3. What's the difference between 126 1/4 and 78 2/3?
O A. 57 7/12
OB. 47 7/12
O C. 58 5/12
O D. 48 1/3

The ordered pairs are (0,8), (1, 7.5), (2, 7), (3,6.5), (4, 6) and (5, 5.5)

The given parameters are:

Initial height, h = 8 inches

Rate = 0.5 inches per hour

The height of the candle at x hour is:

y = Initial - rate * x

This gives

y = 8 - 0.5x

Set x  = 0 to 5

y = 8 - 0.5(0) = 8

y = 8 - 0.5(1) = 7.5

y = 8 - 0.5(2) = 7

y = 8 - 0.5(3) = 6.5

y = 8 - 0.5(4) = 6

y = 8 - 0.5(5) = 5.5

So, the ordered pairs are (0,8), (1, 7.5), (2, 7), (3,6.5), (4, 6) and (5, 5.5)

In (a), we have:

y = 8 - 0.5x

The above is a linear relation.

All linear relations are functions

Hence, the relation is a function.

We have

Initial height, h = 8 inches

New rate = 0.4 inches per hour

The height of the candle at x hour is:

y = Initial - rate * x

This gives

y = 8 - 0.4x

The above is a linear relation.

All linear relations are functions

Hence, the new relation is also a function.

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Answer:

The answer is 1/42 as you take reciprocal of 6=(1/6) and reciprocal of 7=(1/7) and multiply.

Answer:

[tex]\boxed {\frac{1}{42}}[/tex]

Step-by-step explanation:

Reciprocal of 6 : 1/6

Reciprocal of 7 : 1/7

Their product :

Answer:

1277

Step-by-step explanation:

350 * (1.04)^33 =

1276.93338385

algebracom

theo(12211)

Answer: 59

Step-by-step explanation:

The measure of an arc is equal to the measure of the central angle intercepted by it.

If we know that h(x) = (f ° g) (x) = √x + 5, then f(x) = x + 5 and g(x) = √x by applying the binary operation of composition between two functions.

Let be f and g two functions, h is a composition of f with respect to g when the input variable of f is equal to g.  The composed function is h(x) = √x + 5 and there may be more than a solution. One of these solutions are f(x) = x + 5 and g(x) = √x.

If we know that h(x) = (f ° g) (x) = √x + 5, then f(x) = x + 5 and g(x) = √x by applying the binary operation of composition between two functions.

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Answer: K

Step-by-step explanation:

The subtraction with the negatives can cancel out, resulting in a possible positive answer.

Answer:

k

Step-by-step explanation:

K      you CAN get a positive number....

        example  :

     -3   - (-5)   = -3 + 5 = + 2

The cost per unit for each product is given as:
x ≈ 0.0067; and

y ≈ 0.0041. See explanation below.

Given that the current production:

Current cost of production is given as:

Current Total Cost = 150y + 245x where;

if doubling the batch sizes will reduce the cost per unit by 50% then the new cost equation will be:

Thus, New Total Cost of production = (150 x 2) (y/2) + (245 x 2) (x/2)

= (300)(y/2) + (490) (x/2)

Since we are looking for the cost per unit of each product:

f(x) = 300 * (x/2)..........Unit cost of Model Gold

If we make x subject of the formula, then we arrive at:
1/300 = x/2
x = (1/300) * 2

x = 0.00666666666

x ≈ 0.0067

f(x) = 490* (x/2)

If we make y subject of the formula, then we arrive at:

i/490 = y/2

y = (1/490) * 2

y = 0.00408163265306122448979591836735

y ≈ 0.0041

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Answer:

78

Step-by-step explanation:

plug in -3 as x

6(2(-3)^2-5)

6(2(9)-5)

6(18-5)

6(13)

78

Answer:

The cosine function is f(t) = -30sin(π÷3)t + 20

Step-by-step explanation:

Given : The temperature of a chemical reaction ranges between −10 degrees Celsius and 50 degrees Celsius. The temperature is at its lowest point when t = 0, and the reaction completes 1 cycle during a 6-hour period.

To find : What is a cosine function that models this reaction?

General form of cosine function is f(x) = A cos(Bx)+C

Where A is the amplitude

B=2π÷Period

C is the midline    

Now, We have given

The temperature of a chemical reaction ranges between −10 degrees Celsius and 50 degrees Celsius.

A is the average of temperature,

i.e,

A=(-10-50)÷2 = -30

Period of 1 cycle is 6 hour

So,

B = 2π÷6 = π÷3

The temperature is at its lowest point when t = 0 and we know lowest point is -10

So,

f(t) = A cos t + C

-10 = -30 cos 0 + C

Therefore, C = 20

Substituting the values, we get

The cosine function is f(t) = -30sin(π÷3)t + 20

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[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex]\qquad \tt \rightarrow \: 6(3x - 7) = 2[/tex]

Step 1 -

[tex]\qquad \tt \rightarrow \: 18x - 42 = 2[/tex]

[ distributive property ]

Step 2 -

[tex]\qquad \tt \rightarrow \: 18x = 2 + 42[/tex]

[tex]\qquad \tt \rightarrow \: 18x = 44[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

d) Step 1: 18x - 42 = 2

Step 2: 18x = 44

Step-by-step explanation:

Given equation,

→ 6(3x - 7) = 2

Now the value of x will be,

→ 6(3x - 7) = 2

→ 6(3x) - 6(7) = 2

→ 18x - 42 = 2

→ 18x = 2 + 42

→ 18x = 44

→ x = 44/18

→ [ x = 22/9 ]

Hence, value of x is 22/9.

Answer:

[tex]11 - 2 {}^{3} [/tex]

[tex]11 - 8[/tex]

[tex]3[/tex]

Answer:

6

Step-by-step explanation:

I presume you meant

[tex]g(x) = \sqrt{x + 32} \\ g(32) = \sqrt{32 + 4} \\ g(32) = \sqrt{36} \\ g(32) = 6[/tex]

Answer:

Step-by-step explanation:

Answer:

First option.

Step-by-step explanation:

David will be 10 and John will be 9

Answer:

[tex] \cfrac{61}{24} [/tex]

Step-by-step explanation:

Given expression:

[tex] \cfrac{2}{3} + \bigg(\cfrac{5}{2} \bigg) {} ^{ 2} \times \cfrac{3}{10} [/tex]

Solution:

Simplify using PEMDAS.

[tex] = \sf \cfrac{2}{3} + \cfrac{25}{4} \times \cfrac{3}{10} \\ \\ = \cfrac{2}{3} + \cfrac{15}{8} \\ \\ = \cfrac{16 +45 }{24} \\ \\ = \boxed{\cfrac{61}{24} }[/tex]

Done!

Answer:

[tex]\frac{61}{24}[/tex]

Step-by-step explanation:

[tex]\frac{2}{3}[/tex] + ( [tex]\frac{5}{2}[/tex] )² × [tex]\frac{3}{10}[/tex] ← evaluate exponent

= [tex]\frac{2}{3}[/tex] + [tex]\frac{25}{4}[/tex] × [tex]\frac{3}{10}[/tex] ← evaluate multiplication ( cancel 25 and 10 by 5 )

= [tex]\frac{2}{3}[/tex] + [tex]\frac{5}{4}[/tex] × [tex]\frac{3}{2}[/tex]

= [tex]\frac{2}{3}[/tex] + [tex]\frac{15}{8}[/tex] ← evaluate addition

= [tex]\frac{2(8)}{3(8)}[/tex] + [tex]\frac{15(3)}{8(3)}[/tex]

= [tex]\frac{16}{24}[/tex] + [tex]\frac{45}{24}[/tex]

= [tex]\frac{61}{24}[/tex]

The expression in factored form for the polynomial of least possible degree graphed will be y(x) = (x + 3)(x + 2 )(x - 1 )(x - 3 )

From the graph, the zeros of the polynomial of given graph are:

x = -3

x = -2

x = 1

x = 3

Equate the above equations to zero

x + 3 = 0

x + 2 = 0

x - 1 = 0

x - 3 = 0

Multiply the equations

(x + 3)(x + 2 )(x - 1 )(x - 3 ) = 0

Express as a function gives;

y = (x + 3)(x + 2 )(x - 1 )(x - 3 )

Hence, the factored form of the polynomial will be y = (x + 3)(x + 2 )(x - 1 )(x - 3 )

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Answer:

franchise fast-food restaurant located in the Northeast specializing in halfpound hamburgers, fish sandwiches, and chicken sandwiches. Soft drinks and French fries are

also available. The planning department of Bun-and-Run Inc. reports that the distribution of

daily sales for restaurants follows the normal distribution and that the population standard

deviation is $3,000. A sample of 40 showed the mean daily sales to be $20,000. Find the 95%

confidence interval for the population mean.

Answer:

False, distributions having the same mean and standard deviation can have very different shape of distribution.

Answer:

0.98994949366117

√0.98 = 0.98994949366117

Step 1:

Divide the number (0.98) by 2 to get the first guess for the square root.

First guess = 0.98/2 = 0.49.

Step 2:

Divide 0.98 by the previous result. d = 0.98/0.49 = 2.

Average this value (d) with that of step 1: (2 + 0.49)/2 = 1.245 (new guess).

Error = new guess - previous value = 0.49 - 1.245 = 0.755.

0.755 > 0.01. As error > accuracy, we repeat this step again.

Step 3:

Divide 0.98 by the previous result. d = 0.98/1.245 = 0.7871485944.

Average this value (d) with that of step 2: (0.7871485944 + 1.245)/2 = 1.0160742972 (new guess).

Error = new guess - previous value = 1.245 - 1.0160742972 = 0.2289257028.

0.2289257028 > 0.01. As error > accuracy, we repeat this step again.

Step 4:

Divide 0.98 by the previous result. d = 0.98/1.0160742972 = 0.9644963982.

Average this value (d) with that of step 3: (0.9644963982 + 1.0160742972)/2 = 0.9902853477 (new guess).

Error = new guess - previous value = 1.0160742972 - 0.9902853477 = 0.0257889495.

0.0257889495 > 0.01. As error > accuracy, we repeat this step again.

Step 5:

Divide 0.98 by the previous result. d = 0.98/0.9902853477 = 0.9896137535.

Average this value (d) with that of step 4: (0.9896137535 + 0.9902853477)/2 = 0.9899495506 (new guess).

Error = new guess - previous value = 0.9902853477 - 0.9899495506 = 0.0003357971.

0.0003357971 <= 0.01. As error <= accuracy, we stop the iterations and use 0.9899495506 as the square root.

So, we can say that the square root of 0.98 is 0.989 with an error smaller than 0.01 (in fact the error is 0.0003357971). this means that the first 3 decimal places are correct. Just to compare, the returned value by using the javascript function 'Math.sqrt(0.98)' is 0.9899494936611666.

Note: There are other ways to calculate square roots. This is only one of them.

To round it to the tenths, it's 1

To round to the hundredths, it's.99

Thousandth is.990

Answer:

No, the total is 43.5 which is below 50.

Step-by-step explanation:

English: 25% × 48 = 12

Mathematics: 50% × 35 = 17.5

Typing: 5% × 80 = 4

Accounting 20% × 50 = 10

12 + 17.5 + 4 + 10 = 43.5

Total: 43.5

Passing: 50

Answer: No. The total is too low.

Answer:

Step-by-step explanation:The answer is 45

Answer:

[tex]x^{2}-\frac{3}{2} x-\frac{7}{16} =0[/tex]

Step-by-step explanation:

[tex]\begin{cases}\alpha -\beta =2\\ \alpha^{2} -\beta^{2} =3\end{cases}[/tex]

[tex]\Longleftrightarrow \begin{cases}\alpha -\beta =2&\\ \left( \alpha +\beta \right) \left( \alpha -\beta \right) =3&\end{cases}[/tex]

[tex]\Longleftrightarrow \begin{cases}\alpha -\beta =2&\\ \alpha +\beta =\frac{3}{2} &\end{cases}[/tex]

Then

2α = 2 + 3/2 = 7/2

2β = (3/2) - 2 = -1/2

Then

Then

α = 7/4

β = -1/4

Then

a quadratic equation with root α and β can be :

[tex]\left( x+\frac{1}{4} \right) \left( x-\frac{7}{4} \right) =0[/tex]

[tex]\Longrightarrow x^{2}-\frac{3}{2} x-\frac{7}{16} =0[/tex]

Based on the hints of distinguishing between radical and non-radical numbers, we have the following lists:

In this question we must order sets of numbers in ascending order. A hint consists in comparing non-radical numbers with the closest radical numbers whose results are integers.

In consequence, we obtain the following orders:

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Answer:

(2a-b)(3c-d)

Answer:

[tex] \frac{45}{55} = \frac{3}{11} [/tex]

Step-by-step explanation:

I think that is the right answer

Considering the given data-set, it's mean and the formula, the variance is of 870 lbs².

The variance of a data-set is given by the sum of the differences squared between each observation and the mean, divided by the number of values.

The mean is the sum of all observations divided by the number of observations, hence:

M = (145 + 175 + 180 + 205 + 120)/5 = 165.

And the variance, in lbs squared, is given by:

V = [(145-165)² + (175-165)² + (180-165)² + (205-165)² + (120-165)²]/5 = 870.

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The next step in the series is choice D.

Answer:

D

Step-by-step explanation:

if we define the diagrams in terms of their rows and columns, then

1st : 2 by 1

2nd : 3 by 2

3rd : 4 by 3

note that the rows and columns both increase by 1

then the next likely diagram is

5 by 4 , that is diagram D

Answer: d = 40 - 5/2t; 1995

Hope it helps :)