What statement correctly describes this expression

Using percentages and proportion of composition, we know that Lake Stockton lost the least amount of water which is 49%.

What is the proportion of composition?

Here, a fraction of all the lakes after the draught is equal i.e:

Lake  Stockton lost the least amount of water.

Therefore, using percentages and proportion of composition, we know that Lake Stockton lost the least amount of water which is 49%.

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Answer:

y=7x+-9

Step-by-step explanation:

When Mandy tossed a fistful of silver coins into the air, then picked up the 23 coins that landed heads up, this isn't a random sample of the coins.

In statistics, a simple random sample is a subset of individuals chosen at random from a larger set, with all individuals having the same probability. It is the process of selecting a sample at random.

A simple random sample is a subset of a population chosen at random. This sampling method gives each member of the population an exact equal chance of being chosen, reducing the risk of selection bias.

In this case, Mandy only picked heads, this isn't a random sample since it's biased.

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The greatest common factor (GCF) of two or more numbers is the largest number that divides evenly into each of the numbers without leaving a remainder. To find the GCF of 24, 30 and 50, we can use the prime factorization method. The prime factorization of 24 is 2^3 * 3^1, the prime factorization of 30 is 2 * 3^1 * 5^1, and the prime factorization of 50 is 2 * 5^2. We can see that the GCF of these numbers is 2 * 3^1 = 6, since 6 is the highest power of 2 and 3 that divides all three numbers evenly. So, the GCF of 24, 30 and 50 is 6.

I hope this helps :)

Answer:

2

Step-by-step explanation:

I did the work.

Answer:

\(\frac{(a - b)(b + a)}{{a}^{2} }\)

Step-by-step explanation:

\(\frac{(1 - \frac{b}{a} \times \frac{b}{a - b} (1 + \frac{a}{b} ) \times \frac{a}{a - b} }{( \frac{a}{b} - 1) \times \frac{b}{a - b} ( \frac{b}{a - b} + 1) \times \frac{a}{a - b}}\)

Answer:

48

Step-by-step explanation:

The amount of time needed and the amount of wall to paint are directly proportional. So, when we multiply the amount of wall to paint by 8/5 (going from 5000 square feet to 8000 square feet), we multiply the time needed by 8/5. Therefore, we need 30 * 8/5 = 48  minutes to paint the 8000 square foot wall.

We need 48 minutes to paint 8000 square football . The minute is a measure of time that is typically equal to 60 seconds, or 1/60 of an hour.

Given,

8 team members paint 5000square football in 30 min

So,

30*8/5

= 48 minutes

Therefore We need 48 minutes to paint 8000 square football.

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The angle 1 is 19 degrees and angle 2 is 379 degrees. The angles can be found by solving the equation cos(3x + 10) = sin(3x + 26). The two angles, angle 1 and angle 2, can be determined by finding the values of x that satisfy the equation.

To find the angles, we'll solve the equation cos(3x + 10) = sin(3x + 26) for x, taking into account that angles are in degrees.

First, we'll rewrite the equation using the trigonometric identity cos(theta) = sin(90 - theta):

cos(3x + 10) = cos(90 - (3x + 26))

For the angles to be equal, the expressions inside the cosine functions must be equal:

3x + 10 = 90 - (3x + 26)

Simplifying the equation:

3x + 10 = 90 - 3x - 26

Combine like terms:

6x = 54 - 10 - 26

6x = 18

Divide both sides by 6:

x = 3

Now that we have the value of x, we can find the corresponding angles.

Angle 1:

Plugging in x = 3 into the equation:

3x + 10 = 3(3) + 10 = 19

Therefore, angle 1 is 19 degrees.

Angle 2:

To find the second angle, we can use the fact that cosine is a periodic function with a period of 360 degrees. Adding 360 to angle 1 gives us:

19 + 360 = 379

Therefore, angle 2 is 379 degrees.

In summary, angle 1 is 19 degrees and angle 2 is 379 degrees.

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The given statement is correct.

Hence it is true.

We have a statement regarding the quadratic equations.

We have to verify whether it is true or not.

Since we know that,

A quadratic equation is an equation with a single variable of degree 2. Its general form is ax² + bx + c = 0, where x is variable and a, b, and c are constants, and a ≠ 0.

According to the question, we are provided with the standard form of the quadratic equation as -  ax² + bx + c = 0.

If we compare the statement given in the question with the definition discussed above, then it can be concluded that the given statement is true. Equation ax² + bx + c = 0 is the standard form of a quadratic equation with a, b, and c as constant real numbers.

The constant 'a' cannot be 0, as this would reduce the degree of the equation to 1.

Hence, the given statement is correct.

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Answer:

1/40

Step-by-step explanation:

You put 4/1 to put it into a fraction and then flip the fraction to times 1/10 (1/4)

to get the answer of 1/40

The estimated coefficient for the total loans and leases to total assets ratio indicates that holding the total expenses to assets ratio constant, a one unit increase in the total loans and leases to assets ratio is associated with an increase in the odds of being financially weak by a factor of -14.18755183 + 79.963941181 + 9.1732146 = 74.949604981.

This means that as the ratio of total loans and leases to total assets increases, the odds of being financially weak also increase by a significant factor. It is important to note that other factors may also contribute to financial weakness and that the coefficient should be interpreted in conjunction with other relevant data and factors.

The estimated coefficient for the total loans and leases to total assets ratio in terms of the odds of being financially weak can be interpreted as follows:

Holding the total expenses/assets ratio constant, a one unit increase in the total loans and leases-to-assets ratio is associated with an increase in the odds of being financially weak by a factor of 9.1732146.

This means that for each unit increase in the loans and leases-to-assets ratio, the likelihood of the institution being financially weak increases by a factor of 9.1732146, assuming all other factors remain the same.

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Answer:

x = 46°

Step-by-step explanation:

Angles on a straight line sum to 180°.

Therefore, the interior angle of the triangle that forms a linear pair with the exterior angle marked 130° is:

⇒ 180° - 130° = 50°

The interior angle of the triangle that forms a linear pair with the exterior angle marked 96° is:

⇒ 180° - 96° = 84°

The interior angles of a triangle sum to 180°. Therefore:

⇒ 50° + 84° + x = 180°

⇒ 134° + x = 180°

⇒ 134° + x - 134° = 180° - 134°

⇒ x = 46°

Therefore, the size of angle x is 46°.

Explanation

From the graph, we will have the table of values below.

We can then have the explicit formula as;

By observation, the explicit formula becomes

Answer:

Answer:

Step-by-step explanation:

Find the GCD (or HCF) of numerator and denominator. GCD of 1 and 6 is

1 ÷ 16

Reduced fraction: 16. Therefore, 1/6 simplified to lowest terms is 1/6.

Answer:

I have made it in above picture hope it helps

Answer:

Step-by-step explanation:

You want the value of the piecewise function for various values of x.

The first step in evaluating a piecewise function is determining which domain is applicable to the value of x you have. Then you use the corresponding function, evaluating it in the usual way.

For x = -5, the applicable domain is x < -3, so the function is ...

  h(-5) = -4(-5) -18 = 20 -18

  h(-5) = 2

For x = 0, the applicable domain is -3 ≤ x < 1, so the function is ...

  h(0) = 1

For x = 1 or 4, the applicable domain is x ≥ 1, so the function is ...

  h(1) = 1 +2 = 3

  h(4) = 4 +2 = 6

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Answer: Circle 2

Step-by-step explanation:

If you show that angle 2 is equal to angle 3, then since angle 1 is equal to angle 2, angle 1 is equal to angle 3, which proves that the 2 lines are parallel.

(The wording is a bit weird sorry)

Answer:

y = \(\frac{1}{3}\) x

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here slope m = \(\frac{1}{3}\) , then

y = \(\frac{1}{3}\) x + c ← is the partial equation

to find c substitute (- 9, - 3) , that is x = - 9, y = - 3 into the partial equation

- 3 = \(\frac{1}{3}\) (- 9) + c = - 3 + c ( add 3 to both sides )

0 = c

y = \(\frac{1}{3}\) x + 0 , that is

y = \(\frac{1}{3}\) x

Answer: Look below

Step-by-step explanation:

10% = $120.90

1% = $12.09

11% = $132.99

$1,209 + $132.99 = $1,341.99

She made a $132.99 profit or $1,341.99

—————————————————————

8% = 96.72

$1,341.99 - $96.72 = $1245.27

————————————————

Or if it is $96.72 off the price she bought it then it would be

$1,209 - $96.72 = $1,112.28

Answer: y=1/6x

Step-by-step explanation:

1. Identify the type of graph (linear)

2. the linear line equation is y=mx+b

3. find the slope, in this case, 1/6

a. to find the slope follow the equation (y1-y2)/(x1-x2)

b. plug in the x and y of two different points ex: (0,0) and (18,3)

4. plug into the equation the slope and a set of points - 3=18(1/6) +b

5. solve for b (0)

6. plug b and the slope into the original equation

7. y=1/6x

8. Done :)

Answer: D) 15.7

Step-by-step explanation:

Start with the formula C=2 πr

Then solve for r r=C2π = 98.62·π = 15.69(7)204

The radius of the circle is 15.7 mm.

The route or boundary that encircles any shape in mathematics is defined by the shape's circumference.

The measurement of the circle's perimeter, also known as its circumference, is called the circle's boundary. The region a circle occupies is determined by its area. The length of a straight line drawn from the centre of a circle equals the diameter of that circle.

We have,

The circumference of Circle = 2πr

Also, The circumference of a circle is 98.596 millimeters.

So, circumference of Circle = 2πr

98.596 = 2πr

98.596 = 6.28r

r= 98. 596 / 6.28

r = 15.7 mm

Thus, the radius is 15.7 mm.

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The increasing the sample size by a factor of 25 will reduce the width of the confidence interval by a factor of 5.

a. Suppose we have a two-sided confidence interval for the population mean with known variance, given by the equation:

Cl is the confidence interval, x is the sample mean, σ is the population standard deviation, n is the sample size, and zα/2 is the z-score corresponding to the desired level of confidence.

The σ are fixed for a given level of confidence, we can achieve this by increasing n by a factor of 4.

Specifically, if we increase the sample size from n to 4n, then the new confidence interval will have half the width of the original interval.

b. If the sample size is increased by a factor of 25, then the term √n in the denominator of the above equation will be replaced.

Therefore, increasing the sample size by a factor of 25 will reduce the width of the confidence interval by a factor of 5.

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Answer:

Below

Step-by-step explanation:

Pick a bunch of values of 'x' .....calculate the corresponding 'y' values then plot the ordered pairs and connect the dots with a smooth curved line ...

The first part of the trip took approximately 6.39 hours and the second part of the trip took approximately 5.84 hours.

In this problem, we are given the distance, total time, and average speeds for two parts of a plane trip.

Using the formula for average speed

Distance = average speed x time,

We can set up two equations and solve for the times spent flying at each speed.

We define t₁ as the time spent flying at 115 mph and t₂ as the time spent flying at 125 mph.

From the equation

730 miles = 115 mph x t₁,

we solve for t₁ and get

t₁ = 6.391304347826087 hours.

Similarly, from the equation

730 miles = 125 mph x t₂,

we solve for t₂ and get

t₂ = 5.84 hours.

Therefore, the plane flew at an average speed of 115 mph for approximately 6.39 hours and at an average speed of 125 mph for approximately 5.84 hours.

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To know if the classmate’s family is actually wealthy, one will need to know their assets and their debt.

In financial accounting, an asset means a resource that is owned or controlled by a business or an economic entity. An asset is anything that can be used to produce positive economic value.

Assets represent the value of ownership that can be converted into cash and the examples of personal financial assets include cash and bank accounts, real estate, personal property like furniture and vehicles, and investments such as stocks, mutual funds, and retirement plans.

In this case, through the assets, one will be able to know that they're wealthy. The debt is an obligation that requires one party, the debtor, to pay money or other agreed-upon value to another party, the creditor. This is the money that they owe.

The asset should more than the debt.

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Using the given function, it is found that it will take 38.12 years for the tree's height to exceed 17 feet.

The function that models the tree's height after t years is given by:

\(h(t) = 6 + 3\ln{(t + 1)}\)

It will be of 17 feet when h(t) = 17, hence:

\(h(t) = 6 + 3\ln{(t + 1)}\)

\(17 = 6 + 3\ln{(t + 1)}\)

\(3\ln{(t + 1)} = 11\)

\(\ln{(t + 1)} = \frac{11}{3}\)

\(e^{\ln{(t + 1)}} = e^{\frac{11}{3}}\)

\(t + 1 = e^{\frac{11}{3}}\)

\(t = e^{\frac{11}{3}} - 1\)

t = 38.12.

It will take 38.12 years for the tree's height to exceed 17 feet.

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Answer:

√  1. Quadratic

√  2. Quadratic

√  3. Quadratic

x  4. Not quadratic

x  5. Not quadratic

Step-by-step explanation:

A quadratic function is of the form
\(\large {ax^2 + bx + c}\)

where a, b and c are real-valued constants and a ≠ 0

b and c can be 0

The degree of a quadratic function (the highest exponent ) will be 2

#4 has has degree 1

#5 has degree 3

So only 1, 2 and 3 are quadratic functions

Answer:

Each child will receive 22 cookies.

6 tins of cookies x 88 cookies per tin = 528 total cookies

528 total cookies / 4 children = 132 cookies per child

132 cookies per child / 6 cookies in a tin = 22 cookies per child

Answer:

50/77

Step-by-step explanation:

(1÷2 3/4)+(1÷3 1/2)

2 3/4 is same as 11/44

1/2 is same as 7/2

so to divide fraction you have to flip the second number and multiply

so 1 times 4/11=4/11

and 1 times 2/7=2/7

4/11 +2/7=28/77+22/77=50/77

Answer:

x > 4 / 5

Step-by-step explanation:

This is similar to solving 7x = 2x + 4, but instead you have an inequality. The only thing you have to watch out for is if you divide by a negative number, if you do, you have to flip the "alligator" sign.

To solve without having to flip:

\(7x > 2x + 4\\7x - 2x > 2x - 2x + 4\\5x > 4\\5x/5 > 4 / 5\\x > \frac{4}{5}\)

Solving requiring "alligator" flip:

\(7x > 2x + 4\\7x - 7x > 2x - 7x + 4\\0 > -5x + 4\\-4 > -5x\\\frac{-4}{-5} > \frac{-5x}{-5} \\ \frac{4}{5} < x\)

To describe a linear program for finding the largest axis-aligned square that lies entirely inside a polygon (p), we can define the decision variables, objective function, and constraints as follows:

Decision Variables:

Let x be the side length of the square.

Objective Function:

Maximize x. The objective is to find the largest possible side length for the square.

Constraints:

Square Within Polygon Constraint:

For each vertex (xᵢ, yᵢ) of the polygon p, we can define the following set of inequalities:

xᵢ ≤ x, for all vertices of the polygon.

These inequalities ensure that the square lies entirely within the polygon.

Square Symmetry Constraint:

To ensure that the square is axis-aligned, we can impose symmetry constraints. For example, if the coordinates of the center of the square are (c_x, c_y), then we can add the following constraints:

c_x ± (x/2) = constant, for fixed values of c_x.

c_y ± (x/2) = constant, for fixed values of c_y.

These constraints ensure that the sides of the square are parallel to the x and y axes.

Non-Negative Constraint:

x ≥ 0, to ensure a non-negative side length for the square.

By formulating and solving this linear program, we can find the optimal value for x, which represents the largest axis-aligned square that lies entirely within the given polygon p.

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