The measures of two angles of a triangle are 105 and 31 degrees. Find the measure of the third angle.

The answer has one solution:

_______________________________

       →  x = 6 ; y = 7 ;  or, write as:  [6, 7].

_______________________________

Step-by-step explanation:

_______________________________

Given:

y = x + 1;

y = 2x – 5 ;

_______________________________

2x  – 5 = x + 1  ;  Solve for "x" ;

Subtract "x" ; and Subtract "1" ; from Each Side of the equation:

   2x  – x  – 5  – 1 = x  – x  +  1  –  1 ;

to get:  

   x   –  6  =  0  ;

Now, add "6" to Each Side of the equation;

       to isolate "x" on one side of the equation;

        and to solve for "x" :

    x   –  6   +  6 =  0  +  6  ;

to get:

       x  =  6 .

_______________________________

Now, let us solve for "y" ;  

We are given:  

  y =  x + 1  ;

Substitute our solved value for "x" ; which is:  "6" ; for "x" ; into this given equation; to obtain the value for "y" :

 y =  x + 1 ;

    =  6 + 1 ;

 y =  7 .

_______________________________

Let us check our answers by plugging the values for "x" and "y" ;

("6" ; and "7"; respectively);  into the second given equation; to see if these values for "x" and "y" ; hold true:

  Given:  y = 2x –  5 ;

        →  7 =? 2(6) –  5 ??  ;

        →  7 =? 2(6) –  5 ??  ;        

        →  7 =?  12   –  5 ??  ;

        →  7 =?   7 ?? ;

        →  Yes!

_______________________________

The answer has one solution:

       →  x = 6 ; y = 7 ;  or, write as:  [6, 7].

_______________________________

Hope this is helpful!  Best wishes!

_______________________________

Answer:

  50 in²

Step-by-step explanation:

If we assume that 5 inch and 15 inch are the base dimensions, the area formula tells us the area is ...

  A = (1/2)(b1 +b2)h

  A = (1/2)(5 in +15 in)(5 in) = 50 in²

The area of the trapezoid is 50 square inches.

Answer:8.2 x 10^5

Step-by-step explanation:

Answer:

[tex]z=\frac{404-409}{\frac{24}{\sqrt{42}}}=-1.35[/tex]  

The p value for this case is given by:

[tex]p_v =P(z<-1.35)=0.0885[/tex]  

For this case the p value is higher than the significance level given so we have enough evidence to FAIL to reject the null hypothesis and we can't conclude that the true mean is significantly less than 409

Step-by-step explanation:

Information given

[tex]\bar X=404[/tex] represent the sample mean

[tex]\sigma=24[/tex] represent the population standard deviation

[tex]n=42[/tex] sample size  

[tex]\mu_o =409[/tex] represent the value to verify

[tex]\alpha=0.01[/tex] represent the significance level for the hypothesis test.  

z would represent the statistic (variable of interest)  

[tex]p_v[/tex] represent the p value

Hypothesis to test

We want to verify if the true mean is less than 409, the system of hypothesis would be:  

Null hypothesis:[tex]\mu \geq 409[/tex]  

Alternative hypothesis:[tex]\mu < 409[/tex]  

The statistic for this case is given by:

[tex]z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}[/tex] (1)  

Replacing the info we got:

[tex]z=\frac{404-409}{\frac{24}{\sqrt{42}}}=-1.35[/tex]  

The p value for this case is given by:

[tex]p_v =P(z<-1.35)=0.0885[/tex]  

For this case the p value is higher than the significance level given so we have enough evidence to FAIL to reject the null hypothesis and we can't conclude that the true mean is significantly less than 409

Answer:

17x +7y

Step-by-step explanation:

8x + 10y + 9x - 3y

Combine like terms

8x+ 9x          + 10y - 3y

17x                   +7y

8x+9x are like terms    and 10y -3y are like terms

Answer:

17x + 7y

Step-by-step explanation:

8x + 10y + 9x - 3y

Rearrange.

8x + 9x + 10y - 3y

Factor out x and y.

x (8 + 9) + y (10 - 3)

Add or subtract.

x (17) + y (7)

17x + 7y

Answer:

Luther is wrong

Wade is right

Step-by-step explanation:

Luther's case 2^3 = 2x2x2 = 8

Wade's case 3^3 = 3 x 3 = 9

Answer:

Luther is incorrect, while Wade is correct. (2)(2)(2)=8, not 9. (3)(3)= 9.

Step-by-step explanation:

I put that as my answer and it was counted as right.

Question:

You are interested in estimating the the mean age of the citizens living in your community. In order to do this, you plan on constructing a confidence interval; however, you are not sure how many citizens should be included in the sample. If you want your sample estimate to be within 5 years of the actual mean with a confidence level of 97% , how many citizens should be included in your sample? Assume that the standard deviation of the ages of all the citizens in this community is 18 years.

Answer:

61.03

Step-by-step explanation:

Given:

Standard deviation = 18

Sample estimate = 5

Confidence level = 97%

Required:

Find sample size, n.

First find the Z value. Using zscore table

Z-value at a confidence level of 97% = 2.17

To find the sample size, use the formula below:

[tex] n = (Z * \frac{\sigma}{E})^2[/tex]

[tex] n = ( 2.17 * \frac{18}{5})^2 [/tex]

[tex] n = (2.17 * 3.6)^2 [/tex]

[tex] n = (7.812)^2 [/tex]

[tex] n = 61.03 [/tex]

Sample size = 61.03

Answer: (a) Interval where f is increasing: (0.78,+∞);

Interval where f is decreasing: (0,0.78);

(b) Local minimum: (0.78, - 0.09)

(c) Inflection point: (0.56,-0.06)

Interval concave up: (0.56,+∞)

Interval concave down: (0,0.56)

Step-by-step explanation:

(a) To determine the interval where function f is increasing or decreasing, first derive the function:

f'(x) = [tex]\frac{d}{dx}[/tex][[tex]x^{4}ln(x)[/tex]]

Using the product rule of derivative, which is: [u(x).v(x)]' = u'(x)v(x) + u(x).v'(x),

you have:

f'(x) = [tex]4x^{3}ln(x) + x_{4}.\frac{1}{x}[/tex]

f'(x) = [tex]4x^{3}ln(x) + x^{3}[/tex]

f'(x) = [tex]x^{3}[4ln(x) + 1][/tex]

Now, find the critical points: f'(x) = 0

[tex]x^{3}[4ln(x) + 1][/tex] = 0

[tex]x^{3} = 0[/tex]

x = 0

and

[tex]4ln(x) + 1 = 0[/tex]

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

x = [tex]e^{\frac{-1}{4} }[/tex]

x = 0.78

To determine the interval where f(x) is positive (increasing) or negative (decreasing), evaluate the function at each interval:

interval                 x-value                      f'(x)                       result

0<x<0.78                 0.5                 f'(0.5) = -0.22            decreasing

x>0.78                       1                         f'(1) = 1                  increasing

With the table, it can be concluded that in the interval (0,0.78) the function is decreasing while in the interval (0.78, +∞), f is increasing.

Note: As it is a natural logarithm function, there are no negative x-values.

(b) A extremum point (maximum or minimum) is found where f is defined and f' changes signs. In this case:

Then, x=0.78 is a point of minimum and its y-value is:

f(x) = [tex]x^{4}ln(x)[/tex]

f(0.78) = [tex]0.78^{4}ln(0.78)[/tex]

f(0.78) = - 0.092

The point of minimum is (0.78, - 0.092)

(c) To determine the inflection point (IP), calculate the second derivative of the function and solve for x:

f"(x) = [tex]\frac{d^{2}}{dx^{2}}[/tex] [[tex]x^{3}[4ln(x) + 1][/tex]]

f"(x) = [tex]3x^{2}[4ln(x) + 1] + 4x^{2}[/tex]

f"(x) = [tex]x^{2}[12ln(x) + 7][/tex]

[tex]x^{2}[12ln(x) + 7][/tex] = 0

[tex]x^{2} = 0\\x = 0[/tex]

and

[tex]12ln(x) + 7 = 0\\ln(x) = \frac{-7}{12} \\x = e^{\frac{-7}{12} }\\x = 0.56[/tex]

Substituing x in the function:

f(x) = [tex]x^{4}ln(x)[/tex]

f(0.56) = [tex]0.56^{4} ln(0.56)[/tex]

f(0.56) = - 0.06

The inflection point will be: (0.56, - 0.06)

In a function, the concave is down when f"(x) < 0 and up when f"(x) > 0, adn knowing that the critical points for that derivative are 0 and 0.56:

f"(x) =  [tex]x^{2}[12ln(x) + 7][/tex]

f"(0.1) = [tex]0.1^{2}[12ln(0.1)+7][/tex]

f"(0.1) = - 0.21, i.e. Concave is DOWN.

f"(0.7) = [tex]0.7^{2}[12ln(0.7)+7][/tex]

f"(0.7) = + 1.33, i.e. Concave is UP.

Answer:

The 88% confidence interval for the proportion of defectives today is (0.053, 0.123)

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

For this problem, we have that:

[tex]n = 160, \pi = \frac{14}{160} = 0.088[/tex]

88% confidence level

So [tex]\alpha = 0.12[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.12}{2} = 0.94[/tex], so [tex]Z = 1.555[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.088 - 1.555\sqrt{\frac{0.088*0.912}{160}} = 0.053[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.088 + 1.555\sqrt{\frac{0.088*0.912}{160}} = 0.123[/tex]

The 88% confidence interval for the proportion of defectives today is (0.053, 0.123)

Answer:

[tex]-\frac{161}{9}=\\or\\-16\frac{8}{9}[/tex]

Step-by-step explanation:

[tex]-6\frac{4}{9}-3\frac{2}{9}-8\frac{2}{9}=\\\\-\frac{58}{9}-\frac{29}{9}-\frac{74}{9}=\\\\-\frac{161}{9}=\\\\-16\frac{8}{9}[/tex]

Step-by-step explanation:

4m2 - 24m + 8m - 32

4m2 - 16m - 32

Answer:

(a) The value of E (X) is 4/7.

    The value of V (X) is 3/98.

(b) The value of P (X ≤ 0.5) is 0.3438.

Step-by-step explanation:

The random variable X is defined as the proportion of surface area in a randomly selected quadrant that is covered by a certain plant.

The random variable X follows a standard beta distribution with parameters α = 4 and β = 3.

The probability density function of X is as follows:

[tex]f(x) = \frac{x^{\alpha-1}(1-x)^{\beta-1}}{B(\alpha,\beta)} ; \hspace{.3in}0 \le x \le 1;\ \alpha, \beta > 0[/tex]

Here, B (α, β) is:

[tex]B(\alpha,\beta)=\frac{(\alpha-1)!\cdot\ (\beta-1)!}{((\alpha+\beta)-1)!}[/tex]

            [tex]=\frac{(4-1)!\cdot\ (3-1)!}{((4+3)-1)!}\\\\=\frac{6\times 2}{720}\\\\=\frac{1}{60}[/tex]

So, the pdf of X is:

[tex]f(x) = \frac{x^{4-1}(1-x)^{3-1}}{1/60}=60\cdot\ [x^{3}(1-x)^{2}];\ 0\leq x\leq 1[/tex]

(a)

Compute the value of E (X) as follows:

[tex]E (X)=\frac{\alpha }{\alpha +\beta }[/tex]

         [tex]=\frac{4}{4+3}\\\\=\frac{4}{7}[/tex]

The value of E (X) is 4/7.

Compute the value of V (X) as follows:

[tex]V (X)=\frac{\alpha\ \cdot\ \beta}{(\alpha+\beta)^{2}\ \cdot\ (\alpha+\beta+1)}[/tex]

         [tex]=\frac{4\cdot\ 3}{(4+3)^{2}\cdot\ (4+3+1)}\\\\=\frac{12}{49\times 8}\\\\=\frac{3}{98}[/tex]

The value of V (X) is 3/98.

(b)

Compute the value of P (X ≤ 0.5) as follows:

[tex]P(X\leq 0.50) = \int\limits^{0.50}_{0}{60\cdot\ [x^{3}(1-x)^{2}]} \, dx[/tex]

                    [tex]=60\int\limits^{0.50}_{0}{[x^{3}(1+x^{2}-2x)]} \, dx \\\\=60\int\limits^{0.50}_{0}{[x^{3}+x^{5}-2x^{4}]} \, dx \\\\=60\times [\dfrac{x^4}{4}+\dfrac{x^6}{6}-\dfrac{2x^5}{5}]\limits^{0.50}_{0}\\\\=60\times [\dfrac{x^4\left(10x^2-24x+15\right)}{60}]\limits^{0.50}_{0}\\\\=[x^4\left(10x^2-24x+15\right)]\limits^{0.50}_{0}\\\\=0.34375\\\\\approx 0.3438[/tex]

Thus, the value of P (X ≤ 0.5) is 0.3438.

Answer:145

Step-by-step explanation: $19=20 76=80 53=50 23=20 12=10 total = 180 325-180 =145

Answer:

Option C (-4,-1) (In Quadrant III)

Step-by-step explanation:

Coordinate = (-4,1)

=> Reflecting over y-axis will make the coordinate (4,1)

=> Reflecting across x-axis will make the coordinate (4,-1)

=> Rotating 180 will make it (-4,-1)

Answer:

The amount of money separating the lowest 80% of the amount invested from the highest 20% in a sampling distribution of 10 of the family's real estate holdings is $238,281.57.

Step-by-step explanation:

Let the random variable X represent the amount of money that the family has invested in different real estate properties.

The random variable X follows a Normal distribution with parameters μ = $225,000 and σ = $50,000.

It is provided that the family has invested in n = 10 different real estate properties.

Then the mean and standard deviation of amount of money that the family has invested in these 10 different real estate properties is:

[tex]\mu_{\bar x}=\mu=\$225,000\\\\\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}=\frac{50000}{\sqrt{10}}=15811.39[/tex]

Now the lowest 80% of the amount invested can be represented as follows:

[tex]P(\bar X<\bar x)=0.80\\\\\Rightarrow P(Z<z)=0.80[/tex]

The value of z is 0.84.

*Use a z-table.

Compute the value of the mean amount invested as follows:

[tex]\bar x=\mu_{\bar x}+z\cdot \sigma_{\bar x}[/tex]

   [tex]=225000+(0.84\times 15811.39)\\\\=225000+13281.5676\\\\=238281.5676\\\\\approx 238281.57[/tex]

Thus, the amount of money separating the lowest 80% of the amount invested from the highest 20% in a sampling distribution of 10 of the family's real estate holdings is $238,281.57.

Answer:

Length: 18

Width: 9

Step-by-step explanation:

Denote the width as x, hence the length is x+9. As a result, you can create the equation x(x+9) = 162. Solving, you find x = 9.

Answer:

________________________

Answer:

Its D The Last Graph

Step-by-step explanation:

it just is my guy

Answer:

it’s C

Step-by-step explanation:

No, the vertices of the image and pre-image do not correspond

No, the vertices of the image and pre-image do not correspond, Micaela tried to rotate the square 180° about the origin. Hence, option C is correct.

A figure can be rotated by 90 degrees clockwise by rotating each vertex of the figure 90 degrees clockwise about the origin.

Let's take the vertices of a square with points at (+1,+1), (-1,+1), (-1,-1), and (+1,-1), centered at the origin, can be found in the following positions after rotation:

Micaela's rotation must be accurate if it led to the same points. Her rotation is incorrect if the points are different, though.

It is impossible to tell if Micaela's rotation is accurate without more details or a diagram.

Thus, option C is correct.

For more information about rotation about the origin, click here:

https://brainly.com/question/30198965

#SPJ7

Answer:

5.12 x 10¹¹ bit

Step-by-step explanation:

1GB = 8 x 10⁹ bits

so 64gb = 64 x 8 x 10⁹

= 512 x 10⁹

= 5.12 x 10¹¹ bits

scientific notation = 5.12 x 10¹¹ bits

standard Notation = 512 ,000,000,000 bits.

Answer:

[tex] \frac{1}{2} [/tex]

Step-by-step explanation:

[tex]scale \: factor = \frac{5}{10} = \frac{1}{2} \\ [/tex]

Answer:

2

Step-by-step explanation:

Since there are four negative signs, we have -1 multiplying each other 4 times,  multiplying by positive 2. This is then 1 * 2, which is 2.

Answer:

+2

Step-by-step explanation:

=> -(-(-(-2))))

=> -(-(+2))

=> -(-2)

=> +2

Answer:

B) 92.03 < μ < 97.97

99% confidence interval for the mean score of all students.

92.03 < μ < 97.97

Step-by-step explanation:

Step(i):-

Given sample mean (x⁻) = 95

standard deviation of the sample (s) = 6.6

Random sample size 'n' = 30

99% confidence interval for the mean score of all students.

[tex]((x^{-} - Z_{0.01} \frac{S}{\sqrt{n} } , (x^{-} + Z_{0.01} \frac{S}{\sqrt{n} })[/tex]

step(ii):-

Degrees of freedom

ν =   n-1 = 30-1 =29

[tex]t_{0.01} = 2.462[/tex]

99% confidence interval for the mean score of all students.

[tex]((95 - 2.462 \frac{6.6}{\sqrt{30} } , 95 + 2.462\frac{6.6}{\sqrt{30} } )[/tex]

( 95 - 2.966 , 95 + 2.966)

(92.03 , 97.97)

Final answer:-

99% confidence interval for the mean score of all students.

92.03 < μ < 97.97

Answer:

x = 6√2

Step-by-step explanation:

It is a 45°45°90° triangle so you can use the ratio.

x : x√2

x = 6√2

Answer:

  7

Step-by-step explanation:

The number of cells in a tile is 4. If colored alternately, there are 3 of one color and 1 of the alternate color. To balance the coloring, an even number of tiles is needed. Hence the board dimensions must be multiples of 4.

In the given range, there are 7 such boards:

  4×4, 8×8, 12×12, 16×16, 20×20, 24×24, and 28×28

Answer:

[tex] P(X\geq 2)=1- P(X<2)= 1-[P(X=0) +P(X=1)][/tex]

And using the probability mass function we can find the individual probabilities:

[tex]P(X=0)=(8C0)(0.18)^0 (1-0.18)^{8-0}=0.2044[/tex]

[tex]P(X=1)=(8C1)(0.18)^1 (1-0.18)^{0-1}=0.3590[/tex]

And replacing we got:

[tex] P(X\geq 2)=1 -[0.2044 +0.3590]= 0.4366[/tex]

Then the probability that at least 2 disapprove of daily pot smoking is 0.4366

Step-by-step explanation:

Let X the random variable of interest "number of seniors who disapprove of daily smoking ", on this case we now that:

[tex]X \sim Binom(n=8, p=0.18)[/tex]

The probability mass function for the Binomial distribution is given as:

[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]

Where (nCx) means combinatory and it's given by this formula:

[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]

And we want to find this probability:

[tex] P(X\geq 2)=1- P(X<2)= 1-[P(X=0) +P(X=1)][/tex]

And using the probability mass function we can find the individual probabilities:

[tex]P(X=0)=(8C0)(0.18)^0 (1-0.18)^{8-0}=0.2044[/tex]

[tex]P(X=1)=(8C1)(0.18)^1 (1-0.18)^{0-1}=0.3590[/tex]

And replacing we got:

[tex] P(X\geq 2)=1 -[0.2044 +0.3590]= 0.4366[/tex]

Then the probability that at least 2 disapprove of daily pot smoking is 0.4366

Answer:

-3

Step-by-step explanation:

every sequence goes down by -3

Answer:

take away 3. the common difference is 3

Step-by-step explanation:

take away 3

Answer:

X is 3 units.

Step-by-step explanation:

Volume of prism is cross sectional area multiplied by length. So 1/2 ×2× x ×2 into 3x, which is equal to 6x^2. So, 6x^2=54. Therefore, x=3.

Answer:

The full name of the place is the "Danat Jebel Dhanna".  The Jebel Dhanna is currently located in the Abu Dhabi.  It is said that it is one of the most best beach in the UAE, they also say that it is the biggest resort, of course, with a bunch of hotels.

hope this helps ;)

best regards,

`FL°°F~` (floof)