Which of the following is a rational number?

Answer:

Step-by-step explanation:

The probability of drawing a number that is divisible by 3 is 1/3, since there are 3 numbers (3, 6, and 9) out of the 9 possible numbers (1, 2, 3, 4, 5, 6, 7, 8, and 9) that are divisible by 3.

The probability of drawing a 1 after drawing a number that is divisible by 3 is 1/10, since there is only one 1 among the 10 possible digits (0-9) that could be drawn after the first number.

To find the probability of both events happening together (drawing a number divisible by 3 and then drawing a 1), we need to multiply the probability of the first event by the probability of the second event. Therefore, the probability of drawing a number divisible by 3 and then drawing a 1 is:

(1/3) x (1/10) = 1/30

So the probability of drawing a number divisible by 3 and then drawing a 1 is 1/30, or approximately 0.0333, or about 3.33%

Answer:

If I understand this correctly you can draw a 9 and then draw the one if I'm wrong just delete this

Step-by-step explanation:

the distance between Point A (-8,-2) and Point B(6,-1) in Radical form= \(\sqrt{197}\)

Distance formula:
The distance between two points formula uses the coordinates of two points in space. In coordinate geometry, the distance between two points can be calculated using the distance formula, present in a two-dimensional or three-dimensional space. The distance formula for two points is also an application of the Pythagoras theorem

the distance formula is used to find the distance between any two points when we already know the coordinates. The points could be present alone on the x-axis or y-axis or on both axes.

Let us consider, that there are two points say A and B in an XY plane. The coordinates of point A are (x1,y1), and of B are (x2,y2). Then the formula to find the distance between two points PQ is given by:

AB=\(\sqrt{(x2-x1)^{2} +(y2-y1)^{2} }\)

Note: If the coordinates of two points P and Q are such that, (x1, 0) and (x2, 0), the distance between PQ will be given by:

PQ = |x2 – x1|

the distance between point origin O(0,0) and P(x,y) is given by:

OP = √((x2 – 0)² + (y2 – 0)²)

OP = √((x2)² + (y2)²)

or simply,

OP = √(x² + y²)

Solution :

where x and y are coordinates of points other than the origin.

Given :

(x1,y1) = (-8,-2)

(x2,y2)= (6,-1)

Solution:

\(d=\sqrt{x^{2} +y^{2} } \\d=\sqrt{(6+8)^{2} +(-1+2)^{2} } \\d=\sqrt{14^{2}+1^{2} } \\\)

\(d=\sqrt({197)\)

Radical form= \(\sqrt{197}\)

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Answer:

C(x) = 0.2x^5 - x^2 + 6000

Step-by-step explanation:

Given in the question are restated as follows:

Marginal cos = C'(x) = x^4 - 2x ...................... (1)

Note that marginal cost (C'(x)) refers to the change in the total cost (C(x)) as a result of one more unit increase in the quantity produced. That is, MC refers to the additional cost incurred in order to produce one more unit of a good.

Therefore, TC can be obtained by integrating equation (1) as follows:

C(x) = ∫C'(x) = ∫[x^4 - 2x]dx

C(x) = 1/5x^5 - 2/2x^2 + F ................................ (2)

Where F is the fixed cost. Since the fixed cost is given as $6,000 in the question, we substitute it for F into equation (2) and solve as follows:

C(x) = 0.2x^5 - x^2 + 6000 ......................... (3)

Equation (3) is the total cost function​ C.

As per the given data, the number of integers in R ∩ S is 2, and the correct answer is (B) Two.

In mathematics, the intersection of two sets is a set containing all elements that are members of both sets.

In symbols, the intersection of two sets A and B is denoted by A ∩ B, and it contains all elements that belong to both A and B.

The intersection of two sets contains only the elements that are present in both sets. In this case,

R ∩ S = {x | x > 0 and x < 3}

The integers that are present in this set are 1 and 2.

Therefore, the number of integers in R ∩ S is 2, and the correct answer is (B) Two.

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The correct radical form of b^1/5 is 5^√b.

Square root and nth roots are represented by the symbol "radical," which. a square root is a component of a radical expression, which is an expression.

A number's or an algebraic expression's simplest radical form is referred to as this. When a number or algebraic expression contains no elements that are perfect nth powers under the radical, it is said to have an nth root and is said to be in its simplest radical form.

When a number or algebraic expression contains no elements that are perfect nth powers under the radical, it is said to have an nth root and is said to be in its simplest radical form.

Explanation:

Convert to radical form using the formula

a^x/n=n^√a^x

5^√b.

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The radius of curvature is 1410 ft, the velocity is 5.48 ft/s, the normal acceleration is 0.0213 ft/s2, and the magnitude of the acceleration is 0.500 ft/s2 after the particle travels 30 ft along the path to (2.806, 142).

The radius of curvature, r, can be calculated using the formula r = v2/a, where v is the velocity and a is the normal acceleration. The velocity is calculated by integrating the acceleration with respect to time. The normal acceleration is calculated by taking the derivative of the velocity with respect to time. The magnitude of the acceleration is the same as the acceleration given in the problem.

1. Calculate the velocity, v, by integrating the acceleration (0.5 ft/s2) with respect to time:

v = 0.5 * t = 0.5 * 30 s = 15 ft/s

2. Calculate the normal acceleration, a, by taking the derivative of the velocity with respect to time:

a = dv/dt = 0.5 ft/s2

3. Calculate the radius of curvature, r, using the formula r = v2/a:

r = 15 ft/s2/0.5 ft/s2 = 30 ft = 1410 ft

4. The magnitude of the acceleration is the same as the acceleration given in the problem, 0.5 ft/s2.

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Answer: he will be 14

Step-by-step explanation:

Anna is 14 and her brother is 10. Two years ago she was 12. 3/4 of 12 is 9. 9+5 more years is 14. :)))

Answer:

Champs is 64.8, Footlocker is 64. Footlocker is selling them for cheaper. You would go to Footlocker, as it's .8 off.

Then, the number of pounds of food that an adult manatee can eat in "d" days can be represented by the equation: p = r x d.

An equation is a mathematical statement that shows that two expressions are equal. It consists of two parts: the left-hand side (LHS) and the right-hand side (RHS), separated by an equals sign (=). The equals sign indicates that the two expressions are equal, and the goal of solving the equation is to find the value of x that makes this statement true. Equations can be solved using various algebraic techniques, such as simplifying and rearranging the expressions, applying operations to both sides of the equation, and factoring or expanding expressions. Solving an equation involves finding the values of the variables that make the equation true.

Here,

Let's assume that an adult manatee eats "r" pounds of food per day on average. Then, the number of pounds of food that an adult manatee can eat in "d" days can be represented by the equation: p = r x d

Here, "p" represents the number of pounds of food, "r" represents the average amount of food consumed per day, and "d" represents the number of days. So, if we know the average amount of food consumed by an adult manatee per day, we can use this equation to calculate how much food it will eat in any given number of days.

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Answer:

With this P-value, we have statistical evidence to support the claim that there is a relationship between the average number of putts per hole and the player's total winnings.

Step-by-step explanation:

In this case, the hypothesis test has the following hypothesis:

Null hypothesis: there is no relationship between the average number of putts per hole and the player's total winnings.

Alternative hypothesis: there is relationship between the average number of putts per hole and the player's total winnings.

Then, a P-value of 0.0087 is, without doubt, a strong evidence that the null hypothesis is false.

With this P-value, we have statistical evidence to support the claim that there is a relationship between the average number of putts per hole and the player's total winnings.

Answer:

2,540 miles

Step-by-step explanation:

The computation of the fewer miles is given below;

For Space explorer B

= 15,000 miles ÷ 5 hours

= 3,000 miles per hour

For space explorer A

y = 4,600 x

That means in one hour it covered 460 miles

So, the fewer miles would be

= 3,000 - 460

= 2,540 miles

The amount cheaper is the car washes Malcolm orders than the car washes Martha's order is $13.

The correct answer choice is option B.

Malcolm's gift card = $50.

Cost Malcolm's car wash per visit = $7

Martha's gift card = $180

Cost Martha's car wash per visit = Difference between gift card balance of first and second visit

= $180 - $160

= $20

How cheap is the car washes Malcolm orders than the car washes Martha's order = $20 - $7

= $13

Therefore, Malcolm's car wash is cheaper than Martha's car wash by $13

The complete question is attached in the diagram.

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The values of ab, b - c, and c/d are 6, -1, and 4 respectively when a = 2, b = 3, c = 4 and d = 1.Using BODMAS rule, we can simplify the given expression.ab - c/d = 24

Given ab-c/d has a value of 24.Now, we have to find the value ofab, b - c, and c/d.Multiplying d on both sides, we getd(ab - c/d) = 24dab - c = 24d...(1)Now, we can find the value of ab, b - c, and c/d by substituting different values of a, b, c and d.Value of ab when a = 2, b = 3, c = 4 and d = 1ab = a * b = 2 * 3 = 6.

Value of b - c when a = 2, b = 3, c = 4 and d = 1b - c = 3 - 4 = -1Value of c/d when a = 2, b = 3, c = 4 and d = 1c/d = 4/1 = 4Putting these values in equation (1), we get6d - 4 = 24dSimplifying, we get-18d = -4d = 2/9

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Answer:

6 vertices have a triangular prism. I hope I helped:)

A triangular prism has six vertices.

In order to calculate the number of vertices on any type of prism, take the number of corners on one side and multiply by two. For example, a rectangular prism has eight vertices, or two sets of four. read more

I hope this helps =)

Answer:

\(\boxed{\sf Yes}\;;\textsf{because $\angle 9$ and $\angle7$ are \boxed{\sf vertical} angles, $m \angle 9=$ \boxed{\sf 90\; degrees}}\;.\)

\(\textsf{Because $\angle6$ and $\angle8$ are \boxed{\sf complementary} angles, $m\angle6+m\angle8=$\;\boxed{\sf 90\;degrees}}\;.\)

\(\textsf{Thus}, \; \boxed{\sf m\angle9 = m\angle6 + m\angle8}\;.\)

Step-by-step explanation:

Vertical Angles Theorem

When two straight lines intersect, the opposite vertical angles are congruent.

Therefore, ∠9  and ∠7 are vertical angles and:

⇒ m∠9 = m∠7 = 90°

Angles on a straight line sum to 180°

⇒ m∠6 + m∠8 + m∠7 = 180°

⇒ m∠6 + m∠8 + 90° = 180°

⇒ m∠6 + m∠8 = 90°

Complementary Angles

Two angles whose measures sum to 90°.

Therefore, ∠6 and ∠8 are complementary angles and:

⇒ m∠6 + m∠8 = 90°

As  m∠9 = 90°  and  m∠6 + m∠8 = 90°  then:

⇒ m∠6 + m∠8 = m∠9

Answer:

B

Step-by-step explanation:

using the recursive rule \(a_{n}\) = 3\(a_{n-1}\) and a₁ = 10, then

a₁ = 10

a₂ = 3a₁ = 3 × 10 = 30

a₃ = 3a₂ = 3 × 30 = 90

the first 3 terms are 10 , 30 , 90

im pretty sure the answer is 16

Step-by-step explanation:

the drinks are 10

, burgers are 5 and each of the fries are 1. Since there is one of each, it will be like this 10+5+1

Answer:

soda = 10

burger = 5

fri = 2

5 + 2 x 10 = 25

Step-by-step explanation: its 25 cuz its 25

let's take a peek at the picture above, hmmm let's notice the vertex is at (-1 , 2), now let's get a point besides the vertex hmmm let's see it passes through (-2 , -1).

So we can reword that as what's the equation of a quadratic whose vertex is at (-1 , 2) and it passes through (-2 , -1)?

\(~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{a~is~negative}{op ens~\cap}\qquad \stackrel{a~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill\)

\(\begin{cases} h=-1\\ k=2\\ \end{cases}\implies y=a(~~x-(-1)~~)^2 + 2\hspace{4em}\textit{we also know that} \begin{cases} x=-2\\ y=-1 \end{cases} \\\\\\ -1=a( ~~-2-(-1) ~~ )^2 + 2\implies -3=a(-2+1)^2\implies -3=a \\\\\\ ~\hfill~ {\Large \begin{array}{llll} y=-3(x+1)^2 + 2 \end{array}} ~\hfill~\)

Answer:

y = -3(x + 1)^2 + 2

Step-by-step explanation:

y = a(x - h)^2 + k is the vertex form of a quadratic, where

Finding (h, k):

We see from the graph that the vertex is a maximum and its coordinates are (-1, 2).  Thus h is -1 and k is 2.  Since h becomes negative, it will be 1 in the parentheses: (x - (-1) = (x + 1).

Finding a:

In order to find a, we will need to plug in a point on the parabola for (x, y) and (-1, 2) for h and k.  We see that (0, -1) lies on the parabola so we can use this point for (x, y).

-1 = a(0 - (-1))^2 + 2

-1 = a(0 + 1)^2 + 2

-3 = a(1)^2

-3 = a

Thus, a = -3.

Thus, the exact equation in vertex form of the parabola is:

y = -3(x + 1)^2 + 2

I attached a picture from Desmos Graphing Calculator that shows how the equation I provided works and contains the two points you marked on the parabola, including (-1, 2) aka the maximum, and (0, -1) aka the y-intercept.

The probability that the Islanders will win exactly zero is 0.300763

From the question, we have the following parameters that can be used in our computation:

Number of games = 3

Probability of winning = 33%

This means that

Probability of losing = 1 - Probability of winning

Substitute the known values in the above equation, so, we have the following representation

Probability of losing = 1 - 33%

Evaluate

Probability of losing = 67%

The probability that the Islanders will win exactly zero is calculated as

P = Probability of losing^3

So, we have

P = (67%)^3

Evaluate

P = 0.300763

Hence, the probability is 0.300763

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Answer:

first we should add both purchase price

$4.45 + $9.55 = $14

so that

$20 - $14

=$6

The number of minutes to read is 6.25 pages and taking the test will be 5 minutes and 0.50 minutes, respectively.

The rate is the ratio of the amount of something to the unit. For example - If the speed of the car is 20 km/h it means the car travels 20 km in one hour.

It takes you 0.8 of a minute to read each page of your health book. It takes you 5.5 minutes to take the test at the end.

The number of minutes to read 6.25 pages will be given as,

⇒ 6.25 x 0.8

⇒ 5 minutes

The number of minutes to take the test will be given as,

⇒ 5.5 - 5

⇒ 0.50 minute

⇒ 0.50 x 60

⇒ 30 seconds

The number of minutes to read is 6.25 pages and taking the test will be 5 minutes and 0.50 minutes, respectively.

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Answer:

1

Step-by-step explanation:

Answer:

(2/5,0)

Step-by-step explanation:

The equation to find a line is mx+b=y. In this case m is 5, and b is -2.

5x+-2=y

Since we want to find the x-intercept, y has to be 0.

So: 5x+-2=0

5x=2

x=2/5

Answer:

D   28

Step-by-step explanation:

31 own 13-15

3 own 1-3

31 - 3 = 28

Answer:

D. 28

Step-by-step explanation:

1-3 had 31 people and 13-15 had 3 people.

Then we subtract the values (31-3) to get 28.

a. The distance from Carlton to Dalton is 76.61 km

b. The distance from Baxter to Dalton if you take the freeway is 145.61 km

From the question, we are to determine how far it is from Carlton(C) to Dalton(D)

From the given information,

The total distance from Abbott(A) to Dalton(D) is 233 km

Distance from C to D = Distance from A to D - Distance from A to C

Distance from A to C = 76.59 km + 79.8 km

Distance from A to C = 156.39 km

∴ Distance from C to D = 233 km - 156.39 km

Distance from C to D = 76.61 km

Hence, the distance from Carlton to Dalton is 76.61 km

b.

We are to determine the distance from Baxter(B) to Dalton(D) if you take the freeway

Taking the normal route,

Distance from B to D = 79.8 km + 76.61 km

Distance from B to D = 156.41 km

Now, from the given information,

The new freeway shortens the distance by 10.8 km

Thus,

The distance from Baxter(B) to Dalton(D) if you take the freeway

= 156.41 km - 10.8 km

= 145.61 km

Hence, the distance from Baxter to Dalton if you take the freeway is 145.61 km

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Answer:

KC to StL = 300

KC to Den = 600

Step-by-step explanation:

KC to StL was the base distance, so we'll call that x.

KC to Denver is twice as long, so we'll call that 2x.

If we add the together is is 900 miles total.

x + 2x = 900    Combine like terms

3x = 900          Divide by 3

x = 300

If x is 300, then 2x is 600.