Suppose Y Varies Directly As X. If Y = 150 When X = 3, Find Y When X = 5. (2024)

SOLUTIONS

Given: Assume y is the population

[tex]\begin{gathered} t=0=1960,y=14030 \\ t=1=1961,y=14060 \\ so\text{ b = 14000} \\ so\text{ k = 30} \end{gathered}[/tex]

The town grow at the rate of 30 people per year.

[tex]y=kt+14000[/tex][tex]y=30t+14000[/tex]

(A) The population predicted to be in 2030 will be

[tex]\begin{gathered} 2030-1960=70 \\ y=30k+14000 \\ y=30(70)+14000 \\ y=2100+14000 \\ y=16100people \end{gathered}[/tex]

(B) so when y = 15000, find t

[tex]\begin{gathered} y=15000 \\ y=30t+14000 \\ 15000=30t+14000 \\ 15000-14000=30t \\ 1000=30t \\ t=\frac{1000}{30} \\ t\approx33 \\ t=1960+33 \\ t=1993 \end{gathered}[/tex]

ANSWER:

Weekly salary = $300

Commision on sales = 6.0%

Let's find how much she will make in a week if she sold $4,300 worth of merchandise.

To find how much she will make, apply the formula below:

[tex]A=(\text{amount sold }\times commision)+Weekly\text{ earnings}[/tex]

Thus, we have:

[tex]\begin{gathered} A=(4300\times\frac{6}{100})+300 \\ \\ A=(4300\times0.06)+300 \\ \\ A=258+300 \\ \\ A=558 \end{gathered}[/tex]

Therefore, she would make $558 in a work week.

ANSWER:

$558

The controller puts money in 3 places.

First,

He puts money at 2% per year

Let it be "x"

The interest accumulated is

[tex]0.02x[/tex]

Second, he puts 1/3rd of previous at 3% per year.

That will be investing (1/3)x at 3%

The interest accumulated is

[tex]\begin{gathered} 0.03(\frac{1}{3}x) \\ =0.01x \end{gathered}[/tex]

Thirdly, he puts another balance, Let it be "y", at 9% CD.

The interest accumulated is:

[tex]0.09y[/tex]

The sum of all the 3 account interest is $603, thus we can write:

[tex]\begin{gathered} 0.02x+0.01x+0.09y=603 \\ 0.03x+0.09y=603 \end{gathered}[/tex]

This is equation 1.

Also, we are told that the total amount of investments is 10,000, thus we can write:

[tex]\begin{gathered} x+\frac{1}{3}x+y=10000 \\ \frac{4}{3}x+y=10000 \end{gathered}[/tex]

We have to solve these equations simultaneously to find x and y.

Lets solve for y of the 2nd equation and put it into the first equation and solve for x. Shown below:

[tex]\begin{gathered} \frac{4}{3}x+y=10000 \\ y=10000-\frac{4}{3}x \\ \text{ We have} \\ 0.03x+0.09y=603 \\ \text{Substituting, we have:} \\ 0.03x+0.09(10,000-\frac{4}{3}x)=603 \\ \text{Solving for x:} \\ 0.03x+900-0.12x=603 \\ 900-603=0.12x-0.03x \\ 297=0.09x \\ x=\frac{297}{0.09} \\ x=3300 \end{gathered}[/tex]

So, y is:

[tex]\begin{gathered} y=10000-\frac{4}{3}x \\ y=10000-\frac{4}{3}(3300) \\ y=5600 \end{gathered}[/tex]

So,

Answer$3300 invested in first account$1100 invested in second account$5600 invested in third account

We have the expression:

[tex]2\cos x+1=0[/tex]

To find x, first, we solve for cosx by subtracting 1 to both sides of the equation:

[tex]\begin{gathered} 2\cos x+1-1=-1 \\ 2\cos x=-1 \end{gathered}[/tex]

Then, divide both sides by 2:

[tex]\begin{gathered} \frac{2\cos x}{2}=-\frac{1}{2} \\ \cos x=-\frac{1}{2} \end{gathered}[/tex]

Here we have that the value of x is such that the cosine of that value is equal to -1/2.

We can use the inverse cosine to solve for x:

[tex]x=\cos ^{-1}(-\frac{1}{2})[/tex]

And the result is:

[tex]x=2.094[/tex]

And we look in our options which one has the corresponding decimal value:

[tex]\begin{gathered} \frac{\pi}{3}=1.047 \\ \frac{2\pi}{3}=2.094 \\ \frac{4\pi}{3}=4.189 \\ \frac{5\pi}{3}=5.236 \end{gathered}[/tex]

And we can see that 2pi/3 is equal to the value that we got for x, so:

[tex]x=\frac{2\pi}{3}[/tex]

Answer:

[tex]x=\frac{2\pi}{3}[/tex]

Solution.

The problem is an exponential growth problem (Because The number of cells in the tumor doubles every 2.5 months)

The formula for exponential growth is

In the problem given,

a = 1

r = 2

(i) After 2 years, that is ( 2 x 12 months = 24 months)

t = 24/2.5 = 9.6

[tex]\begin{gathered} f(9.6)=1(1+2)^{9.6} \\ =1(3)^{9.6} \\ =38050.822 \\ =38,050(nearest\text{ whole number\rparen} \end{gathered}[/tex]

The number of cell that will be after 2 years = 38,050 cells (nearest whole number)

(ii) After 5 years

5 years = 5 x 12 months = 60 months

t = 60/2.5 = 24

[tex]\begin{gathered} f(24)=1(1+2)^{24} \\ =3^{24} \\ =282,429,536,481 \end{gathered}[/tex]

Solution:

Given:

[tex]\int_0^4|x-2|dx[/tex]

Split the integral;

[tex]\begin{gathered} \int_0^4|x-2|dx=\int_0^2-(x-2)dx+\int_2^4(x-2)dx \\ ==\int_0^2(-x+2)dx+\int_2^4(x-2)dx \end{gathered}[/tex]

Integrating the expression;

[tex]\begin{gathered} =(-\frac{x^2}{2}+2x)|^2_0+(\frac{x^2}{2}-2x)|^4_2 \\ Introducing\text{ the limits;} \\ =[(-\frac{2^2}{2}+2(2))-0]+[(\frac{4^2}{2}-2(4))-(\frac{2^2}{2}-2(2))] \\ =(-2+4)-(0)+(8-8)-(2-4) \\ =2+0+0-(-2) \\ =2+2 \\ =4 \end{gathered}[/tex]

Therefore, the answer is 4.

OPTION D is correct.

Answer:

x = 90 degrees

Explanations:

The sum of interior angle of a heptagon is 900degrees. Taking the sum of all of the interior angles is:

[tex]93+166+127+112+x+76+113+123=900[/tex]

Simplify and solve for the value of "x"

[tex]\begin{gathered} 810+x=900 \\ x=900-810 \\ x=90^0 \end{gathered}[/tex]

Given that y and x vary directly, we have to use the following expression.

[tex]y=kx[/tex]

Where k is the constant of proportionality between the variable.

Let's replace y = 75 and x = 1/5 to find k.

[tex]\begin{gathered} 75=k\cdot\frac{1}{2} \\ k=150 \end{gathered}[/tex]

Then, we use k and x = 2 1/4 to find y.

[tex]\begin{gathered} y=kx \\ y=150\cdot2\frac{1}{4}=150\cdot\frac{9}{4} \\ y=337\frac{1}{2} \end{gathered}[/tex]Hence, the right answer is G.

The given forces are

[tex]F_1=\langle190,160\rangle,F_2=\langle128,-121\rangle[/tex]

To find the angle, the formula for angle between two vectors will be used

[tex]\cos \theta=\frac{a.b}{|a\mleft\Vert b\mright|}[/tex]

Using the given forces, it follows

[tex]\cos \theta=\frac{190(128)+160(-121)}{(\sqrt[]{190^2+160^2})(\sqrt[]{128^2+(-121)^2})}[/tex]

Simplify the equation

[tex]\cos \theta=\frac{24320-19360}{(\sqrt[]{36100+25600})(\sqrt[]{16384+14641})}[/tex]

Simplify further

[tex]\begin{gathered} \cos \theta=\frac{4960}{248.40\times176.1} \\ \cos \theta=0.1134 \end{gathered}[/tex]

Find the value of theta

[tex]\begin{gathered} \theta=\cos ^{-1}(0.1134)_{} \\ \theta=83^{\circ} \end{gathered}[/tex]

Therefore, the required answer is

[tex]\theta=83^{\circ}[/tex]

We have 27 apple slices

each of 4 friends ate the same number of apple slices

there were 3 apple slices left

So we have

x+3=27

but there were 4 friends

so 4x+3=27

The 4x for the number of slices by a friend plus the slices left equal the number of slices

Answer: 4x+3=27

As per given by the question,

The are given that a line on a grapg.

Now,

For the slope of the given graph ;

According to the graph, Donald swan 6 miles at a constant pace .

So,

From the formula of slope,

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Here, point from the graph is,

[tex](x_1,x_2)=(2.5,5),and(y_1,y_2)=(6,\text{ 3)}[/tex]

Now,

[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{6_{}-3_{}}{5_{}-2.5_{}} \\ m=\frac{3}{2.5} \\ m=1.2 \end{gathered}[/tex]

So, the value of slope is 1.2.

Hence, the option d is correct.

We can solve this problem with proportions, by expressing the ratio of the height of the pole and the building to the length of their shadow, like this:

Height of pole / shadow of pole = Height of building / shadow building

when we take x as the height of the building and substitute the values provided by the question, we get:

[tex]\frac{3.5}{1.55}=\frac{x}{45.25}[/tex]

From this expression we can solve for x, like this:

[tex]\begin{gathered} \frac{3.5}{1.55}=\frac{x}{45.25} \\ \frac{3.5}{1.55}\times45.25=\frac{x}{45.25}\times45.25 \\ \frac{3.5}{1.55}\times45.25=\frac{45.25}{45.25}\times x \\ \frac{3.5}{1.55}\times45.25=1\times x \\ \frac{3.5}{1.55}\times45.25=x \\ x=\frac{3.5}{1.55}\times45.25\approx102 \end{gathered}[/tex]

Then, the height of the building is 102 m

We have a system of equations:

[tex]\begin{gathered} x+9=y \\ x=4y-6 \end{gathered}[/tex]

We can solve it by substitution, using the equality of the first equation, replacing y in the second equation:

[tex]\begin{gathered} x=4y-6 \\ x=4(x+9)-6 \\ x=4x+4\cdot9-6 \\ x=4x+36-6 \\ x=4x+30 \\ x-4x=30 \\ -3x=30 \\ x=-\frac{30}{3} \\ x=-10 \end{gathered}[/tex]

With the value of x, we can calculate y as:

[tex]y=x+9=-10+9=-1[/tex]

The solution expressed as ordered pair is (x,y) = (-10,-1).

Answer: (-10, -1)

Answer

Option B is correct.

The probability of getting a multiple of 3 and an even number in one spin of the spinner labelled 1 - 12 is (1/6).

Explanation

The probability of an event is given as the number of elements in the event divided by the number of elements in the sample space.

[tex]\text{Probability of an event = }\frac{Number\text{ of elements in the event}}{Number\text{ of elements in the sample space}}[/tex]

For this question,

Number of elements in the event refers to the numbers out of 1 to 12, that are multiples of 3 and even. The numbers that are multiples of 3 and even are 6 and 12.

Number of elements in the event = 2

Number of elements in the sample space refers to all the possible outcomes.

Number of elements in the sample space = 12

Probability of an event = (2/12) = (1/6)

Hope this Helps!!!

Answer:

bonjour je mappele camellia tu habit tu

Answer:

C'est facile A=20 et B=-30 et C=-30

ANSWER:

72 box with 1-centimeter cubes

STEP-BY-STEP EXPLANATION:

To know how many box with 1-centimeter cubes the figure will fit, you must calculate the total volume of the figure in square centimeters.

The volume of salcula by means of the following formula:

[tex]V=l\cdot w\cdot h[/tex]

Where l is length, w is width, and h is height

l = 6

w = 3

h = 4

Replacing:

[tex]\begin{gathered} V=6\cdot3\cdot4 \\ V=72\operatorname{cm}^3 \end{gathered}[/tex]

Now we calculate the number of boxes, it would be:

[tex]n=\frac{72\operatorname{cm}^3}{1\operatorname{cm}^3}=72[/tex]

Answer

Positive coterminal angle to 140° = 500°

Negative coterminal angle to 140° = -220°

Explanation

Considering that a full revolution is 360°, finding angles that are coterminal with another angle in any given range will involve adding or subtracting 360° from the given angle till we are in the required range.

Basically, these coterminal angles are essentially the same angles, albeit in different revolutions.

For this question, the angle is 140°

For a positive coterminal angle, we go to the revolution that is after 0° to 360°

So, we get there simply by adding 360° to our angle provided.

Positive coterminal angle to 140° = 140° + 360° = 500°

For a negative coterminal angle, we go to the revolution that is before 0° to 360°.

So, we get there simply by subtracting 360° from our angle provided.

Negative coterminal angle to 140° = 140° - 360° = -220°

Hope this Helps!!!

The transformation from figure 1 to figure 2 is shown on the graph.

It is required to choose from the options the composition of transformation that maps figure 1 onto figure 2.

The coordinates of the vertices of figure 1 are (5,2), (5,7), and (8,5).

The coordinates of the vertices of figure 2 are (-2,2), (-7,3), and (-5,5).

Recall the coordinate rule of 90º counterclockwise rotation about the origin:

[tex](x,y)\rightarrow(-y,x)[/tex]

Hence, the rotation of figure 1 90º counterclockwise gives the vertices:

[tex](-2,5),(-7,5),(-5,8)[/tex]

Translate the image 3 units down by subtracting 3 from the y-coordinates to give vertices:

[tex]\begin{gathered} (-2,2),(-7,2),(-5,5) \\ \end{gathered}[/tex]

Notice that these vertices match that of figure 2.

It follows that the sequence of transformation is 90ºcounterclockwise rotation about the origin, followed by a translation three units down.

The answer is B followed by D.

Hello!

Let's analyze it:

Note that the order of the terms was changed, but the final result was still the same.

It is an example of associative property and also commutative property (the order didn't make any difference in the result).

Answer: alternatives B and C.

To solve the system of equations:

[tex]\begin{gathered} -5x-7y=23 \\ 3x+4y=-12 \end{gathered}[/tex]

We can do by adding equations. To do that, we need to make the coefficient of one of the variables the same but with different signs.

We can do that with x by multiplying the first equations by 3 and the second by 5:

[tex]\begin{gathered} -5x+7y=23\leftrightarrow-15x-21y=69 \\ 3x+4y=-12\leftrightarrow15x+20y=-60 \end{gathered}[/tex]

Now, we add them:

[tex]\begin{gathered} -15x-21y=69 \\ 15x+20y=-60 \\ 0x-1y=9 \\ -y=9 \\ y=-9 \end{gathered}[/tex]

Now, we can substitute y into either equation to find out x:

[tex]\begin{gathered} -5x-7y=23 \\ -5x-7\cdot(-9)=23 \\ -5x+63=23 \\ -5x=23-63 \\ -5x=-40 \\ x=\frac{-40}{-5} \\ x=8 \end{gathered}[/tex]

So, the solution is:

[tex]\begin{gathered} x=8 \\ y=-9 \end{gathered}[/tex]

[tex]\frac{F}{H}=M[/tex]

Multiply both-side of the equation by H

[tex]F=MH[/tex]

Answer:

Step-by-step explanation:

Supplementary angles:

They add up to 180º.

So

Answer:v71

Step-by-step explanation:

71717171717171717171717171717171717171717171717171

Answer:

13

Explanation:

The Ratio of miles traveled to gallons of gas used is

[tex]\frac{150}{6}[/tex]

and if we call x the number of gallons required to travel 325 miles, then the ratio of miles travelled to the number of gallons is

[tex]\frac{325}{x}[/tex]

this must equal 150/6; therefore,

[tex]\frac{150}{6}=\frac{325}{x}[/tex]

Cross multipication gives

[tex]150x=325\cdot6[/tex]

dividing both sides by 150 gives

[tex]x=\frac{325\cdot6}{150}[/tex]

which simplifies to give

[tex]\boxed{x=13}[/tex]

which is our answer!

Solution:

Question 1:

80mg was prescribed to the patient.

The dose for the injection is 50mg/2mL

This means for every 2mL, 50mg is prescribed.

[tex]\begin{gathered} 2mL=50mg \\ 50mg=2mL \\ 1mg=\frac{2}{50}mL \\ 1mg=\frac{1}{25}mL \end{gathered}[/tex]

Hence, the volume required for 80mg will be;

[tex]\begin{gathered} 1mg=\frac{1}{25}mL \\ 80mg=\frac{1}{25}\times80mL \\ 80mg=3.2mL \\ =3.20mL\text{ to 2 decimal places} \end{gathered}[/tex]

Therefore, the volume required for the prescribed 80mg will be 3.20mL

Question 2:

48mL of urine sample was measured into a 4-ounce beaker.

[tex]1oz=29.57mL[/tex]

Hence, the 4-ounce beaker will have a full volume of;

[tex]\begin{gathered} 1oz=29.57mL \\ 4oz=29.57\times4mL \\ 4oz=118.28mL \end{gathered}[/tex]

The beaker has a volume of 118.28mL

Since 48mL has been poured into the beaker, the added volume of urine that is needed to fill the beaker up will be;

[tex]\begin{gathered} =118.28-48 \\ =70.28mL \end{gathered}[/tex]

Therefore, 70.28mL more of urine sample is needed to fill up the beaker.

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the given decimal

[tex]6835.048702[/tex]

STEP 2: Round to the nearest integer

Hence, the given decimal number rounded to the nearest integer will be:

[tex]6835[/tex]

Given:

Supply equation is,

[tex]Q_s=-8P+24[/tex]

Demand equation is,

[tex]Q_d=5P+11[/tex]

To determine the equilibrium quantity (Q),

[tex]\begin{gathered} Q_s=Q_d \\ -8P+24=5P+11 \\ 5P+8P=24-11 \\ 13P=13 \\ P=\frac{13}{13} \\ P=1 \end{gathered}[/tex]

Answer: option a) 1

For an exponential function of the form:

[tex]y=a\cdot b^x[/tex]

a = Initial value

b = growth factor = 1 + r

r = Rate of change

So:

[tex]\begin{gathered} f(t)=\frac{1}{3}(1.26)^t \\ b=1+r=1.26 \\ so\colon \\ r=1.26-1 \\ r=(1.26-1)\times100 \\ r=26 \end{gathered}[/tex]

Answer:

26%

[tex]r\approx0.139[/tex]

1) Since this is a Continuously Compounded operation in a 10 yrs period, then we can write out the following equation:

[tex]\begin{gathered} A=Pe^{rt} \\ \end{gathered}[/tex]

2) Plugging into the equation the given data and since Otto is 20 yrs old and he plans to get $4,000 in ten years, we can write out:

[tex]\begin{gathered} 4000=1000e^{\mleft\{10r\mright\}} \\ \frac{4000}{1000}=\frac{1000e^{10r}}{1000} \\ 4=e^{10r} \\ \ln (4)=\ln (e)^{10r} \\ 10r=\ln (4) \\ r=\frac{\ln (4)}{10} \\ r=0.1386 \end{gathered}[/tex]

3) Thus the rate Otto needs is

[tex]r=0.1386\approx0.139[/tex]

Note that since the 0.1386 the six here is greater than 5 then we can round up to the next thousandth, in this case: 0.139. For the 0.1386 is closer to 0.139 (0.004) than to 0.138 (0.006).

Or 13.9%

ANSWER: Letter D. Inverse Property of Addition.

Inverse Property of Addition states that the sum of a number and its opposite is always 0.

[tex]\text{a + (-a) = 0}[/tex]

The length of the cell phone is 74 mm

width of the cell phone is 36mm

Ratio means division

L : W = L/W

L = 74

W = 36

Ratio = 74 / 36

2 is a common factor of both 74 and 36

74/36

= 37/18

= 37 : 18

The answer is 37 : 18 or 2.05