A kangaroo hopped directly toward a lake at a constant velocity for 30seconds. In one-third of that time, the kangaroo hopped 60meters. What was the kangaroo's velocity?

When 36 reindeer are chosen at random, the probability that the mean weight is less than 100 kg is 0.1492.

A standard error is the standard deviation of its sampling distribution or an interpretation of that standard deviation.

Given,

Mean of the weights = 102.4 kg

Standard deviation = 13.9 kg

To determine the probability that the mean weight of 36 reindeer will be less than 100 kg, first compute the standard error using the formula,standard error, [tex]\sigma_x=\frac{\sigma}{\sqrt{n}}[/tex]

Where, [tex]\sigma[/tex]=standard deviation

n= number of reindeer

substitute the values in the formula,

[tex]\sigma_x=\frac{13.9}{\sqrt{36}}\\\\\sigma_x=2.31667[/tex]

Now,

[tex]P(x < 100)=P(x < \frac{100-102.4}{2.316})\\\\=P(z < -1.04)[/tex]

from z-score table,

=0.1492

Thus, the probability the their mean weight is less than 100 kg is 0.1492.

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Your question is incomplete, here is the complete question.

The weight of male reindeer of the R. Santa Claus subspecies is normally distributed with mean 102.4 kg and standard deviation 13.9 kg

if 36 reindeer are randomly selected, what is the probability their mean weight is less than 100kg?

Answer:

16p + 4

Step-by-step explanation:

the first thing you should do when you simplify an equation is to distribute the parenthesis

4p * 4 + 1 * 4

16p + 4

you cannot simplify any further so that is your answer

To get a number point 1 is impossible for any of the team to reach at the end of the described tournament.

As given in the question,

Total number of footballs teams = 3

Each team plays once with other team

Let three teams are Team1, Team2, and Team3

Team1 plays with Team2 and Team3

Team2 will play with Team3

Winning points = 3

Losing team points = 0

Withdraw teams points = 1

To reach in finals suppose Team1 plays with Team2 and Team3 and win

Points of team1 = 3 + 3

                         = 6points

As team plays once with other team , Team1 is out of the game.

Team2 and Team3 play with each other

To reach at the end of the tournament one team has to win let it be Team2

Points of Team2 = 3

Points of Team3 = 0

No withdraw game is possible to reach into finale.

Therefore, point 1 is impossible for any team to reach at the end of the tournament.

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Answer:All I know is that it’s not < or > but It might be ≤

Step-by-step explanation: Bye the way, you can only give brainliest when there is two questions.

[tex]\leq[/tex]

Step-by-step explanation:

Answer: 8

Step-by-step explanation:

8 times 8 is 64

The angle that the line 3y = 2x + 6 makes with the [x] axis is (θ) = 33°69'.

Given is the equation -

3y = 2x + 6

The given equation is -

3y = 2x + 6

y = (2/3)x + (6/3)

y = (2/3)x + 2

Slope of the line -

m = 2/3.

We know slope is also given by -

m = tan(θ)

So -

tan(θ) = 2/3

(θ) = tan⁻¹(2/3)

(θ) = 33°69'

Therefore, the angle that the line makes with the [x] axis is (θ) = 33°69'.

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Theres no point 'Z', so i'm gussing you want the angle of <KLJ?

<K and <M are the same, therefore <M = 130

<J + <K + <M + <L = 360

130 + 130 = 260,  360 - 260 = 100

<J and <L are the same

<MJK = 50 and <KLM = 50

<KLM/2 = <KLJ

50/2 = 25

Answer: 19.71 Million.

The type of linear relationship is positive.

Correlation is a statistical measure that expresses the extent to which two variables are linearly related (meaning they change together at a constant rate). It's a common tool for describing simple relationships without making a statement about cause and effect. The correlation coefficient is a statistical measure of the strength of a linear relationship between two variables. Its values can range from -1 to 1. A coefficient of 1 shows a perfect positive correlation, or a direct relationship. A correlation coefficient of 0 means there is no linear relationship.

The type of linear relationship is positive.

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Answer:

–2.4 + 3.2t

Step-by-step explanation:

= –3.6 – 1.9t + 1.2 + 5.1t

= –3.6 + 1.2 – 1.9t + 5.1t

= –2.4 + 3.2t

i hope this helped

We can conclude that due to the help of nurses, the survival time of patients given drugs was the highest.

The nurse takes the patient's cardiac output and makes a decision on how the patient will react to the medication.

What types of tasks does a nurse perform?

Registered nurses (RNs) administer and supervise patient care, educate the public about various ailments, and provide psychological support and counseling to patients' relatives. Most nurses collaborate to doctors in a variety of contexts.

How many years do such people live?

People who have access for informal health information as having a nurse or doctor in the parents 10% more likely to remain past the age of 80, according study released in a journal article by that of the Directorate of Economic Research.

Therefore, we can conclude that due to the help of nurses, the survival time of patients given drugs was the highest.

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Using the Poisson distribution, the probability of an earthquake in the 0.8-0.9 magnitude range sometime in the next 30 years is

1 - 1.9287 x 10⁻²².

It is given that mean recurrence of an earthquake is the 8.0-9.0 magnitude is approximately 1500 years.

We have to find the probability of an earthquake in this magnitude range sometime in the next 30 years.

Since, an occurrence of an earthquake is a rare event, we can use Poisson distribution here.

Poisson distribution gives the probability of occurrence of any event in a given time interval.

Let the average number of event per year in 30 years of period is λ.

[tex]\lambda = \frac{1500}{30}[/tex]

λ = 50

Let, the occurrence of an earthquake is a random variable x.

Then the probability that at least an earthquake occur in next 30 years is calculated as:

P(x ≥ 1) = 1 - P(x<1)

P(x ≥ 1) = 1- P(x=0)   -----(1)

PDF of Poisson distribution with parameter λ is given as:

[tex]P(X = x) = \dfrac{e^{-\lambda}{\lambda}^x}{x!}[/tex]

So, in this case

[tex]P(x=0)= \dfrac{e^{-50}{(50)}^0}{0!}[/tex]

[tex]P(x=0)= \dfrac{1.9287 \times 10^{-22}}{1}[/tex]

[tex]P(x=0)={1.9287 \times 10^{-22}[/tex]

Substitute this value in equation (1)

P(x ≥ 1) = 1 - 1.9287 x 10⁻²²

Hence, the probability of an earthquake in next 30 years is

1 - 1.9287 x 10⁻²².

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Answer:

B

Step-by-step explanation:

Determine the equation of the line given by the table and compare with given options.

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (2, 9) and (x₂, y₂ ) = (7, 19) ← 2 ordered pairs from the table

m = [tex]\frac{19-9}{7-2}[/tex] = [tex]\frac{10}{5}[/tex] = 2 , then

y = 2x + c ← is the partial equation of the line

to find c substitute any ordered pair from the table into the partial equation.

using (6, 17 ), that is x = 6, y = 17 , then

17 = 12 + c ⇒ c = 17 - 12 = 5

y = 2x + 5 ← equation of line from table, with y- intercept c = 5

thus the function with a y- intercept greater than the table line is B

The first option is true since the item achieved its maximum height of 73.5 feet.

x ax2 + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a 0. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem. The answer could be simple or complicated.

This quadratic equation, which has the form y=a(x-h)2 + k, is referred to as being in vertex form. It is so named because the vertex point (peak point) lies on the graph of this equation (h,k)

We may deduce from the facts above that

-4.9 t2 + 19.6 t + 58.8 = 0

The equation will logically fit into the square upon completion.

y = a(x-h)^2 + k

where h will be the time it takes to get to a height of k.

-[tex]4.9t^{2}[/tex] + 19.6t + 58.8 = 0

-[tex]4.9t^{2}[/tex] + 19.6t = - 58.8

-4.9( [tex]t^{2}[/tex] - 4t ) = -58.8

Now take half the linear term, square it, and add it to both sides.

-4.9( [tex]t^{2}[/tex] - 4t ) = -58.8

-4.9( [tex]t^{2}[/tex] - 4t + 4 ) = -58.8 + 19.6

-4.9 [tex](t-2)^{2}[/tex] = - 78.8

s(t) = -4.9 [tex](t-2)^{2}[/tex] + 78.8

now we have t = 3sec

s(t) = 73.5ft

The object reached its maximum height of 73.5 ft, the first choice is correct.

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The value of (a) r that make sense is 6 in. and (b) the value of A that make sense is 113.1 in²

You should understand that the pizza is fit inside the square box making all circumference of the circle to touch all the sides of the square box

The quadratic function reads

A= πr²

Where A= Area of circle,

π = 22/7

and r= radius of the circle

A= (22/7)*6

Width of the box is 12

Therefore 12/2 = r=6

A= (22*6*6)/7

A=113.1 in²

In conclusion, he value of (a) r that make sense is 6 in. and (b) the value of A that make sense is 113.1 in²

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The vertex (0,2) of the parabola's vertex shape, which can expand upward or downward, equals (x - 0)² + 2.

What is parabola?

Any point on a parabola is at an equal distance from both the focus, a fixed point, and the directrix, a fixed straight line. A parabola is a U-shaped plane curve.

What is a vertex form of an equation?

An equation's conventional vertex form is written as:

f(x) = (x-h)² + k where;

(h, k) is the vertex

Vertex (0,2) should be replaced in the equation's vertex form.

f(x) = (x - 0)² + 2

As a result, vertex (0,2) of the parabola with an opening up or down is equal to (x - 0)² + 2.

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Rick should order part number G371-7 So the option A is the correct Answer

What is a part number ?

Part designs or materials are identified by part numbers, which are sometimes abbreviated as PN, P/N, part no., or part #. Its goal is to make referencing to that thing simpler. A part number clearly identifies a part design both inside and occasionally outside of a single organization. For instance, it is simpler to identify a screw as "HSC0424PP" rather than "Hardware, screw, machine, 4-40, 3/4" long, pan head, Phillips." The part number in this illustration is "HSC0424PP," which may be prefixed in database fields as "PN HSC0424PP" or "P/N HSC0424PP."

A serial number is a specific identifier of a specific instantiation of a part design, much as a part number identifies a component design (regardless of its instantiations). To put it another way, a part number designates each specific (physical) item as having been manufactured to a specific, original design;

As part number G371-7 fits perfectly to the desired requirement of float diameter of less than 8 inches, weigh more than 1 pound, and fit a 5/16-SAE spud connection that's why it is the correct answer

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Step-by-step explanation:

SWT + TWU =180º therefore SWU must be a line. Aka SWU is linear. So SWT and TWU must be a linear pair.

SWT + SWT = 180º therefore 2SWT=180º deviding both sies by 2 we get SWT = 90º Therefore SWT is replacing TWU. SWT is substituted into TWU. So substitution.

SU | TV basically means the line that passes through both points S and U is perpendicular to the line that passes through both points T and V. Therefore it is the Defenition of perpendicular lines.

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The improper fraction 7/8 has no value in the options given

To do this, we must divide the dividend by the divisor in order to change an improper fraction to a mixed number. After division, the acquired quotient becomes the whole numerals, the remainder becomes the new numerator, and the denominator remains the same, resulting in a mixed number.

To convert 7/8 into decimal number;

7/8 = 0.875

2 1/2 = 2.5

1 5/8 = 1.625

4% = 0.04

5 5/8 = 5.625

In the given options, none of them has a value of 7/8

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The total pressure experienced by a diver working 15m below surface of sea is 150000 Pa.

Pressure is the force applied perpendicular to the surface of an object per unit area over which that force is distributed.

We need to find the total pressure experienced by a diver working 15m below surface of sea.

P = h·ρ·g

P = pressure

h = depth = 15 m

ρ = density = 1g/cm³=1000kg/m³

g = acceleration due to gravity = 10 m/s²

Substitute the values in the formula of total pressure.

P=1000×15×10

P=150000Pa

Hence, 150000Pa is the total pressure experienced by a diver working 15m below surface of sea.

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Answer:

4.) a.) 2.01 b.) 404.01

6.) a.) 152.17 b.) 18412.17 c.) 153.14 d.) 18565.60

Step-by-step explanation:

To solve, use the exponential growth formula [tex]A_t=A_0(1+\frac{r}{p})^t[/tex] where

[tex]A_t[/tex] = Amount as a function of time

[tex]A_0[/tex] = Original amount

[tex]r[/tex] = rate

[tex]p[/tex] = period

[tex]t[/tex] = time

For question 4, let

[tex]A_0=400\\r=0.06\\p=12\\t=2[/tex]

So,

[tex]A_t=400(1+\frac{0.06}{12})^2\\A_t=400(\frac{201}{200})^2\\A_t=400(1.01)\\A_t=404.01[/tex]

So, the second-period interest would be 404.01-402=2.01

Question 6 can be solved using the same formula, but let

[tex]A_0=18260\\r=0.025\\p=\frac{12}{4}=3\\t_1=1\\t_2=2[/tex]

So,

[tex]A_t=18260(1+\frac{0.025}{3})^1\\A_t=18260(\frac{121}{120})^1\\A_t=18412.17[/tex]

The first-period interest would be 18412.17-18260=152.17

For the second-period, use [tex]t_2[/tex]:

[tex]A_t=18260(1+\frac{0.025}{3})^2\\A_t=18260(\frac{121}{120})^2\\A_t=18260(1.02)\\A_t=18565.60[/tex]

The second-period interest would be 18565.60-18412.17=153.43

Given that the second student chosen is a girl, the probability that both students are female is 0.175.

The occurrence of likely events is referred to as probability. It is the branch of mathematics concerned with numerical estimates of the likelihood of an event occurring or a statement being true.

Probability is nothing but likelihood of something is to occur. When we are unsure about the outcome of an event, we can discuss the probabilities of certain outcomes—how likely they are.

The probability of selecting a girl from the class is

[tex]= \frac{Number\ of\ girls}{ Total\ number\ of\ students}= \frac{14}{26}\\\\= \frac{7}{13}[/tex]

It is known that the one of the chosen student from 2 students is girl, the probability of having both girls will be:

[tex]= \frac{7}{16} * \frac{6}{15}\\\\= 0.175[/tex]

Hence, the probability is 0.175.

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Your question is incomplete, here is the complete question.

Your statistics class has 26 students in it - 14 girls and 12 boys.Your teacher uses a calculator to select two students at random to solve a problem on the board. Given that the second student chosen is a girl, what is the probability that the first student was also a girl?

The missing statements and reasons to proof that ∠1 is supplementary to ∠3 are:

S1: Line m is parallel to line n.

S2: ∠1 = ∠2

R3:  Corresponding angles postulate

R5: Supplement Postulate

S7:  m∠1 + m∠3 = m∠2 + m∠3

What are Supplementary Angles?

Supplementary angles, when added together will give us a sum of 180°.

Linear pair angles and corresponding angles are supplementary.

Thus, to prove that ∠1 is supplementary to ∠3:

We are given that lines m and n are parallel.

∠1 and ∠3 are corresponding angles.

So therefore, ∠1 = ∠3 by the corresponding angles postulate.

∠2 and ∠3 are linear pair, their sum therefore equals 180° based on the definition of supplementary angles.

Based on the substitution property, we have the following:

m∠2 + m∠3 = m∠1 + m∠3

m∠1+m∠3=180°

Therefore, ∠1 is supplementary to ∠3 based on the definition of supplementary.

The missing statements and reasons to proof that ∠1 is supplementary to ∠3 are:

S1: Line m is parallel to line n.

S2: ∠1 = ∠2

R3:  Corresponding angles postulate

R5: Supplement Postulate

S7:  m∠1 + m∠3 = m∠2 + m∠3

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Brian started cleaning at 3:33 PM and finished at 4:21 PM. The correct answer is 48 minutes

First, we are figuring out what is given we are counting numbers or we can add to get to 4:21 PM.

Counting numbers:

[tex]\boxed{3:33=3:34=3:35=3:36=3:37=3:38=3:39=3:40 }[/tex]

Add the numbers:

[tex]\boxed{3:33+7=3:40+10=3:50+10=4:00+21=4:21}[/tex]

If we add the numbers it would be faster.

Therefore, when we add we get are answer.

Therefore, Brian started cleaning at 3:33 PM and finished at 4:21 PM. The correct answer is 48 minutes

Answer:

48

Step-by-step explanation:

The system of equations is:

3a + 2r + 7b = 21

2a + 6r + b = 29

a + 4r + 5b = 23

What is an equation?

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.

a = price of apples

r = price of oranges (I used r instead of letter o since o can be confused with zero)

b = price of bananas

Sally went to the grocery store and bought 3 lbs. of apples, 2 lbs. of oranges, and 7 lbs. of bananas for $21.

3a + 2r + 7b = 21

Kevin bought 2 lbs. of apples, 6 lbs. of oranges and 1 lb. of bananas for $29.

2a + 6r + b = 29

Heather bought 1 lb. of apples, 4 lbs. of oranges and 5 lbs. of bananas for $23.

a + 4r + 5b = 23

The system of equations is:

3a + 2r + 7b = 21

2a + 6r + b = 29

a + 4r + 5b = 23

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Answer:

See attached image

Step-by-step explanation:

You can graph lines on a website called desmos graphing calculator!

Answer:

Step-by-step explanation:

you replace x with anything you want I will do 0. Then the the first point is (0,-4). Now I am gonna replace x with something else like 4. The second point is (4,8), now connect the two points and you got a line.

The area of the rhombus is  49√6. Option B

The formula for calculating the area of a rhombus is expressed as;

Area = pq/2

Where;

p and q are the diagonals of the rhombus

From the diagram shown, let's determine the value of p

Using the trigonometric identity;

Tan θ = opposite/adjacent

Substitute the values into the formula, we have;

tan 60 = p/7

Find the value of tan 60 and then substitute

√3 = p/7

cross multiply

p = 7√3

But;

Area = 7√3 × 7√3/2

Area = 49√6

Hence, the value is 49√6

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The probability that less than three of the chosen consumers think that currency won't be used in 20 years is 0.293.

According to the statement, 40% of consumers think cash will be unnecessary in 20 years. Let us assume that eight consumers are chosen at random.

We need to determine the likelihood that fewer than three of the chosen consumers think currency will be obsolete in 20 years.

We will use the properties of probability distribution in the given scenario.

We know that for randomly selected variable the properties of combination are used.

P(X=1) + P(X=2) = C¹₈ × 40 × 60⁷ + C²₈ × 40² × 60⁶

P(X=1) + P(X=2) = 0.293

Therefore, there is a 0.293 percent chance that fewer than 3 of the chosen customers think that cash will be obsolete in 20 years.

The ratio of likely outcomes to all scenarios that are feasible, to all possible outcomes is called probability.

Normal distributions are crucial to statistics because they are commonly used in the natural and social sciences to describe real-valued random variables with uncertain distributions. They are important in part because of the central limit theorem.

This claim asserts that under certain conditions, the average of many samples (observations) of a random variable without finite mean and variance is itself a random variable, whose distribution converging to either a normal distribution as the number of samples increases.

Disclaimer: The complete question is :

40% of consumers believe that cash will be obsolete in the next 20 years. Assume that only 8 consumers are randomly selected. Find the probability that less than 3 of the selected consumers believe that cash will be obsolete in the next 20 years .

(Round to three decimal places as needed.)

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