There are 4, 6, and 7 points on three lines. How many quadrilaterals is it possible to create with given points as vertices?

Answer:

[tex]\dfrac{1}{5} $ square foot.[/tex]

Step-by-step explanation:

Area of the Poster =1 sq.ft.

The collage will cover a part of the poster that is [tex]\dfrac{1}{3} ft.$ wide and \dfrac{3}{5} ft.$ long.[/tex]

Area of the Photo Collage Section

=Length X Width

[tex]=\dfrac{1}{3} X \dfrac{3}{5} \\\\=\dfrac{1}{5} $ square foot.[/tex]

[tex]\text{Therefore, the photo collage will cover }\dfrac{1}{5} $ of a square foot.[/tex]

Answer:

58.05% probability that at least 1 of the students is a senior.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

The order in which the captains are chosen is not important. So we use the combinations formula to solve this question.

Combinations formula:

A probability is the number of desired outcomes divided by the number of total outcomes.

In this question:

Either no seniors are captain, or at least one is. The sum of these probabilities is 100%. The easier way to solve this question is finding the probability of no seniors being captain, and subtratcing 100 from this. So

Probability of no seniors being captain:

Desired outcomes:

Four captains, from a set of 18 + 18 + 15 = 51. So

[tex]D = C_{51,4} = \frac{51!}{4!(51-4)!} = 249900[/tex]

Total outcomes:

Four captains from a set of 18 + 18 + 15 + 12 = 63. So

[tex]T = C_{63,4} = \frac{63!}{4!(63-4)!} = 595665[/tex]

Probability:

[tex]p = \frac{D}{T} = \frac{249900}{595665} = 0.4195[/tex]

41.95% probability of no seniors being captains.

Find the probability that at least 1 of the students is a senior.

p + 41.95 = 100

p = 58.05

58.05% probability that at least 1 of the students is a senior.

Answer:

≈103.67cm

Step-by-step explanation:

Shape: Circle

Solved for circumference

Diameter: 33cm

Formula: C=πd

Answer: ≈103.67cm

Hope this helps.

Answer:

C = 33 pi

Step-by-step explanation:

The circumference of a circle is given by

C = pi *d

C = 33 pi

We can approximate pi by 3.14

C = 33*3.14 =103.62

or by using the pi button

C =103.6725576

Answer:

Directional derivative = 1/√2

Step-by-step explanation:

We are given f(x, y) = y cos(xy)

Now, we know that;

∇f(x, y) = ycos xy

Thus, applying that to the question, we have;

∇f(x, y) = [-y² sin xy, cos (xy) - xy sin xy]

At coordinates (0,1),we now have;

∇f(0, 1) = [-1²•sin0, (cos 0) - 0]

∇f(0, 1) = [0, 1]

Now, unit vector indicated by the angle θ is given as; u = [cos θ, sin θ]

From the question, since θ = π/4, thus

u = [cos π/4, sin π/4]

Cos π/4 in surd form is; 1/√2

Also, sin π/4 in surd form is; 1/√2

So, u = [1/√2, 1/√2]

Directional derivative = [∇f(0, 1)] • u

= [0, 1] × [1/√2, 1/√2] = 0 + 1/√2 = 1/√2

Answer:

To get your answer, you need to fix the typos, but the answer is gonna be the closest thing to 13/42 if that is the real value

Step-by-step explanation:

none of these answers are anywhere near to 13/42

Answer:

Option B

Step-by-step explanation:

As property of angle inside circle, arc BC = 2 x angle BDC.

Let's consider triangle ABD.

BAD = 98 deg  

ABD = (1/2) x arc AD = (1/2) x 80 = 40 deg

As the property of sum of 3 angles in a triangle,

=> ADB + ABD + BAD = 180

=> ADB = 180 - ABD - BAD = 180 - 40 - 98 = 42 deg

=> BDC = 70 - 42 = 28

=> arc BC = 2 x 28 = 56 deg

=> Option B is correct

Answer:

x = -4 and x = 6

Step-by-step explanation:

Factor using AC method.

1 × -24 = -24

Factors of -24 that add up to -2 are +4 and -6.

P(x) = (x + 4) (x − 6)

Therefore, zeroes of P(x) are x = -4 and 6.

Answer: 39 minutes 51 seconds

Step-by-step explanation:

Nt=N0 * 2^n

N0=Initial population

n=number of times bacteria divide

700=320*2^n

log2(700/320)=1.129283017=n

45/1.129283017=39.84829252 minutes

0.84829252*60=50.89755135≈51seconds

so the answer is

39minutes and 51seconds

Answer:

B.

Step-by-step explanation:

Recall the properties of logs and once you find the value of x, substitute it into the equation.

Option C ([tex]\frac{10}{27}[/tex]) is the correct alternative.

Given expression is:

→ [tex]3^x = 10[/tex]

By taking log both sides, we get

→ [tex]ln \ 3^x = ln \ 10[/tex]

 [tex]x \ ln \ 3= ln \ 10[/tex]

         [tex]x = \frac{ln \ 10}{ln \ 3}[/tex]

By substituting the value of "x" in "[tex]3^{x-3}[/tex]", we get

→ [tex]3^{x-3}[/tex] = [tex]3^{\frac{ln \ 10}{ln \ 3} -3}[/tex]

          = [tex]\frac{10}{27}[/tex]  

So the above is the right solution.

Learn more:

https://brainly.com/question/47626

SEE BELOW FOR THE CORRECT FORMAT OF THE QUESTION

Answer:

(a) [tex]\mathbf{C_{(t)} =\dfrac{I}{F} [ 1- e \dfrac{-Ft}{v}+ C_oe \dfrac{-Ft}{v} ]}[/tex]

(b) [tex]\mathbf{\lim_{t \to \infty} C_t = \dfrac{I}{F}[1-0+ 0 ] \ = \dfrac{I}{F}}[/tex]

(c) T = 6.02619 years

(d) T = 431.593 years

Step-by-step explanation:

(a)

[tex]\dfrac{dC}{dt} = -\dfrac{F}{v}C + \dfrac{I}{v} \\ \\ \\ \dfrac{dC}{dt} + \dfrac{F}{v}C = \dfrac{I}{v}[/tex]

By integrating the factor of this linear differential equation ; we have :

[tex]= e \int\limits \dfrac{F}{v}t \\ \\ \\ = e \dfrac{Ft}{v}[/tex]

[tex]C* e \frac{Ft}{v}= \int\limits \dfrac{I}{v}*e \dfrac{Ft}{v} dt[/tex]

[tex]C* e \frac{Ft}{v}= \dfrac{I}{v}* \dfrac{e \frac{Ft}{v} }{F/v}+ K[/tex]

[tex]C* e \frac{Ft}{v}= \dfrac{I}{v}* \dfrac{V}{F} e \dfrac{Ft}{v} + K[/tex]

[tex]Ce \dfrac{Ft}{v} = \dfrac{I}{F} \ * \ e \dfrac{Ft}{v} + k \ \ \ \ (at \ t = 0 \ ; C = C_o)[/tex]

[tex]C_o = \dfrac{I}{F} e^o + K[/tex]

[tex]K = C_o - \dfrac{I}{F}[/tex]

[tex]C_{(t)} = [ \dfrac{I}{F}e \dfrac{Ft}{v}+ C_o - \dfrac{I}{F}] e\dfrac{-Ft}{v}[/tex]

[tex]C_{(t)} =\dfrac{I}{F} [ e \dfrac{Ft}{v} * e \dfrac{-Ft}{v}+ C_oe \dfrac{-Ft}{v} - 1* e \dfrac{-Ft}{v}][/tex]

[tex]\mathbf{C_{(t)} =\dfrac{I}{F} [ 1- e \dfrac{-Ft}{v}+ C_oe \dfrac{-Ft}{v} ]}[/tex]

(b)

[tex]\lim_{t \to \infty} C_t = \dfrac{I}{F}[1-e^{- \infty} + C_o e^{- \infty} ][/tex]

since  [tex](e^{- \infty} = 0)[/tex]

[tex]\mathbf{\lim_{t \to \infty} C_t = \dfrac{I}{F}[1-0+ 0 ] \ = \dfrac{I}{F}}[/tex]

(c)

V = 458 km³   and F = 175 km³  , I = 0

[tex]\dfrac{dC}{dt} = - \dfrac{-175}{458}C[/tex]

[tex]= \int\limits \ \dfrac{dC}{C} = - \dfrac{175}{458}\int\limits dt[/tex]

[tex]In (C_{(t)}) = - \dfrac{175}{458} t + K[/tex]

[tex]C_{(t)} = e \dfrac{-175}{458}t + K[/tex]

Let at time t = 0 [tex]C_{(t)}} = C_o \to C_o = e^{0+k} = e^K[/tex]

[tex]C_{(t)} = e \dfrac{-175}{458}t[/tex]

Now at time t = T ; [tex]C_{9t)} = \dfrac{C_o}{10}[/tex]

[tex]\dfrac{C_o}{10} = C_o e \dfrac{-175}{458}T \to \dfrac{1}{10} = e \dfrac{-175}{458}T[/tex]

[tex]In ( \dfrac{1}{10}) = \dfrac{-175}{459}T[/tex]

[tex]- In (10) = \dfrac{175}{458}T[/tex]

[tex]T = \dfrac{458}{175} In (10)[/tex]

T = 6.02619 years

(d) V = 12221 km³

F = 65.2 km³/ year

[tex]\mathbf{T = \dfrac{v}{F}In (10)}[/tex]

[tex]T = \dfrac{12221}{65.2}In (10)[/tex]

T = 431.593 years

Answer:

x=3

Step-by-step explanation:

2x-6=0

2x=0+6

2x=6

2x/2=6/2

x=3

Answer:

Domain: [10, ∞)

Step-by-step explanation:

Domain is the set of x-values that can be inputted into function f(x).

Step 1: Write equation

f(x) = √(x - 10)

We know that if we get negatives under the square root, we would get imaginary numbers.

Our domain to include all x-values would have to be bigger than 10:

f(10) = √(10 - 10) = √0 = 0

If the number is smaller than 10, we get: f(9) = √(9 - 10) = √-1 = i

Therefore, our real numbers domain would be [10, ∞) or x ≥ 10.

Answer:

It is a parallelogram, I don't know what specified method you want us to use

Answer:

a. P(X ≤ 5) = 0.999

b. P(X > λ+λ) = P(X > 2) = 0.080

Step-by-step explanation:

We model this randome variable with a Poisson distribution, with parameter λ=1.

We have to calculate, using this distribution, P(X ≤ 5).

The probability of k pipeline failures can be calculated with the following equation:

[tex]P(k)=\lambda^{k} \cdot e^{-\lambda}/k!=1^{k} \cdot e^{-1}/k!=e^{-1}/k![/tex]

Then, we can calculate P(X ≤ 5) as:

[tex]P(X\leq5)=P(0)+P(1)+P(2)+P(4)+P(5)\\\\\\P(0)=1^{0} \cdot e^{-1}/0!=1*0.3679/1=0.368\\\\P(1)=1^{1} \cdot e^{-1}/1!=1*0.3679/1=0.368\\\\P(2)=1^{2} \cdot e^{-1}/2!=1*0.3679/2=0.184\\\\P(3)=1^{3} \cdot e^{-1}/3!=1*0.3679/6=0.061\\\\P(4)=1^{4} \cdot e^{-1}/4!=1*0.3679/24=0.015\\\\P(5)=1^{5} \cdot e^{-1}/5!=1*0.3679/120=0.003\\\\\\P(X\leq5)=0.368+0.368+0.184+0.061+0.015+0.003=0.999[/tex]

The standard deviation of the Poisson deistribution is equal to its parameter λ=1, so the probability that X exceeds its mean value by more than one standard deviation (X>1+1=2) can be calculated as:

[tex]P(X>2)=1-(P(0)+P(1)+P(2))\\\\\\P(0)=1^{0} \cdot e^{-1}/0!=1*0.3679/1=0.368\\\\P(1)=1^{1} \cdot e^{-1}/1!=1*0.3679/1=0.368\\\\P(2)=1^{2} \cdot e^{-1}/2!=1*0.3679/2=0.184\\\\\\P(X>2)=1-(0.368+0.368+0.184)=1-0.920=0.080[/tex]

Step-by-step explanation:

-3(7 + 5) + 9(2)

-3(12) + 18

-36 + 18

= - 18

In my opinion this should be the answer

Answer:

14

Step-by-step explanation:

Your welcome!

Answer: C. 84

Step-by-step explanation:

In triangles ABD y BCD:

- AD=CD

- Angle BAD = angle BCD

- BD common side

THEN the triangles are equal because they have two sides and the angle opposite the longest side respectively equal.

CBD = ABD = 42 because the triangles ABD y BCD are equal

ABC = CBD+ABD = 42+42= 84

Answer:

C. 84 degrees

Step-by-step explanation:

Answer:

27%

Step-by-step explanation:

6/10*45/100=270/1000 which is 27/100 which is 27%

Answer:

P(CO|M)=0.77 for male

and P(CO|M^c)=0.62 for female

Step-by-step explanation:

When we talk of conditional probability, we refer to the measure of the probability of an event given that another event has occurred

Here, we are to express the results of the survey as a conditional probability.

For the male part of the question, the conditional probability means that, given that the person is a male, the probability that he is a car owner would be;

P(CO|M)=0.77

For the female part of the question, what we have as a conditional probability is that if a person is a female that she is a car owner is;

P(CO|M^c)=0.62

Please kindly understand that the term M^c refers to M complement in words

Answer:

The standard cost of Bramble's product is $69.5 per unit.

Step-by-step explanation:

We can calculate the standard cost per unit of Bramble's product as the sum of the material cost, direct labor cost and overhead cost.

Each unit of product uses 2 pounds of materials, that cost $6 per pound. So the material cost is:

[tex]MC=2\,lb/u\cdot6\,\$/lb=12\,\$/u[/tex]

Each unit needs 2.5 direct labor hours, and they have a cost of $11 per hour, so the direct labor cost is:

[tex]LC=2.5\,h/u\cdot11\,\$/h=27.5\,\$/u[/tex]

The overhead costs are calculated in this case as $12 per direct labor hour. As 2.5 labor hours are needed per unit, we have:

[tex]OC=2.5\,h/u\cdot 12\,\$/h=30\,\$/u[/tex]

The standard cost is then:

[tex]C=MC+LC+OC=12+27.5+30=69.5\,\$/u[/tex]

Answer:

B

Step-by-step explanation:

JK = LM (equidistant from centre)

3x+19=6x+7

19-7=6x-3x

12 = 3x

Dividing both sides by 3

x = 4

JK = 3(4)+19

JK = 12+19

JK = 31

Answer:

31

Step-by-step explanation:

JK = LM (since they are equidistant from centre)

3x + 19 = 6x + 7

- 3x = - 12

x = 4

JK = 3 * (4) + 19

= 12 + 19

= 31

Hope this helps!

Answer:

p = x² − 6x + 10

Step-by-step explanation:

Complex roots come in conjugate pairs.  So if 3−i is a root, then 3+i is also a root.

p = (x − (3−i)) (x − (3+i))

p = x² − (3+i)x − (3−i)x + (3−i)(3+i)

p = x² − 3x − ix − 3x + ix + (9 − i²)

p = x² − 6x + 10

You can check your answer using the quadratic formula.

x = [ -b ± √(b² − 4ac) ] / 2a

x = [ 6 ± √(36 − 40) ] / 2

x = (6 ± 2i) / 2

x = 3 ± i

Answer:

$157.60

Step-by-step explanation:

77 shares + 120 shares = 197 total shares

197/10 = 19.7

19.7 x 8 = 157.60

Answer:

b on edge hope this helps :)

Step-by-step explanation:

Answer:

Step-by-step explanation:

The objective of this question is to known whether the assumptions of the known data set follows normal distribution or not and if it is appropriate to use t-test or not.

TO solve this question ; we construct a box plot for the known data set by using a MINITAB software

The process is as follows to guide you:

Enter your data in the worksheet

Then select Graph→ Boxplot→ EDA→ Boxplot

Under One Y , select simple, Then click OK

In Variables , enter measurements. Then click OK

So; for the first data set (a)  213.03 212.95 213.04 213.00 212.99 213.01 221.03 213.05  as shown in the attached file  in word document for the  boxplot below;

We will observe that there is a outliner present in the data set and the measurement do not meet the normal assumption ; as a result to that ; the t-distribution is not appropriate for this data.

(b) From the document attached below; we will realize and observe that the boxplot doesn't contains an outliner. Also; it is clear and obvious that the shape of the distribution is right skewed. The measurement thus did not meet the assumptions and as a result t- distribution is not appropriate for this data.

(c)

From the document attached below; we will realize and observe that the boxplot doesn't contains an outliner. Also; it is clear and obvious that the shape of the distribution is left skewed. The measurement thus did not meet the assumptions and as a result t- distribution is not appropriate for this data.

(a): The [tex]t-[/tex]distribution is not appropriate for this data.

(b): The [tex]t[/tex]-distribution is not appropriate for this data.

(c): The [tex]t[/tex]- distribution is not appropriate for this data.

A t-test is a statistical test that is used to compare the means of two groups.

Part(a):

Check whether the unknown data set follows the normal distribution or not and is it appropriate to use the [tex]t[/tex]-test or not.

Use the following MS excel instructions to draw a box plot.

Step-1: Enter the data into an excel sheet.

Step-2: Click add-ins-Mega stat-Descriptive statistics.

Step-3: Input the data into the input range box.

Step-4: Click Box-Plot -Click OK

It is observed that there is an outlier in the data set.

The obtained output is as follows:

So, the measurements do not satisfy the normality assumption.

Part(b):

Check whether the known data set follows normal distribution or not and is it appropriate to use the [tex]t[/tex]-test or not.

Use the above MS excel instruction to draw a Box plot.

The obtained output is as follows.

It is observed that there is no outlier in the data set and the shape of the distribution is appears to be right-skewed.

So, the measurement do not satisfy the normality assumption.

Part(c):

Check whether the known data set follows normal distribution or not and is it appropriate to use the [tex]t[/tex]- test or not.

Use the above MS Excel instruction to draw a Box-plot.

The obtained output is as follows.

It is observed that there is no outlier in the data set and the shape of the distribution is appears skewed to the left.

So, the measurement do not satisfy the normality assumption.

Learn more about the topic [tex]t-[/tex]test:

https://brainly.com/question/25999758

Answer:

x = 40

Step-by-step explanation:

The angles are vertical angles.  We know that vertical angles are equal

120 = 3x

Divide each side by 3

120/3 = 3x/3

40 =x

Answer:

40

Step-by-step explanation:

I forgot what you would call this, but basically 3x = 120. both of the angles are the same. So divide both sides of the equation by 3. 3x/3 = 120/3 and your answer is 40.

It's a bad explanation but I hope it helps!

Answer:

5/4   5 ft

Step-by-step explanation:

We are going from 12 to 15

We need to multiply by

15 = k *12

Divide each side by 12

15/12 = k

5/4 = k

The scale factor is 5/4

1 in = 4 ft

Multiply the 4 ft by the scale factor

1 in = 4 * 5/4 = 5 ft

1 in = 5 ft

Answer:

Raphael saw a square patio that was 12-feet long on each side. He wants to build a patio that will be 15-feet long on each side.

The change in the scale factor is  

✔ 4/5

.

The change of scale means that 1 inch represented  4 feet, but now 1 inch represents  

✔ 5

feet.

Answer:

-3

Step-by-step explanation:

We can see that the line passes through (0,3) and (1,0)

So using rise over run we have

-3/1

or

-3

Answer:

h= 1+3d

Step-by-step explanation:

total amount of hairbands equals the 1 hairband she has + 3 times how ever many more she decides to buy