2⁶ × 2⁵ how do i simplify this?​

Answer:

x1 = -4

x2 = 6

Step-by-step explanation:

The 2 vertical lines are "absolute values" meaning whatever they contain has to be positive

For Example

|-3| = 3

So we can ignore if the answer we get is positive or negative because it will forced to be a positive

|3 x 4| = 12

|x - 2| = 4

x1 = 6

x2 = -2

Answer:

(i) 0.32          (ii) 0.85

(iii) 0.3412    (iv) 0.20

(v) 0.29         (vi) 0.12

Step-by-step explanation:

The data provided is as follows:

   Race                    Smoker (S)         Nonsmoker (N)             Row Total

 White(W)                    290                       560                           850

  Black(B)                     30                        120                           150

Column Total                320                       680                        1,000

(i)

Compute the value of P (S) as follows:

[tex]P(S)=\frac{n(S)}{N}=\frac{320}{1000}=0.32[/tex]

P (S) = 0.32.

(ii)

Compute the value of P (W) as follows:

[tex]P(W)=\frac{n(W)}{T}=\frac{850}{1000}=0.85[/tex]

P (W) = 0.85.

(iii)

Compute the value of P (S|W) as follows:

[tex]P(S|W)=\frac{n(S\cap W)}{n(W)}=\frac{290}{850}=0.3412[/tex]

P (S|W) = 0.3412.

(iv)

Compute the value of P (S|B) as follows:

[tex]P(S|B)=\frac{n(S\cap B)}{n(B)}=\frac{30}{150}=0.20[/tex]

P (S|W) = 0.20.

(v)

Compute the value of P (S∩W) as follows:

[tex]P(S\cap W)=\frac{n(S\cap W)}{T}=\frac{290}{1000}=0.29[/tex]

P (S∩W) = 0.29.

(vi)

Compute the value of P (N∩B) as follows:

[tex]P(N\cap B)=\frac{n(N\cap B)}{T}=\frac{120}{1000}=0.12[/tex]

P (S∩W) = 0.12.

[tex]x-1=\dfrac{6}{x}\qquad(x\not=0)\\\\x^2-x=6\\x^2-x-6=0\\x^2+2x-3x-6=0\\x(x+2)-3(x+2)=0\\(x-3)(x+2)=0\\x=3 \vee x=-2[/tex]

Answer5

Step-by-step explanation:

Answer: Check out the diagram below for the filled in boxes

14 goes in the first box (inside A, but outside B)

7 goes in the overlapping circle regions

5 goes in the third box (inside B, outside A)

3 goes in the box outside of the circles

==============================================================

Explanation:

[tex]n(A \cup B) = 26[/tex] means there are 26 items that are in A, B or both.

n(A) = 21 means there are 21 items in A

n(B) = 12 means there are 12 items in B

We don't know the value of [tex]n(A \cap B)[/tex] which is the number of items in both A and B at the same time. This is the intersecting or overlapping regions of the two circles. Let [tex]x = n(A \cap B)[/tex]

It turns out that adding n(A) to n(B), then subtracting off the stuff they have in common, leads to n(A u B) as shown below.

--------

[tex]n(A \cup B) = n(A) + n(B) - n(A \cap B)\\\\26 = 21+12 - x\\\\26 = 33 - x\\\\x+26 = 33\\\\x = 33-26\\\\x = 7\\\\n(A \cap B) = 7\\\\[/tex]

So there are 7 items in both regions.

This means there are [tex]n(A) - n(A \cap B) = 21 - 7 = 14[/tex] items that are in set A only. In other words, 14 items are in circle A, but not in circle B.

Notice how the values 14 and 7 add back up to 14+7 = 21, which represents everything in set A.

Similarly, there are [tex]n(B) - n(A \cap B) = 12 - 7 = 5[/tex] items that are in circle B, but not in circle A. The values 5 and 7 in circle B add to 5+7 = 12, matching with n(B) = 12.

The notation n(A') means the number of items that are not in set A. We're given n(A') = 8. We already know that 5 is outside circle A. So if 5+y = 8, then y = 3 must be the missing value for the box that is outside both circles.

Again the diagram is posted below with the filled in values.

A Venn diagram is an overlapping circle to describe the logical relationships between two or more sets of items.

The filled Venn diagram is given below.

A Venn diagram is an overlapping circle to describe the logical relationships between two or more sets of items.

We have,

n(A) = 21

This is the total of all the items included in Circle A.

n(B) = 12

This is the total of all the items included in Circle A.

n(A') = 8

The items that are not in circle A.

n(A U B ) = 26

The items that are in both circle A and circle B.

Now,

n (A U B) = n(A) + n(B) - n(A ∩ B)

26 = 21 + 12 - n(A ∩ B)

n(A ∩ B) = 33 - 26

n(A ∩ B) = 7

Thus,
The filled Venn diagram is given below.

Learn more about the Venn diagram here:

https://brainly.com/question/1605100

#SPJ2

Answer:

The answer is "[tex]\bold{\frac{1}{4}<k\leq 2+\sqrt{3}}[/tex]"

Step-by-step explanation:

Given:

[tex]\ S_1 = k \\\\ S_{n+1} = \sqrt{4S_n -1}[/tex]   [tex]_{where} \ \ n \geq 1[/tex]

In the above-given value, [tex]S_n[/tex] is required for the monotone decreasing so, [tex]S_2 :[/tex]

[tex]\to \sqrt{4k-1} \leq \ k=S_1\\\\[/tex]

square the above value:

[tex]\to k^2-4k+1 \leq 0\\\\\to k \leq 2+\sqrt{3} \ \ \ \ \ and \ \ 4k+1 >0\\\\[/tex]

[tex]\bold{\boxed{\frac{1}{4}<k\leq 2+\sqrt{3}}}[/tex]

Answer:

x = 0.09

Step-by-step explanation:

[tex] {3}^{x + 2} = {2}^{3} [/tex]

Taking Logarith both sides, we get :

Using the properties of Logarithms:

[tex](x + 2) log(3) = 3 log(2) [/tex]

[tex](x + 2) = 1.91[/tex]

(taking log2= 0.3 and log3= 0.47)

x = 0.09

Answer:

The probability is 2,010,580/13,378,456

Step-by-step explanation:

Here is a combination problem.

We want to 7 cards from a total of 52.

The number of ways to do this is 52C7 ways.

Also, we know there are 12 face cards in a standard deck of cards.

So we are selecting 3 face cards from this total of 12.

So also the number of cards which are not face cards are 52-12 = 40 cards

Out of all these 40, we shall be selecting exactly 4. The number of ways to do this 40C4

Thus, the required probability will be;

(40C4 * 12C3)/52C7 = (91,390 * 220)/133,784,560

= 20,105,800/133,784,560 = 2,010,580/13,378,456

Answer:

35%

Step-by-step explanation:

[tex]Principal = 2500\\\\Simple\:Interest = 3500\\\\Time = 4 \:years\\\\Rate = ?\\\\Rate = \frac{100 \times Simple \: Interest }{Principal \times Time}\\\\Rate = \frac{100 \times 3500}{2500 \times 4} \\\\Rate = \frac{350000}{10000}\\\\ Rate = 35 \%[/tex]

[tex]S.I = \frac{PRT}{100}\\\\ 100S.I = PRT\\\\\frac{100S.I}{PT} = \frac{PRT}{PT} \\\\\frac{100S.I}{PT} = R[/tex]

Answer:

35%

Step-by-step explanation:

I REALLY HOPE I HELPED

HOPE I HELPED

PLS MARK BRAINLIEST

DESPERATELY TRYING TO LEVEL UP

 ✌ -ZYLYNN JADE ARDENNE

JUST A RANDOM GIRL WANTING TO HELP PEOPLE!

                                PEACE!

Answer:

[tex]\huge\boxed{6 ( 3d + 2 )}[/tex]

Step-by-step explanation:

18d + 12

The greatest common factor is 6, So we need to factor out 6

=> 6 ( 3d + 2 ) [Distributive property has been applied and this is the simplest form]

Answer:

6(3d+2)

Step-by-step explanation:

6 is the gcd of the two terms.

Answer:

B

Step-by-step explanation:

Since the power is negative, you automatically know it has to be a or b, because the only way it would be negative is if it was brought from the denominator to the numerator.

The answer is B, because the numerator of the power, is what is inside the square root, while the denominator is what is outside the square root.

Answer:

We conclude that prenatal cocaine exposure is associated with lower scores of four-year-old children on the test of object assembly.

Step-by-step explanation:

We are given that the 190 children born to cocaine users had a mean of 7.3 and a standard deviation of 3.0 The 186 children not exposed to cocaine had a mean score of 8.2 with a standard deviation of 3.0.

Let [tex]\mu_1[/tex] = population mean score for children born to cocaine users.

[tex]\mu_2[/tex] = population mean score for children not exposed to cocaine.

So, Null Hypothesis, : = 490      {means that the prenatal cocaine exposure is not associated with lower scores of four-year-old children on the test of object assembly}

Alternate Hypothesis, : 490     {means that the prenatal cocaine exposure is associated with lower scores of four-year-old children on the test of object assembly}

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

                               T.S.  =  [tex]\frac{(\bar X_1-\bar X_2)-(\mu_1-\mu_2)}{s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex]  ~ [tex]t__n_1_+_n_2_-_2[/tex]

where, [tex]\bar X_1[/tex] = sample mean score of children born to cocaine users = 7.3

[tex]\bar X_2[/tex] = sample mean score of children not exposed to cocaine = 8.2

[tex]s_1[/tex] = sample standard deviation for children born to cocaine users = 3

[tex]s_2[/tex] = sample standard deviation for children not exposed to cocaine = 3

[tex]n_1[/tex] = sample of children born to cocaine users = 190

[tex]n_2[/tex] = sample of children not exposed to cocaine = 186

Also, [tex]s_p=\sqrt{\frac{(n_1-1)\times s_1^{2}+(n_2-1)\times s_2^{2} }{n_1+n_2-2} }[/tex]  = [tex]\sqrt{\frac{(190-1)\times 3^{2}+(186-1)\times 3^{2} }{190+186-2} }[/tex] = 3

So, the test statistics =   ~

                                     =  -2.908

The value of t-test statistics is -2.908.

Now, at a 0.05 level of significance, the t table gives a critical value of -1.645 at 374 degrees of freedom for the left-tailed test.

Since the value of our test statistics is less than the critical value of t as -2.908 < -1.645, so we have sufficient evidence to reject our null hypothesis as the test statistics will fall in the rejection region.

Therefore, we conclude that prenatal cocaine exposure is associated with lower scores of four-year-old children on the test of object assembly.

In the null hypothesis, a test always forecasts no effect, while the alternate theory states the research expectation impact, and calculation as follows:

Calculating the pooled estimator of [tex]\sigma^2[/tex], denoted by [tex]S^2_p[/tex], is defined by

[tex]\to \bold{S^2_p= \frac{(n_1 - 1) S^2_1+ (n_2 - 1)S^2_2}{n_1 + n_2 - 2}}[/tex]

Null hypothesis:

[tex]\to H_0 : \mu_1 - \mu_2 = \Delta_0\\[/tex]

Test statistic:

[tex]\to T_0=\frac{\bar{X_1}- \bar{X_2} -\Delta_0}{S_p \sqrt{\frac{1}{n_1}+\frac{1}{n_2}}} \\\\[/tex]

Alternative Hypothesis:

[tex]H_1 : \mu_1 -\mu_2 \neq \Delta_0\\\\ H_1 : \mu_1 -\mu_2 > \Delta_0\\\\H_1 : \mu_1 -\mu_2 < \Delta_0\\\\[/tex]

Rejection Criterion

[tex]t_0 > t_{\frac{\alpha}{2} , n_1+n_2 -2}\ \ \ or\ \ \ t_0 < - t_{\frac{\alpha}{2} , n_1+n_2 -2} \\\\t_o > t_{\alpha , n_1+n_2 -2} \\\\t_o > -t_{\alpha , n_1+n_2 -2}[/tex]

Given value:

[tex]\to S_p=9\\\\\to \Delta_0=0\\\\\to t_0=-\frac{0.9}{3(\sqrt{(\frac{1}{190}+\frac{1}{186})})}=-2.9\\\\\to t_{0.05,374}=1.645\\\\[/tex]

here

[tex]\to t_0 < -t_{0.05,374}[/tex]

hence rejecting the [tex]H_0[/tex]

Since there should be enough evidence that prenatal cocaine exposure is linked to inferior item assembly scores in 4-year-olds.

Find out more about the alternative hypothesis here:

brainly.com/question/18831983

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:

63 cm

Step-by-step explanation:

If Chubby ran his wheel, which has a diameter of 20cm, we want to find its circumference - this will tell us how far Chubby has ran one one full rotation of the wheel.

The formula for the circumference of a circle is [tex]2\pi r[/tex], where r is the radius. We know the diameter is 20, which is double the radius, so the radius is [tex]20\div2=10[/tex] cm.

We can know substitute inside the formula:

[tex]2\cdot \pi \cdot10\\\\2\cdot 3.14 \cdot10\\\\ 6.28\cdot10\\\\62.8[/tex]

62.8 rounded to the nearest cm is 63.

Hope this helped!

Answer:

6280

Step-by-step explanation:

Answer:

maximum --> 62

median --> 46.5

upper quartile --> 60

lower quartile --> 37

minimum --> 32

Step-by-step explanation:

Forgive me on the explanation as I'm a bit rusty on these types of problems.

First, we need to put the set of numbers in order -->

from: 34, 37, 39, 32, 48, 45, 53, 62, 58, 61, 60, 41 -->

to: 32, 34, 37, 39, 41, 45, 48, 53, 58, 60, 61, 62

maximum = biggest number => thus, 62

median = middle number in a sense => (45+48)/2 => thus, 46.5

upper quartile = median over the median => thus, 60

lower quartile = median under the median => thus, 37

minimum = lowest number => thus, 32

And there we have our 5 answers.

Hope this helps!

Answer:

13 units

Step-by-step explanation:

Use the equation of a circle, (x - h)² + ( y - k )² = r², where (h, k) is the center and r is the radius.

Plug in the values and solve for r:

(5 - 0)² + (12 - 0)² = r²

25 + 144 = r²

169 = r²

13 = r

Answer: The missing number is 5.

Step-by-step explanation:

In the table we can only have numbers between 1 and 9,

The pattern that i see is:

We have sets of 3 numbers.

"the bottom number is equal to the difference between the two first numers, if the difference is negative, change the sign, if the difference is zero, there goes a 9 (the next number to zero)"

Goin from right to left we have:

9 - 6 = 3

6 - 2 = 4

4 - 9 = - 5 (is negative, so we actually use -(-5) = 5)

4 - 4 = 0 (we can not use zero, so we use the next number, 9)

3 - 3 = 0 (same as above)

? - 1 = 4

? = 4 + 1 =  5

The missing number is 5.

Answer:

D. The z scores are numbers without units of measurement.

Step-by-step explanation:

Z-scores are without units, or are pure numbers.

The intervals would contain approximately 95% of the measurements will be (120, 280). Then the correct option is C.

The Gaussian Distribution is another name for it. The most significant continuous probability distribution is this one. Because the curve resembles a bell, it is also known as a bell curve.

In numerical documentation, these realities can be communicated as follows, where Pr(X) is the likelihood capability, Χ is a perception from an ordinarily circulated irregular variable, μ (mu) is the mean of the dispersion, and σ (sigma) is its standard deviation:

The interval for 95% will be given as,

Pr(X) = μ ± 2σ

Pr(X) = 200 ± 2(40)

Pr(X) = 200 ± 80

Pr(X) = (200 - 80, 200 + 80)

Pr(X) = (120, 280)

The intervals would contain approximately 95% of the measurements will be (120, 280). Then the correct option is C.

More about the normal distribution link is given below.

https://brainly.com/question/12421652

#SPJ5

Answer:

14 + 25l + 6l^2

Step-by-step explanation:

(7 + 2i) (2 + 3i)

=> 14 + 4l + 21l + 6l^2

=> 14 + 25l + 6l^2

This is the correct answer

Answer:

Step-by-step explanation:

Answer:

125π ft²

Step-by-step explanation:

1/4π(30)² - 1/4π(20)² = 125π

Answer:

In the error term.

Step-by-step explanation:

A simple linear regression is a regression that has only one explanatory variable. It tries to establish the existing relationship between the variable of interest (dependent variable) and the explanatory variable (independent variable).

Since age is the only explanatory variable, other variables such as faminc would be in the error term. The error term exists because the explanatory variable is never able to on its own to predict the dependent variable perfectly.

Answer:

The  number is  [tex]N =1147[/tex] students

Step-by-step explanation:

From the question we are told that

    The population mean is  [tex]\mu = 281[/tex]

     The standard deviation is  [tex]\sigma = 34.4[/tex]

    The sample size is  n = 2000

percentage of the would you expect to have a score between 250 and 305 is mathematically represented as

      [tex]P(250 < X < 305 ) = P(\frac{ 250 - 281}{34.4 } < \frac{X - \mu }{\sigma } < \frac{ 305 - 281}{34.4 } )[/tex]

Generally  

             [tex]\frac{X - \mu }{\sigma } = Z (Standardized \ value \ of \ X )[/tex]

So  

         [tex]P(250 < X < 305 ) = P(-0.9012< Z<0.698 )[/tex]

       [tex]P(250 < X < 305 ) = P(z_2 < 0.698 ) - P(z_1 < -0.9012)[/tex]

From the z table  the value of  [tex]P( z_2 < 0.698) = 0.75741[/tex]

                                         and  [tex]P(z_1 < -0.9012) = 0.18374[/tex]

     [tex]P(250 < X < 305 ) = 0.75741 - 0.18374[/tex]

      [tex]P(250 < X < 305 ) = 0.57[/tex]

The  percentage is  [tex]P(250 < X < 305 ) = 57\%[/tex]

The  number of students that will get this score is

           [tex]N = 2000 * 0.57[/tex]

           [tex]N =1147[/tex]

Complete Question

In the nation of Gondor, the EPA requires that half the new cars sold will meet a certain particulate emission standard a year later. A sample of 64 one-year-old cars revealed that only 24 met the particulate emission standard. The test statistic to see whether the proportion is below the requirement is:

A -1.645

B -2.066

C -2.000

D-1.960

Answer:

The  correct option is C

Step-by-step explanation:

From the question we are told that

   The  population mean is  [tex]p = 0.50[/tex]

    The sample size is  [tex]n = 64[/tex]

     The  number that met the standard is  [tex]k = 24[/tex]

Generally the sample proportion is mathematically evaluated   as

             [tex]\r p = \frac{24}{64}[/tex]

             [tex]\r p =0.375[/tex]

Generally the standard error is mathematically evaluated as  

       [tex]SE = \sqrt{ \frac{p(1- p )}{n} }[/tex]

=>    [tex]SE = \sqrt{ \frac{0.5 (1- 0.5 )}{64} }[/tex]

=>   [tex]SE = 0.06525[/tex]

The  test statistics is evaluated as

        [tex]t = \frac{ \r p - p }{SE}[/tex]

        [tex]t = \frac{ 0.375 - 0.5 }{0.0625}[/tex]

        [tex]t = -2[/tex]

Answer:

90

Step-by-step explanation:

Answer:

90

Step-by-step explanation:

Here is the equation

[tex]20+3\times(7+4)+5+2\times(7+9)[/tex]

In the order of operations parentheses go first so we get

[tex]20+3\times11+5+2\times16[/tex]

Next we do the multiplication

[tex]20+33+5+32\\[/tex]

And finally we add them all up

[tex]20+33+5+32=90\\[/tex]

Thus, 90 is the answer of [tex]20+3\times(7+4)+5+2\times(7+9)[/tex] or [tex]20+3(7+4)+5+2(7+9)[/tex]

Answer:

6.5

Step-by-step explanation:

The sum of all angles in a triangle are 180 degrees.

=> 10x -10 + 8x + 10x + 8 = 180

=> 28x -2 = 180

=> 28x = 182

=> x = 6.5

So, Angle A = 10 x 6.5 -10 = 65 - 10 = 55 degrees

     Angle B = 8 x 6.5 = 52 degrees

     Angle C = 10 x 6.5 + 8 = 65 + 8 = 73 degrees.

55 + 52 + 73 = 55 + 125 = 180 degrees

Answer:

[tex]Probability = \frac{3}{7}[/tex]

Step-by-step explanation:

Given

Electrician = 6

Mechanic = 8

Required

Determine the probability of selecting an electrician

First, we need the total number of employees;

[tex]Total = n(Electrician) + n(Mechanic)[/tex]

[tex]Total = 6 + 8[/tex]

[tex]Total = 14[/tex]

Next, is to determine the required probability using the following formula;

[tex]Probability = \frac{n(Electrician)}{Total}[/tex]

[tex]Probability = \frac{6}{14}[/tex]

Divide numerator and denominator by 2

[tex]Probability = \frac{3}{7}[/tex]

Hence, the probability of selecting an electrician is 3/7

Answer:

C≈31.42

Step-by-step explanation:

C=2πr

C=2xπx5

C≈31.42

pls mark as brainliest

Answer:

[tex]\boxed{\sf \bf \ \ -2i(6-7i)=-14-12i \ \ }[/tex]

Step-by-step explanation:

Hello, please consider the following.

[tex]-2i(6-7i)=-12i+14i^2=-14-12i[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

A

Step-by-step explanation:

Answer = A