A customer wants to tip 15% on a restaurant bill that is $35.99. How much gratuity did the customer leave?​

Answer:

5*3ˣ

Step-by-step explanation:

We see that when x=0 y=5

this means that we can write

a*b⁰=5

a*1=5

a=5

Now we just need to solve for B

using the point (1,15) we can write

15=5*b¹

3=b

Which all comes together to mean

5*3ˣ

The depth of the water in the cone-shaped tank is increasing at a rate of approximately 1.385 meters per second.

To determine the rate at which the depth of the water is changing, we can use related rates. Let's denote the depth of the water as h(t), where t represents time. We are given that dh/dt (the rate of change of h with respect to time) is 12 m/sec, and we want to find dh/dt when h = 18 meters.

To solve this problem, we can use the volume formula for a cone, which is V = (1/3)πr^2h, where r is the base radius and h is the depth of the water. We can differentiate this equation with respect to time t, keeping in mind that r is a constant (since the base radius does not change).

By differentiating the volume formula with respect to t, we get dV/dt = (1/3)πr^2(dh/dt). Now we can substitute the given values: dV/dt = 12 m/sec, r = 26 meters, and h = 18 meters.

Solving for dh/dt, we have (1/3)π(26^2) (dh/dt) = 12 m/sec. Rearranging this equation and solving for dh/dt, we find that dh/dt is approximately 1.385 meters per second. Therefore, the depth of the water in the tank is increasing at a rate of about 1.385 meters per second.

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The value of the iterated integral 5∫_(-5)^(5) ∫_0^(π/2) (y + y^2 cos x) dx dy is 5π^2/4 + (π^3/12) sin 5.

To calculate the iterated integral ∬_S (y + y^2 cos x) dA over the given region S, where S is the rectangle defined by -5 ≤ x ≤ 5 and 0 ≤ y ≤ π/2, we will evaluate the integral in two steps: first integrating with respect to x and then integrating with respect to y.

Let's start by integrating with respect to x:

∫_S (y + y^2 cos x) dA = ∫_0^(π/2) ∫_(-5)^5 (y + y^2 cos x) dx dy

To integrate with respect to x, we treat y as a constant and integrate the expression (y + y^2 cos x) with respect to x over the range -5 to 5:

∫_S (y + y^2 cos x) dA = ∫_0^(π/2) [(y * x + y^2 sin x)]|_(-5)^(5) dy

Now we have an expression in terms of y only. We substitute the limits of integration for x, which are -5 and 5, into the expression (y * x + y^2 sin x) and evaluate it:

∫_S (y + y^2 cos x) dA = ∫_0^(π/2) [5y + y^2 sin 5 - (-5y - y^2 sin(-5))] dy

Simplifying further:

∫_S (y + y^2 cos x) dA = ∫_0^(π/2) [10y + 2y^2 sin 5] dy

Now we integrate the expression [10y + 2y^2 sin 5] with respect to y over the range 0 to π/2:

∫_S (y + y^2 cos x) dA = [5y^2 + (2/3)y^3 sin 5] |_0^(π/2)

Evaluating the expression at the limits:

∫_S (y + y^2 cos x) dA = [5(π/2)^2 + (2/3)(π/2)^3 sin 5] - [5(0)^2 + (2/3)(0)^3 sin 5]

Simplifying:

∫_S (y + y^2 cos x) dA = [5(π^2/4) + (2/3)(π^3/8) sin 5] - [0]

Finally, we simplify the expression:

∫_S (y + y^2 cos x) dA = 5π^2/4 + (π^3/12) sin 5

Therefore, the value of the iterated integral 5∫_(-5)^(5) ∫_0^(π/2) (y + y^2 cos x) dx dy is 5π^2/4 + (π^3/12) sin 5.

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Answer:

Step-by-step explanation:

false that is not at all true

Answer:  The equation of the line is x = 4.

Step-by-step explanation:  We are given to write the standard form the equation of a line which passes through the point (4, 1) and parallel to the line x = 0.

All the lines parallel to the line x = 0 are given by the following equation

Also, since the line passes through the point (4, 1), so equation (i) must be satisfied by the point (4, 1).

Substituting the point (4, 1) in equation (i), we have

which is the standard equation of the line.

The graphs of the lines x = 0 and its parallel line x = 4 passing through the point (4, 1) are shown in the attached figure.

Thus, the required equation of the line is x = 4.

Answer:

Step-by-step explanation:

-19y=-13x -14 to y=-13/-19 - -14/-19

Answer:

65 degree

Step-by-step explanation:

reason: opposite angles of a parallelogram are equal

Given statement solution is :- The value of m is -98/9.

The correct answer is A. -98/9.

To determine the value of m in the given system of equations, we need to find the condition under which the system has no solutions.

The system of equations can be written in matrix form as:

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Copy code

[  9  -7 ]   [ x ]   [ 11 ]

[ 14   m ] * [ y ] = [  6 ]

For this system to have no solutions, the coefficient matrix [ 9 -7 ; 14 m ] must be singular, which means its determinant must be zero.

Determinant of the coefficient matrix:

det([ 9 -7 ; 14 m ]) = (9 * m) - (-7 * 14) = 9m + 98

Setting the determinant equal to zero, we have:

9m + 98 = 0

Solving for m:

9m = -98

m = -98/9

Therefore, the value of m is -98/9.

So, the correct answer is A. -98/9.

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Answer:0.416667

Step-by-step explanation:

5 inches equal 0.4166666667 feet (5in = 0.4166666667ft). Converting 5 in to ft is easy. Simply use our calculator above, or apply the formula to change the length 5 in to ft.

Answer:

as 1 inch = 0.0833333 ft

so

5inch = 5(0.0833333)

= 0.416667

Step-by-step explanation:

Step-by-step explanation:

so, he predicted he had 12 questions wrong.

that would have been a score of 38.

but he got 42.

that is a difference of 42-38 = 4.

now, accuracy could have different meanings like actual score vs. predicted score, or which questions were right or wrong (for real or predicted), or only looking at the questions that were right (real vs. predicted), ...

I assume it is the first one.

so,

100% = 38 (prediction)

1% = 100%/100 = 38/100 = 0.38

how many % are these 4 questions that his prediction was off from reality ?

4 / 0.38 = 10.52631579...

so, his prediction was off by about 10.53%

Answer:

(1) Executive Administrative Assistant

(2) Receptionist

(3) File Clerk

(4) Administrative Assistant

Step-by-step explanation: edge 2020

Answer: (1) Executive Administrative Assistant (2) Receptionist (3) File Clerk (4) Administrative Assistant

Step-by-step explanation: I just finished and got it correct

Answer:

area = 314 ft²

Step explanation:

20/2 = 10 = radius

10²(3.14) = 314 ft²

The solution is, the solutions using the Zero Product Property: is x =0 and 3/4.

The expression to be solved is:

4x² - 3x = 0

we know that,

The zero product property states that the solution to this equation is the values of each term equals to 0.

now, we have,

4x² - 3x = 0

or, x ( 4x - 3 ) = 0

i.e. we get,

x × ( 4x - 3 ) = 0

so, using the Zero Product Property:

we get,

x = 0

or,

( 4x - 3 ) = 0

so, we have,

x = 0 or, x = 3/4

The answers are 0 and 3/4.

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Answer:

the answer to A,B,C

Step-by-step explanation:

all the points are on the graph

all answers

b) slope -1

intercept 1

c)(x+3)(x-1)

intercepts (-3,0),(1,0)

vertex (-1,-4)

Answer:

6*6+16*20

=320+36

=356 so it's C

Answer:

C: 356 sq ft.

Step-by-step explanation:

Imagine a rectangle filling the empty space in the polygon.

Using this, we get 440 sq ft.

Now subtract the area that you filled in.

440-(14x6)=A

440-84=A

356=A

Answer:

8 weeks

Step-by-step explanation:

433-145=288

288÷36=8

The roots of the auxiliary equation are r = (-1 ± √(1 + 16/x^2)) / x.

The general solution of the differential equation is y(x) = c_1 x^4/16 + c_2 x^(-1/2) cos(ln x) + c_3 x^4/16 + c_4 x^(-1/2) sin(ln x), where c_1, c_2, c_3, and c_4 are arbitrary constants

The auxiliary equation for the given differential equation is obtained by assuming a solution of the form y(x) = e^(rx), where r is a constant. Substituting this solution into the differential equation, we get:

x^2(e^(rx))'' + x(e^(rx))' - 16(e^(rx)) = 0

Differentiating twice, we get:

r^2x^2 e^(rx) + 2rx e^(rx) + x e^(rx) + x e^(rx) - 16 e^(rx) = 0

Simplifying and factoring out e^(rx), we get:

e^(rx) (r^2x^2 + 2rx - 16) = 0

For nontrivial solutions, we must have e^(rx) ≠ 0, which implies that the quadratic expression in the parentheses must be zero. Thus, we need to solve the equation:

r^2x^2 + 2rx - 16 = 0

Using the quadratic formula, we get:

r = [-2x ± √(4x^2 + 64x^2)] / (2x^2) = [-x ± √(x^2 + 16)] / x

The roots of the auxiliary equation are therefore:

r = (-1 ± √(1 + 16/x^2)) / x

To solve the differential equation, we need to find two linearly independent solutions. Since the roots of the auxiliary equation are complex when x > 0, we can write the solutions in terms of exponentials of complex numbers as follows:

y_1(x) = x^4/16 + x^(-1/2) cos(ln x)

y_2(x) = x^4/16 + x^(-1/2) sin(ln x)

Thus, the general solution of the differential equation is:

y(x) = c_1 x^4/16 + c_2 x^(-1/2) cos(ln x) + c_3 x^4/16 + c_4 x^(-1/2) sin(ln x)

where c_1, c_2, c_3, and c_4 are arbitrary constants determined by the initial conditions of the problem.

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tan (0.9269428)

Decimal form=1.33235488...

Answer:

the answer is 2.4 .

Step-by-step explanation:

plug in arccos(5/13) in the calculator and u will get 67.380, then plug that value in for tan and you will get 2.4.

The area of the region shaded with red is 13.02 square inch.

The quadrant of a circle is one fourth part of it.

Its area can be calculated by taking one fourth of the total area of the circle as πr²/4.

The quadrant of a circle subtends right angle to its centre.

The area of the shaded region can be obtained as follows,

Shaded region  area = Area of the region between circles  + Area of one circle

Now, area between the circles is given as,

Area of the square formed by joining the centres - Area of the four quadrants made by them.

When, the centre of the circles are joined,

Each side of square = Diameter of the circle = 3 inches.

Then, the area of square = 3 × 3 = 9

And the area of one quadrant = 1/4 × πr² = 1/4 × π × 1.5² = 1.76

Then, shaded region area =  π × 1.5² + (9 - 4 × 1.76) =  13.02

Hence, the required area is obtained as 13.02 square inch.

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Answer:

y = mx + b

Step-by-step explanation:

The slope intercept formula y = mx + b is used when you know the slope of the line to be examined and the point given is also the y intercept (0, b). In the formula, b represents the y value of the y intercept point.

A person works a standard 40 hour work week, at 30 an hour this would be an annual salary of 62,400

Assuming a person works a standard 40 hour work week, at 30 an hour this would be an annual salary of 62,400 (30 x 40 hours x 52 weeks). This salary also assumes that the person does not take any vacation or sick days.

30 an hour is above the median household income in the United States, which is 59,039 (Source: U.S. Census Bureau, 2017). However, it is important to consider the cost of living in the area in which the person resides. It is possible to live on 30 an hour in some areas, but not in others. For example, according to the cost of living calculator provided by the Missouri Economic Research and Information Center, a person needs an hourly wage of 21.75 to make ends meet in St. Louis, Missouri. In contrast, a person needs an hourly wage of 41.19 to make ends meet in New York City, New York.

To calculate the annual salary of a person making 30 an hour, the following equation can be used: 30 x 40 hours x 52 weeks = $62,400. This equation assumes that the person works a standard 40 hour work week and does not take any vacation or sick days. If the person takes vacation or sick days, this equation would need to be modified to account for the days taken off.

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Answer:

A. plant 3; plant 3

Step-by-step explanation:

Plant 3 was the tallest at the beginning. We know this because it is the plant with the highest recorded height at time = 0.

Plant 1 grew 3.5 inches over 6 weeks.

Plant 2 grew ~ 2.25 inches over 6 weeks.

Plant 3 grew 4 inches over 6 weeks.

> This means that plant 3 grew the most, or had the greatest rate of change, over the 6 weeks.

To determine the cricket population after x months, where the initial population is 40 crickets and it doubles in size every month, the equation is P = 40 * 2^x. After 1 1/2 years (18 months), the population will be 10,485,760 crickets.

The equation P = 40 * 2^x represents the cricket population after x months. The initial population of 40 crickets is multiplied by 2 raised to the power of x, where x represents the number of months. This accounts for the doubling effect of the population each month.
To find the population after 1 1/2 years (18 months), we substitute x = 18 into the equation:
P = 40 * 2^18
Calculating 2^18 gives us 262,144. Multiplying this by the initial population size of 40, we have:
P = 40 * 262,144 = 10,485,760
Therefore, after 1 1/2 years, the cricket population will be 10,485,760 crickets. This demonstrates the exponential growth pattern, as the population doubles in size every month.

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The mean for boxplot #3 should be less than its median. In a negatively skewed distribution, the mean is less than the median.

This is because the few small values in the data pull the mean down, while the median is still at the middle value. A boxplot can give us an idea of the shape of the distribution, and if it is negatively skewed, it suggests that the mean will be less than the median.

It's important to note that without actually seeing the boxplot, this conclusion may not be accurate. There could be other factors that affect the mean and median, such as outliers or the size of the sample. However, based on the information given that the boxplot is negatively skewed, it is likely that the mean will be less than the median.

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Answer: -2.1p + 1.7

2.4 - 6p - 0.7 + 3.9p

Subtract 6p from 3.9p. (-2.1p)

Subtract 0.7 from 2.4. (1.7)

They are used in navigation, astronomy, and surveying. Rays are also used in computer graphics, physics, and optics. In addition, rays are used in the study of optics to describe the behavior of light as it travels through different mediums.

According to the video above, the geometric object called a ray has the characteristics that it has one endpoint and extends in away from that endpoint without end.A ray is a line that starts at a single point and extends in one direction to infinity. Rays are commonly used in geometry to explain lines and line segments. A ray has one endpoint, called the endpoint of the ray, from which it starts. The other end of the ray continues in the direction in which it is pointed without any limit. A ray is named by using its endpoint and another point on the ray, with the endpoint first. For example, if ray A starts at point P and passes through point Q, we write the name of the ray as ray PAQ or ray QAP. Rays can be part of line segments and other geometric objects. They can also be used to explain angles and the direction of a light source. Rays are commonly used in mathematics, science, and engineering.

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Using cdf the following results are obtained of the given function F(x) = 0 x < 0 x2 49 0 ≤ x < 7 1 7 ≤ x

P(X ≤ 5) = 0.7813

P(4.5 ≤ X ≤ 5) = 0.0977

P(X > 5.5) = 0.1211

Median checkout duration = 4.6904

f(x) = (2x/49) for 0 ≤ x < 7, and 0 elsewhere

E(X) = 3.5 hours

V(X) = 2.4231 hours^2, and σ_x = 1.5564 hours

E[h(X)] = 10.9375

(a) P(X ≤ 5) = F(5) - F(0) = (5^2/49) - 0 = 0.7813

(b) P(4.5 ≤ X ≤ 5) = F(5) - F(4.5) = (5^2/49) - (4.5^2/49) = 0.0977

(c) P(X > 5.5) = 1 - F(5.5) = 1 - 1 = 0

(d) Solve 0.5 = F(median) for median, which gives median = 4.6904

(e) f(x) = dF(x)/dx = (4x/49) for 0 ≤ x < 7, and 0 elsewhere

(f) E(X) = ∫x f(x) dx = 3.5 hours

(g) V(X) = ∫(x-E(X))^2 f(x) dx = 2.4231 hours^2, and σ_x = sqrt(V(X)) = 1.5564 hours

(h) E[h(X)] = ∫h(x) f(x) dx = 10.9375

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Answer:

104

Step-by-step explanation:

A rhombus diagonal bisect each other so that means half of the diagonal is equal to the other half.

Applying that, this means

Since they are equal we can divide AC by 2 to find AE and EC.

20/2=10

AE=10, EC=10

Same for DB

48/2=24

DE=24, EB=24

A rhombus diagonals are perpendicular to each other so each middle angle will measure 90 degree.

Looking closer, a rhombus has 4 right triangles. We only need to use one.

Look at triangle AEB. We know AE=10 and EB=24 and Angle E=90. We can apply pythagorean theorem to find side AB.

\( {ae}^{2} + {db}^{2} = {ab}^{2} \)

\( {10}^{2} + {24}^{2} = {ab}^{2} \)

\(100 + 576 = ab {}^{2} \)

\(676 = {ab}^{2} \)

\( \sqrt{676} = 26\)

The perimeter of rhombus is equal to

4a, where a is the length of one side.

One side measures 26 so we can plug that in.

\(26 \times 4 = 104\)