Write an equation for the graph, where
y
depends on
x
.

Answer:

24.5

Step-by-step explanation:

All you have to is Multiply 3 1/2 by 7

3 1/2 x 7= 24.5

Answer: I can't really tell you the answer because you didn't show the graphs...

Step-by-step explanation:

A boat's value over time is given as the exponential function f(x) = 400(0.6)ˣ

An exponential function is in the form:

y = abˣ

Where a is the initial value and b is the multiplication factor.

Given that the boat's value decreasing at a rate of 40% per year, hence:

b = 100% - 40% = 60% = 0.6

A boat's value over time is given as the exponential function f(x) = 400(0.6)ˣ

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Answer:

321

Step-by-step explanation:

Conversion of 86 to base 5 will be done through base 10 to base 5 and it will be (321)₅.

To convert any number to base 10 we have to multiply its unit digit by 10⁰ and its tenth digit by 10¹.

After it, we need to add it. It will give us a number of the 10 bases.

Conversion of any 10 base number into base 5

To convert any number to base 5 we need to divide by 5 and write the remainder each time thus we need to write the quotient from down to up.

Converting 86 to base 10

⇒ 8ₓ10¹ +8ₓ\(10^0\)

⇒ 86₁₀

Converting 86₁₀ into 86₅

When the number 86 is converted in a base of 5 will be (321)₅

Since we need to go down to up to 321₅ will be the correct answer.

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Answer:

$3.32 per shirt of 3.32s has an expression

Step-by-step explanation:

9.95 / 3 ≈ 3.32

3.32s

s = number of shirts

Best of Luck!

Answer:

1/6

the most likely answer

Step-by-step explanation:

Answer:

Step-by-step explanation:

4x + y = - 1 -------------(I)

-5x - 2y = -4 -----------(II)

Multiply the equation (I) by 2 and then add the equations.

(I)*2        8x + 2y = -2

(II)          -5x - 2y = -4  {Now add and y will be eliminated}

             3x         = -6

                       x = -6/3

x = -2

Substitute x = -2 in equation (I)

4*(-2) + y = -1

-8     + y = -1

          y  = - 1 + 8

           y = 7

Answer:

(-2, 7)

Step-by-step explanation:

4x + y = -1

-5x - 2y = -4

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

2(4x + y = -1) = 8x + 2y = -2

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

8x + 2y = -2

-5x - 2y = -4

3x = -6

÷3   ÷3

x = -2

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

4(-2) + y = -1

-8 + y = -1

+8          +8

y = 7

I hope this helps!

The coordinates you would be standing on would be coordinate (-5.71, -3.57).

To discover the arrangement of point "K" that partitions the line section interfacing the beginning point to the coffee shop in a proportion of 5:2, we are able to utilize the concept of the area equation.

We should expect the starting point to be meant as A with orchestrates (- x1, - y1), and the café is implied as B with works with (- x2, - y2). The ratio of 5:2 suggests that segment AB is divided into two parts and five parts, each accounting for 7 percent of the length.

The x-direction of point K can be determined as:

xK = (5 * x2 + 2 * x1)/7

Basically, the y-direction of point K can be determined as:

yK = (5 * y2 + 2 * y1) / 7

Stopping within the arranges of the coffee shop (-8, -5) as (-x2, -y2) and accepting the beginning point as the beginning (0, 0), we have:

xK = (5 * (-8) + 2 * 0) / 7 = -40/7 ≈ -5.71

yK = (5 * (-5) + 2 * 0) / 7 = -25/7 ≈ -3.57

Hence, in case you stood on point K, you'd be around at coordinate (-5.71, -3.57).

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Answer:

5751

Step-by-step explanation:

price per person = 213

213 x 27 = 5751

so, the if 27 people sign up is 5751

Answer:

The expression is given below as

Concept:

To rationalize the denominator, we will multiply by the conjugate given below

The conjugate is given below as

Step 1:

Multiply the expression in the question by the conjugate, we will have

By expanding the brackets, we will have

Step 2:

Factor our the common number and divide

Hence,

The final answer is

OPTION A is the right answer

Answer:

3

Step-by-step explanation:

If 5/8 are eating salads, and 1/4, or 2/8 are eating sandwiches. Add 2/8 and 5/8 to get 7/8. That means only 1/8 are eating neither salads or sandwiches. Divide 24 by eight. You get 3. Since only 1/8 are eating neither sandwiches or salads you multiply 3 times one which gives you 3.

Answer:

Here is a Venn diagram that illustrates the information:

```

           ___________

          |           |

          |    N      |

          |_____  ____|

          |\    ||    /|

          | \   ||   / |

          |  \  ||  /  |

          |   \ || /   |

          |  C \||/ T  |

          |_____\v/____|

              A

```

In the diagram, N represents the set of students who read the novel, C represents the set of students who read the comics, and T represents the set of students who read the textbook. The region labeled A represents the set of students who read all three.

Using the Venn diagram, we can find the number of students who read:

a. comics and novel only: This corresponds to the region of the diagram that is exclusively shaded with the circles for comics and novel, but not for textbook. This region has 9 students.

b. textbook and novel only: This corresponds to the region of the diagram that is exclusively shaded with the circles for textbook and novel, but not for comics. This region has 1 student.

c. none of the 3: This corresponds to the region of the diagram that is outside of all three circles. This region has 13 students.

Therefore, the number of students who read a. comics and novel only is 9, b. textbook and novel only is 1, and c. none of the 3 is 13. Answer: a. 9, b. 1, c. 13.

Answer:

$6.79

Step-by-step explanation:

You add the cost of the first two then subtract that by the total she spent to get the answer

$10.79 + $8.72 = $19.51

$26.30 - $19.51 = $6.79

The prove of the given trigonometric function is given below.

The given trigonometric function is,

(sin⁴(x) - cos⁴(x))/(sin²(x) - cos²(x))

Now proceed left hand side of the given expression:

We can write the expression  as,

⇒[(sin²(x))² - (cos²(x))²]/(sin²(x) - cos²(x))

Since we know that ,

Algebraic identity:

a² - b²  = (a-b)(a+b)

Therefore the above expression be

⇒(sin²(x) - cos²(x))(sin²(x) + cos²(x))/(sin²(x) - cos²(x))

⇒(sin²(x) + cos²(x))

Since we know that,

Trigonometric Identities come in handy when trigonometric functions are used in an expression or equation. Trigonometric identities hold for all values of variables on both sides of an equation. Geometrically, these identities include one or more trigonometric functions (such as sine, cosine, and tangent).

Then,

sin²(x) + cos²(x)² = 1 is an trigonometric identity

Hence,

(sin⁴(x) - cos⁴(x))/(sin²(x) - cos²(x)) = 1

Hence proved.

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Answer:

2x + 1 = y

Step-by-step explanation:

x = Kim

y = Scott's time.

The area of the composite figure is 378.5 square feets.

We can decompose this into a rectangle of 30ft by 10ft and a circle whose diameter is 10ft.

Remember that the area of a rectangle of width W and length L is given by:

A = L*W

So the area of this rectangle is:

A = 30ft*10ft = 300ft²

And the area of a circle whose diameter D is:

A = 3.14*(D/2)²

So in this case the area of the circle is:

A = 3.14*(10ft/2)²

A = 3.14*(5ft)² = 78.5 ft²

Then the total area of the composite figure is:

area = 300ft² + 78.5 ft²

area = 378.5 ft²

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The number of square inches of cardboard that are needed to make one

the container is 18.

We have,

The volume of the triangular prism.

= Area of the triangle x height

Now,

Height = 6 in

And,

To find the area of a triangle, we can use Heron's formula.

A = √(s(s-a)(s-b)(s-c))

where s is the semi-perimeter of the triangle, calculated as:

s = (a + b + c) / 2

In this case, the side lengths of the triangle are 3.2 in, 3.2 in, and 2 in.

Let's calculate the area using Heron's formula:

s = (3.2 + 3.2 + 2) / 2 = 4.2

A = √(4.2(4.2 - 3.2)(4.2 - 3.2)(4.2 - 2))

A = √(4.2 x 1 x 1 x 2.2)

A = √(9.24)

A ≈ 3.04 square inches

Now,

The volume of the triangular prism.

= Area of the triangle x height

= 3.04 x 6

= 18.24 in²

Now,

Area of one cardboard.

= 1² in²

= 1 in²

Now,

The number of square inches of cardboard that are needed to make one

container.

= The volume of the triangular prism / Area of one cardboard

= 18.24 in² / 1 in²

= 18.24

= 18

Therefore,

The number of square inches of cardboard that are needed to make one

the container is 18.

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The volume of the shape is 490cm³

A prism is a solid shape that is bound on all its sides by plane faces. prism is named after the shape of these bases.

The base of this prism is rectangular. The volume of a prism is expressed as;

V = base area × height

base area = 7 × 10 = 70cm²

height = 7cm

the volume of the shape = 70× 7 = 490cm²

therefore the volume of the shape is 490cm³.

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(a) √2 · √8. The simplified surd expression is 4.

(b) √80. The simplified surd expression is  4√5.

(c) √5/√20. The simplified surd expression is  1/2.

(d) √20. The simplified surd expression is  2√5.

The given surd expression is simplified as follows;

(a) √2 · √8

we can simplify it as;

√2 · √8 = √(2 x 8) = √16 = 4

(b) √80

we can simplify it as;

√80 = √ (16 x 5) = √16  x √5 = 4√5

(c) √5/√20

we can simplify it as;

√5/√20  x  √20 / √20

= (√5  x √20 ) /(20)

= √100 / 20

= 10/20

= 1/2

(d) √20

we can simplify it as;

√20 = √4  x √5 = 2√5

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Given statement solution is :- Mathematical models are extremely valuable tools in various fields, including chemistry, biology, and physics. They offer several advantages: Simplification and abstraction, Prediction and simulation, Cost and time efficiency, Insight and understanding.

Mathematical models are extremely valuable tools in various fields, including chemistry, biology, and physics. They offer several advantages:

Simplification and abstraction: Mathematical models allow complex systems or processes to be represented using simplified mathematical equations or algorithms. This simplification helps in understanding the underlying principles and relationships of the system, making it easier to analyze and predict outcomes.

Prediction and simulation: Models enable scientists to make predictions about the behavior of a system under different conditions. They can simulate scenarios that are difficult or impossible to observe in the real world, allowing researchers to explore various hypotheses and make informed decisions.

Cost and time efficiency: Models can be used to explore different scenarios and test hypotheses in a relatively quick and cost-effective manner compared to conducting real-world experiments. They can help guide experimental design by providing insights into the most relevant variables and parameters.

Insight and understanding: Mathematical models often reveal underlying patterns and relationships that may not be immediately apparent from experimental data alone. They provide a framework for organizing and interpreting data, leading to a deeper understanding of the system being studied.

However, mathematical models also have limitations and potential disadvantages:

Simplifying assumptions: Models are based on assumptions and simplifications, which may not fully capture the complexity of the real-world system. If these assumptions are incorrect or oversimplified, the model's predictions may be inaccurate or misleading.

Uncertainty and error: Models are subject to uncertainties and errors stemming from the inherent variability of the system, limitations in data availability or quality, and simplifying assumptions. It is crucial to assess and communicate the uncertainties associated with model predictions.

Validation and verification: Models need to be validated and verified against experimental data to ensure their accuracy and reliability. This process requires rigorous testing and comparison to real-world observations, which can be challenging and time-consuming.

Mathematical models are closely linked to the fields of chemistry, biology, and physics, providing valuable insights and predictions in these disciplines. Here are some examples:

Chemistry: Mathematical models are used to study chemical reactions, reaction kinetics, and molecular dynamics. One example is the use of rate equations to model the kinetics of a chemical reaction, such as the reaction between reactants A and B to form product C.

Biology: Mathematical models play a crucial role in understanding biological systems, such as population dynamics, gene regulation, and the spread of infectious diseases. For instance, epidemiological models like the SIR (Susceptible-Infectious-Recovered) model are used to simulate and predict the spread of diseases within a population.

Physics: Mathematical models are fundamental in physics to describe physical phenomena and predict outcomes. One well-known example is Newton's laws of motion, which can be mathematically modeled to predict the motion of objects under the influence of forces.

Quantum mechanics: Mathematical models, such as Schrödinger's equation, are used to describe the behavior of particles at the quantum level, providing insights into atomic and molecular structures and the behavior of subatomic particles.

Fluid dynamics: Mathematical models, such as the Navier-Stokes equations, are employed to study the behavior of fluids, including airflow, water flow, and weather patterns.

These examples demonstrate the wide range of applications for mathematical models in understanding, predicting, and simulating various phenomena in the fields of chemistry, biology, and physics.

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Answer:

\(t = \frac{3sr}{2a \ + \ 5s}\)

Step-by-step explanation:

Given expression;

\(S = \frac{2at}{3r - 5t}\)

To make "t" the subject of the formula, cross and multiply;

\(S(3r - 5t) = 2at\\\\\)

open the bracket;

3sr - 5st = 2at

collect like terms together;

3sr = 2at + 5st

Factor out "t" on the right hand side;

3sr = t(2a + 5s)

Finally, make "t" the subject of the formula by dividing both sides by (2a + 5s).

\(t = \frac{3sr}{2a \ + \ 5s}\)

Answer:

apples per pound: 0.25

pears per pound: 0.33

Apples give him the best value per pound

Step-by-step explanation:

to find apple per pound: 4/16= 0.25

to find pears per pound: 7/21= 0.33

Step-by-step explanation:

f(10)=(10)²-1

f(10)=100-1

f(10)=99

Answer:

Length of rectangular strip = 12

area of rectangular strip =   2*12 = 24

Area of square =  x^2 = 12^2 = 144

Step-by-step explanation:

Area of square x^2

area of rectangle is given by length * width

Length of rectangular strip = x

width of rectangular strip = 2

area of rectangular strip =  length * width = 2*x = 2x

Area of square piece of paper when  rectangular strip is taken away from it

= Area of square - area of rectangular strip

= \(x^2 -2x\)

It is given that Area of square piece of paper when  rectangular strip is taken away from it is 120 square units.

Thus,

\(x^2 -2x = 120\\=> x^2 -2x -120 = 0\\=> x^2 -12x +10x-120\\=> x(x-12) +10(x-12)\\=> (x+10)(x-12) = 0\\\\\)

Thus,

either x+10 = 0 or x -12= 0

x = -10 or x = 12

but length cannot  be negative hence neglecting x = -10

hence value of x is 12.

Hence,

Length of rectangular strip = 12

area of rectangular strip =   2*12 = 24

Area of square =  x^2 = 12^2 = 144

Compounded Continuously:

A=Pe^{rt}

A=Pe

rt

P=1100\hspace{35px}r=0.051\hspace{35px}t=18

P=1100r=0.051t=18

Given values

A=1100e^{0.051(18)}

A=1100e

0.051(18)

Answer: 2,750

Explanation:

Plug in

A=1100e^{0.918}

A=1100e

0.918

Multiply

A=2754.70450683

A=2754.70450683

Use calculator (with e button)

A\approx 2750

A≈2750

Round to nearest ten dollars

please heart!

VVV                   and rate stars! VVV          :D

The amount of money after 18 years nearest to ten will be $2,750.

Theoretically, long-term average interest means that interest is continuously earned on a current account as well as reinvested into the balance to increase future interest earnings.

The equation is given as,

\(\rm A=P_o \times e^{r \times t}\\\)

Faith invested $1,100 in an account paying an interest rate of 5.1% compounded continuously.

Then the amount after 18 years is calculated as,

\(\rm A = \$1,100 \times e^{0.051 \times 18}\\A = \$1,100 \times e^{0.918}\)

Simplify the equation further, then we have

A = $1,100 x 2.504

A = $2,754.7

The amount of money after 18 years nearest to ten will be $2,750.

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The solution is: the value of x is : x = 98.5.

Formula

<x = 1/2 (arc 1 + arc2)

This is the basic angle formula for the way two chords intersect.

Givens

arc1 = 96

arc2 = 101

Solution

<x = 1/2 (arc1 + arc2)                 Substitute values

<x = 1/2(96 + 101)

<x = 1/2(197)

<x = 98.5

Answer

x = 98.5

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The second pair of points representing the solution set of the system of equations is (-6, 29).

To find the second pair of points representing the solution set of the system of equations, we need to substitute the x-coordinate of the second point into one of the equations and solve for y.

Given the system of equations:

y = x^2 - 2x - 19

y + 4x = 5

Substituting the x-coordinate of the second point (-6) into equation 2:

y + 4(-6) = 5

y - 24 = 5

y = 5 + 24

y = 29

Therefore, the second pair of points representing the solution set of the system of equations is (-6, 29).

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Question

Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.

y = x2 − 2x − 19

y + 4x = 5

The pair of points representing the solution set of this system of equations is (-6, 29) and

_________.

To find the probability that Naomi selects both white balls, we need to consider the total number of possible outcomes and the number of favorable outcomes.

Total number of outcomes:

Naomi selects 2 balls without replacement, so the total number of outcomes is the number of ways she can choose 2 balls out of the total number of balls in the bag. This can be calculated using combinations:

Total outcomes = C(20, 2) = (20!)/(2!(20-2)!) = (20 * 19)/(2 * 1) = 190

Number of favorable outcomes:

Naomi needs to select 2 white balls. There are 2 white balls in the bag, so the number of favorable outcomes is the number of ways she can choose 2 white balls out of the 2 white balls in the bag:

Favorable outcomes = C(2, 2) = 1

Probability = Favorable outcomes / Total outcomes = 1/190

Therefore, the correct answer is (G) 1/190.

The coordinates of each points are:

A = (-0.5, -5)

B = (0.8, -1.8)

C = (-2.6, -2.2)

D = (-1.5, -8.9)

E = (2.5, -6.5)

F = (-1.5, 3.1)

G = (-2.4, 4.1)

H = (1.5, 3)

I = (2.7, 1.5)

J = (-1.5, 0)

K = (-6.5, 0)

We have,

The coordinates of each point are in an ordered form.

i.e

(x, y)

x is the x-axis value.

y is the y-axis value.

Thus,

A = (-0.5, -5)

B = (0.8, -1.8)

C = (-2.6, -2.2)

D = (-1.5, -8.9)

E = (2.5, -6.5)

F = (-1.5, 3.1)

G = (-2.4, 4.1)

H = (1.5, 3)

I = (2.7, 1.5)

J = (-1.5, 0)

K = (-6.5, 0)

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Answer:

Here you go

Step-by-step explanation:

(3 x 10) x 8 = x(10 x 8)

What you do the distributive property so multiply 3x10 and you get 30 and multiply by 8 you get 240 so one side is solved. Now multiply 10x8 you get 80 and remember to multiply the variable x so you get 80x=240 now divide 80 both sides and you will get 3 as your total answer

Answer:

3

Step-by-step explanation:

(3x10)=30

30x8=240

(10x8)=80

240/80=3