Corinne and Deanna decide to race from one corner of an open field to the other. The field is rectangular in shape, 60 meters long and 80 meters wide. Since Corinne is older and faster, she's going to run along the outside of the field, and Deanna will take the diagonal route. If Deanna can run at a rate of 5 meters per second, how fast will Corinne have to run to get there at the same time as Deanna?

The probability that the sample mean would differ from the population mean by greater than 0.5 millimeters is 1

From the question, the given parameters about the distribution are

The standard deviation is the square root of variance

So, we have

Standard deviation = 6

The z-score is calculated using the following formula

z = (x - mean value)/standard deviation

Substitute the given parameters in the above equation

z = (0.5 - 127)/6

Evaluate

z = -21.08

The probability is then calculated as:

P(x > 0.5) = P(z > -21.08)

From the z table of probabilities, we have;

P(x < 0.5) = 1

Hence, the probability is 1.0

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The equivalent monthly rate of the number of security breaches is of 5.31%, using an exponential function.

An increasing exponential function is modeled according to the rule presented by the equation as follows:

[tex]A(t) = A(0)(1 + r)^t[/tex]

In which the parameters of the exponential function are listed as follows:

In the context of this problem, considering the increase at an yearly rate of 86%, the parameter rate r is given as follows:

r = 0.86.

Hence the function is defined as follows:

[tex]A(t) = A(0)(1.86)^t[/tex]

One year is composed by 12 months, hence the monthly increase is calculated as follows:

[tex]r_m = (1.86)^{\frac{1}{12}} - 1 = 0.0531[/tex]

The monthly increase rate is of 5.31%.

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Answer:

The answer is 5.3

The equations using any method for the given situation illustrated that:

Equation for Jordan: 225 + 45w

Equation for RayAnn: 150 + 60w

Let the number of weeks be represented by w.

Jordan saved $225 and continues to save $45 each week. The equation for this will be:

= 225 + (45 × w)

= 225 + 45w

RayAnn saved $150 and continues to save $60 each week. The equation will be:

= 150 + (60 × w)

= 150 + 60w

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Magnitude of an earthquake releasing 3.4*10^14 joules of energy is M ≈ 6.754.

Given:

The magnitude, M, of an earthquake is represented by the equation M=2/3log(E/E0) where E is the amount of energy released by the earthquake in joules and E0=10^4.4 .

E = 3.4*10^14

M = 2/3*log(3.4*10^14 / 10^4.4)

= 2/3*log(13535643798.8)

= 2/3*10.1314

= 20.2628 / 3

M = 6.754

Therefore Magnitude of an earthquake releasing 3.4⋅1014 joules of energy is M ≈ 6.754.

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Answer:

b = 3

Step-by-step explanation:

Given that,

→ a = 27

Forming the equation,

→ 27 = 3b²

Now the value of b will be,

→ 27 = 3b²

→ b² = 27/3

→ b = √9

→ [ b = 3 ]

Hence, the value of b is 3.

⇒Given that a=27 in the equation [tex]a=3b^{2} \\[/tex] in the place of a plug in 27 and solve for b

[tex]27=3b^{2} \\\frac{27}{3} =\frac{3b^{2}}{3} \\b^{2} =9\\b^{2}-9=0\\(b+3)(b-3)=0\\b+3=0\\or\\b-3=0\\b=-3\\or\\b=3[/tex]

⇒Note b can also be -3 but the only option available as the answer is 3

∴ b=3 in this case.

Answer:

|x-7|=3

Step-by-step explanation:

x is 3 units away from 7

x-3=7

x-7=3

x+3=7

3=7-x

|x-7|=3

The amount of pasta and sauce since he wants each bag to have the same amount is 16.

A factor simply means a number that can multiplied with another number which is also.a factor to get the original number.

In this case, Cesar has 32 boxes of pasta and 48 jars of sauce that he will be putting into bags for a food drive.

It should be noted that to get the number in each bag, it means that we have to find the highest common factor for both numbers. This will be:

Factors of 32 = 1, 2, 3, 4, 6, 8, 16 and 32

Factor of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48.

Therefore, the answer is 16.

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Answer:

y=1/3x+6

Step-by-step explanation:

Use the formula "Y=mx+b"

Answer:

y= -1/3x - 6

Step-by-step explanation:

x+3y = -18

3y = -x -18

y= -1/3x - 6

Answer:

-------------------------------

The greatest value of the function is - 3.

The equation of the parabola from the vertex is f(x) = 7(x - 3)² + 5

The equation of the function is given as

f(x) = 7x²

Also, we have

Vertex = (3, 5)

The form of the equation is given as

f(x) = a(x - h)² + k

Where

Vertex = (h, k)

This means that

Vertex = (h, k) = (3, 5)

Substitute (h, k) = (3, 5) in the equation f(x) = a(x - h)² + k

So, we have

f(x) = a(x - 3)² + 5

This also means that

f(x) = 7(x - 3)² + 5

The 7 is gotten from f(x) = 7x²

Hence, the equation of the parabola is f(x) = 7(x - 3)² + 5

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ans=y=8

[tex] \frac{change \: in \: y}{change \: in \: x?} [/tex]

8-8=0

-7--9=2

hence the gradient is 0÷2=0

gradient(0)=

[tex] \frac{y - 8}{x - - 9?} [/tex]

so..,0=y-8

hence the equation is y=8

do you mean 712 or 7.12?

If for 712 it is 1808.48

if for 7.12 it is 18.0848

The expected value of the sum of these events will be 2 / 3.

Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Probability = Number of favourable outcomes / Number of sample

Given that the expected value for getting heads, on 30 coin tosses, is 15. The expected value for rolling a 1, after 30 die rolls is 5.

The probability of the sum will be calculated as,

P = ( 15 / 30 ) + ( 5 / 30 )

P =  ( 20 / 30 )

P = 2 / 3

Therefore, the expected value of the sum of these events will be 2 / 3.

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Answer:

5/11 > 4/9

Step-by-step explanation:

5/11 = 0.45454545....

4/9 = 0.44444444....

The graph of the function  y=3 -1/2x is attached below.

Function:

Function refers the relationship between inputs where each input is related to exactly one output.

Given,

Here we have the function  y=3 -1/2x.

Now, we have to plot the graph of the function.

In order to plot the graph of the function, we have to take some sample values for x.

So, we will take the values of the x as -2, -1, 0, 1, 2.

Now, we have to apply the values on the given function then we get,

=> x = -2 => y = 3 - 1/2(-2) => y = 3 + 1 => y = 4

=> x = -1 => y = 3 - 1/2(-1) => y = 3 + 1/2 => y = 7/2 = 3.5

=> x = 0 => y = 3 - 1/2(0) => y = 3 - 0 => y = 3

=> x = 1 => y = 3 - 1/2(1) => y = 3 - 1/2 => y = 5/2 = 2.5

=> x = 2 => y = 3 - 1/2(2) => y = 3 - 1 => y = 2

When we enter these values into the table, then we get the table like the following.

By using the table we have to plot the graph and then we get the graph like the following.

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Taking into account the definition of a system of linear equations, the number of 2-pointers and 3-pointers Sarah made is 2 and 3 respectively.

A system of linear equations is a set of equations relating two or more unknown values, the goal of which is to determine those values so that the equations are true.

Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. That is to say, the values ​​of the unknowns must be sought, with which when replacing, they must give the solution proposed in both equations.

In this case, a system of linear equations must be proposed taking into account that:

You know:

The system of equations to be solved is

x + y= 10

2x+3y= 24

It is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.

In this case, isolating the variable "x" from the first equation:

x= 10 - y

Replacing this expression in the second equation:

2×(10-y)+3y= 24

Solving:

2×10 -2y +3y= 24

20 -2y +3y= 24

-2y +3y= 24 - 20

y= 4

Remembering that x= 10 -y, you get:

x= 10 -4

x= 6

Finally, the number of 2-pointers Sarah made is 2 and the number of 3-pointers she made is 3.

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The triangles are congruent by ASA(angle side angle) theorem

Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure.

In other words, triangles are congruent when they have exactly the same three sides and exactly the same three angles.

There are different ways to find that out that triangles are congruent.

If two angles and the included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent.

Therefore, the triangles are congruent by ASA(angle side angle) theorem.

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Answer:

addition?

Step-by-step explanation:

Answer:

Math: the science and study of quality, structure, space, and change.

The value of y is 24 when x is -2.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Given,

There are direct variations

y= 24 when x=2

We need to find value of y when x =-2

This can be found by forming an equation.

Let the value of unknown y be a

2/24=-4/a

Apply cross multiplication

2a=24(-2)

2a=-48

We need to divide by 2 on both sides

a=-24

Hence the value of y is 24 when x is -2.

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Answer:

The picture is not Clear. Please provide a better view of the question.

Step-by-step explanation:

The number of degrees of freedom for the chi-square goodness-of-fit test is of:

2.

The number of degrees of freedom for a chi-square goodness-of-fit test is obtained according to the multiplication presented as follows;

df = (r - 1) x (c - 1).

In which the variables are listed as follows:

The table in this problem has three rows, given as follows:

The table has two columns, which are given as follows:

Hence the number of degrees of freedom of the test is given as follows:

df = (3 - 1) x (2 - 1) = 2 x 1 = 2.

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The number of sodas sold is 168

The number of hot dogs sold is 56

Total of sodas and hot dogs=224

Let the number of sodas sold be s, and the number of hot dogs sold be s

So we have the following:

s=3h.................i

s+h=224..........ii

we solve the two equation to find the value of s and h,

From equation ii, s=224-h, replacing this in equation i, we have:

224-h=3h

224=4h

h=56

Now, s=3*56

          =168

s=168

Number of sodas=168

Number of hot dog sold=56

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The complete question is given below;

A vender sold a combined total of 224 sodas and hot dogs. The number of sodas sold was three times the number of hot dogs sold. Find the number of sodas and the number of hot dogs sold.

Answer:

See attached worksheet.

Step-by-step explanation:

The worksheet summarizes the steps for analyzing the data on the graph.  Note that a "line of best fit" was drawn to help illustrate the linear behavior of the data, and to better the question concerning hours of sunshine in another British town.  There are techniques for ensuring a line such as this fits the actual data as closely as possible.  These techniques draw a line that has the least overall deviation from the actual data.  For our purposes, a hand-drawn line appears to match the data reasonably well, so we are able to concule that the relationship is liner:  There is a proportional change in y for every set change in x.  That change is known as the slope.  The slope of this liner would represent the direct relationship between hours of sun and maximum temperature.

Answer:

y = -x + 4

Step-by-step explanation:

The equation of a line follows the form y=mx+c, where x and y are the coordinates, c is the y-intercept (the value of x where the line crosses the y-axis), and m is the slope.

We are given two points/coordinates - (-3,7) and (1,3) - so we know the following is true for our equation:

7=-3m+c

3=m+c

Rearranging the second equation above, we get c=3-m. Sub this into the first one, and we get

7=-3m+3-m

4=-4m

m=-1

Knowing c=3-m, we can say c=3-(-1)=3+1=4

Having found values for m and c, we can now write our equation:

y = -x + 4

Hope this helps :)

Answer: No

Step-by-step explanation: You want to find the unit rate for each bagel. 6/3 is 2 dollars, so each bagel is going to cost 2 dollars. If your getting 24 bagels for 9 dollars, 24/9 is 2 2/3 dollars for each bagel. 2 ≠ 2 2/3 so therefore, they're not the same.

The relation is function because each value in the domain matches only one value in the range, the relationship described above can be thought of as a function.

Given that,

In the picture we can see the domain and range.

We have to find if the domain and range is function or not.

Each of the sets of domain values has precisely one range value, according to the mapping.

Every domain value in a relation must have precisely one range value in order for it to be referred to as a function. It is not recommended to assign or map a domain value to more than one range value.

Therefore, The relation is function because each value in the domain matches only one value in the range, the relationship described above can be thought of as a function.

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The total time it took Jace to out home and return home is 21 minutes and the graph represents that the total distance was 8 blocks.

So, the total number of minutes Jace takes to get back home after going out:

Total minutes:

(Refer to the graph attached below)

Therefore, the total time it took Jace to out of home and return home is 21 minutes and the graph represents that the total distance was 8 blocks.

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