evaluate f*ds where f = <3xy^2,3x^2y,z^3> and m is the surface of the sphere of radius 5 centered at the origin

Hello !

-27/125

= -0.216

= -2.16 * 10⁻¹

Answer:

(x+4)(3x-2)(x+1)

Step-by-step explanation:

Answer:

A.  1/16

Step-by-step explanation:

a^-n = 1/a^n

4^-2 = 1/4² = 1/16

-2/5x - 9 < 9/10

-2/5x-9+9<9/10+9

-2/5x<99/10

(5/-2)*(-2/5 x)<(5/-2)*(99/10)

x>-99/4

Answer: 1287

Step-by-step explanation:

By using given figure, x=9/4 and the length of GH = 21.75.

What is the length ?

Here, in given figure,

BG≈GF and CH≈HE

now by using these similarities, we can write as,

BG≈GF therfore, \(\frac{GF}{BG}\) = 1:1

\(\frac{GF}{BF}\)=\(\frac{4x+8}{34}\)

1/2=\(\frac{4x+8}{34}\)

8x+16=34

8x= 18

x=9/4

if x=9/4 then,

GH= 7x+6 = 7(9/4)+6 =63/4+6 =\(\frac{63+24}{4}\) = 21.75

What is similarity of sides?

similarity of sides refers to the property of two geometric shapes or figures having the same shape but not necessarily the same size. More specifically, two shapes are said to be similar if their corresponding angles are congruent and their corresponding sides are proportional in length.

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Answer:

75%

Step-by-step explanation:

21/28 is the same as 75%

Answer:

(-1,-2) is the correct one but they all are the same

Salutem City would need to build 275 more health centers to match the current city with the most health centers per capita.

What is capita?

In the context of the phrase "per capita", capita refers to the per person or per individual basis. It is a Latin term that means "by the head". When used in statistics or economics, per capita is a measure of a particular variable such as income, health centers, or any other quantity, that is divided by the total population of a given area or country. This measure provides a way to compare variables across different populations or regions, taking into account the differences in their sizes.

To determine how many more health centers Salutem City would need to build to claim the most health centers per capita, we can use the following steps:

Calculate the current number of health centers per capita in Salutem City:

Number of health centers per b = (215 centers / 10,000 people) = 0.0215 centers per person

Calculate the number of health centers needed to match the current leader's ratio:

Number of health centers needed = (0.0215 centers per person) * (250,000 people) = 5,375 centers

Calculate the number of additional health centers Salutem City would need to build:

Additional health centers needed = (5,375 centers) - (5,100 centers) = 275 centers

Therefore, Salutem City would need to build 275 more health centers to match the current city with the most health centers per capita.

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Answer:

y = (3/5)*x

Step-by-step explanation:

First, we can use the slope-intercept form of a line, or y=mx+b

To find the slope, m, we can find

(y₂-y₁)/(x₂-x₁). Denoting (0,0) as (x₁,y₁) and (5,3) as (x₂, y₂) (it is perfectly okay to have (0,0) as (x₂, y₂) and (5,3) as (x₁,y₁) as well), we have

(y₂-y₁)/(x₂-x₁) = (3-0)/(5-0) = 3/5

Therefore, our equation is

y = (3/5)x + b

To solve for b, we can plug any value of (x,y) from the line, e.g. (0,0), and solve from there, resulting in

y = mx + b

0 = (3/5)*0 + b

0 = b

Our equation is therefore

y = (3/5)*x + 0

= (3/5)*x

In this problem, the weight of the items produced by a machine is normally distributed with a mean of 8 ounces and a standard deviation of 2 ounces. The probability that a randomly selected item will weigh between 11 and 12 ounces is required.

Now, we need to find the Z scores for 11 and 12 using the formula given below;

Z = (x-μ)/σwhere μ is the mean, σ is the standard deviation, and x is the value we are finding the Z score for. For 11 ounces;Z1 = (11-8)/2 = 1.5For 12 ounces;

Z2 = (12-8)/2 = 2Now, we need to find the area under the standard normal distribution curve between the Z values we just found. Using the standard normal distribution table or a calculator, we can find that the area between Z1 and Z2 is approximately 0.2334.

Substituting the Z scores found earlier in the formula below;

P(Z1 < Z < Z2) = P(1.5 < Z < 2) = 0.2334

Therefore, the probability that a randomly selected item will weigh between 11 and 12 ounces is 0.2334. Hence, the option (d) 0.0440 is incorrect.

The correct option is (none of the above) since it is not given in the options and the probability of 0.2334 .

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A graph giving us a idea about relationship between the number of days and total amount of sunglasses is mentioned in the image attached below.

In this case, using Microsoft Excel, the number of days would be plotted on the x-axis (x-coordinate) of the scatter plot and the total number of sunglasses would be plotted on the y-axis (y-coordinate).

From the scatter plot (attached image) which shows the relationship between the number of days and total amount of sunglasses, a linear equation for the line of best fit is given by:

y = -2x + 62

Hence, we can reasonably infer and logically deduce that the scatter plot indicates an inverse relationship between the number of days and total amount of sunglasses.

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Answer:C

Step-by-step explanation:

(A) The scale factor of the dilation that transforms Triangle PQR to Triangle P'Q'R'  is 1/2

(B) Coordinates of Δ P"Q"R"

P" (-4,0)

Q"(-3,1)

R"(1,-2)

(C) Triangles PQR and P"Q"R" are not congruent.

Given

ΔPQR is transformed into ΔP'Q'R'

Coordinates of P, Q, R are

P (8,0),

Q(6,2)

R(-2,-4)

Coordinates of P'Q'R' are

P′(4, 0)

Q′(3, 1)

R′(−1, −2)

(A) By Distance formula we can find the distance between P Q and P'Q'

Distance formula = \(D = \sqrt{(x2-x1)^{2} +(y2-y1)^{2} }\)

Where D = Distance between two points

from distance formula we can write that

PQ = \(\sqrt{(6-8)^{2} +(2-0)^{2} } = \sqrt{4+4} =2 \sqrt{2}\)

Similarly

P'Q'= √2

PQ /P'Q' = 2

hence the scale factor of dilation is 1/2 (Compression)

(B )The Coordinates of Reflection about y axis can be written for a point

(x,y) as (-x,y)

So the Coordinated of Δ P"Q"R" can be written as

P" (-4,0)

Q"(-3,1)

R"(1,-2)

(C) ΔPQR  and ΔP"Q"R" are similar triangles but they are not  congruent because their sides  are not equal in size.

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Answer: r² = x² + y²

Step-by-step explanation:

Using the formula \(nCk = n! / (k!(n-k)!)\) the expression gives us the final answer is \(9C4 = 126\)

The expression "\(₉C₄\)" represents the combination of choosing 4 elements from a set of 9 elements.

To evaluate this expression, we can use the formula for combinations, which is given by:
\(nCk = n! / (k!(n-k)!)\)

In this case, n = 9 and k = 4. Plugging these values into the formula, we get:
\(9C4 = 9! / (4!(9-4)!)\)

Now, let's simplify this expression:

\(9! = 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1\\4! = 4 * 3 * 2 * 1\\5! = 5 * 4 * 3 * 2 * 1\)

Simplifying further:

\(9! = 9 * 8 * 7 * 6 * 5 * 4!\\(9-4)! = 5!\)

Substituting these values back into the formula:

\(9C4 = (9 * 8 * 7 * 6 * 5 * 4!) / (4! * 5!)\)

Now, we can cancel out the common factors in the numerator and denominator:

\(9C4 = (9 * 8 * 7 * 6) / (5 * 4 * 3 * 2 * 1)\)

Evaluating this expression gives us the final answer:
\(9C4 = 126\)

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The expression ₉C₄ represents a combination of selecting 4 items from a set of 9 items. To evaluate this expression, we can use the formula for combinations, which is given by: nCr = n! / (r! * (n-r)!). The value of the expression ₉C₄ is 126. This means there are 126 different combinations of selecting 4 items from a set of 9 items.

Where n represents the total number of items and r represents the number of items we want to select. In this case, n = 9 and r = 4. Plugging these values into the formula, we get:

₉C₄ = 9! / (4! * (9-4)!)

Now, let's simplify this expression step by step:

Step 1: Calculate the factorial of 9:
9! = 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 362,880

Step 2: Calculate the factorial of 4:
4! = 4 * 3 * 2 * 1 = 24

Step 3: Calculate the factorial of (9-4):
5! = 5 * 4 * 3 * 2 * 1 = 120

Step 4: Substitute the values into the formula:
₉C₄ = 362,880 / (24 * 120)

Step 5: Simplify the expression:
₉C₄ = 362,880 / 2,880 = 126

Therefore, the value of the expression ₉C₄ is 126. This means there are 126 different combinations of selecting 4 items from a set of 9 items.

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Answer:

gemma gets 6 and zac gets 12

Step-by-step explanation:

zac gets double the about

\( \huge\boxed{ \mathfrak {\red{Answer :}}}\)

Area of equilateral triangle :

=》

\( \huge{ \mathfrak{ \frac{ \sqrt{3} }{2} a {}^{2} }}\)

where,

So,

=》

\( \dfrac{ \sqrt{3} }{2} \times 10\)

=》

\(10 \sqrt{3} \)

\(\huge \boxed{\mathfrak{ \red{hope \: it \: helps}}}\)

Answer:

m<1=1/2 216 =108

then 2 is 180 -108 =72

Answer:

Assuming the number is 1/(y^(-1/4)):  y^(1/4)

Step-by-step explanation:

1/(y^(-1/4))

Bring the y^(-1/4) by subtracting it's exponent:

1*y^-(-1/4)

y^(1/4)

Answer:

it will come with time, you are too young

Step-by-step explanation:

you need minimum math for life experience, the rest, if not that interesting, might help in some circumstances but you will have someone to help if needed

Answer: Some things will.

Step-by-step explanation:

For example learning about money will help you in adulthood. But on the other hand, the Pythagorean theorem won't help you unless your an architect or study measurement.

Answer:

$60.42

Step-by-step explanation:

0.06 x $57 = $3.42

$57 + $3.42 = $60.42

Hope this helped! :)

Yes, the result is a binomial probability distribution.

Therefore, the answer is D

An experiment is said to follow a binomial distribution if the following conditions are adequately met.

i. The experiment should consist of a definite number of independent and identical trials.

ii. Each trial should generate two outcomes- one success, and the other failure.

iii. The likelihood of success should be determined by a value that should remain constant throughout the experiment.

In the given experiment, we see that the 500 voters were selected randomly from the population of registered voters. This implies that n = 500 trials are independent and identical. Each trial generated into two outcomes- Political party A (success) and B (failure). The probability of success is 0.5, and it remains constant throughout the experiment. Thus the experiment is a binomial probability distribution.

The answer is D.

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In an illustration of a normal probability distribution, a shaded area represents probability. The probability of the event occurring within that range is equal to the area of the shaded region.

A normal probability distribution is a type of continuous probability distribution that follows a bell-shaped curve. The total area under this curve is equal to 1, which means that the probability of any given event occurring is always between 0 and 1. When a shaded area is shown in an illustration of a normal probability distribution, it represents the probability of a specific event occurring within a certain range. For example, if the shaded area represents the area under the curve between two specific points, the probability of the event occurring within that range is equal to the area of the shaded region.

In statistics, probability is a fundamental concept that is used to measure the likelihood of an event occurring. A normal probability distribution is a common type of distribution that is used in many areas of statistics, including hypothesis testing, confidence intervals, and regression analysis. The normal distribution is characterized by its bell-shaped curve, which is symmetrical and has a peak at the center. The curve is also continuous, which means that there are no gaps or jumps in the data. The standard deviation of the distribution determines the width of the curve, while the mean determines the center. One of the key features of the normal distribution is that it is completely determined by its mean and standard deviation. This means that if you know these two parameters, you can calculate the probability of any event occurring within the distribution.

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A table that matches the data in the graph include the following:

Correct answers       Points

0                                   0

5                                   30

12                                  72

18                                  108

20                                 120

In Mathematics, a proportional relationship produces equivalent ratios and it can be represented by the following mathematical equation:

y = kx

Where:

Next, we would determine the constant of proportionality (k) for the data points contained in the table as follows:

Constant of proportionality, k = y/x = t/d

Constant of proportionality, k = 30/5 = 72/12 = 108/18 = 120/20

Constant of proportionality, k = 6.

Therefore, the required equation is given by;

y = kx

y = 6x

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer: a and c

Step-by-step explanation:

Using proportions, the estimate of the per capita consumption from 2011 was 29.25 gallons.

A proportion is a fraction of the total amount, the measures are related using a rule of three.

The amount in 2012 was an increase of 5.3% from 2011,

105.3% = 1.053 of x,

The consumption per capita was 30.8 gallons,

hence:

1.053x = 30.8

x = 30.8/1.053

x = 29.25 gallons.

(ii) The sales in 2011

= 9.1 billion gallons in 2011.

(iii) The per capita consumption from 2011

= 9.1 / 11.8

= 0.77 billion

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The coefficient of x³y² in the expansion of (2x+y)5 is 80.

Given data :

The coefficients of terms of (p+q)^n can be found by the Pascal's triangle for small values of n.  Pascal's triangle will start with (1,1)  = coefficients of (p,q)^n =1.  For n=2, we add successive terms of the previous value of n.  Thus for n-2, we have (, 1+1,11=(1,2,1), for n=3, we have (1,3,3,1), giving the following pattern:

(1,1)

(1,2,1)

(1,3,3,1)

(1,4,6,4,1)

(1,5,10,10,5,1)

meaning for n=5, the binomial expansion for (P+Q)^5 is

P^5+5P^4Q+10P^3Q^2+10P^2Q^3+5PQ^4+Q^5

Setting P=2x, Q=y in the term 10P^3Q^2, we get a term

10(2x)^3(y)^2

=10(8x^3)(y^2)

=80x^3y^2

So the required coefficient is K=80.

We can also find the coefficient 10 by binomial expansion of

n=5, x=3 in

C(n,x) = n! / (x! (n-x)!) = 5! / (2!3!) = 5*4*3/(1*2*3) = 10

Then again substituting 10(2x)^3(y)^2 = 80x^3y^2

to get the coefficient K=80.

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P = 90 is the solution for the given equation.

Given: Qd=95−4

PQs=5+P

To find Qd if P=5:

Put P = 5 in the equation

Qd=95−4P

Qd = 95 - 4 x 5

Qd = 75

So, Qd = 75.

To find P if Qs = 20:

Put Qs = 20 in the equation

Qs = 5 + PP

= Qs - 5P

= 20 - 5P

= 15

So, P = 15.

To solve Qd=Qs, substitute Qd and Qs with their respective values.

Qd = Qs

95 - 4P = 5 + P

Subtract P from both sides.

95 - 4P - P = 5

Add 4P to both sides.

95 - P = 5

Subtract 95 from both sides.

- P = - 90

Divide both sides by - 1.

P = 90

Thus, P = 90 is the solution for the given equation.

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