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The function in terms of the time (t) is t=d/r and the value of the time (t) for the given values is 5.

An equation can be represented by a linear function. The standard form for the linear equation is: ax+b , for example, y=2x+7. Where:

a= the slope

b=constant term that represents the y-intercept.

For the given example: a=2 and b=7.

In the exercise is asked the equation for the time (t) in the function of the distance (d) and the rate (r).

Thus, if d=rt, we will have t= d/r

Replacing the variables for the given values for finding t. The question gives:

distance (d) =40

rate (r) = 8

Thus, you will have t= 40/8. Then, t=5

Therefore, the answer is the fourth option.

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Based on the random sample of beach lengths taken, the probability of a randomly selected beach having a length of 12 miles is C. 0.

Beach length is considered a continuous variable which takes a numerically positive form because it can have any one of infinite possible values.

As a result, there is no possibility that a beach chosen at random will have a given length of 12 miles which means that the probability is 0.

In conclusion, the probability that a selected beach has a length of 12 miles is 0.

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1) Given - This is given in the question.

2) Reflexive Property of Equality - Anything is equal to itself

3) Substitution Property of Equality - Due to the given, substituting 118° for m∠1 and 62° for m∠2 will not change the equality of the equation

4) Simplify - No need to explain as they have already given this

5) Definition of Supplementary Angles - Two angles are supplementary only when the sum of their measures is 180°.

6) Converse of Same-side Interior Angles Theorem - If there is a transversal intersecting two lines and the same-side interior angles formed are supplementary, then the lines are parallel.

1) Given - It is given in the question

2) Vertical Angles Theorem - Vertical angles have the same measure, making their angles congruent

3) Transitive Property of Congruence - Since it's given that [tex]\angle1\cong\angle3[/tex] and in step 2 we showed that [tex]\angle3\cong\angle4[/tex], we can say that [tex]\angle1\cong\angle4[/tex]

4) Transitive Property of Congruence - Since we proved that [tex]\angle1\cong\angle4[/tex] and it's given that [tex]\angle4\cong\angle5[/tex], we can say that [tex]\angle1\cong\angle5[/tex]

5) Converse of Alternate Interior Angles Theorem - If a transversal intersects two lines and the measures of alternate interior angles formed are equal, then the lines are parallel.

The rectangular representation of the polar point of (4 , 300) is (2,- 2√3)

According to the statement

we have given a coordinates of the rectangle and we have to find the polar coordinates.

So, For this purpose, we know that the

We Use the conversion formulas to convert from polar coordinates to rectangular coordinates which are

x = rcosθ

y = rsinθ

Substitute the given values in it then

x=(4)cos(300)

y=(4)sin(300)

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.

x=(4)cos(60) -(1)

y= - (4)sin(60) -(2)

And then

x=(4)cos(60)  

x=(4)(1/2)

x = 2 -(3)

and

y= - (4)sin(60)

y= - (4)(√3/2)

y= - 2√3 -(4)

Replace (3) with (1) and (4) with (2)

then it becomes

x = 2 and y= - 2√3

The rectangular representation of the polar point of (4 , 300) is (2,- 2√3)

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Answer:

Step-by-step explanation:

<E = <T                                Given

M is the midpoint of TE      Given

TM = ME                               Definition of a  midpoint

<TMI = <RME                        Property of Vertically Opposite Angles

ΔTMI = ΔRME                       ASA = ASA

MI = ME                                 Corresponding parts of Congruent triangles                                    are Congruent

answer:                              reasoning:

<E = <T                                given

M is the midpoint of TE      given

TM = ME                               definition of a  midpoint

<TMI = <RME                        property of Vertically Opposite Angles

ΔTMI = ΔRME                       ASA = ASA

MI = ME                                 corresponding parts of congruent triangles                                    are Congruent

hope this helps!

Answer:

Step-by-step explanation:

Option C.

Step-by-step explanation:

Initial number of clients = 18

Number of Increase per week = 4

We need to use an arithmetic sequence to write a function.

So, the required arithmetic sequence for four weeks is

18, 22, 26, 30

Here, first term is 18 and common difference is 4. The range is  [18,30].

The explicit formula of n arithmetic sequence is

where, a is first term and d is common difference.

Substitute a=18 and d=4 in the above formula.

The function notation is

The function is f(x)=4x+14 and the range is  18 ≤ y ≤ 30.

Therefore, the correct option is C.

Answer: $2250

Step-by-step explanation:

Given information

Dimension of the room = 20 feet × 15 feet

Cost of tiles = $7.50 / ft²

Derived formula from the given information

Total cost = Floor area × Cost of tiles

Substitute values into the formula

Total cost = Floor area × Cost of tiles

Total cost = (20 × 15) × (7.5)

Simplify by multiplication

Total cost = 300 × (7.5)

[tex]\Large\boxed{Total~cost~=~2250~Dollars}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

True

Step-by-step explanation:

Plotting the point of any linear equation on a graph gives a straight line

One way to capture the domain of integration is with the set

[tex]D = \left\{(x,y) \mid 0 \le x \le 1 \text{ and } -x \le y \le 0\right\}[/tex]

Then we can write the double integral as the iterated integral

[tex]\displaystyle \iint_D \cos(y+x) \, dA = \int_0^1 \int_{-x}^0 \cos(y+x) \, dy \, dx[/tex]

Compute the integral with respect to [tex]y[/tex].

[tex]\displaystyle \int_{-x}^0 \cos(y+x) \, dy = \sin(y+x)\bigg|_{y=-x}^{y=0} = \sin(0+x) - \sin(-x+x) = \sin(x)[/tex]

Compute the remaining integral.

[tex]\displaystyle \int_0^1 \sin(x) \, dx = -\cos(x) \bigg|_{x=0}^{x=1} = -\cos(1) + \cos(0) = \boxed{1 - \cos(1)}[/tex]

We could also swap the order of integration variables by writing

[tex]D = \left\{(x,y) \mid -1 \le y \le 0 \text{ and } -y \le x \le 1\right\}[/tex]

and

[tex]\displaystyle \iint_D \cos(y+x) \, dA = \int_{-1}^0 \int_{-y}^1 \cos(y+x) \, dx\, dy[/tex]

and this would have led to the same result.

[tex]\displaystyle \int_{-y}^1 \cos(y+x) \, dx = \sin(y+x)\bigg|_{x=-y}^{x=1} = \sin(y+1) - \sin(y-y) = \sin(y+1)[/tex]

[tex]\displaystyle \int_{-1}^0 \sin(y+1) \, dy = -\cos(y+1)\bigg|_{y=-1}^{y=0} = -\cos(0+1) + \cos(-1+1) = 1 - \cos(1)[/tex]

Answer:

  305 °F

Step-by-step explanation:

The core temperature of the object after 4 hours can be found using an exponential decay formula to model the decay of the difference between core temperature and ambient.

The solution to the differential equation described by Newton's law of cooling is the exponential equation ...

  y = ab^t +c

where 'a' is the initial core temperature difference from ambient, 'b' is the decay factor of that difference in 1 unit of time period t. 'c' is the ambient temperature.

For this problem, the ambient temperature is c=80, and the differences of interest are ...

  a = 1200 -80 = 1120

  b = (830 -80)/1120 = 75/112

Using these values in the model gives ...

  y = 1120(75/112)^t +80 . . . . . . where y(t) is the core temperature at time t

Note that units of time are hours.

We want y when t=4.

  y = 1120(75/112)^4 +80 ≈ 1120(0.20108) +80 ≈ 305.212

The core temperature after 4 hours is about 305 °F.

__

Additional comment

The differential equation will have a solution of the form ...

  [tex]T-T_R=(T_0-T_R)e^{kt}[/tex]

where k = ln(75/112) ≈ -0.40101

In the above, we defined b = e^k = 75/112. Accuracy with this fraction can be better than using a truncated value of k.

The distance and direction of the ship from its original point of course correction is 33 miles and 23° respectively.

An equation is an expression that shows the relationship between two or more numbers and variables.

Pythagoras theorem is used to show the relationship between the sides of a right angled triangle.

Let x represent the distance travelled, hence:

x² = 14² + 30²

x = 33 miles

tanФ = 14/33

Ф = 23°

The distance and direction of the ship from its original point of course correction is 33 miles and 23° respectively.

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109×50

100×50+9×50=5000+450

5450

Answer:

5450

Step-by-step explanation:

You can just use a caculater to get the answer.

He needs to run with approximately 6429 for a distance of 9 km

The given parameters are:

Length of stride = 1.4 m

Distance for marathon = 9 km

The number of strides needed is then calculated as:

Number of stride = Distance for marathon/Length of stride

Substitute the known values in the above equation

Number of stride = 9km/1.4m

Convert km to m

Number of stride = 9000m/1.4m

Evaluate the quotient

Number of stride = 6428.57143

Approximate the estimate

Number of stride = 6429

Hence, he needs to run with approximately 6429 for a distance of 9 km

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Answer:

60

Step-by-step explanation:

60 + y + y = 180

2y = 120

y = 60

Answer: Madison can travel 2.2 miles less than Anthony on one gallon of gas.

Step-by-step explanation:

The equation y = 39.1[tex]x[/tex] represents the number of miles, [tex]y[/tex], that madison can drive her car for every x gallons of gas.

Question: Madison can travel _ miles _ than Anthony on one gallon of gas.

Lets find how much Madison travels on 1 gallon of gas.

39.1(1) = 39.1

Therefore, Madison travels 39.1 miles on one gallon of gas.

Now lets solve for Anthony

Anthony travels 380.7 miles on 9 gallons of gas.

Therefore we can set up the equation:

9x = 380.7 to show that 9 gallons equates to 380.7 miles

to solve divide 9 from both sides

[tex]\frac{9x}{9} =\frac{380.7}{9}[/tex]

x = 41.3

So, Anthony travels 41.3 miles on one gallon of gas

Now find whether Madison travels more or less than Anthony on one gallon.

39.1 - 41.3 = -2.2

This means that Anthony can travel 2.2 miles more than Madison.

For your answer, this means that:

Madison can travel 2.2 miles less than Anthony on one gallon of gas

Hope this helped and have a nice day :)

The probability that it will rain on exactly one of the three days they are there is 0.375.

Given that Hiking Club plans to go camping in a State park where the probability of rain on any given day is 50%.

The binomial distribution is used when there are exactly two outcomes of a trial that are mutually exclusive.

Use binomial probability:

P = ⁿCʳ pʳ (1−p)ⁿ⁻ʳ

where n is the number of trials,

r is the number of successes,

and p is the probability of success.

probability of rain on any given day =p =0.50

total number of ways,n=3

let X is number of days with rain out of 3 days

So, [tex]X\sim Bin(3,0.50)[/tex]

P(x=X)=ⁿCₓpˣ(1-p)ⁿ⁻ˣ

P(x=1)=³C₁(0.50)¹(1-0.50)³⁻¹

P(x=1)=3×0.50×(0.5)²

P(x=1)=1.5×0.25

P(x=1)=0.375

Hence, the probability that it will rain on exactly one of the three days they are there where the probability of rain on any given day is 50% is 0.375.

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The expression that represents the number of reams of paper the company produced during the second year is 4.704 × 10¹⁰. The correct option is D. 4.704 × 10¹⁰

From the question, we are to determine the expression that represents the number of reams of paper the company produced during the second year

From the given information,

During the first year of operation,

The company produced 8.4 × 10⁹ reams of paper

And

During the second year,

the company produced 5.6 times the number of reams of paper that it produced during the first year.

Thus,

The number of reams of paper the company produced during the second year = 5.6 × 8.4 × 10⁹ reams of paper

The number of reams of paper the company produced during the second year = 47.04 × 10⁹ reams of paper

= 4.704 × 10¹ × 10⁹ reams of paper

= 4.704 × 10¹⁰ reams of paper

Hence, the expression that represents the number of reams of paper the company produced during the second year is 4.704 × 10¹⁰. The correct option is D. 4.704 × 10¹⁰

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the height of the pentagonal pyramid is 5. 70 meters

The formula for determining the volume of a regular pentagonal pyramid is given as;

V=5/12tan(54°)ha^2

Where

We have the volume to be;

volume = 82. 5 cubic centers

height = h

a = 5m

Substitute the values

[tex]82. 5 = \frac{5}{12}[/tex] × [tex]tan 54[/tex] × [tex]h[/tex] ×[tex]5^2[/tex]

[tex]82. 5 = 0. 42[/tex] × [tex]1. 3764[/tex] × [tex]25[/tex] × [tex]h[/tex]

Make 'h' subject of formula

[tex]h = \frac{82. 5}{14. 45}[/tex]

h = 5. 70 meters

The height of the pentagonal pyramid is 5. 70 meters

Thus, the height of the pentagonal pyramid is 5. 70 meters

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Answer:

The value of b equals to

[tex] \frac{5}{72} [/tex]

Step-by-step explanation:

steps given below

given expression

[tex]b + \frac{3}{8} = \frac{4}{9} \\ [/tex]

subtract

[tex] \frac{3}{8} [/tex]

from both sides

[tex]b + \frac{3}{8} - \frac{3}{8} = \frac{4}{9} - \frac{3}{8} \\ b = \frac{4}{9} - \frac{3}{8} [/tex]

To, continue find the L.C.M of 9 and 8 thus, it's 72

So, plug 72 and solve the expression as follows

[tex]let \: \frac{a}{c} - \frac{b}{c} = \frac{a - b}{c} \\ b = \frac{32 - 27}{72} = \frac{5}{72} [/tex]

Hope it helps!

Answer:

answer

Step-by-step explanation:

To see whether or not two lines are parallel, we must compare their slopes. Two lines are parallel if and only if their slopes are equal. The line 2x – 3y = 4 is in standard form. In general, a line in the form Ax + By = C has a slope of –A/B; therefore, the slope of line q must be –2/–3 = 2/3.

Answer:

72 Degrees

Step-by-step explanation:

10 / 50 = 0.2

A circle has 360 degrees.

0.2 X 360 = 72

Answer:

B

Step-by-step explanation:

• the opposite sides of a parallelogram are congruent , then

ZY = WX , that is

5x - 6 = 4x + 1 ( subtract 4x from both sides )

x - 6 = 1 ( add 6 to both sides )

x = 7

• the diagonals bisect each other , then

ZT = TX = 2x = 2 × 7 = 14

Using proportions, it is found that the two cities are 27.5 miles apart.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

From the given scale, we have that each inch of distance represents 10 miles. Hence the distance in miles for a distance of 2 and 3/4 miles = 2.75 miles is given by:

D = 10 x 2.75 = 27.5 miles.

Hence, the two cities are 27.5 miles apart.

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Answer:

a = 3

b = -9

c = -3

d = 22

e = 49 - 9

f = a^2 -3

Step-by-step explanation:

Please no more questions :(

Answer:

0.28

Step-by-step explanation:

Depreciation Expense per mile:

= (Cost of delivery truck - Salvage value) ÷ Expected miles driver

=(33000-2760)÷108000=0.28 per mile

The slope of the graph is 1 / 5.

A slope of a line is the change in y coordinate with respect to the change in x coordinate.

Slope describes the steepness of a line. The slope of any line remains constant along the line.

Therefore,

slope  = y₂ - y₁ / x₂ - x₁

Hence, let's take two coordinates in the graph,

(2, 2)(7, 3)

x₁ =  2

x₂ = 7

y₁ = 2

y₂ = 3

Therefore,

slope = 3 - 2 / 7 - 2

slope = 1 / 5

Therefore, the slope of the graph is 1 / 5.

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The percentages for each outcome are given as follows:

a) 34.4%.

b) 29.4%.

The percentage of an amount a over a total amount b is given by a multiplied by 100% and divided by b, that is:

P = a/b x 100%

For this problem, we already have the percentages, hence we just combine them.

For item a, he can be late in two ways, one that happens 24.4% of the time(waking up late), and the other 10%(stuck in traffic), hence the percentage is of 34.4%, as 24.4% + 10% = 34.4%.

For item b, the percentage stuck in traffic is of 5%, hence the percentage that he will be late is 24.4% + 5% = 29.4%.

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