Solve for x.

14x + 18 + x = −112(x + 36) + 13

A
x = −6

B
x = −3

C
x = 3

D
x = 6

Answer:

Arf ( its 128 units)

Step-by-step explanation:

(a)  Total urine volume is excreted during this time period is 442.34 mL.

(b) Equations for the velocity of urine is v = (-3 x \(V_t\) + 7.35) / 2.46 x \(10^{-5}\)

(a) To determine the total urine volume excreted during this time period, we need to integrate the flow rate function over the given time period. However, we are given two different equations for the flow rate for different ranges of time:

For t < 12 seconds, V = -0.306 x  \((t-7)^2\)  + 15

For 12 ≤ t < 26.7 seconds, V = -3 x \(V_t\)  + 7.35

To find the total urine volume, we need to first determine the time at which the flow rate changes from the first equation to the second.

We can do this by setting the two equations equal to each other and solving for t:

-0.306 x  \((t-7)^2\)  + 15 = -3 x \(V_t\) + 7.35

0.306 x  \((t-7)^2\) + 3 x \(V_t\)  = 7.65

0.306 x \((t-7)^2\) = 7.65 - 3 x \(V_t\)

\((t-7)^2\) = (7.65 - 3 x \(V_t\) ) / 0.306

t = 7 +/- \(\sqrt{((7.65 - 3 \times Vt) / 0.306)}\)

Since t < 12 for the first equation, we can ignore the negative root and use the positive root to find the time at which the flow rate changes:

t = 7 + \(\sqrt{((7.65 - 3 \times 12) / 0.306)}\)= 10.76 seconds

Now we can integrate each equation separately over their respective time ranges:

For 0 ≤ t < 10.76 seconds:

∫ V dt = ∫ (-0.306 x \((t-7)^2\) + 15) dt

= [-0.102 x \((t-7)^3\) + 15t] from t=0 to t=10.76

= 121.86 mL

For 10.76 ≤ t < 26.7 seconds:

∫ V dt = ∫ (-3 x \(V_t\) + 7.35) dt

= [-1.5 x \(V_t^2\) + 7.35t] from t=10.76 to t=26.7

= 320.48 mL

Therefore, the total urine volume excreted during this time period is:

121.86 mL + 320.48 mL = 442.34 mL

(b) To develop equations for the velocity of urine as it exits the body, we need to use the continuity equation, which states that the flow rate (V) is equal to the cross-sectional area (A) multiplied by the velocity (v):

V = A x v

We are given that the urethra has a diameter of 5.6 mm, which means the radius is 2.8 mm (or 0.0028 m).

The cross-sectional area can be calculated using the formula for the area of a circle:

A = π x \(r^2\)

A = 3.14 x \((0.0028)^2\)

A = 2.46 x   \(10^{-5}\) \(m^2\)

Now we can rearrange the continuity equation to solve for the velocity:

v = V / A

Substituting the given equations for V, we get:

For t < 12 seconds:

v = (-0.306 x \((t-7)^2\) + 15) / 2.46 x  \(10^{-5}\)

For 12 ≤ t < 26.7 seconds:

v = (-3 x  \(V_t\) + 7.35) / 2.46 x \(10^{-5}\)

Note that the velocity will be in units

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Question:-

The flow of urine from the bladder, through the urethra, and out of the body, is induced by increased pressure in the bladder resulting from muscle contractions around the bladder with simultaneous relaxation of the muscles in the urethra. The mean pressure in the bladder can be estimated using the velocity of urine as it exits the body. Assume that the bladder is about 5 cm above the external urethral orifice. (This height is different for males and females.) The flow rate of urine from the bladder can be approximately described with the following equations, where t is time in seconds, and V is flow rate in mL/s:

V = -0.306 X (t – 7)2 + 15 Osts 12

V = -3 X Vt 12 + 7.35 12 st < 26.7

(a) How much total urine volume is excreted during this time period?

(b) Develop equations for the velocity of as it exits the body. Assume that the urethra is 5.6 mm in diameter.

Answer:

a=-2

Step-by-step explanation:

\(2(3a + 4) = - 8 \\( 2 \times 3a = 6a)(2 \times 2 = 4) \\ - 8 - 4 = - 12 \\ 6a \div - 12 = - 2\)

Considering the given function, we have that:

a) F(4) = 1416.

b) There were 1832 employees in 2010.

c) There were 1032 employees in 2020.

The function is given by:

F(x) = 4x² - 120x + 1832

It represents the number of new employees in x years after 2010.

Then:
F(4) = 4(4)² - 120(4) + 1832 = 1416.

The number of employees in 2010 is:

F(0) = 4(0)² - 120(0) + 1832 = 1832.

There were 1832 employees in 2010.

The number of employees in 2020 is:

F(10) = 4(10)² - 120(10) + 1832 = 1032.

There were 1032 employees in 2020.

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The volume of the given combined solids is 675 cm³.

The given combined solid is made up of two solids. A rectangular solid and a triangular prism. The dimensions of the rectangular solid are length, width, and height 15 cm, 6 cm, and 5 cm, respectively, while the triangular prism has a height of 6 cm and a base of 5 cm.

The rectangular solid is placed on the triangular prism such that the rectangular solid's width coincides with the base of the prism's triangle.Find the volume of the given combined solids.

Since the rectangular solid is on top of the triangular prism, we will compute the two volumes separately and then add them together to obtain the combined volume.

Volume of rectangular solid = l × w × h= 15 cm × 6 cm × 5 cm= 450 cm³

Volume of triangular prism= 1/2 × base × height × length= 1/2 × 5 cm × 6 cm × 15 cm= 225 cm³

To get the combined volume, we add the two volumes together:Combined volume= 450 cm³ + 225 cm³= 675

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(a) The probability that a randomly chosen nucleotide from the first region is the same as a randomly chosen nucleotide from the second region is 1/4.

(B) The chance that the triple chosen from the first region will be identical to the triple chosen from the second region is 1/4096.

(a) If we assume that there are four possible nucleotides (A, C, G, T) and that each nucleotide is equally likely to occur in each region, then the probability that a randomly chosen nucleotide from the first region is the same as a randomly chosen nucleotide from the second region is 1/4, since there is a 1 in 4 chance that the nucleotide chosen from the first region will be the same as the nucleotide chosen from the second region.

(b) If we again assume that there are four possible nucleotides (A, C, G, T) and that each nucleotide is equally likely to occur in each region, then the probability of choosing a particular three-nucleotide sequence is (1/4)³ = 1/64.

The probability of choosing the same three-nucleotide sequence from both regions is the product of the probabilities of choosing that sequence from each region, or (1/64) x (1/64) = 1/4096. Therefore, the chance that the triple chosen from the first region will be identical to the triple chosen from the second region is 1/4096.

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Step-by-step explanation:

there are several things to be considered to solve this.

the strategy is to caucuses the volume of the full "box", and then to deduct the 3-dimensional triangle that is "cut off" from the oil.

then we know the volume of the pool.

next step is to calculate the volume of a "box" with the same layout but is only 20 cm deep.

then we know how much volume can be pumped out in 30 minutes.

and then we divide the whole volume by that small volume to see how many 30-minues units are needed to empty the whole pool.

and then we transform the 30- minutes units into actual minutes or hours.

so, let's begin :

the whole box's volume is

2×1×1.4 = 2.8 m³

the volume of the 3-D triangle we need to subtract is the area of the triangle × width of the pool (this pool width is the height of the 3-D triangle).

2×(1.4 - 0.6) × 1 / 2 = 2×0.8 × 1 / 2 = 1.6/2 = 0.8 m³

so, the volume of the pool is

2.8 - 0.8 = 2 m³

now, how much volume can the pump eliminate in 30 minutes ?

the content of a box

1×2×0.2 = 0.4 m³

as 20 cm = 0.2 m

so, the pump pumps out 0.4 m³ in 30 minutes.

and we need to empty 2 m³.

that means we need

2 / 0.4 = 5

30-minues units = 5×30 = 150 minutes = 2.5 hours.

Colin has to wait 2.5 hours (150 minutes) to empty the complete pool.

Answer:

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

Step-by-step explanation:

the coordinates are what you have to look for

If there is at-least one-song liked by those two girls but disliked by the third, then the "different-ways" this is possible is 132 ways.

There are ⁴C₃ ways to choose the "3-songs" which are liked by "3-pairs" of girls.

There are 3! ways to find the three songs are liked by which pair of girls.

In total, there are ⁴C₃×3! possibilities for the first "3-songs".

There are "3-cases" for fourth song, let that song be "D".

Case 1: Song "D" is disliked by all three girls means there is only one possibility.

Case 2: Song "D" is liked by exactly one girl means there are three possibility.

Case 3: Song "D" is liked by exactly two girls means there are three pairs of girls to choose from.

However, there is an overlap when "other-song" is liked by "same-pair" of girl is counted as "fourth-song" at some point, in which "case-D" will be counted as one of first "three-songs" liked by same girls.

Counting the overlaps, there are "three-ways" to choose pair with overlaps and 4×3=12 ways to choose what the other "two-pairs" like independently.

In total, there are 3×12=36 over-lapped possibilities,

Therefore, there are ⁴C₃ × 3! ×(3+1+3)-36 = 132 ways for the songs to be likely by the girls.

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The general solution of the second-order differential equation y′′−3y′+2y = 0 is y(x) = C₁e^(2x) + C₂e^x, where C₁ and C₂ are arbitrary constants.

To find the general solution of the given second-order differential equation y′′−3y′+2y = 0, we assume a solution of the form y(x) = e^(mx). By substituting this into the differential equation, we get the characteristic equation m² - 3m + 2 = 0. Factoring the quadratic equation, we find two roots: m₁ = 2 and m₂ = 1. Therefore, the general solution is y(x) = C₁e^(2x) + C₂e^x, where C₁ and C₂ are arbitrary constants determined by initial or boundary conditions. This solution represents a linear combination of exponential functions with the roots of the characteristic equation. The constants C₁ and C₂ can be determined by applying any given initial or boundary conditions.

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\(\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=\sqrt{a^2 + b^2} \qquad \begin{cases} c=hypotenuse\\ a=\stackrel{adjacent}{7}\\ b=\stackrel{opposite}{4}\\ \end{cases} \\\\\\ c=\sqrt{7^2 + 4^2}\implies c=\sqrt{65}\)

The purpose of using prefix in the metric system is to properly sale the basis of the unit so large numeric values can be used effectively.

If the metric system is not properly prefixed it can lead to various inconsistencies in the the numeric values. for example if you go to a computer store and you do not know the scale like (kb, mb, gb, tb) you will get quite confused about what is the sales representative saying

Consider you went to a store to get sugar and you do not know the metric system say(gram, kg, mg) you would not know how much sugar you need directly by taking it in your hands.

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Answer:

b.34% interest rate

Step-by-step explanation:

Because you can move the decimal point to the right side.

Tq.

Answer:

not 100% sure, but I think it's A) 3.4% interest rate

Step-by-step explanation:

you can move the decimal place to the right 2 times = 3.4

Answer:

S= t/2+9/2

Hope This Helps :-)

Answer:14.42

How to get it:Use Pythagorean Theorem to solve this problem. Since a squared plus b squared =c squared and we have an and c we can work backwards. Start by squaring 17 (17x17) which would be 289. Then do 9 squared (9x9) to get 81. Subtract 289-81 to get 208, square root this for your answer 14.4222 round to 14.42. You can check this by doing 14.4222 squared plus 9 squared then square root it and you should get approximately, but not exactly 17.

Answer:

h = -7

Step-by-step explanation:

I hope this helps!

Answer:

4 + 11 = 15

Step-by-step explanation:

brainliest plz

Your answer is B.

It states that 4 people signed up to go bowling, then 11 more people did.

So that means the equation would be \(\left[\begin{array}{ccc}4+11=15\end{array}\right]\)

If this helped please mark me as brainliest!

\(\left[\begin{array}{ccc}Thanks,\\JustSomeIdiot\end{array}\right]\)

Answer:

CORRECT ANSWER IS B " Y - 1/2 x - 2 "

Step-by-step explanation:

Price of 3 kg carrots = 1.80

Price of 1 kg carrots = 1.80 ÷ 3 = 0.6

Price of 2 kg carrots = 0.6 x 2 = 1.2

Remaining amount = 3.45 - 1.2 = 2.25

Price of 5 kg potatoes = 2.25

Price of 1kg potatoes = 2.25 ÷ 5 = 0.45

Now

Cost of 4 kg of carrots = 0.6 x 4 = €2.4

Cost of 2 kg of potatoes = 0.45 x 2 = €0.9

The total cost of 4kg of carrots and 2 kg of potatoes is £3.30

Total cost is the product of the cost of each unit and the number of units purchased.

As it is given that the cost of 3 kg carrot is £1.80, therefore, the cost of 1 kg of carrot can be written as,

\(\text{Cost of 1 kg carrot}=\dfrac{\text{Total cost of carrot}}{\text{Total amount of carrot}}\)

                              \(=\dfrac{\£1.80}{3}\\\\= \£0.60\)

Thus, the cost of 1 kg carrot is £0.60.

Now., as it is given that the cost of 2 kg carrot and 5 kg potatoes is £3.45, therefore, the cost of 5 kg potatoes can be written as,

\(\text{Total cost}=\text{Cost of 2 kg carrot}+\text{Cost of 5 kg potatoes}\)

\(3.45= (0.60 \times 2) + \text{Cost of 5 kg Potatoes}\\\\\text{Cost of 5 kg Potatoes} = 2.25\)

Further, the cost of each kg of potatoes can be written as,

\(\text{Cost of 1kg of potatoes}=\dfrac{\text{Cost of 5 kg Potatoes}}{\text{Total amount of potatoes}}\)

                                      \(=\dfrac{2.25}{5}\\\\=0.45\)

Thus, the cost of each kg of potatoes is £0.45.

Further,  the total cost of 4kg of carrots and 2 kg of potatoes can be written as,

\(\text{Total cost }=\text{Cost of 4kg of carrots} +\text{Cost of 2 kg of potatoes} \\\\\text{Total cost }=(4 \times 0.60)+(2\times 0.45)\\\\\text{Total cost }= 2.24+0.90=\£3.3\)

Hence, the total cost of 4kg of carrots and 2 kg of potatoes is £3.30

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If a bottle weighs 300g and can hold 630ml, then it will weigh approximately 930g when filled with water.

As per the question statement, a bottle weighs 300g and can hold 630ml.

We are required to find out the weight of the bottle when it is filled up with water.

To solve this question, we need to know about the concept of density of a substance, i.e.,

\(Density=\frac{Mass}{Volume}\\ or, Mass=[Density*Volume]\).

And density of water is 1gm/ml, i.e., 1gm of water has a mass of 1ml.

Using the above info, we will calculate the mass of 630ml of water and then we will have to add up the mass of water and the mas of the bottle to obtain our desired answer.

Using the unitary method, if 1ml of water has a mass of 1gm, then,

630 ml of water has a mass of \((630*1)=630\\\) gms.

Hence, total weight of the bottle filled with water will be

\((630+300)=930\) gms.

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Answer: 7

Step-by-step explanation:

The slope is the number being multiplied by x

One possible solution that could be used to address the problems caused by the Electoral College is "electoral reform."

Popular Vote: One approach is to replace the Electoral College with a system where the President is directly elected by a popular vote. This would eliminate the possibility of a candidate winning the presidency while losing the popular vote, as has happened in some elections.

Proportional Representation: Another option is to implement a proportional representation system, where the allocation of electors is based on the percentage of votes a candidate or party receives in each state. This would ensure a more proportional representation of voters' preferences and reduce the influence of winner-takes-all mechanisms.

National Popular Vote Interstate Compact: This reform proposal aims to work within the existing Electoral College framework. States that join the compact agree to allocate their electoral votes to the winner of the national popular vote, effectively ensuring that the candidate who receives the most votes nationwide becomes the President.

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This graph represents a function Because it passes the vertical line test.

Let us first understand the Vertical Line Test.

In this test, we draw a few random vertical lines on a graph and check whether any one or more than one lines intersect the graph, no matter once or more.

If there exists a line that intersects the graph, we say the graph passes the vertical line test.

The vertical line test is a visual way to determine if a curve is a graph of a function or not. A function can only have one output, y, for each unique input, x.

Hence this graph passes the vertical line test because there are many vertical lines that intersect it.

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Answer:

5/100 , 7/2 ,4/5 321/100,  35/100, 607/1000, 3/2, 52/1

Step-by-step explanation:

Answer:

7. To perform a t-test when the sample size is small, the sample must show no evidence of strong skewness and must contain no outliers.

Step-by-step explanation:

These are the two conditions required for performing a t test

- Sample Size: A small sample size can reduce the statistical power of a t-test, making it more challenging to detect significant differences between groups. Generally, a larger sample size is desirable to obtain more reliable and representative results.

- Skewness: Skewness refers to the asymmetry of the distribution of data. In a t-test, assuming normality of the data is important for accurate results. If the data exhibits strong skewness, the assumption of normality may be violated. In such cases, alternative non-parametric tests or transformations of the data may be more appropriate.

- Outliers: Outliers are extreme values that significantly differ from the rest of the data. They can have a disproportionate impact on the results of a t-test, particularly when the sample size is small. Outliers can distort the mean and affect the assumptions of normality and homogeneity of variance.

While the presence of skewness or outliers does not prohibit the use of a t-test with a small sample size, it is important to interpret the results with caution and consider alternative approaches if necessary. Robust statistical methods, such as non-parametric tests or bootstrapping, can be useful when dealing with non-normal or outlier-prone data, especially with small sample sizes. Additionally, visual inspection of the data distribution, such as through histograms or box plots, can help identify potential skewness or outliers.

From the calculation carried out below, the number of children admitted was 1,400 and the number of adults admitted was 700.

How do we calculate the different numbers of people admitted?

This question can be solved using the substitution method as follows:

x = Number of children admitted

y = Number of adults admitted

x + y = 2,100 ............................................. (1)

1.50x + 4y = 4,900 ................................ (2)

From equation (1), we have:

x = 2,100 - y ................................................. (3)

Substituting x = 2,100 - y into equation (2) and solving for y, we have:

1.50(2,100 - y) + 4y = 4,900

3,150 - 1.50y + 4y = 4,900

2.50y = 4,900 - 3,150

2.50y = 1,750

y = 1,750 / 2.50

y = 700

Substituting y = 700 into equation (3), we have:

x = 2,100 - 700

x = 1,400

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The solution to the equation is x= -10 and y= 5.

We have Equations,

2x + 6y = 10............(1)

3x - 2y = -40............(2)

Now, solving equation (1) and (2) we get

2x + 6y = 10

9x - 6y = -120

+    +       +

__________

   11x = -110

      x = -10

and, 3(-10) - 2y= -40

-30 - 2y= -40

-2y = -10

y=5

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The expected activity time for the given statement is = 5.33

The average amount of time required for an activity when it is repeatedly performed is known as the expected time. The weighted average of the three estimated times, i.e., the optimistic time, the most probable time, and the pessimistic time, is used in project management analysis to determine the expected time of activity.

A network model called the Program Evaluation and Review Technique (PERT) allows for randomness in the timing of activity completion. PERT was created in the late 1950s again for a massively labor-intensive Polaris project for the US Navy. It might shorten a lot of time and cost needed to finish a project.

optimistic = 2

most likely = 5

pessimistic = 10.

We will use the following formula to calculate the anticipated time for each activity in order to solve this problem:

Expected Time = (Optimistic Time + (4 x Most likely) + Pessimistic Time) / 6

Putting the values into formula:

= (2 + (4 x 5) + 10)/ 6

= (2 + 20 + 10) / 6

= 5.33

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(a) The probability of having all six children be girls is (1/2)^6, or 1/64.
(b) The probability of having all six children be the same sex (either all boys or all girls) is (1/2)^6 + (1/2)^6, or 2/64, or 1/32.
(c) The probability of having at least one boy is 1 - 1/64, or 63/64

The probability of having a child of a particular sex is 50%. Given a family with six children, we can calculate the probability of each event as follows:
(a) All the children being girls: the probability is (1/2)^6, or 1/64.
(b) All the children being the same sex (either all boys or all girls): the probability is (1/2)^6 + (1/2)^6, or 2/64, or 1/32.
(c) At least one boy being in the family: the probability is 1 - (1/2)^6, or 63/64. This can be calculated by finding the probability of having no boys (all girls) and then subtracting it from 1.
In summary, the probability of having a particular outcome in a family with six children depends on the number of children of each sex and can be calculated using the formula (1/2)^n, where n is the number of children of a particular sex.


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Complete question:

Assume that the probability of the birth of a child of a particular sex is 50%. In a family with six children, find the probability of each event.

(a) All the children are girls.

(b) All the children are the same sex.

(c) There is at least one boy.