MP Reason Inductively A student said you
can add the same number to both terms of
a ratio to find an equivalent ratio. Is the
student correct? Explain why or why not.

Answer:

x = 27

Step-by-step explanation:

You need to cube each side.

[tex]\sqrt[3]{x} ^{3}[/tex] = [tex]3^{3}[/tex]

x = 27

Answer:

41.61

Step-by-step explanation:

Just divide.

[tex]\begin{matrix}4\overline{|\smallspace166.44}\:\:\:\:\:\:\:\end{matrix}[/tex]

Answer: We have the equation:

166.44 ÷ 4 = 41.610

Calculated to 3 decimal places.

 0 4 1. 6 1 0

4 1 6 6. 4 4 0

− 0          

 1 6        

− 1 6        

   0 6      

 −   4      

     2 4    

   − 2 4    

       0 4  

     −   4  

         0 0

       −   0

           0

Step-by-step explanation: hope this helps

Simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.

Exact Form: 10√21 where t = 10 and u =21

Answer:

63 crayons are broken

Step-by-step explanation:

84 ÷ 4 = 21

21 x 3 = 63

can be checked by 84 - 63 = 21

a. The formula solved for t is t = I/Pr

b. The value of t in the table is 3 years

From the question, we are to solve for t in the given formula

The given formula is the formula for simple interest

I = Prt

To solve for t, we will divide both sides of the equation by Pr

That is,

I/Pr = Prt/Pr

I/Pr = t

∴ t = I/Pr

The formula solved for t is t = I/Pr

b. We are to find the value of t when

I = $75

P = $500

r = 5% = 0.05

From

t = I/Pr

t = 75/(500×0.05)

t = 75/25

t = 3 years

Hence, the value of t in the table is 3 years

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Answer:

12, 3/5, 25%, -1/12, -0.17

Step-by-step explanation:

The simplest way to do this is to convert all of the numbers into either a fraction, decimal, or a percentage. In my opinion, it is easier to use a percentage here.

25% is already a percentage

-0.17 = -17%

3/5 = 60%

-1/12 (you can use a calculator to divide and find the percentage here) = -8.33

12 = 1200%

Now that the rational numbers are all in the same unit, it is easier to sort them. In the end, we get this list (from greatest to least):

12, 3/5, 25%, -1/12, -0.17

FINAL ANSWER: 12, 3/5, 25%, -1/12, -0.17

Answer:

91/7=13

so x=11×13

x=143

The interquartile range of the players' weights = 48 pounds.

The boxplot attached to this question is missing. It was obtained online and is attached to this solution of the question.

It should be noted that the following is true for a boxplot.

A box plot gives a visual representation of the distribution of the data, showing where most values lie and those values that greatly differ from the rest, called outliers.

The elements of the box plot are described thus;

The bottom side of the box represents the first quartile, and the top side, the third quartile. Therefore, the width of the central box represents the inter-quartile range.

The horizontal line inside the box is the median.

The lines extending from the box reach out to the minimum and the maximum values in the data set, as long as these values are not outliers. The ends of the whiskers are marked by two shorter horizontal lines.

Variables in the dataset, higher than Q3+(1.5×IQR) or lower than Q1-(1.5×IQR) are considered outliers and are usually shown using dots above the top whisker or below the bottom whisker.

So, it is evident that for this question,

First quartile = 174 pounds

Third quartile = 222 pounds

Inter Quartile Range = (Third quartile) - (First quartile)

= 222 - 174

= 48 pounds.

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The amount of fruit in the smoothie will be 3/2 .

It is given in the question that a smoothie calls for 4/6 of a peach, 1/2 of a banana, and 2/6 of a kiwi.

We have to find the amount of fruit in the smoothie.

We know that,

Amount of fruit in the smoothie = Amount of peach in the smoothie +  Amount of banana in the smoothie +  Amount of kiwi in the smoothie

Hence,

Amount of fruit in the smoothie = 4/6 + 1/2 + 2/6

Adding all the fractions, we get,

4/6 + 3/6 + 2/6 = 9/6 = 3/2

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Answer: -15x+30

Step-by-step explanation:

-3(5x-10)=

-3*5x-10(-3)=

-15x-(-30)=-15x+30

Answer:

-15x-30

Step-by-step explanation:

Just multiply -3 by 5 in 5x and get -15 and then put x back with -15. thhen multiply -3 by 10 and get -30

Answer :                                                                                                              500,000                                                                                                                       450,000                                                                                                                        453,000                                                                                                                                       452,900                                                                                                                                         452,910                                                                                                                                                                                                                                                                                step-by-step explanation:

look to the right one digit of the place they are asking to round . if it is either greater than or equal to5, then you round up the place they want. if it is not, then it says the same. then all he number to right of it becomes 0s.

So the percentage would be 9500/15000 = 63.333333333... = 63.3...%

10 m/s can be expressed as 36km/h.

Here, we are given an expression for speed, that is: 10 meter per second.

Now, as per the rules of mathematics,

1 kilometer = 1000 meters

⇒ 1 meter = 1/1000 kilometers

or 1 meter = 0.001 kilometers

and also, 1 hour = 60 mins

and 1 min = 60 seconds

⇒ 60 mins = 60 × 60 seconds

= 3600 seconds

Thus, 1 hour = 60 mins = 3600 seconds

⇒ 1 second = 1/3600 hours

Now, we need to convert meter per second into kilometer per hour,

1 meter/ 1 second =  [tex]\frac{0.001}{\frac{1}{3600} }[/tex]

= (0.001 × 3600)/ 1

= 3.6

This 1 meter per second = 3.6 kilometer per hour

⇒ 10 meter per second = 3.6 × 10 = 36 kilometers per hour

Thus, 10 m/s is 36km/h.

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Answer:

Step-by-step explanation:

The angles lie on a straight line summing to total 180 degrees.

Form an equation:

m∠1 + m∠2 = 180

2x + x + 72 = 180

and solve:

3x + 72 = 180

3x = 180 - 72

3x = 108

x = 36

Answer:

see below

Step-by-step explanation:

We are here given a straight line which is splitted into two parts by a line , such that it makes two angles.

Also we know that the angle measure of a straight line is 180° . Therefore; here the sum of angles 1 and 2 will be 180° .

So that,

==> angle 1 + angle 2 = 180°

==> 2x + x + 72° = 180°

==> 3x = 180° - 72°

==> 3x = 108°

==> x = 108°/3

==> x = 36° .

The equation which we used to solve the problem is ,

==> Equation = 2x + x + 72° = 180°

For finding the individual angels substitute the value of x into their expressions , as ;

==> angle 1 = 2x = 2(36°) = 72°

==> angle 3 = x + 72° = 36° + 72° = 108° .

And we are done!

The solution of the given equation are (1/2 , 17/2) and (-3 , 12)

The two equation that we have been given are :

    y = 9 – x            (1)

    y = 2x² + 4x + 6       (2)

We will solve this simultaneously, from equation (1) we will equate the value of y in equation (2) we get

       9 – x = 2x² + 4x + 6

        3 = 2x² + 5x

2x² + 5x – 3 = 0

Now to find the factors of the value x we will use quadratic formula.

   x = (-b±√b² – 4ac)/2a

   x = [ -5 ± √25 + 24 ]/4

   x = [ -5 ± 7 ]/4

x = (-5 + 7)/4              and                 x = (-5 – 7)/4

x = 1/2     and    x= -3

putting the required value of x in equation (1) we get

y = 9 – 1/2            and             y = 9 – (-3)

y = 17/2      and    y = 12

Hence the solution of the equation is (1/2 , 17/2) and (-3 , 12)

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The results of the equations are listed below:

In this problem we must make use of given formulas and substitute all known variables to determine all the required information:

Case 1

The temperature in Celsius scale in terms of the temperature in Fahrenheit scale is defined by the following formula:

T' = (5 / 9) · (T - 32)

T' = (5 / 9) · (68 - 32)

T' = 20 °C

Case 2

The area of the circle in terms of its radius is presented below:

A = π · r²

A = π · (6 m)²

A ≈ 113.097 m²

Case 3

The area of the triangle as a function of its base and its height is shown in the following formula:

A = 0.5 · b · h

A = 0.5 · (8 ft) · (25 ft)

A = 100 ft²

Case 4

The traveled distance is the product of the velocity and time:

s = v · t

s = (62.5 mi / h) · (5 h)

s = 312.5 mi

Case 5

The simple interest formula is equal to the product of the invested amount, interest rate and time divided by 100:

C' = (C · r · t) / 100

C' = [(300) · (5) · (8)] / 100

C' = $ 120

Case 6

C' = (C · r · t) / 100

C' = [(200) · (2) · (10)] / 100

C' = $ 40

Case 7

s = v · t

s = (45 mi / h) · (0.5 h)

s = 27.5 mi

Case 8

T' = (5 / 9) · (T - 32)

T' = (5 / 9) · (212 - 32)

T' = 100 °C

Case 9

C' = (C · r · t) / 100

C' = [(1200) · (2.5) · (2)] / 100

C' = $ 60

Case 10

The area of the rectangle is equal to the product of its base and its height:

A = b · h

A = (14 ft) · (8 ft)

A = 112 ft²

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Answer:

173, 339.10

Step-by-step explanation:

Move the decimal from 157,581.00 to the left to give you 10% of 15,758.10.

Add 15,758.10 to 157,581.00 to give you the total from last month.

Or, convert 10% to a decimal.

157,781 x 0.10 = 15,758.10

15,758.10 + 157,581 = 173,339.10

Answer:

C. integers

Step-by-step explanation:

integers are similar to whole numbers : all numbers without any fractional part, but including negative numbers.

whole numbers only include positive numbers (incl. 0) without any fractional part.

natural numbers (I guess, that is the meaning of "counting numbers") are all positive numbers (but without 0) without any fractional part.

so, C is correct, because A contains also -1.

Answer:

B

Step-by-step explanation:

it cat be a whole number because whole number are set of positive number from 0 and above excluding fraction , negative integer or decimal.

integers include both positive and negative numbers excluding fraction and decimal

Answer: 25=0.011x+13

The two vectors and a vector and a scalar which shows that H is not a subspace of [tex]R^2[/tex] are [tex]\bold{\left[\begin{array}{c}\frac{1}{5} \\\frac{1}{4} \end{array}\right]}[/tex] , [tex]\bold{\left[\begin{array}{c}\frac{1}{6} \\\frac{1}{7} \end{array}\right]}[/tex]  and [tex]\left[\begin{array}{c}\frac{1}{6} \\\frac{1}{3} \end{array}\right][/tex] and 6.

Given the set, [tex]H=\{\left[\begin{array}{c}x\\y\end{array}\right] :8x^2+5y^2\leq 1\}[/tex] which represents the set of points on and inside an ellipse in the xy-plane.

We have to show that H is not a subspace.

We can show that this set is not closed under vector addition of two vectors by finding those vectors.

[tex]\left[\begin{array}{c}\frac{1}{5} \\\frac{1}{4} \end{array}\right][/tex] and [tex]\left[\begin{array}{c}\frac{1}{6} \\\frac{1}{7} \end{array}\right][/tex] are two vectors in H, since it satisfies the given condition, [tex]8x^2+5y^2\leq 1[/tex].

i.e., [tex]8\times(\frac{1}{5})^2 + 5\times (\frac{1}{4})^2 = 0.6325\leq 1[/tex] and [tex]8\times(\frac{1}{6})^2 + 5\times (\frac{1}{7})^2 = 0.3242\leq 1[/tex]

[tex]\left[\begin{array}{c}\frac{1}{5} \\\frac{1}{4} \end{array}\right][/tex] + [tex]\left[\begin{array}{c}\frac{1}{6} \\\frac{1}{7} \end{array}\right][/tex] = [tex]\left[\begin{array}{c}\frac{11}{30} \\\frac{11}{28} \end{array}\right][/tex]

But  [tex]8\times(\frac{11}{30})^2 + 5\times (\frac{11}{28})^2 =1.847 \geq 1[/tex]

So the vector  [tex]\left[\begin{array}{c}\frac{11}{30} \\\frac{11}{28} \end{array}\right][/tex] does not belongs to H.

So It is not closed under addition.

Now we will prove that H is not closed under scalar multiplication of a vector and a scalar either.

[tex]\left[\begin{array}{c}\frac{1}{6} \\\frac{1}{3} \end{array}\right][/tex] is a vector in H. But [tex]6\left[\begin{array}{c}\frac{1}{6} \\\frac{1}{3} \end{array}\right][/tex] does not belongs to H, where 6 is a scalar.

This is because [tex]6\left[\begin{array}{c}\frac{1}{6} \\\frac{1}{3} \end{array}\right][/tex]  = [tex]\left[\begin{array}{c}1 \\2 \end{array}\right][/tex] and  [tex]8\times1^2 + 5\times 2^2 =28 \geq 1[/tex].

So the two vectors are [tex]\bold{\left[\begin{array}{c}\frac{1}{5} \\\frac{1}{4} \end{array}\right]}[/tex] and [tex]\bold{\left[\begin{array}{c}\frac{1}{6} \\\frac{1}{7} \end{array}\right]}[/tex]  and one vector and a scalar are [tex]\left[\begin{array}{c}\frac{1}{6} \\\frac{1}{3} \end{array}\right][/tex] and 6.

The question is incomplete. Find the complete question below:

Let  [tex]H=\{\left[\begin{array}{c}x\\y\end{array}\right] :8x^2+5y^2\leq 1\}[/tex], which represents the set of points on and inside an in the xy-plane. Find two specific examples two vectors, and a vector and a scalar to show that H is not a subspace of  [tex]R^2[/tex].

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The branch of statistics that uses sample statistics to estimate a population parameter or test a hypothesis about such a parameter is best referred to as inferential statistics.

Therefore, the branch of statistics that uses sample statistics to estimate a population parameter or test a hypothesis about such a parameter is best referred to as inferential statistics.

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our ordered pair is ( 2 , 1/2).

What is linear equations in two variables?

Let's first move the y's to the left side in the first equation.

4x - y  = 3y + 7

4x - 4y = 7

Dividing both sides by 4,

x - y  = 7/4

Our other equation is

x + 8y = 4

Subtracting the first equation from the second, we get

 9y = 9/4

   y = 1/4

We plug this into one of the equations

  x + 2 = 4

   x =  2

So our ordered pair is ( 2 , 1/2)

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Answer:

(2/3)^4 = 2^4/3^4

(2/3)^1 = 2/3

(-3/4)^0 = 1

(-0.4)^8/(-0.4)^4 = (-0.4)^4

Step-by-step explanation:

(2/3)^4 = 2^4/3^4

(2/3)^1 = 2/3

(-3/4)^0 = 1

(-0.4)^8/(-0.4)^4 = (-0.4)^4

Answer:

-2(7+2n) +4 = 5

step by step explantation:

-2(7-n) +4

-2×7 =-14

-2x-n = 2n

14+2n = 4

2n = 14 - 4

2n/ 2= 10/2

n= 5

The number can be -3, -2, -1, 0 ,1

Here, we are given that twice a number is increased by three and the result is between negative three and seven.

Let the number be x

Twice of the number = 2x

Four more than twice the number = 2x + 4

This number is between -3, 7

⇒ -3 < 2x +4 < 7

subtracting 4 from both sides we get

-3 -4 < 2x < 7 - 4

-7 < 2x < 3

Dividing both sides by 2 we get

-7/2 < x < 3/2

- 3.5 < x < 1.5

Thus the original number lies between -3.5 and 1.5

This means that it can take 5 values-

-3, -2, -1, 0 ,1

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The buffer will probably be destroyed by the addition of HCN.

A weak acid and the conjugate base of the weak acid, or a weak base and the conjugate acid of the weak base, are combined to form the buffer solution, a water-based solvent solution. They withstand being diluted or having modest amounts of acid or alkali added to them without changing their pH.

Given that a 1.0 l buffer solution is 0.15 m in HCN and 0.10 m in NaCN.

We need to find a action which one destroy the buffer solution.

A buffer is a substance made of salt and a weak acid that is beneficial. From the aforementioned chemicals, HCN is a potent acid and NaCN is a salt between HF and NaCN. Therefore, the buffer will probably be destroyed by the addition of HCN.

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Ricky had 176 cookies initially

Let Ricky has x number of cookies

Cookies left after he ate 1/8 of his cookies and additional 14 cookies:

x - (1/8x + 14)

Cookies left after he ate 3/10 of the remaining cookies and an additional 24 cookies on Saturday:

x - (1/8x + 14) - 3/10(x - (1/8x + 14)) + 24)

Cookies left after he ate 40 more cookies on Sunday

x - (1/8x + 14) - 3/10(x - (1/8x + 14)) + 24) - 40 ------(1)

Cookies left with him at the end = 34

Therefore, equating equation (1) with 34

(7/10)((7x/8) - 14) - 64 = 34

x = 176

Thus Ricky had 176 cookies intially

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Answer:

square of the following

2×2=4

3×3=9

4×4=16

2×2×2=8

now

square root

√4

√2×2

=2 answer likewise other

again

cube root

√8

=√2×2×2

=2 through that you can find these

at first you should know square and cube of different numbers from 1 to 20 is the required you should know then you can easily find out answer

Answer:

Piecewise

Step-by-step explanation:

It is basically made up of 2 linear functions