PLEASE SHOW WORK…!!!!!!!

His speed for the remaining 26 km of the course is given as follows:

24.3 km/h.

The relation between velocity, distance and time states that the velocity is obtained by the quotient of the distance by the time, as follows:

v = d/t.

In which the parameters are given as follows:

The time is obtained as the distance divided by the velocity, hence:

t = d/v.

Then the time taken for the first 29 km is given as follows:

t = 29/15

t = 1.93 hours.

180 minutes = 3 hours, hence he took 1.07 hours for the remaining 26 km, hence the velocity is of:

v = 26/1.07

v = 24.3 km/h.

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The area of rhombus KLMN is 287.3 in²

A rhombus is a quadrilateral whose four sides all have the same length. Another name is equilateral quadrilateral, since equilateral means that all of its sides are equal in length.

Given that, a rhombus KLMN with diagonals KM and NL,

Since, the diagonals of a rhombus bisects each other at a right angle,

Let they bisect at O, so, KM = 2MO = 2KO = 2×11.4 = 22.8 in

Therefore, Δ KON is a right triangle,

Using Pythagoras theorem,

KN² = KO² + ON²

ON = √17²-11.4²

ON = 12.611 in

LN = 2×12.611

LN = 25.22 in

Area of a rhombus = 1/2 × diagonal 1 × diagonal 2

Area = 1/2 × 25.22 × 22.8

= 287.3 in²

Hence, the area of rhombus KLMN is 287.3 in²

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Answer:

There are 31 quarters.  

There are 47 dimes.  

Step-by-step explanation:

let q = number of quarters

let d = number of dimes

d = 16 + q      

.10d + .25q = 12.45  Multiply through by 100

10d + 25q = 1245       Substitute 16 + q for d

10(16 + q) + 25q = 1245    Distribute the 10

160 + 10q + 25q = 1245  Combine like terms

160 + 35q = 1245  Subtract 160 from both sides

160 - 160 + 35q = 1245 - 160

35q = 1085  Divide both sides by 35

q = 31

There are 31 quarters.    

Substitute 31 for q

d = 16 + 31

d = 47

There are 47 dimes.

Check:

d = 16 + q

47 = 16 + 31

47 = 47  Checks

.10d + .25q = 12.45

.10(47) + .25(31) = 12.45

4.70 + 7.75 = 12.45

12.45 = 12.45  Checks.

Answer:

There are 31 quarters and 47 dimes.

Step-by-step explanation:

To solve this problem, we can create and solve a system of equations.

Define the variables:

Values of the coins:

Given a coin bank contains $12.45 in quarters and dimes:

Given there are 16 more dimes than quarters:

Therefore, the system of equations that represents the problem is:

[tex]\begin{cases} 0.25q + 0.10d = 12.45\\d = q + 16\end{aligned}[/tex]

Substitute the second equation into the first equation to eliminate d:

[tex]0.25q+0.10(q+16)=12.45[/tex]

Solve the equation for q to find the number of quarters:

[tex]\begin{aligned}0.25q+0.10(q+16)&=12.45\\0.25q+0.10q+1.6&=12.45\\0.35q+1.6&=12.45\\0.35q&=10.85\\q&=31\end{aligned}[/tex]

Therefore, there are 31 quarters.

Substitute the found value of q into the second equation and solve for d:

[tex]\begin{aligned}d &= q + 16\\&= 31 + 16\\&= 47\end{aligned}[/tex]

Therefore, there are 47 dimes.

Answer:

Step-by-step explanation:

There are 16 ounces in 1 pound. Take 3/4 and multiply it by 16.

3/4 x 16 ounces = 12 ounces

There are 12 ounces in 3/4 lb.

The chef uses 1/8 of the 12 ounces (or 3/4 lb) of cheese for the top of the lasagna.

1/8 of 12 ounces

1/8 x 12 ounces = 1.5 ounces

The chef uses 1.5 ounces for the top of the lasagna.

To convert the ounces to pounds, use 1 lb/16 ounces. The ounces cancel and you are left with pounds.

1.5 ounces x (1 lb/16 ounces) = 0.09375 lb

Answer:

Step-by-step explanation:

The volume of a cube is the edge length cubed (S^3)

To find the edge length when the volume is known find the cubic root of the volume.

Edge = ∛1/27

Edge = 1/3 ft.

Answer:

Depreciation is the decrease in value of an asset over time. We know that the value of the equipment depreciates at a rate of 20% per year, and after 5 years the equipment is worth $98,304. We can use this information to set up an equation to find the original value of the equipment.

Let X be the original value of the equipment.

We know that:

X * (1 - 0.20)^5 = 98304

Where (1 - 0.20) is the depreciation rate, and the exponent 5 is the number of years.

We can solve for X by using the following steps:

X * (1 - 0.20)^5 = 98304

X * (0.8)^5 = 98304

X = 98304 / (0.8)^5

X = $143,680

So, the original value of the equipment was $143,680.

Step-by-step explanation:

Answer:

Given;

Total number of pencil=55

number of pencil lost=11

Then,

percentage of pencil lost=((Number of pencil lost/Total number of pencil)*100)

% of pencil lost= ((11/55)*100)

% of pencil lost=0.2*100

% of pencil lost=20%

Therefore,

The percentage of pencil lost is 20%

The probability of getting at least one question wrong on a 6 question multiple-choice test is 0.9874

Probability is the function that measures the chances that an outcome of a random event will be as expected. In this way you can measure how likely it is that an event will happen.

Probability requested is equivalent to:

P(get one question right) = 1/2

P (get all questions right) = (1/2)^6

P(get one question wrong) = 1 - P (get all questions right)

P(get one question wrong) = 1 - (1/2)^6

P(get one question wrong) = 0.9874

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As per the standard deviation the proportion of observations is in the interval between each pair of values is 190 and 310

The term in math known as standard deviation is defined as a measure of how dispersed the data is in relation to the mean.

Here we have know that the mean of a population is 250 and its standard deviation is 20.

Then the proportion of observations is in the interval between each pair of values is calculated as,

We have interval (190,310) and we can express this interval as:

=> (190,310) = (250−3⋅20, 250+3⋅20)

According to this interval , we have that k=3.

Based on the value of the constant the required percent of observations in interval(190,310) is at least 88.9%

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30 hot dogs would contribute $60 to the GDP and 20 hamburgers would also contribute $60 to the GDP.

The calculation for the number of hamburgers that would contribute the same to the GDP as 30 hot dogs is as follows:

GDP (Hot Dogs) = 2 x 30 = 60

GDP (Hamburgers) = 3 x x = 60  

Therefore, the number of hamburgers needed to equal the GDP of 30 hot dogs is equal to 20:

GDP (Hamburgers) = 3 x 20 = 60

Therefore, the answer is C) 20.

To explain this in more detail, Gross Domestic Product (GDP) is a measure of the total value of all goods and services produced in a country during a specific period of time. It is calculated by multiplying the price of a good or service by the amount produced. In this case, the price of a hot dog is $2 and the price of a hamburger is $3. Therefore, 30 hot dogs would contribute $60 to the GDP and 20 hamburgers would also contribute $60 to the GDP.

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The statement which is strictly true for algorithms is :

Option d. Each step of algorithms should be very clear and unambiguous.

Therefore, the option d. each step of algorithms represents steps clearly and unambiguous is the true statement of algorithms.

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The integral function is equal to, Integral [tex]\int\limits^[/tex] y[tex]e^{6y}[/tex] dy = [tex]\frac{1}{36}[/tex] [ 7[tex]e^{-2}[/tex] - 1 ]

An integral in mathematics is either a numerical value equal to the area under the graph of a function for some interval or a new function, the derivative of which is the original function (indefinite integral).

In calculus, an integral is a mathematical object that can be interpreted as an area or a generalization of area. Integrals, together with derivatives, are the fundamental objects of calculus. Other words for integral include antiderivative and primitive.

Given that,

Integral [tex]\int\limits^[/tex] y[tex]e^{6y}[/tex] dy

=  [tex]\int\limits^[/tex] y d([tex]e^{6y}[/tex])

= [ y ([tex]\frac{e^{6y} }{6}[/tex]) - [tex]\int\limits^[/tex] (1)  ([tex]\frac{e^{6y} }{6}[/tex]) ]

= [tex]\frac{ye^{-6y} }{6}[/tex] + [tex]\frac{e^{-6y} }{36}[/tex]  where, 0 and 1

= [ [tex]\frac{1}{6e^{2} }[/tex] + [tex]\frac{1}{36e^{2} }[/tex] ] - [1/36]

= [ 7/36[tex]e^{2}[/tex] ] - [1/36]

= [tex]\frac{1}{36}[/tex] [ 7[tex]e^{-2}[/tex] - 1 ]

Therefore,

The integral function is equal to, Integral [tex]\int\limits^[/tex] y[tex]e^{6y}[/tex] dy = [tex]\frac{1}{36}[/tex] [ 7[tex]e^{-2}[/tex] - 1 ]

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Answer:

c = 3n + 5

Step-by-step explanation:

The equation c = 3n + 5 fits the data in the table. When n = -7, c = -7 * 3 + 5 = -16. When n = -6, c = -6 * 3 + 5 = -13. When n = 3, c = 3 * 3 + 5 = 14. When n = 5, c = 5 * 3 + 5 = 20. And when n = 9, c = 9 * 3 + 5 = 32. All the values of c in the table match the values predicted by the equation c = 3n + 5. Therefore, c = 3n + 5 is the correct equation for the data.

Answer:2 + √3

Step-by-step explanation:

The value of tan 5pi/12 in decimal is 3.732050807. . .. Tan 5pi/12 can also be expressed using the equivalent of the given angle (5pi/12) in degrees (75°).

We know, using radian to degree conversion, θ in degrees = θ in radians × (180°/pi)

⇒ 5pi/12 radians = 5pi/12 × (180°/pi) = 75° or 75 degrees

∴ tan 5pi/12 = tan 5π/12 = tan(75°) = 2 + √3 or 3.7320508

If in the survey of a survey of a community, 55%. The percentage of the people who don't like to listen to the radio as well as watch the television​ is 15%.

The number of people who like to listen to the radio as well as watch the television = 35%.

So,

The number of people who like to listen to the radio but don't like to watch the television

=  55% - 35%

= 20%

The number of people who like to watch television but don't like to listen to the radio =  65% - 35% = 30%.

The percentage of people who don't like to listen to the radio as well as watch the television

= 100% - (35% + 20% + 30%)

= 100% - 85%

= 15%

Therefore  15% of the people in the community don't like to listen to the radio or watch the television.

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If we change the symbols, the system will have one solution.

x ≥ 2

x ≤ 2

Where the solution is x = 2.

Here we have the system of inequalities:

x > 2

x < 2

So, x can be smaller than 2 or larger than 2. Is easy to see that there are no values of x that are solutions of both inequalities, but if we replace both symbols by ≤ and ≥, then x = 2 will be a solution of both inequalities, and thus, a solution of the system.

x ≥ 2

x ≤ 2

That system has one solution.

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Answer:

768

Step-by-step explanation:

2 gallons is 32 cups. Times 32 by the servings which is 24. 32 times 24 equals 768

The correct answer of this expression is (b) g>-6.

A finite combination of symbols that are well-formed in accordance with context-dependent principles is referred to as an expression or mathematical expression. Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

a formula expression with the first part signifying a mathematical item and the second part signifying a statement about mathematical objects

given that;

-3 (g + 5) > 3

divide both side by -3, we get

⇒ g + 5 > 3/-3

⇒ g + 5 > -1

subtract both side by 5

⇒ g > -1 -5

⇒ g > -6

so the correct answer is g > -6

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36 yards wide is the actual picnic area.

The drawing's length, a colon (":"), and the actual length that corresponds to it are used to illustrate the scale.

Given that this illustration is scaled at "1:10," everything depicted with a size of "1" would have a size of "10" in the real world, a measurement of 150 mm on the image would be 1500 mm on the actual horse.

One unit in the picture equals 100 actual units. In other words, you would draw the table on a piece of paper at a scale of 2 cm if we were to draw it at a scale of 1:50 and it was 100 cm wide by 200 cm long.

width of actual picnic area = 12 × 3 = 36 yards

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Using distributive property, each expressions are write in an appropriate form. The expression are shown below.

This characteristic states that multiplying the total of two or more addends by a number will provide the same outcome as multiplying each addend separately by the number and then combining the results collectively.

According to the property, the outcomes are the same whether the numbers in parenthesis are added before or after multiplication. In situations when the polynomial cannot be combined together before being multiplied, the distributive property is very helpful. Using this property the following expression are solved.

4(6 + 7) = 4.6 + 4.7

14.1 - (14 - 9) = 14 (1 - 9)

5 (z - 10) = 5.z - 5.10

8.6 + 8.2 = 8 (6 + 2)

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The equation of line J that is perpendicular to line K is: 3. y = 1/2x + 6.

Perpendicular lines have slopes that are negative reciprocals to each other, that is, if the slope of one is 3, the other will be -1/3.

Given that the slope of line K is -2, the slope of line J that is perpendicular to line K would be 1/2.

Substitute m = 1/2 and (x, y) = (6, 9) into y = mx + b to find b:

9 = 1/2(6) + b

9 = 3 + b

9 - 3 = b

6 = b

b = 6

Substitute b = 6 and m = 1/2 into y = mx + b:

y = 1/2x + 6.

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Alan would have to sell less than 540 boxes to earn less than $2050.

A transaction known as "selling" occurs when a product or service is traded for cash. The act of convincing a person or group to purchase something is sometimes referred to as persuasion. Your selling efforts should be concentrated on explaining the benefits to the customer if you're trying to sell a good or service. Selling's goal is to persuade customers to acquire something so they can use it. The course becomes further in-depth to explain the distinctions between traditional and consultant sales, two major schools in the field of sales. Transactional selling is one of the four forms of selling.

Selling solutions.

selling with consultation.

provocative sales tactics.

So, from the graph given it state that: Alan would have to sell less than 540 boxes to earn less than $2050.

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The par coupon rate of four-year, default-free security with annual coupon payments is 112%.

The par coupon rate of a four-year, default-free security with annual coupon payments can be calculated by taking the present value of all future coupon payments, plus the face value of the security, and dividing that amount by the face value of the security.

Par Coupon Rate = (Present Value of Coupon Payments + Face Value) / Face Value

Annual interest payment = [tex]\frac{12}{100} *1000[/tex]

Annual interest payment = $120

A face value of $1,000 and the present value of all future coupon payments is $120, the par coupon rate for this security would be 112%.

Par Coupon Rate = ($120 + $1,000) / $1,000

Par Coupon Rate = 1120 / 1000

Par Coupon Rate = $1.12

Par Coupon Rate = 112/100

Par Coupon Rate = 112 %.

Therefore,

The par coupon rate of four-year, default-free security with annual coupon payments is 112%.

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The percentage decrease is 19.4%

In contrast to being expressed as a fraction, a percentage is a portion of a total expressed as a number between 0 and 100. The percentages are as follows: 100% of everything, 0% of nothing, 50% of something, and 0% of nothing. Divide the component by the total, then multiply the result by 100 to get the percentage.

(Original Cost - New Cost) / Original Cost x 100 equals the percentage decrease.

In this case, the original cost is $36 and the new cost is $29, so we plug these values into the formula:

Percentage decrease = ($36 - $29) / $36 x 100 = $7 / $36 x 100 = 0.1944 x 100 = 19.44%

We can round the answer to the nearest tenth of a percent:

19.44% rounded to the nearest tenth is 19.4%

So the percentage decrease is 19.4%

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The tire will need to rotate 38.2 times to travel the whole length of the street.

We will first compute the tire's circumference in order to determine how many times it will need to revolve while traveling the distance of the roadway.

The formula for determining a circle's circumference may be used to get the tire's circumference because it is circular.

The circumference of a circle is given by

C = πd

Where C is the circumference and d is the diameter

From the question d = 3.5ft and π = 3.14

∴ C = 3.14 × 3.5

C = 10.99ft

Therefore, the circumference of the tire is 10.99ft

The tire will need to turn 38.2 times to travel the whole length of the street. We will now divide the street's length by the tire's circumference to determine how many times it tire will need to turn to go its whole length.

Number of times the tire will have to turn = Length of the street ÷ Circumference of the tire

Number of times the tire will have to turn = 420 ft ÷ 10.99 ft

Number of times the tire will have to turn = 38.2165 times

Number of times the tire will have to turn ≅ 38.2 times

Hence,  the number of times the tire will have to turn in travelling the length of the street is 38.2 times

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1. The variable in the solution is the population every year

2. The model can be presented as

y= 1175-20x

3. The value of slope is -20 which says that the population decreases by 20 members for every one year increase from 2010

Let y be the population after x years from 2010

So, the model can be presented as

y= 1175-20x

Now for example, in year 2011

x= 2011-2010= 1

The population is y = 1175-20(1) = 1155

The population in year 2012 is

x= 2012-2010= 2

Population is y= 1175-20(2) = 1135

The result obtained is satisfactory and hence ok

The population follows a linear trend with slope of -20 and intercept of 1175.

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The rock that has a mass of 35.4 g has a density of: 5.06 g/ cm^3

It is a physical quantity that expresses the ratio of the body mass to the volume it occupies.

The density formula and the procedure we will use is:

d = m/v

Where:

Information about the problem:

Applying the density formula we get:

d = m /v

d = 35.4 g / 7.0 cm^3

d = 5.06 g/ cm^3

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Correctly written question:

If a rock has a mass of 35.4 g and a volume of 7.0 cm^3. What is the density of the rock in g/cm3

The instantaneous voltage across the capacitor is 4/53 * (-cos (106 t - 25)) (volts).

The instantaneous voltage across a capacitor is given by v(t) = 1/C * integral(i(t)dt) where C is the capacitance of the capacitor.

For the current i(t) = 4 sin (106 t - 25), the voltage across the capacitor can be found using the following definite integral:

v(t) = 1/C * integral(4 sin (106 t - 25)dt) from 0 to t

v(t) = 4/106C * (-cos (106 t - 25)) from 0 to t

So, the instantaneous voltage across a 2-F capacitor for this current will be:

v(t) = 4/53 * (-cos (106 t - 25)) (volts)

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The required equation is 2x + 2 = 6x and the value of 'x' is 1/2.

The total length covered by the outline or boundary of a rectangle is known as the perimeter of the rectangle. And the formula is given by

Where l = length and b = breadth  

Here we have

Rectangle-A and rectangle-B  

Dimensions of Rectangle-A are (x + 2) × x  

=> Perimeter of Recatngle-A = 2(x + 2 + x)

= 2(2x + 2)

Dimensions of Rectangle-B are 4x × 2x  

=> Perimeter of Rectangle-B = 2(4x + 2x)

= 2(6x)    

Given that both rectangles have the same perimeter

=> 2(2x + 2) = 2(6x)

=> 2x + 2 = 6x  [ Divide by 2 ]    

∴ The required equation is 2x + 2 = 6x

We can solve the above equation as follows

=> 2x + 2 = 6x

=> [ 2x + 2 - 2x] = 6x - 2x         [ Subtract -2x from both sides  ]

=> 4x = 2

=> x = 2/4

=> x = 1/2

Therefore,

The required equation is 2x + 2 = 6x and the value of 'x' is 1/2.

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