There are 5 one-digit numbers in a set of data. The mean is 3, the mode is 1, and the median is 4. What are the numbers in the set of data?

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Hello! In this question, we were given an expression and would have to express it without the use of exponents.

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Explanation:

In the question, we were given:

(3a³)²

In order to express the expression without the exponents, we would have to first simplify it and then expand the expression.

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Solve:

[tex](3a^3)^2[/tex]

Simplify by "squaring" the variable inside the parenthesis, in which in this case we would multiply the "2" to the "3".

[tex]3a^6[/tex]

Now in this step, we would have to expand the expression in a different form to get rid of the exponent.

To get rid of the exponent, we would expand the " [tex]a^6[/tex] " term.

Note that the term [tex]a^6[/tex] is the same thing as a · a · a · a · a · a, it is just the expanded version of the exponent.

This means that our expressed expression without exponents, including our constant "3" would be:

3 · a · a · a · a · a · a

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Answer:

3 · a · a · a · a · a · a

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Additional Info:

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Answer:

False

Step-by-step explanation:

3 x 1/3

3/1 x 1/3 = 1

Answer:false

Step-by-step explanation: i did the test

Answer:

E

Step-by-step explanation:

Say the distance is 'd'

time for going  =  d/15

time for returning  = d/30

average speed =  total distance / ( total time)

                           =  2d / ( d/15 + d/30 )  

                                 solve for average speed  = 20 mi/hr

Answer:

  6.1 cm

Step-by-step explanation:

You want to know the remaining side of the irregular figure such that the perimeter is 110 cm.

The perimeter of a plane figure is the sum of the lengths of the sides. Working clockwise from the upper left corner, we have ...

  34.6 +8.6 +17.3 +11.6 +? +11.6 +11.6 +8.6 = 110

  103.9 +? = 110 . . . . collect terms

  ? = 6.1 . . . . . . . . . subtract 103.9

The length of the missing side is 6.1 cm.

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Additional comment

If the angles that appear to be right angles actually were right angles, the perimeter would be 109.6 cm. The perimeter is longer than this, so at least three of the angles are not right angles.

Answer:

x>3

Step-by-step explanation:

2x+6-6 > 12-6    ditch the 6

2x/2 > 6/2          divide by 2

x>3

Answer:

Step-by-step explanation:

31320=x+0.08x

31320=1.08x

swap the sides

1.08x=31320

Divide by 1.08

x=29000

The two fractions are equivalent.

When two fractions have the same value, they are said to be equivalent, meaning that even though the numbers in the two fractions are different, their overall value is the same.

Fractions that are not equal to one another are referred to as nonequivalent fractions. The same cross multiplication procedure must be used to determine whether two fractions are comparable or not.

Consider these two fractions,

x = ( m / 4n ) and y = ( 2m / 8n )

Now when the fraction x is multiplying and dividing by 2.

We get,

x = ( m / 4n ) × ( 2 / 2 )

x = 2m / 8n

Therefore, x = y

Hence, the fractions are equivalent.

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Number 50 in the Jack's equation represents the rate of change in the oven's temperature over time (per minute) or with respect to time by using the slope form concept.

As per the question statement, Jack is preheating his oven before using it to bake. He wants to predict the final temperature after [tex]x[/tex] minutes.

He wrote the equation [tex]y =50x+78[/tex] , where [tex]y[/tex]  represents the final temperature in [tex]fahrenheit[/tex]. We are supposed to tell the significance of number 50 in the given equation.

As we know that the equation which is in the form of [tex]y=mx+c[/tex], or the slop form equation, m is called the slope or the rate of change of value of [tex]y[/tex] with respect to value of [tex]x[/tex].

And the given equation [tex]y =50x+78[/tex] is also of the form of [tex]y=mx+c[/tex] hence we conclude that 50 is the slope or the  rate of change of value of [tex]y[/tex] with respect to value of [tex]x[/tex].

As y is the temperature in Fahrenheit therefore x is the time hence "50 Degrees Fahrenheit change of temperature per unit minute" is the significance of 50.

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The inequality graph of the system of inequalities is graph (a)

Inequality expressions are mathematical statements that are represented by variables, coefficients and operators where the opposite sides are not equal

The system of inequalities is given as

-2x + 3y < 9

x^2 - y <= 10

4x + y > 3

In the above system of inequalities, there are two linear inequalities and a parabola inequality

The inequality symbols in the linear inequalities are opposite

This means that the region between both lines would be shaded

Also, for the parabola; the upper part would be shaded.

This is so because when y is made the subject of the formula, the symbol  becomes >=

Using the above as a guide, the inequality graph of the system of inequalities is graph (a)

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Answer: 3√6

Step-by-step explanation:

√54​=

√(9*6)=3√6

If a person is chosen at random, there is a 71% probability that he or she has run a red light in the last year.

So, to find the probability:

Apply values in the formula:

Therefore, if a person is chosen at random, there is a 71% probability that he or she has run a red light in the last year.

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Answer: -4

Step-by-step explanation:

it is -4 because we are looking for like the opposite so the opposite of 4 is -4

Answer:

Absolute value of |4| = 4

Step-by-step explanation:

The absolute value of a number is always positive

Given that the triangle is a right triangle, the value of sin (n) is √5/5.

Hence, option D)√5/5 is the correct answer.

Trigonometry is simply a branch in mathematics that looks into the relationships between angles and side lengths of a triangle.

Given the data in the question;

To determine the value of sine n, we will use one of six functions of an angle commonly used in trigonometry.

Sine of angle n = Opposite of angle n / Hypotenuse

sin(n) = Opposite / Hypotenuse

Plug in the given values and simplify

sin(n) = Opposite / Hypotenuse

sin (n) = 2 / 2√5

Next, rationalize the denominator.

Cancel out the common factor 2.

sin (n) = 2 / 2√5

sin (n) = 1 /√5

Multiply both the numerator and the denominator by √5.

sin (n)  = (1×√5) / (√5 × √5)

sin (n)  = √5/5

Given that the triangle is a right triangle, the value of sin (n) is √5/5.

Hence, option D)√5/5 is the correct answer.

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Answer:

146 centimeters or 1.46 meters.

Step-by-step explanation:

1m = 100cm

2m = 200cm

200 - 54 =146

Hope this helps!

Answer:

3/4 of 5. It equals 3 3/4.

Step-by-step explanation:

The question asks for 3/4 of 5 cups of milk.

Answer:

0.0058543

Step-by-step explanation:

58.543/10,000 = 58.543 divide 10,000

Answers:  

2.857142 mph

4.190476 ft per second

Both values are approximate

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Work Shown:

21 min = 21/60 = 0.35 hrs which is exact

distance = rate*time

rate = distance/time

rate = (1 mile)/(0.35 hrs)

rate = (1/0.35) mph

rate = 2.857142 mph which is approximate

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21 min = 21*60 = 1260 seconds

1 mile = 5280 ft

rate = distance/time

rate = (5280 ft)/(1260 seconds)

rate = (5280/1260) ft per second

rate = 4.190476 ft per second approximately

Answer: 2.857 miles/hr

4.19 ft/sec

Step-by-step explanation:

60 min=1 hr.

1 mi/21 min*60 min=

60 min*1 mi/21 min=2.857 miles/hr

60 sec=1 min

60*60 sec=1 hr

1 hr=3600 sec

2.857 miles/hr=

2.857/3600 miles/sec=0.00079 miles/sec

1 mile=5280 ft

0.00079 miles/sec=

0.00079*5280 ft/sec=4.19 ft/sec

Answer:

Steve: $138.00

Jenna: $72.00

Step-by-step explanation:

Steve:

[tex]\frac{23}{35}[/tex] x 210 = 138

Jenna:

[tex]\frac{12}{35}[/tex] x 210 = 72

I'm not really sure what this means, but i'll do what i think is right!

Answer:

Steve: $138

Jenna: $72

Step-by-step explanation:

If you're doing it so they each get what they sold, you would have to first add the total number of chocolate bars, giving you 35. To see how much each bar costs, you just have to divide $210 ÷ 35, giving you $6 per chocolate bar.

To give each what they gained, you multiply $6 by whichever amount you chose, 23 or 12, which will give you that person's amount. Steve will get $138 and Jenna will get $72.

hope this helps!

Given that XZ is the perpendicular bisector of segment WY, the numerical value of k is 4.

A bisector divides an angle or segment into two equal halves.

Given the data in the question;

Since XZ is a  perpendicular bisector of segment WY,

Segment WX is equal to Segment XY

Segment WX = Segment XY

Plug in the given values and solve for k.

6k + 8 = 11k - 12

Collect like terms

6k - 11k = -12 - 8

-5k = -20

Divide both sides by the coefficient of k

-5k/-5 = -20/-5

k = 4

Given that XZ is the perpendicular bisector of segment WY, the numerical value of k is 4.

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The total bill for 3.18 pounds of apples, 1.45 pounds of peaches, and 1.71 pounds of pears is $6.78  .

In the given question

The price of 1 pound apple = $0.99

The price of 1 pound Peaches = $1.09

The price of 1 pound Pears = $1.19

Total pounds of apples bought = 3.18 pounds

price of 3.18 pounds of apple = ( pounds of apple bought)*(price of 1 pound apple)

=3.18*0.99

=$3.15    ...(i)

Total pounds of Peaches bought = 1.45 pounds

price of 1.45 pounds of peaches = 1.45*1.09

                                                 = $1.59    ...(ii)

Total pounds of Pears bought = 1.71 pounds

price of 1.71 pounds of pears = 1.71*1.19

                                                = $2.04     ...(iii)

Total bill = price of 3.18 pounds of apple + price of 1.45 pounds of peaches + price of 1.71 pounds of pears.

Substituting the values from equation (i),(ii)and (iii) we get ,

Total bill = $3.15 + $1.59 + $2.04  

= $6.78

Therefore , the total bill for 3.18 pounds of apples, 1.45 pounds of peaches, and 1.71 pounds of pears is $6.78  .

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The banker should invest $ 30,000 at 6 % interest rate to earn an interest of 3800 per year from both the investments.

Principal 1 = $ 50,000

Rate 1 = 4 %

Let principal 2 be x

Rate = 6 %

Time = 1 year

Interest = 3800

Using simple interest, we get that:

SI = p × r × t

3800 = ( 50,000 × 0.04 × 1) + ( x × 0.06 × 1)

3800 = 2000 + 0.06 x

0.06 x = 3800 - 2000

0.06 x = 1800

6 x = 180000

x = 180000 / 6

x = 30,000

Therefore, we get that, the banker should invest $ 30,000 at 6 % interest rate to earn an interest of 3800 per year from both the investments.

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The lateral area of the cone is 394 square inches

The formula for lateral area of a cone is expressed as;

Lateral area = πr √h² + r²

Given that;

Substitute the values into the formula

Lateral area = 3. 142(6) √20² + 6²

Lateral area = 18. 85 √436

Lateral area = 18. 85 × 20. 8

Lateral area = 394 square inches

Thus, the lateral area of the cone is 394 square inches

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Answer:

2 and 3 and y

Step-by-step explanation:

2x2x4x y x 1x2x3x3x3

-2x7x y x 2x3x z x3x3

2,290,000 in scientific notation is 2.29 x 10⁶.

Scientific notation is a way of expressing numbers that are too large or too small (usually would result in a long string of digits) to be conveniently written in decimal form. It may be referred to as scientific form or standard index form, or standard form in the United Kingdom. This base ten notation is commonly used by scientists, mathematicians, and engineers, in part because it can simplify certain arithmetic operations.

Converting a number in these cases means to either convert the number into scientific notation form, convert it back into decimal form or to change the exponent part of the equation.

Now the given number is,

2,290,000

To convert 2,290,000 into scientific notation, 2,290,000 must be converted into into decimal and multiples of 10.

So, factorizing 2,290,000 we get,

2,290,000 = 229 x 10,000

Now converting 10,000 into multiples of 10

Since, 10,000 = 10 x 10 x 10 x 10

So, 2,290,000 can be written as,

2,290,000 = 229 x 10 x 10 x 10 x 10

Multiplying and divide 229 by 100 we get,

2,290,000 = (229 x 100 x 10 x 10 x 10 x 10) / 100

Rearranging we get,

2,290,000 = (229 x 100) / 100 x (10 x 10 x 10 x 10)

Since, (229 x 100) / 100 = 2.29 x 100

2,290,000 = (2.29 x 100) x (10 x 10 x 10 x 10)

And 100 = 10 x 10

Therefore we get,

2,290,000 = 2.29 x 10 x 10 x 10 x 10 x 10 x 10

Since 10 x 10 x 10 x 10 x 10 x 10 = 10⁶

Therefore we get,

⇒ 2,290,000 = 2.29 x 10⁶

this is the required scientific notation of 2,290,000 .

Thus, 2,290,000 in scientific notation is 2.29 x 10⁶.

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In the given situation (A) the median is a good measure regardless of whether the outlier is included.

To find the median:

Therefore, in the given situation (A) the median is a good measure regardless of whether the outlier is included.

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The correct question is given below:

The following dataset represents the dollar amounts of donations collected at the entrance to a free museum for one hour.

(Refer to the table given below)

Is the median a reasonably good measure of central tendency for this dataset? What if the outlier were removed from consideration?

Select the correct answer below:

(A) The median is a good measure regardless of whether the outlier is included.

(B) The median is a very poor measure regardless of whether the outlier is included.

(C) The median is a good measure when the outlier is included, but it would be a very poor measure if the outlier were removed from consideration.

(D) The median is a very poor measure when the outlier is included, but it would be a good measure if the outlier were removed from consideration.