Carlos had 194 seeds and 11 flower pots. He put the same number of seeds in each flower pot. Which is the best estimate for the number of seeds in each flower pot?
a:10
b:20
c:30
d:40

The value of x is -2 and the value of y is -7. The correct option is C.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the equations are y = x - 5 and y = 5x + 3. The value of x and y will be calculated by solving the equations,

y=x-5

y=5x+3

x -5 = 5x + 3

-4x = 8

x = -2

The value of y will be calculated as,

y = x - 5

y = -2 - 5

y = -7

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The augmented matrix represents the following system of linear equations:

Use back substitution. It means, use the value of z given in the last equation, to find y in the second equation, and then, use these values to find x in the first equation:

The solution of the system is (x, y, z)=(7, 0, -5)

The surface area of the prism is 1440 mm²

Given,

Triangular prism

Height of the prism = 32 mm

Base  of the prism = 24 mm

Length of the prism = 7 mm

We have to find the surface area of the prism;

Surface area, SA = bh + (b₁ + b₂ + b₃) l

Here,

Base, b = 24 mm

Height, h = 32 mm

Length, l = 7 mm

b₁ = 24 mm

b₂ = 32 mm

b₃ = [tex]\sqrt{b_{1} ^{2} + b_{2} ^{2} }[/tex] = [tex]\sqrt{24^{2}+ 32^{2} }[/tex] = [tex]\sqrt{576 + 1024}[/tex] = √1600 = 40 mm

Then,

Surface Area = bh + (b₁ + b₂ + b₃) l

SA = 24 x 32 + (24 + 32 + 40) 7

SA = 768 + 96 x 7

SA = 768 + 672

SA = 1440 mm²

That is,

The surface area of the prism is 1440 mm²

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The mean number of miles that the employees in a department live from work is 24.

What is a z-score?

The z-score is a numerical measurement used in statistics of the value's relationship to the mean of a group of values, measured in terms of standards from the mean.

The z-score is given as

x = 29

s = 3.6

z = -1.5

Then the mean will be

[tex]-1.5 = \frac{29-u}{3.6}[/tex]

μ = 29 - 5.4

μ = 23.6 ≅ 24

Hence the answer is the mean number of miles that the employees in a department live from work is 24.

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A Quadrilateral has four-sides, it is 2-dimensional (a flat shape), closed (the lines join up), and has straight sides.

We have special types of quadrilaterals which are,

1) Rectangle

2) Square

3) Rhombus

4) Parallelogram

5) Trapezium

6) Kite

Some types are also included in the definition of other types! For example a square, rhombus and rectangle are also parallelograms.

An isosceles trapezoid has left and right sides of equal length that join to the base at equal angles.

Below is the diagram of an Isosceles trapezoid

The ordered pair that is a solution for the inequality 2x + 3y < 12 and

3x - 2y ≥ 18 is

The solution is sought by substituting to each of the pair to the equation and comparing the answers

for  D. (4,-9)

2 * 4 + 3 * -9 < 12

-19 < 12   correct

3x - 2y ≥ 18

3 * 4 - 2 * -9 ≥ 18

30  ≥ 18 correct

This proves that option D is the correct option

trying for A. (5,0)

2 * 5 + 3 * 5 < 12

25 < 12   incorrect

3x - 2y ≥ 18

3 * 5 - 2 * 0 ≥ 18

15  ≥ 18 incorrect

trying for B. (3,-1)

2 * 3 + 3 * -1 < 12

3 < 12   correct

3x - 2y ≥ 18

3 * 3 - 2 * -1 ≥ 18

11  ≥ 18 incorrect

When any part is incorrect the pair is not a solution

trying for C. (-1,3)

2 * -1 + 3 * 3 < 12

7 < 12   correct

3x - 2y ≥ 18

3 * -1 - 2 * 3 ≥ 18

-9  ≥ 18 incorrect

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Given

Monthly deposit = $98

Rate = 6.1%

Number of years = 21

Find

Total value of the annuity in 21 years.

Explanation

Total value of annuity is given by

where FV is a future value

so ,

now solve this to obtain the future value .

Final Answer

Therefore , the future value is $49904.27

The height of cone is 10 inches.

What is cone?
A cone is indeed a three-dimensional geometric shape with a smooth transition from a flat base—often but not always circular—to the point at the top, also known as the apex or vertex. A cone is made up of a collection of line segments, half-lines, as well as lines that connect the apex—the common point—to every point on a base that is in a plane other than the apex. The base may only be a circle, any closed one-dimensional figure, any one-dimensional quadratic shape in the plane, or any combination of the above and furthermore all the enclosed points, depending on the author.

What is the formula for finding the height of a cone?

We know that

If two figures are similar, then the ratio of its corresponding sides is proportional

Let x----> the height of cone B

using proportionality

3/2 = 15/x

x = 2 * 15/3

x = 10 inches

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ANSWER:

A. 2.2%

STEP-BY-STEP EXPLANATION:

We can calculate the probability using the quotient of the area of the small circle and the area of the entire rectangular sector, like this:

In the circle the radius is 6 inches and in the rectangle the length is 84 inches and the width is 60 inches.

Therefore we replace and we have:

Answer:25

Step-by-step explanation:

1. you place the numbers in order from least to greatest so 1,1,3,8,12

2. then you add those all up

3.then you divide how many numbers there are together

1+1+3+8+12=25

then you divide by 5 because that's how many numbers are shown for the daily snow fall

HOPE THIS HELPS

Before finding the probability of being dealt 4 Aces of cards, let's find the probability of being dealt an Ace card on each draw.

The probability of getting an specific card from a deck is given by the ratio between the amount of this specific card and the total amount of cards. We have 4 Aces in a deck, and 52 cards, therefore, the probability of getting an Ace is

Since the cards are replaced, it is the same probability of getting an Ace on each draw.

Each draw is an independent event, the probability of them happening simultaneously is given by their product. The probability of being dealt 4 Aces of cards with a replacement is

Dependent Events where what happens depends on what happened before, such as taking cards from a deck makes less cards each time.

Independent Events which we learn about here.

Bill flipping a coin and rolling a dice are independent events. Flipping a coin doesn't depend on rolling a die.

Independent

Answer:

Step-by-step explanation: if the width is x then the length is 2x+3

The perimeter is 2x+2(2x+3)=42

then 6x+6=42

6x=36

x=6

Then the length is 2*6+3=15

The slope of the given line is 2

What is slope of a line?

Slope of a line is the tangent of the angle which the line makes with the positive direction of x axis

If [tex]\theta[/tex] is the angle which the line makes with the positive direction of x axis, then slope of the line is given by

m = [tex]tan\theta[/tex]

If the line passes through [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex]

slope = [tex]\frac{y_2-y_1}{x_2 - x_1}[/tex]

The given line passes through ( 0, 5) and  (-2, 1) .

Slope of the line  =

                               [tex]\frac{1-5}{-2-0}\\\\\frac{-4}{-2}\\\\2[/tex]

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Answer: 20

Step-by-step explanation: They are both equal to each other, so 3x+50=6x-10. Then just solve for x by canceling out both sides.

The total number of cards in a deck of cards is: 52

The total number of club cards is: 13

The total number of cards that less than 5 is: 8.

The probability of selecting a club card is,

The probability of selecting a card that is less than five is,

The total number of club card that is less than 5 is 3.

The probability of selecting a club card and a card that is less than 5 is,

The probability of selecting a card that is a club or less than 5 is,

Thus, the probability of selecting a club card or card that is less than 5 is 9/26.

We can notice that the graph of function g(x) = 1/2 f(x) is below the graph of function f(x) = x in the 1st quadrant but above in the 3rd quadrant, and they both intersect at 0.

So, the difference in the graph of the given functions:

Plot on the graph as follows:

(Refer to the graph attached below)

Therefore, we can notice that the graph of function g(x) = 1/2 f(x) is below the graph of function f(x) = x in the 1st quadrant but above in the 3rd quadrant, and they both intersect at 0.

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Answer:

1) B, 2) C

===========

As per definition, functions have only one y-value per x-value.

Let's test it with given sets and tables.

A)

x y

0 1

0 2

1 3

2 3

B)

x y

1 0

2 0

3 1

3 2

C)

x y

​​−1 −1

0 −1

2 0

3 2

D)

x y

−1 −1

−1 0

0 2

2 3

1) The set of ordered pairs that represents y as a function of x is;

B; {(−1, 1), (−2, 0), (−3, 4), (−3, 3)}

2) The table that represents y as a function of x is; Table 3

An ordered pair is defined as a composition of the x coordinate called the abscissa and the y coordinate called the ordinate having two values written in a fixed order within parentheses.

1) The first function given as  {(−1, 0), (−1, 1), (−2, 2), (0, 3)} ; This cannot be regarded as a function because the input x = - 1 is repeated with different output values.

The second function {(−1, 1), (−2, 0), (−3, 4), (−3, 3)} ; This cannot be regraded as a function because the input x = -3 is repeated with different output values.

The third function {(0, 0), (1, 1), (2, 2), (3, 3)};  This is a function because each input has unique output values.

The fourth function {(0, 0), (1, 0), (2, 4), (2, 3)} ;  This cannot be regraded as a function because the input x = 2 is repeated with different output values.

2) Table 1 cannot be regarded as a function because the input x = 0 is repeated with different output values.

Table 2 cannot be regarded as a function because the input x = 3 is repeated with different output values.

Table 3 is a Function because each input has unique output values.

Table 4 cannot be regarded as a function because the input x = -1 is repeated with different output values.

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Answer:

-20x9= -180.    2 to the power of three =8  if you want the quotient it would be -22.5

Step-by-step explanation:

We need to find the center and the radius of

The general circle equation is the following

where

(h,k) is the center and

r is the radius

1. rearrange the equation

2. Add 25 on both sides

3. Factor

Now we have an equation that is very similar to the circle equation, so let's compare them

Center -> (h,k) = (5,-11)

radius -> r = 5

STEP 1: Identify and Set Up

We are required to get the angle subtended by the arc DE.

We first acknowledge that it is part of the angles in a quadrant as this will help us find it.

STEP 2: Execute

First find angle DAE

Answer:

12. 0 = 11

No Solution

21. 0 = -132

No Solution

Step-by-step explanation:

12.

5 - 8x = 16 - 8x

-8x + 5 = -8x + 16

      - 5 =        -  5

-8x = -8x + 11

-8x = -8x

0 = 11

No Solution

21.

12x + 32 = 12x - 100

      - 32           -  32

12x = 12x - 132

-12x   -12x

0 = -132

No Solution

A quantity that is compounded continuously follows the next equation:

Where:

Now, the interest rate in decimal notation is determined by dividing the percentage by 100:

Now, we are asked to determine the time required for the quantity to double. Therefore, we need to determine "t" when:

Substituting in the formula we get:

Now, we can cancel out the "P":

Now, we solve for "t". First, we take the natural logarithm to both sides:

Now, we use the following property of logarithms:

Applying the property we get:

We have that:

Therefore:

Now, we divide both sides by "r":

Now, we substitute the value of "r":

Solving the operations:

Therefore, the right option is A.

Given: The bearing and distance of a ship from Akron(A) through Bellville(B) to Compton(C)

To Determine: The distance travelled and the angles

Solution

The diagram of the journey can be represented as shown below

Let us solve for BC using cosine rule

The total distance travelled is

Using sine rule, we can determine the measure of angle C

Also know that the sum of angles in a triangle is 180 degree. Therefore

The bearing of Compton from Bellville(B) is

The bearring of Akron(A) from Compton(C) is

In summary

The total distance travelled is 676km

The bearing of Compton from Bellville is 124.4 degrees, and the bearing of Akron from Compton is 304.4 degrees

On solving the equation 2x+y=-4 and 43x-12y=-4 for y we get the value of y=-164/67 as the definition of solution of equation says "A solution to an equation is a number that can be plugged in for the variable to make a true number statement".

A group of equations involving one or more variables is known as a system of equations. The variable mappings that cause all component equations to be satisfied or intersected are the solutions to systems of equations.

Here,

2x+y=-4

43x-12y=-4

43(2x+y=-4)

2(43x-12y=-4)

86x+43y=-172

86x-24y=-8

subtracting equation,

67y=-164

y=-164/67

As stated in the definition of equation solution, "A solution to an equation is a number that can be plugged in for the variable to make a true number statement," we arrive at the value of y=-164/67 after solving the equations 2x+y=-4 and 43x-12y=-4 for y.

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Answer:

[tex]2 {d}^{2} + 5d - 7 [/tex]

[tex](2d + 7)(d - 1)[/tex]

Given

(1,7) and (4,1)

y=-2x+9

The model is a linear function that shows $3.25 money that  Ilya has all together

The phrase linear function relates to two distinct but related concepts in mathematics:

Some authors use the term "linear function" only for linear mappings that accept values in the scalar field; these are more frequently known as linear forms.

Calculus' "linear functions" qualify as "linear mappings" when (and only when) f(0,..., 0) = 0, or, equivalently, when the aforementioned constant b equals zero.

A linear function in calculus and related fields is one whose graph is a straight line, that is, a polynomial function of degree zero or one. The word affine function is commonly used to distinguish such a linear function from the other idea.

A linear function is also known as a linear map in linear algebra, mathematical analysis, and functional analysis.

Given,

Ilya goes to the store with $1.40 in his pocket and $1.85 in his wallet.

Total money=$1.40+$1.85

=$3.25

The model is a linear function that shows $3.25 money that  Ilya has all together.

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A Cylinder can be used to model the surface area of the caterpillar with Surface area of 117.3 cm²

A full-grown monarch caterpillar is of cylinder shape . so , the option 4th is correct for first blank.

Surface area of cylinder is 2πrh + 2πr²

where r is radius of circle and h is height of cylinder

here , length of caterpillar is 5cm and radius is 2.5cm

Surface area = 2πrh + 2πr²

= 2π(5)(2.5) + 2π(2.5)²

= 2π(12.5) + 2π(6.25)

putting π = 3.14

=78.5+39.25

=117.8 cm²

Rewriting the sentence

A cylinder can be used to model the surface area of the caterpillar. Based on the model, the caterpillar has an approximate surface area of 117.8 square centimeters.

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Answer: A Cylinder can be used to model the surface area of the caterpillar with Surface area of 117.8 square centimeters

(if your on PLATO) if not then 117.8

Answer: 2.5, 5.4

Step-by-step explanation:

[tex]-16t^2 +126t=213\\\\16t^2 -126t+213=0\\\\t =\frac{-(-126) \pm \sqrt{(-126)^2 -4(16)(213)}}{2(16)}\\\\t \approx 2.5, 5.4[/tex]