find the median of the list 12,18,21,25,30,43

Answer:

The area of the quadrilateral ABCD is 114 square units

Step-by-step explanation:

We must calculate the area of each triangle and then add these areas so we calculate the area of the quadrilateral ABCD

First for the BAD right triangle:

AD = sqrt [BD ^ 2 - AB ^ 2]

AD = sqrt [15 ^ 2 - 12 ^ 2]

AD = sqrt [225-144]

AD = sqrt [81]

AD = 9

The area of a triangle is half the product of the base times the height, that is:

A1 = AB * AD / 2 = 12 * 9/2 = 54

Then for the second triangle in the right triangle BDC:

DC = sqrt [BC ^ 2 - BD ^ 2]

DC = sqrt [17 ^ 2 - 15 ^ 2]

DC = sqrt [289 - 225]

DC = sqrt [64] = 8

We calculate the area

A2 = DC * BD / 2 = 8 * 15/2 = 60

The total area then is:

AT = A1 + A2

AT = 54 + 60 = 114

Which means that the area of the quadrilateral ABCD is 114 square units

Answer:

X ≥ 3   (D)

Step-by-step explanation:

I got it right on Khan Academy :)

Answer:

AAAAAAAAAAAAAAAAAAAA

Step-by-step explanation:

x < 7

Answer:

18.333

Step-by-step explanation:

Answer:

The solutions to the system of equations are [tex]y=4,\:x=5[/tex].

Step-by-step explanation:

To solve the system [tex]\begin{bmatrix}4x+5y=40\\ 6x+3y=42\end{bmatrix}[/tex]

First,

[tex]\mathrm{Multiply\:}4x+5y=40\mathrm{\:by\:}3\:\mathrm{:}\:\quad \:12x+15y=120\\\\\mathrm{Multiply\:}6x+3y=42\mathrm{\:by\:}2\:\mathrm{:}\:\quad \:12x+6y=84[/tex]

[tex]\begin{bmatrix}12x+15y=120\\ 12x+6y=84\end{bmatrix}[/tex]

Subtract the first equation from the second equation

[tex]12x+6y=84\\\underline{-12x-15y=-120}\\-9y=-36[/tex]

Solve [tex]-9y=-36[/tex] for y:

[tex]\frac{-9y}{-9}=\frac{-36}{-9}\\y=4[/tex]

For [tex]12x+15y=12[/tex] plug in [tex]y=4[/tex] and solve for x

[tex]12x+15\cdot \:4=120\\12x=60\\x=5[/tex]

The solutions to the system of equations are:

[tex]y=4,\:x=5[/tex]

Answer:

6.14125(0.15) = 0.9211875 (below 1)

6.14125 - 0.92118 = 5.22007

Step-by-step explanation:

Given data

1. 10(.15)=1.5

2. 10-1.5=8.5

3. 8.5 (.15)=1.275

4. 8.5-1.275=7.225

continuation the sequence

5)    7.225 (0.15) = 1.08375

6)    7.225 -  1.08375 = 6.14125

7)   6.14125(0.15) = 0.9211875   (below -one)

8 ) 6.14125 - 0.9211875 = 5.2200625 (get number 5)

9)   5.2200625(0.15) = 0.783009

10) 5.2200625 - 0.783009 = 4.4370532

Answer:

10 x 17.1 = 171

Step-by-step explanation:

10 x 17.1 = 17.1

Answer:

a) [tex] z = \frac{40-35.33}{1.794}= 2.60[/tex]

b) [tex] z = \frac{40-35.33}{1.794}= 2.60[/tex]

c) [tex] z = \frac{30-35.33}{1.794}= -2.97[/tex]

Step-by-step explanation:

For this case we know that the mean for the random variable of interest is [tex]\mu = 35.33[/tex] and the variance [tex]\sigma^2 = 3.22[/tex] so then the deviation would be [tex]\sigma = \sqrt{3.22}= 1.794[/tex]

The z score is given by thsi formula:

[tex] z = \frac{X -\mu}{\sigma}[/tex]

Part a

We want this probability:

[tex] P(X>40)[/tex]

And if we find the z score we got:

[tex] z = \frac{40-35.33}{1.794}= 2.60[/tex]

And we can find this probability: [tex] P(Z>2.60)[/tex]

Part b

We want this probability:

[tex] P(X<40)[/tex]

And if we find the z score we got:

[tex] z = \frac{40-35.33}{1.794}= 2.60[/tex]

And we can find this probability: [tex] P(Z<2.60)[/tex]

Part c

We want this probability:

[tex] P(X<30)[/tex]

And if we find the z score we got:

[tex] z = \frac{30-35.33}{1.794}= -2.97[/tex]

And we can find this probability: [tex] P(Z<-2.97)[/tex]

Answer:

Check the explanation

Step-by-step explanation:

Kindly check the attached image below to see the step by step explanation to the question above.

Answer:

3

Step-by-step explanation:

Well, first off I'm assuming that by "scar factor" you mean scale factor. So if the two squares are similar then that means the sides are also similar, that means that they are equivalent. So all you have to do is 12/4 to get 3. So then to check it, you do 4 times 3 which gets you to 12.

So the final answer is 3

Answer:

Step-by-step explanation:

A general equation of a hyperbola is

 x^2     y^2

-------- - ------- = 1   (This applies only when the center of the hyperbola

 a^2     b^2                               is at (0, 0)  ).

You must compare the given equations to this standard form to identify which represents the hyperbola shown, and also you must share the illustration of the hyperbola.

The equation represents the hyperbola shown in the graph is  (y - 1)² / 9 - (x + 4)² / 4  = 1

A hyperbola is a type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set.

A hyperbola has two pieces, called connected components or branches, that are mirror images of each other and resemble two infinite bows.

Given that, a graph, showing hyperbola, we need to find the equation,

We have the general equation for up - down facing hyperbola as

(y - k)² / b²- (x - h)² / a²  = 1.

Let's start listing the properties of this graph -

Taking a look at the graph we see that the center point of our hyperbola here is (- 4, 1).

Therefore, (h, k) = (- 4,1).

This is the semi distance from the center to one of the vertices. Here it will be the distance from points (- 4,1) and (- 4,4) or 3 unit difference.

Therefore, a = 3.

That gives asymptotes. Now remember that it will be in the form

y = ± b / a.

We already know a = 3, so we have to find b.

Looking at this graph we can say that another point besides (- 4,1) that lies on the "dotted line" is (- 2, - 2).

Calculating the slope of the dotted line would be as follows,

Given: (- 4,1) and (- 2, - 2)

Slope = - 2 + 4 / - 2 - 1 = 2 / 3

We have the equation y = 2 / 3x.

Therefore, b = 2.

Let's substitute to equation...

h = - 4, k = 1, b = 2, a = 3

(y - 1)² / (3)²- (x + 4)² / (2)²  = 1

(y - 1)² / 9 - (x + 4)² / 4  = 1

Hence, the equation represents the hyperbola shown in the graph is  (y - 1)² / 9 - (x + 4)² / 4  = 1

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The complete question is attached

Answer:

The point of estimate for the true difference would be:

[tex] 186-171= 15[/tex]

And the confidence interval is given by:

[tex] (186-171) -1.77 \sqrt{\frac{33^2}{8} +\frac{23^2}{7}}= -10.753[/tex]

[tex] (186-171) +1.77 \sqrt{\frac{33^2}{8} +\frac{23^2}{7}}= 40.753[/tex]

Step-by-step explanation:

For this case we have the following info given:

[tex] \bar X_1 = 186[/tex] the sample mean for the first sample

[tex] \bar X_2 = 171[/tex] the sample mean for the second sample

[tex]s_1 =33[/tex] the sample deviation for the first sample

[tex]s_2 =23[/tex] the sample deviation for the second sample

[tex]n_1 = 8[/tex] the sample size for the first group

[tex]n_2 = 7[/tex] the sample size for the second group

The confidence interval for the true difference is given by:

[tex] (\bar X_1 -\bar X_2) \pm t_{\alpha/2}\sqrt{\frac{s^2_1}{n_1} +\frac{s^2_2}{n_2}}[/tex]

We can find the degrees of freedom are given:

[tex] df = n_1 +n_2 -2 =8+7-2= 13[/tex]

The confidence level is given by 90% so then the significance would be [tex]\alpha=1-0.9=0.1[/tex] and [tex]\alpha/2=0.05[/tex] we can find the critical value with the degrees of freedom given and we got:

[tex] t_{\alpha/2}= \pm 1.77[/tex]

The point of estimate for the true difference would be:

[tex] 186-171= 15[/tex]

And replacing into the formula for the confidence interval we got:

[tex] (186-171) -1.77 \sqrt{\frac{33^2}{8} +\frac{23^2}{7}}= -10.753[/tex]

[tex] (186-171) +1.77 \sqrt{\frac{33^2}{8} +\frac{23^2}{7}}= 40.753[/tex]

Answer:

Total textbook cost of tuition fees per month will be $ 2,356 and 25 cents

Step-by-step explanation:

To solve the exercise, we will first define the total cost per quarter.

cost of 1 credit hour = $ 601

then we solve the following:

cost of 15 credit hours = $ 601 * 15 = $ 9015

textbooks = $ 410

then we solve the following:

total cost = 9015 + 410 = $ 9425

total cost for 3 quarters = 3 * $ 9425 = $ 28275 for 12 months

we calculate as follows

Total textbook cost of tuition fees per month will be

$ 28,275 / 12 = $ 2,356 and 25 cents

Answer:

A'B'= 3 cm and B'D' = 1.6 cm

Step-by-step explanation:

First of all, we are told that the scale factor = 1/5

Now,we know that If the scale factor is less than 1, then the dilation is a reduction.

Thus, in this question the dilation is a reduction.

For us to calculate the dimensions of the dilated rectangle, we'll multiply the original dimensions by the scale factor

Thus;

A'B' = AB(1/5)

A'B' = 15(1/5) = 3 cm

B'D' = BD(1/5) = 8(1/5) = 1.6 cm

Thus, The length of each side of the dilated rectangle are;

A'B'= 3 cm and B'D' = 1.6 cm

Answer:  D. p(d) = 3(10000)p​

Step-by-step explanation:

The function is p(d) = 3(10000)p, where p is the bacteria population and the number of days, d. The correct answer would be option (D).

The function is defined as a mathematical expression that defines a relationship between one variable and another variable.

As per the given situation, we can write the function would be as:

⇒ p(d) = 3(10000)p

It states that the population of the bacteria, p, is equal to the starting population of 10,000 multiplied by 3 number of days, d. This function correctly represents the idea that the population triples each day.

Hence, the correct answer would be an option (D).

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Answer:

We conclude that the true average estimated calorie content in the population sampled exceeds the actual content.

Step-by-step explanation:

We are given that an article reported on a pilot study in which each of 58 individuals in a sample was asked to estimate the calorie content of a 12 oz can of beer known to contain 153 calories.

The resulting sample mean estimated calorie level was 193 and the sample standard deviation was 88.

Let [tex]\mu[/tex] = true average estimated calorie content in the population sampled.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] [tex]\leq[/tex] 153 calories     {means that the true average estimated calorie content in the population sampled does not exceeds the actual content}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 153 calories     {means that the true average estimated calorie content in the population sampled exceeds the actual content}

The test statistics that would be used here One-sample t test statistics as we don't know about the population standard deviation;

                             T.S. =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~ [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample mean estimated calorie level = 193 calories

            s = sample standard deviation = 88

            n = sample of individuals = 58

So, the test statistics  =  [tex]\frac{193-153}{\frac{88}{\sqrt{58} } }[/tex]  ~ [tex]t_5_7[/tex]

                                       =  3.462

The value of t test statistics is 3.462.

Since, in the question we are not given the level of significance so we assume it to be 5%. Now, at 0.05 significance level the t table gives critical value of 1.6725 at 57 degree of freedom for right-tailed test.

Since our test statistic is more than the critical value of t as 3.462 > 1.6725, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the true average estimated calorie content in the population sampled exceeds the actual content.

Answer:

hes

56 inches

hope it helps

Answer:

The theoretical probability of drawing a red marble is 1/3.

Step-by-step explanation:

1. Add all of the marbles together to get total marbles. 16 + 12 + 8 = 36.

2. Create a fraction, with numerator being favorable outcomes and denominator being total possible outcomes. In this case it would be 12/36.

3. Since it is asking for a reduced fraction, simplify 12/36 to 1/3.

The meaning of each parameter is given as follows:

Then the yearly percent increase is of:

4%.

C(3) represents the cost in 2015, which was of $33,746.

a) The expression to represent the cost in 2007 is of: C(-5).

b) The cost was of: $24,658.

An exponential function is defined as follows:

y = ab^x.

In which:

For this problem, the function is defined as follows:

y = 30000(1.04)^x.

In which:

C(3) represents the cost in 2015 and is obtained as follows:

C(3) = 30000(1.04)^3 = $33,746.

C(-5) represents the cost in 2007 and is obtained as follows:

C(-5) = 30000(1.04)^(-5) = $24,658.

(as 2007 was five years before 2012).

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Answer:

x + (x+1) + (x+2) = 114

3x = 111

x = 37

the numbers are 37, 38 and 39

the smallest number is 37

Step-by-step explanation:

Answer:3

Step-by-step explanation:

edg

Answer:

radius-8 inches cause math

circumference-50.27

Step-by-step explanation:

Answer:

2x³ - 17x² + 13x + 11

Step-by-step explanation:

(2x + 1)(x² - 9x + 11)      Distribute the 2x then the 1

2x³ - 18x² + 22x + x² - 9x + 11       Combine like terms

2x³ - 17x² + 13x + 11

If this answer is correct, please make me Brainliest!

Answer: [tex]1\frac{1}{2} *9=\frac{3}{2}*9=\frac{27}{2}=13\frac{1}{2}[/tex]

Step-by-step explanation:

Answer:             27

                        -------  

                           2

Step-by-step explanation:

Step-by-step explanation:

-2a + 2a + 7 = 8

Solving like terms

7 = 8

= 8 - 7 = 1

Has one solution

Answer:

x-intercept: -13/6

y-intercept: 13

General Formulas and Concepts:

Algebra I

Equality Properties

Coordinate Planes

Slope-Intercept Form: y = mx + b

Terms/Coefficients

Step-by-step explanation:

Step 1: Define

Identify.

y = 6x + 13

Step 2: Find y-intercept

Compare given equation to slope-intercept form.

y = 6x + 13 ↔ y = mx + b

Slope m = 6

y-intercept b = 13

Step 3: Find x-intercept

Substitute y = 0.

Answer:

Black Line     y = 3 + 2x ,     y = 2x +3

Red Line       y = -2 - .5x.     y = -.5x -2

vice versa

Step-by-step explanation:

For the black line, the lines intersects y at coordinate (0,3) and that would be b. To find the slope, use the equation rise / run. It rises 4 and runs 2. Putting this into an equation 4/2, it would be 2 as the constant. In other words, it would be 2x. Therefore, the function for the black line is y = 3 + 2x

For the red line, using the same explanation from the black line, the line intersects y at -2, and the slope would be -.5x, since it runs downwards 2 and runs 4, and since it runs downwards, a negative sign would be necessary in front of the slope.

Answer:

I also belive for Part A the second one is the answer because it equals 120 Part B is 120 pints! Good Luck! And I hope this Helps!

Answer:

B

Step-by-step explanation: