Hannah is the oldest of four siblings whose ages are consecutive integers. If the sum
of their ages is 86, find Hannah's age.

Taking into account the definition of a system of linear equations, there were 4 adult dinosaurs and 12 baby dinosaurs.

A system of linear equations is a set of linear equations that have more than one unknown, related by the equations and that can appear in all of them or only in some of the equations.

Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. This is, ystems of linear equations have as a solution set all ordered pairs (x, y) that satisfy the equation, where x and y are real numbers.

In this case, a system of linear equations must be proposed taking into account that:

You know:

The system of equations to be solved is

15b + 7a= 208

b= 3a

There are several methods to solve a system of equations, it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.

In this case, substituting the second equation in the first you get:

15×3a + 7a= 208

45a + 7a= 208

52a= 208

a= 208÷ 52

a= 4

Remembering that b= 3a, you get

b=3×4

b= 12

Finally, there were 4 and 12 adult dinosaurs and baby dinosaurs respectively.

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Answer: 78.3 ft.

Step-by-step explanation: If I am looking at it right, it would be 8.7 ft x 9 ft because A= L x W. Hope this helps.

Julia paid a total of $94.07 for the service she received at the salon

Service tax: Service tax is a type of indirect Tax that you are liable to pay to the government once you. The consumer pays the service tax to the service provider while paying the bill (for example, your restaurant bill has a component of service tax). The government in turn collects the tax from the service providers.

Service charge for Julia at a beauty salon = $72.60

The rate of sales tax taken = 8%

Percentage of tips she added to the service charge before sales tax= 20%

Then amount of tips given by Julia = (20/100)x72.60

                                                      = (1/5)x72.60

                                                      = 14.52 dollars

Then the amount in total paid by Julia before adding service tax =

(72.60 + 14.52) dollars=87.12dollars

Now the sales tax of 8% has to be calculated on the amount of $87.12

Then

Amount of sales tax given by Julia = (8/100)x87.12

                                                      = 696.96/100

                                                      = 6.969

                                                      = 6.97 dollars

So the total amount paid by Julia for the service at the salon =

(87.12 + 6.97) dollars = 94.07 dollars

Julia paid a total of $94.07 for the service received by her at the salon

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Yes, the equation 6x²-2y=7 will give a straight line.

Let's put the some values in equation for proof,

put x = 0, find y

6x² - 7 = 2y

6(0)² - 7 = 2y

y = -3.5

put x = 1, find y

6(1)² - 7 = 2y

y = -1/2 or -0.5

put x = 2, find y

6(2)² - 7 = 2y

y = 8.5

we get the some of the points to plot in graph,

The points are (0, -3.5) (1, -0.5) (2, 8.5)

Plot these points on graph you'll get a straight line.

Therefore, we can say that 6x²-2y=7 will give a straight line.

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The probability of getting exactly four heads when a fair coin is flipped 10 times is 20.51%.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.

A coin is filliped 10 times. Each of the flips is independent.

Let's say X is the number of heads in 10 tosses.

Then X is distributed as n = 10 and the probability that the head comes after a single flip is 1/2.

Therefore, the probability of X being exactly 4 will be:

P( X = 4 ) = ₁₀C₄ ( 1/2 )⁴ ( 1 - 1/2 )⁶

P( X = 4 ) = 210 × ( 1/16 ) × ( 1/2 )⁶

P( X = 4 ) = 210 × ( 1/16 ) × ( 1/64 )

P( X = 4 ) = 210/1024

P( X = 4 ) = 105/512

P( X = 4 ) = 0.2051

Hence, the probability is 20.51%.

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The value ∠L, ∠M and ∠N is 59°, 105° and 16° respectively.

∠L = (4x - 5)°, ∠M = (7x-7)° and ∠N = x°

The summation of all three angles of a triangle is equal to 180°

∠L+ ∠M + ∠N = 180°

4x - 5 + 7x -7 + x = 180

12x - 12 = 180

12x = 192

x = 192/12

x = 16

∠L = 4x - 5

= 4(16) - 5

= 64 - 5

= 59°

∠M = 7x - 7

= 7(16) - 7

= 112 - 7

= 105°

∠N = x = 16°

Therefore the value ∠L, ∠M and ∠N is 59°, 105° and 16° respectively.

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%, which is a relative figure used to denote hundredths of any quantity. Since one percent (symbolized as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified.

When expressing a proportionate share of a total, percentages are frequently utilized. (Similarly, the term "per mile" or the sign "" can be used to denote a number as a fraction of 1,000.)

Answer:

The percentage of water in a 64-ounce bottle of orange juice is higher.

Detailed explanation:

Case 1: There are 32 ounces of water in an 80-ounce container of apple juice.

80 ounces total are contained in the bottle.

32 ounces of water, please.

Therefore, Percent of Water =32/80x100

                                                = 40%

Case 2) There are 48 ounces of water in a 64-ounce bottle of orange juice.

64 ounces total are contained in the bottle.

Water measurement is 48 ounces.

Therefore, Percent of Water =48/64x100

                                              =75%

The percentage of water in a 64-ounce bottle of orange juice is therefore higher.

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Answer:

$2.50

Step-by-step explanation:

Answer:

Each notebook cost $2.50

Step-by-step explanation:

We can turn the problem into an equation

1. We have a magazine for $5, and then 4 notebooks, with the price x. They all equal to the amount $15.

5 + 4x = 15

4x = 15 - 5

4x = 10

x = 4/10

x = 2.5

2. Just to check, we can plug in 2.5 for x in the equation

5 + 4(2.5) = 15

5 + 10 = 15

15 = 15

The total cost of the birdfeeder which poni wants to buy including the sales tax is $21.54.

Given poni wants to purchase a birdfeeder that costs $19.95.

sales tax rate in her city is = 8.12%

total cost of the birdfeeder = ?

The pre-tax price of an item must first be multiplied by the sales tax percentage once it has been converted into a decimal form in order to determine the amount of sales tax that will apply to the purchase. To get the item's final cost, the sales tax must first be computed, and then it must be added to the pre-tax price.

sales tax rate = 8.12% = 0.0812

Round it off to two decimal places.

= 0.08

Now, in order to determine the cost of the sales tax, we must multiply the item's pre-tax price by this amount.

sales tax = 0.08×$19.95

sales tax = $1.596

Since our total is in dollars and cents, round to two decimal places.

sales tax = $1.59

now total cost = pre tax value+sales tax.

= $19.95+1.59

=$21.54

Hence the total cost of the birdfeeder is $21.54.

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Let's begin by listing out the information given to us:

3 treasure chests contain: 34 jewels, 48 jewels & 18 jewels

Total jewels = 34 + 48 + 18 = 100 jewels

Five explorers plan to share them equally:

To know how many jewels does each get, we divide the total number of jewels by the number of explorers

Total jewels / number of explorers = 100/5 = 20 jewels

Therefore each explorer gets 20 jewels

Answer:

x = 1 , x = 13

Step-by-step explanation:

(x - 7)² = 36 ( take square root of both sides )

x - 7 = ± [tex]\sqrt{36}[/tex] = ± 6 ( add 7 to both sides )

x = 7 ± 6

then

x = 7 - 6 = 1

x = 7 + 6 = 13

The time taken for the mixture to find the right amount of additive per gallon is 12.869 minutes.

The total amount of diesel into the tank = 1700 gallons

The mixture is added at the rate of 0.28 ounces per gallon.

The mixture is added at the rate of 25 gallon per minute.

Let us consider that the time taken is t minutes.

A mixture is a substance made up of two or more distinct chemical components that are not chemically bonded together. A mixture is a mixture of two or more substances that retain their identities while being mixed in the form of solutions, suspensions, and colloids.

Now in t minutes the mixture = 25 × .28 ×t = 7t

Now we will use the second part of the equation as:

The rate of 20gal/min. if there should be 14oz of additive for every 120 gallons of diesel fuel, how long will it take to reach the right mixture

Now we will use the mixture formula to calculate the e amount of diesel in the mixture.

Hence 0.20 × 14×120=336  × 65.11 = 21877.3

Now the diesel mixture will have

Therefore the equation formed is :

336t +7t = 21877.3

Solving we get t=21877.3.

Hence the time taken for the mixture to find the right amount of additive per gallon is 12.869 minutes.

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Answer:

y = (-1/3)x + 4

Step-by-step explanation:

Slope Intercept equation for a line is

y = mx + b

where m = slope and y = y-intercept

Slope = rise/run

Rise = y2 - y1 for any two points (x1,y1) and (x2, y2) on the line

Run = x2 - x1 for the same two points

We are told the line passes through 2 points
(-6, 6) and (9,1)

For these two points,

rise = 1 - 6 = -5

run = 9 - (-6) = 9 + 6 = 15

Slope = -5/15 = -1/3

Equation of line is

y = (-1/3) x + b

We only have to calculate b to get the whole equation. To find b, plug in the x, y coordinates of any of the two points into the above equation and solve for b

Choose point(9, 1)
y = 1 when x = 9

1 = (-1/3)(9) + b

1 = -3 + b

b = 1 + 3 = 4

So equation of line is

y = (-1/3)x + 4

Answer: y=[tex]-\frac{1}{10} x-7[/tex]

Step-by-step explanation: The slope of a perpendicular line is always negative and the reciprocal (opposite fraction) of the regular slope so the slope would be [tex]-\frac{1}{10}[/tex]. If the line passes through (-10,-6) then the y intercept would be (0,-7) because every time x goes 10 right y goes down 1 because of the slope.

The mean, median, and mode, of the given data set, are 5.25, 5.5, and 7.

So, the data set from ascending to descending form:

Mean: Sum of terms/ number of terms

The mean is 5.25.

Median: (Even terms) Average of 2 middle terms:

The Median is 5.5.

Mode: The most repetitive term

The mode is 7.

Therefore, the mean, median, and mode, of the given data set are 5.25, 5.5, and 7.

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Given

A section of a circle has both endpoints on the circle.

To find: What is the section of the circle.

Explanation:

It is given that,

A section of a circle has both endpoints on the circle.

Since A chord is a line segment with both end points on the circle.

Final result: Then, the section of the circle is called Chord.



Answer: chord

Step-by-step explanation:

The offer percentage on that online site on the book  is 20%

What is the dollar amount of discount?

The dollar value of the discount given by the online site is difference between the normal price of the  book which is $25 and the offer price of the online site of $20 as shown below:

discount offered=$25-$20

discount offered=$5

Now that the offer discount has been ascertained, the discount offer in percentage terms relates the dollar value of the discount to the normal price to arrive at the percentage given off the normal price

offer percentage=discount offered/normal selling price

offer percentage=$5/$25

offer percentage=20%

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Answer:

Option D is right

Step-by-step explanation:

It is correct .

The probability that the person smoked 11 to 20 cigarettes per day is 15273/100450.

The likelihood of choosing at random one study participant who smoked between 11 and 20 cigarettes per day is equal to the frequency of those who smoke between 11 and 20 cigarettes divided by the total number of study participants.

1. People smoking at most ten cigarettes per day,

African American: 9886

Native Hawaiians: 2745

Latinos: 12831

Japanese Americans: 8378

Whites: 7650

2. People who smoke 11 to 20 cigarettes per day.

African Americans: 6514

Native Hawaiians: 3062

Latinos: 4932

Japanese Americans: 10680

Whites: 9877

3. People smoking 21 to 30 cigarettes per day,

African Americans: 1671

Native Hawaiians: 1419

Latinos: 1406

Japanese Americans: 4715

Whites: 6062

4. People smoke at least 31 cigarettes per day.

African Americans: 759

Native Hawaiians: 788

Latinos: 800

Japanese Americans: 2305

Whites: 3970

Therefore, the total will be:

Group                       Total

[0 - 10]                      41,490

[11 - 20]                     35,065

[21 -30]                     15,273

[31 and more]            8,622

Total           100,450

Therefore, the probability that a person smoked 11 to 20 cigarettes per day will be:

P = 15,273/100,450

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The complete question is mentioned below:

An article in the New England Journal of Medicine, reported about a study of smokers in California and Hawaii. In one part of the report, the self-reported ethnicity and smoking levels per day were given. Of the people smoking at most ten cigarettes per day, there were 9,886 African Americans, 2,745 Native Hawaiians, 12,831 Latinos, 8,378 Japanese Americans, and 7,650 Whites. Of the people smoking 11 to 20 cigarettes per day, there were 6,514 African Americans, 3,062 Native Hawaiians, 4,932 Latinos, 10,680 Japanese Americans, and 9,877 Whites. Of the people smoking 21 to 30 cigarettes per day, there were 1,671 African Americans, 1,419 Native Hawaiians, 1,406 Latinos, 4,715 Japanese Americans, and 6,062 Whites. Of the people smoking at least 31 cigarettes per day, there were 759 African Americans, 788 Native Hawaiians, 800 Latinos, 2,305 Japanese Americans, and 3,970 Whites. Suppose that one person from the study is randomly selected. Find the probability that person smoked 11 to 20 cigarettes per day. (Enter your probability as a fraction.)

Area of standard football pitch is 7140 square m.

What is the area and perimeter of the rectangle?

Perimeter  is the total distance of the rectangle moves outside of it. The Perimeter  basically indicates the length of the shape. A rectangle has four sides, so the perimeter of the rectangle is the sum of all four sides. Perimeter is a linear measure, so rectangle perimeter units are meters, centimeters, inches, feet, and so on.

perimeter, P = 2 ( a+b) units

area = length × width = a × b

Area can be defined as the region covered by the rectangle in two-dimensional space. The area of ​​a rectangle can also be defined as the number of square units required to completely fill the rectangle.

Length of the standard football pitch = 105 m

Breadth of the standard football pitch = 68 m

Using, area of rectangle = Length × breadth

Area of standard football pitch = 105 × 68 = 7140 square m.

Hence, area of standard football pitch is 7140 square m.

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The distance that should be drwan on a scale plan of 1:100000 is = 32m

Distance can be defined as the area that is covered by the movement of an object without reference to its direction.

From the scale given,

1cm : 100000cm on the scale plan of the map

The given distance = 32km

Convert km to cm by multiplying by 100000

32km = 32× 100000 = 3,200,000

To determine the equivalent ratio,

1 cm = 100000

n cm = 3,200,000

n cm= 3,200,000/100000

n cm= 32cm

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Answer:

0.000752739974

by the way  i used a calculator

       I hope this helps :)

================================================

Work Shown:

x = original price of the calculator

x+6.20 = original price of calculator and binder

0.85(x+6.20) = price after discount, see note below

0.85(x+6.20) = 107.27

Solving for x.

0.85(x+6.20) = 107.27

0.85x+0.85*6.20 = 107.27

0.85x+5.27 = 107.27

0.85x = 107.27-5.27

0.85x = 102

x = 102/0.85

x = 120 dollars is the original price of the calculator

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

Checking the answer:

Before the discount, Justin would pay 120+6.20 = 126.20 dollars for the calculator and binder. He saves 15%, which means he saves 0.15*126.20 = 18.93 dollars and the final price would be 126.20-18.93 = 107.27 which matches up with the value in the instructions.

Or a shortcut would be 0.85*126.20 = 107.27 and that confirms the answer as well.

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

note: If Justin saves 15% then he pays the remaining 85% (since 15+85 = 100). So that's why there's a 0.85

Answer:

Original price of the calculator = $120

Step-by-step explanation:

Given:

If the original price of the binder was reduced by 15%, then the sale price is 85% of the original price (since 100% - 15% = 85%).

[tex]\begin{aligned}\implies \textsf{Sale price of the binder}& = \sf 85\% \;of\; \$6.20\\&= \sf 0.85 \times \$6.20\\&= \sf \$5.27\end{aligned}[/tex]

If Justin spent a total of $107.27:

[tex]\begin{aligned}\implies \textsf{Sale price of the calculator}&= \sf Total\;spent-Sale\;price\;of\;the\;binder\\ & = \sf \$107.27 - \$5.27 \\ & = \sf \$102.00\end{aligned}[/tex]

Remembering that the sale price of the calculator is 85% of its original price:

[tex]\begin{aligned}\implies \sf 85\% \; \textsf{of original price}&=\sf \$102.00\\\sf 0.85 \times original \; price &=\$102.00\\\sf Original \; price & = \sf \$102.00 \div 0.85\\\sf Original \; price &= \sf \$120.00\end{aligned}[/tex]

Therefore, the original price of the calculator was $120.

Answer:

3.46410

Step-by-step explanation:

Option (C) It means the technician charges a fixed amount of $75 for the repair is correct.

A straight line is a combination of endless points joined on both sides of the point.

The slope 'm' of any straight line is given by:

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

The graph of the equation is given:

From the graph the equation of the straight line will be:

y = 45x + 75

For the y-intercept plug x = 0

y = $75

The y-intercept represents the technician charging a fixed amount of $75 for the repair.

Thus, option (C) It means the technician charges a fixed amount of $75 for the repair is correct.

The graph is attached is in the picture.

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The relative rate of population change after seven years from now is a) 1.7 % (rounded off to 1 decimal place) b) Yes, the relative rate of population change will reach 2.3% in 19.21 years

The function for population t years from now is P(t)= 2+ 1.2e^(0.04t)

a) relative rate of change of population

= P'(t) / P(t)

= (0+1.2e^(0.04t) * 0.04 )/ ( 2+ 1.2e^(.04t) )

= 0.048 e ^(0.04t) / (2 + 1.2e^(0.04t) )

Relative rate of change of population 7 years from now

= 0.048 e ^(0.04 * 7) / (2+ 1.2e^(0.04*7))

=0.0177 = 0.177 * 100 = 1.7 % per year (rounded off to one decimal place

b) For the relative rate of change to reach 2.3 %

P'(t) / P(t) = 2.3 % = 0.023

⇒(0+1.2e^(0.04t) * 0.04 )/ ( 2+ 1.2e^(0.04t) ) = 0.023

⇒0.048e ^(0.04t) = 0.046 + 0.0267e^(0.04t)

⇒e ^(0.04t) = 0.958 + 0.556e ^(0.04t)

⇒e ^(0.04t) ( 1 - 0.556) = 0.958

⇒e ^(0.04t) ( 0.444) = 0.958

⇒e ^(0.04t) = 2.157

⇒0.04t = ln(2.157)           (applying ln on both sides)

⇒t = 19.21 years

The relative rate of population change is 2.3% in 19.21 years

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The slope of the line would be - 3/2 which passes through the points (−3, 1) and (1, −5) which is the correct answer would be an option (C).

The slope of a line is defined as the angle of the line. It is denoted by m

Slope m = (y₂ - y₁)/(x₂ -x₁ )

Consider two points on a line—Point 1 and Point 2. Point 1 has coordinates (x₁,y₁) and Point 2 has coordinates (x₂, y₂)

The required slope of the line that passes through the points (−3, 1) and (1, −5)

Let

x₁ = -3, y₁ = 1

x₂ = 1, y₂ = -5

∵ Slope m = (y₂ - y₁)/(x₂ -x₁ )

Substitute values in the formula, and we get

m = (-5 - 1)/(1 - (-3))

m = -6 /(1 + 3)

m = -6 / 4

m = - 3/2

Therefore, the slope of the line would be - 3/2.

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