This equation is an example of:

A. Dividing two binomials
B. FOIL
C. Vertical multiplication
D. Complex conjugates

Answer:

930.91

Step-by-step explanation:

931 x 99% = 921.69

921.69 x 101% = 930.9069

Answer:

930.91

Step-by-step explanation:

931*99%=921.69

921.69*101=930.91

Answer:

a) The velocity at which the water leaves the gun = 37.66 m/s

b) The volume rate of flow = (1.183 × 10⁻⁴) m³/s

c) The water hits the ground 18.64 m from the point where the water gun was shot.

Step-by-step explanation:

a) Using Bernoulli's equation, an equation that is based on the conservation of energy.

P₁ + ½ρv₁² + ρgh₁ = P₂ + ½ρv₂² + ρgh₂

The two levels we are considering is just inside the water reservoir and just outside it.

ρgh is an extension of potential energy and since the two levels are at the same height,

ρgh₁ = ρgh₂

Bernoulli's equation becomes

P₁ + ½ρv₁² = P₂ + ½ρv₂²

P₁ = Pressure inside the water reservoir = 8 atm = 8 × 101325 = 810,600 Pa

ρ = density of water = 1000 kg/m³

v₁ = velocity iof f water in the reservoir = 0 m/s

P₂ = Pressure outside the water reservoir = atmospheric pressure = 1 atm = 1 × 101325 = 101,325 Pa

v₂ = velocity outside the reservoir = ?

810,600 + 0 = 101,325 + 0.5×1000×v₂²

500v₂² = 810,600 - 101,325 = 709,275

v₂² = (709,275/500) = 1,418.55

v₂ = √(1418.55) = 37.66 m/s

b) Volumetric flowrate is given as

Q = Av

A = Cross sectional Area of the channel of flow = πr² = π×(0.001)² = 0.0000031416 m²

v = velocity = 37.66 m/s

Q = 0.0000031416 × 37.66 = 0.0001183123 m³/s = (1.183 × 10⁻⁴) m³/s

c) If the height of gun above the ground is 1.2 m. Where does the water hit the ground?

The range of trajectory motion is given as

R = vT

v = horizontal component of the velocity = 37.66 m/s

T = time of flight = ?

But time of flight is given as

T = √(2H/g) (Since the initial vertical component of the velocity = 0 m/s

H = 1.2 m

g = acceleration due to gravity = 9.8 m/s²

T = √(2×1.2/9.8) = 0.495 s

Range = vT = 37.66 × 0.495 = 18.64 m

Hope this Helps!!!

Question:

The geometric sequence ; is defined by the formula: [tex]a_1 =10[/tex] ; [tex]a_i =a_{i-1} * \frac{9}{10}[/tex] Find the sum of the first 75 terms in the sequence .

Answer:

[tex]S_{75} = 99.963001151[/tex]

Step-by-step explanation:

Given

[tex]a_1 =10[/tex]

[tex]a_i =a_{i-1} * \frac{9}{10}[/tex]

Required

Find the sum of 75 terms

Given that the sequence is geometric;

First, the common ratio has to be calculated;

The common ratio is defined as follows;

[tex]r = \frac{a_{i}}{a_{i-1}}[/tex]

Let [tex]i = 2[/tex]

[tex]r = \frac{a_{2}}{a_{2-1}}[/tex]

[tex]r = \frac{a_{2}}{a_{1}}[/tex]

So,

[tex]a_i =a_{i-1} * \frac{9}{10}[/tex] becomes

[tex]a_2 =a_{2-1} * \frac{9}{10}[/tex]

[tex]a_2 =a_{1} * \frac{9}{10}[/tex]

Divide through by [tex]a_1[/tex]

[tex]\frac{a_2}{a_1} =\frac{a_{1} * \frac{9}{10}}{a_1}[/tex]

[tex]\frac{a_2}{a_1} = \frac{9}{10}[/tex]

Recall that [tex]r = \frac{a_{2}}{a_{1}}[/tex]

So, [tex]r = \frac{9}{10}[/tex]

Given that r < 1;

The sum of n terms is calculated as thus;

[tex]S_n = \frac{a(1-r^n)}{1-r}[/tex]

To calculate the sum of the first 75 terms, we have the following parameters

[tex]n = 75\\a = a_1 = 10\\r = \frac{9}{10} = 0.9[/tex]

[tex]S_n = \frac{a(1-r^n)}{1-r}[/tex] becomes

[tex]S_{75} = \frac{10(1-0.9^{75})}{1-0.9}[/tex]

[tex]S_{75} = \frac{10(1-0.9^{75})}{0.1}[/tex]

[tex]S_{75} = 100(1-0.9^{75})[/tex]

[tex]S_{75} = 100(1-0.00036998848)[/tex]

[tex]S_{75} = 100(0.99963001151)[/tex]

[tex]S_{75} = 99.963001151[/tex]

Answer:

Step-by-step explanation:

Total surface of the cube = 6a²

                                          = 6 * 42 * 42

                                          = 10584 cm²

Hole that is drilled out, will make a cylinder shape in the middle of the cube

Volume  of iron in the cube = Volume of cube  - volume of cylinder

Volume of cube = a³

                          = 42 * 42 * 42

                         = 74088 cm³

Cylinder:

r = 14/2 = 7 cm

h = sideof the cube = 42 cm

Volume = πr²h

            [tex]=\frac{22}{7}*7*7*42\\\\=22*7*7*6[/tex]

           = 6468 cm³

Volume  of iron in the cube = Volume of cube  - volume of cylinder

                                             = 74088 - 6468

                                             = 67620 cm³

Answer:

a. P(CWC)=0.046875

b.  P(WCC)=0.046875

    P(CCW)=0.046875

c. P=0.140625

Step-by-step explanation:

By the rule of multiplication there are 64 forms to answer three questions. This is calculated as:

    4 _          *            4               *             4            = 64

1st question      2nd question     3rd question

Because there are 4 options for every question. At the same way, from that 64 options, 3 are CWC and it is calculated as:

    1 _          *            3               *             1            = 3

1st question      2nd question     3rd question

Because there is just one answer that is correct for the first question, there are 3 answers wrong for the second question and there are 1 answer correct for the third question.

So, the probability P(CWC) is equal to:

[tex]P(CWC)=\frac{3}{64}=0.046875[/tex]

Then, the complete list of the different possible arrangements of two correct answers and one wrong answer are: CWC, WCC and CCW

Therefore, the probabilities P(WCC) and P(CCW) are calculated as:

[tex]P(WCC)=\frac{3*1*1}{64}=\frac{3}{4}= 0.046875[/tex]

[tex]P(CCW)=\frac{1*1*3}{64}=\frac{3}{4}= 0.046875[/tex]

Finally, the probability of getting exactly two correct answers is the sum of the probabilities calculated before.

[tex]P=P(CWC)+P(WCC)+P(CCW)\\P=0.046875+0.046875+0.046875\\P=0.140625[/tex]

Answer: The volume of the​ sculpture is 141.84 cubic-feet

Step-by-step explanation: Please see the attachments below

Answer:

Se requiere un 20 por ciento de descuento.

Step-by-step explanation:

(This exercise has been presented in Spanish and for that reason explanation will be held in the same language)

Sea [tex]p_{o}[/tex] el precio original del computador portatil, el nuevo precio es:

[tex]p_{1} =\left(\frac{100\,\% + 25\,\%}{100\,\%} \right)\cdot p_{o}[/tex]

[tex]p_{1} = 1.25\cdot p_{o}[/tex]

Si [tex]p_{2} = p_{o}[/tex], entonces el porcentaje requerido para recuperar el precio original es:

[tex]r = \left(1-\frac{p_{2}}{p_{1}} \right)\times 100\,\%[/tex]

[tex]r = \left(1-\frac{p_{o}}{1.25\cdot p_{o}} \right)\times 100\,\%[/tex]

[tex]r = \left(1-\frac{1}{1.25} \right)\times 100\,\%[/tex]

[tex]r = 20\,\%[/tex]

Se requiere un 20 por ciento de descuento.

Answer:

Step-by-step explanation:

so much for bein a college student.

Answer:

f(n)=-5-3n

Step-by-step explanation:

Given the recursive formula of a sequence

f(1)=−8

f(n)=f(n−1)−3

We are to determine an explicit formula for the sequence.

f(2)=f(2-1)-3

=f(1)-3

=-8-3

f(2)=-11

f(3)=f(3-1)-3

=f(2)-3

=-11-3

f(3)=-14

We write the first few terms of the sequence.

-8, -11, -14, ...

This is an arithmetic sequence where the:

First term, a= -8

Common difference, d=-11-(-8)=-11+8

d=-3

The nth term of an arithmetic sequence is determined using the formula:

T(n)=a+(n-1)d

Substituting the derived values, we have:

T(n)=-8-3(n-1)

=-8-3n+3

T(n)=-5-3n

Therefore, the explicit formula for f(n) can be written as:

f(n)=-5-3n

Answer:

72+9(n−1)

Step-by-step explanation:

I hope this helps, Its from khan <3

Answer:

3136

Step-by-step explanation:

Thats the answer please I don't have time to write the explanation

Answer:

The onject 1/8 of the length of the path 3/4 in second.

Using the ratio and proportion to find the total time does it take the object to travel the entire length of the path as following

Length:time

X:(total time )

Total time x.(3/4)/(1/8x)=(3/4)/(1/8) = 6 seconds

Answer:

4(x - 1) = 6(x + 3)

x = -11

Step-by-step explanation:

x represents “the number” so we would substitute this with a variable.

(I hope this helps! Have a great day AND STAN BTS)

Answer:

C

Step-by-step explanation:

(x, y) -> (1/2x, 1/2y)

When you dilate a side, point, etc, you are multiplying the original dimension by the scale factor. That is represented in option C: the original x and y are multiplied by the scale factor, 1/2! Hope that helps! :)

Answer:

C. (x,y) → (1/2x,1/2y)

Step-by-step explanation:

Dialation means to multiply each coordinate by scale factor and in this case it's 1/2

Answer:

73.2 miles i am not so sure

Step-by-step explanation:

Answer:

5.94% of customers carries a balance of GH¢100 or lower.

82.64% of customers carries a balance of GH¢500 or lower.

0% of current account customers carries average daily balances exactly equal to GH¢500.

76.7% of customers maintains account balance between GH¢100 and GH¢500

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

[tex]\mu = 350, \sigma = 160[/tex]

What percentage of customers carries a balance of GH¢100 or lower?

This is the pvalue of Z when X = 100. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{100 - 350}{160}[/tex]

[tex]Z = -1.56[/tex]

[tex]Z = -1.56[/tex] has a pvalue of 0.0594

5.94% of customers carries a balance of GH¢100 or lower.

What percentage of customers carries a balance of GH¢500 or lower?

This is the pvalue of Z when X = 500.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{500 - 350}{160}[/tex]

[tex]Z = 0.94[/tex]

[tex]Z = 0.94[/tex] has a pvalue of 0.8264

82.64% of customers carries a balance of GH¢500 or lower.

What percentage of current account customers carries average daily balances exactly equal to GH¢500?

In the normal distribution, the probability of finding a value exactly equal to X is 0. So

0% of current account customers carries average daily balances exactly equal to GH¢500.

What percentage of customers maintains account balance between GH¢100 and GH¢500?

This is the pvalue of Z when X = 500 subtracted by the pvalue of Z when X = 100.

From b), when X = 500, Z = 0.94 has a pvalue of 0.8264

From a), when X = 100, Z = -1.56 has a pvalue of 0.0594

0.8264 - 0.0594 = 0.767

76.7% of customers maintains account balance between GH¢100 and GH¢500

Answer:

$4.20

Step-by-step explanation:

Calculation for the standard deviation of the fare passengers pay of Blue Cab Company:

T = Total amount of the cab fare

Formula for Standard deviation of T will be:

T = σa+bX= bσX.

To convert the rate to dollars per mile from dollars per tenth of a mile, it will be:

b= 3

Hence,

Standard deviation of T is :

3.00(1.4) = $4.20.

Answer:

x=2

Step-by-step explanation:

f(x) = -3x + 5.

f(x) =-1

-1 = -3x+5

Subtract 5 from each side

-1 -5 = -3x+5-5

-6 = -3x

Divide each side by -3

-6/-3 = -3x/-3

2 =x

Answer:graph C is the answer because if you put the both values from the graph it satisfies the equation

Answer:

Graph C

Step-by-step explanation:

The given equation is in the form y=mx+b

This is slope-intercept form.

This is where m represents the slope, and b represents the y-intercept.

Therefore, the slope is 3 and the y-intercept is 2.

Let's first name all the equations with a y-intercept of 2.

That would be B and C.

Now, let's find the equation with a slope of 3.

Let's find the slope for B.

The formula for slope is: y1-y2/x1-x2

A point is: (x coordinate, y coordinate)

In the formula,

y1 is the y coordinate of the first point

y2 is the y coordinate of the second point

x1 is the x coordinate of the first point

x2 is the x coordinate of the second point

This said, we can plug our points in.

6-2/2-0

4/2

2

The slope for Graph B is 2, so it is incorrect.

Let's find the slope for Graph C.

2-(-1)/0-(-1)

2+1/0+1

3/1

3

The slope for Graph C  is 3, and it has a y-intercept of 2, so Graph C is the correct choice.

Answer:

i

Step-by-step explanation:

Answer:

im going to say a wallaby because they are smaller and lighter and if you think of the weight then less power is needed for a wallaby

idk lol XD

Step-by-step explanation:

Answer:

13 miles

Step-by-step explanation

27 miles in 2 hours

x miles in 1 hours

2x=27

x=13.5

Complete Question

The complete question is  shown on the first uploaded image

Answer:

Option D is the correct answer

Step-by-step explanation:

   Now looking at the bar chart we see that a greater number of employee over the age of 45 preferred the 4-day work week compared to the number of employee between 30- 45 who preferred to have a flexible work hour and employee below 30  who' s preference are the same for both type of work hours

Answer:

D

Step-by-step explanation:

Answer:

The probability that a randomly selected student didn’t take economics but did take statistics is 13%.

Step-by-step explanation:

Let the event that a student offers Economics be E.

The event that a student does NOT offer Economics is E'.

Let the event that a student offers Statistics be S.

The event that a student does NOT offer Statistics be S'.

P(E) = 13.5% = 0.135

P(S) = 24.7% = 0.247

P(E n S) = 11.7% = 0.117

Find the probability that a randomly selected student didn’t take economics but did take statistics

This probability = P(E' n S)

Since E and E' are mutually exclusive events,

P(S) = P(E' n S) + P(E n S)

P(E' n S) = P(S) - P(E n S)

P(E' n S) = 0.247 - 0.117 = 0.13 = 13%

Hope this Helps!!!

Answer:

answer B [tex]\boxed{ \ 569 \ }\\[/tex]

Step-by-step explanation:

f(8)=-2*8+5=-11

g(8)=9*8*8+4=580

f(8)+g(8)= -11+580=569

Answer:

$ 14.08

Step-by-step explanation:

We have that the policy costs $ 94 and with life insurance with coverage of $ 120,000, to calculate the expected value, we must subtract the value of that life insurance multiplied with the probability of dying (complement of the probability of living) and the policy value multiplied by the probability of staying alive) like this:

120000 * (1 - 0.9991) - 94 * 0.9991 = 14.0846

Which means that the expected value of the policy is $ 14.08

The probability that more than half of the 8 randomly chosen blood donors have Type A blood is approximately 0.2533 or 25.33%.

To calculate the probability that more than half of the 8 randomly chosen blood donors have Type A blood, we can use the binomial probability formula:

[tex]\mathrm{P(X > n/2) = \sum [ P(X = k) ]}[/tex]

where the sum is taken from k = (n/2 + 1) to k = n

In this case, n represents the number of trials (8 blood donors) and p is the probability that a single blood donor has Type A blood (0.40).

P(X = k) is the probability of getting exactly k donors with Type A blood, and it is given by the binomial probability formula:

[tex]\mathrm {P(X = k) = (n, k) \times p^k \times (1 - p)^{(n - k)}}[/tex]

where (n choose k) represents the number of combinations of n items taken k at a time, and it is given by:

[tex]\mathrm {(n, k) = \frac{n!}{(k! \times (n - k)!)}}[/tex]

Now, let's calculate the probability that more than half (i.e., 5 or more) of the donors have Type A blood:

[tex]\mathrm{P(X > 4) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8)}[/tex]

[tex]\mathrm {P(X = k) = (8, k) \times 0.40^k \times (1 - 0.40)^{(8 - k)}}[/tex]

[tex]\mathrm{P(X = 5)} = (8, 5) \times 0.40^5 \times (1 - 0.40)^{(8 - 5)}\\\\= 56 \times 0.01024 \times 0.343\\\\= 0.1961984[/tex]

[tex]\mathrm{P(X = 6)} = (8, 6) \times 0.40^6 \times (1 - 0.40)^{(8 - 6)}\\\\= 28 \times 0.004096 \times 0.36\\\\= 0.0516608[/tex]

[tex]\mathrm {P(X = 7)} = (8, 7) \times 0.40^7 \times (1 - 0.40)^{(8 - 7)}\\\\= 8 \times 0.0016384 \times 0.4\\\\= 0.0052224[/tex]

[tex]\mathrm {P(X = 8)} = (8, 8) \times 0.40^8 \times (1 - 0.40)^{(8 - 8)}\\\\= 1 \times 0.00065536 \times 0.4\\\\= 0.000262144[/tex]

Now, add all these probabilities together to get the final result:

[tex]\mathrm {P(X > 4)} = 0.1961984 + 0.0516608 + 0.0052224 + 0.000262144\\\\= 0.253343344[/tex]

Therefore, the probability that more than half of the 8 randomly chosen blood donors have Type A blood is approximately 0.2533 or 25.33%.

Learn more about probability click;

https://brainly.com/question/32117953

#SPJ4

Answer:

  6750 - 3894 = 2856

Step-by-step explanation:

You have to make use of the arithmetic facts you know.

The least-significant asterisk must be 0, because the sum of 4 and 6 is 10.

The 10s asterisk must be 9,so that the sum 5 + 9 + 1 has a least-significant digit of 5.

The 100s asterisk must be 7, because that is the least-significant digit of the sum 8 + 8 + 1 = 17.

The 1000s asterisk must be 3, so that 2 + 3 + 1 = 6.

(The "1" in each of these sums is the carry from the sum of the digits with the next lower place value.)

So, the subtraction problem is ...

  6750 - 3894 = 2856

_____

Comment on the solution method

For the most part, we worked this as an addition problem. The sum of the last two numbers must be equal to the first: 6570 = 3894 +2856. For some of us, addition facts are easier to work with than subtraction facts. The carry/borrow can be less confusing that way.

Answer:

Explained below.

Step-by-step explanation:

A compound event is an event in which has possible outcomes more than one.  

To determine the probability of compound events on has to compute the sum of the probabilities of all the individual events and, if required, remove any coinciding probabilities.

Examples of compound events are:

The number of favorable outcome is rolling a 5, is 1.

The total number of outcomes of rolling a die is 6.

Then the probability of rolling a 5 is 1/6.

The number of favorable outcome of pulling a heart is 13.  

The total number of outcomes is 52.

The probability of pulling a heart from a standard deck is 13/52 or 1/4.

Thus, the procedure is to compute the sum of the probabilities of all the individual events and, if required, remove any coinciding probabilities.