What is the equation of the line represented by the table below?

x y
-3 1
6 4
12 6
30 12

The expected number of cards Percy turns over before stopping = 3.78≈3

Probability refers to the chance of occurrence of an event E.

Let E be an event and P(E) be the probability of E occurring.

Then, P(E) = \(\frac{Number Of Favourable Outcomes Of E}{Total Number Of Outcomes}\)

Now, given a 52-card deck; cards are turned over till a spade comes up.

Then, the number of cards turned over is the sum of all card over 'kth' card, having probability \(P_{k}\), where, the card 'k' comes up if no previous card was a spade.

=> \(P_{k}=\frac{\binom{39}{k}}{\binom{52}{k}} = \frac{39!(52-k)!}{52!(39-k)!}\)

\(\sum^{39}_{k=0} (P_{k})=\frac{39!}{52!} \sum^{39}_{k=0}(\frac{(52-k)!}{(39-k)!}=\frac{53}{14} = \frac{52+1}{13+1}=3.78\)

Hence, after 3.78≈3 cards, Percy will stop turning the cards.

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Therefore, the value of x is x = -2 / m + 3.

Supporting Answer: We have to find the equation of the line that passes through the point (3, 7) and has a slope of m. We use the point-slope form of the equation of the line, which is :y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope of the line. Thus, the equation of the line is: y - 7 = m(x - 3). Now, we are given that point A(x, 5) lies on the line. Hence, we substitute y = 5 and solve for x:x - 3 = (5 - 7) / mx - 3 = -2 / mmx = -2 / m + 3.

Equations act as a scale of balance. If you've ever seen a balancing scale, you know that it needs to have an equal amount of weight on both sides in order to be deemed "balanced". The scale will tip to one side if we just add weight to one side, and the two sides will no longer be equally weighted. Equations use the same reasoning. Anything on one side of the equal sign must have the exact same value on the opposite side in order for it to not be considered unequal.

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The area of the shaded sector is 4π square units.

To find the area of the shaded sector, we need to calculate the central angle formed by the sector. In this case, we are given that the angle JIK is 90 degrees, which means it forms a quarter of a full circle.

Since a full circle has 360 degrees, the central angle of the shaded sector is 90 degrees.

Next, we need to determine the radius of the circle. The line segment IJ represents the radius of the circle, and it is given as 4 units.

The formula to calculate the area of a sector is A = (θ/360) * π * r², where θ is the central angle and r is the radius of the circle.

Plugging in the values, we have A = (90/360) * π * 4².

Simplifying, A = (1/4) * π * 16.

Further simplifying, A = (1/4) * π * 16.

Canceling out the common factors, A = π * 4.

Hence, the area of the shaded sector is 4π square units.

Therefore, the area of the shaded sector, expressed as a fraction times π, is 4π/1.

In summary, the area of the shaded sector is 4π square units, or 4π/1 when expressed as a fraction times π.

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Answer:

graphing

Step-by-step explanation:

ez

we have to add 7775000 to make 7800000 from 25000 which is calculated by using Substraction method.

Subtraction in mathematics is the process of subtracting one integer from another. In other terms, the result of subtracting two from five is three. After addition, subtraction is usually the second process you learn in math class.Subtraction is the action or procedure of determining the difference between two quantities or figures. The phrase "taking away one number from another" is also used to describe the process of subtracting one number from another.

Distance to be covered altogether= 7800000 m
THE distance has covered= 25000 m.

We can calculate the thousands needs to be added in 25000 to make it 7800000 by using Substraction method:-

7800000-25000= 7775000m

hence, to make 7800000 from 25000 we have to add 7775000.

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ANSWER

First quadrant

EXPLANATION

Those two trigonometric functions are the reciprocal of the sine and cosine functions:

Therefore:

sinθ is greater than zero for the first and second quadrants.

Also:

cosθ is greater than zero for the first and fourth quadrants.

Hence, for cscθ>0 and secθ>0, angle θ lies in the first quadrant.

Answer:

Step-by-step explanation:

1)

∠AOB + ∠BOC = ∠AOC

(x + 7) + (x + 7) = 7x - 1

7 + 7 + 1 = 7x - x - x

15 = 5x

x = 15/5

x  = 3

2)

5x = 7x - 20

5x - 7x = -20

x = -20 / -2

x = 10

∠TAD = 180 - 5x

∠TAD  = 180 - 5(10)

∠TAD  = 130°

The three workers can produce 25 thingamajigs if they split their time evenly between producing widgets and thingamajigs.

Step 1: Calculate the production rate of each workerFirstly, calculate the production rate of each worker for both widgets and thingamajigs. In one hour, Karen can make 1 widget or 3 thingamajigs. In one hour, Sue can make 1 widget or 1 thingamajig. Lastly, Peter can make 3 widgets or 1 thingamajig in one hour.Karen's hourly production rate: 1 widget or 3 thingamajigsSue's hourly production rate: 1 widget or 1 thingamajigPeter's hourly production rate: 3 widgets or 1 thingamajig

Step 2: Calculate the total hourly production of the groupSecondly, calculate the hourly production of the entire group. To split their time evenly, they will have to spend 5 hours each producing widgets and thingamajigs.In 5 hours, Karen can produce 5 widgets or 15 thingamajigs (since her hourly production rate is 1 widget or 3 thingamajigs).In 5 hours, Sue can produce 5 widgets or 5 thingamajigs (since her hourly production rate is 1 widget or 1 thingamajig).In 5 hours, Peter can produce 15 widgets or 5 thingamajigs (since his hourly production rate is 3 widgets or 1 thingamajig).Step 3:

Calculate the total number of thingamajigsLastly, add up the total thingamajigs produced by each worker in 5 hours and you'll have the answer:15 (Karen's production) + 5 (Sue's production) + 5 (Peter's production) = 25 thingamajigsIn total, the three workers can produce 25 thingamajigs if they split their time evenly between producing widgets and thingamajigs.

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The angle of each measure is:

m<DEC= 129°

m∠BCE = 51°

m∠ADE = 57°

m∠EDB = 123°

m∠DBC = 57°

Angle of measure is the measure of an angle formed by two rays with a common endpoint. Angle of measure is important to many mathematical and scientific fields, including geometry, trigonometry, and physics.

In geometry, angles are used to define shapes and measure the size of an object. For example, angles are used to determine the angles of a triangle, or the angles between the sides of a rectangle. Angle of measure is also important in trigonometry, as it is used to calculate the lengths of sides and angles in a triangle, as well as the area of a triangle.

Angle of measure is also used in engineering, navigation, and surveying. When designing a building or structure, angles are used to determine the strength and stability of the structure, as well as the angles of the beams and walls. In navigation, angles are used to calculate the direction of a ship or aircraft. Finally, in surveying, angles are used to measure the angles between points on a map or a landscape.

Given,

m∠DEC= (12x-3)°, m∠BCE= (7x-26)°, and m∠DAE= 72°

∠DEC+∠BCE = 180°

12x-3+7x-26 = 180°

19x - 29 = 180°

19x = 180+29

x = 209/19

x = 11

Substitute x=11 in m∠DEC= (12x-3)°, we get

m∠DEC= 129°

Substitute x=11 in m∠BCE= (7x-26)°, we get

m∠BCE = 51°

To find m∠ADE,

m∠ADE + m∠DAE + m∠DEA=180°

m∠ADE + 72° + 51° = 180°

m∠ADE = 57°

To find m∠EDB,

m∠EDB + m∠ADE=180°

m∠EDB = 180° - 57°

m∠EDB = 123°

To find m∠DBC,

m∠DBC = m∠ADE are corresponding angles, so

m∠DBC = m∠ADE = 57°

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Pauline needs to work for 75 hours to make $600

Given that Pauline worked 35 hours and made $280, this can be written as:

35 hours = $280

If Pauline’s company makes $600 a week, this can be expressed as:

x = $600

35/x = 280/600

35/x = 28/60

28x = 35 * 60

28x = 2100

x = 2100/28

x = 75

This means that Pauline needs to work for 75 hours to make $600

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Answer:

Step-by-step explanation:

Answer:

b=(28+a²)^½

Step-by-step explanation:

but i couldnt find the numerical value of b since the value of a wasn't given

Answer:

I think it would be 11.2

Step-by-step explanation:

because if I is 10 and it only goes across to the other side then it would only be 11.2

The given triangles are obtuse = 36 m, right angled = 225 m and right angled = 2500 m.

Triangle can be defined in which it consists of three sides, three angles and sum of three angles is always 180 degrees.

7.) This triangle is obtuse.

To see this, we can use the Pythagorean theorem:

4*4 + 5*5 = 16 + 25 = 41

6*6 = 36 m

Since 41 > 36, we know that the triangle is obtuse.

8.) This triangle is right.

To see this, we can again use the Pythagorean theorem:

11*11 + 12*12 = 121 + 144 = 265

15*15 = 225 m

Since 265 = 225 + 40, we know that the triangle is right.

9.) This triangle is also right.

We can use the same method as before:

30*30 + 40*40 = 900 + 1600 = 2500

50*50 = 2500 m

Since 2500 = 2500, we know that the triangle is right.

Therefore, The given triangles are obtuse , right angled and right angled.

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Notice that if both \(x,y\) are positive, then

\(xy = 3 \implies \sqrt{xy} = \sqrt x \sqrt y = \sqrt3\)

We also have the binomial expansion

\(x + 2\sqrt{x}\sqrt{y} + y = \left(\sqrt x\right)^2 + 2 \sqrt x \sqrt y + \left(\sqrt y\right)^2 = \left(\sqrt x + \sqrt y\right)^2\)

Then

\(\left(\sqrt x + \sqrt y\right)^2 = (x + y) + 2\sqrt{xy} = 5 + 2\sqrt3 \\\\ \implies \sqrt x + \sqrt y = \boxed{\sqrt{5 + 2\sqrt3}}\)

Let's see if we can denest the radical. Suppose we could write

\(\sqrt{5 + 2\sqrt3} = a + b \sqrt c\)

for some non-zero integer constants \(a,b,c\) (and \(c>0\)). Squaring both sides gives

\(5 + 2\sqrt3 = a^2 + 2ab\sqrt c + b^2c\)

Let \(c=3\) and \(ab=1\). Then \(a^2 + b^2c = 5\), which gives

\(a^2 + 3b^2 = 5\)

\(a^2 + \dfrac3{a^2} = 5\)

\(a^4 - 5a^2 + 3 = 0\)

We can solve this with the quadratic formula. However, it'll lead to non-integer solutions for \(a,b\), so we cannot denest after all.

Answer:

the answer would be 4 because you multiply

Answer:

\(x >12\)

\((12, \infty)\)

\(\{x\in\mathbb{R} : x>12 \}\)

Step-by-step explanation:

\(\dfrac{4}{9} x - 3 > \dfrac{7}{3}\)

\(\dfrac{4}{9} x > \dfrac{7}{3}+3\)

Multiply both sides by 9

\(4 x > 21+27\)

\(4 x > 48\)

Divide both sides by 4

\(x >12\)

Answer:

By the Substitution property, the measure of angle ABC is equal to GHI.

Step-by-step explanation:

According to the Question,

Since we have,

On substituting the value of from equation (1) to equation (2)

We get, ∠ABC = ∠GHI ∴ ∠ABC ≅ ∠GHI

Thus, By the Substitution property  

The measure of angle ABC is equal to angle GHI.

(a) If the current distribution is Ps all other Pa 0.2, then in the next period, all states will have the same probability of 0.2, because the frog has a 0.2 probability of moving to any state.

(b) If the current distribution is Pz 0.5, Ps 0.5 all other Pa 0.2, then in the next period, the probabilities of being in state z and state s will each be 0.5 * 0.5 = 0.25, and the probabilities of being in all other states will be 0.2.

(c) If the current distribution is Pz 0.225, Pa 0.25, Pa 0.5, all other P; 0.2, then in the next period, the probabilities of being in each state will be the sum of the products of the current probability of being in that state and the transition probabilities from that state.

(d) If the current distribution is P: Pz 0.22, Pa 0.22, Pa 0.22, Ps 0.22. P6 0.2, then in the next period, the probabilities of being in each state will be the same as in the current period, because the frog has an equal probability of moving to any state.

Note that in each case, the probabilities must add up to 1, as they represent the entire possible states of the frog.

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Answer: 149 - m

He gave some away so we subtract

The favorable outcome is the number of all-women groups (126) and the total possible outcomes are all possible groups (3003). Therefore, P(all-women) = 126/3003 ≈ 0.0419 (rounded to four decimal places).

(a) To determine the number of different groups of applicants that can be selected for the positions, we use the combination formula: C(n, k) = n! / (k!(n-k)!) where n is the total number of applicants (9 women + 6 men = 15) and k is the number of positions (5). So, C(15, 5) = 15! / (5!(15-5)!) = 3003.

(b) To find the number of different groups of trainees consisting entirely of women, we use the same formula but with only the 9 women as applicants: C(9, 5) = 9! / (5!(9-5)!) = 126.

(c) To calculate the probability that the trainee class will consist entirely of women, we can use the formula P(event) = Number of favorable outcomes / Total possible outcomes. In this case, the favorable outcome is the number of all-women groups (126) and the total possible outcomes are all possible groups (3003). Therefore, P(all-women) = 126/3003 ≈ 0.0419 (rounded to four decimal places).

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Answer:

Step-by-step explanation:

First let's find the value of x :

We khow that the area of this triangle is 400 and it is given by the product of the base and the height over 2

Let's find the hypotenuse :

The pythagorian theorem :

(i) The number of infected plants among 5 plants follows a binomial distribution with parameters n = 5 and p.

We observed 4 infected plants. To determine the probability of a result at least as extreme as the observed data, we need to calculate the probabilities of 4 and 5 infected plants for a range of values of p and add them up.

The probability of 4 infected plants is:

P(X = 4) = 5C4 * p^4 * (1-p)^1 = 5p^4 * (1-p)

The probability of 5 infected plants is:

P(X = 5) = 5C5 * p^5 * (1-p)^0 = p^5

Therefore, the probability of a result at least as extreme as the observed data is:

P(X >= 4) = P(X = 4) + P(X = 5) = 5p^4 * (1-p) + p^5

(ii) To determine if p = 0.3 or p = 0.2 lie within the 95% confidence interval, we need to find the range of values of p such that the probability of a result at least as extreme as the observed data is less than or equal to 0.025. We can solve this numerically using the expression derived in part (i):

For p = 0.3:

P(X >= 4) = 5(0.3)^4 * (1-0.3) + (0.3)^5 = 0.0765

Since 0.0765 > 0.025, we cannot conclude that p = 0.3 lies within the 95% confidence interval.

For p = 0.2:

P(X >= 4) = 5(0.2)^4 * (1-0.2) + (0.2)^5 = 0.01024

Since 0.01024 < 0.025, we can conclude that p = 0.2 lies within the 95% confidence interval.

(iii) If we observed five infected plants out of five, then the probability of a result at least as extreme as the observed data is simply P(X = 5) = p^5. To determine if p = 0.3 lies within the 95% confidence interval, we need to find the range of values of p such that the probability of observing five infected plants is less than or equal to 0.025:

p^5 <= 0.025

p <= (0.025)^(1/5)

p <= 0.551

Since 0.3 < 0.551, we can conclude that p = 0.3 does not lie within the 95% confidence interval.

(i) The number of infected plants among 5 plants follows a binomial distribution with parameters n = 5 and p. We observed one infected plant. To determine if p = 0.6 or p = 0.7 lie within the 95% confidence interval, we need to find the range of values of p such that the probability of a result at least as extreme as the observed data (i.e., zero or one infected plants) is less than or equal to 0.025:

For p = 0.6:

P(X <= 1) = P(X = 0) + P(X = 1) = (0.4)^5 + 5(0.6)(0.4)^4 = 0.07808

Since 0.07808 > 0.025, we cannot conclude that p = 0.6

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Answer:

Question 1:

\({ \tt{1 \: in = 2.54 \: cm}} \\ { \tt{5.36 \: in = (5.36 \times 2.54) \: cm}} \\ { \tt{ diameter= 13.6144 \: cm}} \\ \\ { \tt{radius = ( \frac{1}{2} \times 13.6144)}} \\ \\ { \tt{radius = 6.8072 \: cm}}\)

Question 2:

\({ \tt{ \frac{3.00 \times {10}^{8} \: m}{1 \: s} = \frac{( \frac{1}{1609}) \times 3.00 \times {10}^{8} \: mi }{( \frac{1}{3600} ) \: h} }} \\ \\ = { \tt{(1.86 \times {10}^{5}) \times 3600 }} \\ \\ = { \tt{ 6.71 \times {10}^{8} \: mi {h}^{ - 1} }}\)

Question 3;

\({ \tt{ \frac{25.0 \: mi}{1 \: } = \frac{1.609 \times 25.0 \: km}{3.785 \: l} }} \\ \\ { \tt{ = 10.627 \: km {l}^{ - 1} }}\)

Answer:

124.5

Step-by-step explanation:

All you need to do is multiply.

15*8.3=124.5

This is because The total water in Ari's fish tank has 15 gallons, and each gallon has 8.3, so you multiply.

Step-by-step explanation:

Volume of Washing machine = Volume of Rectangle

= Length x Width x Height

= 5 x 6 x 6

\( = 180ft^{3} \)

Answer:

10 hours at $140

Step-by-step explanation:

Well, uhh...

"same amount of money" means the same value on the y axis

looking at the graph one can see they intercept at point (10,140)

so if they both work 10 hours, their total individual money will be $140

Answer:

10 hour because you will need to find the time the line intercect(meaning cross each other) and it was at 10 hour for 140 dollar

Step-by-step explanation:

Reject the claim by accepting H0.

What is null hypothesis and alternate hypothesis?

The null hypothesis and the alternative hypothesis are types of conjectures used in statistical tests, which are formal methods of reaching conclusions or making decisions on the basis of data.

Explanation for the answer:

Mean of observations, x bar \(=\frac{(23+19+23+23)}{4}=22\)

Then for each number: subtract the Mean and square the result:

\(1+9+1+1=12\)

Sample Variance:

       \(\frac{12}{3} = 4\)

Sample Standard Deviation:

\(\sqrt{4} = 2\)\((\sqrt{4})^{0.5} = 1.1412\)

Standard error,

  \(se = (\frac{s}{n} )^{0.5}\)

\(se = (\frac{1.1412}{4} )^{0.5}\)

\(se = 0.5341\)

Hypothesis,

\(H_0: Xbar \geq 21, against\)

\(H_1: Xbar < 21\\\)  (Lower tailed test)        

t-statistic:  

\(t-statistic=\frac{xbar-Xbar}{se}=\frac{22-21}{0.5341}=1.8723\)

p value for 3 (=n-1) degrees of freedom = 0.039805 or 3.9805%

As p-value < 1% (level of significance), so, we reject the null hypothesis. Hence, the mean running time of runners is not significantly atleast 21 miles.    

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