal to 240 meters, so it would take Helen 1 minute to run 240 meters. We also know that there is 60 seconds in 1 minute. So 240/60 is equal to 4.

So Therefore we know it would take 1 second to run 4 meters

Answer:

104ft

Step-by-step explanation:

First - find the area of triangles.

h = hight

b = base
h • b / 2

5 • 8 /2 = 20ft

And

4 • 6 /2 = 12ft

And then area of the rectangle.
l • w

9 • 8 = 72 ft

Than add. Them all together

The solution to the system of equations is (-1, 6) and the determinants are D = -13, Dx = 13 and Dy = -78

The system of equations is given as

3x + 5y = 27

2x - y = -8

Remove the variables x and y from the equation

So, we have the following representation

3    5   27

2    -1   -8

Calculate the determinant D

So, we have

D = 3 * -1 - 5 * 2

D = -13

Replace the first column with x

27    5

-8    -1

Calculate the determinant Dx

So, we have

Dx = 27 * -1 - 5 * -8

Dx = 13

Replace the second column with y

3    27

2     -8

Calculate the determinant Dy

So, we have

Dy = 3 * -8 - 27 * 2

Dy = -78

So, we have

x = Dx/D and y = Dy/D

This gives

x = 13/-13 = -1

y = -78/-13 = 6

Hence, the solution is (-1, 6)

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Answer:

We can use the normal distribution to estimate the number of babies that weighed less than 3.2 kg and between 2.8 kg and 3.4 kg. We will assume that the weights of the babies are normally distributed.

Step-by-step explanation:

a) To estimate the number of babies that weighed less than 3.2 kg, we can use the z-score formula:

z = (x - μ) / σ

where x is the weight we want to estimate (3.2 kg), μ is the mean weight (3.0 kg), and σ is the standard deviation (0.2 kg).

z = (3.2 - 3.0) / 0.2 = 1

We can look up the probability corresponding to a z-score of 1 in a standard normal distribution table or use a calculator. The probability of a baby weighing less than 3.2 kg is approximately 0.8413.

So, the estimated number of babies that weighed less than 3.2 kg is:

0.8413 x 545 = 458.9

We can round this to the nearest whole number and estimate that about 459 babies weighed less than 3.2 kg.

b) To estimate the number of babies that weighed between 2.8 kg and 3.4 kg, we can use the same formula and find the probabilities corresponding to the z-scores for 2.8 kg and 3.4 kg.

z1 = (2.8 - 3.0) / 0.2 = -1

z2 = (3.4 - 3.0) / 0.2 = 2

The probability of a baby weighing less than 2.8 kg (corresponding to a z-score of -1) is approximately 0.1587. The probability of a baby weighing less than 3.4 kg (corresponding to a z-score of 2) is approximately 0.9772. So, the probability of a baby weighing between 2.8 kg and 3.4 kg is:

0.9772 - 0.1587 = 0.8185

The estimated number of babies that weighed between 2.8 kg and 3.4 kg is:

0.8185 x 545 = 446.2

We can round this to the nearest whole number and estimate that about 446 babies weighed between 2.8 kg and 3.4 kg.

1. The estimated price of vest is $30.

The amount of discount is $10.

1) 25% of $40 is $10.

2) The discount percent is 25%.

What is discount?

A discount is a reduction in the regular selling price of a good or service, either in terms of money or as a percentage.

To estimate the sale price of a vest, we can round the original price of $42 to a convenient value, such as $40.

The amount of the discount can be calculated as 25% of the rounded price -

Discount = 0.25 x $40 = $10

Subtracting the discount from the rounded price gives us the sale price -

Sale price = $40 - $10 = $30

Therefore, the estimated sale price of a vest is $30.

25% of $40 = 0.25 x $40 = $10

Subtracting the discount of $10 from the rounded price of $40 gives us the sale price -

Sale price = $40 - $10 = $30

Therefore, the estimated sale price of a vest is $30.

The discount percent is 25%.

This is the percentage by which the original price is reduced to obtain the sale price.

Since the sale price is 75% of the original price, the discount is 25% of the original price.

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The correct proportion from the given expressions is option d. 12/15 = 21/25.

Two ratios are said to be equal when a proportion is used. When comparing two numbers or values, ratios can be stated as a fraction, with the first item represented by the numerator and the second by the denominator. In mathematics, proportions are used to establish analogous ratios and find the missing value in situations involving unknown numbers.

Cross multiply the proportions to check the proportionality we see that:

12 x 25 = 15 x 21

300 = 300

Hence, the correct proportion is option d. 12/15 = 21/25.

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Greg should expect to choose a yellow pebble 12 times out of 75. The closest option among the given answer choices is A) 11.

What is addition ?

Addition is a mathematical operation that involves combining two or more numbers to get a total or sum. It is one of the four basic arithmetic operations, along with subtraction, multiplication, and division.

Based on the given table, we can calculate the probability of choosing a yellow pebble from the box as follows:

The total number of pebbles = 8 + 7 + 10 + 14 + 5 + 6 = 50

The total number of yellow pebbles = 8

The probability of choosing a yellow pebble = 8/50 = 0.16

To find how many times Greg should expect to choose a yellow pebble, we can multiply the probability by the number of times he chooses a pebble:

Expected number of yellow pebbles = 0.16 x 75 = 12

Therefore, Greg should expect to choose a yellow pebble 12 times out of 75. However, since the answer choices do not include 12, the closest option would be A) 11.

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For the equation, the ordered pairs of coordinate points are (7, 9) and (1, 9).

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

To solve the system algebraically, we need to find the values of x that satisfy both equations -

f(x) = (x - 4)²

g(x) = 9

Since g(x) is a constant, we can solve for x by setting f(x) equal to 9 -

(x - 4)² = 9

Taking the square root of both sides, we get -

x - 4 = ±3

Adding 4 to both sides, we get -

x = 7 or x = 1

Therefore, the solutions as ordered pairs are (7, 9) and (1, 9).

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The graph that shows a reflection over the line k is the first one.

If we have a figure and we reflect it over a line, the perspective of the image with respect to that line shouldn't change.

For example, in this case we can see that the blue triangle has a "white corner" pointing towards the line k.

Then the image after the reflection also should have the white corner pointing to the line.

And the parallel to the line (the top vertex) shouldn't change, with these two things we can conclude that the correct option is the first one.

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The approximate number of water bottles that Charlotte sold was 31.

Suppose the value of which a thing is expressed in percentage is "a' the percent that considered thing is of "a" is b%. Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts.

We need to find the approximate number of water bottles that Charlotte sold

It can be written by

[tex]62\% \ \text{of} \ 50[/tex]

[tex]\dfrac{62}{100} \times 50[/tex]

[tex]0.62 \times 50 = 31[/tex]

so, 62% of 50 is 31. However, it is to the nearest 10, it would be about 31 water bottles.

She sold about 31 water bottles.