which is a characteristic of any function created by the product of two linear factors?

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).

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Answer:

what is the question??????

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.

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Answer:

H0: μ=7.6

Ha: μ>7.6

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

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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;

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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:

30

Step-by-step explanation:

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

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

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Answer:

$8.75 for one ticket

Step-by-step explanation:

Since this is just plain division, you'd divide 52.50 by 6 and get your answer of 8.75.

Hope I helped!

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.

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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%.

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The recent college graduate upon passing her exam with a probability will be as follows:

(a) Let the event where she passes the exam be denoted as [tex]E_{i}[/tex] and by i-th exam.

P(passes all exams) = P([tex]E_{3} E_{2} E_{1}[/tex]) = P([tex]E_{3} | E_{2} E_{1}[/tex])P([tex]E_{2} | E_{1}[/tex])P([tex]E_{i}[/tex])

= (0.7)(0.8)(0.9)

= 0.504

(b) By calculating,

[tex]P (E_{1} E_2^{c} | (E_{1} E_{2} E_{3})^{c})[/tex] = [tex]\frac{P (E_{1} E_2^{c} | (E_{1} E_{2} E_{3})^{c})}{P((E_{1} E_{2} E_{3})^{c})}[/tex]

= [tex]\frac{P(E_{1} E^{c}_{2}) }{P((E_{1} E_{2} E_{3})^{c})}[/tex]

= [tex]\frac{P(E^{c}_{2} | E_{1)}P(E_{1 )} } {{P((E_{1} E_{2} E_{3})^{c})}}[/tex]

= [tex]\frac{(1- P (E_{2}|E_{1})) P(E_{1})}{1-P(E_{1} E_{2} E_{3} }[/tex]

= [tex]\frac{(1-0.8) X 0.9}{1-0.504}[/tex]

where we know the denominator from part (a)

≈ 0.3629

Probability theory deals with numerical representations of the likelihood that an event will happen or that a statement is true. A probability is a number between 0 and 1, where 0 essentially signifies an event's impossibility and 1 generally denotes certainty. The likelihood that something will happen is what is commonly referred to as probability. We can talk about the likely of one outcome, or the likelihood of a few outcomes, when we don't know how an event will turn out. An event's probability distribution is studied in statistics.

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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.

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The error is not using PEMDAS in right order and the answer is 75.

PEMDAS is a method of operation in which operations are done in the order of parentheses first , then exponents, multiplication, division, addition and subtraction in the respective manner.

Given expression, 62 + 3 + 5 x 2

By using PEMDAS,

Step.1 - Firstly do the multiplication;

             62 + 3 + 5 x 2 = 62 + 3 + 10

Step.2 - Now add the remaining terms;

             62 + 3 + 10 = 75

Therefore, the answer is 75 .

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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.

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Answer: 21.78

Step-by-step explanation:

25.65 - 3.87 = 21.78

Answer:

  GCF = 6; sum = 6(1 +3)

Step-by-step explanation:

You want the greatest common factor of 6 and 18.

The greatest common factor is the largest factor common to both numbers. Here, we can factor the numbers as ...

  6 = 6·1

  18 = 6·3

The factor 6 is common to both numbers. (Other numbers, such as 1, 2, and 3 are also common factors, but 6 is the largest.)

The GCF is 6.

In terms of the GCF, the sum can be written ...

  6 +18 = 6(1 +3)

__

Additional comment

If the smaller number is not a factor of the larger, then the next value to check is the difference between the larger and smaller.

Euclid's algorithm tells you the remainder from division of the larger by the smaller will be zero when the divisor is the GCF. Otherwise, the remainder can be used to replace the larger number for trying again.

Here, 18/6 = 3 r 0, so 6 is the GCF.

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.

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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:

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

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:39cm

Step-by-step explanation:

The formula to convert the sample mean to a z score is, z = (x−μ)/σ/√n

a) Probability that the sample average sediment density is at most 3 is 0.9525 and probability between 2.69 and 3.00 is 0.4525..

b) Large Sample size is approx. 4 ..

We have given that,

Suppose the sentiment density of a randomly selected specimen from a certain region is normally distributed with

Sample mean , X-bar = 2.69

Sample size , n = 25

Standard deviations, σ = 0.74

a) we have to see what's the probability that the sample average setiment is at most 3 and then we're going to calculate between 2.69 and 3 point, so the firstly we have to calculate the standard error.

standard error = σ/√n = 0.74/√25

=> standard error = 0.148

the probability that x is between 2.69 and 3 in the probability of 2.69, i.e P (2.69<z <3)

P(at most 3 ) = P( X-bar <3) = P( X-bar - u /σ /√n<( 3 - 2.69) /0.74/5 )

=> P(z< 1.67) = 0.9525

P (2.69<z <3) = P( 2.69 - 2.69/0.74/5<z< 1.67)

=> P( <z< 1.67) = 0.4525

b) A large sample size is needed to make sure the first probability is 0.99.

If P(X-bar <3) = 0.99

=> P( 0<z<(3-2.69)/0.74/√n ) = 0.99

=> (3 - 2.69 )/0.74 /√n = 2.33

=> 0.31 √n /0.25 = 2.33

=> n = ( 2.33×0.25/0.31)² = 3.5 ~ 4

Hence, sample size is 4 and P( <z< 1.67) is 0.4525

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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.

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Yes, These data suggest a statistically significant difference between the proportions of drug-resistant cases in the two cities.

In first city, the drug-resistant proportion is significant while In other city, It is not significant.

What is Ratio and proportion ?

A ratio is an ordered pair of numbers a and b, expressed as a / b, where b is not equal to 0. A percentage is an equation in which two ratios are made equal to one another.

Let the first city to be City A and the other city as City B.

In city A, 14 cases are of drug-resistant out of total 221 cases.

In city B, 6 cases are of drug-resistant out of total 322 cases.

We'll find the proportion of drug-resistant cases of both cities,

City A = 14 / 221 = 0.06 > 0.02

City B = 6 / 322 = 0.018 < 0.02

If use a 0.02 level of significance then,

City A has significant drug-resistant cases while City B does not have significant cases.

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Answer: 350 meters

Step-by-step explanation: if she can run 2100 meters in 6 minutes to get 1 minute you can to divide by 6. so 6 minutes turn to 1 minute and 350 meters.

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.

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.

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Answer to question 1:
2/5

Explanation:
This square is a 10 by 10 graph, meaning there is 100 total blocks, and 40 of the squares are shaded in, making 40/100 of the squares shaded. 40/100 is then simplified to 2/5.

Answer to question 2:
0.6

Explanation:
As previously stated, the graph has a total of 100 squares, and 60 of the squares are not shaded, making it 60/100 squares unshaded. 60/100 is then converted to a decimal of 0.6.

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]