30 POINTS, WILL GIVE BRAINLIEST IF ONLY RIGHT
Which of these expressions is equivalent to log 200?

A) 2 + log 2
B) 2 + log 20
C) log 50 + log 150
D) log 250 – log 50

Because the demographic group is dictated by location of the college. In this case the students are all college bound and have like socio ecconomic backgrounds.

What do you mean by sampling?

Sampling is the process of choosing the group from which you will actually collect data for your study. For instance, you could interview a sample of 100 students if you were examining the viewpoints of students at your university. With the help of sampling, you can test a statistical hypothesis on the features of a population.

According to the question,

A true sampling would be a mixed demographic group. A sampling from several like areas:

e.g. infront of the student store, infront of the regular store, infront if a food pantry, infront of ... or even better do a blind survey.

Because the demographic group is dictated by location of the college. In this case the students are all college bound and have like socio ecconomic backgrounds.

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Answer:

\(|RS| = \sqrt[3]{19}\)

Step-by-step explanation:

The computation of the magnitude is shown below:

Data provided in the question

Given points

R(3,7,-1), S(10,-4,0)

Now the distance lies between R and S

RS = (10 ,-4, 0) - ( 3 ,7, -1 )

     = (10 - 3, -4 - 7, 0 - (- 1))

     = (7, - 11, 1 )

After that, the magnitude is determined by using the following calculation part

\(|RS| = \sqrt{(7)^2 + (-11)^2 + (1)^2} \\\\ = \sqrt{49 + 121 + 1} \\\\ = \sqrt{121}\\\\ = \sqrt[3]{19}\)

The absolute minimum of the function z = f(x, y) = 5x^2 - 20x + 5y^2 - 20y on the domain D: x^2 + y^2 ≤ 121 is achieved at the point (-11, 0), and the absolute maximum is achieved at the point (11, 0).

To find the absolute maximum and absolute minimum of the function \(z = f(x, y) = 5x^2 - 20x + 5y^2 - 20y\) on the domain \(D: x^2 + y^2 \leq 121\), we need to consider the critical points and boundary of the domain.

First, we find the critical points by taking the partial derivatives of \(f\) with respect to \(x\) and \(y\) and setting them equal to zero:

\(\frac{\partial f}{\partial x} = 10x - 20 = 0\),

\(\frac{\partial f}{\partial y} = 10y - 20 = 0\).

Solving these equations, we get the critical point \((2, 2)\).

Next, we examine the boundary of the domain \(D: x^2 + y^2 \leq 121\), which is a circle centered at the origin with radius 11. We can parameterize the boundary as \(x = r \cos(\theta)\) and \(y = r \sin(\theta)\), where \(r = 11\) and \(0 \leq \theta \leq 2\pi\).

Substituting these parameterizations into \(f(x, y)\), we obtain \(z = g(\theta) = 5(11\cos(\theta))^2 - 20(11\cos(\theta)) + 5(11\sin(\theta))^2 - 20(11\sin(\theta))\).

To find the absolute maximum and minimum on the boundary, we need to find the critical points of \(g(\theta)\). We take the derivative of \(g(\theta)\) with respect to \(\theta\) and set it equal to zero:

\(\frac{dg}{d\theta} = -220\cos(\theta) + 110\sin(\theta) = 0\).

Simplifying this equation, we get \(\tan(\theta) = \frac{220}{110} = 2\).

Thus, the critical points on the boundary occur at \(\theta = \arctan(2)\) and \(\theta = \arctan(2) + \pi\).

Now, we evaluate the function \(f(x, y)\) at the critical points and compare them to determine the absolute maximum and minimum.

At the critical point \((2, 2)\), we have \(f(2, 2) = 5(2)^2 - 20(2) + 5(2)^2 - 20(2) = -40\).

At the critical points on the boundary, we have \(z = f(11\cos(\theta), 11\sin(\theta))\).

Evaluating \(f\) at \(\theta = \arctan(2)\), we get \(f(11\cos(\arctan(2)), 11\sin(\arctan(2)))\).

Similarly, evaluating \(f\) at \(\theta = \arctan(2) + \pi\), we get \(f(11\cos(\arctan(2) + \pi), 11\sin(\arctan(2) + \pi))\).

Comparing the values of \(f\) at the critical points and the critical point \((2, 2)\), we can determine the absolute maximum and minimum.

In summary, the absolute minimum of the function \(z = f(x, y) = 5x^2 - 20x + 5y^2 - 20y\) on the domain \(

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Answer:

8 hours

Step-by-step explanation:

Because Jack is riding at 5km/hr (15km/3hr), then in order for him to get 40 km it would take him 8 hours

Answer:

Ounces of green paint needed = 13.8

Step-by-step explanation:

Blue paint : green paint = 25 : 115

how many ounces of green paint should she mix with 3 ounces of blue paint?

Let

Ounces of green paint needed = x

Blue paint : green paint = 3 : x

Equate both ratios

25 : 115 = 3 : x

25/115 = 3/x

25 * x = 115 * 3

25x = 345

x = 345/25

x = 13.8 ounces

Ounces of green paint needed = 13.8

Answer:

651/100

Step-by-step explanation:

Answer:6 51/100

Step-by-step explanation:I dont really feel like explaining lol

Answer:

Options (1), (2), (4) and (5) are correct.

Step-by-step explanation:

Characteristics of the given hyperbola,

1). Vertex of the given hyperbola are at (-3, 6) and (-3, 4).

2). Since center of a hyperbola is the center of a line joining vertices of the hyperbola,

Center of the given parabola will be,

\((\frac{-3-3}{2},\frac{6+4}{2})\) ⇒ (-3, 5)

3). Vertical line joining the foci of the hyperbola is the transverse axis.

4). A line perpendicular to the transverse axis and passing through the center will be the conjugate axis.

5). Directrices of a horizontal hyperbola are the horizontal lines.

Therefore, Options (1), (2), (4) and (5) are correct.

Answer:

check photo. <3

Step-by-step explanation:

A department store chain that is entering a new area is looking at 16 possible locations for the placement of its 7 outlets. There are 57657600 many possible ways to the sites for the new stores.

Given that,

A department store chain that is entering a new area is looking at 16 possibility locations for the placement of its 7 outlets.

We have to find how many different possibility are there to choose the locations for the new businesses, provided that each site has an equal chance of being chosen.

By multiplying the number of possibilities each store has, we may determine the total number of ways.

It can be put on 16 sites for store 1. 15 locations can accommodate Store 2 (since store 1 is already on site 1). Up until shop 7, which has 10 sites, store 3 can be situated on 14 sites.

The quantity of ways is thus:

= 16 × 15 × 14 × 13 × 12 × 11 × 10

= 57657600

Therefore, there are 57657600 many possible ways to the sites for the new stores.

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The number of additional gifts Jeff can buy with the remaining cost is 1.

Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,

As per the given,

Total cost = $15 + $20 = $35

Total spent = $50

Remaining = $50 - $35 = $15

Since one gift cost $10

Thus, 15/10 = 1.5 since the number of gifts will be the whole number so it will be round to bottom 1 gift.

Hence "With the money still available, Jeff can purchase 1 more present".

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Answer:

45

Step-by-step explanation:

Draw an imaginary line from F to S. We then break this into 2 parts:

1. Evaluate the area of triangle SFN

The base of the triangle is FS, who has length 9. The height is the vertical line that passes through point N and FS, and that line has length 6. The area would then be 9*6/2=27.

2. Evaluate the area of rectangle SCWF

WC has length 9. FW has length 2. The area would then be 9*2=18.

The correct statement regarding the triangles is given as follows:

Triangle ABC is similar to triangle A prime B prime C prime. because triangle A prime B prime C prime. is obtained by dilating Triangle ABC. by a scale factor of 1 over 4. and then rotating it about the origin by 180 degrees.

Similar triangles are triangles that share these two features presented as follows:

For this problem, we have that the transformations are given as follows:

The angle measures weren't changed, meaning that they are congruent, and thus the triangles are similar.

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Explanation:

Concept:

The zero of a function is any replacement for the variable that will produce an answer of zero. Graphically, the real zero of a function is where the graph of the function crosses the x‐axis; that is, the real zero of a function is the x‐intercept(s) of the graph of the function.

Hence,

From the graph below,

We can see that the graph cuts the x-axis at two points

Therefore,

The zeroes of the graph are

Answer:

A. 5 hours

Step-by-step explanation:

Therefore, the compound interest of the annuity due of BD 400 paid each 4 months for 6.2 years at a nominal rate of 3% per annum is BD 40,652.17.

Compound interest of an annuity due can be calculated using the formula:A = R * [(1 + i)ⁿ - 1] / i * (1 + i)

whereA = future value of the annuity dueR = regular paymenti = interest raten = number of payments First, we need to calculate the effective rate of interest per period since the nominal rate is given per annum. The effective rate of interest per period is calculated as

:(1 + i/n)^n - 1 = 3/1003/100 = (1 + i/4)^4 - 1

(1 + i/4)^4 = 1.0075i/4 = (1.0075)^(1/4) - 1i = 0.0303So,

the effective rate of interest per 4 months is 3.03%.Next, we can substitute the given values in the formula:

A = BD 400 * [(1 + 0.0303)^(6.2 * 3) - 1] / 0.0303 * (1 + 0.0303)A = BD 400 * [4.227 - 1] / 0.0303 * 1.0303A = BD 400 * 101.63A = BD 40,652.17

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Answer:

750.88 (rounded to 2 d.p.)

Step-by-step explanation:

100% --- 731

100% + 7% --- \(\frac{100+7}{100}\) × 731 = 782.17

100% --- 782.17

100% - 4% --- \(\frac{100-4}{100}\) × 782.17 = 750.88 (rounded to 2 d.p.)

The comparison distribution in a t test for dependent means is a distribution of the differences between the pairs of scores on the dependent variable.

This distribution is used to determine whether the observed differences between the means of two related groups are statistically significant or could have occurred by chance. The t statistic is calculated by dividing the mean difference between the pairs of scores by the standard error of the mean difference, which is based on the variance of the differences in the sample. The t statistic is then compared to a t distribution with degrees of freedom equal to the number of pairs of scores minus one to determine the probability of obtaining the observed difference by chance.

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Let x be the price per pound of apples and y be the price per pound of potatoes.

For Ethan, the total cost for apples was $25.50 - 5y and the total cost for potatoes was $25.50 - 8x.

So, we have the following two equations:

8x + 5y = 25.5

3x + 10y = 18.5

Solving this system of linear equations, we get:

x = 1.71 and y = 2.36.

So, the ordered pair (x,y) = (1.71, 2.36) represents the price per pound of apples and potatoes.

Answer:

x=52

Step-by-step explanation:

One of the properties of parallelograms is that angle A = Angle C

5y-54 = 3x eq1

Another property of parallelograms is that angle A + angle B = 180 degrees

5y-54+2y-60 = 180

7y = 180+114 = 294

y = 42

Putting this value in eq1

3x = 5*42-54 = 210-54 = 156

x = 52

Answer:

Since BD Bisects ABC,

Hence,

Angle CBD=Angle DBA

-> 55°=x°+12°

-> x° =55°-12°

-> x° =43°

The domain of the function \(f(x) = \sqrt{\frac{1}{3}x + 2\) is (d) x  ≥ -6

From the question, we have the following parameters that can be used in our computation:

\(f(x) = \sqrt{\frac{1}{3}x + 2\)

Set the radicand greater than or equal to 0

So, we have

1/3x + 2 ≥ 0

Next, we have

1/3x  ≥ -2

So, we have

x  ≥ -6

Hence, the domain of the function is (d) x  ≥ -6

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Answer:

$43,512

Step-by-step explanation:

3.6% = 0.036

0.036 * 42,000 = 1,512

42,000 + 1,512 = 43,512

Farm Joe used \(7\frac{6}{15}\) kg of soil in this month.

The total weight of soil that Farm Joe ordered was:

3 bags x 4 2/5 kg/bag = 12 6/15 kg = 12 2/5 kg

The weight of the first bag used was 4 2/5 kg.

The weight of the second bag remaining is 2 3/4 kg.

The weight of the third bag remaining is 7/8 kg.

The total weight of soil used in this month can be found by subtracting the weight of the second and third bags remaining from the total weight of soil ordered:

12 2/5 kg - 2 3/4 kg - 7/8 kg

Converting all fractions to fifteenths:

12 8/15 kg - 5 1/15 kg - 1/15 kg = 7 6/15 kg

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Answer:

-5(t - 70) = -60

t - 70 = 12 -- Divide by -5

t = 82 -- Add 70

88 because you multiply 66 by 8 then divide by 6 and you get 88

Answer:

88

Step-by-step explanation:

6:8=66:x

66×6=528

528=6x

x=88

Answer: natural; whole; integer; rational; real

Step-by-step explanation:

16/4=4

Natural: numbers that are greater than 0.

4 is greater than 0

Whole: numbers that are equal or greater than 0

4 is equal or greater than 0

Integer: numbers that have no decimal points

4 has no decimal points

Rational: numbers that can be written as fraction

4=16/4 which is fraction

It is already rational, so it will not be irrational.

Real: all number you can name are real number

4 is four

Answer:

21

Step-by-step explanation:

The Jacobian of this transformation is given by  

∂(x,y) / ∂(r,θ) = r

Integrating with respect to y first, then x, we have

,∫∫D e^(-x)² dA= ∫[0,π/4]∫[0,81] e^(-r cosθ)² r dr dθ= ∫[0,π/4] ∫[0,81] r e^(-2r cosθ) dr dθ = ∫[0,π/4] e^(-2r cosθ)  [r²/(-2 cosθ)]∣[0,81] dθ= -1/2 ∫[0,π/4] r² e^(-2r cosθ) d(cosθ)= -1/4 ∫[0,π/4] r² e^(-2r cosθ) d(-2cosθ)= 1/8 ∫[0,π/4] r² e^(2r cosθ) d(cosθ) = 1/16 [ e^(2r cosθ) r² ]∣[0,π/4] = 1/16 [ e^(81√2) - 1 ]

And therefore, 27 e^(72)² - 1 / 156^(78)² ∫∫D e^(-x)² dA = 27 e^(72)² - 1 / 156^(78)²  1/16 [ e^(81√2) - 1 ] = [27 e^(72)² - 1]/16×156^(78)² [ e^(81√2) - 1 ]

Therefore, ∫∫D e^(-x)² dA = [27 e^(72)² - 1]/16×156^(78)² [ e^(81√2) - 1 ]

Given, if D is the triangle with vertices (0,0), (78,0), (78,27), then we have to find the value of

∫∫D e^(-x)² dA

= Let us discuss the concept used to solve the above integral in detail below:The integral is of the form

∫∫D e^(-x)² dA,

where D is the triangle with vertices

(0,0), (78,0), (78,27)

Now, use the change of variable from Cartesian to Polar coordinate Let

(x, y) = (r cosθ, r sinθ)

where 0 ≤ r ≤ √(78²+27²)

= √(6561)

= 81

and 0 ≤ θ ≤ π/4

Then the Jacobian of this transformation is given by

∂(x,y) / ∂(r,θ)

= r

Integrating with respect to y first, then x, we have

,∫∫D e^(-x)² dA

= ∫[0,π/4]∫[0,81] e^(-r cosθ)² r dr dθ

= ∫[0,π/4] ∫[0,81] r e^(-2r cosθ) dr dθ

= ∫[0,π/4] e^(-2r cosθ)  [r²/(-2 cosθ)]∣[0,81] dθ

= -1/2 ∫[0,π/4] r² e^(-2r cosθ) d(cosθ)

= -1/4 ∫[0,π/4] r² e^(-2r cosθ) d(-2cosθ)

= 1/8 ∫[0,π/4] r² e^(2r cosθ) d(cosθ)

= 1/16 [ e^(2r cosθ) r² ]∣[0,π/4]

= 1/16 [ e^(81√2) - 1 ]

And therefore,

27 e^(72)² - 1 / 156^(78)² ∫∫D e^(-x)² dA

= 27 e^(72)² - 1 / 156^(78)²  1/16 [ e^(81√2) - 1 ]

= [27 e^(72)² - 1]/16×156^(78)² [ e^(81√2) - 1 ]

Therefore,

∫∫D e^(-x)² dA

= [27 e^(72)² - 1]/16×156^(78)² [ e^(81√2) - 1 ]

which is the final answer.Note: Here, we have used the result from integration by parts which is given by

∫e^ax dx

= 1/a e^ax + c

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Certainly! Here's the solution to find the equation of the cubic polynomial with zeros at 0, 1, and 2:

Since the zeros of the polynomial are 0, 1, and 2, we can express the polynomial in factored form as:

\( \sf f(x) = (x - 0)(x - 1)(x - 2) \\\)

Simplifying the expression, we get:

\( \sf f(x) = x(x - 1)(x - 2) \\\)

Expanding the product, we have:

\( \sf f(x) = (x^2 - x)(x - 2) \\\)

Using the distributive property, we can further simplify:

\( \sf f(x) = (x^3 - 2x^2 - x^2 + 2x) \\\)

Combining like terms, we get:

\( \sf f(x) = (x^3 - 3x^2 + 2x) \\\)

Therefore, the equation of the cubic polynomial with leading coefficient 1 and zeros at 0, 1, and 2, in standard form, is:

\( \sf f(x) = x^3 - 3x^2 + 2x \\\)

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