8
Evaluate 3n+ 7.
n = 3
Find the indicated sum? Help!

Answer:

x=½

y=5

Step-by-step explanation:

(8x+7y=39)2

16x+14y=78

4x-14y=-68 add the two equations

20x=10.

divide both sides by 20

x=½

8x+7y=39

4+7y=39

7y=39-4

7y=35

y=5

The value of x and y in the system of equation using elimination method is 1 / 2and 5 respectively.

8x + 7y = 39

4x – 14y = –68

Multiply by 2

16x + 14y = 78

-14y + 14y = 0

4x + 16x = 20x

-68 + 78 = 10

20x = 10

x = 1 / 2

8(1 / 2) + 7y = 39

4 + 7y = 39

7y  = 35

y = 35 / 7

y = 5

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Answer:

The time spent studying is the response variable.

Step-by-step explanation:

The response variable, also known as the dependent variable is the main question which the experiment wants to provide an answer for. Usually, the predictors determine or affect the response variable.  In the study where Teresa investigates the effect of grade level on time spent studying, the response variable is the time spent studying, while the predictor which is the grade level provides an explanation as to the time spent studying.

The changes or variations on time spent studying depends on the grade level. This means that the grade level provides an explanation of the length of time dedicated to studying.

Answer:

Option (1)

Step-by-step explanation:

Since the length of arc YZ = 12 units

m∠YXZ = one third of the full circle = [tex]\frac{360}{3}[/tex] = 120°

From the formula of arc length,

Length of arc = [tex]\frac{\theta}{360}(2\pi r)[/tex]

Where θ = Central angle subtended by the arc

r = radius of the circle

By substituting these values in the formula,

12 = [tex]\frac{120}{360}(2\pi r)[/tex]

12 = [tex]\frac{2}{3}\pi r[/tex]

[tex]18=\pi r[/tex]

r = [tex]\frac{18}{\pi }[/tex]

r = 5.73

r ≈ 6 units

Therefore, Option (1) will be the answer.

Answer:

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

Step-by-step explanation:

The n th term of an arithmetic sequence is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference , thus

a₇ = a₁ + 6d

a₄ = a₁ + 3d

Given a₇ - 2a₄ = 1 , then

a₁ + 6d - 2(a₁ + 3d) = 1, that is

a₁ + 6d - 2a₁ - 6d = 1

- a₁ = 1 ( multiply both sides by - 1 )

a₁ = - 1

Given a₃ = 0 , then

a₁ + 2d = 0 , thus

- 1 + 2d = 0 ( add 1 to both sides )

2d = 1 ( divide both sides by 2 )

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

Answer:

The sample mean is 6.1

Step-by-step explanation:

Margin of Error (E) = (upper limit - lower limit)/2 = (6.8 - 5.4)/2 = 1.4/2 = 0.7

Sample mean = lower limit + E = 5.4 + 0.7 = 6.1

Answer: B) 3:7

Step-by-step explanation:

104/78 = .75

so for everyone 3 males there are 4 females,

then for every 7 people there are 3 males so the answer is B

<!> Brainliest is appreciated! <!>

The ratio between the males and the total number of persons will be 03:7

It is a kind of relationship between two variables. It represents the weightage of one variable in comparison to other.

Number of males present=78

Number of females present=104

Total number of people present=182

Ratio=number of males: number of people

=78:182=39:91=3:7

Hence the ratio of males to total people is 3:7

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Answer:

C.) 60°

Step-by-step explanation:

The triangle is an equilateral triangle. So that means that all the angles measure the same. And we have to remember that a triangle always equals 180°

So, to find out the measure of an angle. We must divide 180 by 3. Which is 60

=60°

Hope this helps you out! : )

Step-by-step explanation:

The given sequences are;

2,7,12,17......

difference =5

by using formula,

we get,

tn=a+(n-1)d

tn= 2+(n-1)5

Therefore, tn is 5n-3 is required formula for this arithmetic sequences.

Hope it helps....

Answer:

solution,

Volume of cylinder=304 cm^3

height=10 cm

Radius=?

Now,

[tex]volume = \pi {r}^{2} h \\ or \: 304 = 3.14 \times {r}^{2} \times 10 \\ or \: 304 = 31.4 \times {r}^{2} \\ or \: {r}^{2} = \frac{304}{31.4} \\ or \: {r}^{2} = 9.68 \\ or \: r = \sqrt{9.68} \\ or \: r = \sqrt{ {(3.11)}^{2} } \\ r = 3.11 \: cm[/tex]

Hope this helps..

Good luck on your assignment..

Answer:

Step-by-step explanation:

First you need to find the slope of the line that contains those 2 points.

[tex]m=\frac{0-8}{0-(-4)}=\frac{-8}{4}=-2[/tex]

So the slope is -2. Now we can pick one of those points and sub it into the point-slope formula to find the equation:

y - 0 = -2(x - 0) gives us an equation of

y = -2x

If the integral as written in my comment is accurate, then we have

[tex]I=\displaystyle\int_{3/2}^2\sqrt{(x-1)(3-x)}\,\mathrm dx[/tex]

Expand the polynomial, then complete the square within the square root:

[tex](x-1)(3-x)=-x^2+4x-3=1-(x-2)^2[/tex]

[tex]I=\displaystyle\int_{3/2}^2\sqrt{1-(x-2)^2}\,\mathrm dx[/tex]

Let [tex]x=2-\cos\theta[/tex] and [tex]\mathrm dx=\sin\theta\,\mathrm d\theta[/tex]:

[tex]I=\displaystyle\int_{\pi/3}^{\pi/2}\sqrt{1-(2-\cos\theta-2)^2}\sin\theta\,\mathrm d\theta[/tex]

[tex]I=\displaystyle\int_{\pi/3}^{\pi/2}\sqrt{1-\cos^2\theta}\sin\theta\,\mathrm d\theta[/tex]

[tex]I=\displaystyle\int_{\pi/3}^{\pi/2}\sqrt{\sin^2\theta}\sin\theta\,\mathrm d\theta[/tex]

Recall that [tex]\sqrt{x^2}=|x|[/tex] for all [tex]x[/tex], but for all [tex]\theta[/tex] in the integration interval we have [tex]\sin\theta>0[/tex]. So [tex]\sqrt{\sin^2\theta}=\sin\theta[/tex]:

[tex]I=\displaystyle\int_{\pi/3}^{\pi/2}\sin^2\theta\,\mathrm d\theta[/tex]

Recall the double angle identity,

[tex]\sin^2\theta=\dfrac{1-\cos(2\theta)}2[/tex]

[tex]I=\displaystyle\frac12\int_{\pi/3}^{\pi/2}(1-\cos(2\theta))\,\mathrm d\theta[/tex]

[tex]I=\dfrac\theta2-\dfrac{\sin(2\theta)}4\bigg|_{\pi/3}^{\pi/2}[/tex]

[tex]I=\dfrac\pi4-\left(\dfrac\pi6-\dfrac{\sqrt3}8\right)=\boxed{\dfrac\pi{12}+\dfrac{\sqrt3}8}[/tex]

You can determine the more general result in the same way.

[tex]I=\displaystyle\int_p^q\sqrt{(x-a)(b-x)}\,\mathrm dx[/tex]

Complete the square to get

[tex](x-a)(b-x)=-(x-a)(x-b)=-x^2+(a+b)x-ab=\dfrac{(a+b)^2}4-ab-\left(x-\dfrac{a+b}2\right)^2[/tex]

and let [tex]c=\frac{(a+b)^2}4-ab[/tex] for brevity. Note that

[tex]c=\dfrac{(a+b)^2}4-ab=\dfrac{a^2-2ab+b^2}4=\dfrac{(a-b)^2}4[/tex]

[tex]I=\displaystyle\int_p^q\sqrt{c-\left(x-\dfrac{a+b}2\right)^2}\,\mathrm dx[/tex]

Make the following substitution,

[tex]x=\dfrac{a+b}2-\sqrt c\,\cos\theta[/tex]

[tex]\mathrm dx=\sqrt c\,\sin\theta\,\mathrm d\theta[/tex]

and the integral reduces like before to

[tex]I=\displaystyle\int_P^Q\sqrt{c-c\cos^2\theta}\,\sin\theta\,\mathrm d\theta[/tex]

where

[tex]p=\dfrac{a+b}2-\sqrt c\,\cos P\implies P=\cos^{-1}\dfrac{\frac{a+b}2-p}{\sqrt c}[/tex]

[tex]q=\dfrac{a+b}2-\sqrt c\,\cos Q\implies Q=\cos^{-1}\dfrac{\frac{a+b}2-q}{\sqrt c}[/tex]

[tex]I=\displaystyle\frac{\sqrt c}2\int_P^Q(1-\cos(2\theta))\,\mathrm d\theta[/tex]

(Depending on the interval [p, q] and thus [P, Q], the square root of cosine squared may not always reduce to sine.)

Resolving the integral and replacing c, with

[tex]c=\dfrac{(a-b)^2}4\implies\sqrt c=\dfrac{|a-b|}2=\dfrac{b-a}2[/tex]

because [tex]a<b[/tex], gives

[tex]I=\dfrac{b-a}2(\cos(2P)-\cos(2Q)-(P-Q))[/tex]

Without knowing p and q explicitly, there's not much more to say.

Answer:

The Matlab code along with the plot of slope field for the given differential equation is provided below.

Step-by-step explanation:

Matlab quiver function:

The Matlab's quiver function may be used to plot the slope field lines for any differential equation.

The syntax of the function is given by

quiver(x, y, u, v)

Where matrices x, y, u, and v must all be the same size and contain corresponding position and velocity components.

Matlab Code:

[t,y] = meshgrid(0:0.2:2, 0:0.2:2);

v = sin(y) + sin(t);

u = ones(size(v));

quiver(t,y,u,v)

xlabel('t')

ylabel('y(t)')

xlim([0 2])

ylim([0 2])

Output:

The plot of the given differential equation is attached.

Answer:

[tex] {9}^{1} = 9 \\ {3}^{1} = 3 \\ {1}^{3} = 1[/tex]

Answer:

Argument is valid.

Step-by-step explanation:

Let M, C and S represent the premises. The the statements can be represented using these letters as:

M: Microchips are made from diamond wafers.

C: Computers will generate less heat.

S: Synthetic diamonds will be used for jewelry.

1st premises:

If microchips are made from diamond wafers, then computers will generate less heat.

Notice that the above statement is a conditional statement. So to represent such relationship, the material implication is used which has ⊃ symbol.

This can be translated into symbolic form using the horseshoe operator ⊃ as:

M ⊃ C

2nd premises:

Computers will not generate less heat and microchips will be made from diamond wafers.

Notice that the above statement is a compound statement. It has two part joined together with "and" i.e.  Computers will not generate less heat "and" microchips will be made from diamond wafers. These are two conjuncts and   both should be true for the premises/compound statement to be true. So to represent such relationship, the Conjunction is used which has • symbol.

This can be translated into symbolic form using the dot • symbol as:

Computer will not generate less heat is represented as ~C because C states that Computer will generate less heat and ~C states that Computer will not generate less heat. So ~C is the negation of C. Now the complete symbolic form is:

~C • M

third premises:

Therefore, synthetic diamonds will be used for jewelry is represented as:

S

This is basically the conclusion statement.

Truth Tables:

For M:

M

T

T

T

T

F

F

F

F

For C:

C

T

T

F

F

T

T

F

F

For ~C:

It reverses the truth values of C

~C

F

F

T

T

F

F

T

T

For S:

S

T

F

T

F

T

F

T

F

For M ⊃ C:

The above mentioned premise formed with this connective is true unless the left the antecedent is true and right the consequent is false.

M       C        M ⊃ C

T         T             T

T         T             T

T         F             F

T         F             F

F         T             T

F         T             T

F         F             T

F         F             T

For ~C • M

The truth table of conjunction of ~C and M is formed using truth table of reverse of C i.e.  ~C and that of M. The conjunction is true when both conjuncts are true and if either of the two conjuncts is false then whole conjunction is false.

M       ~C        ~C • M

T         F             F

T         F             F

T         T             T

T         T             T

F         F             F

F         F             F

F         T             F

F         T             F

Now combining all to check the validity:

M       C       S        M ⊃ C     ~C • M             S

T         T        T             T               F                T

T         T         F            T               F                F

T         F         T            F               T                T

T         F         F            F               T                F

F         T         T            T               F                T

F         T         F            T               F                F

F         F         T            T               F                T

F         F          F           T               F                 F

The given argument is valid. The is because it is impossible for the above premises to be true and the conclusion to be false. You can see that when the premises M ⊃ C  and ~C • M are true the conclusion S is also true.

We check validity by checking in the truth table if there is a row that has all true premises and a false conclusion. If there is then argument is invalid. Here in the truth table you can see that no row has all the premises true and a false conclusion. So the argument is valid.

Answer:

1.79% probability that the number of times that the coin lands tails will be less than 40

Step-by-step explanation:

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

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

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].

Fair coin:

Equally as likely to be heads or tails, so [tex]p = 0.5[/tex]

100 times

[tex]n = 100[/tex]

Then

[tex]\mu = E(X) = np = 100*0.5 = 50[/tex]

[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{100*0.5*0.5} = 5[/tex]

What is the probability that the number of times that the coin lands tails will be less than 40

Using continuity correction, this is [tex]P(X < 40 - 0.5) = P(X < 39.5)[/tex], which is the pvalue of Z when X = 39.5.

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

[tex]Z = \frac{39.5 - 50}{5}[/tex]

[tex]Z = -2.1[/tex]

[tex]Z = -2.1[/tex] has a pvalue of 0.0179

1.79% probability that the number of times that the coin lands tails will be less than 40

Answer:

Use a graphing calc or desmos

Step-by-step explanation:

Answer:

  m less-than-or-equal-to 28

Step-by-step explanation:

Xander's charge for m miles will be (3 +1.50m). He wants this to be no more than $45, so ...

  3 +1.50m ≤ 45

  1.50m ≤ 42 . . . . . . subtract 3

  m ≤ 28 . . . . . . . . . .divide by 1.5

Answer: M is less than or equal to 28 or C

Step-by-step explanation:

GOT RIGHT ON E D G

Answer:

4.9 hours = 4 hours 54 minutes

Step-by-step explanation:

speed = distance/time

time * speed = distance

time = distance/speed

time = (284 miles)/(58 mph) = 4.9 hours

4.9 hours - 4 hours = 0.9 hours

0.9 hours * (60 minutes)/(1 hour) = 54 minutes

4.9 hours = 4 hours 54 minutes

Answer:

a. 0.48

b. 0.14

c. 0.47

Step-by-step explanation:

Data provided in the question

0 - 2        0.48

3 - 5        0.26

6 - 8        0.12

9- 11        0.09

12- 14       0.05

Based on the above information

a. The probability for fewer than three phobias is

= P( x < 3)

= 0.48

b.  The probability for more than eight phobias is

= P( x >8)

= 0.09 + 0.05  

= 0.14

c. Probability between 3 and 11 phobias is  

= P(3 < x < 11)

= 0.26 + 0.12  + 0.09

= 0.47

Answer:

E. P(W | H)

Step-by-step explanation:

What each of these probabilities mean:

P(H): Probability of the game being at home

P(W): Probability of the game being a win.

P(H and W): Probability of the game being at home and being a win.

P(H|W): Probability of a win being at home.

P(W|H): Probability of winning a home game.

Which of the following probabilities do you need to find in order to determine the proportion of at-home games that were wins?

This is the probability of winning a home game. So the answer is:

E. P(W | H)

Answer:

(-1, 6)

(0, 7)

Step-by-step explanation:

Easiest and fastest way to do this is to graph both equations and analyze the graph for when they intersect each other.

Answer:

  g(-6) = 8; g(0) = 5; g(6) = 0; g(12) = 6

Step-by-step explanation:

We assume your function definition is ...

  [tex]g(x)=\left\{\begin{array}{ccc}-\dfrac{1}{2}x+5&\text{for}&x<6\\x-6&\text{for}&x\ge 6\end{array}\right.[/tex]

For each given value of x, determine which segment applies, then evaluate.

For x = -6 and for x = 0, the first segment applies:

  g(-6) = (-1/2)(-6) +5 = 3 +5 = 8

  g(0) = (-1/2)(0) +5 = 5

For x = 6 and x = 12, the second segment applies:

  g(6) = (6) -6 = 0

  g(12) = (12) -6 = 6

In summary, ...

  g(-6) = 8; g(0) = 5; g(6) = 0; g(12) = 6

Answer:

-2

Step-by-step explanation:

The slope of a line is

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

   = (-2 -4)/(-1 - -4)

   = -6/ ( -1 +4)

   = -6 /3

    =-2

Answer:

[tex]= - 2 \\ [/tex]

Step-by-step explanation:

[tex]( - 4 \: \: \: \: \: \: \: \: \: \: \: 4) = > (x1 \: \: \: \: \: \: y1) \\ ( - 1 \: \: \: \: - 2) = > (x2 \: \: \: \: \: \: y2)[/tex]

Now let's find the slope

[tex]slope = \frac{y1 - y2}{x1 - x2} \\ = \frac{4 - ( - 2)}{ - 4 - ( - 1)} \\ = \frac{4 + 2}{ - 4 + 1} \\ = \frac{6}{ - 3} \\ = - 2[/tex]

hope this helps you.

brainliest appreciated

good luck! have a nice day!

Answer:

-3

Step-by-step explanation:

I'm not sure what the 0s are all about, but I can help with the equation;

To do this, we can do substitution. By equaling x-4 to 3x+2, we get

x-4=3x+2

By isolating the x, we get

-2x=6

x=-3

Hope this helped!

Answer:

75%

Step-by-step explanation:

There are 3 numbers that fit this rule, 3, 5, and 6. There is a 3/4 chance spinning one or a 75% chance.

Answer:

75%

Step-by-step explanation:

The numbers 6 or odd are 3, 5, and 6.

3 numbers out of a total of 4 numbers.

3/4 = 0.75

Convert to percentage.

0.75 × 100 = 75

P(6 or odd) = 75%

Answer:

The solution to this expression is 61,224.74

Step-by-step explanation:

To solve we initially have to convert the percentage to a decimal:

[tex]1.8\% = \frac{1.8}{100} = 0.018[/tex]

So

56000*(1+1.8%)^5 = 56000(1+0.018)^5 = 56000(1.018)^5 = 61,224.74

The solution to this expression is 61,224.74

Answer:

b. not all the children can be above average

d. half the children must be below average

Step-by-step explanation:

In theory, all women could be strong and all men could be good looking, however, since the average is calculated based on the town children, it is not possible for all children to be above average.

Assuming a normal distribution, half the children must be at or below average, while the other half must be at or above the average.

Therefore, the correct answers are:

b. not all the children can be above average

d. half the children must be below average

Answer:

Second and last options are correct choices.

Step-by-step explanation:

If all the children are above average, then the average should not include the average of the children. Because it is impossible for a data set to be have values greater than it's average.

Best Regards!

Answer:

$15

Step-by-step explanation:

Each cup is 50 cents which is basically $0.50

Multiply $0.50 by 120= $60

Because you and your three friends equal 4 total people,

divide 60 by 4 to get your own profit:

60/4=15

-2

0

2

Answered on edge

Answer:

-2, 0, 2

Step-by-step explanation:

edge 2020

Answer:pete

Step-by-step explanation: