If a function has rate of change
4
5 and y=6 when x=5​, write its equation

Answer:

I believe it would be 16.75 but ik not completely sure

The meaning of f(7) is that a vehicle is parked for 7 hours, and the cost of parking for 7 hours will be $16.75.

A function assigns the value of each element of one set to the other specific element of another set.

Given that the function for the cost of parking in the garage for 2 hours or more is f(x)=8+1.75(x–2), where x is the number of total hours parked in the garage.

Now, the meaning of f(7) is that a vehicle is parked for 7 hours in the parking garage. And its value can be found by substituting the value of x as 7 in the given function,

f(x) = 8 + 1.75(x – 2)

f(7) = 8 + 1.75(7 – 2)

     = 8 + 1.75(5)

     = 8 + 8.75

     = 16.75

Hence, the meaning of f(7) is that a vehicle is parked for 7 hours, and the cost of parking for 7 hours will be $16.75.

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The second difference of the given number table is: Option A: -2

The second difference method can be used to determine a quadratic model.  In order for us to calculate the second difference, we will select 3 consecutive y-values, and then subtract the first y-value from the second and the second y-value form the third. Then we will find the difference of these two resulting values. That difference is what we refer to as the second difference.

Thus, Applying the second difference concept to our problem, we have:

First difference:

-4 - (-9) = 5

-1 - (-4) = 3

Thus, second difference is:

3 - 5 = -2

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The distance between points C and D is given as follows:

5 units.

Suppose that we have two points of the coordinate plane, and the ordered pairs have coordinates \((x_1,y_1)\) and \((x_2,y_2)\).

The shortest distance between them is given by the equation presented as follows, derived from the Pythagorean Theorem:

\(D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

The coordinates for this problem are given as follows:

(-4, -6) and (1, -6).

Hence the distance is given as follows:

\(D = \sqrt{(-4 - 1)^2 + (-6 - (-6))^2}\)

D = 5 units.

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Answer:

x=20

Step-by-step explanation:

Complementary means =90 degrees, so with that being said, you need to write the equation as follows:

2x+10+x+20=90

Then add like terms:

3x+30=90

Subtract 30 from both sides (30 and 90)

3x=60

Divide both sides by 3

x=20

I hope this helps!!

Answer:

-6

Step-by-step explanation:

Trust me fam

Answer: C

Step-by-step explanation: -14 * -6 = 84 so -14 goes into 84 -6 times.

Answer:

$8.40

Step-by-step explanation:

Answer:36.4

Step-by-step explanation:

Answer:

56 possible outcomes

Step-by-step explanation:

Order does not matter in this case, so we will find all the possible combinations:

8 nCr 3 = 8! / ((8 – 3)! 3!) = 40320 / 720 = 56

Therefore, there are 56 possible outcomes.

The volume of the cylindrical water tank that has a length of 20 feet and a radius of 12 feet is about 9,048 cubic feet.

The correct option is option d;

d. 9,048

The volume of a solid indicates the amount of space the solid takes at a location.

The formula for finding the volume of the cylindrical tank is presented as follows;

V = π·r²·L

Where;

r = The radius of the tank

L = The length of the tank

From a similar question on the website, we have;

The length of the tank, L = 20 feet

Therefore;

The volume of the tank, V = π × 12² × 20 ≈ 9048

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Answer: $3,833.20

Step-by-step explanation:

Mortgages interest and property tax are both federal deductions so they will reduce taxes:

= 10,260 + 3,430

= $13,690

The tax saving is therefore:

= 13,690 * tax rate

= 13,690 * 28%

= $3,833.20

Answer:

The Concert Tickets are less. Concert Tickets cost 7.30 per ticket and is 20cents different from the movie tickets.

Step-by-step explanation:

Movie Tickets : 4

30.00/4 = 7.50$

Concert Tickets : 5

36.50/5 = 7.30$

Hope this helps <3

Answer:

. Concert Tickets cost 7.30

Step-by-step explanation:

The value of integral is 3.

Let's evaluate the integral over the positive half of the interval:

∫[0 to π] (cos(x) / √(4 + 3sin(x))) dx

Let u = 4 + 3sin(x), then du = 3cos(x) dx.

Substituting these expressions into the integral, we have:

∫[0 to π] (cos(x) / sqrt(4 + 3sin(x))) dx = ∫[0 to π] (1 / (3√u)) du

Using the power rule of integration, the integral becomes:

∫[0 to π] (1 / (3√u)) du = (2/3) . 2√u ∣[0 to π]

Evaluating the definite integral at the limits of integration:

(2/3)2√u ∣[0 to π] = (2/3) 2(√(4 + 3sin(π)) - √(4 + 3sin(0)))

(2/3) x 2(√(4) - √(4)) = (2/3) x 2(2 - 2) = (2/3) x 2(0) = 0

So, the value of integral is

= 3-0

= 3

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Answer:

\(3-\displaystyle \int^{\pi}_{-\pi} \dfrac{\cos x}{\sqrt{4+3 \sin x}}\; \text{d}x\approx 0.806\; \sf (3\;d.p.)\)

Step-by-step explanation:

First, compute the indefinite integral:

\(\displaystyle \int \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x\)

To evaluate the indefinite integral, use the method of substitution.

\(\textsf{Let} \;\;u = 4 + 3 \sin x\)

Find du/dx and rewrite it so that dx is on its own:

\(\dfrac{\text{d}u}{\text{d}x}=3 \cos x \implies \text{d}x=\dfrac{1}{3 \cos x}\; \text{d}u\)

Rewrite the original integral in terms of u and du, and evaluate:

\(\begin{aligned}\displaystyle \int \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&=\int \dfrac{\cos x}{\sqrt{u}}\cdot \dfrac{1}{3 \cos x}\; \text{d}u\\\\&=\int \dfrac{1}{3\sqrt{u}}\; \text{d}u\\\\&=\int\dfrac{1}{3}u^{-\frac{1}{2}}\; \text{d}u\\\\&=\dfrac{1}{-\frac{1}{2}+1} \cdot \dfrac{1}{3}u^{-\frac{1}{2}+1}+C\\\\&=\dfrac{2}{3}\sqrt{u}+C\end{aligned}\)

Substitute back u = 4 + 3 sin x:

                            \(= \dfrac{2}{3}\sqrt{4+3\sin x}+C\)

Therefore:

\(\displaystyle \int \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x= \dfrac{2}{3}\sqrt{4+3\sin x}+C\)

To evaluate the definite integral, we must first determine any intervals within the given interval -π ≤ x ≤ π where the curve lies below the x-axis. This is because when we integrate a function that lies below the x-axis, it will give a negative area value.

Find the x-intercepts by setting the function to zero and solving for x in the given interval -π ≤ x ≤ π.

\(\begin{aligned}\dfrac{\cos x}{\sqrt{4+3\sin x}}&=0\\\\\cos x&=0\\\\x&=\arccos0\\\\\implies x&=-\dfrac{\pi }{2}, \dfrac{\pi }{2}\end{aligned}\)

Therefore, the curve of the function is:

So to calculate the total area, we need to calculate the positive and negative areas separately and then add them together, remembering that if you integrate a function to find an area that lies below the x-axis, it will give a negative value.

Integrate the function between -π and -π/2.

As the area is below the x-axis, we need to negate the integral so that the resulting area is positive:

\(\begin{aligned}A_1=-\displaystyle \int^{-\frac{\pi}{2}}_{-\pi} \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&=- \left[\dfrac{2}{3}\sqrt{4+3\sin x}\right]^{-\frac{\pi}{2}}_{-\pi}\\\\&=-\dfrac{2}{3}\sqrt{4+3 \sin \left(-\frac{\pi}{2}\right)}+\dfrac{2}{3}\sqrt{4+3 \sin \left(-\pi\right)}\\\\&=-\dfrac{2}{3}\sqrt{4+3 (-1)}+\dfrac{2}{3}\sqrt{4+3 (0)}\\\\&=-\dfrac{2}{3}+\dfrac{4}{3}\\\\&=\dfrac{2}{3}\end{aligned}\)

Integrate the function between -π/2 and π/2:

\(\begin{aligned}A_2=\displaystyle \int^{\frac{\pi}{2}}_{-\frac{\pi}{2}} \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&= \left[\dfrac{2}{3}\sqrt{4+3\sin x}\right]^{\frac{\pi}{2}}_{-\frac{\pi}{2}}\\\\&=\dfrac{2}{3}\sqrt{4+3 \sin \left(\frac{\pi}{2}\right)}-\dfrac{2}{3}\sqrt{4+3 \sin \left(-\frac{\pi}{2}\right)}\\\\&=\dfrac{2}{3}\sqrt{4+3 (1)}-\dfrac{2}{3}\sqrt{4+3 (-1)}\\\\&=\dfrac{2\sqrt{7}}{3}-\dfrac{2}{3}\\\\&=\dfrac{2\sqrt{7}-2}{3}\end{aligned}\)

Integrate the function between π/2 and π.

As the area is below the x-axis, we need to negate the integral so that the resulting area is positive:

\(\begin{aligned}A_3=-\displaystyle \int^{\pi}_{\frac{\pi}{2}} \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&= -\left[\dfrac{2}{3}\sqrt{4+3\sin x}\right]^{\pi}_{\frac{\pi}{2}}\\\\&=-\dfrac{2}{3}\sqrt{4+3 \sin \left(\pi\right)}+\dfrac{2}{3}\sqrt{4+3 \sin \left(\frac{\pi}{2}\right)}\\\\&=-\dfrac{2}{3}\sqrt{4+3 (0)}+\dfrac{2}{3}\sqrt{4+3 (1)}\\\\&=-\dfrac{4}{3}+\dfrac{2\sqrt{7}}{3}\\\\&=\dfrac{2\sqrt{7}-4}{3}\end{aligned}\)

To evaluate the definite integral, sum A₁, A₂ and A₃:

\(\begin{aligned}\displaystyle \int^{\pi}_{-\pi} \dfrac{\cos x}{\sqrt{4+3\sin x}}\; \text{d}x&=\dfrac{2}{3}+\dfrac{2\sqrt{7}-2}{3}+\dfrac{2\sqrt{7}-4}{3}\\\\&=\dfrac{2+2\sqrt{7}-2+2\sqrt{7}-4}{3}\\\\&=\dfrac{4\sqrt{7}-4}{3}\\\\ &\approx2.194\; \sf (3\;d.p.)\end{aligned}\)

Now we have evaluated the definite integral, we can subtract it from 3 to evaluate the given expression:

\(\begin{aligned}3-\displaystyle \int^{\pi}_{-\pi} \dfrac{\cos x}{\sqrt{4+3 \sin x}}\; \text{d}x&=3-\dfrac{4\sqrt{7}-4}{3}\\\\&=\dfrac{9}{3}-\dfrac{4\sqrt{7}-4}{3}\\\\&=\dfrac{9-(4\sqrt{7}-4)}{3}\\\\&=\dfrac{13-4\sqrt{7}}{3}\\\\&\approx 0.806\; \sf (3\;d.p.)\end{aligned}\)

Therefore, the given expression cannot be zero.

The difference between their yearly incomes is $31,304.

To calculate each person's yearly income, we need to multiply their weekly income by the number of weeks in a year. Assuming there are 52 weeks in a year, the yearly income can be calculated as follows:

For the student who drops out of high school:

Yearly Income = Weekly Income x Number of Weeks

= 451 x 52

= 23,452

For someone with a bachelor's degree:

Yearly Income = Weekly Income x Number of Weeks

= 1053 x 52

= 54,756

The difference between their yearly incomes can be found by subtracting the student's yearly income from the bachelor's degree holder's yearly income:

Difference = Bachelor's Yearly Income - Student's Yearly Income

= 54,756 - 23,452

= 31,304

Therefore, the difference between their yearly incomes is $31,304.

It is important to note that these calculations are based on the given information and assumptions. The actual yearly incomes may vary depending on factors such as work hours, additional income sources, deductions, and other financial considerations.

Additionally, it is worth considering that educational attainment is just one factor that can influence income, and there are other variables such as experience, job type, and market conditions that may also impact individuals' earnings.

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Answer:

g = 4.5

Step-by-step explanation:

8g = 36

g = 36/8

g = 4.5

The place value of the digit "6" in the given number 760,000 is Ten thousand's i.e., sixty thousand.

Definition of place value

The numerical value of the digit in the given number is based on its position in the number.

The place values are:

Hundred thousands(Hth) - 100,000

Ten thousands(Tth) - 10,000

Thousands(Th) - 1,000

Hundreds(H) - 100

Tens(T) - 10

Ones(O) - 1

Given number is 760,000

The place values for the given number are:

Hth  Tth  Th  H  T  O

7       6     0    0  0  0

So, the digit '6' is in the ten thousand's place. So, its place value is "ten thousand" i.e., "sixty thousand".

In math, every digit in more than a few has an area cost. place value can be described as the value represented by a digit in quite a number on the premise of its position within the number.

for instance, the region value of seven in 3,743 is 7 loads or seven-hundred. but, the place value of seven in 7,432 is 7 thousands or 7,000. here, we will see that despite the fact that the digits are identical in both the numbers, it’s region cost adjustments with the exchange in it’s position.

area value Chart is a completely beneficial table format that helps us in finding the place value of each digit primarily based on it’s function in various.

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Answer:

Step-by-step explanation:

False. They have one point in common meaning there is only 1 solution.

Answer:

1.07 > 0.007

Step-by-step explanation:

Greater than

Plz mark as brainliest if correct! Have a nice day!!!

-Lil G

Given statement solution is :- The present value of R13,000 per year invested for 8 years at 10% compound interest is approximately R69,776.60.

To calculate the present value of an investment with compound interest, we can use the formula for the present value of an annuity:

PV = A *\((1 - (1 + r)^(-n)) / r\)

Where:

PV = Present value

A = Annual payment or cash flow

r = Interest rate per period

n = Number of periods

In this case, the annual payment (A) is R13,000, the interest rate (r) is 10% per year, and the investment is made for 8 years (n).

Using the formula and substituting the given values, we can calculate the present value:

PV = \(13000 * (1 - (1 + 0.10)^(-8)) / 0.10\)

Calculating this expression:

PV = \(13000 * (1 - 1.10^(-8)) / 0.10\)

= 13000 * (1 - 0.46318) / 0.10

= 13000 * 0.53682 / 0.10

= 6977.66 / 0.10

= 69776.6

Therefore, the present value of R13,000 per year invested for 8 years at 10% compound interest is approximately R69,776.60.

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Answer:

a

 \(z-score = 1.57\)

b

 \(z-score_s = -3.36\)

Step-by-step explanation:

From the question we are told that

   The sample size is  n =  103  

    The  sample mean of  sag is  \(\= x_1 = 353\)

     The sample mean of swells is  \(\= x_2 = 184\)

    The standard deviation of  sag is  \(s_1 = 30\)

     The standard deviation of swells is  \(s_2 = 25\)

     The number of swell for a randomly selected transformer is  k  =  100

      The number of sag for a randomly selected transformer is  c  =  400

Generally the z-score for the number of swells is mathematically represented as

     \(z-score_s = \frac{ k - \= x_2}{s_2}\)

=>   \(z-score_s = \frac{ 100- 184}{25}\)

=>     \(z-score_s = -3.36\)

Generally the z-score for the number of sags is mathematically represented as    

      \(z-score = \frac{ c - \= x_1}{s_1}\)

     \(z-score = \frac{ 400 - 353}{30}\)

     \(z-score = 1.57\)

The z-score for the number of sags for this transformer is 1.57.

And the z-score for the number of swells for this transformer is -3.36.

Given that,

The power quality of transformers built in Turkey was investigated in Electrical Engineering (Vol. 95, 2013).

For a sample of 103 transformers built for heavy industry, the mean number of sags per week was 353 and the mean number of swells per week was 184.

Assume the standard deviation of the sag distribution is 30 sags per week that the standard deviation of the swell distribution is 25 swells per week.

Suppose one of the transformers is randomly selected and found to have 400 sags and 100 swells in a week.

We have to find,

Find the z-score for the number of sags for this transformer.

Find the z-score for the number of swells for this transformer.

According to the question,

For a sample of 103 transformers built for heavy industry, the mean number of sags per week was 353,

the standard deviation of the sag distribution is 30 sags per week.

the transformers is randomly selected and found to have 400 sags.

Therefore,

The z-score for the number of sags for this transformer,

\(\rm Z_s_c_o_r_e = \dfrac{Randomely \ selected \ transformers \ of \ sags- Mean \ number \ of \ sags }{Standard \ deviation \ of \ sags}\\\\ Z_s_c_o_r_e= \dfrac{400-353}{30}\\\\ Z_s_c_o_r_e= \dfrac{47}{30}\\\\ Z_s_c_o_r_e= 1.57\)

Sample of 103 transformers built for heavy industry, the mean number of sags per week was 184,

the standard deviation of the sag distribution is 25 sags per week.

the transformers is randomly selected and found to have 100 sags

Therefore,

The z-score for the number of sags for this transformer,

\(\rm Z_s_c_o_r_e = \dfrac{Randomely \ selected \ transformers \ of \ swells - Mean \ number \ of \ swells }{Standard \ deviation \ of \ sweels}\\\\ Z_s_c_o_r_e= \dfrac{100-184}{25}\\\\ Z_s_c_o_r_e= \dfrac{-84}{25}\\\\ Z_s_c_o_r_e= -3.36\)

Hence, The z-score for the number of sags for this transformer is 1.57 and the z-score for the number of swells for this transformer is -3.36.

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Answer:

10 (8-x)(8+x)

Step-by-step explanation:

640-10x^2

Factor out 10

10 (64 - x^2)

Notice that inside the parentheses is the difference of squares

10 ( 8^2 - x^2)   and a^2 - b^2 = (a-b) (a+b)

10 (8-x)(8+x)

Answer:

10(8 - x)(8 + x)

Step-by-step explanation:

Given

640 - 10x^2

Solution

Take out 10 on each side of the minus sign

10(64 - x^2)

The expression in the brackets is a difference of squares which factors as

a^2 - b^2 = (a + b)(a - b)

Factor the expression inside the brackets as a difference of squares.

64 = 8*8

x^2 = x*x

10(8 - x)(8 + x)

The area of the smaller rectangle (KLMN) is 16.

Since rectangles ABCD and KLMN are similar, their corresponding sides are proportional.

Let's assume the length of side AB in rectangle ABCD is x, and the length of side KL in rectangle KLMN is y.

We can set up the proportion:

(x/y) = (20/16)

To find the area of the smaller rectangle, we need to determine the ratio of their areas.

Since the area of a rectangle is given by the product of its length and width, the ratio of the areas will be equal to the square of the ratio of their sides:

(Area of ABCD)/(Area of KLMN) = (x²)/(y²)

We are given that the area of ABCD is 25, so we have:

25/(Area of KLMN) = (x²)/(y²)

To find the area of KLMN, we need to substitute the values of x and y from the proportion:

25/(Area of KLMN) = (20/16)²

Simplifying the right side:

25/(Area of KLMN) = (5/4)²

25/(Area of KLMN) = 25/16

Cross-multiplying:

25 × 16 = 25 × (Area of KLMN)

400 = 25 × (Area of KLMN)

Dividing both sides by 25:

16 = Area of KLMN

Therefore, the area of the smaller rectangle (KLMN) is 16.

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Answer:

c )

Step-by-step explanation:

To find equivalent inequalities, we are looking to isolate x on the left side.

a) x < 4 ✅

b) x -1 < 3 add 1 to both sides  x -1 +1 < 3 +1 result x < 4 ✅

c) x + 1 < 4 subtract 1 from both sides x + 1 -1 < 4 -1 result x < 3 ❌

d) x - 2 < 2 add 2 to both sides x - 2 +2 < 2+2 result x < 4 ✅

To find a book it is necessary to write the name "a vacation trip" in the search engine and add the word PDF to obtain better results.

To download a book from the Internet it is necessary to review various pages since some do not contain the complete book and others may have some type of virus that can damage the device.

In the same way, there are some platforms or applications that require a subscription payment to be able to access the content in an unlimited way.

¡Hope this helped!

Answer:

\( \sqrt{7x + 2} \\ \)

for answer please see

9514 1404 393

Answer:

  inverse

  y = 10/x

Step-by-step explanation:

Inverse variation is described by an equation of the form ...

  y = k/x

The value of k is a constant equal to ...

  k = xy = 5·2 = 10·1 = 15·2/3 = 20·1/2 = 10

__

Here, the products of the x- and y-values are all 10, so the inverse variation equation is ...

  y = 10/x

The number of bacteria after 8 hours is approximately 2,713.

Let's apply the exponential growth formula:

N = N0 * e(rt),

N is the number of bacteria at a particular period. N0 is the initial bacterial population, e is the mathematical constant (about equal to 2.71828), r is the growth rate, and t is the amount of time that has passed.

The information provided in the problem can be used to determine the growth rate:

N1 = N0 * e(r*2)

N2 = N0 * e(r*4)

To get eliminate N0, divide the second equation by the first equation:

N2/N1 = e(r4) / e(r2)

385/135 = e(r4) / e(r2)

If we condense this expression, we get:

e(r*2) = 385/135

e(r*2) = 2.8519

When we take the natural logarithm of both sides, we get:

r*2 = ln(2.8519)

r = ln(2.8519)/2

r = 0.5457 (rounded to 4 decimal places)

The number of bacteria after 8 hours can now be determined using the exponential growth algorithm once more:

N = N0 * e(rt)

N = 135 * e(0.5457*8)

N = 2,713 (rounded to the nearest whole number)

Therefore, the number of bacteria after 8 hours is approximately 2,713.

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Answer:

Step-by-step explanation:

The temperature T of the coffee after 10 minutes is 100.

Two or more expressions with an Equal sign is called as Equation.

change of temperature of an object is proportional to the difference between its temperature and the temperature of its surroundings.

dT/dt = -k(T - t)

dT/dt is the rate of change of temperature,

T is the temperature of the coffee,

t is the temperature of the room, and k is a constant of proportionality

We need to find the temperature of coffee after 10 minutes

∫(dT/T - kdt) = -∫kdt

ln(T) - kt = -kt + C

we can use the initial condition that the temperature of the coffee is 100°C at t = 0:

ln(100) - 0 = -0 + C

C = ln(100)

ln(T) - kt = -kt + ln(100)

ln(T) = -kt + ln(100) + kt

ln(T) = ln(100)

T = 100e⁰

T = 100

Hence, the temperature T of the coffee after 10 minutes is 100.

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Answer:

745.5 ft

Step-by-step explanation:

Reference angle (θ) = angle of depression = angle of elevation = 28° (alternate angles are congruent)

Opposite side = 350 ft

Hypotenuse = x

Apply the trigonometric function, SOH:

Sin θ = Opp/Hyp

Sin 28° = 350/x

x = 350/Sin 28

x = 745.5 ft (nearest tenth)

Answer:

use BODMAS

brackets

of

division

multiplication

addition

subtraction

or Americans would use BEDMAS I think

so it'll be 8 + 4 ÷ (-24) × (3) - 4 = 35

u can break the brackets down further

Answer:

Its a on ed

Step-by-step explanation: