Solve. −3 2/3x=−2 1/5 What is the solution to the equation? Enter your answer as a simplified fraction in the box. x =

Answer:

90pi

Step-by-step explanation:

SA = pi r l +B

we know the radius is 5

We need to find the slant height using the Pythagorean theorem

a^2+b^2 = c^2

5^2+12^2 = l^2

25+144= l^2

169 = l^2

Taking the square root of each side

sqrt(169) = sqrt(l^2)

13 = l

B is the area of the base

B = pi r^2 = pi (5)^2 = 25 pi

SA = pi r l +B  = pi (5)*13 + 25pi

                       =65pi +25pi = 90pi

Answer:

90 pi

Step-by-step explanation:

Just in case the other answer was confusing. Just put it in, and it marked it right. 90 is the answer

SA= 90

Hypatia has read 4.4 CHAPTERS out of her book.

However, without (at least) an estimated guess of the amount of pages per chapter it can't be known how many pages that Hypatia has read.

----------------------------------------------------------------------------------------------------------------Hope you get this right.

<3

Miri

The area of the figure ABDECA, and the coordinates of the points on the quadrilateral are;

1. The area is about 15.16 units²

2. The coordinates of the points are;

(i) B(5, 8)

(ii) C(8.58, 4)

(ii) D(8,58, 1.21)

A quadrilateral is a four sided polygon.

1. The coordinate of the point C can be found as follows;

Let (x, y) represent the coordinates of the C, we get;

(x + 8)/2 = 5

x = 2 × 5 - 8 = 2

(y + 8)/2 = 6

y = 2 × 6 - 8 = 4

The coordinates ot the point C (2, 4)

The length of the segment BC = √((8 - 2)² + (8 - 4)²) = 2·√(13)

Length of the side AB = √((8 - 6)² + (8 - 11)²) = √(4 + 9) = √(13)

The area of the triangle ABC = (1/2) × 2·√(13) × √(13) = 13

CE is perpendicular to DE, let (a, b), represent the coordinates of the point E, therefore;

(4 - y)/(2 - x) = -(5 - x)/(6 - y)

y - 4 = (-4/7)(x - 2)

y - 6 = (7/4)(x - 5)

(-4/7)(x - 2) + 4 = (7/4)(x - 5) + 6

x = (17/5) = 3.4

y = (7/4)((17/5) - 5) + 6 = 3.2

The coordinates of the point E is (3.4, 3.2)

The length of the side DE = √((5 - 3.4)² + (6 - 3.2)²) = √(10.4)

Length of the side CE = √((3.2 - 2)² + (3.4 - 4)²) = √(1.8)

Area of the triangle ΔCDE = (1/2) × √(10.4) × √(1.8)

Area of the figure is therefore;

2. The equation of the line AB is; y - 6 = (1/3)·(x - (-1))

y - 6 = (1/3)·(x + 1)

y = (1/3)·(x + 1) + 6

The slope of the segment AE = (4 - 6)/(3 - (-1)) = -1/2

Slope of the segment BE = -1/(-1/2) = 2

Equation of BE is; y - 4 = 2·(x - 3)

y = 2·(x - 3) + 4 = (1/3)·(x + 1) + 6

Therefore, x = 5

y = (1/3)·(5 + 1) + 6 = 8

(ii) Area of the triangle EBC = 24 unit²

EB = (1/2) × √((5 - 3)² + (8 - 4)²) = √20

Therefore;

BC = 24/(√20) = 12/√5 = 12·√5/5 = √(28.8)

(x - 5)² + (y - 8)² = 28.8

y = 4, therefore;

(x - 5)² + (4 - 8)² = 28.8

(x - 5)² = 28.8 - (4 - 8)² = 12.8

x = √(12.8) + 5

(iii) The equation of the segment AD is; y - 4 = (-1/2)(x - 3)

x = √(12.8) + 5

Therefore;

y - 4 = (-1/2)((√(12.8) + 5) - 3)

y = (-1/2)((√(12.8) + 5) - 3) + 4 ≈ 1.21

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The probability P(-0.5 ≤ z ≤ 0.5) is the greatest for a standard normal distribution, and the value of P(-0.5 ≤ z ≤ 0.5) is 38.2% option second is correct.

It's the probability curve of a continuous distribution that's most likely symmetric around the mean. On the Z curve, at Z=0, the chance is 50-50. A bell-shaped curve is another name for it.

We have a statement:

Which of the following probabilities is the greatest for a standard normal distribution:

The options are:

P(-1.5 ≤ z ≤ -0.5)

P(-0.5 ≤ z ≤ 0.5)

P(0.5 ≤ z ≤ 1.5)

P(1.5 ≤ z ≤ 2.5)

As we know from the normal distribution curve we can find the probability between the range given. At Z=0, the chance is 50-50.

From the Z-curve:

P(-1.5 ≤ z ≤ -0.5)  = 9.2% + 15% = 24.2%

P(-0.5 ≤ z ≤ 0.5) = 19.1% + 19.1% = 38.2%

P(0.5 ≤ z ≤ 1.5) = 15% + 9.2% = 24.2%

P(1.5 ≤ z ≤ 2.5) = 4.4% + 1.7% = 6.1%

Thus, the probability P(-0.5 ≤ z ≤ 0.5) is the greatest for a standard normal distribution, and the value of P(-0.5 ≤ z ≤ 0.5) is 38.2% option second is correct.

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Answer:

B) P (-0.5 <= z <= 0.5)

Step-by-step explanation:

Answer: 72.36

Step-by-step explanation:

To find the total amount of salt in the bowl after Omar poured 13.2 grams, we need to add the initial amount of salt in the bowl to the amount of salt Omar added.

The initial amount of salt in the bowl was 59.16 grams.

Omar added 13.2 grams of salt to the bowl.

To find the total amount of salt in the bowl now, we add these two amounts: 59.16 + 13.2 = 72.36

Therefore, the bowl contains 72.36 grams of salt now.

Answer:

The answer is  M< A= -2.

Answer:

C 18

Hope this helps

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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its c

Step-by-step explanation:

Answer:

the answer us 8/9

1/3 times 8/3= 8/9

Answer:

Step-by-step explanation:

we have 2 area rugs, and each has a length of 4 yards

Rug 1 has a area of 16 square yards, meaning that the width is also 4 yard(L*w=16, where Length=4)

Rug 2 has a Length of L=4 but the area is just 12 square yards, so here we have the width of 3 yards (12/4=3)

the rug number 2 will fit in tucker's bedroom

Answer: 189 people preferred running.

Step-by-step explanation: 35% is equal to 35/100. Since 540 people were surveyed, we can multiply 35/100 by 540 to find that 189 people out of 540 preferred running. Hope this helps!

Answer:

10,369.04

Step-by-step explanation:

Sorry if i'm wrong i got a little confused with this

Answer:

√43

Step-by-step explanation:

Implement the Pythagorean formula to solve for sides of a right triangle: a^2 + b^2 = c^2, where "a" and "b" are the legs and "c" is the hypotenuse.

a = √6 and c = 49

√6^2 + b^2 = 49

6 + b^2 = 49

b^2 = 43

b = √43

Answer:

The square root of 43

Step-by-step explanation:

 I did this in class the other day

Answer:

\(2 \frac{2}{15} - 1 \frac{2}{3}\)

\( = \frac{32}{15} - \frac{5}{3} \)

\( = \frac{32 \times 1 - 5 \times 5}{15} \)

\( = \frac{32 - 25}{15} \)

\( = \frac{7}{15} \)

To determine the area of the remaining piece of cardboard expressed in terms of x when a square of side length x inches is cut out from a rectangular piece of cardboard having a length of 6x+2 inches and a width of 2x-4 inches, use the following steps.

Draw and label a diagram of the problem. The rectangle should be labeled as 6x+2 inches by 2x-4 inches, and the square cut out should be labeled as x inches by x inches. This is how the diagram looks like: Determine the area of the rectangle, Arect.

The area of the rectangle is given by the product of its length and width. Thus, Arect = (6x + 2)(2x - 4) Determine the area of the square, Asq. The area of the square is given by the square of its side length. Thus, Asq = x²Step 4: Determine the area of the remaining cardboard after the square is cut out, Ar.

This is the difference between the area of the rectangle and the area of the square. Thus, Ar = Arect - Asq= (6x + 2)(2x - 4) - x²= 12x² - 20x - 16

Simplify the expression. The final answer is given in terms of x. Thus, Ar = 12x² - 20x - 16.The area of the remaining piece of cardboard is expressed in terms of x as 12x² - 20x - 16.

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Sara needs to reduce the price by approximately 33.33% to provide the same value for money as Zak's idea.

To find the percentage by which Sara needs to reduce the price to provide the same value for money as Zak's idea, we need to compare the original price and the new price under Zak's idea.

Let's assume the original price of a box of pet food is P and the original amount of pet food in each box is A.

According to Zak's idea, the company will put 50% more pet food into each box without changing the price. Therefore, the new amount of pet food in each box will be 1.5A.

To calculate the value for money under Zak's idea, we divide the amount of pet food by the price:

Value for money (Zak's idea) = (1.5A) / P

Now, let's consider Sara's idea. She wants to reduce the price but keep the amount of pet food unchanged. Let's assume Sara reduces the price by a percentage represented by x.

Under Sara's idea, the new price of a box of pet food will be P - (x/100)P = P(1 - x/100).

Since Sara wants her idea to provide the same value for money as Zak's idea, we can equate the two value for money expressions:

(1.5A) / P = (A) / (P(1 - x/100))

Cross-multiplying and simplifying the equation:

1.5A * P(1 - x/100) = A * P

1.5(1 - x/100) = 1

Simplifying further:

1 - x/100 = 2/3

-x/100 = -1/3

x/100 = 1/3

x = 100/3

Therefore, Sara needs to reduce the price by approximately 33.33% to provide the same value for money as Zak's idea.

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answer:

\(\frac{-23}{6}\) or -3.8333 (repeating)

Answer:

x=10, y=4

Step-by-step explanation:

3x-3y=18

(-)3x-(-)8y=-(-)2   -3x+8y=2   add to first equation to eliminate x

5y=20

y=4

substitute y with 4

3x-3(4)=18

3x=30

x=10

x=10,y=4

Answer:

Step-by-step explanation:

The bell boy added $270 and $20 incorrectly. The $20 bill was something that was returned due to overcharching. On the other hand, $270 was the amount that they paid for their room. This only means that $20 should be deducted from $270 and that's the amount that they paid for their room while $30 and $20 are the amount that the bell boy received as a tip

Total money of the three men: 3($100) = $300

They paid $270 for the room: $300 - $270 = $30

Tip for the bell boy: $30 - $30 = $0

Amount overcharged to them: $0 + $20 = $20

Tip to the bell boy: $20 - $20 = $0

They were left with no more money from the original $300.

Rounding to the nearest whole number. The correct option is D) 216 m²; 244 m².

Since the prism has a rectangular base, we know that its lateral faces are all rectangles with heights equal to the height of the prism. Let's first find the lateral area of the prism using the formula:

Lateral Area = Perimeter of Base * Height

The perimeter of the base is the sum of the lengths of all four sides of the rectangle. Since there are two bases, we will add their perimeters together. The length and width of each base are 12 m and 7 m, respectively, so:

Perimeter of Base = 2 * (Length + Width) = 2 * (12 + 7) = 38 m

The height of the prism is given as 10 m, so:

Lateral Area = 38 * 10 = 380 m²

Next, we need to find the surface area of the prism. This consists of the lateral area we just found, plus the areas of the two bases. Each base has an area of 12 * 7 = 84 m², so:

Surface Area = 2 * Base Area + Lateral Area = 2 * 84 + 380 = 548 m²

Rounding to the nearest whole number, we get:

Lateral Area ≈ 380 m²

Surface Area ≈ 548 m²

Therefore, the answer is option D) 216 m²; 244 m².

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The middle 95% of Jace's finishing times in the 400 meter race is between 82 and 92 seconds.

Approximately 68% of the data falls within 1 standard deviation of the mean (i.e., between μ - σ and μ + σ).

Approximately 95% of the data falls within 2 standard deviations of the mean (i.e., between μ - 2σ and μ + 2σ).

Approximately 99.7% of the data falls within 3 standard deviations of the mean (i.e., between μ - 3σ and μ + 3σ).

We want to find the interval of times that represents the middle 95% of Jace's finishing times, which means we want to find the interval that falls between μ - 2σ and μ + 2σ.

Substituting the given values, we get:

μ - 2σ = 87 - 2(2.5) = 82

μ + 2σ = 87 + 2(2.5) = 92

Therefore, the middle 95% of Jace's finishing times in the 400 meter race is between 82 and 92 seconds.

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Answer:

10x10x10 or 10*3......

Step-by-step explanation:

Hey there!

Given;

The measure of angle B is 45°.

And AB = 14.

Taking refrence angle as B, we get;

AC = perpendicular

AB = hypotenuse

Using ratio of sin,

\( \sin(45°) = \frac{p}{h} \)

Put all values.

\( \sin(45°) = \frac{ac}{14} \)

Simplify it to get answer.

\( \frac{1}{ \sqrt{2} } = \frac{AC}{14} \)

\( \sqrt{2} AC = 14\)

\(AC = \frac{14}{ \sqrt{2} } \)

\(AC= \frac{14 \times \sqrt{2} }{ \sqrt{2} \times \sqrt{2} } \)

\(AC = \frac{14 \sqrt{2} }{2} \)

\(AC = 7\sqrt{2} \)

Therefore the answer is option B.

Hope it helps...

Answer:

The augmented matrix is:

\(\left[\begin{array}{cccc}-2&-2&5&1\\-5&-5&7&4\end{array}\right]\)

Step-by-step explanation:

This system of two equations with three unknowns will generate an augmented matrix that consists of two rows and four columns:

\(\left[\begin{array}{cccc}-2&-2&5&1\\-5&-5&7&4\end{array}\right]\)

Answer:

(x, y) = (-38/5, -38/5)

Step-by-step explanation:

6y - 9x = 24

-3y + 2x = 7 $\Rightarrow$ -6y + 4x = 14.

Adding the two equtions together, we get:

(6y - 9x) + (-6y + 4x) = 24 + 14.

Simplifying, we get:

-9x + 4x = 38

-5x = 38

x = -38/5.

So, 6y - 9 * (-38/5) = 24

y = -37/5

Answer:

Step-by-step explanation:

6y - 9x = 24

-6y + 6x = 21

-3x = 45

x = -15

-3y - 30 = 7

-3y = 37

y = -37/3

The central angle of Bathing = 108 degrees.

In the given pie chart,

Since we know,

A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle possesses rotational symmetry around the center.

The whole circle is 360 degrees

which represents 100%.

It is given that,

Bathing = 30%

So have need to find 30% of 360 degrees.

Therefore,

Bathing = (30/100)x360

            =  (30/10) x 36

            = 3x36

            = 108

Hence,

The central angle = 108 degrees.

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The complete question is:

To the nearest degree, what is the measure of the central angle for bathing?

Given

The function is

\(f(x)=3\sqrt{x}\)

The function g(x) transform by shifting f(x) right 3 units.

To find:

The function g(x).

Step-by-step explanation:

The translation is defined as

\(g(x)=f(x+a)+b\)

where, a is horizontal shift and b is vertical shift.

If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.

If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.

The function f(x) shifts only 3 units right. So,

\(a=-3,b=0\)

Now,

\(g(x)=f(x+(-3))+0\)

\(g(x)=f(x-3)\)

\(g(x)=3\sqrt{x-3}\)               \([\because f(x)=3\sqrt{x}]\)

Therefore, the required function is \(g(x)=3\sqrt{x-3}\).

(A)

\(\dfrac{\partial f}{\partial x}=-16x+2y\)

\(\implies f(x,y)=-8x^2+2xy+g(y)\)

\(\implies\dfrac{\partial f}{\partial y}=2x+\dfrac{\mathrm dg}{\mathrm dy}=2x+10y\)

\(\implies\dfrac{\mathrm dg}{\mathrm dy}=10y\)

\(\implies g(y)=5y^2+C\)

\(\implies f(x,y)=\boxed{-8x^2+2xy+5y^2+C}\)

(B)

\(\dfrac{\partial f}{\partial x}=-8y\)

\(\implies f(x,y)=-8xy+g(y)\)

\(\implies\dfrac{\partial f}{\partial y}=-8x+\dfrac{\mathrm dg}{\mathrm dy}=-7x\)

\(\implies \dfrac{\mathrm dg}{\mathrm dy}=x\)

But we assume \(g(y)\) is a function of \(y\) alone, so there is not potential function here.

(C)

\(\dfrac{\partial f}{\partial x}=-8\sin y\)

\(\implies f(x,y)=-8x\sin y+g(x,y)\)

\(\implies\dfrac{\partial f}{\partial y}=-8x\cos y+\dfrac{\mathrm dg}{\mathrm dy}=4y-8x\cos y\)

\(\implies\dfrac{\mathrm dg}{\mathrm dy}=4y\)

\(\implies g(y)=2y^2+C\)

\(\implies f(x,y)=\boxed{-8x\sin y+2y^2+C}\)

For (A) and (C), we have \(f(0,0)=0\), which makes \(C=0\) for both.

The side length of the cube is 5.6 feet (rounded to the nearest tenth).

We can calculate the side length of a cube with a volume of 141 cubic feet using the formula for cube volume , which is \(V = s^3\), where V is the volume and s is the side length.

We can calculate s by taking the cube root of both sides of the equation:

\(s = (V)^{(1/3)\)

Substituting V = 141, we get:

\(s = (141)^{(1/3)\)

By using a calculator to evaluate this expression, we may determine:

s ≈ 5.6

As a result, the cube's side length is roughly 5.6 feet (rounded to the closest tenth). This indicates that if we increase the side length by three, it will become longer. (\(s^3\)), we will get the volume of the cube, which is 141 cubic feet.

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