The numbers of dots in the four triangular arrays form a sequence...​

Population distribution is probability distribution that measures the frequency of sample provided. For the given problem condition I and III are met for the inference but condition II does not met. Thus the option A is correct option.

Total students 500.

Total students surveyed by the counselor is 20.

Population distribution is probability distribution that measures the frequency of sample provided.

[tex]P=\dfrac{10\times500}{100}[/tex]

[tex]P=50[/tex]

Here the 10 percent of the population size is 50. Our sample size is 20. Thus the sample size is less than 10 percent of the population size.Hence the condition III is met for the inference.

Hence, for the given problem condition I and III are met for the inference but condition II does not met. Thus the option A is correct option.

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Answer:

No because there is sufficient statistical evidence to suggest that the mean contents of cola bottles is equal to 300 ml as advertised

Step-by-step explanation:

Here we have the measured contents as

299.4

297.7

301.0

298.9

300.2

297.0

Total = 1794.2

∴ Mean = 299.03

Standard deviation = 1.5

We have

[tex]z=\frac{\bar{x}-\mu }{\frac{\sigma }{\sqrt{n}}}[/tex]

Where:

[tex]\bar x[/tex] = Mean of sample = 299.03 ml

μ = Mean of population = 300 ml

σ = Standard deviation of population = 3 ml

n = Sample size = 6

α = 5% = 0.05

We set our null hypothesis as H₀ = 300 ml

Our alternative hypothesis is then Hₐ < 300 ml

Therefore,  z = -0.792

The probability from z table is P = 0.2142

Since the P value, 0.2142 is > than the 5% significance level, 0.05 we accept the null hypothesis that the mean contents of cola bottles is 300 ml.

Answer:

a) pi/3

Step-by-step explanation:

-11pi/3 + 4pi

(-11+12)pi/3

pi/3

Answer:

A

Step-by-step explanation:

We see that the angle is -11[tex]\pi[/tex]/3, which means that when drawing this angle on the graph, we need to move clockwise from 0 (see the drawing).

We see that this angle is actually the exact same as an angle in the first quadrant. This angle is [tex]\pi[/tex]/3.

Thus, the answer is A.

Hope this helps!

Answer:

(3x + 5)(x + √3)(x - √3)

Answer:

a = 4

Step-by-step explanation:

(3x+5) is a factor of the polynomial (a-1)x³ + (a+1)x² - (2a + 1)x - 15

Means x = -5/3 is a root

(a-1)(-5/3)³ + (a+1)(-5/3)² - (2a + 1)(-5/3) - 15 = 0

-125a/27 + 125/27 + 25a/9 + 25/9 + 10a/3 + 5/3 - 15 = 0

a(-125/27 + 25/9 + 10/3) = 15 - 5/3 - 25/9 - 125/27

a(40/27) = 160/27

a = 4

Answer:

Given

Number of stacks = 2

Stack 1 = 6 cups; h1 = 15cm

Stack 2 = 12 cups; h2 = 23cm

Let's first find the average:

[tex] \frac{H_1 - H_2}{ n_1 - n_2}[/tex]

[tex]= \frac{15-23}{6-12} [/tex]

[tex] = \frac{-8}{-6} = \frac{4}{3} [/tex]

With an average of 4/3, to obtain the number of cups needed to obtain a height of 50m, we have:

50 / (4/3)

= 50 * 3/4

= 150/4

= 37.5

From the answer, we can see that the number of cups is not really proportional to the height of the stack, because the average of stack one and stack 2 are different.

Answer:

  94.76°

Step-by-step explanation:

Assuming the coordinates are <E, N>, the total distance from the start is ...

  5<5, -2> +<-1, 8> = <5·5 -1, 5(-2) +8> = <24, -2>

These coordinates represent a vector south of east, so the bearing measured clockwise from north will be greater than 90°. The reference angle (with respect to a north-south line) will be ...

  arctan(24/2) = 85.24°

The bearing is 180° -85.24° = 94.76°.

Answer:

Not proportional

Step-by-step explanation:

Hope it helps you in your learning process.

[tex] \frac{6}{6}=1\\\\

\frac{8}{24}= \frac{1}{3}\\\\

\frac{10}{50}= \frac{1}{5}\\\\

\frac{12}{84}= \frac{1}{7}\\\\

\therefore \frac{6}{6}\neq \frac{8}{24}\neq \frac{10}{50}\neq \frac{12}{84}[/tex]

Hence, given ratios are not proportional.

Answer:

You right in this one.

Step-by-step explanation:

Answer:

D) secant

Step-by-step explanation:

NL doesn't pass through the centre, so not radius or diameter

Passes through two points on the circle so not a tangent

Extends to a point outside the circle, so not a chord

Answer:

Step-by-step explanation:

Answer:

86 cars

Step-by-step explanation:

1,500/17.50=85.71 so you just round it a little

He must wash 86 cars.

The division is one of the basic arithmetic operations in math in which a larger number is broken down into smaller groups having the same number of items. It is the process of repetitive subtraction. It is the inverse of the multiplication operation. It is defined as the act of forming equal groups.

Example: 4 / 2 = 2.

Given, Ryan charges his neighbors $17.50 to wash their car.

So, he earns $17.50 per car.

Let Ryan washes x cars to earn $1500

$17.50(x)=$1500

x = $1500/$17.50

x = 85.71 ≈ 86

Hence, Ryan needs to wash 86 cars to earn at least $1500.

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Answer:

Step-by-step explanation:

on the box chart it shows that shelter A has the lightest dog

hope i helped :D

Answer:

shelter A. shelter B. Both shelters have a dog with the lowest weight of 8 pounds.

Step-by-step explanation:

Hope this helps :)

Answer:

400

Step-by-step explanation:

Answer:

800*400/80=400

Step-by-step explanation:

To work this out you would first start with 40/80. This is because when using BODMAS / BIDMAS you would start with whatever operation that comes first out of all the operations in the question. This gives you 0.5. Then you would multiply 0.5 by 800, this gives you 400.

1) Find what operation you should do first.

B- Brackets

O -Orders

D-Division

M-Multiplication

A-Addition

S-Subtraction

2) Divide 40 by 80.

[tex]40/80=0.5[/tex]

3) Multiply 0.5 by 800.

[tex]0.5*800=400[/tex]

Answer:

4.5 kg

Step-by-step explanation: if you have 4.050 take off the zero and it is only 4.05 which is less then 4.5 or 4.50

Final answer:

When comparing 4.5 kg to 4.050 kg, 4.5 kg is the larger weight since both are in kilograms and 4.5 is greater than 4.050.

Explanation:

The question asks which number is larger, 4.5 kg or 4.050 kg. In the metric system, weights are compared directly as they are expressed in the same units. Here, we compare 4.5 to 4.050. Since 4.5 can also be thought of as 4.500 when considering the decimal places, it becomes clear that 4.5 kg is the larger value because both represent kilograms, and 4.5 is greater than 4.050.

Answer:

-12

Step-by-step explanation:

x-9.37+5.77=1.3x

Answer:

I had to look up the problem B4 because your image doesn't show the rest of the information

B4 = 12

B5 = 1,738

Step-by-step explanation:

if you need help on any other questions on this, i can't see them in the image

Answer:

The numbers are 1 and 17

Step-by-step explanation:

The only factors of 17 are 1 and 17 since 17 is a prime number

1*17 =17

1+17 =18

The two numbers that multiply to 17 and add to 18 are 1 and 17.

To find two numbers that satisfy the conditions of multiplying to 17 and adding to 18, we can set up a system of equations based on these criteria.

Let the two numbers be x and y .

1. Set up the equations:

  - [tex]\( xy = 17 \)[/tex] (product of the numbers)

  - [tex]\( x + y = 18 \)[/tex] (sum of the numbers)

2. Solve the system of equations:

  From x + y = 18, express y in terms of x :

  [tex]\[ y = 18 - x \][/tex]

  Substitute y = 18 - x into [tex]\( xy = 17 \)[/tex]:

  [tex]\[ x(18 - x) = 17 \][/tex]

  [tex]\[ 18x - x^2 = 17 \][/tex]

  [tex]\[ x^2 - 18x + 17 = 0 \][/tex]

3. Find the roots of the quadratic equation:

  Use the quadratic formula [tex]\( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \)[/tex], where a = 1 , b = -18, and c = 17:

  [tex]\[ x = \frac{-(-18) \pm \sqrt{(-18)^2 - 4 \cdot 1 \cdot 17}}{2 \cdot 1} \][/tex]

  [tex]\[ x = \frac{18 \pm \sqrt{324 - 68}}{2} \][/tex]

  [tex]\[ x = \frac{18 \pm \sqrt{256}}{2} \][/tex]

  [tex]\[ x = \frac{18 \pm 16}{2} \][/tex]

  So, [tex]\( x = \frac{34}{2} = 17 \)[/tex] or [tex]\( x = \frac{2}{2} = 1 \)[/tex].

4. Determine the corresponding y values:

  - If x = 17, then [tex]\( y = 18 - 17 = 1 \)[/tex].

  - If x = 1 , then [tex]\( y = 18 - 1 = 17 \)[/tex].

Therefore, the two numbers that multiply to 17 and add to 18 are 1 and 17.

The numbers 1 and 17 satisfy the conditions of multiplying to 17 and adding to 18, providing a clear solution based on the given criteria of the problem.

Answer:

12 inches

Step-by-step explanation:

Volume = length × width × height

336 = 4 × 7 × height

height = 12

Answer:

12 cubic inches.

Step-by-step explanation:

Since volume is length x width x height, you just do 7 x 4 (28) and then the total, 336 and divide that by 28. So, 12 cubic inches!

Answer:

There are 100 boys and 300 girls in School A and there are 300 boys and 500 girls in School B .

Step-by-step explanation:

The ratio of the boys in school A and the boys in school B is 1:3

Let the ratio be x

No. of boys in School A = x

No. of boys in School B = 3x

We are given that The number of boys in school B is 200 higher than the number of boys in school A.

So,[tex]x+200=3x[/tex]

[tex]200=3x-x[/tex]

[tex]200=2x[/tex]

[tex]\frac{200}{2}=x[/tex]

100=x

So, No. of boys in School A = x = 100

No. of boys in School B = 3x =3(100)=300

We are given that the ratio of the girls in school A and the girls in school B is 3:5.

Let the ratio be y

So, No. of girls in School A = 3y

No. of girls in School B = 5y

So, Total No. of students in School A= No. of boys in school A + No. of girls in school A=100+3y

Total No. of students in School B= No. of boys in school B + No. of girls in school B=300+5y

We are given that The number of pupils in school A is equal to half the number of pupils in school B.

So, [tex]100+3y=\frac{1}{2}(300+5y)[/tex]

[tex]200+6y=300+5y[/tex]

[tex]y=100[/tex]

No. of girls in School A = 3y=3(100)=300

No. of girls in School B = 5y=5(100)=500

Hence there are 100 boys and 300 girls in School A and there are 300 boys and 500 girls in School B .

Answer: 100 boys, 300 girls in School A. 300 boys,500 girls in School B

Step-by-step explanation:

Answer:

y = 2m-5

Kim's age now is y = 2m-5

Step-by-step explanation:

Let m represent martas age now and y represent Kim's age now

Given;

Five years ago Kim's age was twice as great as martas age.

(y-5) = 2(m-5)

Solving for y;

y-5 = 2m-10

y = 2m-10+5

y = 2m-5

Kim's age now is y = 2m-5

Final answer:

Kim's current age is represented by the expression 2m - 5, where m is Marta's current age. This is determined by considering the age difference and relationship of their ages five years ago.

Explanation:

The question is about determining Kim's current age given that Marta is currently m years old and five years ago Kim's age was twice that of Marta's. To solve this, we can follow these steps:

Let's represent Marta's age five years ago as m - 5.

Since Kim's age was twice Marta's age five years ago, we express Kim's age at that time as 2(m - 5).

To find Kim's current age, we add five years to her age at that time: 2(m - 5) + 5.

Simplifying the expression gives us Kim's current age as 2m - 5.

Therefore, the expression that represents Kim's age now, given that Marta is m years old, is 2m - 5.

Answer:

The answer is 20,358,520

Step-by-step explanation:

Selecting 6 numbers from a collection of 52 numbers regardless of order involves a combination.

Note: if regards was taken into order of selection, this would be a permutation.

Hence, the different 6 number selections out of 52 is

52C6 = 52! / [6!*(52-6)!]

= 52!/(6!*46!)

= 20,358,520

Answer:

x = 2sqrt(5)

Step-by-step explanation:

We can use the Pythagorean theorem to solve

The legs are x and 8/2 =4

and the hypotenuse is 6

a^2 + b^2 = c^2

x^2 +4^2 = 6^2

x^2 +16 = 36

Subtract 16 from each side

x^2 +16-16=36-16

x^2 = 20

Take the square root of each side

sqrt(x^2) = sqrt(20)

x = sqrt(4*5)

x = sqrt(4) sqrt(5)

x = 2sqrt(5)

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

The equation is already in standard form [ ax² + bx + c = y ] so we can find the values of each variable.

a = 1

b = 10

c = 3

y = 0

Quadratic formula: [tex]x = \frac{-b+-\sqrt{b^2-4ac} }{2a}[/tex]

Solve using the formula:

[tex]x=\frac{-10+-\sqrt{10^2-4(1)(3)} }{2(1)}[/tex]

[tex]x=\frac{-10+-\sqrt{100 - 12} }{2}[/tex]

[tex]x=\frac{-10+-\sqrt{88} }{2}[/tex]

[tex]x=-5+-\sqrt{22}[/tex]

Therefore, the answer is [ x = -5 ± √22 ]

Best of Luck!

Answer:

The volume of cone is increasing at a rate 1808.64 cubic cm per second.

Step-by-step explanation:

We are given the following in the question:

[tex]\dfrac{dr}{dt} = 12\text{ cm per sec}\\\\\dfrac{dh}{dt} = 12\text{ cm per sec}[/tex]

Volume of cone =

[tex]V = \dfrac{1}{3}\pi r^2 h[/tex]

where r is the radius and h is the height of the cone.

Instant height = 9 cm

Instant radius = 6 cm

Rate of change of volume =

[tex]\dfrac{dV}{dt} = \dfrac{d}{dt}(\dfrac{1}{3}\pi r^2 h)\\\\\dfrac{dV}{dt} = \dfrac{\pi}{3}(2r\dfrac{dr}{dt}h + r^2\dfrac{dh}{dt})[/tex]

Putting values, we get,

[tex]\dfrac{dV}{dt} = \dfrac{\pi}{3}(2(6)(12)(9) + (6)^2(12))\\\\\dfrac{dV}{dt} =1808.64\text{ cubic cm per second}[/tex]

Thus, the volume of cone is increasing at a rate 1808.64 cubic cm per second.

Final answer:

The volume of a cone can be found using the formula V = πr²h³. To find the rate at which the volume is increasing, we differentiate the volume formula with respect to time and substitute the given values into the derivative formula. The volume is increasing at a rate of 15552π cubic centimeters per second.

Explanation:

To find the rate at which the volume is increasing, we need to differentiate the volume formula with respect to time.

Let's differentiate the volume formula V = πr²h³ with respect to time t:

dV/dt = π(2rh³(dr/dt) + r²h²(dh/dt))

Given that dr/dt = dh/dt = 12 cm/sec, r = 6 cm, and h = 9 cm, we substitute these values into the derivative formula:

dV/dt = π(2(6)(9³)(12) + (6²)(9²)(12))

dV/dt = π(11664 + 3888)

dV/dt = 15552π

Therefore, the volume is increasing at a rate of 15552π cubic centimeters per second.

Answer:

A.)129/7

Step-by-step explanation:

25/4 + 24/7 + 35/4

I will add the two with common denominator together first

25/4 + 35/4     +24/7

60/4   +24/7

15  + 24/7

We need to get a common denominator of 7

15 *7/7  + 24/7

105/7  + 24/7

129/7

There are 4 out of the 7 cards that are odd numbers.

As a fraction: 4/7

As a percent: 57.14%

As a decimal: 0.57

Answer:

Step-by-step explanation:

The domain is the horizontal extent: all real numbers. -∞ < x < ∞.

The range is the vertical extent: all numbers greater than zero. 0 < y < ∞. (The graph never actually touches y=0, but comes arbitrarily close.)

Answer:

23.5

Step-by-step explanation:

you put it in order and find the middle in this case is  23 and 24 then you add them and divide by two and get 23.5

The estimated size of the lemur population can be calculated using the mark and recapture technique.

The estimated size of the lemur population can be calculated using the mark and recapture technique. The formula to estimate population size is:

N = (M * C) / R

where N is the estimated population size, M is the number of marked individuals in the second capture, C is the total number of individuals in the second capture, and R is the number of marked individuals recaptured in the second capture.

In this case, the number of marked individuals in the second capture is 11, the total number of individuals in the second capture is 49, and the number of marked individuals recaptured is 11. Plugging these values into the formula:

N = (11 * 49) / 11 = 49

Rounding to the nearest whole number, the estimated size of the lemur population is 49.

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