Claire left her home at 11 a.m. travelling along route 1 at 30 miles per hour. At 1 pm,Her counsin Valerie left home and started after her on the same road at 45 miles per hour.At what time did Valerie catch up with Claire ?
(Please give a step by step explanation and answer correctly)

Answer:

[tex]\frac{51}{4}[/tex]

Step-by-step explanation:

Since they are similar we can set up direct proportions

FE:CB=DE:AB

y:6=17:8

[tex]\frac{y}{6} =\frac{17}{8}[/tex]

cross multiply

8y=17*6

divide by 8 each side

[tex]\frac{51}{4}[/tex]

Answer:625/27

Step-by-step explanation:

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{\dfrac{5^4}{3^3}}[/tex]

[tex]\mathsf{= \dfrac{5\times5\times5\times5}{3\times3\times3}}[/tex]

[tex]\mathsf{= \dfrac{25\times25}{9\times3}}[/tex]

[tex]\mathsf{= \dfrac{625}{27}}[/tex]

[tex]\huge\text{Therefore, your answer is: \boxed{\mathsf{\dfrac{625}{27}}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

1. A conditional statement can be written as

The hypothesis is: It is sunny

The conclusion is: there is daylight

2. The converse of the conditional statement

3. The inverse of the conditional statement

4. The contrapositive of the conditional statement

5. The biconditional statement and can be written because the statement and the converse are both true

6. The biconditional statement is

A conditional statement is a term used in logic that refers to the type of statement that has "if-then". It is sometimes called if-then statements. Conditional statement are of two parts the hypothesis required to ensure that the conclusion. Other forms of conditional statements are

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Since , X lies between W and Y, the location of X so that the ratio of WX to XY is 1 to 7 is 7.01.

In regards to math's, position is seen as the looking through a given location and it is one that is pertaining to another kind of thing or the lines.

Note that from the question:

W = -31

Y= -7

So -  7 - (-31) = 38

Now:

WX: XY = 1 :7

XY =  7K

WZ = K

Then 7k + K = 38

K = 38/7

K  = 5.43

So XY = 5.43 x 7

= 38.01

So position of X = 38.01 + (-31)

X = 7.01

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After solving the equation the value of x is 13/5.

So, we can see that both triangles are congruent under the SAS condition.

Since both triangles are congruent, then we can conclude that side BC will be congruent to side DE under CPCT (Corresponding parts of congruent triangles).

Then, we can form the equation:

Now, solve the equation as follows:

Therefore, after solving the equation the value of x is 13/5.

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If the website advertised an Airpod rental of $5 a week with a down payment of $10, then the total cost he paid if he rented the Airpod for 6 months is $130

The amount he paid for down payment = $10

The rent amount for the airpod for one week = $5

We know,

There are 4 weeks in a month

Number of weeks in 6 month = 6×4

= 24 weeks

The total amount her paid for if he rented the airpod for 6 months = The amount he paid for down payment + (The rent amount for the airpod for one week ×24)

= 10+5×24

= 10+120

= $130

Hence, if the website advertised an Airpod rental of $5 a week with a down payment of $10, then the total cost he paid if he rented the Airpod for 6 months is $130

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Sector length is the distance between two points along a section of a curve.

Answer:

Arc length is calculated using the relation : Arc length = l = (θ/360) × 2πr. Therefore, Perimeter of a Sector = 2 Radius + ((θ/360) × 2πr )

Answer:

0.25 Months =7.6099 Days= 7 Days, 14 Hours, 38 Minutes and 19 Seconds

In Spanish

0.25 Meses =7.6099 Días= 7 Días, 14 Horas, 38 Minutos y 19 Segundos

Call the two offers offer A and B respectively.

For offer A, the list price is 5000 pesos with a 15% discount. So you will pay:

For offer B, the list price is 5200 with a 20% discount. So you will pay:

So the first deal is costing 4250 pesos and second one costs 4160 pesos.

Hence the second deal is better by 4250-4160= 90 pesos.

The second deal is the better deal by 90 pesos.

The number is 17.

Let's assume that the number is x.

So according to the question twice a number is 34 less than 4 times the number.

Then, the equation formed will be as follows

⇒ 2x = 4x - 34

Solving the equation we get the value of x which is the respective number.

Combine the like terms then proceed with calculations.

⇒ 4x - 2x = 34

⇒ 2x = 34

Divide both sides of the equation by 2.

⇒ x = 17

Hence the number whose twice is 34 less than 4 times the number is 17.

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Answer:

The value of the 8 in the front is 800 000 and the value of the second is 80 000. The front value is ten times as big as the second  value.

Step-by-step explanation:

The location of the point B on the line with the endpoints is 63

On the segment, we have the following endpoints

A = -3

C = 8

Rewrite the endpoints of the line segment as

A = (-3,0) and C = (8,0)

The ratio of the line is given as

Ratio, A : B = 1 :5

This means that

Point C = A/A + B

So, we have

C = 1/1 + 5

Evaluate

C = 1/6

The coordinate of point C on the line segment is calculated using

Point C = C * (B - A) + A

So, we have

8 = 1/6 * (B + 3) - 3

This gives

1/6 * (B + 3) = 11

So, we have

B + 3 = 66

Subtract 3

B = 63

Hence, the coordinate of the point B on the line segment is  63

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Possible question

if point c divides a directed line segment from point A to point B in a 1 : 5 ratio, what are the coordinates of point B?

A = -3  and C = 8

Parametric equation of the give cartesian equation x(y) = 3log(y)+y is

x(t) =3log(t)+t

y(t) = t

The given cartesian equation x(y) = 3log(y)+y

The cartesian equation is an equation of the curve in which variables are the Cartesian coordinates of a point on the curve or surface.

Here we have to convert the cartesian equation into parametric equation.

We can converting the cartesian equation into parametric equation by changing the independent variable in the cartesian equation to t.

The cartesian equation x(y) = 3log(y)+y

Here x is expressed as the function of y.

Define y = t

x(t) = 3log(t)+t

y(t) = t

Hence, the Parametric equation of the give cartesian equation x(y) = 3log(y)+y is

x(t) =3log(t)+t

y(t) = t

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Answer:

When data points are marked on the chart, all data points within a single dependent variable are connected with a line, making it very useful tool for analyzing changes over time for one or more variables.

Step-by-step explanation:

the equation given

we can rewrite the equation as

to solve this question, we can use any of the given mehod known to solve quadratic equations which are

1. factorization

2. completing the squares

3. using quadratic equation

for the purpose of this tutoring session, i'll use quadratic equation also know as quadractic formula

the formula is given as

next we proceed to identify the variables

now we can input the values into the equation (formula) above

from the calculations above, x = -1/3 or x = -4

Answer:7.5 inches

Step-by-step explanation:

69.75/9.3=7.5

A physics concept called frequency describes how many cycles a wave completes each second. As a result, the following expression is used to get the lower note's frequency [tex]\frac{2}{3}[/tex] f

A wave is a phenomena that moves through a physical medium without leaving any lasting impression on the molecules therein. Energy is transferred from one end of the medium to the other. Sound waves, light waves, electromagnetic waves, etc. are some examples.

Frequency develops during wave propagation. This can be characterized as the number of cycles a wave makes in a second. It's also measured in Hertz.

Let f stand for the upper note's frequency and for the lower note's frequency we have [tex]f_{1}[/tex]. We therefore have;

[tex]f_{1}[/tex] =[tex]f\frac{2}{3}[/tex]

Therefore, the expression for the frequency of the lower notes is [tex]\frac{2}{3}[/tex] f.

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Answer:

9495.221

Step-by-step explanation:

16000=Pe^(0.11x5)

Step-by-step explanation:

a)

[tex]f(x+h) = 2(x+h)-9[/tex]

[tex]f(x+h)=2x+2h-9[/tex]

b)

[tex]f(x+h)-f(x)=2x+2h-9-(2x-9)[/tex]

[tex]f(x+h)-f(x)=2x+2h-9-2x+9[/tex]

[tex]f(x+h)-f(x)=2h[/tex]

c)

[tex]f(x+h)-f(x)h=2x+2h-9-h(2x-9)[/tex]

[tex]f(x+h)-f(x)h=2x+2h-9-2hx+9h[/tex]

[tex]f(x+h)-f(x)h=-2hx+11h+2x-9[/tex]

We have two relations between length of the trench and time.

Case: we want to know how many feet we can dig in a certain amount of time.

In this case, and in most of the cases, time is the independent quantity.

Therefore, the dependent quantity is the other variable: length of the trench.

For example, we can write a proportional relationship between time (x) and length (y) as:

We know that when x=40 min, y=36 ft, according to the machine advertisement.

Then, we can find k as:

And we can write the relation as:

Answer: the independent quantity is time (in minutes).

NOTE:

Which variable is which depends on what we want to calculate.

If we want to know how much it will take to make a certain length of trench, the independent quantity is the length of the trench. The dependent variable is, in this case, time, as we calculate it from the information about the length of the trench.

If we want to calculate the length of the trench we can dig in a certain time, the independent quantity is time and the dependent quantity is the length of the trench.

Answer:

It is forever, and it does not end.

Step-by-step explanation:

Infinity is the concept of no beginning and no end. It is the concept of all things and everything. So when you think of a deity ( Ex. God ) you think of them being infinite. They have no beginning or end, and have limitless possibilities. They live forever, and they can do anything. That is infinity in a nutshell.

Hope this helps.

Answer: 68/9 which simplifies into 7 6/9

Answer:

16000

Step-by-step explanation:

3984:24.9*100 =

(3984*100):24.9 =

398400:24.9 = 16000

When the graph of a relationship shows a line that passes through the origin, then it is proportional.

If a connection's graph is a line that runs through its origin, it is proportional. If there isn't a line or ray that does this, the ratio isn't proportional. The equation for the proportionality constant is K = y/x.The equation that describes the slope of a straight line in relation to its origin is identical to this one.

When the graph of a proportional connection passes through the origin, any ratio in the proportional relationship can be found.

A relationship is proportional if its graph is a line or ray that passes through the origin. It is not proportional if the line or ray does not go through the origin.

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Answer:

x = 26/5

Step-by-step explanation:

Distribute

 5x - 25  : -5x + 27

Add 25 to both sides

 5x = -5x +52

Add 5x to both sides

 10x = 52

Divide by 10

x = 52/10

Simplify

x = 26/5

no answer for this question

Based on the number of items in the simple random sample, and the sample mean, the standard error of the mean can be found to be 1.12

The standard error of a simple random sample can be found by the formula:

= Population standard deviation / √Number of items in simple random sample

Solving for the standard error gives:

= 5 / √20

= 5 / 4.4721359549995793928183473374626

= 1.118

= 1.12

We can therefore conclude that the standard error of this sample is 1.12.

Rest of the question:
What is the standard error of the mean?

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Answer:

200 children.

180 adults.

Step-by-step explanation:

let x=Children and y=Adults

create 2 equations.

x+y = 380

2.50x+5.80y = 1544

solve for x in the first equation and plug into the second equation.

x = 380-y

2.50(380-y) +5.80y = 1544

distribute and simplify.

950 + 3.3y = 1544

simplify

3.3y = 594

y = 180

plug y back into first equation and you get that there were 200 children.

Answer:  My bill was 17 dollars.  I gave four tokens of equal monetary value to the cashier who gave me in return 3 one dollar bills.  How much was each token worth?  

Step-by-step explanation:  4x - 3 = 17.

                                             add 3 to both sides

                                             4x = 20

                                              x = 5.  Each token was worth $5.