A tower that is 106 feet tall casts a shadow 141 feet long. Find the angle of elevation of the sun to the nearest degree.

Answer:

The price of season ticket last year was 1,840.

Step-by-step explanation:

Given:

Price of season tickets this year = 2024

Also given:

The Price of season tickets this year is 10% more than amount paid last year.

We need to find the Price of season tickets last year.

Solution:

Let the Price of season tickets last year be 'x'.

Now we know that;

The Price of season tickets this year is 10% more than amount paid last year.

so equation can be framed as;

[tex]x+ \frac{10}{100}x=2024\\\\x+\frac{x}{10}=2024\\\\x+0.1x=2024\\\\1.1x=2024[/tex]

Now dividing both side by 1.1 we get;

[tex]\frac{1.1x}{1.1}=\frac{2024}{1.1}\\\\x= 1840[/tex]

Hence The price of season ticket last year was 1,840.

Answer:

X>-9

X is greater than -9

Step-by-step explanation:

4(X-3)+4<10+6X

By clearing up the bracket :

4X-12+4<10+6X

Collecting like terms:

4X-6X<10+12-4

-2X<18

Dividing both sides by -2:

-2X/-2>18/-2

Therefore, X>-9

The mission step is in combining like terms which is 4X-8<10+6X instead of 4X-6X<10+8.

The missing step in solving the given inequality 4(x – 3) + 4 < 10 + 6x is; x > -9

We are given the inequality as:

4(x – 3) + 4 < 10 + 6x

The steps are given as:

The next step in solving the inequality is to apply the division property of inequality by dividing both sides by -2.

This gives; x > -9

Thus, the missing step in the inequality is x > -9

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Answer:

The recycle percent as a rate per 100 is 0.03 per hour.

And 12 dolls are recycled each hour during production.

Step-by-step explanation:

The question is incomplete so below is the complete question:

A factory produces toy dolls at a rate of 400 per hour and has to recycle 3% of them because the clothes are torn. Express the recycle percent as a rate per 100. How many dolls are recycled each hour during production?

Now, to express the recycle percent as a rate per 100, And to find the number of dolls are recycled each hour during production.

Number of dolls factory produces at rate per hour = 400.

Percent of recycle = 3%.

So, to express the recycle percent as a rate per 100:

[tex]3\%\ per\ 100[/tex]

[tex]=\frac{3}{100} \ per\ hour[/tex]

[tex]=0.03\ per\ hour.[/tex]

So, to get the number of dolls are recycled each hour during production:

3% of number of dolls factory produces at rate per hour.

[tex]=\frac{3}{100} \times 400[/tex]

[tex]=0.03\times 400[/tex]

[tex]=12.[/tex]

The dolls are recycled each hour = 12.

Therefore, the recycle percent as a rate per 100 is 0.03 per hour.

And 12 dolls are recycled each hour during production.

Answer:

The answer to this question is the wall is 45.95 yards tall

Step-by-step explanation:

To solve this, we list out the given variables and the unknowns thus

Height of ball at launch = 8 yards

Distance of net from the ball = 80 yards

Distance of the wall down the path = 75%

Maximum height of the ball= 80 yards

equation of Motion of the ball = parabolic motion =

v² = u² - 2gS

S = 80 - 8 = 72 yards

at maximum height v = 0 thus u² = 2×9.81×72 =1412.64

u = 37.59 m/s

also v = u - gt and again at max height v = 0

Therefore 37.59 = 9.81×t or t = 3.83 s

If the motion of the ball is free of obstruction then time of flight before the ball just reaches the 8 yards off the ground = 3.83×2 = 7.66 seconds

Taking the initial velocity as zero at maximum height and from the equation

S = ut + 0.5×gt² we get, where S is the heigt of the ball from touching the actual field ground which is 80 yards we have

80 = 0.5×9.81×t²

so that t² = 2×80÷9.81 = 16.31 or t = 4.04s

Therefore the total time of flight = 4.04 + 3.83 = 7.87 seconds

if the ball is considered as having a constant horizontal velocity, therefore

at 75% of the way the time it took will be 0.75×7.87 = 5.9 seconds

However time it took  the  ball to reach maximum height and then starts descent = 3.83s, and the time at which the ball is directly over the wall = 2.07 seconds on the second half just after reaching mximum height

Thus at 2.07 seconds the distance trvelled from the maximum height is

S = ut +0.5gt² as before where u = 0

hence S = 0.5×9.81×2.07² = 21.05 yards or (80 -21.05) yards off the ground =  58.95 yards

As stated in the question, the ball cleared the wall by 13 yards therefore the height of the wall is 58.95 - 13 = 45.95 yards

In this exercise we have to use the knowledge of finance to identify the best cost benefit is to buy a new car or a used car, thus we find that:

The new car costs more, that can be prove if;

Manny drives an average of 110 miles per week with his old car. The old car gets 16 miles per gallon. The cost per gallon is [tex]\$2.65[/tex] repair and maintainance costs an average of [tex]\$740[/tex] per year. For the old car, to find the amount spent on the car we have:

[tex](110/16) * (2.65) = \$18.21875 / week[/tex]

There are 52 weeks in a year. We have:

[tex](10.21875)*(52) = \$ 947.375\\947.375 + 740 = \$1687.375\\(1687.357) * (3) = \$5062.125[/tex]

The new car cost [tex]\$6500[/tex] over a three year loan process. The car gets 28 miles per gallon. It requires a maintenance of [tex]\$10[/tex] per month. For the new car to find the amount, we have:

[tex](110)*(28) * (2.65) *(52) = \$541.357\\541.357 + 10*(12) + 6500 = \$ 7161.357[/tex]

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Answer:

Day Weather Temperature Humidity Wind Play?

1 Sunny Hot High Weak No

2 Cloudy Hot High Weak Yes

3 Sunny Mild Normal Strong Yes

4 Cloudy Mild High Strong Yes

5 Rainy Mild High Strong No

6 Rainy Cool Normal Strong No

7 Rainy Mild High Weak Yes

8 Sunny Hot High Strong No

9 Cloudy Hot Normal Weak Yes

10 Rainy Mild High Strong No

Step-by-step explanation:

The statement 'the number of new clients (x) is 154% of the number of old clients (y)' can be translated into a linear equation in the standard form 'ax + by = c' as '-1.54y + x = 0' or '-154y + 100x = 0' where a, b, and c are constants.

To translate the given statement into a linear equation, we need to interpret the percentages as a ratio. When we say 'the number of new clients (x) is 154% of the number of old clients (y)', it means 'x is equivalent to 1.54 times y'. So, we can write that as a linear equation:

x = 1.54y

However, that's not in the form 'ax + by = c'. To get it into that form, we can write it as:

Or alternately you might prefer, if you wish to avoid decimals:

Where a = -154, b = 100 and c = 0.

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Answer: C. Keeps taxes lower for Georgians

Step-by-step explanation:

Since the road system allows the bulky products to be shipped inexpensively this must apply that the taxes are lower for georgians otherwise this might not have been the case.

Answer:

B

Step-by-step explanation:

i just did it

Answer:

12%

Step-by-step explanation:

0.9/7.5 *100

= 12%

Answer:

I = 0.0631 W/m²

Step-by-step explanation:

Value in Decibel = 10 Log [tex]\frac{I}{10^{-12} }[/tex]

108 / 10 = Log [tex]\frac{I}{10^{-12} }[/tex]

10.8 = Log [tex]\frac{I}{10^{-12} }[/tex]

[tex]\frac{I}{10^{-12} }[/tex] = [tex]10^{10.8}[/tex]

I =  [tex]10^{10.8}[/tex] x [tex]10^{-12}[/tex]

I = 0.0631 W/m²

Answer: a drink costs $5.5

Step-by-step explanation:

Let x represent the cost of one bag of popcorn.

Let y represent the cost of one drink.

Kylie spends a total of $125.50 on 12 bags of popcorn and 7 drinks. This means that

12x + 7y = 125.50 - - - - - - - - - - 1

Amelia spends a total of $87.50 on 6 bags of popcorn and 8 drinks. This means that

6x + 8y = 87.50 - - - - - - - - - -- - - 2

Multiplying equation 1 by 1 and equation 2 by 2, it becomes

12x + 7y = 125.50

12x + 16y = 175

Subtracting, it becomes

- 9y = - 49.5

y = - 49.5/ - 9

y = 5.5

Substituting y = 5.5 into equation 2, it becomes

6x + 8 × 5.5 = 87.50

6x + 44 = 87.5

6x = 87.5 - 44 = 43.5

x = 43.5/6 = 7.25

Answer:

(x+8)² + (y+13)² = 169

Step-by-step explanation:

Equation of circle:

(x-h)² + (y-k)² = r²

(h,k) is the centre, r is the radius

(x-(-8))² + (y-(-13))² = 13²

(x+8)² + (y+13)² = 169

Answer: the equation of the circle is

(x + 8)² + (y + 13)² = 169

Step-by-step explanation:

A circle is the set of all points in a plane equidistant from a fixed point called the origin or center.

The center of the circle is (-8, -13)

The formula for determining the equation of a circle us expressed as

(x - h)² + (y - k)² = r²

Where

r represents the radius of the circle

h and k represents the x and y coordinates of the center of the circle. Comparing with the given points,

h = - 8 and k = - 13

Radius, r = 13

Substituting into the formula, it becomes

(x - h)² + (y - k)² = r²

(x - - 8)² + (y - - 13)² = 13²

(x + 8)² + (y + 13)² = 169

The probability of selecting a red marble and then a green marble, without replacement, is 33/325.

The probability in this case is being calculated as the outcome of two independent events - selecting a red marble first and then selecting a green marble. The total number of marbles in the jar is the sum of green, red, and blue marbles which is 11+6+9 = 26.

First, let's calculate the probability of drawing a red marble. There are 6 red marbles out of a total 26 marbles, so the probability is 6/26 (which reduces to 3/13).

Next, the jar now has 25 marbles left, and 11 of them are green. So, our probability of drawing a green marble after a red one is 11/25.

For both events to happen one after the other, we multiply the individual probabilities together. Hence, the combined probability of these two events would be (3/13) * (11/25), which equals 33/325.

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The probability of first selecting a red marble and then a green marble from a jar containing 11 green, 6 red, and 9 blue marbles is 33/325.

The subject of this question is probability, which is a branch of mathematics. The problem involves calculating the probably of two events occurring in sequence: selecting a red marble and then a green one from a jar of colored marbles. In total there are 26 marbles: 11 green, 6 red, and 9 blue.

The probability of selecting a red marble first is 6/26 as there are 6 red marbles and 26 total marbles in the jar. Once you've chosen a red marble, it's removed from the jar. So for the second event, there are now 25 marbles in the jar, with 11 of them being green. So, the probability of selecting a green marble is 11/25.

The probability of both events (Choosing a red marble then a green one) happening one after the other is the product of the individual probabilities. So, the probability is (6/26) × (11/25) which simplifies to 33/325.

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Answer:

If you`re trying to figure out how many gifts Maggie can get without the fee going over the budget, then I would say that she can buy 3 gifts. 4 times 3 is 12, and when you add 7 it equals 19. Of course, if 3 is pushing it, Maggie can also buy 1 or 2 gifts, and she`d be fine. Hope this helps!

Step-by-step explanation:

Answer:

Step-by-step explanation:

We would apply the formula for determining compound interest which is expressed as

A = P(1+r/n)^nt

Where

A = total amount in the account at the end of t years

r represents the interest rate.

n represents the periodic interval at which it was compounded.

P represents the principal or initial amount deposited

From the information given,

A = 7614

r = 10% = 10/100 = 0.1

n = 1 because it was compounded once in a year.

P = 3673

Therefore,

7614 = 3673(1+0.1/1)^1 × t

7614/3673 = 1.01^t

2.073 = 1.01^t

Taking log of both sides, it becomes

Log 2.073 = log 1.01^t

0.3166 = t × 0.0043

t = 0.3166/0.0043

t = 73.3

Answer:

x=3

y=8

Step-by-step explanation:

y-x=5

2y-x=13

subtract

-y=-8

y=8

8-x=5

x=8-5=3

Answer:

3

Step-by-step explanation:

y-x=5 2y-x=13 subtract -y=-8 y=8 8*5 y=8-5=3

Answer:

(A)  [tex]f=\frac{k}{L}[/tex]

(B) Frequency becomes half.

Step-by-step explanation:

We have been given that the frequency f of vibration of a violin string is inversely proportional to its length L. The constant of proportionality k is positive and depends on the tension and density of the string.

(A) We know that two inversely proportional quantities are in form [tex]y=\frac{k}{x}[/tex], where y is inversely proportional to x and k is constant of proportionality.

Upon substituting our given values, we will get:

[tex]f=\frac{k}{L}[/tex]

Therefore, our required equation would be [tex]f=\frac{k}{L}[/tex].

(B) For part, we have been given that length is twice, so our new frequency will be [tex]f_n[/tex] and new length [tex]L_n[/tex] is [tex]2L[/tex].

Upon substituting [tex]2L[/tex] in our equation as:

[tex]f_n=\frac{k}{L_n}[/tex]

[tex]f_n=\frac{k}{2L}[/tex]

[tex]f_n=\frac{1}{2}\cdot \frac{k}{L}[/tex]

[tex]f_n=\frac{1}{2}\cdot f[/tex]

Upon comparing [tex]f_n[/tex] with [tex]f[/tex], we can see that [tex]f_n[/tex] is half the value of [tex]f[/tex].

Therefore, the frequency of vibration of violin gets half, when we double the length of the string.

The frequency f of a vibrating string is represented by the equation f = k/L, where k is a constant and L is the string's length. If the length of the string is doubled, the frequency of the string's vibration is halved due to the inverse relationship.

(A) Considering the problem describes the frequency f of a vibrating string being inversely proportional to its length L, we can represent this information mathematically with the equation f = k/L, where k is a constant of proportionality. This constant is positive and depends on the tension and density of the string.

(B) Because frequency and length are inversely proportional, if you double the length of the string (L), the frequency (f) will halve. This is due to the inverse relationship, with the longer string taking more time to complete each vibration and thus reducing the frequency of vibration.

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Answer:

Special Lenses For Special Effects. ... These specialty lenses may be designed with movable focal planes for amazing depth of field, or built to focus extremely close to tiny subjects for macro enlargements, or even to produce a specific type of soft focus that's flattering for portraits

The meaning of photo editing is the act of altering an image, simply put. But that’s oversimplifying a subject which is quite complex.

For example, some photo editing techniques are done manually, while others are conducted through automated software. Some photo editing is even done offline, on actual photographs, posters or other printed collateral.

Other terms for photo editing:

Image editing

Post-processing

Image/photo manipulation

Photoshopping

Image/photo enhancement

Explanation:

so they both are alike because they can both be used to edit photos and both are great to use

Step-by-step explanation:

They both are alike because they can both be used to edit photos and both are great to use.

The procedure used to change a picture, including digital photography, analog photography, and graphics is referred to as image editing.

Special Lenses For Special Effects. These specialty lenses may be designed with movable focal planes for amazing depth of field, built to focus extremely close to tiny subjects for macro enlargements, or even to produce a specific type of soft focus that's flattering for portraits.

The meaning of photo editing is the act of altering an image, simply put. But that’s oversimplifying a subject that is quite complex.

For example, some photo editing techniques are done manually, while others are conducted through automated software. Some photo editing is even done offline, on actual photographs, posters, or other printed collateral.

Other terms for photo editing:

Image editing

Post-processing

Image/photo manipulation

Photoshopping

Image/photo enhancement

Therefore, both are alike because they can both be used to edit photos and both are great to use.

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Answer:

96 books

Step-by-step explanation:

Given:

Dan reads 12 books over winter break.

Dan reads 8 times the number of books he read over winter break.

Question asked:

How many books did Dan read over summer break ?

Solution:

By doing multiplication:

Dan reads  number of books over winter break = 12

Dan reads  number of books over summer break = 8 times of winter break

                                                                                        [tex]= 8\times12\\\\= 96[/tex]

Therefore, 96 books is read by Dan over summer break.

Final answer:

Dan read 96 books over summer break by multiplying the 12 books he read during winter break by 8.

Explanation:

The question asks us to calculate how many books Dan reads over summer break given that he reads 8 times the number of books he read over winter break. To find the answer, we need to multiply the number of books Dan read in winter break by 8. Dan read 12 books during winter break, so for summer break, we will calculate:

12 books × 8 = 96 books

Therefore, Dan read 96 books over summer break.

Answer:

20 days

Step-by-step explanation:

Expected Task duration

= (O + 4 M + P)/6

Where O = best case scenario = 15 days

P = worst case scenario = 25 days

M = Usual scenario = 20 days

Therefore, expected task duration

= [15 + 4 (20) + 25] ÷ 6

= 120 ÷ 6

= 20 days.

Therefore expected task duration is 20 days.

Answer:

Option c) Because the p-value is greater than the significance level, there is convincing evidence that the population mean number of ounces dispensed into a bottle is 12 ounces.

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 12 ounces

Sample size, n = 50

Alpha, α = 0.05

First, we design the null and the alternate hypothesis

[tex]H_{0}: \mu = 12\\H_A: \mu < 12[/tex]

We use one-tailed  test to perform this hypothesis.

P-value = 0.08

Since the p value is greater than the significance level, we fail to reject the null hypothesis and accept it.

Thus, the machine is working properly and dispense 12 ounces of a beverage into a bottle.

Option c) Because the p-value is greater than the significance level, there is convincing evidence that the population mean number of ounces dispensed into a bottle is 12 ounces.

Since the p-value found is more than the level of significance, thus in such case, we can't reject the null hypothesis, and thus accept it.

Thus:

"Option C): c. Because the p-value is greater than the significance level, there is convincing evidence that the population mean number of ounces dispensed into a bottle is 12 ounces.

Given that:

Since the p-value found is more than the level of significance, thus in such case, we can't reject the null hypothesis, and thus accept it.

Null hypothesis is the favored hypothesis which we test. The test's result just tells whether the null hypothesis is acceptable or not. The alternative hypothesis is accepted when the null hypothesis is rejected, else we accept the null hypothesis.

Thus,  [tex]H_0 : \mu = 12 = \mu_0[/tex]   is accepted as  [tex]\text{p-value} = 0.08 > 0.05 = \alpha[/tex]   and we deduce that:

"Option C: Because the p-value is greater than the significance level, there is convincing evidence that the population mean number of ounces dispensed into a bottle is 12 ounces."

is correct option.

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Answer:  False

Step-by-step explanation:

Answer:

False

Step-by-step explanation:

Answer:

a. 0.26

b. 0.7

c. 0.38

Step-by-step explanation:

For a)

For sponsored studies: 62 %  found the products favorable. The percentage is 0.62.

For non-sponsored studies 46% found the products favorable. The percentage is 0.46

Total probability = P(A) × P (B)

                           = 0.46 × 0.62

                           = 0.2604

For b)

Probability for the food industry = 0.7

For c) 1 - ( 0.62) = 0.38

The overall probability that a participant finds the product favorable is 57.2%. If the product was found favorable, the probability the study was industry-sponsored is 75.8%. If the product was found unfavorable, the probability the study was not industry-funded is 71.7%.

The first step to answer the given question is understand that this is a problem of conditional probability, related to the concept of favorability or unfavorability towards products based on industry-sponsored studies and non-sponsored studies.

To find the overall probability of a participant finding the product favorable, we add the probabilities of a product being favorable under both industry funding and no industry funding, weighted by their respective chances of occurrence.

To work out the conditional probabilities:

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Triangle ABC is similar to triangle CEF.

Explanation:

Diagram is inserted for the reference.

ABCD is a rectangle.

ABC is a right angled triangle because all the angles of the rectangle are 90◦ - (a)

CEF is a right angled triangle because FE is perpendicular to DC – (b)

In triangles ABC and CEF,

1. Angle ABC = Angle CEF = 90◦ (Both are right angles from a and b)

2. Angle BCA = Angle EFC (Alternate angles on parallel lines are equal on intersection)

Hence using Similarity property of AA (Angle, Angle), Triangle ABC and CEF are similar.

ΔABC and ΔCEF are similar triangles by the AA similarity theorem.

The angle-angle similarity theorem (AA) states that when two triangles have two pairs of corresponding congruent angles, both triangles are similar triangles.

In ΔABC and ΔCEF, we have the following:

Two pairs of corresponding congruent angles - ∠FEC ≅ ∠ABC (right angles) and ∠FCE ≅ ∠BAC

Therefore, ΔABC and ΔCEF are similar triangles by the AA similarity theorem.

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Answer:

In Mozambique a currency crisis led the government to mandate that citizens from Mozambique could only spend up to $13,600 on their credit or debit cards when shopping abroad. This is an example of a(n) ______________.

A. import tariff

B. quota

C. self-reference criterion

D. embargo

E. exchange control

The correct answer is E. exchange control

Step-by-step explanation:

Exchange controls are government imposed controls on the selling, buying or transfer of foreign currencies by residents of the country and on the selling and buying of the country's local currency by nonresidents, as well as control of cross border currency transfer.

Exchange contrl is meant for in-country economic management to prevent exchange rate volatility and is common in countries with developing economies.

Generally types of exchange controls are as follows:

1.  Allowing foreign exchange transaction through only government approved channels

2. Placing a ban on the possession of foreign currency

3. Placing a ban on the use of foreign currency within the country

4. setting fixed exchange rates

5. Placing a restriction on the amount of currency flow across border

Answer: a) yNA/100

b) NA(y-x)/100

c) (NA)/B

Step-by-step explanation:

a) The total amount of dollars owned by the shares' owner = N number of shares × A dollars per share = NA dollars

This total is then transferred to buy B shares which then appreciates by y%.

The amount of increase in portfolio from January to June = y% of total dollars invested = y% of NA dollars = yNA/100

b) If the shares were left with A, the increase in portfolio from January to June would be x% and = x% of the total Dollar amount = x% of NA dollars = xNA/100

How much more money made in that time would be the difference in interest, between taking the dollars to invest in share B or keeping the dollars on investment A

That is, (yNA/100) - (xNA/100) = NA(y-x)/100

c) Total dollars available after sale of the A stock = NA

Number of B stock this dollar can buy = Total dollars available/amount of B stock per share

That is, (NA)/B

QED!

Answer:

Incomplete question

Complete question: Jaclyn plays singles for South's varsity tennis team. During the match against North, Jaclyn won the sudden death tiebreaker point with a cross-court passing shot. The 57.5-gram ball hit her racket with a northward velocity of 26.7 m/s. Upon impact with her 331-gram racket, the ball rebounded in the exact opposite direction (and along the same general trajectory) with a speed of 29.5 m/s.

a. Determine the pre-collision momentum of the ball.

b. Determine the post-collision momentum of the ball.

c. Determine the momentum change of the ball.

Answer:

A. 1.5353kgm/s

B. 1.6963kgm/s

C. 0.161kgm/s

Step-by-step explanation:

A. The pre-collision momentum of the ball = mass of ball × velocity of ball

Mass of ball = 57.5g = 0.0575kg

Velocity of ball = 26.7m/s

Pre-collision momentum of ball = 0.0575×26.7

= 1.5353kgm/s

B. Post collision momentum of the ball = mass of ball × velocity of ball after impact

Velocity of ball after impact = 29.5m/s

Post collision momentum of ball after impact = 0.0575×29.5

= 1.6963kgm/s

C. Momentum change of ball = momentum after impact - momentum before imlact

= 1.6963kgm/s - 1.5353kgm/s

= 0.161kgm/s

Some parts are missing in the queston. Find attached the picture with the complete question

Answer:

                   [tex]\large\boxed{\large\boxed{161}}[/tex]

Explanation:

Let's put the information in a table step-by step.

                                                (number of remaining students)

                                                        Juniors          Seniors

Condition

At the end, there were 8 more seniors than juniors:

Now you have obtained one equation, which you can solve to find S, the number of senior students, and then the number of junior students.

Solve the equation:

[tex]2/3\times (S - 15) - 1/4\times 2(S - 15) = 8[/tex]

[tex]8(S - 15)-6(S - 15)=96[/tex]

[tex]8S-120-6S-90=96[/tex]

[tex]8S-6S=96+120+90[/tex]

[tex]2S=306[/tex]

[tex]S=306/2=153[/tex]

That is the number of senior students that came out to the information meeting, but the number of students remaining to perform in the school musical is (from the table above):

[tex]2/3\times (S-15)+1/4\times 2(S-15)[/tex]

Just substitute S with 153 fo find the number of students that remained to perfom in the musical:

          [tex]2/3\times (153-15)+1/4\times 2(153-15)\\ \\ 2/3(138)+1/2(138)[/tex]

          [tex]161[/tex]

Answer:

Amount invested at 6% equals $35200; Amount invested at 10% equals $17600

Step-by-step explanation:

For simple interest; A = P (1 + rt), where;

A= final amount, P=principal , r = rate , t = time in years

Let the amount invested in the 6% yielding account be 'x' and the amount invested in the 10% yielding account be 'y'.

From the question, the man invests twice as much in the lower yielding, Therefore;

⇒ x = 2y

Interest = A - P = Prt

Total interest = (Interest for 6% yielding account) + (Interest for 6% yielding account)

⇒ 3872 = ( [tex]x[/tex] X 0.06 x 1) + ( [tex]y[/tex] X 0.10 x 1)

⇒ 3872 = (2[tex]y[/tex] x 0.06 x 1) + ([tex]y[/tex] x 0.10 x 1)

⇒ 3872 = 0.12[tex]y[/tex] + 0.10[tex]y[/tex]

⇒ y = $17600

⇒ x = 2y = $ 35200

Answer: Amount invested at 6% equals $35200

Amount invested at 10% equals $17600

Step-by-step explanation:

Let x represent the amount invested at 6%.

Let y represent the amount invested at 10%.

He puts twice as much in the lower-yielding account because it is less risky. This means that

x = 2y

The formula for determining simple interest is expressed as

I = PRT/100

Where

P represents the principal

R represents the rate of investment

T represents the time in years.

Considering the amount invested at 6%,

I = (x × 6 × 1)/100 = 0.06x

Considering the amount invested at 10%,

I = (y × 10 × 1)/100 = 0.1y

If his annual interest is $3872, it means that

0.06x + 0.1y = 3872 - - - - - - - - - - - -1

Substituting x = 2y into equation 1, it becomes

0.06 × 2y + 0.1y = 3872

0.12y + 0.1y = 3872

0.22y = 3872

y = 3872/0.22

y = 17600

x = 2y = 2 × 17600

x = 35200

Answer:

(C) X<5

Step-by-step explanation:

Set of all old integers less than 5=(1,3)

X will represent this in inequality :

X<5.

Therefore, the answer is C.