Learning task 1

week 7

I think its (B)

V = four-thirds pi r cubed = Four-thirds (3.14) (5) cubed

Answer:

4.35

Step-by-step explanation:

The expected value can be defined as: [tex]\sum{x_i*p_i}[/tex] where x_i = the payout, and p_i = the probability of it occurring.

This gives us the expression: [tex](1 * 0.35) + (2 * 0.2) + (5 * 0.1) + (8 * 0.2) + (10 * 0.15) = 0.35 + 0.4 + 0.5 + 1.6 + 1.5 = 4.35[/tex]

So the expected payout is 4.35

Answer:

b = 21

Step-by-step explanation:

In general for these trig problems look for the angle whose measure you are given or need to find and for the sides you are given lengths or whose sides you need to find.

Given:

side AB = 10 cm

m<C = 25°

Find:

side AC

The angle of interest here is <C whose measure is 25°.

Now look at the given side and the side you are looking for with respect to angle C, the given angle.

For angle C, AC is the adjacent leg.

For angle C, AB is the opposite leg.

Which trig function relates the opposite leg to the adjacent leg?

It is the tangent, since, in general, tan X = opp/adj.

tan C = opp/adj

tan 25° = AB/AB

tan 25° = 10 cm/b

Solve for b.

b × tan 25° = 10 cm

b = 10 cm / tan 25°

Using your calculator, divide 10 by the tangent of 25°.

b = 21.44506...

Answer: b = 21

Answer:

[tex]b = \bf 21 \space\ cm[/tex]

Step-by-step explanation:

• To solve for a side using SOH CAH TOA, first check the angle whose measure is given.

In this case, we know ∠ C is 25°.

• Next we have to figure out the relationships between the given angle and two sides: one side whose length we know, and the other whose length we have to find.

In this case, the side opposite to ∠ C is known to be 10 cm, and the side adjacent to ∠ C is AC, whose length, b, we have to find.

• The trigonometric ratio that relates the adjacent and opposite sides of an angle is tan, where:

[tex]\boxed{tan \theta = \frac{opposite}{adjacent} }[/tex] .

We can use this relationship to calculate the value of b:

⇒ [tex]tan (25 \textdegree) = \frac{10}{b}[/tex]

Solving for b:

⇒ [tex]b \cdot tan (25 \textdegree) = 10[/tex]

⇒ [tex]b = \frac{10}{tan (25 \textdegree)}[/tex]

⇒ [tex]b = 21.45[/tex]

⇒ [tex]b \approx \bf 21 \space\ cm[/tex]  (rounded to the nearest whole number)

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Using it's concept, the probability that a student attended the game, given that the student if fro North Beach is:

B. 0.65.

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

In this problem, we have that 170 people attended the game, out of which 110 are from North Beach, hence the probability is:

p = 110/170 = 0.65.

Hence option B is correct.

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Answer:0.55 is the correct answer

Step-by-step explanation:

The information that Clark is asking me to provide for him regarding the property is called  Brokers Price Opinion (BPO).

The term BPO refers to Brokers Price Opinion. It is the opinion of a genuine real estate professional regarding the accurate pricing of a property.

The information that Clark is asking me to provide for him regarding the property is called  Brokers Price Opinion (BPO).

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As per definition

In. a function every domain has an unique range of it

Here

f(10) has two corresponding values hence it's not a function

Answer:

40%

8%

15%

37%

Step-by-step explanation:

The solutions are in the image

Mean = 3.5

Median = 3

Distribution is negatively skewed.

What is skew in the distribution?

The distribution has no skewness if the mean and median are equal.

The median exceeds the mean in a favorably skewed distribution.

The distribution is also negatively skewed if the median is lower than the mean.

Given,

Data set : 1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 6, 8

Mean = [tex]\frac{1+1+2+2+2+3+3+3+3+4+4+4+5+5+6+8}{16}[/tex]

Mean = [tex]\frac{56}{16}[/tex]

Mean = [tex]3.5[/tex]

Median = mid value of the data set when the values are arranged in   ascending order

Here,

the two mid values = [tex]3, 3[/tex]

Median = [tex]\frac{3+3}{2}[/tex]

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

Median = [tex]3[/tex]

Now, as the mean is larger than the median therefore the distribution will be skewed negatively.

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The data in the distribution is positively skewed (skewed to the right). If the writer writes for two more days and creates 5 and 7 comic strips, respectively, the difference between the mean and the median for the new data set is 0.28.

ヾ(•ω•`)o

A possible critical point of the function f(x) is given by: (0,-2)

The critical points of a function are the values of x for which:

[tex]f^{\prime}(x) = 0[/tex]

At these points, the function can change from decreasing to increasing, or vice-versa.

For the table described, we have that the function is decreasing until (0,-2), then it starts to increase, hence there can be a critical point at (0,-2).

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Answer:

The answer is B.

Step-by-step explanation:

The function F(x) = x would be the “parent function”. Meaning the +4 we see in G(x) would be a translation, because the function is not multiplied.

if you have ever seen the formula y = mx + b then you should be able to see that +4 would be referencing b in the linear equation, and because m is the same in both lines, we can say that the two functions only change is b, because b represents the y-intercept, if b was 0 in f(x)=x and was 4 in g(x)=x+4, the graph would be shifted 4 units up.

if you want to learn how to understand functions and linear equations, I recommend using khan academy. It is really helpfull in explaining topics of math.

The first 3 iterates of the function are D. 3, -3, 9.

The function given is:

f(x) = -2x + 3

= -2(0) + 3

= 3

When x = 3

f(x) = -2x + 3

= -2(3) + 3

= -6 + 3

= -3

When x = -3

f(x) = -2x + 3

= -2(-3) + 3

= 9

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Answer:

12/13

Step-by-step explanation:

there are 4 7's in a 52 card deck, that means the other 48 cards are not 7's. 48/52 = 12/13

The probability that 5 boys would be selected would be 5/6720

From the information given, the probability can be calculated using permutation

The formula for permutation is given as;

Permutation = [tex]\frac{n!}{n - r!}[/tex]

Where;

Substitute the values into the formula

Permutation = [tex]\frac{8!}{8 - 5!}[/tex] = [tex]\frac{8!}{3!}[/tex] = [tex]\frac{40, 320}{6}[/tex] = 6720

The probability that 5 boys would be selected is 5/6720

Thus, the probability that 5 boys would be selected would be 5/6720

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Answer:

y = -1.3x + 10

Step-by-step explanation:

x_avg = (-2 + -1 + 1 + 2 + 3 + 4)/6 = 1.166666...

y-avg = (21 + 8.6 + 1 + 1 + 5 + 14.3) = 8.48333...

x      y       x-x_avg       y-y_avg          (x-x+avg)²           (x-x_avg)(y-y_avg)

-2    21     -3.1666        12.51666       10.02777                    -39.63611

-1    8.6     -2.1666        0.11666        4.69444                     -0.252777

1      1        -0.1666       -7.48333        0.02777                     1.247222

2      1       0.83333     -7.48333         0.69444                    -6.236111

3      5       1.8333        -3.48333        3.3611111                     -6.386111

4     14.3    2.8333        5.81666         8.02777                     16.480555

sum of (x-x_avg)(y-y_avg) = -34.858

sum of (x+x_avg)² = 26.8333

slope = [(x-x_avg)(y-y_avg)/[(x+x_avg)²]

slope = -34.858/26.8333

slope = -1.29907

y = mx + b

y_avg = m(x_avg) + b

8.48333 = -1.3(1.1666) + b

b = 9.9989

y = -1.3x + 10

Answer:

2

Step-by-step explanation:

We can find the slope of the line by using the slope formula

m = ( y2-y1)/(x2-x1)  where ( x1,y1) and (x2,y1) are points on the line

Using the points  (0,-4) and  (2,0)

m = ( 0 - -4)/ ( 2 - 0)

   = ( 0+4)/( 2-0)

   = 4/2

    = 2

Answer:

CORRECT graph is Graph C.

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HOPE IT HELPS

50^99 is greater than 99!

The numbers are given as:

99! and 50^99

When the above numbers are estimated using a calculator, we have:

99! = 9.332622e+155

50^99 = 1.577722e+168

Next, we compare the exponents

168 and 155

168 is greater than 155

Hence, 50^99 is greater than 99!

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The time taken by Millie to catch up with Ben is 6 minutes, solved using the linear equation in one variable and the unit rates provided.

We assume the minutes taken by Millie to catch up with Ben to be x minutes.

The number of words Ben has already typed = 180.

The unit rate for Ben for the typing of words = 30 per minute.

Therefore, words typed by Ben in x minutes = 30x words.

Therefore, the total number of words typed by Ben = 180 + 30x words.

The number of words Millie has already typed = 60.

The unit rate for Millie for the typing of words = 50 per minute.

Therefore, words typed by Millie in x minutes = 50x words.

Therefore, the total number of words typed by Millie = 60 + 50x words.

As Millie needs to catch up with Ben after x minutes, the total number of words typed by them needs to be equal, that is, 60 + 50x = 180 + 30x, which is the required linear equation in one variable.

To find the minutes taken by Millie to catch up with Ben, we solve this linear equation in one variable as follows:

60 + 50x = 180 + 30x,

or, 60 + 50x - 30x = 180 + 30x - 30x {Subtracting 30x from both sides},

or, 60 + 20x = 180 {Simplifying},

or, 60 + 20x - 60 = 180 - 60 {Subtracting 60 from both sides},

or, 20x = 120 {Simplifying},

or, 20x/20 = 120/20 {Dividing both sides by 20},

or, x = 6 {Simplifying}.

Thus, the time taken by Millie to catch up with Ben is 6 minutes, solved using the linear equation in one variable and the unit rates provided.

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Answer:

5.4 ft to nearest tenth.

Step-by-step explanation:

We know the adjacent side  of the right triangle  and we need the hypotenuse so we use the cosine:

cos 50 = 3.5/x

x = 3.5 / cos 50

  = 5.445 ft.

The solutions of the equations x - 5y = 0 and 15x + 10y = 17 at x and y is 1 and 1/5 respectively.

Two algebraic expressions separated by an equal symbol in between them and with the same value of the expression are called equations.

Given that:

The linear equations are:

x - 5y = 0

15x + 10y = 17

Solve the equations using elimination method:

Multiply equation 1 by 2

2(x - 5y) = 0

15x + 10y = 17

This can be solved as:

2x-10y = 0.....(1)

15x + 10y = 17....(2)

On subtracting equation 1 from 2

17x = 17

x = 1

The value of x is 1.

Substitute the value of x in equation (1)

2(1)-10y = 0

2=10y

y = 1/5

Thus, the value of x and y is 1 and 1/5 respectively.

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Answer: 22.5

Step-by-step explanation:

[tex]\sin 64^{\circ}=\frac{x}{25}\\\\x=25 \sin 64^{\circ}\\\\x \approx 22.5[/tex]

The factored form of the equation are as follows;

Converting a quadratic function to factored form is called factoring.

Therefore,

let's factor the equation,

a.

d² - 7d + 6 = 0

d² - d - 6d + 6 = 0

d(d - 1) - 6(d - 1) = 0

(d - 6)(d - 1) = 0

b.

x² + 18x + 81 = 0

x² + 9x + 9x + 81 = 0

x(x + 9) + 9(x + 9) = 0

(x + 9)(x + 9) = 0

c.

u² + 7u - 60 = 0

u² - 5u + 12u - 60 = 0

u(u - 5) 12(u - 5) = 0

(u + 12)(u - 5) = 0

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Profit function : p(x) = 53 x - 12

Cost is the total cost of producing the output.

The cost function consists of two different types of costs:

- Variable costs

- Fixed costs.

Variable costs vary with output (number of units produced). Total variable costs can be

expressed as the product of variable costs per unit and the number of units produced. If there are multiple items

manufactured costs are higher.

Fixed costs usually do not vary with performance.

Revenue is the total payment received from the sale of goods or the provision of a service.

The revenue function R() reflects the revenue from selling “” quantity of output items at price

"p" after item.

() =

Profit functions

The profit function P() is the difference between the revenue function R(x) and the total cost function C()

So P() = R() – C()

=−

Now, Profit = Revenue - Cost

= 60 x - ( 12 + 7 x)

= 60 x -12 -7 x

Profit = 53 x - 12

Hence, Profit function : p(x) = 53 x - 12

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Answer:

6 [tex]units^{2}[/tex]

Step-by-step explanation:

The formula for the area of a triangle is A = [tex]\frac{1}{2} bh[/tex]. The base in this case is the length of DE, 4 - 1 = 3 units. The height of this triangle is 1 + 3 = 4 units.

A = [tex]\frac{1}{2} bh[/tex] = [tex]\frac{1}{2} *3*4[/tex] = 6

The equation of the line is 3x + y = 1

The points are given as:

(5, −2) and (3, 4)

Start by calculating the slope (m)

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

This gives

m = (4 + 2)/(3 - 5)

Evaluate

m = -3

The equation is then calculated as:

y = m(x - x1) + y1

This gives

y = -3(x + 2) +5

So, we have:

y = -3x - 6 + 5

Evaluate the like terms

y = -3x - 1

Rewrite as:

3x + y = 1

Hence, the equation of the line is 3x + y = 1

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Answer:

Vertical shift up 3

Horizontal shift to the right 2

Brainliest, please :)

Answer:

Step-by-step explanation:

f(x) is moved 2 units to the right followed by 3 units up,

The cost of 2 chairs is = $30

The cost of 1 table = $60

Step-by-step explanation:

Let a table represent x

A chair represents y

4x + 3y = 225.......eq 1

3x + 4y = 195........eq 2

Use elimination method

x - y = 30

x= 30 + y...... Eq 3

Substitute the value of x into equation 1

4(30+ y) + 3y= 225

120 + 4y + 3y= 225

7y + 120= 225

7y= 225-120

7y= 105

y= 15

Substitute the value of y in eq 2

3x + 15 = 195

3x= 195-15

3x= 180

x= 60

Therefore, the cost of 2 chairs is 15 * 2= $30

The cost of 1 table = $60

Answer:

65

Step-by-step explanation:

Answer:

See picture below.

Step-by-step explanation:

Interchange x and y

[tex]\\ \tt\leadsto x=\dfrac{1}{9}y-2[/tex]

[tex]\\ \tt\leadsto \dfrac{1}{9}y=x+2[/tex]

[tex]\\ \tt\leadsto y=9(x+2)[/tex]

[tex]\\ \tt\leadsto y=9x+18[/tex]

[tex]\\ \tt\leadsto f^{-1}(x)=9x+18[/tex]

Answer:

[tex]f^{-1}(x)=9x+18[/tex]

Step-by-step explanation:

[tex]f^{-1}(x)[/tex] is the notation for the inverse of a function.  

The inverse of a function is its reflection in the line y = x.

Given function:

[tex]f(x)=\dfrac{1}{9}x-2[/tex]

To find the inverse of the given function:

Replace f(x) with y to get an equation for y in terms of x:

[tex]\implies y=\dfrac{1}{9}x-2[/tex]

Rearrange the equation to make x the subject:

[tex]\implies y+2=\dfrac{1}{9}x[/tex]

[tex]\implies 9(y+2)=x[/tex]

[tex]\implies x=9y+18[/tex]

Replace x with [tex]f^{-1}(x)[/tex] and y with x:

[tex]\implies f^{-1}(x)=9x+18[/tex]

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