As a young professional in the future, it is good to start saving money to have a
security for the future and have something to use when emergency cases happen
related to the need of cash. The Philippine Average Family income last 2015 was
around P276,000 per year. Lets say every year you earn the same amount and save
P76,000 yearly in your frusted bank giving 4% compounded interest annually. How much
will the account worth in the future after 40 years?
a. Solve for the future value of the account:
FV=PMT
[tex]( \frac{(1 + i) ^{n} - 1 }{i} )[/tex]
​

Answer:

10,000 books

Step-by-step explanation:

Let x be the number of print runs per year and let y the number of books per print run.

Thus, xy = 100,000.

Now from the question, we only start a new print run when we have sold all books in the storage. Thus;

Per print run we now have a cost of;

(x * 1)/(y * 2)

This is because right after the print run, we have y books that last 1/n years (until the next print run). Now, if we plot number of books in storage vs time, we will see a sawtooth pattern where the spikes begin at each print run and will linearly decrease to 0 until the next sprint run which implies constant demand. The area of each triangle will be how many book⋅years we have to pay the storage for. This area is;

(y * (1/x))/2

We'll have to multiply this number by 1 so we can then we get the storage cost per printrun:

(y * (1/x))/2 * 1 = y/2x

Since we do x print runs, the total storage costs is; y/2x * x = y/2

The total print run cost is (500 * x). Therefore, the total cost is;

C_total = (500x) + (y/2)

From initially, we saw that;

xy = 100000

So,x = 100,000/y

C_total = (500*100,000/y) + (y/2)

C_total = 50000000/y + y/2

To minimize its total storage and setup​ costs, we will find the derivative of the total cost and equate to zero.

So;

dC/dx = -50000000/y² + 1/2

At dC/dx = 0,we have;

0 = -50000000/y² + 1/2

50000000/y² = 1/2

2 × 50000000 = y²

y = √2 × 50000000

y = 10,000 books

Answer:

No solutions.

Step-by-step explanation:

5x = 8x^-1/3

Divide 8 into both sides.

5/8x = x^-1/3

Divide both sides by x.

5/8 = x^-4/3

Multiply both sides by the exponent -3/4.

5/8^-3/4 = x

1.422624 = x

Plug in 1.422624 for x to check.

It does not work. There are no real solutions.

Answer:  c) rotation of 180° & shift right 1 unit and down 2 units

Step-by-step explanation:

Rotation of 180° changes the signs of x and y

(x, y)   →   (-x, -y)

Shift right one unit adds 1 to x, Shift two down subtracts 2 from y

(-x, -y)   →   (-x + 1, -y - 2)

  (x, y)          (-x + 1, -y - 2)  

(-1, -2)    →       (2, 0)

(-4, -1)    →       (5, -1)

(-4, -3)   →       (5, 1)

Answer:

75435912

Step-by-step explanation:

1495486+73940426

= 75435912

Answer:

75,435,912

Step-by-step explanation:

=> 1495486 + 73940426

Using Calculator

=> 75,435,912

Answer:

True

Step-by-step explanation:

3y=5x

Put x as 3 and y as 5.

3(5) = 5(3)

15 = 15

Hence, true.

Answer:

X=3

y=15

[tex]3y = 5x \\ 3 \times 5 = 5 \times 3 \\ 15 = 15[/tex]

Proved.

Hope it helps..

Answer:

reflection of the axis y=4

Step-by-step explanation:

becuase it is reflected on itself

Answer:

Reflect Triangle A by the line y = 4

Step-by-step explanation:

The answer is reflect Triangle A by y = 4 because the two triangles are symmetric.

Answer:

The minimum sample size required to estimate that average is 51

Step-by-step explanation:

In order to calculate the minimum sample size required to estimate that average we would have to calculate the following formula:

minimum sample size required to estimate that average =(z∝/2σ/E)∧2

According to the given data we have the following:

z∝/2=1.645

E=5

σ=21.6

Therefore, minimum sample size required to estimate that average =(1.645*21.6/5)∧2

minimum sample size required to estimate that average =51

The minimum sample size required to estimate that average is 51

Answer:

Step-by-step explanation:

Let the five courses with their corresponding credit hours be represented as shown;

FST 201 = 4

FST 203 = 5

FST 112 = 1

FST 219 = 5

FST 223 = 4

If a student earned grades of​ B, B,​ A, C, and D respectively in those courses with the following grading system  A =​4, B =​3, C =​2, D =​1, and F =0, before we can get the student GPA, we need to know the total credit point for the five courses.

Credit point for each course = Number of credit hour * point for each grade

FST 201 = 4 * 4 = 16points (A)

FST 203 = 5 * 4 = 20points (A)

FST 112 = 1 * 4  = 4points (A)

FST 219 = 5 * 4 = 20points (A)

FST 223 = 4 * 4 = 16points (A)

Total credit point = 16+20+4+20+16 = 76points

Total credit point gotten by the student is calculated as thus;

FST 201 = 4 * 3 = 12points (B)

FST 203 = 5 * 3 = 15points (B)

FST 112 = 1 * 4  = 4points (A)

FST 219 = 5 * 2 = 10points (C)

FST 223 = 4 * 1 = 4points (D)

Total credit point gotten by the student = 45points.

student's Grade Point Average​ (GPA) = Total credit point/Total credit point gotten by the student = 76/45 = 1.69 (to 2dp)

Answer:

Exponential model

Y = y0e-0.693(t½)

Amount remaining after 4 days

5.9413 grams

Step-by-step explanation:

The formula will he given by

Y = y0e-k(t½)

The half life t½ for this radioactive substance is a day.

Initial mass y0 = 95 grams

Mass after one day = 95/2

Mass after one day = 47.5

.

Value of the decay constant k is not given, let's look for k.

Y = y0e-k(t½)

47.5= 95e-k(1)

47.5/95= e-k(1)

0.5= e-k(1)

In 0.5 = -k

-0.693= -k

0.693 = k

Y = y0e-0.693(t½)

Amount remaining after 4 days

Y = y0e-0.693(t½)

Y = 95e-0.693(4)

Y= 95e-2.772

Y= 95(0.06254)

Y= 5.9413 grams

Answer:

140

Step-by-step explanation:

The maximum is the furthest the line that goes out the furthest, the minimum would be about 83-84

Answer:

the other person is correct!

Step-by-step explanation:

Answer:

-12+28i+3i-7i-65i+28

14 -41i

Answer:

Step-by-step explanation:

a) You're trying to justify that two sums equal to 180° are equal to each other. The Transitive Property of Equality is that justification.

__

b) You're trying to justify that angles 3 and 6 are congruent. These are between the parallel lines, so are "interior" angles. They are on opposite sides of the transversal, so are "alternate" angles. They do not share a vertex, so cannot be vertical angles. The applicable theorem is the Alternate Interior Angles Theorem.

Answer:

Step-by-step explanation:

Answer:

this lesson, we will investigate the relationship between the distance traveled, the rate or speed or travel, and the time that it takes to travel that distance at that rate.  We will also look at a few other related products.

Distance  =  (Rate)(Time)

The equation that relates distance, rate, and time is

        d  =  rt

Where d is the distance traveled, r is the rate, and t is the time.  On the CAHSEE exam, you will be given two of these and will be asked to use the above equation to find

Answer:

2.5 hours

Step-by-step explanation:

First, try rewriting Jenny's speed in it's fraction form: 6 mi/hr

Next, use the units to set up an equation that relates Jenny's speed to the distance they want to travel. Let's call the unknown time t:

6mi/hr=15mi/t

1/t=6/15 (mi/hr•1/mi)

t=15/6 (hrs/mi•mi)= 15/6 (hrs•mi/mi)= 15/6 hrs

t=2.5hrs

So it'd take Jenny 2.5hrs at 6mph to go 15 miles. The key here is to keep track of the units. You can treat them like fractions and reduce them away as if they were numbers or variables.

Answer:

Exponent Product Rule

Step-by-step explanation:

Exponent multiplication: (a^b)(a^c)= a^(b+c)

t^3=(t^2)t

Because t=t^1, we have

t^2+t^1=t^3

This can be shown by the Exponent Product Rule

Answer:   t²⁺¹

Step-by-step explanation:

The law of exponents states that when multiplying terms with the same base, you ADD the exponents.  Note that "t" has an exponent of 1.

t³ = (t²)t¹ = t²⁺¹

I hope this is what you were looking for.

Answer:

The tangent line to the point P(x0,y0) and the line OP are perpendicular

Step-by-step explanation:

To show that the tangent line to the point P(x0,y0) is perpendicular to the line OP, of the circle with center at 0(0,0), you first use implicit differentiation on the equation of a circle, as follow:

[tex]x^2+y^2=r^2[/tex]     (1)

equation of a circle with center at (0,0) and constant radius r.

The implicit derivative of the equation (1) is:

[tex]\frac{d}{dx}(x^2+y^2)=\frac{d}{dx}r^2\\\\2x+2y\frac{dy}{dx}=0[/tex]

You solve the previous equation for dy/dt:

[tex]\frac{dy}{dx}=-\frac{x}{y}[/tex]

The derivative dy/dx is also the slope of the tangent line, for the point P(x0,y0) you obtain:

[tex]\frac{dy}{dx}=m=-\frac{x_o}{y_o}[/tex]

The slope m' of the OP line is given by:

[tex]m'=\frac{y-0}{x-0}[/tex]

for the point P(x0,y0) you obtain:

[tex]m'=\frac{y_0}{x_0}[/tex]

In order to know if the lines OP and tangent line to the point P, are perpendicular between them, the you verify the following relation:

[tex]m'=-\frac{1}{m}[/tex]         (2)

In fact, you relace the values of m and m':

[tex]\frac{y_o}{x_o}=-\frac{1}{x_o/y_o}\\\\\frac{y_o}{x_o}=\frac{y_o}{x_o}[/tex]

The tangent line to the point P(x0,y0) and the line OP are perpendicular

Answer:

352 cm/s

Step-by-step explanation:

circ = 44pi

speed = distance * time

distance = circ * 4 = 176pi

speed = 176pi/0.5

Answer:

≈ 1106 cm/s

Step-by-step explanation:

linear speed = angular speed x radius of the rotation

v = ωr

v = linear speed (m/s)

ω = angular speed (radians/s)

r = radius of the rotation (m)

------------

Given:

Linear speed is:

Answer: a. 1320

b.495

Step-by-step explanation:

Complete question is provided in the attachment.

Total members on the board = 12

a. Persons to chose : chairperson, first vice​ chairperson, second vice​ chairperson, and​ secretary

i.e. Total 3 posts in an order.

Number of ways to choose 3 persons from 12 in an order = [tex]^{12}P_3[/tex]  [By permutation]

[tex]=\dfrac{12!}{(12-3)!}\\\\=\dfrac{12!}{7!}\\\\=12\times11\times10\\\\=1320[/tex]

hence, 1320 different slates of candidates are​ possible .

b. number of ways to choose 4 members out of 12 ( order not matters)=[tex]^{12}C_{4}[/tex] [By combinations]

[tex]=\dfrac{12!}{4!8!}\\\\=\dfrac{12\times11\times10\times9}{24}\\\\=495[/tex]

Hence, the number of different subcommittees are​ possible =495

Answer:

The answer is 1.

Step-by-step explanation:

Given the expression:

[tex]|z-6|-|z-5|,\ if\ z<5[/tex]

To find:

The expression without absolute value.

Solution:

First of all, let us learn about the absolute value function:

[tex]y = f(x) = |x| =\left \{ {{x\ if\ x>0} \atop {-x\ if\ x<0}} \right.[/tex]

i.e. value is x if x is positive

value is -x if x is negative

Here the given expression contains two absolute value functions:

[tex]|z-6|[/tex] and [tex]|z-5|[/tex]

Using the definition of absolute value function as per above definition.

[tex]|z-5| =\left \{ {{(z-5)\ if\ z>5} \atop {-(z-5)\ if\ z<5}} \right.[/tex]

[tex]|z-6| =\left \{ {{(z-6)\ if\ z>6} \atop {-(z-6)\ if\ z<6}} \right.[/tex]

Now, it is given that z < 5 that means z will also be lesser than 6 i.e. z < 6

So, given expression [tex]|z-6|-|z-5|,\ if\ z<5[/tex] will be equivalent to :

[tex]-(z-6) - (-(z-5))\\\Rightarrow -z+6 +z-5 = \bold{1}[/tex]

So, the expression is equivalent to 1.

Answer:

25%

Step-by-step explanation:

The probability of having a boy is 50%

To calculate the probability of him having 2 boys, multiply the probabilities together

0.5(0.5) = 0.25

Answer:

D. Quadratic parent function.

Step-by-step explanation:

Answer:

Date X, Month Y, payroll taxes expense

Dr FICA (OASDI) taxes expense 2,058

Dr FICA (Medicare) taxes expense 514.50

Dr FUTA taxes expense 84.80

Dr SUTA taxes expense 572.40

    Cr Dr FICA (OASDI) taxes payable 2,058

    Cr FICA (Medicare) taxes payable 514.50

    Cr FUTA taxes payable 84.80

    Cr SUTA taxes payable 572.40

Step-by-step explanation:

The amount of employer's FICA taxes expense is the same as the FICA taxes withheld from employees' salaries. Since the question asked for the journal entry to record payroll taxes, wages expense is not included.

Answer:

8.005 km

Step-by-step explanation:

There are 1000 meters in a kilometer, so:

5/1000 = 1/200 = 0.005

8 km + 0.005 km = 8.005 km

Answer:

$200

I hope this helps!

Answer:

200rupees

Step-by-step explanation:

according to the question ,kajol has 75 rupees

amount earned=3/8* amount earned

                        =75/3*8

                         =200 rupees

Answer:

a. Local maximum = 50 units per week.

b. The graph is never concave upward.

c. (0, 80)

Step-by-step explanation:

a. The revenue function is:

[tex]R(x) = 1275x-0.17x^3[/tex]

The derivate of the revenue function for which R'(x) = 0 gives us the local extrema:

[tex]R'(x) =0= 1275-0.51x^2\\x=\sqrt{2,500}\\x=50[/tex]

The second derivate of the revenue function determines if x =50 is local maximum or minimum:

[tex]R''(x) = -1.02x\\R''(50) = -1.02*50=-51\\[/tex]

Since the second derivate yields a negative value, x = 50 units per week is a local maximum.

b. Since there are no local minimums in the range of 0 < x < 80, the graph is never concave upward.

c. Since there is only one local maximum  in the range of 0 < x < 80, the graph is concave downward from x>0 to x<80 or (0, 80)

Answer:

134 sneakers and 66 sandals

Step-by-step explanation:

Sneakers= x, sandals= y

Profit rate:

Sneakers are more profitable, so it should be maximized.

Cost:

8x+14y≤2000

x+y≤200

if we assume the maximum of 200 shoes stocked, then:

x= 200-y

8(200-y)+14y ≤ 2000

1600 - 8y +14y ≤ 2000

6y≤400

y≤66 and x=134 is the best option

Answer:

Step-by-step explanation:

hello,

we need to evaluate f(15) so

f(15)=4*15-3=60-3=57

Hope this helps

Answer:

Division property of equality.

Answer:

Domain: - infinity, + infinity. Range All real numbers less than -3

Step-by-step explanation:

The domain of the graph of a quadratic function with vertex (1, -3) is all real numbers and range belongs to the number less then equal to -3.

Vertex form of quadratic equation, is used to find the coordinate of vertex points at which the quadratic crosses its symmetry.

The standard equation of the vertex form of quadratic is given as,

[tex]y=a(x-h)^2+k[/tex]

Here, (h, k) is the vertex point.

The graph of a quadratic function with vertex (1, -3) is shown in the figure below.  Put the value in the above equation,

[tex]y=a(x-1)^2+(-3)\\y=a(x-1)^2-3[/tex]

One point of this function is passes from (0,-4) as shown in graph. Put this value in above expression to solve it for a,

[tex]-4=a(0-1)^2-3\\-4+3=a\\-1=a\\a=-1[/tex]

Put the value of a, we get,

[tex]y=-1(x-1)^2-3\\y=-(x-1)^2-3\\y=-x^2-1+2x-3\\y=-x^2+2x-4[/tex]

The domain of the above function is all real number as there is no undefined point and nor domain constraint. Thus, the domain is,

[tex](-\infty < x < \infty)[/tex]

In the above function, the coefficient of the term with the highest degree is -1. Put this value as,

[tex]y=-(1)^2+2(1)-4\\y=-1+2-4\\y=-3[/tex]

Hence, the range of the function,

[tex]f(x)\le-3[/tex]

Thus, the domain of the graph of a quadratic function with vertex (1, -3) is all real numbers and range belongs to the number less then equal to -3.

Learn more about the vertex form here;

https://brainly.com/question/17987697

#SPJ2

Question Correction

The table represents an exponential function. What is the multiplicative rate of change of the  function?

(A)1/3 (B)2/3 (C)2 (D)9

[tex]\left|\begin{array}{c|c}x&y\\--&--\\1&9\\2&6\\3&4\\4&\dfrac83\\\\5&\dfrac{16}{9}\end{array}\right|[/tex]

Answer:

(B)  [tex]\dfrac{2}{3}[/tex]

Step-by-step explanation:

An exponential function is a function of the form

[tex]y= a (b)^{x}[/tex]

where a is the initial value and b is the multiplicative rate of change

When  x=2, y=6, we have:

[tex]6= a (b)^{2}[/tex]

When  x=3, y=4, we have:

[tex]4= a (b)^{3}[/tex]

Dividing the two equations:

[tex]\dfrac{a (b)^{3}}{a (b)^{2}} =\dfrac{6}{9} \\b=\dfrac{6}{9}\\b=\dfrac{2}{3}[/tex]

The multiplicative rate of change, b is [tex]\dfrac{2}{3}[/tex].

The correct option is B.

Answer: It's B) 2/3

Hope it helps :3