How long is the wire from the top of the telephone pole to the ground?

The five-number summary comprehends the minimum and maximum values, the 1st and 3rd quartiles and the median.

1st step: is to arrange the data sets from least to greatest.

Sherelle:

26 39 56 58 60 62 65 66 66 68 71 72 72 73 74 75 81 83 84 85

Venita:

44 45 51 51 53 53 55 57 58 62 65 66 69 69 70 73 75 77 78 79

2nd step: To calculate each quartile you have to determine their position and then identify which observation sits in that position:

Quartile 1:

PosQ₁: n/4= 20/4= 5

Quartile 2 (Median)

PosMe: n/2= 20/2= 10

Quartile 3

PosQ₃: n*(3/4)= 20*(3/4)= 15

Since both samples have the same size, the 1st quartile will be the fifth observation of each sample, the median will be the tenth observation and the 3rd quartile will be the fifteenth.

Sherelle:

Q₁: 60

Me: 68

Q₃: 74

Minimum: 26

Maximum: 85

Venita:

Q₁: 53

Me: 62

Q₃: 70

Minimum: 44

Maximum: 79

Answer:

22 students

Step-by-step explanation:

Answer:

64

Step-by-step explanation:

Answer:

40

Step-by-step explanation:

Since 30% of the bag is blue, you can setup the equation, \(\frac{3}{10}x=12\) where x is the total number of gumballs in the bag because that is what you are looking for. Simplify and you get \(x=40\). Checking this you get \(12=12\) which is true.

Answer:

Square Root of 162 ~ 12.727

Step-by-step explanation:

Simply do the Pythagorean Theorem!

a^2 + b^2 = c^2

This case we're solving for the long side which is the hypothenuse.

9^2+9^2= c^

81+81=c^

162=c^

Square root of 162

Which is 12.727

Step-by-step explanation:

........................

Answer:

root of 162

Step-by-step explanation:

i hope this helps please put brainliest im only 9

Answer:

c = number of chimes

12c = amount gotten from the sale of the chimes.

To make a profit what she gets from the sales must be greater than her expenses.

12c > 530

c > 44.166666

She must sell each chime for more than 44 an one-sixth cent.

Step-by-step explanation:

Answer:

X=13

Step-by-step explanation:

So if ΔABC ≅ ΔDEC, then that means that ∠B is ≅ ∠E. Therefore you would write the equation 3x=6x-39 and solve for X to get 13.

To say that two variables are negatively correlatted means that when one variable increases, the other variable decreases.

Negative correlation refers to a relationship between two variables where they tend to move in opposite directions. When one variable increases, the other variable tends to decrease, and vice versa. This negative relationship indicates an inverse association between the two variables.

Option A, "When one variable increases, the other decreases," accurately describes negative correlation. As one variable increases, the other variable decreases, reflecting the negative relationship between them.

Negative correlation does not imply that both variables change at the same rate (Option D). In negative correlation, the relationship is characterized by the opposite direction of change, not necessarily the same magnitude or rate of change.

Option B, "When variable increases, the other also," suggests a positive correlation, where both variables move in the same direction. This is not the case in negative correlation.

Option C, "When one variable decreases, the other also decreases," is a misinterpretation of negative correlation. In negative correlation, when one variable decreases, the other variable tends to increase, not decrease.

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Answer:

They are not equivalent.

Step-by-step explanation:

Before we solve the question, we need to know that from the laws of indices:

A^x x A^y = A^(x+y).

7 to the power of 8th power means 7^8

7^8 times 7 means 7^8 x 7. From the laws of indices we have 7^8 x 7 = 7^9.

7 to the power of 3rd power means 7^3

7^3 times 7 to the power of 3rd power means 7^3 x 7^3. From the laws of indices we have 7^3 x 7^3 = 7^6.

Obviously, 7^9 ≠ 7^3 therefore, they are not equivalent.

Answer:

only 5 of her friends will play

Step-by-step explanation:

8-3=5

Answer:

The answer 5

Step-by-step explanation:

8 friends minus the three that dont want to play

Answer:

12,853.85568

Step-by-step explanation:

\(A=P(1+\frac{r}{n})^{nt}\)

A= final amount

P= inital principal balance

r= interest rate

n= number of times interest applied per time period

t= numbers of period

\(A=3,686(1+\frac{.07}{4})^{(4)(18)}\)

The system of equations for x^3 - 2x^2 + 5x - 6 = -4x^2 + 14x + 12.

Carlos graphed the system of equations that can be used to solve the equation x^3 - 2x^2 + 5x - 6 = -4x^2 + 14x + 12.

To graph this system of equations, we need to set the equation equal to zero. So, the equation becomes:

x^3 - 2x^2 + 5x - 6 + 4x^2 - 14x - 12 = 0

Combining like terms, we get:

x^3 + 2x^2 - 9x - 18 = 0

To graph this equation, you can use a graphing calculator or plot points manually. Here are the steps to manually plot the graph:

1. Choose a range for x, for example, from -5 to 5.
2. Pick a few values for x within the chosen range and substitute them into the equation to find the corresponding y-values.
3. Plot the points (x, y) on a coordinate plane.
4. Connect the plotted points to create a smooth curve.

By following these steps, you can graph the system of equations for x^3 - 2x^2 + 5x - 6 = -4x^2 + 14x + 12.

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811-354

you are taking away 354 from 811

answer: 547

please consider giving be brainliest, i need it to level up

Step-by-step explanation:

Let x and y be the two positive numbers.

Now according to the given condition we have:

x.y=9........(1)

1/x=4.1/y......(2)

Now from (1) we have,

1/x=y/9

Substituting 1/x=y/9 in (2) we have,

y/9=4/y

Solving this we have

y^2=36

y=+6 and y=-6

But neglecting the negative value as we are given in the question that the numbers are positive. So

y=6

Substituting y=6 in (1) we have,

x.6=9

Solving which gives

x=3/2

So the numbers are 3/2 and 6

9514 1404 393

Answer:

  ac

Step-by-step explanation:

The length of the base is the x-distance between E and H, so is ...

  base = a - 0 = a

The height is the y-distance between E and F, so is ...

  height = c - 0 = c

The area of the parallelogram is the product of base and height.

  A = base×height

  A = a×c

The area of the parallelogram is ac.

Answer:

4) a = 6

5) m = 1

Step-by-step explanation:

4) use FOIL, First Inside Outside Last, when you cross multiply.

\(\frac{a+4}{a-1} =\frac{a-2}{a-4}\)

\((a+4)(a-4) = (a-1)(a-2)\)

I'm going to do the left side first.

\((a+4)(a-4)\\a^2-4a+4a-16\\a^2-16\)

Now I'm going to do the right side.

\((a-1)(a-2)\\a^2-2a-1a+2\\a^2-3a+2\)

Next I'm going to rewrite back as the equation and solve for a.

\(a^2 - 16 = a^2 -3a +2\\a^2 - a^2 -16 = a^2-a^2-3a+2\\-16-2=-3a+2-2\\-18=-3a\\-18/-3=-3a/-3\\a=6\)

5) I'm going to use distributive propoerty when I cross multiply. Then I will setup an equation like number 4 and solve for m.

\(\frac{5m-2}{3}=\frac{8-3m}{5} \\\)

\(5(5m-2)=3(8-3m)\\25m-10=24-9m\\25m+9m-10=24-9m+9m\\34m-10=24\\34m-10+10=24+10\\34m=34\\34m/34=34/34\\m=1\)

Answer:

x+1 , x<-1

x²-bx-4  , -1≤x≤4

1/2 x +a

substitute x=-1 , continuous everywhere

x+1=x²-bx-4 when x=-1

-1+1=-1²-b-4

then for :

x²-bx-4=1/2 x +a for x=4

4²-4b-4=1/2x+a

16-4(3)-4=4/2+a

16-12-4-2=a

the equations will be :

x+1

x²-3x-4

1/2x-2

I hope this help

Answer:

the degree of f(x) is 3

Step-by-step explanation:

fundamental theorem of algebra

The degree of function f(x) is at least 3.

The function has n intercepts i.e. it touches the x-axis n times, then the function will have at least n roots.

And as we know if the degree of the function is n then the number of roots of the function is n.

So, if the function has n intercepts, then the function has at least n degrees.

Here given that the polynomial function f(x) has 3 intercepts.

Then from above, it is clear that the function will have at least 3 roots.

And the function will have at least 3 degrees.

Therefore If the polynomial f(x) has 3 intercepts, then The degree of function f(x) is at least 3.

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1   Y is distributed as N(aμ + b, a^2σ^2), as desired.

2  We have shown that under these conditions, E[XY] = E[X]E[Y].

To prove that Y is distributed as N(aμ + b, a^2σ^2), we need to show that the mean and variance of Y match those of a normal distribution with parameters aμ + b and a^2σ^2, respectively.

First, let's find the mean of Y:

E(Y) = E(aX + b) = aE(X) + b = aμ + b

Next, let's find the variance of Y:

Var(Y) = Var(aX + b) = a^2Var(X) = a^2σ^2

Therefore, Y is distributed as N(aμ + b, a^2σ^2), as desired.

We can use the definition of covariance to prove that E[XY] = E[X]E[Y]. By the properties of expected value, we know that:

E[XY] = ∫∫ xy f(x,y) dxdy

where f(x,y) is the joint probability density function of X and Y.

Then, we can use the fact that X and Y are independent to simplify the expression:

E[XY] = ∫∫ xy f(x) f(y) dxdy

= ∫ x f(x) dx ∫ y f(y) dy

= E[X]E[Y]

where f(x) and f(y) are the marginal probability density functions of X and Y, respectively.

Therefore, we have shown that under these conditions, E[XY] = E[X]E[Y].

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Answer:

120 = 2 * 2 * 2 * 3 * 5 = 2^3 * 3 * 5

180 = 2 * 2 * 3 * 3 * 5 = 2^2 * 3^2 * 5

300 = 2 * 2 * 3 * 5 * 5 = 2^2 * 3 * 5^2

Step-by-step explanation:

Here, we want to write the given numbers as the product of their prime numbers

Prime numbers are numbers divisible by 1 and itself

We have the prime factorization as follows;

120 = 2 * 2 * 2 * 3 * 5 = 2^3 * 3 * 5

180 = 2 * 2 * 3 * 3 * 5 = 2^2 * 3^2 * 5

300 = 2 * 2 * 3 * 5 * 5 = 2^2 * 3 * 5^2

Answer:

To determine how many miles Naomi's car can go on one gallon of gas, we first need to determine how many gallons of gas the car used to travel 15\tfrac{1}{2}15 2 1 ​ miles. We are told that the car used \frac{2}{5} 5 2 ​ of a gallon to travel this distance, so we can multiply this value by 15\tfrac{1}{2}15 2 1 ​ to get the total number of gallons used:

\frac{2}{5} \cdot 15\tfrac{1}{2} = 9

Therefore, the car used 9 gallons of gas to travel 15\tfrac{1}{2}15 2 1 ​ miles. To determine how many miles the car can go on one gallon of gas, we need to divide the total number of miles traveled by the number of gallons used:

15\tfrac{1}{2} \div 9 = \frac{31}{18}

This means that the car can go 31/18 miles on one gallon of gas. Since this fraction is not in simplest form, we can further simplify it by dividing the numerator and denominator by the greatest common factor, which is 3:

\frac{31}{18} \div \frac{3}{3} = \frac{31}{18} \cdot \frac{3}{3} = \frac{31 \cdot 3}{18 \cdot 3} = \frac{93}{54}

Therefore, the car can go 93/54 miles on one gallon of gas. This fraction can be further simplified by dividing the numerator and denominator by the greatest common factor, which is 1:

\frac{93}{54} \div \frac{1}{1} = \frac{93}{54} \cdot \frac{1}{1} = \frac{93 \cdot 1}{54 \cdot 1} = \frac{93}{54}

Therefore, the final answer is that the car can go 93/54 miles on one gallon of gas.

Answer: BC=22cm

Step-by-step explanation:

5d-3=3d+7

2d=10

d=5

plug 5 into the equation for BC, and you get 22

Answer:

Segment BC is (3d + 7)cm, where d=5. So, BC= 22cm.

Step-by-step explanation:

Segment BC is (3d + 7)cm, where d=5. You find this through these steps:

(5d-3)=(3d+7)           Subtract 3d from 5d, which equals 2d.

2d-3=7                     Now, add 3 to 7.

2d=10                       Divide 10 by 2.

d=5                          The solution is 5.

Plug 5 into the equation of Segment BC:

3(5) + 7

BC= 22

The approximate surface area of a cone is 204 inches².

It is a shape of a Christmas tree where there is a base of radius r and a top point called the apex.

We have,

The surface area of a cone is πr (r + √(h² + r²) )

Now,

Diameter = 10 inches

Radius = 5 inches

Slant height = 8 inches

Now,

The surface area of a cone is πr (r + √(h² + r²) )

Slant height = √(h² + r²) = 8 inches

So,

= πr (r + √(h² + r²) )

= π x 5 (5 + 8)

= 3.14 x 5 x 13

= 204 inches²

Thus,

The surface area of a cone is 204 inches².

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The approximate surface area of the cone is 227 square inches.

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

The diameter of a cone's circular base measures 10 inches

Radius of cone is 5 inches.

Slant height = 8 inches

A=πr(r+√h²+r²)

A=3.14×5(5+√64+25)

A=3.14×5(5+√89)

A=3.14×5(5+9.43)

A=3.14×5(14.43)

A=226.61

Hence, the approximate surface area of the cone is 227 square inches.

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Answer:

  a) see attached

  b) 15015 meters

Step-by-step explanation:

You want the voltage, current, resistance, and power for each component of the circuit shown in the diagram.

The relevant circuit relations are ...

Given current and resistance for element 1, we immediately know its voltage is ...

  V = IR = (4)(10) = 40 . . . . volts

Given the voltage on element 3, we know that parallel element 2 has the same voltage: 30 volts.

Given the voltage at T is 90 volts, the sum of voltages on elements 1, 2, and 4 must be 90 volts. That means the voltage on element 4 is ...

  90 -(40 +30) = 20

The current in elements 1, 4, and T are all the same, because these elements are in series. They are all 4 amperes.

That 4 ampere current is split between elements 2 and 3. The table tells us that element 2 has a current of 1 ampere, so element 3 must have a current of ...

  4 - 1 = 3 . . . . amperes

The resistance of each element is the ratio of voltage to current:

  R = V/I

Dividing the V column by the I column gives the values in the R column.

Note that power source T does not have a resistance of 22.5 ohms. Rather, it is supplying power to a circuit with an equivalent resistance of 22.5 ohms.

Power is the product of voltage and current. Multiplying the V and I columns gives the value in the P column.

Note that the power supplied by the source T is the sum of the powers in the load elements.

We found that the transmitter is receiving a power of 90 watts, so its operating frequency is ...

  (90 W)×(222 Hz/W) = 19980 Hz

Then the wavelength is ...

  λ = c/f

  λ = (3×10⁸ m/s)/(19980 cycles/s) ≈ 15015 m/cycle

The wavelength of the broadcast is about 15015 meters.

__

Additional comment

The voltage and current relations are "real" and used by circuit analysts everywhere. The relationship of frequency and power is "made up" specifically for this problem. You will likely never see such a relationship again, and certainly not in "real life."

Kirchoff's voltage law (KVL) means the sum of voltage rises (as at T) will be the sum of voltage drops (across elements 1, 2, 4).

Kirchoff's current law (KCL) means the sum of currents into a node is equal to the sum of currents out of the node. At the node between elements 1 and 2, this means the 4 amps from element 1 into the node is equal to the sum of the currents out of the node: 1 amp into element 2 and the 3 amps into element 3.

As with much of math and physics, there are a number of relations that can come into play in any given problem. You are expected to remember them all (or have a ready reference).

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Answer:

x=28 bottom left angle is 60, bottom right is 70

Step-by-step explanation:

the angles add up to 180

lets set up an equation

x+32+x+42+50=180

2x+124=180

2x=56

x=28

So the value of the vector product 3C . (2A × B) = 1242.

Given that the vectors are,

A = 4 i + 3 j - 3 k

B = - 3 i + 2 j + 4 k

C = 8 i - 9 j

So, now calculating the required we get,

2A = 2 (4 i + 3 j - 3 k) = 8 i + 6 j - 6 k

3C = 3 (8 i - 9 j) = 24 i - 27 j

So, cross product is given by,

2A × B

= \(\left[\begin{array}{ccc}i&j&k\\8&6&-6\\-3&2&4\end{array}\right]\)

= [(6) (4) - (2) (- 6)] i - [(8) (4) - (- 3) (- 6)] j + [(8) (2) - (- 3) (6)] k

= [24 + 12] i - [32 - 18] j + [16 + 18] k

= 36 i - 14 j + 34 k

So the dot product is given by

3C . (2A × B) = (24 i - 27 j) . (36 i - 14 j + 34 k ) = 24 * 36 + (- 27) * (- 14) = 1242

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The question is not clear. The clear question will be -

"For the following three vectors, what is 3⋅C⋅(2A × B)?

A=4.00i+3.00j−3.00k; B=−3.00i+2.00j+4.00k; C=8.00i−9.00 j"

Answer:

$200 and $450

Step-by-step explanation:

We can start by assigning variables to our unknowns.

Our unknowns are the price for a DVD player and the price for a television.

x= price of a television

y= price of a DVD player

Next, let's translate the given information into a system of equations.

two televisions and three DVD players for $1750

2x+3y=1750

four televisions and one DVD player for $1250

4x+y=1250

Since the instructions did not specify, I will use substitution to solve, however you can also use elimination.

First, from the second equation, we subtract 4x from both sides.

4x+y-4x=1250-4x

y=1250-4x

Now we plug 1250-4x for y in the first equation.

2x+3y=1750

2x+3(1250-4x)=1750

Distribute.

2x+3*1250-3*4x=1750

Simplify.

2x+3750-12x=1750

Combine like terms.

-10x+3750=1750

Subtract 3750 from both sides

-10x+3750-3750=1750-3750

-10x=-2000

Divide both sides by -10

x=200

A television costs $200.

Now using that, we can plug that into one of the original equations. I'll use the second one.

4x+y=1250

4(200)+y=1250

800+y=1250

Subtract 800 from both sides.

y=450

A DVD player costs $450

You can plug those values back into the other equation (the first one) to double-check if you'd like as well.