what’s the correct answer for this question?

Answer:

i

Step-by-step explanation:

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:

boys = 9 ( eighth grade ) + 1 ( seventh grade) = 10 boys

girls = 3 (eight grade) + 9 ( seventh grade) = 12

probability = 22÷ 2

= 1/11

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:

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:

Step-by-step explanation:

so much for bein a college student.

Answer:

13 miles

Step-by-step explanation

27 miles in 2 hours

x miles in 1 hours

2x=27

x=13.5

Answer:

<BAR ≅<CAR

Step-by-step explanation:

Just took the test

Answer:

A edg 2020

Step-by-step explanation:

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

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

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

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

Answer:

3136

Step-by-step explanation:

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

Answer:

The initial temperature of the coffee was 90°C.

Step-by-step explanation:

The function representing the temperature of the coffee after x minutes is:

[tex]T(x)=70\cdot(0.80)^{x}+20[/tex]

T is the temperature in degree Celsius.

The initial temperature of the coffee will be at x = 0.

Compute the value of T (x) at x = 0 as follows:

[tex]T(x)=70\cdot(0.80)^{x}+20[/tex]

[tex]T(0)=70\cdot (0.80)^{0}+20[/tex]

        [tex]=70\times 1+20\\=70+20\\=90[/tex]

Thus, the initial temperature of the coffee was 90°C.

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:

b. 0.02

Step-by-step explanation:

The smaller the p-value, the stronger the evidence that you should reject the null hypothesis. In this case, this will mean rejecting that the proportions are not significantly different.

Usually, a p-value is considered to be statistically significant when p ≤ 0.05.

From the answer options provided, alternative b. 0.02 is the only one that represents the difference in proportions to be statistically significant (there is only a 2% chance that the proportions are not significantly different).

Therefore, the answer is b. 0.02

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:

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:

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!!!

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.

Answer:

D

Step-by-step explanation:

Answer:

a. x<3

b. 3,4,5,6

c.x>6

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:

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:

It’s E

Step-by-step explanation:

The length of the diagonal of the figure considered is given by: Option E: 5√2

If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:

[tex]|AC|^2 = |AB|^2 + |BC|^2[/tex]

where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).

Consider the figure attached below.

The triangle ABC is a right angled triangle as one of its angle is of 90 degrees.

Thus, we can use Pythagoras theorem here to find the length of the diagonal line AC.

Since it is given that:
|AB| = 5 units = |BC|, thus, we get:

[tex]|AC|^2 = |AB|^2 + |BC|^2\\\\|AC| = \sqrt{5^2 + 5^2} = \sqrt{2 \times 5^2} = \sqrt{5^2} \times \sqrt{2} = 5\sqrt{2} \: \rm units[/tex]

We didn't took negative of root as length cannot be negative.

Thus, the length of the diagonal of the figure considered is given by: Option E: 5√2

Learn more about Pythagoras theorem here:

https://brainly.com/question/12105522

Answer:

7.5 in

Step-by-step explanation:

Step one

This problem bothers on the mensuration of solid shapes, a sphere.

We know that the volume of a sphere is expresses as

V= (4/3) πr³

Given that the volume of the sphere is

1767.1459 in³

To solve for the radius r we need to substitute the value of the volume in the expression for the volume we have

Step two

1767.1459= (4/3) πr³

1767.1459*3= 4πr³

5301.4377/4*3.142=r³

421.82031=r³

Step three

To get r we need to cube both sides we have

r= ³√421.82031

r= 7.49967589711

To the nearest tenth

r= 7.5 in

Answer:

[tex] y = 5x[/tex]

And we need to ee what happen if we increase the value of x by a factor of 2. So then for this case we can set up the equation like this:

[tex] y_f = 5(2x) = 10x[/tex]

And if we find the ratio between the two equations we got:

[tex] \frac{y_f}{y} =\frac{10x}{5x} =2[/tex]

So then if we increase the value of x by a factor of 2 then the value of y increase also by a factor of 2

Step-by-step explanation:

For this case we have this equation given:

[tex] y = 5x[/tex]

And we need to ee what happen if we increase the value of x by a factor of 2. So then for this case we can set up the equation like this:

[tex] y_f = 5(2x) = 10x[/tex]

And if we find the ratio between the two equations we got:

[tex] \frac{y_f}{y} =\frac{10x}{5x} =2[/tex]

So then if we increase the value of x by a factor of 2 then the value of y increase also by a factor of 2

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:

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:

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.