HCF and LCM of two numbers are 15 and 180 respectively. If they are in the ratio 3;4,find the numbers​

Answer:

(6,-2)

Step-by-step explanation:

The point is now 6 units to the right of the y axis.  That would be 6, but the y value would be the same 2 units below the x axis.

a)The two way table is shown in figure,

b)The success rate of the three treatments in preventing cardiac arrests are 90.91% , 79.41% and 70%.

c)The expected cell count are as shown in the figure,

d)No. There is no difference among the treatments.

e) The brief summary is mentioned below.

Given,

The total number of people is 107.

33 people are enrolled in a stress management programme.

3 people had cardiac events as a result of the stress management programme.

34 people are in the exercise group.

The number of cardiac events in the exercise group was 7 people.

40 people receive routine care.

12 people had cardiac events while receiving standard care.  

a)

The two-way table for the given information is shown in the figure

b)

During the same time period, 7 of the 34 people in the exercise group and 12 of the 40 patients in usual care experienced such events.Success rate can be determined by,

[tex]Success=\frac{no.\ of\ people\ who\ did not\ suffered\ in\ group}{Total\ number\ of people\ in\ group}[/tex]

For stress management:-

[tex]Success\ rate = \frac{30}{33}=0.9091=90.90\%[/tex]

For exercise program:-

[tex]Success\ rate = \frac{27}{34}=0.7941=79.41\%[/tex]

For usual care:-

[tex]Success\ rate = \frac{28}{40}=0.7=70\%[/tex]

c)

Expected cell count can be calculated by formula,

[tex]Expected\ value=\frac{row\ total*column\ total}{table\ total}[/tex]

then,

Expected value for the people who suffered cardiac arrest,

Under stress management:-

[tex]E= \frac{22*23}{107}=6.79[/tex]

Under exercise group:-

[tex]E=\frac{22*34}{107}=6.99[/tex]

Under usual care:-

[tex]E=\frac{22*40}{107}=8.22[/tex]

Expected value for the people who did not suffered cardiac arrest :-

Under stress management:-

[tex]E=\frac{85*33}{107}=26.21[/tex]

Under exercise group:-

[tex]E=\frac{85*34}{107}=27.01[/tex]

Under usual care:-

[tex]E=\frac{85*40}{107}=31.78[/tex]

The expected cell count is mentioned in the table

d)

The null and alternate hypothesis are

[tex]H_0[/tex] :There is no difference in the actual success rates of the three treatments.

[tex]H_1[/tex] :The three treatments differ in terms of actual success rates.

The test statistic can be calculated by

[tex]x^2=\sum \frac{(O-E)^2}{E}[/tex]

Where,

O=observed value

E=Expected value

Under null hypothesis,

[tex]x^2=\frac{(3-.679)^2}{6.79}+\frac{(7-6.99)^2}{6.99}+\frac{(12-8.22)^2}{8.22}+\frac{(30-26.21)^2}{26.21}+\frac{(27-27.01)^2}{27.01}+\frac{(28-31.78)^2}{31.78}\\\\=4.8514[/tex]

The p-value for the test is [tex]P(x_2 > 4.8514)=0.0884[/tex]

There is no statistically significant difference in the success rates of the three treatments.

e)

Because the p-value is greater than 0.05 (at the 5% level of significance), there is insufficient evidence to reject the null hypothesis and conclude that there is no difference in the actual success rates for the treatments.

To learn more about test statistic refer here

https://brainly.com/question/14082240

#SPJ4

Making predictions about your data requires the usage of a hypothesis. They aid data analysts in determining what they want to verify or dispute.

Given,

A senior data analyst requests that a junior data analyst offer two hypotheses for a project involving data analytics.

The rationale for a hypothesis must be explained;

This is,

Hypothesis testing is a sort of statistical reasoning that uses information from a sample to draw conclusions about a population parameter or population probability distribution. The parameter or distribution is initially best guessed.

Here,

A hypothesis seeks to infer something from your data. Data analysts use them to show or refute what they want to prove.

Learn more about hypothesis here;

https://brainly.com/question/17099835

#SPJ4

Answer:

11.3

Step-by-step explanation:

Angles A & B are each 45 degrees because if you subtract 90 from 180 and divide that by 2 you get 45 then you do:

sin(45) times 16 which is 11.3

SIN = opposite over hypotenuse.

Each candy costs $3 and each pretzel costs $4.25

From the question, we are to determine the price of each candy and the price of each pretzel

Let the price of each candy be x and the price of each pretzel be y

From the given information,

3 candies and 2 pretzels cost $17.50

Then, we can write that

3x + 2y = 17.50          ----------- (1)

Also,

9 candies and 4 pretzels cost $44

Then,

9x + 4y = 44              ------------ (2)

Solve the equations simultaneously

Multiply equation (1) by 2 and subtract it from equation (2)

2 × [3x + 2y = 17.50

6x + 4y = 35

Subtract from equation (2)

9x + 4y = 44

- [6x + 4y = 35

---------------------------------

3x + 0 = 9

3x = 9

Divide both sides by 3

3x/3 = 9/3

x = 3

substitute the value of x into equation (2)

9x + 4y = 44  

9(3) + 4y = 44  

27 + 4y = 44

4y = 44 - 27

4y = 17

y = 17/4

y = 4.25

Hence, the cost of the candy is $3 and the cost of the pretzel is $4.25

Learn more on Calculating costs here: https://brainly.com/question/28671876

#SPJ1

Answer:

y=35

Step-by-step explanation:

3y+25+2y+30+2y-5+y+30=360

Combine like terms then you will get
8y+80=360
8y=280

y=35

Answer:

35°

Step-by-step explanation:

the sum of the angles in a quadrilateral is 360 degrees

let 's make and solve the equation

3y + 25 + 2y + 30 + 2y - 5 + y +30 = 360

Combine like terms then you will get

(3y + 2y + 2y + y) + (25 + 30 - 5 + 30) = 360

8y + 80 = 360

8y + 80 - 80 = 360 - 80

8y = 280

y = 280:8

y= 35

Answer: 480 are teenagers

Step-by-step explanation:

To find a percentage of a number, I like to convert the percentage into its decimal form, so I do...

10% = .1 because a percentage is out of a whole number. 100% = 1.

Next, multiply your sum by the percentage you are looking for, so...

[tex]4800*.1=480[/tex]

Answer: 21.78

Step-by-step explanation:

25.65 - 3.87 = 21.78

When a pair of dice is rolled, there is a 1/6 chance that the result will be less than 5.

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we might discuss the likelihood or likelihood of several outcomes. Statistics is the study of occurrences that follow a probability distribution. The probability is computed by dividing the total number of possible outcomes by the number of possible ways the event might occur. Probability and odds are two distinct ideas. Odds are calculated by dividing the likelihood of an event by the likelihood that it won't.

Here,

Total possibility=36

To calculate the probability correctly, the list should be,

(1,1),(1,2),(1,3),(2,1),(2,2),(3,1)

Total cases=6

probability of getting a sum less than 5,

=6/36

=1/6

The probability of getting a sum less than 5 when a pair of dice is rolled will be 1/6.

To know more about probability,

https://brainly.com/question/11234923

#SPJ4

The null hypothesis is that the mean is equal to 7.6 lbs while the alternate hypothesis of the valve is that it is not equal to 7.6lbs.

What is a Hypothesis in statistics?

This term is used to refer to a statement which is made that is tested to be true or untrue during the study.

The Null hypothesis

H0: μ = 7.6

The alternate hypothesis:

H1: μ ≠ 7.6

The null hypothesis says the valve produces a mean pressure of 7.6 lbs. The alternate hypothesis on the other hand says that it does not equal to 7.6lbs.

To know more about Hypothesis in statistics visit,

https://brainly.com/question/13446219

#SPJ4

Answer:

H0: μ=7.6

Ha: μ>7.6

Answer:

30

Step-by-step explanation:

9-(-21) = 9+21 = 30

Using the binomial distribution, it is found that there is a 0.5954 = 59.54% probability that at least 1 is defective.

What is the binomial distribution?

A collection of numerous independently distributed Bernoulli trials with equal distributions results in the binomial distribution. The experiment in a Bernoulli trial is said to be random and can only result in one of two outcomes: success or failure.

For each phone, there are only two possible outcomes, either it is defective, or it is not. The probability of a phone being defective is independent of any other phone, which means that the binomial distribution is used to solve this question.

Binomial probability distribution

[tex]P(X = x) = C_n, x. p^{x.(1-p)^n-x}[/tex]

[tex]C_n, x = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

x is the number of successes.

n is the number of trials.

p is the probability of success on a single trial.

In this problem:

0.11 probability of a single phone is defective, hence

6 phones are selected at random, hence

The probability that at least 1 is defective is:

P(X >= 1) = 1 - P(X = 0)

In which

[tex]P(X = x) = C_n, x. p^{x.(1-p)^n-x}[/tex].

P(x = 0) = C₆,₀.(0.11)⁰ (0.86)⁶ = 0.4046

Then:

P(X >= 1) = 1 - P(X = 0) = 1 - 0.4046 = 0.5954

Hence, the 0.5954 = 59.54% probability that at least 1 is defective.

To learn more about the binomial distribution visit,

https://brainly.com/question/9325204

#SPJ4

Answer:

Usually we write the final answer with positive exponents.

[tex]\frac{1}{x^{2} }[/tex]

Step-by-step explanation:

[tex]\frac{x^{5} }{x^{7} }[/tex]

When we are dividing powers with the same bases, we subtract the exponents.

[tex]x^{5-7}[/tex] = [tex]x^{-2}[/tex] or [tex]\frac{1}{x^{2} }[/tex]

Answer:39cm

Step-by-step explanation:

The one - year standard deviation is, 10.45%.

what is standard deviation?

The standard deviation in statistics is a measurement of how much a set of values can vary or be dispersed. A low standard deviation suggests that values are typically close to the set's mean, whereas a high standard deviation suggests that values are dispersed over a wider range.

Given:

A portfolio has a 3-year standard deviation of 18.1%.

We have to find the one - year standard deviation.

One - year SD = Variance / number of years.

Here,

Variance = square of standard deviation = (18.1)^2 = 327.61

So,

One - year SD = 327.61 / (3/1)

One - year SD = 109.20

Now,

(109.2)^(1/2) = 10.45%

Hence, the one - year standard deviation is, 10.45%.

To know more about standard deviation, click on the link

https://brainly.com/question/475676

#SPJ4

Answer:

x = -2, y = -3

Step-by-step explanation:

Solve for y:

If -3x + 9y = -21, and -3x +8y = -18, then -21 - y = -18

Add 18 to both sides:

-3 - y = 0, so y = -3

reconstruct new equation:

-3x + 9(-3) = -21, -3x + 8(-3) = -18

-3x + -27 = -21, -3x + -24 = -18

Using the new equation, solve for x:

add 24 to both sides of each equation :

-3x + -3 = 3, -3x = 6

x=-2

Applying the distance formula, the distance between the two points (7, 4) and (3, 3) is: 4 units.

If we have two given points with their coordinates, to find the distance between these two points, apply the distance formula that is expressed as:

d = [tex]\sqrt{(y_2 - y_1)^2 + (x_2 - x_1)^2}[/tex].

Given the two points:

(7, 3) = [tex](x_1, y_1)[/tex]

(3, 3) = [tex](x_2, y_2)[/tex]

Substitute the values into the distance formula:

d = √[(3−7)² + (3−3)²]

d = √[(−4)² + (0)²]

d = √16

d = 4 units.

The distance is: 4 units.

Learn more about the distance formula on:

https://brainly.com/question/661229

#SPJ1

Answer:

b)-8

Step-by-step explanation:

Because the absolute value of -8 is 8 and it will have an greater number then all of them

The odds in favor of her selecting a red marble = 6/7

Here, Madison has a bag with 30 red marbles and 5 green marbles. she chooses one at random.

We need to decide the odds in favor of her selecting a red marble.

Total number of marbles = 30 + 5

Total number of marbles = 35

So, the odds in favor of her selecting a red marble would be,

p = number of favourable outcomes / total number of outcomes

p = 30/35

p = 6/7

Therefore, the probability that she select a red marble is 6/7

Learn more about probability here:

https://brainly.com/question/11234923

#SPJ4

Answer:

what is the question??????

Answer:

1/2x+3/4y=10

ANS:

x=

−3

2

y+20

Let's solve for x.

1

12

12x+

12x+3

12x+34

12x+34y=10

Step 1: Add (-3)/4y to both sides.

1

12

12x+

12x+3

12x+34

12x+34y+

12x+34y+−3

12x+34y+−34

12x+34y+−34y=10+

12x+34y+−34y=10+−3

12x+34y+−34y=10+−34

12x+34y+−34y=10+−34y

12x+34y+−34y=10+−34y1

12x+34y+−34y=10+−34y12

12x+34y+−34y=10+−34y12x=

12x+34y+−34y=10+−34y12x=−3

12x+34y+−34y=10+−34y12x=−34

12x+34y+−34y=10+−34y12x=−34y+10

Step 2: Divide both sides by 1/2.

1

2

x

x1

x12

x12=

x12=−3

x12=−34

x12=−34y+10

x12=−34y+101

x12=−34y+1012

x12=−34y+1012x=

x12=−34y+1012x=−3

x12=−34y+1012x=−32

x12=−34y+1012x=−32y+20

Answer:

Answer:x=

Answer:x=−3

Answer:x=−32

Answer:x=−32y+20

question

Answer: 67 87 34

Step-by-step explanation:

Answer: 8

Step-by-step explanation:

We only need to take  672/84 = 8

So there are 8

If you can please give me a Brainliest, I only need 1 more to become an Ace, thank you!

Answer:

x=8

Step-by-step explanation:

Lets assume that the number of 84 is x

as given in this equation

total values given in the question be 672

then the equatiuon becomes

84 multiplied by x is 672

simplify above the equation

84x=672

[tex]x=\frac{62}{84}[/tex]

x=8

Therefore, the number of 84 is 672 is 8.

(Hope this helped! :D)

The population size after four days is 121.

Given that,

a population of protozoa with a constant relative growth rate of 0.8603 per member per day

let P be the population size and let t be the time interval then the given system modeled by the differential equation

[tex]\frac{dP}{dt}[/tex] = 0.8603

by solving the separable equation and expifying both sides we get,

P = A [tex]e^{0.8603t}[/tex]

From the condition that on day zero the population consist of four members,

i.e. P(0) = 4, A = 4

Therefore population size after four days is

P(4) = 4[tex]e^{4(0.8603)}[/tex]

      = 4 [tex]e^{3.441}[/tex]  

      = 4 × 30.295

P(4) =  121.2

nearest whole number is 121

i.e P(4) = 121

Hence the population size after four days is 121.

To know more about population size here

https://brainly.com/question/15290034

#SPJ4

The maximum error in the area is 33.933 sq cm. The relative error is 0.0148. The percent error will be 1.48%.

The measurement that indicates the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the border of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.

Here,

1)  A = pi(r²)

dA = 2(pi)r(dr)

= 2(3.14)(27)(0.2) sq cm

= 33.93 sq. cm

2)  Relative error is the above divided by actual area

actual area=3.14*27*27

=2289.06 sq cm

Relative error=0.0148

3) % error -- convert the above to a % by appropriate shifting of decimal point

% error=0.0148*100

=1.48%

The area's largest inaccuracy is 33.933 sq cm. 0.0148 is the relative inaccuracy. There will be a 1.48% error percentage.

To know more about area,

https://brainly.com/question/22469440

#SPJ4

A system of linear inequalities for the number of packages of both hot dogs and hamburgers that can be bought is as follows:

x + y ≥ 3.

4x + 5y ≤ 20.

In order to write a system of linear inequalities to describe this situation, we would assign variables to the number of packages of hot dogs and number of packages of hamburgers respectively, and then translate the word problem into algebraic equation as follows:

Since you will need at least 3 packages of both hot dogs and hamburgers, the linear inequality to represent this is as follows:

x + y ≥ 3.

For the cost of both hot dogs and hamburgers, and the maximum amount you can spend;

4x + 5y ≤ 20.

Read more on inequality here: brainly.com/question/29115398

#SPJ1

5.94 minutes is the half-life, or the amount of time it takes to half the substance to degrade (about 6 minutes).

When we use the formula A = A0(1 - r)t,

(1/2)A₀ = A₀(1 - 0.11)t

[Divide both sides by A₀ results in:

1/2 = (0.87)t

Using the log of both sides;:

log(1/2) = log(0.87)t

Using a logarithm property, we can bring the "t" to the front, giving us:

log(1/2) = t.log(0.89)

[Dividing both sides with log(0.89) gets us:

t =  log(1/2)/log(0.89)

Using calculator for soling the values.

t = 5.94 seconds

Thus, 5.94 minutes is the half-life, or the amount of time it takes to half the substance to degrade (about 6 minutes).

To know more about the half-life of a radioactive substance, here

https://brainly.com/question/1160651

#SPJ4

The basketball player made 15 errors in  100 games as of the given condition.

Given that,
A baseball player made 9 errors in 60 games, how many errors would we expect the player to make in 100 games is to be determined.

The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.

Here,
Let the error be x, for 100 games,
Now, according to ot the question,
9/60= x / 100
x = 15

Thus, the basketball player made 15 errors in  100 games.

Learn more about ratios here:

brainly.com/question/13419413

#SPJ1

The lengths of the bamboo sticks obtained using the quadratic formula are;

33.06 cm and 16.94 cm

The quadratic formula used to find the solution of quadratic equations can be presented as follows;

[tex]x = \dfrac{-b \pm \sqrt{b^2 - 4\times a \times c} }{2 \times a}[/tex]

The area of the rhombus = 280 cm²

The length of the stick = 50 cm

Let x represent a length of the sticks , therefore;

The length of the other stick = 50 - x

The rhombus consists of two  triangles

The height of the triangles is half the length of the diagonal of the rhombus, therefore;

Area =  x × (50 - x) × 0.5 = 280

-0.5·x² + 25·x = 280

x² - 50·x + 560 = 0

x = (50 ± √((-50)² - 4 × 1 × (560))/(2)

x ≈ 33.06, or x ≈ 16.94

The lengths of the bamboo sticks are;

Learn more about quadratic equations in algebra here:

https://brainly.com/question/29478725

#SPJ1