Two students, Jack and Remi, were running laps around a track. They ran at constant speeds. Jack ran 2 laps in 6 minutes 10 seconds. Remi ran 3 laps in 9 minutes 6 seconds. Who ran faster, Jack or Remi?

The probability of rolling a total of 9 is 1/9.

The probability of rolling a total of 10 is 1/12.

The probability of rolling a total of 11 is 1/18.

We have,

To calculate the probabilities of rolling specific totals with a pair of dice, we need to consider all possible combinations of numbers on each die.

Probability of rolling a total of 9:

There are four combinations that can result in a total of 9: (3, 6), (4, 5), (5, 4), and (6, 3).

Since each die has six sides, there are 6 * 6 = 36 equally likely outcomes when rolling two dice.

The probability of rolling a total of 9 is 4/36, which can be simplified to 1/9.

Probability of rolling a total of 10:

There are three combinations that can result in a total of 10: (4, 6), (5, 5), and (6, 4).

The probability of rolling a total of 10 is 3/36, which can be simplified to 1/12.

Probability of rolling a total of 11:

There are two combinations that can result in a total of 11: (5, 6) and (6, 5).

The probability of rolling a total of 11 is 2/36, which can be simplified to 1/18.

Thus,

The probability of rolling a total of 9 is 1/9.

The probability of rolling a total of 10 is 1/12.

The probability of rolling a total of 11 is 1/18.

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Answer:

2.4 put a bar over the 4 because it is repeating

Step-by-step explanation:

22/9 =

22 divided by 9

equals

The correct answers are:

The explanation for each response can be given as:

a. The population of this study would be all AIDS patients who have revealed symptoms and are receiving the new AIDS antibody drug.

b. Two reasons why the data may differ are:

  1. Variability in the patient's overall health and response to the treatment.

  2. Differences in the time of diagnosis and initiation of treatment among the patients.

c. It is not possible to determine if one researcher is correct and the other is incorrect solely based on the collected data. Multiple factors, such as the patient's individual characteristics and treatment protocols, could influence the outcomes.

d. The data may not be identical because each researcher is following a different set of patients, and individual patient experiences and outcomes can vary. Additionally, differences in data collection methods or other external factors could contribute to variations.

e. The sampling method used by the first researcher, randomly selecting \(40\) states and then selecting one person from each state, is a combination of stratified sampling (based on states) and simple random sampling (within each state).

f. The second researcher used a non-random sampling method by choosing \(40\) patients they knew. This method is known as convenience sampling. Concerns regarding this data set include potential bias in patient selection, as the researcher's personal knowledge could introduce subjectivity and may not represent a diverse range of patients receiving the treatment.

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Mrs. Horwitz needs 670 square inches of wrapping paper to wrap the present.

We have,

To figure out how much wrapping paper Mrs. Horwitz needs, she should find the surface area of the rectangular prism box.

The surface area of a rectangular prism is given by the formula:

Surface Area = 2lw + 2lh + 2wh

Given dimensions:

Length (l) = 13 in

Width (w) = 8 in

Height (h) = 11 in

Plugging these values into the formula, we get:

Surface Area = 2(13)(8) + 2(13)(11) + 2(8)(11)

Surface Area = 208 + 286 + 176

Surface Area = 670 in²

Therefore,

Mrs. Horwitz needs 670 square inches of wrapping paper to wrap the present.

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Answer:

Volume = 111.33 in.³

Step-by-step explanation:

The volume of the shape = volume of the rectangular prism part + volume of the triangular prism part

✔️volume of the rectangular prism part:

V = L*W*H

Where,

L = 5.1 in.

W = 3.4 in.

H = 5.9 in.

V = 5.1*3.4*5.9

V = 102.306 in.³

✔️volume of the triangular prism part:

V = ½*b*h*l

b = 6 - 5.1 = 0.9 in.

h = 5.9 in.

l = 3.4 in.

V = ½*0.9*5.9*3.4

V = 9.027 in.³

✅Volume of the shape = 102.306 + 9.027

= 111.333 in.³

≈ 111.33 in.³ (approximated to 2 decimal places)

9514 1404 393

Answer:

  C. x^2 + 3

Step-by-step explanation:

Substitute for f(x) and g(x) and simplify.

  (f -g)(x) = f(x) -g(x)

  (f -g)(x) = (2x^2 +2) -(x^2 -1) = 2x^2 +2 -x^2 +1

  (f -g)(x) = x^2 +3

Answer: 3^3 Square root 3

Step-by-step explanation:

Answer:

positive, leaner association

Step-by-step explanation:

Answer: please carify

Step-by-step explanation:I will change my anwser when you clarify

Answer:

its 4

Step-by-step explanation:

4 dude 4

Answer:

(3, 0) (7, 0)

Step-by-step explanation:

the parabola intersects the x-axis at these points

Answer:

The x intercepts are 3 and 7

Step-by-step explanation:

The x intercepts are where the line intersects with the x axis

Therefore the two intercepts are 3 and 7

Answer:

Y > 30

Step-by-step explanation:

Answer: 28.25%

Step-by-step explanation:

113/400=0.2825=28.25%

The confidence interval captures p with a given probability.

A confidence interval is used to estimate an unknown population proportion p. The endpoints of the interval will vary with each new sample taken, as the sample proportion p can vary. The probability that p is in the interval is equal to the level of confidence chosen for the interval, which is usually 95%, though it can be adjusted depending on the desired accuracy. However, whether the interval captures p is not known with certainty. The population proportion p is fixed, but the sample proportion p can vary from sample to sample and so the interval can either capture p or not capture p. Thus, the researcher cannot know with certainty whether the interval captures p or not. In order to obtain an accurate estimate of the population proportion, the researcher should take multiple samples, each with a high level of confidence, to ensure that the interval captures p.

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Answer:

$26

Step-by-step explanation:

17+9=26

Answer:

\(x=750m\)

Step-by-step explanation:

\(Assuming\) \(That\):

\(1m=3.3ft\)

We can make the conversion from feet per second to meters per second with this procedure:

\((165 \frac{ft}{s} ) (\frac{1m}{3.3ft} )=50\frac{m}{s}\)

Let \(x\) be the amount of meters the parachutist will fall during 15 seconds of free fall

Having that in 1 second the parachutist falls 50 meters, we can calculate \(x\) :

\(x=(50\frac{m}{s} )(15s)\)

\(x = 750 m\)

Brainliest?!

​

The x-intercept is 2 and the y-intercept is -6. The solution has been obtained by using the concept of intercepts.

What are intercepts?

An intercept is a location on the y-axis where the slope of the line crosses.

X and Y intercepts are the two main intercepts. The x-intercept and y-intercept of the line are the locations where it intersects the x and y axes, respectively.

We are given an equation as 3x - y = 6.

The x - intercept will be when y = 0.

So, on substituting y = 0, we get

⇒3x - y = 6

⇒3x - 0 = 6

⇒3x = 6

⇒x = 2

So, the x - intercept is 2.

Similarly, putting x = 0, we get

⇒3x - y = 6

⇒3(0) - y = 6

⇒-y = 6

⇒y = -6

So, the y - intercept is -6.

The graph for the same has been attached below.

Hence, the x-intercept is 2 and the y-intercept is -6.

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Answer:

n=4

Step-by-step explanation:

f(x+n)=3(x+n)^2-7=3x^2+24x+41

3x^2+3n^2+6xn-7=3x^2+24x+41

Comparing and we will get, n=4

Answer:

x          y

9         0

8         2

5         8

Step-by-step explanation:

(9, 0) , (8, 2) , and (5, 8) --> all three points satisfy the equation 2x + y = 18.

Answer:

Plug the equation into a graphing calculator, and you'll get these:

(9, 0) , (8, 2) , and (5, 8)

The probability that the mean battery life would be greater than 526.4 minutes if in a sample of 81 batteries having a variance of, 2916 and a mean life of 518 minutes is 0.0808.

The ratio of good outcomes to all possible outcomes of an event is known as probability. A lot of successful results for an experimental with 'n' results can be represented by the symbol x.

Given:

The variance = 2916,

The mean life of a battery, m = 518 min,

The total number of samples, n = 81

Calculate the probability of a mean battery life of lower than 526.4 minutes by the following formula,

z = x - m / (σ / √ n)

Here, x is the expected value, σ is the deviation, and z is the probability.

Substitute the values,

z = 526.4 - 518 / (54 / √81)         [σ = √ variance = √2916  = 54]

z = 1.4

Consult the cumulative standard normal table

P (z < 526.4) = 0.9192,

But we know that

P (z > 526.4) = 1 - P (z < 526.4)

P (z > 526.4) = 1 - 0.9192 = 0.0808

Therefore, The probability that the mean battery life would be greater than 526.4 minutes if in a sample of 81 batteries having a variance of, 2916 and a mean life of 518 minutes is 0.0808.

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Answer:

see below

Step-by-step explanation:

80 - 71 = 9

That means 9 studied neither language

25+14 = 39 studied only 1 language

71 - 39 =32

32 studied both

The length of the rope is A. 10.3 ft.

Now, the length of the rope, L, the height of the tent , h and the distance of point on ground, d form a right-angled triangle with hypotenuse side length of rope,L

Using Pythagoras' theorem which states that in any right-angled triangle, the square of the hypotenuse side equals the sum of the squares of the other two sides.

So, L² = h² + d²

L = √(h² + d²)

Since h =  5ft and d = 9 ft

Substituting the values of the variabes into the equation, we have

L = √(h² + d²)

L = √(5² + 9²)

L = √(25 + 81)

L = √106

L = 10.29 ft

L ≅ 10.3 ft

So, the length of the rope is A. 10.3 ft.

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The values of the determinants D, Dx, Dy, and Dz are -17, -52, 13, and -4, respectively.

To solve this system of equations using determinants, we need to set up the coefficient matrix and the augmented matrix. The coefficient matrix is the matrix of the coefficients of the variables, and the augmented matrix is the matrix of the coefficients and constants.

The coefficient matrix A is:

| 1 1 -1 |

| 3 4 -3 |

| 9 -3 4 |

The augmented matrix [A|B] is:

| 1 1 -1 | 4 |

| 3 4 -3 | 16 |

| 9 -3 4 | 14 |

To find the determinants D, Dx, Dy, and Dz, we need to use the following formulas:

D = det(A)

Dx = det([B|A1])

Dy = det([A0|B|A2])

Dz = det([A0|A1|B])

where A0, A1, and A2 are the columns of A, and [B|A1], [A0|B|A2], and [A0|A1|B] are the augmented matrices with the corresponding columns replaced by the constants.

Using these formulas, we get:

D = det(A) = -17

Dx = det([B|A1]) = -52

Dy = det([A0|B|A2]) = 13

Dz = det([A0|A1|B]) = -4

Therefore, the values of the determinants D, Dx, Dy, and Dz are -17, -52, 13, and -4, respectively.

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For X ≤ 15, n = 20, π = .70 ; compound event probability is approximately 0.0008 .

For X > 8, n = 11, π = .65 ; compound event probability is  approximately 0.9198.

For X ≤ 1, n = 13, π = .40 ; compound event probability is  approximately 0.6646 .

a. To calculate the probability of the event X ≤ 15, n = 20, π = .70, we will use the binomial distribution formula:

P(X ≤ 15)

=  ∑_(k=0)¹⁵〖(20Ck)(0.70)^k (0.30)^(20-k) 〗

Using a binomial distribution calculator, we can find this probability to be approximately 0.0008 (rounded to 4 decimal places).

b. To calculate the probability of the event X > 8, n = 11, π = .65, we will first find the probability of X ≤ 8, and then subtract this value from 1 to find the complement probability:

P(X > 8) = 1 - P(X ≤ 8)

= 1 - ∑_(k=0)⁸〖(11Ck)(0.65)^k (0.35)^(11-k)〗

Using a binomial distribution calculator, we can find the probability of X ≤ 8 to be approximately 0.0802.

Therefore, the probability of X > 8 is approximately 0.9198 (rounded to 4 decimal places).

c. To calculate the probability of the event X ≤ 1, n = 13, π = .40, we will use the binomial distribution formula:

P(X ≤ 1)

= ∑_(k=0)¹〖(13Ck)(0.40)^k (0.60)^(13-k)〗

Using a binomial distribution calculator, we can find this probability to be approximately 0.6646 (rounded to 4 decimal places).

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Answer:

20 dollars

Step-by-step explanation:

I think 20+20+20=60 then 60-40=20

Answer:

S₁₆ = 344

Step-by-step explanation:

the sum to n terms of an arithmetic sequence is

\(S_{n}\) = \(\frac{n}{2}\) [ 2a₁ + (n - 1)d ]

where a₁ is the first term and d the common difference

here a₁ = - 1 and d = a₂ - a₁ = 2 - (- 1) = 2 + 1 = 3 , then

S₁₆ = \(\frac{16}{2}\) [ (2 × - 1) + (15 × 3) ]

     = 8 (- 2 + 45)

     = 8 × 43

     = 344

Answer:

PK=15

RJ=9

Step-by-step explanation:

PK and RJ are angle bisector because they also bisect their side lengths.

QK=2(PQ)=10

PK=5+10=15

QJ=2(QR)=6

RJ=6+3=9

RJ=9

The needed number of days at 10 degrees is given as follows:

11 days.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

In which:

For this problem, we have that when x decreases by 5, y increases by 2, hence the slope m is given as follows:

m = -2/5

m = -0.4.

Hence the time needed for a temperature of 10 degrees is given as follows:

9 + 2 = 11 days.

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