A metal bar is to be divided into two pieces so that one piece is 3 centimeters longer than twice the length of the other. If the sum of the squares of the two lengths is 109 square centimeters, find the two lengths

Answer:

z=2.27

Step-by-step explanation:

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

where z is the deviation from mean.

mean (μ) = 35 inches

standard deviation (σ) = 11 inches

last year snow fall (x) = 60 inches

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

[tex]z=\frac{60-35}{11}[/tex]

z=2.27

now, the standard deviation for the 60 inches snow from the mean is calculated to be 2.27

Answer:

Amount theta she is putting in Checking account is 2272.80

Step-by-step explanation:

Given:

Amount on check = 2941

Amount that he want in cash = 100

Amount she put in saving account = 20% of remaining after getting cash

Remaining Amount she put in checking account.

To find: Amount in her Checking Account.

Amount left after taking cash = 2941 - 100 = 2841

Amount that she put in saving account = 20% of 2841 = [tex]\frac{20}{100}\times2841[/tex] =  568.20

Amount in her checking account = 2941 - 100 - 568.20  = 2272.8

Therefore, Amount theta she is putting in Checking account is 2272.80

ANSWER

[tex]36k^{8} -13{k}^{6} -64k^{4} + 30 {k}^{2} [/tex]

EXPLANATION

Recall the distributive property:

[tex](a + b + c)(d + e) = a(d + e) + b(d + e) + c(d + e)[/tex]

We apply this property multiple times to simplify

[tex](9k^{6}+8k^{4}-6k^{2})(4k^{2}-5)[/tex]

This implies that:

[tex]9k^{6}(4k^{2}-5)+8k^{4}(4k^{2}-5)-6k^{2}(4k^{2}-5)[/tex]

We apply the distributive property again:

This time: a(b+c)=ac+ab

[tex] \implies \: 9k^{6} \times 4k^{2}-5 \times 9 {k}^{6} +8k^{4} \times 4k^{2}-5 \times 8 {k}^{4} -6k^{2} \times 4k^{2} + 5 \times 6 {k}^{2} [/tex]

[tex]\implies \: 36k^{8} -45{k}^{6} +32k^{6} -40 {k}^{4} -24k^{4} + 30 {k}^{2} [/tex]

[tex]\implies 36k^{8} -13{k}^{6} -64k^{4} + 30 {k}^{2} [/tex]

NB: [tex]k^{n}\times{k}^{m}=k^{m+n} [/tex]

[tex]_7C_3\cdot {_{13}C_2}=\dfrac{7!}{3!4!}\cdot\dfrac{13!}{2!11!}=\dfrac{5\cdot6\cdot7}{2\cdot3}\cdot\dfrac{12\cdot13}{2}=2730[/tex]

The number of ways the student can select 5 books such that at least 3 are English novels can be calculated as the sum of combinations of 3 English and 2 American, 4 English and 1 American, and all 5 being English.

The subject matter of this question is based in the mathematics field, specifically combinatorics. To tackle this problem, we will utilize the concept of combination, which is a way of selecting items from a larger set where order does not matter.

The student has to select 5 books out of 16 (9 American and 7 English novels). But at least 3 should be English novels. It means the student can pick 3, 4 or all 5 novels as English novels. Let's calculate each possibility:

So, the total number of ways = [C(7,3)*C(9,2)] + [C(7,4)*C(9,1)] + C(7,5). Here C(n,r) denotes combination and is equal to n! / [(n-r)!*r!], where '!' denotes factorial.

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To find the area of a triangle with given vertices, calculate the cross product of two vectors representing the sides of the triangle. The magnitude of this cross product gives the area of the parallelogram, and half of this value is the triangle's area.

The area of a triangle with vertices (1, 0, 0), (0, 2, 0), and (0, 0, 1) can be calculated using the cross product of two vectors that represent two sides of the triangle. First, we find the vectors AB and AC by subtracting the coordinates of the points:

Next, we calculate the cross product AB x AC:

|i    j    k|
|-1  2  0|
|-1  0  1|

This results in a new vector (2, -1, -1). The magnitude of this vector gives us the area of the parallelogram formed by vectors AB and AC.

Area of parallelogram = |(2, -1, -1)| = √(2^2 + (-1)^2 + (-1)^2) = √(6)

Since the area of the triangle is half the area of the parallelogram, we get:

Area of triangle = ½ √(6) = √(1.5).

Answer:

Given relations defined on the set {a, b, c, d},

S= { (a, b), (a, c), (c, d), (c, a)}

R={ (b, c), (c, b), (a, d), (d, b)},

Since, SoR(x) = S(R(x)),

So, SoR(a) = S(R(a)) = S(d) = ∅,

SoR(b) = S(R(b)) = S(c) = d and a,

SoR(c) = S(R(c)) = S(b) = ∅,

SoR(d) = S(R(d)) = S(b) = ∅,

Thus, SoR = { (b,d), (b,a) }

RoS(a) = R(S(a)) = R(b) = c and RoS(a) = R(S(a)) = R(c) = b,

RoS(b) = R(S(b)) = R(∅) = ∅,

RoS(c) = R(S(c)) = R(d) = b and RoS(c) = R(S(c)) = R(a) = d

RoS(d) = R(S(d)) = R(∅) = ∅,

Thus, RoS = { (a, c), (a, b), (c,d), (c, b) },

SoS(a) = S(S(a)) = S(b) = ∅ and SoS(a) = S(S(a)) = S(c) = d and a

SoS(b) = S(S(b)) = S(∅) = ∅,

SoS(c) = S(S(c)) = S(d) = ∅ and SoS(c) = S(S(c)) = S(a) = b and c

SoS(d) = S(S(d)) = S(∅) = ∅,

SoS = { (a, d), (a, a), (c, b), (c, c) }

The composition of relations S and R mentioned in the question are SoR: { (a, c), (c, b)}, RoS: { (b, d), (a, b)} and SoS: { (a, d), (c, b)}.

The question is asking for the composition of relations. So, composition of relations S and R, denoted as 'SoR' or 'S ◦ R', is the set of ordered pairs where the first element is related to the second element through the combination of relations S and R. In this case the relations S and R on the set {a, b, c, d} are: S= { (a, b), (a, c), (c, d), (c, a)} and R={ (b, c), (c, b), (a, d), (d, b)}.

By the rule of composition SoR will be: { (a, c), (c, b)}.

Similarly, for RoS will be: { (b, d), (a, b)}.

And for SoS it will be: { (a, d), (c, b)}.

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To calculate the value of 715 × 211, you can use the standard multiplication method by multiplying each digit of the two numbers and summing up the results.

To find the value of 715 × 211, you can use the standard multiplication method. Start by multiplying the ones digit of 715 (5) by each digit of 211 (1, 1, and 2), and write down the results. Then, multiply the tens digit of 715 (1) by each digit of 211, and write down the results one place to the left of the previous results. Finally, multiply the hundreds digit of 715 (7) by each digit of 211 and write down the results two places to the left. Sum up the columns and you will get the final product.

Here's how it looks:

   715
× 211
--------
 715
 1430  
+1425
--------
 150665

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Answer:

its E none of the above

Step-by-step explanation:

Answer:

  The junction law is based on the conservation of charge.

Step-by-step explanation:

Kirchhoff's current law, or junction law, (1st Law) states that current flowing into a node (or a junction) must be equal to current flowing out of it. This is a consequence of charge conservation—charge is not created or destroyed in a closed system.

Answer: 0.116

Step-by-step explanation:

The Poisson distribution probability formula is given by :-

[tex]P(X=x)=\dfrac{e^{-\lambda}\lambda^x}{x!}[/tex], where \lambda is the mean of the distribution and x is the number of success

Given : The number of inclusions in one cubic millimeter = 3.2

Then , the number of inclusions in two cubic millimeters=[tex]\lambda=2\times3.2=6.4[/tex]

Now, the probability of exactly four inclusions in 2.0 cubic millimetres is given by :-

[tex]P(X=4)=\dfrac{e^{-6.4}(6.4)^4}{4!}\\\\=0.11615127195\approx0.116[/tex]

Hence, the probability of exactly four inclusions in 2.0 cubic millimetres = 0.116

Answer:  216

Step-by-step explanation:

Given : We like to make a salad that consists of​ lettuce, tomato,​ cucumber, and onions.

The number of varieties of lettuce = 9

The number of varieties of tomatoes = 4

The number of varieties of cucumbers = 2

The number of varieties of onions = 3

Now, the number of different salads we can make is given by :-

[tex]9\times4\times2\=216[/tex]

Hence, we can make 216 different types of salads.

Step-by-step explanation:

There are 20 chips in total.

P(red) = 8/20 = 2/5

P(not green) = 16/20 = 4/5

P(yellow or green) = 9/20

Answer: 208

Step-by-step explanation:

Given : An advertising company wishes to estimate the population mean of the distribution of hours of television watched per household per day.

Standard deviation : [tex]2.8\text{ hours}[/tex]

Margin of error : [tex]\pm0.5\text{ hour}[/tex]

Significance level : [tex]\alpha=1-0.99=0.01[/tex]

Critical value : [tex]z_{\alpha/2}=2.576[/tex]

The formula to calculate the sample size is given by :-

[tex]n=(\dfrac{z_{\alpha/2}\sigma}{E})^2[/tex]

[tex]\Rightarrow\ n=(\dfrac{2.576\times2.8}{0.5})^2=208.09793536\approx208[/tex]

Hence, the minimum required sample size must be 208.

Suppose [tex]y_p=a_0+a_1t[/tex] is a solution to the ODE. Then [tex]{y_p}'=a_1[/tex] and [tex]{y_p}''=0[/tex], and substituting these into the ODE gives

[tex]a_1-4(a_0+a_1t)=7t+5\implies\begin{cases}-4a_1=7\\-4a_0+a_1=5\end{cases}\implies a_0=-\dfrac{27}{16},a_1=-\dfrac74[/tex]

Then the particular solution to the ODE is

[tex]y_p=-\dfrac{27}{16}-\dfrac74t[/tex]

We know that speed is defined as the ratio of distance to time.

i.e.

[tex]Speed=\dfrac{Distance}{Time}[/tex]

Let the distance traveled to work be: x m.

Now, while going to work it takes a person 20 minutes.

This means that the speed of the person while going to work is:

[tex]S_1=\dfrac{x}{20}[/tex]

Also, the time taken to come back home is: 30 minutes.

This means that the speed of person while riding to home is:

[tex]S_2=\dfrac{x}{30}[/tex]

Also, it is given that  the rate back is 8 mph slower than the trip to work.

This means that:

[tex]S_1-S_2=8[/tex]

i.e.

[tex]\dfrac{x}{20}-\dfrac{x}{30}=8\\\\i.e.\\\\\dfrac{30x-20x}{600}=8\\\\i.e.\\\\\dfrac{10x}{600}=8\\\\i.e.\\\\\dfrac{x}{60}=8\\\\i.e.\\\\x=480\ \text{m}[/tex]

Hence, the distance to work is:  480 m.

Also, the rate while going to work is:

[tex]=\dfrac{480}{20}\\\\=24\ \text{mph}[/tex]

and the trip back to home is covered with the speed:

[tex]=\dfrac{480}{30}\\\\=16\ \text{mph}[/tex]

Answer:

6

Step-by-step explanation:

96x5

Answer:

32x(2)         (squared)

Step-by-step explanation:

GCF of 96 and 64:

  64 = (2)(2)(2)(2)(2)(2)

  96 = (2)(2)(2)(2)(2)(3)

  GCF = (2)(2)(2)(2)(2) = 32

GCF of x5 and x2:

x5 = (x)(x)(x)(x)(x)

x2 = (x)(x)

GCF = (x)(x) = x2

Answer: The z score that corresponds to the value x=22 is 0.4 .

Step-by-step explanation:

Given : A normal distribution has a mean 20 and standard deviation 5.

i.e. [tex]\mu=20[/tex]

[tex]\sigma=5[/tex]

Let x be the random selected variable.

We know that to find the z-score corresponds to the value x is given by :-

[tex]z=\dfrac{x-\mu}{\sigma}[/tex]

For x = 22, we have

[tex]z=\dfrac{22-20}{5}=\dfrac{2}{5}\\\\\Rightarrow\ z=0.4[/tex]

Hence, the z score that corresponds to the value x=22 is 0.4

A z-score in a normal distribution measures the number of standard deviations a value is from the mean. To calculate it, use the formula z = (x - μ) / σ for the specific values provided, such as half a standard deviation below the mean, 5 points above the mean, three standard deviations above the mean, and 22 points below the mean.

The calculation of a z-score within a normal distribution is a common task in statistics, allowing one to determine how many standard deviations a particular value, x, is from the mean, μ, of the distribution. The z-score is calculated using the formula:

z = (x - μ) / σ

where x is the value in question, μ is the mean, and σ is the standard deviation. Now, we will calculate the z-scores for the given situations:

Remember, when you use these calculations for specific numerical values, you need to insert the actual values of mean and standard deviation into the formula.

Answer:

a) Arthur Penn

Step-by-step explanation:

There are three feature films based on Bonnie and Clyde they are the following:

"The Bonnie Parker Story"  released in 1958 was directed by William Witney.

"Bonnie and Clyde" released in 1967 was directed by Arthur Penn.

Warren Beaty is primarily an actor who has directed six films including a tv movie and five feature films.

"The Highwaymen" was directed by John Lee Hancock released 2019.

Answer:

A. Arthur Penn

Step-by-step explanation:

Bonnie and Clyde A defining film of the New Hollywood generation was Bonnie and Clyde (1967). Produced by and starring Warren Beatty and directed by Arthur Penn, its combination of graphic violence and humor, as well as its theme of glamorous disaffected youth, was a hit with audiences.

Step-by-step explanation:

Consider the first sequence:

15, 20, 25, 30, 35,...

Note that each term is increased by 5 from its previous term.

Therefore,

[tex]a_n=a_{n-1}+5[/tex]

If the pattern continue, the next three term of the sequence will be:

[tex]a_6=a_{6-1}+5[/tex]

[tex]a_6=a_{5}+5[/tex]

[tex]a_6=35+5[/tex]

[tex]a_6=40[/tex]

Similarly,

[tex]a_7=a_{7-1}+5[/tex]

[tex]a_7=a_{6}+5[/tex]

[tex]a_7=40+5[/tex]

[tex]a_7=45[/tex]

Similarly,

[tex]a_8=a_{8-1}+5[/tex]

[tex]a_8=a_{7}+5[/tex]

[tex]a_8=45+5[/tex]

[tex]a_8=50[/tex]

Thus, the next three term of the sequence 15, 20, 25, 30, 35,... is 40, 45, and 50.

Now, consider the second sequence:

5, 9, 13, 17, 21,...

Note that each term is increased by 4 from its previous term.

Therefore,

[tex]a_n=a_{n-1}+4[/tex]

If the pattern continue, the next three term of the sequence will be:

[tex]a_6=a_{6-1}+4[/tex]

[tex]a_6=a_{5}+4[/tex]

[tex]a_6=21+4[/tex]

[tex]a_6=25[/tex]

Similarly,

[tex]a_7=a_{7-1}+4[/tex]

[tex]a_7=a_{6}+4[/tex]

[tex]a_7=25+4[/tex]

[tex]a_7=29[/tex]

Similarly,

[tex]a_8=a_{8-1}+4[/tex]

[tex]a_8=a_{7}+4[/tex]

[tex]a_8=29+4[/tex]

[tex]a_8=33[/tex]

Thus, the next three term of the sequence 5, 9, 13, 17, 21,... is 25, 29, and 33.

Answer:

Dear, Have a look at pic

Answer:

  yes

Step-by-step explanation:

The line intersects each parabola in one point, so is tangent to both.

__

For the first parabola, the point of intersection is ...

  y^2 = 4(-y-1)

  y^2 +4y +4 = 0

  (y+2)^2 = 0

  y = -2 . . . . . . . . one solution only

  x = -(-2)-1 = 1

The point of intersection is (1, -2).

__

For the second parabola, the equation is the same, but with x and y interchanged:

  x^2 = 4(-x-1)

  (x +2)^2 = 0

  x = -2, y = 1 . . . . . one point of intersection only

___

If the line is not parallel to the axis of symmetry, it is tangent if there is only one point of intersection. Here the line x+y+1=0 is tangent to both y^2=4x and x^2=4y.

_____

Another way to consider this is to look at the two parabolas as mirror images of each other across the line y=x. The given line is perpendicular to that line of reflection, so if it is tangent to one parabola, it is tangent to both.

[tex]\dfrac{x^4-2x^3+x^2+3x-2}{x^2-2x+1}[/tex]

The degree of the numerator exceeds the degree of the denominator, so first you have to divide:

[tex]x^2+\dfrac{3x-2}{x^2-2x+1}[/tex]

Now, [tex]x^2-2x+1=(x-1)^2[/tex], so the remainder term can be expanded to get

[tex]\boxed{x^2+\dfrac a{x-1}+\dfrac b{(x-1)^2}}[/tex]

The probability that a truck drives between 100 and 157 miles in a day within a normal distribution can be calculated using z-scores. The z-scores for 100 and 157 miles are computed relative to the mean and standard deviation, and the corresponding probabilities are obtained from the standard normal distribution table. The final probability is the difference of these two probabilities.

Given that the distribution of trucks' daily mileage is normally distributed, we can approach this problem by using the principles of normal distribution and z-scores. The z-score is a measure of how many standard deviations an element is from the mean.

First, we calculate the z-scores for both 100 miles and 157 miles:

Next, we look up these z-scores in the standard normal distribution table (or use a calculator with a normal distribution function), which will give us the probabilities P(Z To arrive at four decimal places precision, this process typically involves using a statistical calculator or software.

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I hope I've helped

In this photo you can find de probabilities

Answer:

The flow rate is 267ml/hour

Step-by-step explanation:

Hello, great question. These types are questions are the beginning steps for learning more advanced Equations.

To solve this we first need to find out how many ml the Rottweiler needs over 12 hours. We do this by using the Rule of Three property.

[tex]\frac{40ml}{1kg} = \frac{x}{80kg}[/tex]

[tex]\frac{40ml*80kg}{1kg} =x[/tex]

[tex]3200ml = x[/tex]

So the Rottweiler needs 3200 ml over a 12 hour period. We now need to find the flow rate per hour. We can solve this by simply dividing 3200 ml by 12 hours.

[tex]3200ml / 12hours = 266.67ml/hour[/tex]

So the flow rate is 267 ml/hour (rounded to the nearest whole number)

I hope this answered your question. If you have any more questions feel free to ask away at Brainly.

Answer:

Step-by-step explanation:

1. Greater density means the sphere has more mass in the same volume. The volume of water that must be displaced to equal that increased mass must be increased, causing the water level to rise.

__

2. Less mass means less water must be displaced to equal the mass of the new sphere, causing the water level to fall.

__

3. More mass is the same as higher density (see 1). The water level will rise.

Archimedes' principle states that the upward force acting on a body floating or immersed in a fluid is equal to the weight of the displaced fluid

The level of the water in the three situations are as follows;

Situation 1; Falls or stays the same, E: f or s

Situation 2; Falls, B: f

Situation 3, Rises A: r

The reason for the above selection is as follows;

The given details of the arrangements are;

The mass of the solid homogeneous sphere = m₀

The radius of the sphere = r₀

The density of the sphere = ρ₀

The location the sphere is placed = Floating in a container of water

The required parameter;

The provision of an estimate of the water level when the sphere is replaced with a new sphere with different physical parameters

Notation;

r = The water level rises

f = The water level falls

s = The water level stays the same

Situation 1; The mass of the new sphere, m = m₀

The density of the new sphere, ρ > ρ₀

Here, the denser sphere of equal mass = Smaller sphere, r < r₀

if the sphere floats, then the volume of the water displaced is equal to the

mass of the sphere, which is therefore, equal to the volume of the water

displaced by the original sphere

Therefore, the water level remains the same, s

However, if the sphere sinks, then the water displaced is less than the

mass m = m₀, of the sphere and therefore, the level falls, f

Therefore, the correct option is E: f or s

Situation 2: The mass of the new sphere, m < m₀

The radius of the new sphere, r = r₀

Here, we have equal radius and therefore equal volume and lesser density

Given that the volume of the water displaced for a floating body is equal to

the weight of body, and that the mass of the new sphere is less than the

mass of the original sphere, the mass of the water displaced and therefore,

the volume of water displaced is less and therefore, the water level falls

The correct option is therefore B: f falls

Situation 3: The mass of the new sphere, m > m₀, and the radius r = r₀

therefore the new sphere is denser than the original sphere and the

therefore, the mass of the water displaced where the sphere floats is m >

m₀, which is more than the water displaced for the original sphere and the

level of water rises, r, and the correct option is A: r

Therefore;

In situation 1, we have option E: f or s

In situation 2, the correct option is B: f

In situation 3, the correct option is A: r

Learn more about Archimedes' principle here:

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Answer:

6 people

Step-by-step explanation:

Suppose A represents the event of going on Saturday,

B represents the event of going on Sunday,

According to the question,

n(A)=11

n(B)=14

n(A∪B)=20

We know that,

n(A∪B) = n(A) + n(B) - n(A∩B)

By substituting values,

20 = 11 + 14 - n(A∩B)

⇒ n(A∩B) = 25 - 20 = 5,

Hence, the number of people who can only go to the game on Saturday = n(A) - n(A∩B) = 11 - 5 = 6.

Answer:

x = 250 units

Step-by-step explanation:

We can easily solve this problem by using a graphing calculator or any plotting tool.

We must find the minimum point in the graph. This corresponds to the number of machines that produce the minimum cost.

The equation is

C (x) = 1.2x^2 -600x + 89,966

Please see attached image below

By producing x = 250 units, we obtain the minimum cost

Answer:

Step-by-step explanation:

Correlation means that two or more events happen together. They are related to one another by being caused by the same thing.

Causation has a definite order. The first event has some cause that is comes before the second event. One event caused the other.

Answer:

415

Step-by-step explanation:

Confidence Level = 98%

Z-value for this confidence level = z = 2.326

Margin of error = E = 0.08

Mean = u = 6.6

Standard deviation = [tex]\sigma=0.7[/tex]

Required Sample Size = n = ?

The formula for margin of error is:

[tex]E=z\frac{\sigma}{\sqrt{n}}[/tex]

Re-arranging the equation for n, and using the given values we get:

[tex]n=(\frac{z\sigma}{E} )^{2}\\\\ n=(\frac{2.326 \times 0.7}{0.08} )\\\\ n=415[/tex]

Thus, the minimum sample size required to create the specified confidence interval is 415

The minimum sample size required to construct a 98% confidence interval with an error of no more than 0.08 is 255.

To determine the minimum sample size required to construct a 98% confidence interval with an error of no more than 0.08, we can use the formula:

n = (Z * sigma / E) ^ 2

where n is the sample size, Z is the Z-score corresponding to the desired confidence level, sigma is the standard deviation, and E is the desired margin of error.

In this case, the Z-score for a 98% confidence level is approximately 2.33. Substituting the given values of sigma = 0.7 and E = 0.08 into the formula, we can calculate the minimum sample size:

n = (2.33 * 0.7 / 0.08) ^ 2

n ≈ 254.43

Rounding up to the next integer, the minimum sample size required is 255.

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