In the past, the mean running time for a certain type of flashlight battery has been 8.0 hours. The manufacturer has introduced a change in the production method and wants to perform a hypothesis test to determine whether the mean running time has increased as a result. The hypotheses are: H0 : µ = 9.8 hours Ha : µ > 9.8 hours Suppose that the results of the sampling lead to rejection of the null hypothesis. Classify that conclusion as a Type I error, a Type II error, or a correct decision, if in fact the mean running time has not increased.

Answer:

142 mL

Step-by-step explanation:

In order to find the answer for this question, we'll need to find the average of the two values, because that will tell us how much each person will have after the exchange. We can then subtract that from Theo's initial amount to get what he gives to Poppy. There are other ways to do this, this is just one way.

To find the average, we'll first add the two values together. 500 + 216 = 716.

Then, we divide this by 2, as that's the number of values we initially added together. 716 / 2 = 358.

Finally, we subtract this from Theo's initial value. 500 - 358 = 142.

That gives us our final answer of 142 mL. We can add this to Poppy's initial value to check our answer, 216 + 142 = 358.

Hope this helps! Let me know if you have any questions :D

The probability of having exactly 3 women on a jury selected randomly from a pool of 25 men and 25 women in a county with very few people can be calculated as approximately 0.324.

To calculate the probability, we need to determine the number of favorable outcomes (jury configurations with exactly 3 women) and the total number of possible outcomes (all possible jury configurations).

Determining the number of favorable outcomes:

We can select 3 women from a pool of 25 women in $\binom{25}{3}$ ways (using the binomial coefficient formula).

Similarly, we can select 9 men from a pool of 25 men in $\binom{25}{9}$ ways.

To obtain the total number of favorable outcomes, we need to multiply these two numbers together: $\binom{25}{3} \times \binom{25}{9}$.

Determining the total number of possible outcomes:

The total number of jurors we can select from the pool of 50 people is $\binom{50}{12}$ (selecting 12 jurors from a total of 50).

Calculating the probability:

The probability of having exactly 3 women on the jury is the ratio of the number of favorable outcomes to the total number of possible outcomes:

(

25

3

)

×

(

25

9

)

(

50

12

)

≈

0.324

(

12

50

​

)

(

3

25

​

)×(

9

25

​

)

​

≈0.324

Therefore, the probability of having exactly 3 women on the jury selected at random from a pool of 25 men and 25 women in a county with very few people is approximately 0.324.

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Answer:

h= -15

Step-by-step explanation:

you have to move the negative from the h to the other side :)

so hmmm say A(-10 , 5) , B(8 , 2) and the point that partitions them is point C.

\(\textit{internal division of a line segment using ratios} \\\\\\ A(-10,5)\qquad B(8,2)\qquad \qquad \stackrel{\textit{ratio from A to B}}{1:2} \\\\\\ \cfrac{A\underline{C}}{\underline{C} B} = \cfrac{1}{2}\implies \cfrac{A}{B} = \cfrac{1}{2}\implies 2A=1B\implies 2(-10,5)=1(8,2)\)

\((\stackrel{x}{-20}~~,~~ \stackrel{y}{10})=(\stackrel{x}{8}~~,~~ \stackrel{y}{2}) \implies C=\underset{\textit{sum of the ratios}}{\left( \cfrac{\stackrel{\textit{sum of x's}}{-20 +8}}{1+2}~~,~~\cfrac{\stackrel{\textit{sum of y's}}{10 +2}}{1+2} \right)} \\\\\\ C=\left( \cfrac{ -12 }{ 3 }~~,~~\cfrac{ 12}{ 3 } \right)\implies \boxed{C=(-4~~,~~4)}\)

Answer:

r² = (9 - 4)² + (6 - 4)² = 5² + 2² = 25 + 4 = 29

So the equation of this circle is

(x - 4)² + (y - 4)² = 29

In thsi question, the confidence coefficient when the level of significance is 0.03 is C. 0.9700.

In statistics, the confidence coefficient is the complement of the level of significance (α) used in hypothesis testing. The confidence coefficient represents the confidence level or the degree of certainty associated with a confidence interval.

The level of significance, denoted by α, is the probability of rejecting the null hypothesis when it is true. It is typically chosen before conducting a statistical test and determines the critical value or the cutoff point for decision-making.

To find the confidence coefficient, we subtract the level of significance from 1. In this case, the level of significance is 0.03. Subtracting 0.03 from 1 gives us a confidence coefficient of 0.97, which can be written as 0.9700 when rounded to four decimal places.

Therefore, the correct answer is C. 0.9700, which represents the confidence coefficient when the level of significance is 0.03.

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Answer:

Hope it will help you a lot.

Answer:

\(\huge\boxed{\sf 63}\)

Step-by-step explanation:

\(= x^2+10x + 24\)

Put x = 3

= (3)² + 10(3) + 24

= 9 + 30 + 24

= 63

\(\rule[225]{225}{2}\)

Answer:

Option D) 63 is the correct answer.

Step-by-step explanation:

where :

\( \quad\sf{\dashrightarrow{{x}^{2} + 10x + 24}}\)

Substituting the value of x :

\( \quad\sf{\dashrightarrow{{(3)}^{2} + 10 \times 3 + 24}}\)

\( \quad\sf{\dashrightarrow{(3 \times 3) + 30 + 24}}\)

\( \quad\sf{\dashrightarrow{(9) + 54}}\)

\( \quad\sf{\dashrightarrow{9 + 54}}\)

\( \quad\sf{\dashrightarrow{63}}\)

\(\quad{\star{\underline{\boxed{\sf{\pink{63}}}}}}\)

Hence, the answer is 63.

The general form of the equation Kareem can use to represent the data include the following: B. y = ab^x.

Generally speaking, an equation is a linear equation when the first difference between the y-values of an equation are the same. Additionally, an equation is an exponential equation when the common ratio between y-values of an equation are the same.

Furthermore, an equation is a quadratic equation when the second difference between the y-values of an equation are the same.

For the first difference between the y-values, we have:

First difference = 1/4 - 1/8 = 1/8

First difference = 1/2 - 1/4 = 1/4

Therefore, this equation is not a linear equation.

Next, we would determine the common ratio between y-values;

Common ratio = 1/4/(1/8) = 2

Common ratio = 1/2/(1/4) = 2

Therefore, this equation is not an exponential equation with the general form of y = ab^x.

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Answer:

B

Step-by-step explanation:

Answer:

10 or 70

Step-by-step explanation:

10= 40-30=10

70=40+30=70

Answer:

1) is greater than

2) is equal to

3) is equal to

4) is less than

Please mark as brainliest if answer is right

Have a great day, be safe and healthy  

Thank u  

XD  

Answer:

f^-1(x) = -4 / x - 2

Step-by-step explanation:

First swap the x and y values. This is done by setting f(x) to x, and x to y.

f(x) = (2x - 4) / x → x = (2y - 4) / y

*Then solve for y like you would for a normal equation*

x = (2y - 4) / y

×y ×y

(multiplication property of equality)

*This will isolate the extra y term*

__________________________

xy = 2y - 4

-2y -2y

(subtraction property of equality)

*This is done to group the like terms together, because they both share a y term now*

_____________________________

xy - 2y = -4

| |

v v

( x - 2 )

(GCF)

*In this case the GCF is y because it is the factor held in common, reverse distributive property*

________________________________

y(x-2) = -4

÷(x-2) ÷(x-2)

(Division property of equality)

*This is the last and final step to isolate the y term completely, so we can find the inverse*

y = -4/x-2

*This is the inverse*

Now just set it in function form as an inverse:

y = -4/x-2 → f^-1(x) = -4/x-2

From the steps below, it has been proven that; CB ≅ BE because the corresponding parts of congruent triangles are congruent.

Triangles are said to be congruent when they fulfill any of the 5 primary congruency postulates.

From the image, we see that;

AB = BD = 30 ft

CA ║DE

We want to prove that CB ≅ BE,

In ΔBDE and ΔBAC, we see that;

AB = BD = 30 ft

∠DBC = ∠ABC because they are vertically opposite angles

∠BED = ∠BCA because they are alternate interior angles

ΔBAC ≅ ΔBDE by AAS Congruency Postulate

Thus, CB ≅ BE because the corresponding parts of congruent triangles are congruent.

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Complete question is;

Keisha, Dwayne, and Lonzell are planning for a new bridge to replace the old bridge. The new bridge will start at point B, where Dwayne is standing, and end at point C, where Keisha is standing. Lonzell walks to point  and then walks parallel to the river until he reaches point D where he sees Dwayne and Keisha are aligned. Why is the distance from  E to  B the length of the new bridge?

It is given that

because they are vertical angles

because they are alternate interior angles. Therefore,

is congruent to ΔBDE

by

So CB ≅ BE,

because the corresponding parts of congruent triangles are congruent. This means that the distance from  E to B  is the length of the new

bridge.

Answer:

Domain:  \(-3\leq x\leq 1\)

Range:  \(-4\leq y\leq 0\)

Step-by-step explanation:

If you find the coordinate of the graph you can get the domain and range

(-3,0), (-2,-4), (-1,-2), (0,0), (1, -4)

Now that we have that find the domain and range

Domain -  x coordinate

Range - y coordinate

Domain: (-3, -2, -1, 0, 1)

Range: (-4, -2, 0)

Since the domain ranges from -3 to 1 you can use the inequality \(-3\leq x\leq 1\) to represent the domain and \(-4\leq y\leq 0\) for the range

Answer:

this is not questions you mind is deie

When both groups are shifted to a situation in which they earn an alternative reward after being trained to navigate a runway for food, the group that received three food pellets will continue to perform the task at a high level while the group that received one food pellet will experience difficulty.

It is known that rats have a natural preference for higher rewards. As a result, the group that received three pellets will be more motivated to complete the task since they have already tasted a higher reward. Therefore, they will continue to perform at a high level in the new environment.

On the other hand, the group that received only one pellet may find it challenging to adapt to the new situation since they are now receiving a lower reward. As a result, they may struggle to complete the task, and their performance may decrease.

In conclusion, the group that received three pellets will perform better than the group that received one pellet when both groups are shifted to a situation in which they earn an alternative reward. This is because the rats have a natural preference for higher rewards.

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The density of the mixture (liquid C) is 1.44 g/cm³ (rounded to 2 decimal places).

What is density ?

Density is a physical property of matter that describes how much mass is contained within a given volume. It is defined as the amount of mass per unit volume of a substance. In other words, density tells us how tightly packed the molecules or particles of a substance are.

The formula for density is:

density = mass / volume

where mass is the amount of matter in an object or substance, and volume is the amount of space it occupies.

According to the question:
To find the density of the mixture, we need to use the formula:

density of mixture = (mass of liquid A + mass of liquid B) / (volume of liquid A + volume of liquid B)

We can find the masses of the liquids by using their densities and volumes:

mass of liquid A = density of A x volume of A = 1.09 g/cm³ x 43 cm³ = 46.87 g

mass of liquid B = density of B x volume of B = 1.53 g/cm³ x 166 cm³ = 254.58 g

Now we can substitute the values into the formula:

density of mixture = (mass of liquid A + mass of liquid B) / (volume of liquid A + volume of liquid B)

density of mixture = (46.87 g + 254.58 g) / (43 cm³ + 166 cm³)

density of mixture = 301.45 g / 209 cm³

Therefore, the density of the mixture (liquid C) is 1.44 g/cm³ (rounded to 2 decimal places).

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Greetings from Brasil...

According to the properties of the radiation:

X^(a/b) = \(\sqrt[b]{X^a}\)

So

X^(2/3) = \(\sqrt[3]{X^2}\)

And

Y^(-3/4) = 1/Y^(3/4)

so 1/Y^(-3/4) = Y^(3/4) = \(\sqrt[4]{Y^3}\)

Then we get

\(\sqrt[2]{X^3} .\sqrt[4]{Y^3}\)

Answer:2.4 chapters

Step-by-step explanation:

To find the consumer surplus, we need to first find the equilibrium quantity at the given sales level of 800. To do this, we set the demand function equal to 800 and solve for q:

770 - 0.3q - 0.0004q^2 = 800

0.0004q^2 + 0.3q - 30 = 0

Using the quadratic formula, we get:

q = (-0.3 ± sqrt(0.3^2 - 4(0.0004)(-30))) / (2(0.0004))

q = 387.97 or q = -77.47

Since the negative quantity doesn't make sense in this context, we can disregard it and conclude that the equilibrium quantity at a sales level of 800 is approximately 388.

To find the consumer surplus, we need to calculate the area between the demand curve and the price line up to the quantity of 388. We can do this by taking the integral of the demand function from q = 0 to q = 388 and subtracting the total revenue earned at the quantity of 388:

CS = ∫[770 - 0.3q - 0.0004q^2]dq - (770 - 0.3(388)) * 388

CS = 217,829.32 - 66,224 = 151,605.32

Rounding to two decimal places, the consumer surplus is $151,605.32.

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The first 5 elements of set H, which contains numbers in G that are also elements of F are {4, 16, 36, 64, 100}.

The intersection of two sets has been the set that includes each of the elements which are shared by both sets.

The symbol for set intersection is  "∩''. The intersection, A ∩ B (read as A intersecting B) lists all the items that really are present in both sets and constitute the common elements of A and B for any two sets A and B.

Now, according to the question;

Set G is the set of positive integers divisible by 4, and

Set F is the set of perfect squares;

Then,

G = {4; 8; 12; 16; 20; 24; 28; 32; 36; 40; 44; 48; 52; 56; 60; 64; 68; 72; 76; 80; 84; 88; 92; 96; 100; 104; ...}

F = {1; 4; 9; 16; 25; 36; 49; 64; 81; 100; ...}

So, by the intersection of the sets;

G ∩ F - a intersection of the two sets, that is, what numbers are present in both sets at the same time.

G ∩ F = {4; 16; 36; 64; 100}

Therefore, The first 5 elements of set H, which have the same numbers in G as elements of F are {4, 16, 36, 64, 100}.

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Answer: ?

Step-by-step explanation: ?

Glow costs 16/27 dollars, which is equal to 59.3 cents per volume unit.

Let's start by assigning variables to the unknown prices and volumes of the toothpastes. Let x be the price per unit volume of Fresh, y be the price per unit volume of Glow, and z be the price per unit volume of Bright. Let v1 be the volume of Fresh, v2 be the volume of Glow, and v3 be the volume of Bright. From the information given in the problem, we can set up the following equations:

z = 1.6y (a tube of Bright is 60% more expensive than a tube of Fresh)

v3 = 0.75v2 (a tube of Bright has 25% less volume than Glow)

y = 0.75z (a tube of Glow is 25% less expensive than a tube of Bright)

v2 = v1 + 100/3 (a tube of Glow has 100/3 more volume than Fresh)

We can substitute the first equation into the second equation to eliminate z:

v3 = 0.75v2

(substitute v2 = 0.75z and v1 = 1)

0.75v2 = 0.75(0.75z + 100/3)

0.75v2 = 0.5625z + 25

(substitute z = 1.6y and v2 = v1 + 100/3)

0.75(v1 + 100/3) = 0.5625(1.6y) + 25

0.75v1 + 25/3 = 0.9y + 25

0.75v1 = 0.9y + 50/3

We can substitute the third equation into the fourth equation to eliminate y:

v2 = v1 + 100/3

(substitute y = 0.75z)

0.75z = 0.75(0.75y) + 100/3

z = y + 16/9

(substitute z = 1.6y)

1.6y = y + 16/9

y = 16/27

Therefore, the price per unit volume of Glow is 16/27 dollars, or 59.3 cents per unit of volume.

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(a) Total 288 different arrangements of the committee are possible if the rowers and basketballers both sit together in groups, but no rower sits next to a basketballer.

(b) If the conditions in a apply, 1/24 is the probability that these two members of the committee will sit next to one another.

(a) Considering the four rowers as a single person, the three basketball players as a single person, and the cricketers as two unique people (So, a total of 4 persons).

Number of configurations for a round table of n people = (n-1)!

Number of configurations for a round table of n people = (4-1)!

Number of configurations for a round table of n people = 6 ways

Let's leave out the number of arrangements that the basketball players and rowers will have.

Assuming that a basketball player and a rower are one person, they will sit together = (3-1)! × 2!

Assuming that a basketball player and a rower are one person, they will sit together = 4

There are therefore numerous arrangements for the groups where basketball players and rowers sit together = 2

No. of ways to arrange basketball players in a group = 3!

No. of ways to arrange basketball players in a group = 6

There are numerous number of methods to arrange rowers within a group = 4!

There are numerous number of methods to arrange rowers within a group = 24

Hence, total number of ways = 2×6×24

Total number of ways = 288

No. of ways are 288

b) The definition of an event's probability is as follows:

Probability = No. of Successful Outcomes / Total no. of Outcomes

Number of ways a cricketer can take a seat = 2! = 2 ways

Number of arrangements for the remaining rowers when he is seated next to the cricket player = 3!

Number of arrangements for the remaining rowers when he is seated next to the cricket player = 6 ways

Total number of possible ways = 6×2

Total number of possible ways = 12 ways

Probability = 12/288

Probability = 1/24

Hence, the required probability is 1/24.

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Answer:

  14 cm

Step-by-step explanation:

The applicable formula is ...

  s = rθ

  s = (7 cm)(2) = 14 cm