Which statements are true about the ordered pair (10, 5) and the system of equations? {2x−5y=−5 x+2y=11 Select each correct answer. The ordered pair (10, 5) is a solution to the first equation because it makes the first equation true. The ordered pair (10, 5) is a solution to the second equation because it makes the second equation true. The ordered pair (10, 5) is not a solution to the system because it makes at least one of the equations false. The ordered pair (10, 5) is a solution to the system because it makes both equations true.

Step-by-step explanation:

Below is an attachment containing the solution.

Answer:

a) [tex]\mu = 24,\sigma = 3.46[/tex]

b) Significantly low:

[tex]x < 17.08[/tex]

Significantly high:

[tex]x > 30.92[/tex]

c) 42 girls are significantly high.                                      

Step-by-step explanation:

We are given the following in the question:

[tex]p = 0.5[/tex]

a) mean and the standard deviation for the numbers of girls in groups of 48 births

[tex]\mu = np = 48(0.5) = 24\\\sigma = \sqrt{np(1-p)} = \sqrt{48(0.5)(1-0.5)} = 3.46[/tex]

b) Range rule of thumb

Significantly low: According to this rule the observations lying below two standard deviation of mean is considered significantly low.

[tex]x = \mu - 2\sigma\\x = 24 - 2(3.46) = 17.08[/tex]

Significantly high: According to this rule the observations lying above two standard deviation of mean is considered significantly high.

[tex]x = \mu + 2\sigma\\x = 24 + 2(3.46) = 30.92[/tex]

c) Significance of 42 girls

[tex]42 > \mu + 2\sigma[/tex]

Since 42 is greater than 30.92, 42 girls are significantly high. Thus, the method is not significant.

Answer:

Investments in order by least risk to greatest risk: A, C, E, D, F, B.

Step-by-step explanation:

Answer:

is d

Step-by-step explanation:

Answer:

One cubic foot of the stone weigh 10 tons.

Step-by-step explanation:

There is a mistake in the question, thus it is corrected:

A typical stone on the lowest level of the great pyramid in Egypt was a rectangular prism 5 feet long by 5 feet high by 6 feet deep and weighed 15 tons. What was the volume of the average stone and how much did it one cubic foot of the stone weigh?

Now, to find the volume of average stone and how much one cubic foot of stone weigh.

Dimension of rectangular prism:

Length = 5 feet.

Height = 5 feet.

Width = 6 feet.

Now, to get the volume of stone which was a rectangular prism we put formula:

[tex]Volume=length\times width\times height[/tex]

[tex]Volume=5\times 6\times 5[/tex]

[tex]Volume=150\ cubic\ feet.[/tex]

The volume of the average stone was = 150 cubic feet.

Weight of stone = 15 tons.

Now, to get one cubic foot of the stone weigh we divide the volume of the average stone by weight of stone:

The volume of the average stone ÷ weight of stone

[tex]150\div 15[/tex]

[tex]=10\ tons.[/tex]

Therefore, one cubic foot of the stone weigh 10 tons.

Answer:

The measure of each angle is 143 degrees.  

Step-by-step explanation:

We are given the following in the question:

A nonagon in which measure of seven angles are:

138, 154, 145, 132, 128, 147, 130.

Angle sum property of a nonagon:

Let the two equal angle of nonagon be x degrees. Thus, we can write:

[tex]138+154+ 145+132+ 128+ 147+ 130+2x = 1260\\\Rightarrow 974 + 2x = 1260\\\Rightarrow 2x = 1260 - 974\\\Rightarrow 2x = 286\\\Rightarrow x = 143[/tex]

Thus, the measure of two equal angles is 143 degrees.

Final answer:

Using the formula for the sum of interior angles of a polygon and subtracting the sum of the seven given angles from the total, we find that the remaining two equal angles in a nonagon each measure 111 degrees.

Explanation:

The measure of the seven angles in a nonagon are given as 138, 154, 145, 132, 128, 147, and 130 degrees. To find the measure of each of the remaining two equal angles, we first need to calculate the sum of the angles in a nonagon. Using the formula for the sum of interior angles (S = (n-2) × 180 degrees, where n is the number of sides), we find that a nonagon has interior angles that add up to 1260 degrees. We then sum the seven given angles and subtract this total from 1260 to find the total measure of the remaining two angles. Finally, we divide this result by 2 to get the measure of each of the two equal angles. This allows us to determine that the measure of each of the two equal angles in the nonagon is 111 degrees.

Answer:

Step-by-step explanation:

Two train traveling in opposite direction

Distance apart the train is 120miles

Train A

Speed =30mph

Train B

90mph

What is common to the train is the same time, they will meet at the same time

Let assume they meet at distance x from from Washington

Then A has travelled x mile distance

Then, B has travelled 120-x mile distance

Time for train A to get to x,, = time for train B to get 120-x

Time=distance/speed

da/Sa=db/Sb

Let da be distance of train A

And db be distance of train B

Sa be speed of train A

Sb be speed of train B

Then,

da/Sa=db/Sb

x/30=120-x/90

Cross multiply

90x=3600-30x

90x+30x=3600

120x=3600

Then, x=3600/120

x=30miles

Then will meet at 30miles from Washington

Second part of the questions

Train B is faster than train A

Train B has already travelled 90miles while train B travels 30 miles

This shows that train A will not get to Baltimore before train B catch up

Then, let train A travel y distance

Then B will have to complete the 30 miles and then with another 30 miles that A has travel and then y

Total distance B travel will be

db=30+30+y

db=60+y

And da=y

Therefore,

da/Sa=db/Sb

y/30=60+y/60

Cross multiply

60y=1800+30y

60y-30y=1800

30y=1800

Then, y=1800/30

y=60miles

That means they will meet at 60miles from both Washington and Baltimore, or they are at mid points

Answer:

  a) linear. Cost per minute is a constant.

  b) f(x) = 40 -0.15x

  d) f(100) = 25. The remaining value is $25 after using 100 minutes.

Step-by-step explanation:

a) Since the cost per minute is a constant, the remaining dollar value of the phone decreases by the same amount for each minute used. The cost as a function of minutes used is a linear function with a constant rate of change.

__

b) The value starts at $40 and decreases by $0.15 for each increment of x (minutes used). The function can be written as ...

  f(x) = 40 -0.15x

__

d) Put 100 where x is in the function definition and do the arithmetic.

  f(100) = 40 -0.15×100 = 40 -15

  f(100) = 25

According to the variable and function definitions, x=100 means 100 minutes have been used; f(x) = 25 means the remaining value of the phone is 25 dollars.

  f(100) = 25 means the phone's remaining value is $25 when 100 minutes have been used.

Answer:

t=2652

Step-by-step explanation:

The type of Function shown in the graph

Step-by-step explanation:

1.The vertical line test can be used to determine whether a graph represents a function. A vertical line includes all points with a particular x value. The y value of a point where a vertical line intersects a graph represents an output for that input x value.

2.Different types of graphs depend on the type of function that is graphed. The eight most commonly used graphs are linear, power, quadratic, polynomial, rational, exponential, logarithmic, and sinusoidal. Each has a unique graph that is easy to visually differentiate from the rest.

3.we can represent a function using a graph. Graphs display many input-output pairs in a small space. The visual information they provide often makes relationships easier to understand. We typically construct graphs with the input values along the horizontal axis and the output values along the vertical axis.

Answer:

y= 1/2 csc (x)

Step-by-step explanation:

probably

Answer:

SAS

Step-by-step explanation:

Answer:

The answer to your question is x = 64; y = 20

Step-by-step explanation:

Angles    2x + 2  and 130° are vertical angles so they measure the same.

                           2x + 2 = 130

- Solve for x

                           2x = 130 - 2

                           2x = 128

                             x = 128/2

                             x = 64

Angles  3y - 10 and 50° are vertical angles, so they measure the same.

                           3y - 10 = 50

                           3y = 50 + 10

                           3y = 60

                             y = 60/3

                            y = 20

Answer:

  x^2 -11x +30 = 0

Step-by-step explanation:

If these two integers are solutions of the quadratic, then its factors are ...

  (x -5)(x -6) = 0

Multiplying this out, we get ...

  x^2 -11x +30 = 0

Answer:

cluster sampling

Step-by-step explanation:

ideal groups of objects are naturally chaos arranged in groups, and randomly selected. Unlike class sampling, with homogeneously arranged groups and only a few randomly selected objects from each group, in cluster sampling, each group is allocated in a chaotic and all objects in the group become part of the sample.

Answer:

x  =  25    Total worked hours by welder winning 34 $ /h

y  =  21    Total worked hours by welder winning 39 $ /h

Step-by-step explanation:

Let call

"x" numbers of hours worked by welder winning 34 $/h

"y" numbers of hours worked by welder winning 39 $/h

Then according to problem statement

x  +  y  = 46      ⇒     y  = 46  -  x

1669  =  34*x  +  39*y     ⇒  

We got a two equation system, solving

1669  =  34*x  +  39* ( 46  -  x )  ⇒   1669   =  34*x  + 1794 - 39*x

1669 - 1794  = - 5*x      ⇒  -125 = - 5*x

x = 125/5   ⇒  x = 25

And as         y = 46 - x       y  =  46  -  25   ⇒  y  = 21  

The two problems are almost identical: you have to set up a system, and then solve it.

In the first case, let [tex]g[/tex] and [tex]b[/tex] be, respectively, the number of girls and boys.

We know that [tex]g=2b+4[/tex] (the number of girls in the Spanish Club is four more than twice the number of boys). Also, we know that [tex]g+b=61[/tex] (there are 61 students in total).

So, we have the system

[tex]\begin{cases}g=2b+4\\g+b=61\end{cases}[/tex]

We can use the first equation to substitute in the second

[tex]g+b=61 \iff (2b+4)+b=61 \iff 3b+4=61 \iff 3b=57 \iff b=19[/tex]

And then solve for [tex]g[/tex]:

[tex]g=2b+4=2\cdot 19+4=38+4=42[/tex]

For the second problem, let [tex]c[/tex] and [tex]j[/tex] be the number of pins knocked down by, respectively, Carrie and John. Just like before, we have the system

[tex]\begin{cases}c=j+12\\c+j=230\end{cases}[/tex]

And you can solve it in the very same way we solved the previous one.

To find out how many packs of construction paper Ms. Perkins will need, divide the total number of pieces needed by the number of pieces in each pack. Using long division, we find that she will need at least 16 packs of construction paper.

To find out how many packs of construction paper Ms. Perkins will need, we can divide the total number of pieces she needs (8,000) by the number of pieces in each pack (495). This will give us the number of packs required.

Using long division, we divide 8,000 by 495:

Since the remainder is less than 495, we stop here. Therefore, Ms. Perkins will need at least 16 packs of construction paper.

Answer:

Rolling case achieves greater height than sliding case

Step-by-step explanation:

For sliding ball:

- When balls slides up the ramp the kinetic energy is converted to gravitational potential energy.

- We have frictionless ramp, hence no loss due to friction.So the entire kinetic energy is converted into potential energy.

- The ball slides it only has translational kinetic energy as follows:

                                   ΔK.E = ΔP.E

                                   0.5*m*v^2 = m*g*h

                                    h = 0.5v^2 / g

For rolling ball:

- Its the same as the previous case but only difference is that there are two forms of kinetic energy translational and rotational. Thus the energy balance is:

                                  ΔK.E = ΔP.E

                                  0.5*m*v^2 + 0.5*I*w^2 = m*g*h

- Where I: moment of inertia of spherical ball = 2/5 *m*r^2

             w: Angular speed = v / r

                               0.5*m*v^2 + 0.2*m*v^2 = m*g*h

                               0.7v^2 = g*h

                               h = 0.7v^2 / g

- From both results we see that 0.7v^2/g for rolling case is greater than 0.5v^2/g sliding case.

A ball will reach a greater height when it slides up a frictionless ramp and is then rolled without slipping up another frictionless ramp with the same slope angle.

A ball will reach a greater height when it slides up a frictionless ramp and is then rolled without slipping up another frictionless ramp with the same slope angle. This is because, when the ball slides up, it gains potential energy which is then converted to kinetic energy as it rolls up the second ramp. The ball will reach a greater height because it retains some of the initial energy it gained from sliding up the first ramp.

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Answer:

1. f₁(x)=-x²+2x-2

2. f₂(x)=-x²+6x-10

3. f₃(x)=-x²-2  

4. f₄(x)=-x²+10x-26

5. f₅(x)=-x²-2x-2

6. f₆(x)=-x²

Step-by-step explanation:

1. we have that f(x) is translated right by 1 unit , also

according to the graph f(x) has a vertex P(0,-1) then P₁ ( 1,-1) to f₁(x) therefore y-y₁ = -(x-x₁)² ⇒ y-y₁ = -(x-x₁)² ⇒ y+1 = -(x-1)² ⇒ y=-(x²-2x+1)-1 =-x²+2x-2

2. f(x) is reflected across the x-axis 3, same as in 1., P₂(3,-1) to f₂(x)

y+1 = -(x-3)² ⇒ y=-(x²-6x+9)-1 =-x²+6x-10

3. f(x) is translated down by 1 unit, P₃(0,-2) to f₃(x)

y+2 = -(x)² ⇒ y=-x²-2  

4. f(x) is reflected across the y-axis 5, P₄(5,-1) to f₄(x)

y+1 = -(x-5)² ⇒ y=-(x²-10x+25)-1 =-x²+10x-26

5. f(x) is translated left by 1, P₅(-1,-1) to f₅(x)

y+1 = -(x+1)² ⇒ y=-(x²+2x+1)-1 =-x²-2x-2

6. f(x) is translated up by 1 unit, P₆(0,0) to f₆(x)

y+0 = -(x+0)² ⇒ y=-x²

Answer:

70

Step-by-step explanation:

Answer:

(A) 0.15625

(B) 0.1875

(C) Can't be computed

Step-by-step explanation:

We are given that the amount of time it takes for a student to complete a statistics quiz is uniformly distributed between 32 and 64 minutes.

Let X = Amount of time taken by student to complete a statistics quiz

So,   X ~ U(32 , 64)

The PDF of uniform distribution is given by;

    f(X) = [tex]\frac{1}{b-a}[/tex] ,  a < X < b      where a = 32 and b = 64

The CDF of Uniform distribution is P(X <= x) = [tex]\frac{x-a}{b-a}[/tex]

(A) Probability that student requires more than 59 minutes to complete the quiz = P(X > 59)

   P(X > 59) = 1 - P(X <= 59) = 1 - [tex]\frac{x-a}{b-a}[/tex] = 1 - [tex]\frac{59-32}{64-32}[/tex] = [tex]1-\frac{27}{32}[/tex] = 0.15625

(B) Probability that student completes the quiz in a time between 37 and 43 minutes = P(37 <= X <= 43)  = P(X <= 43) - P(X < 37)

    P(X <= 43) = [tex]\frac{43-32}{64-32}[/tex] = [tex]\frac{11}{32}[/tex] = 0.34375

    P(X < 37) = [tex]\frac{37-32}{64-32}[/tex] = [tex]\frac{5}{32}[/tex] = 0.15625

    P(37 <= X <= 43) = 0.34375 - 0.15625 = 0.1875

(C) Probability that student complete the quiz in exactly 44.74 minutes

     = P(X = 44.74)

The above probability can't be computed because this is a continuous distribution and it can't give point wise probability.

Answer:

a) 9(t - u)

Step-by-step explanation:

x = 10t + u

y = 10u + t

x - y = 10t + u - 10u - t

= 9t - 9u

= 9(t - u)

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. The recursive formula for an arithmetic sequence is an = a1 + (n-1)d, and the explicit formula is an = a1 + (n-1)d.

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. The recursive formula for an arithmetic sequence is given by: an = a1 + (n-1)d, where an is the nth term, a1 is the first term, n is the position of the term, and d is the common difference. The explicit formula for an arithmetic sequence is given by: an = a1 + (n-1)d. The explicit formula allows you to directly find any term in the sequence without having to find the previous terms.

Answer: the ship unloaded 1455 tons of cargo at the bahamas.

Step-by-step explanation:

Let x represent number of tons of cargo that the ship unloaded at the bahamas.

The initial number of tons of cargo in the ship is 5678 tons. If it unloads x tons of cargo, the number of tons of cargo left would be

5678 - x

The crew also loads three times the quantity of cargo that was unloaded. This means that the number of tons of cargo that it loaded is 3x. The total number of tons of cargo in the ship would be

5678 - x + 3x

= 5678 + 2x

If the ship holds 8588 tons now, it means that

5678 + 2x = 8588

2x = 8588 - 5678

2x = 2910

x = 2910/2

x = 1455 tons of cargo

Answer:

a) Water height, H(g) = 8g^2 + 3g -4 - [9g^2 -2g -5] = 8g^2 + 3g -4 -9g^2 + 2g +5 = -g^2 +5g +1

b) g = 1

H(g) = -(1)^2 + 5(1) + 1 = -1 + 5 + 1 = 5

g=2

H(g) = -(2)^2 + 5(2) + 1 = -4 + 10 + 1 = 7

g=3

H(g) = -(3)^2 + 5(3) + 1 = -9 +15 +1 = 5

c) Greatest height

Find the vertex of the parabole

The vertex is at the mid point between the two roots.

To find the roots you can use the quadratic equation

The result is g = 5/2 + [√29]/2 and g = 5/2 - [√29]/2

The middle poin is 5/2 = 2.5

Now find H(2.5) = -(2.5)^2 + 5(2.5) + 1 = 7.5 ≈ 7.3

hope this helps

Answer:

a. E(F)=0.875

b. 99.9976%

c. P(X=2)=0.1683

Step-by-step explanation:

a. We notice that this is a binomial distribution with the probability of success;

[tex]p=\frac{5}{40}=0.125[/tex]

#We are given the sample size, n=7. The Expected value is calculated as:

[tex]E(X)=np\\\\E(F)=np , n=7, p=0.125\\\\E(F)=7\times 0.125\\\\=0.875[/tex]

Hence the expectation, E(F)=0.875

b. To calculate the probability of the range of F, we need to calculate all possible outcomes of F in the given sample;

[tex]P(X\leq 5)=1-P(X=6)-P(X=7)\\\\=1-{7\choose 6}(0.125)^6(1-0.125)^1-{7\choose 7}(0.125)^7(1-0.125)^0\\\\=1-0.000023365-0.000000476\\\\=0.999976158\\\\=99.9976\%[/tex]

Hence, the range of F is 99.9976%

c. The probability that F=2 is calculated  using the binomial distribution function as:

[tex]P(X=2)={7\choose 2}(0.125)^2(1-0.125)^5\\\\=0.1683[/tex]

Hence, the probability of F=2 is 0.1683

Using the hypergeometric distribution, it is found that:

a) E(F) = 0.875

b) The range is {0, 1, 2, 3, 4, 5}

c) 0.1741 = 17.41% probability that F = 2.

The computers are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

In this problem:

Item a:

The expected value of the hypergeometric distribution is:

[tex]E(F) =  \frac{nk}{N}[/tex]

Hence:

[tex]E(F) = \frac{35}{40} = 0.875[/tex]

Item b:

The range is the possible values that F can assume, which is from 0 to k, hence 0 to 5.

Item c:

The probability is P(X = 2), applying the hypergeometric distribution.

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 2) = h(2,40,7,5) = \frac{C_{5,2}C_{35, 5}}{C_{40,7}} = 0.1741[/tex]

0.1741 = 17.41% probability that F = 2.

You can learn more about the hypergeometric distribution at https://brainly.com/question/25303388

Answer:

Oliver read in two months = 945 minutes

Step-by-step explanation:

Oliver read in this month = 450 minutes

Goal for the next month = 10 % more than this month = [tex]\frac{110}{100}[/tex] × 450

⇒ Oliver read in next month = 495 minute

⇒ Oliver total  read in two months = 450 + 495  = 945 minutes

Thus Oliver read in two months = 945 minutes

Answer:

Oliver will read 945 minutes in 2 months.

Step-by-step explanation:

Given:

Number of minutes read this month = 450 mins

Percent of minutes to read next month = 10%

We need to find the number of minutes he read in two months.

Solution:

First we will find the number of minutes he read in next month.

number of minutes he read in next month is equal to Number of minutes read this month plus Percent of minutes to read next month multiplied by Number of minutes read this month.

framing in equation form we get;

number of minutes he read in next month = [tex]450+\frac{10}{100}\times 450 =450+45 =495\ mins[/tex]

Now  number of minutes he read in two months is equal to sum of Number of minutes read this month and number of minutes he read in next month.

framing in equation form we get;

number of minutes he read in two months = [tex]450+495 = 945\ mins[/tex]

Hence Oliver will read 945 minutes in 2 months.

Answer:

yes

Step-by-step explanation:

It depends on how accurate you want your answer to be, but basically yes, imagine we set our numerator to be x, and our denominator to be 2x, if we built our fraction we will get that:

[tex]\frac{x}{2x}=\frac{1}{2}[/tex]

If the denominator of a fraction is exactly twice the numerator, then the fraction will be simplified to 1/2 or 0.5.

Now, the greater the denominator is, the closer the fraction will get to zero.

Take for example I had an fraction like this:

[tex]\frac{3}{6}=0.5[/tex]

which approximates to 0. If we made the denominator bigger, let's say 7, we would get:

[tex]\frac{3}{7}=0.43[/tex]

notice the answer is closer to 0 this time, so it's valid to round it to zero. If we made the denominator greater, let's say 25, we would get:

[tex]\frac{3}{25}=0.12[/tex]

and so on. So it is true that if the denominator of a fraction is greater than twice the numerator, we can always replace the fraction with a 0 (depending on how accurate you want your answer to be).

If the denominator is more than twice the numerator, the number is therefore less than halve, 1/2 but cannot always be replaced with a 0.

An example;

Suppose we have a numerator, 2.

Then, we have a denominator which is more than twice the numerator; say 5

The resulting fraction is therefore;

The fraction 2/5 is definitely less than 1/2 but cannot always be replaced with a 0.

Read more on fractions:

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Answer:

So if the parameter 's value  is 7 or 803 or 141 the function returns true . But if the parameter 's value  is -22 or -57, or 0, the function returns false .

My Code:

bool is Positive ( int x ) {  

if ( x > 0 )  

{  

 return true;  

}  

else {  

 return false ;  

}  

}