Calculate the length of ac to 1 decimal place below

Answer:

b=7

Step-by-step explanation:

3-5b=-32

-5b=-32-3

-5b=-35

Divide both sides by -5

b=7

( I also had trouble with these kind of expressions)

The value of e is 33/5 or 6.6 era.

It is given in the question that:-

e*i = 9r

Where,

e represents era

i represents the number of innings pitched, and

r represents the number of earned runs allowed

Also, we are given that:-

i = 45 innings, and

r = 33 earned runs allowed

We have to find the value of e for the given data.

Hence, applying the formula given in the question, we get

e*45 = 9*33

Now, as only one variable is left in the equation, it has become a linear equation in one variable.

Hence, solving the linear equation, we get

e = (9*33)/45

e = 33/5

e = 6.6 era

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Arrangement of students from shortest to tallest is

Kim 56.03 < Roy 56.14 < Alexa 56.3 < Tom 57.1.

As given in the question,

Number of students =  4

Height of the students

Kim = 56.03 units

Alexa = 56.3 units

Roy = 56.14 units

Tom = 57.1 units

Arrange the students from shortest to tallest

56.03 < 56.14 < 56.3 < 57.1

Kim < Roy < Alexa < Tom

Therefore, arrangement of students from shortest to tallest is

Kim 56.03 < Roy 56.14 < Alexa 56.3 < Tom 57.1.

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Answer: 0.75km

Step-by-step explanation:

Answer:

all of them are terminating decimals

Step-by-step explanation:

5/2=2.5

4/5=1.25

2/7=3.5

4/5=1.25

4/3=0.75

5/2=2.5

4/5=1.25

2/7=3.5

4/3=0.75

they are terminating decimals because they have a finite end

Answer:

9

Step-by-step explanation:

6 / 2(1+2)

6 / 2 (3)

6 / 2 * 3

3 * 3

9

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Answer: 176 miles

Step-by-step explanation:

m=mile.

97 cents=

97/100 dollars=$0.97

190.67=19.95+0.97m

170.72=0.97m

m=176 miles

Answer:

13/25

Step-by-step explanation:

hope this helps :)

If the speed of car is 44 feet per second and the speed of emergency vehicle is 74 feet per second,then they the driver of the car will hear the siren after 8.48 seconds after cover the distance of 1000 feet.

Given that the speed of car be 30 mph or 44 feet per second, the speed of emergency vehicle be 50 mph or 74 feet per second and the distance between both is 1000 feet apart.

We are required to find the seconds after which the driver of the car first hear the siren.

Speed is basically the distance that a vehicle covers in a particular period of time.

Speed=Distance/Time

Time=Distance/Speed

Total speed in feet per second=44+74=118 feet per second

Time=1000/118

=8.48 seconds

Hence if the speed of car is 44 feet per second and the speed of emergency vehicle is 74 feet per second,then they the driver of the car will hear the siren after 8.48 seconds.

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Answer:

19, 29, 29, 37, 41

Step-by-step explanation:

1. What we know: x y 29 z 41

(x+y+29+z+41)/5 =31

x y and z each >9 and prime

Possibile numbers: 11, 13, 17, 19, 23, 29, 31, 37, 41

2. (x+y+29+z+41)/5 =31

x+y+29+z+41 = (31×5)

x+y+z = (31×5) -29 -41

x+y+z = 85

z>=29

x<=29

y<=29

x and y can be 11, 13, 17, 19, 23, 29

z could be 29, 31, 37, 41

At least one if them must equal 29 because it's the mode.

So two of them must equal 56

11+29=40 so both numbers cannot be less than or equal to 40

This means y is 29 because x + z has to equal 56 and that wouldn't be possible if x equals 29.

Now we know x+z=56

Possible numbers: 19+37

I found these by doing 56- each possible number for x and seeing if that equaled a possible number for z. For example 56-11=45 but z cannot be 45 therefore x cannot be 11 and so on.

Then you just plug in the numbers!

19, 29, 29, 37, 41

This was so much fun to solve! I hope this is helpful, let me know if you have any questions! You got this :)

The function which represents the taxi fare in terms of distance d in meter is f(d) = 3.50 ×[tex]\frac{d-500}{300}[/tex] + 40 .

According to the question,

For first 500 meters cost is  40.00 and For each additional 300 meters cost is 3.50 .

Let, the total distance of taxi ride = d meters

Now, representing the equation of taxi fare in terms of distance when distance is less than 500

taxi fare = 3.50 ×  [tex]\frac{d-500}{300}[/tex]  + 40

∴  f(d) = 3.50 ×  [tex]\frac{d-500}{300}[/tex] + 40

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Answer:6

Step-by-step explanation:

The length of ac is 20 and the length of ab is 14 so all you have to do is 20-14=6

The total hours worked on each day of his normal work week is 7.5 hours.

The total hours worked is a function of the total hours worked during the week and the hours worked on Saturday.

The equation that represents the total hours that Diego worked is:

Total hours = total hours worked during the five days + hours worked on Saturday

52 = (5 X H) + 7 + H

52 = 5H + 7 + H

In order to determine the value of H, take the following steps:

Combine similar terms together: 52 - 7 = 5H + H

Add similar terms together: 45 = 6h

Divide both sides of the equation by 6 : H = 45 /6

H = 7.5 hours

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The given statement "The median of a quantitative data set is always one of the individual data values" is false.

When a given data set is arranged in ascending order the observation which at the between of the data is the median of that data set. It is a value in the set whose left and right both have the same number of observations.

The given statement is not true, this is because the median is the mid-value of any data set.

Hence, the given statement "The median of a quantitative data set is always one of the individual data values" is false.

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The driver B has the fastest typical race time.

It is required to find which driver's race times were the most variable.

A statement is a declarative sentence that is either true or false but not both. A statement is sometimes called a proposition. The key is that there must be no ambiguity. To be a statement, a sentence must be true or false, and it cannot be both.

Given:

From the options presented, driver B has the fastest typical race time because he recorded the smallest time taken to complete an individual race.

Also from the standard deviation given 3.96  seconds  for driver B, it shows that the individual time spread from the standard deviation is minimal and that the driver maintained a fairly consistent time of race throughout the racing period.

Therefore, the driver B has the fastest typical race time.

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Answer:

Negative

Step-by-step explanation:

Because knowing that a positive number times a negative number equals negative.

Answer:

5.14 minutes

Step-by-step explanation:

4 pages / 7 minutes = 0.57 minutes per page

0.57 minutes/pg * 9 pages = 5.14 minutes

Satisfactory internal control reduces the probability of errors or frauds in the accounts.

What functions may a strong internal control system perform?

Why are internal controls necessary?

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Answer: Derivative of f(x) =3x+5=3

Step-by-step explanation:

By the Sum Rule, the derivative of 3x+5 with respect to x is d/dx[3x]+d/dx[5]

d/dx[3x]+d/dx[5]

evaluate:  d/dx[3x]

Since 3 is constant with respect to x, the derivative of 3x with respect to x is 3d/dx[x].

3d/dx[x]+d/dx[5]

Differentiate using the power rule

which states that d/dx[[tex]x^{n}[/tex]] is [tex]nx^{n-1}[/tex]    where n=1.

3⋅1+d/dx[5]

Multiply 3 by 1.

3+d/dx[5]

Differentiate using the Constant Rule.

Since 5 is constant with respect to x, the derivative of 5 with respect to x is 0.

3+0

Add 3 and 0 = 3

So, derivative of f(x) =3x+5=3

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The amount raised by a booster club compared with the number of  raffle tickets sold shows a constant rate of change;

A constant rate of change is realized when a change in one situation always results in a change in another. In the scenario of a booster club that regularly sells raffle tickets, the more tickets it sells, the higher the club gets.

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Answer:

(A) is correct.

Step-by-step explanation:

As we know,

The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).

From the first graph:

The line goes through the points:

(-2, 2) and (2, 1)

y - 1 = (1-2)/(2+2)[x -2]

y - 1 = (-1/4)[x -2]

y = -x/4 + 1/2 + 1

y = -x/4 + 3/2

The constant additive rate of change = -1/4

Thus, the function shown in graph (A) has a constant additive rate of change is -1/4 option (A) is correct.

The number of students take both AP European History and AP US History is 19 students

A Venn diagram is an illustration of the relationships between and among sets, groups of objects that share something in common.

Let the students take both AP European History and AP US History be x such that;

n(U) = 29 - x + 50 - x

If 60 high school seniors taking AP classes, then n(U) = 60. Substitute to have:

60 = 29 - x + x + 50 - x

60 = 79 - x

-x = 60 - 79

-x =-19

x = 19

Therefore the number of students take both AP European History and AP US History is 19 students

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The function ƒ(x) = e^(2x + 1) when graphed could be described as; an increasing exponential graph.

The graphs of exponential functions are nonlinear—because their slopes are always changing, they look like curves, not straight lines.

Now, we are given the exponential function as;  ƒ(x) = e^(2x + 1)

Now, as the exponent increases, the curves get steeper and the rate of growth increases respectively. Thus, we can see that the exponent we are given increases as seen in the exponent attached to it.

Thus, we can conclude that The function ƒ(x) = e^(2x + 1) when graphed could be described as; an increasing exponential graph.

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Taking into account the definition of speed, Monica will complete the triathlon in 12.62 hours.

Speed can be defined as the amount of space traveled per unit of time with which a body moves and can be calculated using the expression:

speed= distance traveled÷ time

In this case, you know

Replacing these values ​​in the speed definition:

Solving:

Swim: 1.8 mph×time to swim= 2.4 miles

time to swim= 2.4 miles÷ 1.8 mph

time to swim= 1.33 h

Ride a bike: 19.2 mph× time to ride a bike = 112 miles

time to ride a bike= 112 miles÷ 19.2 mph

time to ride a bike=5.83 h

Run: 4.8 mph× time to run= 26.2 miles

time tu run= 26.2 miles÷ 4.8 mph

time to run= 5.46 h

The time to complete the triathlon is the sum of each of the stages:

Total time= time to swim + time to ride a bike + time to run

Total time= 1.33 h + 5.83 h + 5.46 h

Total time= 12.62 h

In summary, Monica will complete the triathlon in 12.62 hours.

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The equivalent expression of 8^-1 is 1/8

The expression is given as

8^-1

The above represents 8 exponent -1

The rule for negative exponents states that

a^-1 = 1/a

This means that

8^-1 = 1/8

Hence, the equivalent expression of 8^-1 is 1/8

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Answer:

X=3

Step-by-step explanation:

Remember to get all your variables on one side by doing the "Reverse function" etc...

Once youve got your variables on one side (and only 1 is remaining) you should get rid of whats BESIDE the variable by dividing it by *whatever it is thats beside the variable!* AND REMEMBER TO DO THIS ON BOTH SIDES OF THE EQUATION SO THAT THEYRE EQUAL!!

The measure of each angle are m∠ABC =  40.4 and m∠DEF =  49.6

The given parameters are

m∠ABC = (2x+4)∘ and m∠DEF = (3x−5)∘,

Complementary angles add up to 90 degrees

So, we have

2x + 4 + 3x - 5 = 90

Evaluate the like terms

5x = 91

Divide by 5

x = 18.2

Substitute x = 18.2 in m∠ABC = (2x+4)∘ and m∠DEF = (3x−5)∘,

m∠ABC = (2 x 18.2 + 4) = 40.4

m∠DEF = (3 x 18.2 − 5)∘ = 49.6

Hence, the measure of each angle are m∠ABC =  40.4 and m∠DEF =  49.6

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