(-1, 4) and (-2, 2).

Answer:

Step-by-step explanation:

[tex] \mathsf{(x - 2)(x - 3)}[/tex]

Multiply each term in the first parentheses by each term in the second parentheses ( FOIL )

[tex] \mathsf{x×x - 3x - 2x - 2 × ( - 3 )}[/tex]

Calculate the product

[tex] \mathsf{ {x}^{2} - 3x - 2x - 2 \times (- 3)}[/tex]

Multiply the numbers

[tex] \mathsf{ {x}^{2} - 3x - 2x + 6 }[/tex]

Collect like terms

[tex] \mathsf{ {x}^{2} - 5x + 6}[/tex]

Hope I helped!

Best regards!

Answer:

$5

Step-by-step explanation:

Let the notebook cost x, then Mark spent:

Notebook costs $5

Answer:

The answer is "Analysis the information by chart and number processes".

Step-by-step explanation:

They already have articulated a query and also gathered information unless you are searching only at the distribution of your results. Those who are ready to analyze your results for all are there.

Answer:

C. -8, -6, -4, -2, ...

Step-by-step explanation:

An arithmetic sequence increases by the same amount every time through addition or subtraction. There is a common difference.

A: -2, 4, -6, 8, ... If there were a common difference, the numbers would not switch between being positive and back to negative. The numbers would either keep going positive or keep going negative.

B: 2, 4, 8, 16, ... The common difference between 16 and 8 is 16 - 8 = 8. The difference between 8 and 4 is 8 - 4 = 4. Since the difference changes between the numbers, this is not an arithmetic sequence.

C. -8, -6, -4, -2, ... The common difference between -2 and -4 is -2 - (-4) = -2 + 4 = 2. The difference between -4 and -6 is -4 - (-6) = -4 + 6 = 2. The difference between -6 and -8 is -6 - (-8) = -6 + 8 = 2. Since the common difference is always two, this is an arithmetic sequence.

Hope this helps!

Answer:

Mean= 242.5 pounds

Median= 236 pounds

Mode= 208 and 278 pounds

Range=117 pounds

Mid-range= 58.5 pounds

B. The results are likely to be representative because a championship team is most likely representative of the entire league.

Step-by-step explanation:

278 303 186 292  276 205 208 236 278 198 208

Arranged in ascending order is

186 198 205 208 208 236 276 278 278 292 303

Mean = (186 +198+ 205+ 208 +208 +236 + 276+ 278 +278+ 292 +303)/11

Mean =2668/11

Mean= 242.5 pounds

Median = the middle number

Median= 236 pounds

Mode = highest occuring number(s)

Mode= 208 and 278 pounds

Range= highest number- smallest number

Range=303-186

Range=117 pounds

Mid-range= range/2

Mid-range= 117/2

Mid-range= 58.5 pounds

Answer:

15/225

Step-by-step explanation:

The number of chaperones for the group of students can be represented with a ratio - 15:225 or 15/225.

Because there are 15 chaperones for the 225 students, you can state what the ratio does - for every 225 students, there are 15 chaperones.

However, 15/225 can be reduced to 1/15, so for every 15 students, there is 1 chaperone.

Answer:

33.53

Step-by-step explanation:

OB is a radius of the circle, and OC is also a radius of the circle, so both are equal length.  That makes ΔOBC an isosceles triangle.

If we cut ΔOBC in half, the angle formed is 125° / 2 = 62.5°.

Therefore:

sin 62.5 = (x/2) / 18.9

x = 37.8 sin 62.5

x ≈ 33.53

Answer:

33.5

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given

Garden: [tex]x^2+18x+81[/tex]

One Bag: [tex]x^2 - 81[/tex]

Requires

Determine the number of bags to cover the whole garden

This is calculated as thus;

[tex]Bags = \frac{x^2+18x+81}{x^2 - 81}[/tex]

Expand the numerator

[tex]Bags = \frac{x^2+9x+9x+81}{x^2 - 81}[/tex]

[tex]Bags = \frac{x(x+9)+9(x+9)}{x^2 - 81}[/tex]

[tex]Bags = \frac{(x+9)(x+9)}{x^2 - 81}[/tex]

Express 81 as 9²

[tex]Bags = \frac{(x+9)(x+9)}{x^2 - 9\²}[/tex]

Evaluate as difference of two squares

[tex]Bags = \frac{(x+9)(x+9)}{(x - 9)(x+9)}[/tex]

[tex]Bags = \frac{(x+9)}{(x - 9)}[/tex]

Hence, the number of bags is [tex]Bags = \frac{(x+9)}{(x - 9)}[/tex]

Answer:

Step-by-step explanation:

Following the cardinal points as regards location of points, the sketch of Musah's movement can be as what is attached to this answer.

Answer:

Step-by-step explanation:

The exponential equation for the fraction remaining after x years can be written as ...

  y = (1/2)^(x/30)

A) For x=1, the fraction remaining is ...

  y = (1/2)^(1/30) ≈ 0.97716 = 1 - 0.0228

Of the original amount, 0.0228 decays each year.

__

B) The continuous decay rate is the natural log of the growth factor, so is ...

  ln(0.97716) = -0.0231

The continuous decay rate is 0.0231 of the present amount (per year).

__

C) For y=.10 (1/10 of the original amount) we find x to be ...

  .1 = .5^(x/30)

  ln(.1) = (x/30)ln(.5) . . . . . take the natural log

  30ln(0.1)/ln(0.5) = x ≈ 100 . . . years

It will take 100 years for a 10-gram sample to decay to 1 gram.

__

D) As x goes to infinity, y goes to zero.

_____

The relationship between growth rate and growth factor is ...

  growth factor = 1 + growth rate

When the growth rate is negative, it is called a decay rate.

Answer:

1/2 mi

Step-by-step explanation:

Fairfax to Greenwood is equal to one mile

Now think of it as an equation and substitute 1/2 for fairfax and x for greenwood

1/2 + x = 1

This means that x = 1/2

Because of this from Arcadia to Greenwood it is 1/2 mi

Answer:

[tex](5 - 2y) \div 12 > 1 - 6y[/tex]

[tex]5 - 2y > 12 - 72y[/tex]

[tex] - 7 > - 70y[/tex]

[tex]7 < 70y[/tex]

[tex]y > 1 \div 10 = 0.1[/tex]

Answer:

Size of |E n B| = 2

Size of |B| = 1

Step-by-step explanation:

I'll assume both die are 6 sides

Given

Blue die and Red Die

Required

Sizes of sets

- [tex]|E\ n\ B|[/tex]

- [tex]|B|[/tex]

The question stated the following;

B = Event that blue die comes up with 6

E = Event that both dice come even

So first; we'll list out the sample space of both events

[tex]B = \{6\}[/tex]

[tex]E = \{2,4,6\}[/tex]

Calculating the size of |E n B|

[tex]|E n B| = \{2,4,6\}\ n\ \{6\}[/tex]

[tex]|E n B| = \{2,4,6\}[/tex]

The size = 3 because it contains 3 possible outcomes

Calculating the size of |B|

[tex]B = \{6\}[/tex]

The size = 1 because it contains 1 possible outcome

Answer: x=3.2     AC= 42.8

Step-by-step explanation:

As point B lies at segment AC      AC=AB+BC

Otherwise we can write the equation

5x+9x-2=11x+7.6

14x-2=11x+7.6

14x-2+2=11x+7.6+2

14x=11x+9.6

14x-11x=11x-11x+9.6

3x=9.6

x=9.6:3

x=3.2

AC= 11*x+7.6= 11*3.2+7.6=35.2+7.6=42.8

Answer:

Yes

Step-by-step explanation:

18 × 200 = 3600

120 × 25 = 3000

270 × 5 = 1350

in total 7950

tickets = 10 × 1000 = 10000

7950 < 10000

Answer: The correct answer is 19 sit ups.

Step-by-step explanation: Given that the regression equation to find a  a relationship between hours of TV watched per day (x) and number of situps a person can do (y) was done.

The result was

y = ax+b

Correlation coefficient = 0.865

To predict the number of situps a person who watches 3 hours of TV

y = -1.23(3)+22.738

= 19.048

Approximately 19 situps.

Answer:

[tex]\Large \boxed{\sf 17 \ and \ 18}[/tex]

Step-by-step explanation:

The product means multiplication.

There are two positive consecutive integers.

Let the first positive consecutive integer be x.

Let the second positive consecutive integer be x+1.

[tex](x) \times (x+1) =306[/tex]

Solve for x.

Expand brackets.

[tex]x^2 +x =306[/tex]

Subtract 306 from both sides.

[tex]x^2 +x -306=306-306[/tex]

[tex]x^2 +x -306=0[/tex]

Factor left side of the equation.

[tex](x-17)(x+18)=0[/tex]

Set factors equal to 0.

[tex]x-17=0[/tex]

[tex]x=17[/tex]

[tex]x+18=0[/tex]

[tex]x=-18[/tex]

The value of x cannot be negative.

Substitute x=17 for the second consecutive positive integer.

[tex](17)+1[/tex]

[tex]18[/tex]

The two integers are 17 and 18.

The product of two consecutive positive integers is 306.

We need to find the integers

solution : Let two consecutive numbers are x and (x + 1)

A/C to question,

product of x and (x + 1) = 306

⇒x(x + 1) = 306

⇒x² + x - 306 = 0

⇒ x² + 18x - 17x - 306 = 0

⇒x(x + 18) - 17(x + 18) = 0

⇒(x + 18)(x - 17) = 0⇒ x = 17 and -18

so x = 17 and (x +1) = 18

Therefore the numbers are 17 and 18.

Hope it helped u if yes mark me BRAINLIEST

TYSM!

Answer:

(-5/9, 16/9)

Step-by-step explanation:

2y = -x + 3

-y = 5x + 1

To find the intersection, you need to substitute the y-value from the second equation into the first equation.  Rearrange the second equation so that it is equal to y.

-y = 5x + 1

-1(-y) = -1(5x + 1)

y = -5x - 1

Substitute this equation into the y-value of the first equation.

2y = -x + 3

2(-5x - 1) = -x + 3

-10x - 2 = -x + 3

(-10x - 2) + 2 = (-x + 3) + 2

-10x = -x + 5

(-10x) + x = (-x + 5) + x

-9x = 5

(-9x)/(-9) = (5)/(-9)

x = -5/9

Plug this x value into one of the equations and solve for y.

2y = -x + 3

2y = -(-5/9) + 3

2y = 5/9 + 3

2y = 32/9

(2y)/2 = (32/9)/2

y = 32/18 = 16/9

The ordered pair is (-5/9, 16/9).

Answer:

6h + 12 = 30

Step-by-step explanation:

Hence, the equation obtained for number of hours worked is given as  12 + 6h = 30.

A linear equation for the given case can be written by assuming any variable as the unknown quantity. Then, as per the given data the required operations are done and it is equated to some value.

The total money required is given as $30.

Suppose the number of hours for babysitting be h.

Then, the money earned by doing it is $6h.

And, the total money with Karl is 12 + 6h.

As per the question, the following equations can be written as,

12 + 6h = 30

Hence, the equation for finding the number of hours is given as 12 + 6h = 30.

To know more about linear equation click on,

https://brainly.com/question/11897796

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Answer:

0.9773

Step-by-step explanation:

Here, we start by calculating the z-scores statistic

Mathematically;

z-score = (x-mean)/SD/√n

From the question, we have;

x = 71, mean = 70, SD = 5 and n = 100

Plugging these values in the equation above, we have;

z-score = (71-70)/5/√100 = 1/5/10 = 1/0.5 = 2

So the probability we want to calculate is that;

P(z > 2)

This is obtainable from the standard normal distribution table

P(z > 2) = 0.97725 which is 0.9773 to 4 decimal places

Answer:hope it helps

Step-by-step explanation:

Result:

0.6

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Number line:

Number line

Rational form:

3/5

Answer:

  [tex]\dfrac{3}{(y+2)^3}[/tex]

Step-by-step explanation:

Maybe you want this written using math symbols. It will be ...

  [tex]\boxed{\dfrac{3}{(y+2)^3}}[/tex]

Answer:a

a

   [tex]336.04 < \mu < 443.96[/tex]

b

  The  margin of error will increase

c

The  margin of error will decreases

d

The 99% confidence interval is  [tex]0.4107 < p < 0.4293[/tex]

Step-by-step explanation:

From the question we are  told that

   The sample size  [tex]n = 19[/tex]

    The sample mean is  [tex]\= x = \$\ 390[/tex]

    The  standard deviation is  [tex]\sigma = \$ \ 120[/tex]

Given that the confidence level is  95% then the level of significance is mathematically represented as

           [tex]\alpha = 100 - 95[/tex]

          [tex]\alpha = 5 \%[/tex]

          [tex]\alpha = 0.05[/tex]

Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table

    So  

         [tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]

The  margin of error is mathematically represented as

      [tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma}{\sqrt{n} }[/tex]

=>    [tex]E = 1.96 * \frac{120}{\sqrt{19} }[/tex]

=>   [tex]E = 53.96[/tex]

The 95% confidence interval is  

     [tex]\= x - E < \mu < \= x + E[/tex]

=>   [tex]390 - 53.96 < \mu < 390 - 53.96[/tex]

=>  [tex]336.04 < \mu < 443.96[/tex]

When the confidence level increases the [tex]Z_{\frac{\alpha }{2} }[/tex] also increases which increases the margin of error hence the confidence level becomes wider

Generally the sample size mathematically varies with margin of error as follows

         [tex]n \ \ \alpha \ \ \frac{1}{E^2 }[/tex]

So if the sample size increases the margin of error decrease

The  sample proportion is mathematically represented as

       [tex]\r p = \frac{210}{500}[/tex]

       [tex]\r p = 0.42[/tex]

Given that the confidence level is 0.99 the level of significance is  [tex]\alpha = 0.01[/tex]

The critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table is  

      [tex]Z_{\frac{\alpha }{2} } = 2.58[/tex]

  Generally the margin of error is mathematically represented as

       [tex]E = Z_{\frac{\alpha }{2} }* \sqrt{ \frac{\r p (1- \r p )}{n} }[/tex]

=>   [tex]E = 0.42 * \sqrt{ \frac{0.42 (1- 0.42 )}{ 500} }[/tex]

=>     [tex]E = 0.0093[/tex]

The 99% confidence interval  is

     [tex]\r p - E < p < \r p + E[/tex]

     [tex]0.42 - 0.0093 < p < 0.42 + 0.0093[/tex]

     [tex]0.4107 < p < 0.4293[/tex]

Answer:

If we have an integer number N, the opposite of N will be:

-1*N = -N.

Then, the opposite of 0°C is:

-1*0°C = 0°C.

The number 0 is it's own opposite.

And for 32F, the opposite is:

-1*32F = -32F

So, while the numbers 0°C and 32F physically represent the same thing (the same temperature), mathematically, they behave differently.

Answer:

We conclude that the population mean is equal to 490.

Step-by-step explanation:

We are given that a random sample of 15 observations is selected from a normal population. The sample mean was 495 and the sample standard deviation 9.

Let [tex]\mu[/tex] = population mean.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 490      {means that the population mean is equal to 490}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu\neq[/tex] 490     {means that the population mean is different from 490}

The test statistics that will be used here is One-sample t-test statistics because we don't know about population standard deviation;

                               T.S.  =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~ [tex]t_1_4[/tex]

where, [tex]\bar X[/tex] = sample mean = 495

            s = sample standard deviation = 9

             n = sample of observations = 15

So, the test statistics =   [tex]\frac{495-490}{\frac{9}{\sqrt{15} } }[/tex]  ~ [tex]t_1_4[/tex]

                                     =  2.152

The value of t-test statistics is 2.152.

Now, at a 0.01 level of significance, the t table gives a critical value of -2.977 and 2.977 at 14 degrees of freedom for the two-tailed test.

Since the value of our test statistics lies within the range of critical values of t, so we have insufficient evidence to reject our null hypothesis as the test statistics will not fall in the rejection region.

Therefore, we conclude that the population mean is equal to 490.

Answer:

Since x= 12 (0.006461) does not fall in the critical region so we accept our null hypothesis and conclude that the coin is fair.

Step-by-step explanation:

Let p be the probability of heads in a single toss of the coin. Then our null hypothesis that the coin is fair will be formulated as

H0 :p 0.5   against   Ha: p ≠ 0.5

The significance level is approximately 0.05

The test statistic to be used is number of heads x.

Critical Region: First we compute the probabilities associated with X the number of heads using the binomial distribution

Heads (x)        Probability (X=x)                        Cumulative     Decumulative

0                        1/16384 (1)             0.000061     0.000061

1                         1/16384  (14)         0.00085             0.000911

2                       1/16384 (91)           0.00555             0.006461

3                       1/16384(364)         0.02222

4                       1/16384(1001)         0.0611

5                       1/16384(2002)       0.122188

6                        1/16384(3003)      0.1833

7                         1/16384(3432)      0.2095

8                        1/16384(3003)       0.1833

9                        1/16384(2002)       0.122188

10                       1/16384(1001)        0.0611

11                       1/16384(364)        0.02222

12                      1/16384(91)            0.00555                             0.006461

13                     1/16384(14)              0.00085                           0.000911

14                       1/16384(1)            0.000061                            0.000061

We use the cumulative and decumulative column as the critical region is composed of two portions of area ( probability) one in each tail of the distribution. If  alpha = 0.05 then alpha by 2 - 0.025 ( area in each tail).

We observe that P (X≤2) =   0.006461 > 0.025

and

P ( X≥12 ) = 0.006461 > 0.025

Therefore true significance level is

∝=  P (X≤0)+P ( X≥14 ) = 0.000061+0.000061= 0.000122

Hence critical region is (X≤0) and ( X≥14)

Computation x= 12

Since x= 12 (0.006461) does not fall in the critical region so we accept our null hypothesis and conclude that the coin is fair.

Answer:

[tex]\large \boxed{\mathrm{1/2 \ boxes}}[/tex]

Step-by-step explanation:

Subtract the fractions.

[tex]\frac{9}{16}-\frac{1}{16}=\frac{8}{16} =\frac{1}{2}[/tex]

Vicky had 1/2 of a box more baking powder yesterday.

Answer:

B. 4.61 miles

Step-by-step explanation:

midpoint is (-3+4)/2, (2+8)/2 = (1/2, 5)

distance = √(-3-1/2)² + (2 - 5)² = 4.609772299

Answer: 247.92 euros

Step-by-step explanation:

Given, Varia is required pay $3,500 (in US dollars) per year to the university.

If she must pay in euros , then we convert $3,500 into euros.

Current rate : 1 US dollar = 0.85 euro

Then,  $3,500 = ( 0.85 x 3500) euros

= 2975 euros

She can expect 2975 euros to pay per year.

Also, [tex]2975\div 12\approx247.92[/tex]   [ 1 years = 12 months]

Hence, She can expect 247.92 euros to pay per month to the university.