How do you do this question?

Answer:

[tex]x<-\frac{1}{2}\text{ or } x>1[/tex]

Step-by-step explanation:

So we have the equation:

[tex]|-4x+1|>3[/tex]

First, note that since the sign is greater than, this is an or inequality (not an "and" inequality). This is the student's first mistake.

So, let's solve this inequality.

Case 1:

[tex]-4x+1>3[/tex]

Subtract 1 from both sides:

[tex]-4x>2[/tex]

Divide both sides by -4:

[tex]x<-\frac{1}{2}[/tex]

The student did not flip the sign when doing this step, hence the incorrect answer.

You correctly spotted the student's mistake. Nicely done!

Case 2:

[tex]-4x+1<-3[/tex]

This is what you're missing: for this second instance, we must flip the sign to less than right away. This is because we are essentially multiplying the 3 by a negative. So, we must flip the sign in order to be correct.

Now solve. Subtract 1 from both sides:

[tex]-4x<-4[/tex]

Divide both sides by -4. Since we're dividing by a negative, flip the sign:

[tex]x>1[/tex]

So, our solutions are:

[tex]x<-\frac{1}{2}, x>1[/tex]

As mentioned previously, this is an or inequality. Therefore, our final answer is:

[tex]x<-\frac{1}{2}\text{ or } x>1[/tex]

Edit: Improved Answer

Answer:

<8 and <6 are congruent to each other.

Step-by-step explanation:

A protractor was used to determine the answer.  They both measured to 140 degrees.  

Step-by-step explanation:

Mile Per Hour to Foot Per Second Conversion Table

Miles Per Hour Feet Per Second

16 mph 23.47 ft/s

17 mph 24.93 ft/s

18 mph 26.4 ft/s

19 mph 27.87 ft/s

(h + k)(2) = 5

(h - k)(3) = 9

evaluate 3h(2) + 2k(3) = 17

The composition of functions is solved

a) ( h + k ) ( 2 ) = 5

b) ( h - k ) ( 3 ) = 9

c) 3h ( 2 ) + 2k ( 3 ) = 17

Evaluation of a function at the value of another function is known as Composition of function. A function composition is a process in which two functions, f and g, form a new function, h, in such a way that h(x) = g(f(x)). This signifies that function g is being applied to the function x. So, in essence, a function is applied to the output of another function.

Given data ,

Let the first function be represented as f ( x )

Now , the value of f ( x ) is

h ( x ) = x² + 1

Let the second function be represented as g ( x )

Now , the value of g ( x ) is

k ( x ) = x - 2

Now , the composition of function is

To calculate (h+k)(2), we substitute x = 2 in both h(x) and k(x), add them together and simplify:

h(2) = 2² + 1 = 5

k(2) = 2 - 2 = 0

(h+k)(2) = h(2) + k(2) = 5 + 0 = 5

To calculate (h-k)(3), we substitute x = 3 in both h(x) and k(x), subtract k(x) from h(x), and simplify:

h(3) = 3² + 1 = 10

k(3) = 3 - 2 = 1

(h-k)(3) = h(3) - k(3) = 10 - 1 = 9

To evaluate 3h(2)+2k(3), we substitute x = 2 and x = 3 in h(x) and k(x), respectively, and simplify:

3h(2) + 2k(3) = 3(5) + 2(3-2) = 15 + 2 = 17

Therefore , ( h + k ) ( 2 ) = 5 , ( h - k ) ( 3 ) = 9, and 3h( 2 ) + 2k( 3 ) = 17

Hence , the composition of functions is solved

To learn more about composition of functions click :

https://brainly.com/question/17673639

#SPJ5

Answer:

The answer is 3

Step-by-step explanation:

Answer:

Calculated t=  0.011659

t ≥ t ( 0.025,11) = 2.201

So the null hypothesis is accepted.

Step-by-step explanation:

Student     Math      Writing            Difference                            d²

                                             math score − writing score

1                 540          474               66                                      4356

2                432         380                52                                      2704

3               528           463              65                                       4225

4               574             612             -38                                  1444

5               448            414              34                                    1156

6               502            526            -24                                   576

7               480            430              50                                 2500

8              499            453             46                                    2116

9              610             615             -5                                       25

10             572             541             31                                      961

11              390             335            55                                  3025

12             593             613          -20                                     400            

∑              6168          5856          312                                     23488                

1) We state our null and alternative hypothesis as

H0: ud= 0                   Ha: ud≠0

2) The significance level alpha is set at α= 0.05

3) The test statistic under H0 is

t= d`/ sd/√n

which has t distribution with n-1 degrees of freedom.

4) The critical region is t ≥ t ( 0.025,11) = 2.201

5) Computations

d`= ∑di/n= 312/12= 31.2

Variance = ∑(di- d`)²/n-1= 1/n-1 [ ∑di²-( ∑di)²/n]

= 1/11[ 23488- (312)²/12]

= 1/11[ 23488- 8112] = 1/11[15376]= 5976.7272

Standard Deviation= √ 5976.7272= 77.2510= 77.25

Now t= 3.12/77.25/√12= 0.011659

The calculated t value= 0.011659 falls in the acceptance region . So we accept our null hypothesis  and reject the alternative hypothesis.

Answer:

15.05

Step-by-step explanation:

8.6 is 100% of 8.6.

To increase it by 75%, you'll end up with 175% of 8.6

175% of 8.6 =

= 1.75 * 8.6

= 15.05

Answer:

  22

Step-by-step explanation:

In order to get one of the answer choices, it appears we need to interpret your input as ...

  [tex](q^{16}q^{-5})^2 = (q^{16-5})^2=q^{11\cdot 2}=q^{22}[/tex]

The value of n is 22.

__

The applicable rules of exponents are ...

  (a^b)(a^c) = a^(b+c)

  (a^b)^c = a^(bc)

Answer:

6

Step-by-step explanation:

Answer

about 15 min to 1 hour

Answer:

BC, BD, BQ, CB, CD, CQ, DB, DC, DQ, QB, QC, QD

Step-by-step explanation:

"BC, BD, BQ, CB, CD, CQ, DB, DC, DQ, QB, QC, QD" Are all the possible rays on line c.

Answer:

mZCAD=310°

Step-by-step explanation:

M2BAC=1,m2DAE=3 and m-BAE=0 therefore solution will be 310°

Answer:

4

Step-by-step explanation:

Answer: The answer is D

Step-by-step explanation:

I divided 24 by 3 and it gave me 8 which is a whole number.

Answer:

nos   agoi o se

Step-by-step explanation:

Answer:

[tex]\boxed{\bold{\huge{\boxed{x = 10}}}}[/tex]

Step-by-step explanation:

=> [tex]\sf \frac{3}{4} x + \frac{5}{6} = 5x - \frac{125}{3}[/tex]

Combining like terms

=> [tex]\sf \frac{3x}{4} - 5x = -\frac{125}{3} - \frac{5}{6}[/tex]

Taking LCM to make the denominator same

=> [tex]\sf \large{\frac{3x-20x}{4} = \frac{-250-5}{6} }[/tex]

=> [tex]\sf \frac{-17x }{4} = \frac{-255}{6}[/tex]

=> [tex]\sf \frac{17x }{4} = \frac{255}{6}[/tex]

Cross Multiplying

=> [tex]\sf 17x * 6 = 4 * 255[/tex]

=> [tex]\sf 102x = 1020[/tex]

Dividing both sides by 102

=> x = 10

Answer:

Y=- 6

3(y-5)+2=5

multiply

3y-15+2=5

add

3y-13=5

add pos 13 to the neg 13 to

cancel it out and add +13 to 5

3y=18

divide -3 to pos 3 and 18 to cancel it out

y= -6

Answer:

The answer is

Step-by-step explanation:

To find an equation of a line in point slope form when given the slope and a point we use the formula

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

where

m is the slope

( x1 , y1) is the point

From the question the point is (-2,-2) and slope 42

The equation of the line is

[tex]y + 2 = 42(x + 2) \\ y + 2 = 42x + 84 \\ y = 42x + 84 - 2[/tex]

We have the final answer as

[tex]y = 42x + 82[/tex]

Hope this helps you

Difference means subtract.

Set up the equation:

K - 8.1 > 24

Solve for k by adding 8.1 to both sides:

K > 32.1

Answer:

Total length of shoes in feet = 2 feet

Length of each shoe = 1 feet

Step-by-step explanation:

Given:

Length of each shoe = 12 inches

Find:

Total length of shoes in feet

Computation:

Total length of shoes = [12 + 12] inches

Total length of shoes = 24 inches

12 inches = 1 feet

Total length of shoes in feet = 24 / 12

Total length of shoes in feet = 2 feet

Length of each shoe = 1 feet

Answer:

The sideways E is used for indcating that a point, object, or number belongs to a certian set.

Step-by-step explanation:

Answer: 2

Step-by-step explanation:            

Answer:

12.5in.

x=.5t+11

Step-by-step explanation:

First of all, create the equation so you can solve both questions at once. We know that Sydney had eleven inches of snow on her lawn, and it doesn't dissapear, so it starts with x=11. Then every hour she gets .5 inches per hour, and the amount of hours is t, so that will translate to .5t. that makes the equation x=.5t+11. To find out how much she would have in three hours, substitute 3 for t, which which goes like this: x=.5(3)+11

x=1.5+11

x=12.5

Answer:

Snow after 3 hours: 12.5

Snow after t hours: 11+0.5t

Answer:

1.5 MPH

Step-by-step explanation:

3/4 = 0.75

3/4 x 2 = 0.75 x 2 = 1.5

Step 1) Set up a proportion to find how much Peter spent

45 cards / x dollars = 3 cards / 2 dollars

Step 2) Cross-multiply to solve the proportion

3x = 90

x = $30

Step 3) Set up a proportion to find how much Peter made

45 cards / x dollars = 5 cards / 4 dollars

5x = 180

x = $36

Step 4) Subtract the amount Peter made by the amount he spent

36 - 30 = $6

Answer: Peter made $6

($2/3) * 45 = $30

($4/5) * 45 = $36

$36 - $30 = $6

Answer:

[tex]x = 1.28[/tex]

Step-by-step explanation:

Given

[tex]95 = 35^x[/tex]

Required

Solve for x

[tex]95 = 35^x[/tex]

Take Log of both sides

[tex]Log95 = Log35^x[/tex]

Apply law of logarithm

[tex]Log95 = xLog35[/tex]

Divide both sides by Log35

[tex]x = \frac{Log95}{Log35}[/tex]

[tex]x = \frac{1.97772360529}{1.54406804435}[/tex]

[tex]x = 1.28085262338[/tex]

Approximate

[tex]x = 1.28[/tex]

Answer:

115°

Step-by-step explanation:

Measure of the degree of the angle represented by section B on the chart = percentage in the pie chart ÷ 100 × 360. A full circle makes 360°.

Section B represents 32% of the pie chart, therefore, number of degrees for section B = [tex] \frac{32}{100}*360 = \frac{32*360}{100} [/tex]

[tex] = 115.2 [/tex]

Section B = 115° (to the nearest whole number)

Answer:

A) 0.2967

B) 0.0747

C) 0.2637

D)0.6933

Step-by-step explanation:

We are told the box contains four 40-watt light bulbs, five 60-watt bulbs, and six 75-watt bulbs.

Thus, total number of bulbs = 4 + 5 + 6 = 15 bulbs

This is a combination problem.

Thus;

A) probability that exactly one of the selected bulbs are rated 75-watt will be = ((6C2) × (9C1))/(15C3)

= (15 × 9)/455

= 0.2967

B) probability that all three of the elected bulbs have the same rating;

Number of ways to select three 40 watt bulbs out of the 4 in the box = 4C1 = 4!/(3! × 1!) = 4

Number of ways to select three 60 watt bulbs out of the 5 in the box = 5C1 =

5!/(3! × 2!) = 10

Number of ways to select 75 watt bulbs out of the 6 in the box = 6C1 = 6!/(3! × 3!) = 20

Total number of ways = 4 + 10 + 20 = 34.

Thus, probability that all three of the elected bulbs have the same rating = 34/15C3 = 34/455

= 0.0747

C) probability that one bulb of each type is selected =

[(4C1) × (5C1) × (6C1)]/(15C3)

= (4 × 5 × 6)/455

= 0.2637

D) probability that at least two of the selected bulbs are rated 75-watt =

[(4C1 × 5C1 × 6C2)/15C3] + 6C3/15C3

= (4 × 5 × 15/455) + 20/455

= 0.6493 + 0.044

= 0.6933

Answer:

50

Step-by-step explanation:

When parethesis are next to each other than you need to multiply them.

- times - is positive so -5*--10 would be 50.

Answer:

The answer is "Option b".

Step-by-step explanation:

In the calculation of engineering or modeling, it is used to assess its necessary system, that performance, and also used to evaluate the distribution network adjustments, which is used to accommodate the slew of other distribution network adjustments, that's why except "choice b" all were incorrect.

Answer:

two raised to the power of -3

Two to the power of negative 3

Step-by-step explanation:

[tex]2^-^3 = \frac{1}{2^3}[/tex]

1 divided by 2 to the power of 3

Answer:it is the tens place

Step-by-step explanation:

Answer:

2 represents the the tenths place

Step-by-step explanation:

You have 168,526 remember your tenth hundred and thousands 2 is in the tenth place that is what represents

Hope that answers ur question