Lesson 4 Solving One Variable Equation


2. What value makes the equation 3b + 15 = – 26 – 20 true?

The Least Common Denominator of the fractions 5/8, 1/2, and 5/6 is 24.

The smallest number that can serve as a common denominator for a group of fractions is known as the least common denominator (LCD), also known as the lowest common denominator. The "smallest non-zero common number," a multiple of both numbers, is the least common multiple of two numbers.

Here, the given fractions are 5/8, 1/2, and 5/6.

So, we have to find the least common multiple of 8, 2, and 6 [Since they are the denominators of our given fractions].

8 = 2*2*2

2 = 2*1

6 = 2*3

So LCM of 8, 2, and 6 is 2*2*2*3 = 24

Therefore the Least Common Denominator of the fractions 5/8, 1/2, and 5/6 is 24.

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Answer:

0.7% of 77 = 0.54 0.7%

Step-by-step explanation:

hope this helps

Answer:

12 meters

Step-by-step explanation:

Given

[tex]Scale= 1cm:2m[/tex]

Required

Determine the measurement when the scale reads 6cm

Represent this scale with x;

Such that:

[tex]Scale = 6cm:x[/tex]

Equate

[tex]Scale= 1cm:2m[/tex] and [tex]Scale = 6cm:x[/tex]

[tex]1cm:2m = 6cm:x[/tex]

Express as fraction

[tex]\frac{1cm}{2m} = \frac{6cm}{x}[/tex]

Cross Multiply

[tex]x * 1cm = 6cm * 2m[/tex]

[tex]x * 1 = 6 * 2m[/tex]

[tex]x = 6 * 2m[/tex]

[tex]x = 12m[/tex]

Answer:

Hypothesis

Step-by-step explanation:

 a polygon has five sides Conclusion: it is a pentagon If a polygon has five sides, then it is a pentagon.

hope this helps

Answer:

[tex]y = \frac{1}{4}x +\frac{7}{4}[/tex]

Step-by-step explanation:

Given

[tex]f(-3) = 1[/tex]

[tex]f(13) = 5[/tex]

Required

Determine the linear function

A function is of the form:

[tex]y = f(x)[/tex]

Writing the given parameters in (x,y) format, we have:

[tex]f(-3) = 1[/tex] implies (-3,1)

[tex]f(13) = 5[/tex] implies (13,5)

So, the x and y values are:

(-3,1) and (13,5)

i.e.

[tex](x_1,y_1) = (-3,1)[/tex]

[tex](x_2,y_2) = (13,5)[/tex]

First, we need to determine the slope using:

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

[tex]m = \frac{5 - 1}{13 - -(3)}[/tex]

[tex]m = \frac{4}{13 +3}[/tex]

[tex]m = \frac{4}{16}[/tex]

[tex]m = \frac{1}{4}[/tex]

The equation is calculated as thus:

[tex]y - y_1 = m(x - x_1)[/tex]

Where

[tex](x_1,y_1) = (-3,1)[/tex]

[tex]m = \frac{1}{4}[/tex]

[tex]y - 1 = \frac{1}{4}(x - (-3))[/tex]

[tex]y - 1 = \frac{1}{4}(x +3)[/tex]

[tex]y = \frac{1}{4}(x +3) + 1[/tex]

[tex]y = \frac{1}{4}x +\frac{3}{4} + 1[/tex]

[tex]y = \frac{1}{4}x +\frac{3+4}{4}[/tex]

[tex]y = \frac{1}{4}x +\frac{7}{4}[/tex]

Answer:

1/2

Step-by-step explanation:

Answer:

Step-by-step explanation:

x-7=18 because x would be the number with "7 less"  being the "-7."

Answer:

the answer is 4.98

Step-by-step explanation:

you subtract 0.17 from 5.15 you will get 4.98

Answer:

d

Step-by-step explanation:

it would be 5 x 4/1 and u would get 20/1

- when dividing with a fraction u have to do keep, change, flip

or just plug it into a calculator :))

Answer:

D. 20

Step-by-step explanation:

5 / (1/4) =20

5/.25=20

Answer:

Step-by-step explanation:

Answer:

The age of pluto is:

5,560,000,000 years old = 5.56 × 10⁹ years old

x = 5.56

y = power of 9

Step-by-step explanation:

Pluto is 5,560,000,000 years old. Estimate the age of Pluto by writing it in the form of x×10y years, where x and y are single-digit numbers.

We write this in standard form or scientific notation.

5,560,000,000 years old = 5.56 × 10⁹ years old

x = 5.56

y = power of 9

Answer:

98 + 99 + 100 = 297

Step-by-step explanation:

Answer:

Decision rule  is  

Fail to reject the null hypothesis

 The conclusion is  

There is sufficient evidence that indicate that there is a significant difference between the two treatments

Step-by-step explanation:

From the question we are told that  

    The sample size is  n =  12

    The first  mean is  [tex]M_1  =  55[/tex]

    The variance is  [tex]s^2_1 =  8[/tex]

    The second mean is  [tex]M_2  =  52[/tex]

     The second variance is [tex]s^2_2 =  4[/tex]

Let the level of significance be  [tex]\alpha  =  0.05[/tex]

The null hypothesis is  [tex]H_o  :  M_1 = M_2[/tex]

The alternative hypothesis is [tex]H_a  :  M_1 \ne M_2[/tex]

  Generally the test statistics is mathematically

     [tex]t = \frac{M_1 - M_2 }{ \sqrt{\frac{s_1^2}{n_1} +\frac{s_2^2}{n_2}} }[/tex]

=>   [tex]t = \frac{55 - 52 }{ \sqrt{\frac{8}{12} +\frac{4}{12 }} }[/tex]

=>   [tex]t = 1.1619 [/tex]

Generally the degree of freedom is mathematically represented as

      [tex]df = 12 -1[/tex]

=>    [tex]df = 11 [/tex]

Generally  from the t- distriibution table the critical  value  of  [tex]\alpha[/tex] at a degree of freedom of [tex]df = 11 [/tex]  is

    [tex]t_{0.05 , 11} =  2.20098516[/tex]

Here given that the critical value is greater than the t statistics value the

Decision rule  is  

Fail to reject the null hypothesis

 The conclusion is  

There is sufficient evidence that indicate that there is a significant difference between the two treatments

Answer:

x=3

Step-by-step explanation:

Hope this helps u..

Answer:

The 3 in the tens place is worth 10 times the 3 in the ones places.

Step-by-step explanation:

Have a great day :)

Answer:

75  14  12,600  781  128  399  26.13  40.80    12,750

Step-by-step explanation:

Hope this helps

Answer:

7. 100

8. 14

9. 12600

10. 639

11. 128

12. 399

13. Discount price= 12.87 Sale price= 26.13

14. 40.80

15. 12,750

I'm not 100% on #15 but the rest are good.

Step-by-step explanation: When you multiply the percent by the other number that gives you the difference. So then get the original number and either add or subtract the difference from the original number to get your answer. Add if increase Subtract if decrease.

So 7-11 you just have to multiply the percent by the other number.

7. 25*300% or 25*3 = 75  25 + 75 = 100

8. 56*.75 = 42  56-42= 14

9. 12000*.05 = 600 (since it is an increase add 600 to 12000) = 12600

10. 710*.10= 71 (71 is the difference so do this) 710-71= 639

11. 160*.20 = 32 (decrease) 160-32= 128

12. 380*.05=19 (increase) 380+19 = 399

13. 39*.33= 12.87 (decrease)

Discount price = 12.87

Sale price= 39-12.87= 26.13

14. 48*.15 = 7.20 (decrease) 48-7.20= 40.80

15. 3,000*3.25 = 9750 (increase) 9750 + 3000= 12,750

Answer:

12 only

Step-by-step explanation:

It means x is zero, and the only point on x=0 is 12 :)

According to the graph the function  f(0) is  12 only .

The x-intercept is the point where a line crosses the x-axis or at y = 0, and the y-intercept is the point where a line crosses the y-axis or at x =0.

According to the question

The graph shows the function in which

f(0) is

i.e

x = 0  or y intercept

Now, according to the graph

at x = 0 , y = 12

Or

f(0) = 12

Hence, The function  f(0) is  12 only .

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Step-by-step explanation

x=-1

x=4

f(x)= x^3+5x^2

Answer:

a

  [tex]P(a | e') =  0.22[/tex]

  [tex]P(b | e') =  0.28[/tex]

  [tex]P(c | e') =  0.33[/tex]

b

  [tex]P(a | e' , d' , b') = 0.57  [/tex]

Step-by-step explanation:

From the question we are told that

   The probabilities are

Supplier  chosen            A                     B                    C            

Probability                P(a) = 0.20       P(b) =  0.25   P(c) =  0.15      

                                       D                      E

                                P(d) =  0.30     P(e) = 0.10

Generally the new probability of companies A being chosen as the sole supplier this year given that supplier E goes out of business is mathematically represented as below according to Bayes theorem

[tex]P(a | e') =  \frac{P (a \  and \  e')}{P(e')}[/tex]

      [tex]P(a | e') =  \frac{P (a)}{P(e')}[/tex]

     [tex]P(a | e') =  \frac{P (a)}{1- P(e)}[/tex]

=>   [tex]P(a | e') =  \frac{ 0.20}{1- 0.10}[/tex]

=>   [tex]P(a | e') =  0.22[/tex]

Generally the new probability of companies B  being chosen as the sole supplier this year given that supplier E goes out of business is mathematically represented as below according to Bayes theorem

[tex]P(b | e') =  \frac{P (b \  and \  e')}{P(e')}[/tex]

      [tex]P(b | e') =  \frac{P (b)}{P(e')}[/tex]

     [tex]P(b | e') =  \frac{P (b)}{1- P(e)}[/tex]

=>   [tex]P(b | e') =  \frac{ 0.25}{1- 0.10}[/tex]

=>   [tex]P(b | e') =  0.28[/tex]

Generally the new probability of companies C  being chosen as the sole supplier this year given that supplier E goes out of business is mathematically represented as below according to Bayes theorem

[tex]P(c | e') =  \frac{P (c \  and \  e')}{P(e')}[/tex]

      [tex]P(c | e') =  \frac{P (c)}{P(e')}[/tex]

     [tex]P(c | e') =  \frac{P (c)}{1- P(e)}[/tex]

=>   [tex]P(c | e') =  \frac{ 0.15}{1- 0.10}[/tex]

=>   [tex]P(c | e') =  0.17[/tex]

Generally the new probability of companies D  being chosen as the sole supplier this year given that supplier E goes out of business is mathematically represented as below according to Bayes theorem

[tex]P(d | e') =  \frac{P (d \  and \  e')}{P(e')}[/tex]

      [tex]P(d | e') =  \frac{P (d)}{P(e')}[/tex]

     [tex]P(d | e') =  \frac{P (d)}{1- P(e)}[/tex]

=>   [tex]P(d | e') =  \frac{ 0.30}{1- 0.10}[/tex]

=>   [tex]P(c | e') =  0.33[/tex]

Generally the probability that  B, D , E  are not chosen this year is mathematically represented as

      [tex]P(N) =  1 - [P(e) +P(b) + P(d) ][/tex]

=>       [tex]P(N) =  1 - [0.10 +0.25  +0.30 ][/tex]

=>       [tex]P(N) =  0.35[/tex]

Generally the probability that A is chosen given that E , D , B  are rejected this year is mathematically represented  as

      [tex]P(a | e' , d' , b') =  \frac{P(a)}{P(N)}[/tex]

=>     [tex]P(a | e' , d' , b') =  \frac{0.20 }{0.35 }[/tex]    

=>     [tex]P(a | e' , d' , b') = 0.57  [/tex]

Answer:

They are called powers of ten

Step-by-step explanation:

Answer:

The decision rule is

Fail to reject the null hypothesis

The conclusion is  

There is no sufficient evidence to conclude that the mean CPA of all students who vote is lower than the CPA of students who do not vote

Step-by-step explanation:

From the question we are told that

       The first sample size  is  [tex]n_1 =  114[/tex]

       The sample mean is  [tex]\= x_1 =  2.71[/tex]

       The standard deviation is  [tex]s_1 =  0.64[/tex]

      The second sample size is   [tex]n_2 =  123 [/tex]

      The sample mean is   [tex]\= x_2 =  2.79[/tex]

      The level of significance is  [tex]\alpha  =  0.05[/tex]

      The standard deviation is   [tex]s_2 =  0.56 [/tex]

The null hypothesis is  [tex]H_o  :  \mu_1 = \mu _2[/tex]

The alternative hypothesis is  [tex]H_a :  \mu_1 <  \mu_2[/tex]

Generally the test hypothesis is mathematically represented as

      [tex]t =  \frac{\= x_1 - \= x_2}{ \sqrt{ \frac{s_1^2 }{n_1} + \frac{s_2^2}{n_2}  } }[/tex]

=> [tex]t =  \frac{2.71 - 2.79}{ \sqrt{ \frac{0.64^2 }{ 114} + \frac{0.56^2}{123}  } }[/tex]

=> [tex]t =  -1.01 [/tex]

Generally given that variance are not equal (the standard deviation  squared of both population are not equal ) the degree of freedom  is mathematically represented as

[tex]df  =  \frac{[\frac{s_1^2}{n_1 } + \frac{s_2^2}{n_2}  ]}{\frac{[\frac{s_1^2}{n_1}]^2 }{n_1 - 1} + \frac{[\frac{s_2^2}{n_2}]^2 }{n_2 - 1}}[/tex]

=>  [tex]df  =  \frac{[\frac{0.64^2}{114} + \frac{0.56^2}{123}  ]}{\frac{[\frac{0.64^2}{114}]^2 }{114 - 1} + \frac{[\frac{0.56^2}{123}]^2 }{123 - 1}}[/tex]

=>  [tex]df  =  225[/tex]

Generally from the t distribution table the the probability of  (t < -1.01) at a degree of freedom of [tex]df  =  225[/tex]is  

      [tex] p-value  = P(t <  -1.01 ) =  0.15679[/tex]

Generally the value obtained we see that  [tex]p-value  > \alpha[/tex] so

The decision rule is

Fail to reject the null hypothesis

The conclusion is  

There is no sufficient evidence to conclude that the mean CPA of all students who vote is lower than the CPA of students who do not vote

Answer:

c  5x -15y =1

Step-by-step explanation:

5x-15y=1

-5x -15y= 1 -5x     change the signs on both sides of the equation

     15y = -1 +5x      divide both sides by 15

         y = -1/15 + 1/3 x    Reorder the terms

         y = 3x-15

              :)

All options are wrong here.

Given equation is  [tex]y=3x-15[/tex].

the equation given here is in form of [tex]y=mx+c[/tex] . The general equation of any straight line where m is the gradient of the line (how steep the line is) and c is the y -intercept (the point in which the line crosses the y -axis) .

We have to write [tex]y=3x-15 \\[/tex] in standard form.

The standard form for linear equations in two variables is Ax+By=C.

Now we convert [tex]y=3x-15[/tex] in standard form.

Here [tex]y=3x-15\\[/tex]

[tex]y-3x=-15\\\\-y+3x=15[/tex]

[tex]3x-y=15[/tex]

But no options match with the above standard form of equation.

Hence all options are wrong here.

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Answer:

C

Step-by-step explanation:

 [tex]\bold{Hello!}\\\bold{Your~Answer~Is~Below!}[/tex]

______________________________

 [tex]\bold{Solutions~Steps:}[/tex]

[tex]1.)~Simplify~everything~into~decimal~form:[/tex]

[tex]2.)~Round~to~the~nearest~hundredth :[/tex]

[tex]3.)~Order~them~in~decreasing~order,~(Greatest~to~Least:)[/tex]

______________________________

 [tex]\bold{Answer:}[/tex]

______________________________

 [tex]\bold{Hope~this~helps,}\\\bold{And~best~of~luck!}\\\\\bold{~~~~~-TotallyNotTrillex}[/tex]

Answer:

hehaw

Step-by-step explanation:

0.19, 91 hundredths, then the equation

Answer:

-1.4

Step-by-step explanation:

opposite of -1.4 = 1.4

opposite of the opposite of -1.4 = the opposite of 1.4 = -1.4

Answer:

The square root of 16=4, 4x2=8, x2=8.

Step-by-step explanation:

Answer:

there is no solution for this equation