2.a. What type of angles are shown?
1 point
70-
(х + 16)"
Corresponding
Alternate Interior
ОООО
Same Side Interior/Consecutive Interior Angles
Alternate Exterior

Answer:

1,000 cm

Step-by-step explanation:

5 x 200 = 1000

Answer:

75.4

Step-by-step explanation:

2·π·12

75.36

The equation for finding the circumference of a circle is 2pi times the radius.

The radius is already given, so we multiply it by 2.

12*2

= 24

After that, we multiply 24 by pi.

24*3.14

= 75.36

Answer:

D - 16%

Step-by-step explanation:

percent change = (new number - old number)/(old number) * 100%

percent change = (87 - 75)/75 * 100%

percent change = 12/75 * 100%

percent change = 4/25 * 100%

percent change = 16%

Answer: D - 16%

The speed of the boat in still water is 18mph and the speed of the current is 9mph. The solution has been obtained using speed-distance-time relationship.

What is speed-distance-time?

Speed is calculated by dividing the distance travelled by the time taken to travel it. It gives the distance travelled as well as the time it took to travel that distance.

Inversely correlated with time is speed and directly correlated with distance.

We are given that a boat tracked 162 miles downstream and back.

The trip downstream took 6 hours.

So, the speed of the boat downstream is

⇒S = D/T

⇒S = 162/6

⇒S = 27mph

The trip back took 18 hours.

So, the speed of the boat upstream is

⇒S = D/T

⇒S = 162/18

⇒S = 9mph

The speed of boat in still water is

⇒S = (27 + 9)/2

⇒S = 36/2

⇒S = 18mph

The speed of the current is

⇒S = (27 - 9)/2

⇒S = 18/2

⇒S = 9mph

Hence, the speed of the boat in still water is 18mph and the speed of the current is 9mph.

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The probability of the event between two and five lines, inclusive, are in use is 0.85.

Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.

Given that,

x         0         1         2       3        4         5         6

p(x)   0.12    0.18   0.20  0.20  0.20   0.07   0.03

a) At most three lines are in use

Here we need to find the probability for x≤3.

P(x≤3)=P(x=0)+P(x=1)+P(x=2)+P(x=3)

= 0.12+0.18+0.20+0.20

= 0.70

b) Fewer than three lines are in use

Here we need to find the probability for x<3.

P(x<3)=P(x=0)+P(x=1)+P(x=2)

= 0.12+0.18+0.20

= 0.50

c) At least three lines are in use

Here we need to find the probability for x≥3.

P(x≥3)=P(x=3)+P(x=4)+P(x=5)+P(x=6)

= 0.20+0.20+0.07+0.03

= 0.50

d) Between two and five lines, inclusive, are in use

Here we need to find the probability for 2≤x≤5.

P(2≤x≤5)= P(x=2)+P(x=3)+P(x=4)+P(x=5)

= 0.18+0.20+0.20+0.20+0.07

= 0.85

Therefore, the probability of the event between two and five lines, inclusive, are in use is 0.85.

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The volume of the composite figure in this problem is given as follows:

76 ft³.

The volume of a rectangular prism, with dimensions defined as length, width and height, is given by the multiplication of these three defined dimensions, according to the equation presented as follows:

Volume = length x width x height.

The figure in this problem is composed by two prisms, with dimensions given as follows:

Hence the volume is given as follows:

2 x 6 x 3 + 2 x 4 x 5 = 76 ft³.

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Step-by-step explanation:

Let's assume that Andrew had $5x at first, and Paul had $2x.

After Andrew gave $30 to Paul, Andrew has $5x-$30, and Paul has $2x+$30.

We are told that they had an equal amount of money each after the transaction. This means:

5x - 30 = 2x + 30

Solving for x, we get:

3x = 60

x = 20

So Andrew had $5x = $100 at first, and Paul had $2x = $40.

After the transaction, Andrew had $100-$30 = $70, and Paul had $40+$30 = $70.

Together, they had $70+$70 = $140.

Therefore, they had $140 altogether.

We can plοt the pοints (0,1) and (1,-11) οn the line tο graph the functiοn p(x) = 1 - 12x.

A functiοn frοm a set X tο a set Y is an assignment οf an element οf Y tο each element οf X. The set X is called the dοmain οf the functiοn and the set Y is called the cοdοmain οf the functiοn.

A functiοn, its dοmain, and its cοdοmain, are declared by the nοtatiοn f: X→Y, and the value οf a functiοn f at an element x οf X, denοted by f(x), is called the image οf x under f, οr the value οf f applied tο the argument x.

Functiοns are alsο called maps οr mappings, thοugh sοme authοrs make sοme distinctiοn between "maps" and "functiοns" (see § Other terms).

Tο plοt twο pοints οn the line fοr the functiοn p(x) = 1 - 12x, we can chοοse any twο values οf x and find the cοrrespοnding values οf p(x).

Fοr example, if we chοοse x = 0, then p(0) = 1 - 12(0) = 1, sο the pοint (0,1) is οn the line.

If we chοοse x = 1, then p(1) = 1 - 12(1) = -11, sο the pοint (1,-11) is οn the line.

Therefοre, we can plοt the pοints (0,1) and (1,-11) οn the line tο graph the functiοn p(x) = 1 - 12x.

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Answer:

if this is a fraction, then negative 5 over a⁶

Answer:

70/100 = 105/X ---> 70X = 10,500 ---> X = 150 games played.

Step-by-step explanation:

\( - 2( - 2x + 3) = - 3 x+ 10\)

\(4x - 6 = - 3x + 10\)

\(4x + 3x = 16\)

\(7x = 16\)

\(x = \frac{16}{7} \)

\(x = 2.2857\)

\(x = 3\)

(a) Clicks Width of Door (inches)

1 3.3

2 3.63

3 3.99

4 4.39
(b) The function is y = 3  (1.1)ˣ.

(c) It would take about 15 clicks of the zoom-in button to make the door approximately 3 feet wide on the screen.

(d) It would take about 12 clicks of the zoom-out button to transform the display of the door from 3 feet wide back to a width of approximately 3 inches.

(a)

Clicks Width of Door (inches)

1 3.3

2 3.63

3 3.99

4 4.39

(b) Let x be the number of clicks and y be the width of the door on the screen. Then, we can write the algebraic rule as:

y = 3  (1.1)ˣ

(c) To make the door approximately 3 feet wide on screen, we need to convert 3 feet to inches, which is 36 inches. Then, we need to solve for x in the equation:

3 (1.1)ˣ = 36

Dividing both sides by 3, we get:

(1.1)ˣ = 12

Taking the logarithm of both sides (with base 1.1), we get:

x = log(12) / log(1.1) ≈ 14.7

So, it would take about 15 clicks of the zoom-in button to make the door approximately 3 feet wide on the screen.

(d) To transform the display of the door from 3 feet wide back to a width of approximately 3 inches, we need to find the number of clicks of the zoom-out button that will result in a width of approximately 3 inches. We can use the same formula as before, but with the initial width of 36 inches (since we are zooming out):

36 (0.9)ˣ = 3

Dividing both sides by 36, we get:

(0.9)ˣ = 1/12

Taking the logarithm of both sides (with base 0.9), we get:

x = log(1/12) / log(0.9) ≈ 11.5

So, it would take about 12 clicks of the zoom-out button to transform the display of the door from 3 feet wide back to a width of approximately 3 inches.

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The area that Mr. Adams needs to paint is 34ft².

Given that the toy box measures 4 feet long, 1.5 feet wide, and 2 feet high. Since the area that mr Adams needs to paint is the outside area of this box, therefore, the area he needs to paint is the total surface area of the toy box.
Surface area of the box

= 2 [ (Length×Width) + (Height×Width) + (Length×height)]

= 2[ (4 ft ×1.5 ft) + (2ft × 1.5 ft) + (4 ft × 2 ft)]

= 2( 6 ft² + 3 ft² + 8 ft² )

= 34 ft²

Hence, the area is 34ft².

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The complete question must be:

Mr Adams is painting the outside of his son’s toy box, including the top and bottom. The toy box measures 4 feet long, 1.5 feet wide, and 2 feet high. What is the total area that Mr Adams needs to paint?

Answer:

False. The product of two negative integers is a positive integer.

Answer:

4 1/10 when u have a inproper fraction like that every 10 is one whole number

Answer:

A = 60 cm²

Step-by-step explanation:

Given that,

The area of a circle, A = 20 cm²

It is enlarged 3 times.

We need to find the area of the enlarged circle.

Area of the enlarged circle,

A = 20×3

= 60 cm²

So, the area of the enlarged circle is equal to 60 cm².

Answer: \(5\sqrt 5\)

Step-by-step explanation:

Sol \(\sqrt 125\) = \(\sqrt{25.5}\)

= \(\sqrt{25}\)  x  \(\sqrt{5}\)

\(5 \sqrt{5}\)

Answer:

Assuming you had a bill of $120 when you went to the restaurant with your three friends, the 20% tip would come out to $24.

What would be the tip?

First, assume an amount that the meal you ate the cost. Let's assume that amount is $120.

If the tip rate is 20%, it means that you need to find out what 20% of the bill of $120 is.

If you don't want to use a calculator, there are other ways you can calculate the tip.

An easy method would be to find 10% of the bill. To find 10%, all you have to do is to move the decimal point from right to left.

The decimal point in $120 is at the far right so the 10% amount would be:

= $12.0

Now that you have the 10% amount, remember that 20% is simply twice the amount of 10% so:

= 12 x 2

= $24

The total amount then becomes:

= 120 + 24

= $144

In conclusion, your tip amount would be $24.

Step-by-step explanation:

Hey there! I'm happy to help!

Let's look at all of the perfect squares (numbers with integer square roots) so that we can see where the square root of 12 lies.

√1=1

√4=2

√9=3

√16=4

√25=5

√36=6

√49=7

√64=8

√81=9

√100=100

We see that √12 would be in between √9 and √16 (3 and 4), so the square root of 12 is in between 3 and 4.

I hope that this helps! Have a wonderful day! :D

The square root of 12 lies between the whole numbers 3 and 4.

The value of a number's power 1/2 is the number's square root. It is the number whose product by itself yields the original number, to put it another way.

Let's look at all of the perfect squares (numbers with integer square roots) so that we can see where the square root of 12 lies.

√1=1

√4=2

√9=3

√16=4

√25=5

√36=6

√49=7

√64=8

√81=9

√100=100

We see that √12 would be in between √9 and √16 (3 and 4), so the square root of 12 is in between 3 and 4.

Therefore, the square root of 12 lies between the whole numbers 3 and 4.

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On solving the provided question we can say that to plot data - dread = $0.16; Turkey = $1.24; Cheese = $0.30

The most typical approach to display data using a chart is a graph that shows the relationship between two additional variables. Diagrams created by hand or on a computer are also acceptable. Move 2 units to the right after starting at the origin before going 3 units up. The coordinates for the points 2, 3, should be shown on the coordinate plane. Clearly state your points. The pink dot with the letter P thus stands for 2.3. Before creating a line chart, you need first generate a number line for each value in your data collection. Put an X (or dot) over each value of the data on the number line after that. For each instance when a value appears in a record, place an X over the corresponding number.

to plot data -

dread = $0.16

Turkey = $1.24

Cheese = $0.30

Lettuce = $0.06

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Answer:

Step-by-step explanation:

Set a system of equations.

c- correct, i- incorrect.

Add the equations together:

Then find the value of i:

Answer:

The length will be 4.5 × 3.5 = 15.75 feet

The width will be 6 × 3.5 = 21 feet

So the area will be

15.75 feet × 21 feet = 330.75 square feet

Answer:

20.

Step-by-step explanation:

60 - 40 = 20

Answer:

There are 5 prime numbers between 40 and 60.

Step-by-step explanation:

A prime number is a number that is ONLY divisible by itself and 1 with no remainder. For example 3 can only be divided by 1 or 3 without a remainder left.

Between 40 and 60 there are 5 prime numbers: 41, 43, 47, 53, and 59.

Answer:

As the P-value (0.086) is greater than the significance level (0.01), the effect is  not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the return rate is less than 15%.

Step-by-step explanation:

This is a hypothesis test for a proportion.

The claim is that the return rate is less than 15%.

Then, the null and alternative hypothesis are:

\(H_0: \pi=0.15\\\\H_a:\pi<0.15\)

The significance level is 0.01.

The sample has a size n=5000.

The sample proportion is p=0.143.

\(p=X/n=717/5000=0.143\)

The standard error of the proportion is:

\(\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.15*0.85}{5000}}\\\\\\ \sigma_p=\sqrt{0.000026}=0.005\)

Then, we can calculate the z-statistic as:

\(z=\dfrac{p-\pi+0.5/n}{\sigma_p}=\dfrac{0.143-0.15+0.5/5000}{0.005}=\dfrac{-0.007}{0.005}=-1.366\)

This test is a left-tailed test, so the P-value for this test is calculated as:

\(P-value=P(z<-1.366)=0.086\)

Answer:

\(z=\frac{0.1434 -0.15}{\sqrt{\frac{0.15(1-0.15)}{5000}}}=-1.307\)  

Now we can calculate the p value with the following probability:

\(p_v =P(z<-1.307)=0.0956\)  

For this case the p value is lower than the significance level provided of 0.1 so then we can reject the null hypothesis and we can conclude that the the return rate is significantly less than 15%.

Step-by-step explanation:

Information provided

n=5000 represent the random sample taken

X=717 represent the surveys returned

\(\hat p=\frac{717}{5000}=0.1434\) estimated proportion of urvyes returned

\(p_o=0.15\) is the value to verify

\(\alpha=0.01\) represent the significance level

z would represent the statistic

\(p_v\) represent the p value

System of hypothesis

We want to verify if the return rate is less than 15% the system of hypothesis are.:  

Null hypothesis:\(p \geq 0.15\)  

Alternative hypothesis:\(p < 0.15\)  

The statistic is given by:

\(z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}\) (1)  

Replacing the info we got:

\(z=\frac{0.1434 -0.15}{\sqrt{\frac{0.15(1-0.15)}{5000}}}=-1.307\)  

Now we can calculate the p value with the following probability:

\(p_v =P(z<-1.307)=0.0956\)  

For this case the p value is lower than the significance level provided of 0.1 so then we can reject the null hypothesis and we can conclude that the the return rate is significantly less than 15%.

The rope will hit the ground in about 4.37 seconds.

The correct order to solve for when the rope will hit the ground is:

1. Use the kinematic equation for the vertical motion of an object: h(t) = -4.9t^2 + vt + h0, where h0 is the initial height and v is the initial velocity (in meters per second).

2. Substitute h0 = 50 m and v = 10 m/s into the equation: h(t) = -4.9t^2 + 10t + 50.

3. Find the time t when the rope hits the ground by solving the equation h(t) = 0.

4. Use the quadratic formula to solve for t: t = (-10 ± sqrt(10^2 - 4(-4.9)(50))) / (2(-4.9)).

5. Select the positive value of t, since the time must be positive: t ≈ 4.37 seconds.

Therefore, the rope will hit the ground in about 4.37 seconds.

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Answer:

4x²=2(x-4)

2x²=x-4

2x²-x+4=0​

x=1+√31​/ 4, 1-√31​/4

Step-by-step explanation:

1. Cancel log on both sides

2. Divide both sides by 2

3. Move all terms to one side

4. Use the quadratic formula

Answer:

6

Step-by-step explanation

The only f(0) answer in table is 6

Answer:

6

Step-by-step explanation:

f(0) = 6.  That is, when the input (x) is 0, the output (y) is 6.

There are 12 face cards (kings, queens and jacks) and the total number of cards in a deck is 52, then the probability of drawing a face card is:

P(face card) = 12/52 = 3/13

Since there is a replacement after the first card is drawn, the total number of cards still 52, the probability of getting a 2 knowing that there are 4 cards with a 2 in a deck is:

P(2 card) = 4/52 = 1/13

Then, the probability is the multiplication of P(face card) and P(2 card) , then we get:

P = P(face card)×P(2 card) = (3/13)×(1/13) = 3/169

the answer is 3/169, which is equivalent to 1.8%

The relationship between the distance that birds fly in relation to the time they do so, is positive.

There are about 3 outliers but for the most part, the relationship is positive.

The graph which shows the distance that birds fly in relation to the time they do, shows that there is a positive relationship because as the time increases, the distance that the birds have flown also increases.

There are some outliers such as the bird that flew 1 mile in 7 hours but in general, as the time increases, the distance increases as well. There are two clusters of distance as well.

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