which of the following demonstrates how the first 21 on the left side of the triangle is calculated using the combination pattern?

Answer:

Q.2 [tex]4\sqrt2[/tex] units

Q.3 [tex]10\sqrt2[/tex] units

Step-by-step explanation:

Given that points:

C(-1, 3) and D (-5, 7)

E(0, -5) and F(10, -15)

To find:

Q.2. Distance between C and D

Q.3. Distance between E and F

Solution:

First of all, let us solve the question marked as number 2 in the attached image.

C(-1, 3) and D (-5, 7)

[tex]x_2 = -5\\x_1 = -1\\y_2 = 7\\y_1 = 3[/tex]

To find the distance 'd' between the points, we can use distance formula:

[tex]d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

[tex]d = \sqrt{(-5-(-1))^2+(7-3)^2}\\\Rightarrow d = \sqrt{(-4)^2+(4)^2}\\\Rightarrow d =\sqrt{16+16}\\\Rightarrow d =\sqrt{32} = 4\sqrt2\ units[/tex]

First of all, let us solve the question marked as number 3 in the attached image.

E(0, -5) and F(10, -15)

[tex]x_2 = 10\\x_1 = 0\\y_2 = -15\\y_1 = -5[/tex]

To find the distance 'd' between the points, we can use distance formula:

[tex]d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

[tex]d = \sqrt{(10-0)^2+(-15-(-5))^2}\\\Rightarrow d = \sqrt{10^2+(-10)^2}\\\Rightarrow d =\sqrt{100+100}\\\Rightarrow d =\sqrt{200} = 10\sqrt2\ units[/tex]

Please find attached image for the answers filled in the boxes.

Answer:

There is sufficient evidence to support the claim that the standard deviation is less than 14.7.

Step-by-step explanation:

From the question we are told that that the null hypothesis is

       [tex]H_o : \sigma < 14.7[/tex]

Now given from the question that this null hypothesis was rejected, it mean, in non technical term that there is sufficient evidence to support the claim that the standard deviation is less than 14.7.

Answer:

The answer is option C.

Step-by-step explanation:

- 9x - 3 > 51

Group like terms

- 9x > 51 + 3

- 9x > 54

Divide both sides by -9

x < - 6

Hope this helps you

Answer:

a)  Y = 350 + 130X

b) C. The symbol [tex]\hat {y}[/tex] represents the predicted value of price.

Step-by-step explanation:

The equation of a regression line is given as:

Y = a + bX

Where Y is the dependent variable, X is the independent variable, a is the intercept on the y axis when X = 0 and b is the slope of the regression line.

a)  The regression equation has a slope of 130 and a y-intercept of 350. From Y = a + bX, the equation of the regression line is:

Y = 350 + 130X

b) From the question x represents the ratings of different hotels in a certain area and [tex]\hat {y}[/tex] represents the price of the different hotels based on their ratings. Since a regression line is drawn, y represents the predicted value of price

Answer:

proper because the numerator is lower than the denominator

Answer:

9.941*10^-6

Step-by-step explanation:

Probability of at most 1 means not more than 1 defective= probability of 1 or probability of 0

Probability of 1 = 50C1(0.25)(0.75)^49

Probability= 50(0.25)*7.55*10^-7

Probability= 9.375*10^-6

Probability of 0

= 50C0(0.25)^0(0.75)^50

= 1(1)(0.566*10^-6)

= 0.566*10^-6

Total probability

= 9.375*10^-6+ 0.566*10^-6

= 9.941*10^-6

Answer:

T(n) = 5n + 20

Step-by-step explanation:

1 candy has a mass of 5 g.

n candies have a mass of 5n grams.

The box has a mass of 20 grams.

total mass = mass of candies + mass of box

T(n) = 5n + 20

n         T(n)

0           20

25         145

50         270

75          395

100        520

Answer:

y = -15

Step-by-step explanation:

x-5y=-15x−5

Let x = -5

-5 -5y = -15 * -5 -5

Combine like terms

-5 -5y = 75-5

-5 -5y = 70

Add 5 to each side

-5y = 75

Divide by -5

y = -15

Answer:

B. 3

Step-by-step Explanation:

To find the average rate of change of the exponential function represented by the table of values above can be calculated using the general formula for average rate of change of a function, which is given as [tex] m = \frac{f(b) - f(a)}{b - a} [/tex]

Where,

[tex] a = 1, f(1) = 7 [/tex]

[tex] b = 3, f(3) = 13 [/tex]

Plug in the above values in the average rate of change formula:

[tex] m = \frac{13 - 7}{3 - 1} [/tex]

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

[tex] m = 3 [/tex]

Average rate of change is B. 3

Answer:

3

Step-by-step explanation:

Answer:

It would be B. Circle

Answer:

Step-by-step explanation:

A linear graph with y values (height of tree) going up 2.5 with each increase of x (growing season)

This is the model that best fits the graph describing a growth of a plant

Answer:

240

Step-by-step explanation:

You should go to the value 50 °F and see the value that match it

here it's 240 students

Based on the line of best fit, the number of students who wear a jacket to school when the temperature is 50°F is 240.

A graph is a way to represent a lot of data in such a visual format that it is easy for the user to understand the complete information in one go. Usually, the line of the graph is a function that follows the graph.

Given that The graph shows a line of best fit for data collected on the number of students who wear a jacket to school and the average daily temperature in degrees Fahrenheit.

Now, Based on the line of best fit, the number of students who wear a jacket to school when the temperature is 50°F can be found by simply observing the graph when the average daily temperature is 50°F as shown below, and then looking the value of y at that temperature.

Hence,  Based on the line of best fit, the number of students who wear a jacket to school when the temperature is 50°F is 240.

Learn more about Graph:

https://brainly.com/question/21608293

#SPJ5

Answer:

s = 0     OR     s = 2

Step-by-step explanation:

=> [tex]-s^2+2s = 0[/tex]

=> [tex]-s(s-2)=0[/tex]

So, Either:

=> -s = 0   OR    s-2 = 0

=> s = 0     OR     s = 2

Answer:

s=0,2

Step-by-step explanation:

-s^2+2s=0

Factor out -s

-s ( s-2) =0

Using the zero product property

-s =0  s-2 =0

s=0   s=2

Answer: Regression line equation:  [tex]\hat{y}=-1.008x+39.1704[/tex]

Step-by-step explanation:

Equation of least-squares regression line for predicting y :

[tex]\hat{y}=b_1x+b_o[/tex]

, where [tex]\text{Slope} (b_1)=r\dfrac{s_y}{s_x}[/tex] ,  [tex]\text{intercept}(b_0)=\bar{y}-b_1\bar{x}[/tex]

Given: [tex]\bar{x}=8.8,\ s_x=1.5,\ s_y=1.8,\ \bar{y}=30.3,\ r=-0.84[/tex]

Then,

[tex]b_1=(-0.84)\dfrac{ 1.8}{ 1.5}\\\\\Rightarrow\ b_1=-1.008[/tex]

Now,

[tex]b_0=30.3-(-1.008)(8.8)=30.3+8.8704\\\\\Rightarrow\ b_0=39.1704[/tex]

Then, Regression line equation:  [tex]\hat{y}=-1.008x+39.1704[/tex]

Answer:

59 accidents were investigated.

Step-by-step explanation:

The question above is a probability question that involves 2 elements: causes of accidents.

Let

A = Alcohol

E = Excessive speed

In the question, we are given the following information:

18 accidents involved Alcohol and Excessive speed =P(A ∩ E)

26 involved Alcohol = P(A)

12 accidents involved excessive speed but not alcohol = P( E ) Only

21 accidents involved neither alcohol nor excessive speed = neither A U B

We were given P(A) in the question. P(A Only) = P(A) - P(A ∩ E)

P(A Only) = 26 - 18

= 8

So, only 8 accident involved Alcohol but not excessive speed.

The Total number of Accidents investigated = P(A Only) + P( E only) + P(A ∩ E) + P( neither A U B)

= 8 + 12 + 18 + 21

= 59

Therefore, 59 accidents were investigated.

Answer:

Standard form = y = mx + c

m = Δy/Δx

m = 5/2

y = 5/2 x + c

Sub in (4,2)

2 = 10 + c

c = -8

y = 5/2 x - 8  

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]\frac{sin~x}{sec~x+1} =\frac{sin~x}{\frac{1}{cos~x}+1 } =\frac{sin~x~cos~x}{1+cos~x} \\=\frac{sin~x~cos~x}{1+cos~x} \times \frac{1-cos~x}{1-cos~x} \\=\frac{sin~x~cos~x(1-cos~x)}{1-cos^2 x} \\=\frac{sin~x~cos~x(1-cos~x)}{sin^2x} \\=\frac{cos~x(1-cos~x)}{sin~x} \\=cos ~x(csc~x-cot~x)\\or\\=cot~x(1-cos~x)[/tex]

Answer:

18.4°

Step-by-step explanation:

Use law of cosine.

a² = b² + c² − 2bc cos A

11² = 20² + 28² − 2(20)(28) cos A

121 = 1184 − 1120 cos A

cos A = 0.949

A = 18.4°

Answer:

a)the proportion of student is 0.1082

b)

H1: p = .08

H2: p not equal to 0.08

H1: p =0 .08

H2: p < .08

H1: p =0 .08

H2: p >0 .08

c)z=1.45

d) the p value is 0.1470

e)null hypothesis cannot be accepted,There is no enough evidence to reject the  null hypothesis.

Step-by-step explanation:

CHECK THE ATTACHMENT FOR DETAILED EXPLANATION

Answer:

a)x - 4y -14 =0

5x - y - 13 =0

Step-by-step explanation:

Using substitution method to solve equation above gives:

x - 4y - 14 =0 ....eq1

5x - y -13 =0 ....eqn2

From eqn1, making x the subject formula:

x - 4y - 14 =0

x - 4y =14

x = 14+4y ...eqn3

From eqn2, substitute value of x and solve for y:

5(14+4y)-y-13 =0

70+20y-y-13 =0

70+19y-13 =0

70 - 13 = -19y

57 = -19y

divide both sides by -19

-57/19 = -19y/-19, then

y = -3

From eqn1:

x = 14 + 4y

substitute the value of y in the expression above

x = 14 + 4(-3)

x = 14 + (-12)

x = 14 - 12

x = 2

Answer:

The probability is  [tex]P(X \ge 20 ) = 0.3707[/tex]

Step-by-step explanation:

From the the question we are told that

    The population proportion is  p =  0.60

    The sample size is  n  =  31

The  mean is evaluated as

       [tex]\mu = n * p[/tex]

substituting values  

       [tex]\mu = 31 *0.60[/tex]

       [tex]\mu = 18.6[/tex]

The standard deviation is evaluated as

    [tex]\sigma = \sqrt{n * p * (1- p )}[/tex]

substituting values  

    [tex]\sigma = \sqrt{31 * 0.6 * (1- 0.6 )}[/tex]

    [tex]\sigma = 2.73[/tex]

The  the probability that at least 20 of them have looked at their score in the past six months is mathematically represented as

     [tex]P(X \ge 20) = 1- P(X < 20)[/tex]

 applying normal approximation we have that

     [tex]P(X \ge 20) = 1- P(X < (20-0.5))[/tex]

   Standardizing

         [tex]1 - P(X < 20) = 1 - P(\frac{X - \mu }{\sigma} < \frac{19.5 - \mu }{\sigma } )[/tex]

         [tex]1 - P(X < 20) = 1 - P(Z < \frac{19.5 - 18.6 }{2.73 } )[/tex]

         [tex]1 - P(X < 20) = 1 - P(Z < 0.33)[/tex]

Form the standardized normal distribution table we have that

      [tex]P(Z < 0.0512)[/tex] = 0.6293

=>   [tex]P(X \ge 20 ) = 1- 0.6293[/tex]

=>   [tex]P(X \ge 20 ) = 0.3707[/tex]

Answer:

A=64340 dollars

Step-by-step explanation:

A=p(1+r)^t     p principal, t= time period, r is the rate

A=21000(1+0.0775)^15= 64339.61

A=64340 dollars

Answer:

Step-by-step explanation:

The side lengths are equal - supposedly

30                          25

?                              ?

25 + ? = 45

-25        - 25

? = 20

45 - 30 = 15

The question mark should be equal to 15.

Hope this helps,

Kavitha

Answer:

2x - 4.

Step-by-step explanation:

4 less than twice a number is the same thing as a number times 2 minus 4. Let's say that the number is represented by x.

2 * x - 4 = 2x - 4.

Hope this helps!

We're told (and we can confirm) that [tex]v_3=2v_1-3v_2[/tex], so [tex]v_3[/tex] is a linear combination of the other two vectors.

This means H is sufficiently spanned by [tex]\{v_1,v_2\}[/tex]; no need for the third vector.

But this also means we can write either [tex]v_1[/tex] as a linear combination of [tex]\{v_2,v_3\}[/tex], and [tex]v_2[/tex] as a lin. com. of [tex]\{v_1,v_3\}[/tex]. So any set of these three vectors taken two at a time will span the subspace H. Hence all of b, c, and d are acceptable.

Answer:

[tex]\huge\boxed{slope=\dfrac{1}{2}=0.5}[/tex]

Step-by-step explanation:

The formula of a slope:

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

We have the points

[tex](-5;\ 3)\to x_1=-5;\ y_1=3\\(7;\ 9)\to x_2=7;\ y_2=9[/tex]

Substitute:

[tex]m=\dfrac{9-3}{7-(-5)}=\dfrac{6}{7+5}=\dfrac{6}{12}=\dfrac{6:6}{12:6}=\dfrac{1}{2}[/tex]

Answer:

1/2

Step-by-step explanation:

We can use the slope formula since we have 2 points

m = ( y2-y1)/(x2-x1)

    = (9-3)/( 7 - -5)

    = (9-3) /( 7+5)

   = 6/ 12

  = 1/2

Answer:

201 miles

Step-by-step explanation:

Base fee =  $15.95

Mileage fee = $ 0.95  per/mile

Paid = $206.90

Distance= ?

--------------

Equation to calculate miles:

Answer:

(-2, -(2pi)/3)

Step-by-step explanation:

a p ex

In da pic :)))))))))

Answer:

Step-by-step explanation:

Recursively Defined Function               Sequence

f(1) = 13 f(n) = f(n - 1) + 26 for n ≥ 2         13, 39, 65, 91, ...

f(1) = 13 f(n) = 3 · f(n - 1) for n ≥ 2

f(1) = -24 f(n) = -4 · f(n - 1) for n ≥ 2

f(1) = 28 f(n) = f(n - 1) - 84 for n ≥ 2

f(1) = 28 f(n) = -4 · f(n - 1) for n ≥ 2         28, -112, 448, -1,792, ...

f(1) = -24 f(n) = 4 · f(n - 1) for n ≥ 2         -24, -96, -384, -1,536, ...

__

The initial values are easily seen. They match f(1). The recursive functions can be tested to see if they match the offered sequences.

  sequence 1 has a common ratio of 4 (not -4)

  sequence 2 has a common ratio of -4 (it is not arithmetic)

  sequence 3 has a common difference of 26 (it is not geometric)

Answer:

1 is sequence 3

5 is sequence 2

6 is sequence 1

(These r not included in the test, so don't use them)

 |

\ /

2 is no matching sequence

3 is no matching sequence

4 is no matching sequence

Step-by-step explanation:

PLATO

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            Hi my lil bunny!

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Let's solve this step by step.

[tex]2^x + 4^x + 8^x = -14[/tex]

              ↓

In order to factor an integer, we need to repeatedly divide it by the ascending sequence of primes (2, 3, 5...).

The number of times that each prime divides the original integer becomes its exponent in the final result.

    Prime number 2 to the power of 2 = 4                

[tex]2^x + (2^2)^x + (2^3) ^x = -14[/tex]

                    ↓

Prime number 2 to the power of 3 = 8

[tex]2^x + 2^2x + 2^3x = -14[/tex]

                    ↓

We need to exponentiate the power.

The following rule is applied:

           [tex](A^B) ^C = A^BC[/tex]

In our example,

   A is equal to 2,

   B is equal to 2 and

   C is equal to x.

[tex]( 2^x + 2^2x + 2^3x ) + 14 = -14 + 14[/tex]

                         ↑

In order to solve this non-linear equation, we need to move all the terms to the left side.

In our example,

- term −14, will be moved to the left side.

Notice that a term changes sign when it 'moves' from one side of the equation to the other.

___________________

We need to get rid of expression parentheses.

If there is a negative sign in front of it, each term within the expression changes sign.

Otherwise, the expression remains unchanged.

In our example, there are no negative expressions.

                                  ↓

            [tex]2^x + 2^2x + 2^3x + 14 = 0[/tex]

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Hope this helped you.

Could you maybe give brainliest..?

❀*May*❀