Answers
Answer:
739 m²
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{9 cm}\underline{General form of an Exponential Equation}\\\\$y=ab^x$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $b$ is the base (growth/decay factor) in decimal form.\\\end{minipage}}[/tex]
The given scenario can be modelled as an exponential equation.
Let y be the area the fire covers (in meters squared).
Let x by the time (in hours).
If the fire currently covers an area of 32 m² then the initial value, a, is 32.
If the area covered by the fire increases by 17% each hour, then the growth factor, b, is 1.17 (since an increase of 17% is 117% of the previous amount).
Therefore:
a = 32b = 1.17Substitute the values of a and b into the exponential formula:
[tex]y=32(1.17)^x[/tex]
To find the area that the first covers in 20 hours' time, simply substitute x=20 into the equation:
[tex]\implies y=32(1.17)^{20}[/tex]
[tex]\implies y=32(23.1055991...)[/tex]
[tex]\implies y=739.37917...[/tex]
Therefore, the area the fire will cover in 20 hours' time is 739 m² (nearest 1 m²).
Related Questions
Thank you sooo much for the help if you do
WHAT IS IMAGE ABOUT? STEM AND LEAF
Answers
Answer:
A
Step-by-step explanation:
A stem and leaf plot is a way of representing data (it might be helpful to look up a video—the organic chemistry tutor has a good one).
The column on the left shows the first digit of each number, and the column on the right is the different ones place digits.
Take the number 31. It would go at the bottom, where the 3 (from the tens place) is in the left column and the 1 (from the ones place) is in the right column.
3 would be in the first row as 03.
You have three nines in your list of data, and only A has three nines.
I hope this helps!
jamal wants to estimate the distance across the gorge shown in the diagram below. He stands at point Y and locates a tree at point X directly across the gorge to the north. He then walks west along the gorge 500ft and marks point A. After walking another 500ft in the same direction, he turns 90 degrees and walks south, perpendicular to the gorge. He stops when his location appears to form a straight line with points A and X. Jamal measures the distance BC as 327 ft.
Answers
Answer:
Step-by-step explanation:
To estimate the distance across the gorge, Jamal can use the following steps:
First, he can draw a diagram to represent the situation. He can label points Y, X, A, and B on the diagram and draw the lines YX and AB to represent the locations of the tree and the points he marked.
Next, he can use the Pythagorean Theorem to find the distance AC. The theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In this case, the side AC is the hypotenuse, and the sides YA and YC are the other two sides. Therefore, he can use the theorem to find AC as follows:
AC^2 = YA^2 + YC^2
He knows the values of YA (500ft) and YC (327ft), so he can substitute these values into the equation and solve for AC:
AC^2 = 500^2 + 327^2
AC^2 = 250000 + 107649
AC^2 = 357659
AC = √357659
AC ≈ 597.56 ft
Finally, he can use the distance AC to estimate the distance across the gorge. The distance across the gorge is equal to the distance from X to Y, which is equal to the sum of the distances from X to A and A to Y. Therefore, he can estimate the distance across the gorge as follows:
distance across gorge = XA + AY
distance across gorge = AC + YA + YC
distance across gorge = 597.56 ft + 500 ft + 327 ft
distance across gorge ≈ 1424.56 ft
This is Jamal's estimate of the distance across the gorge.
in a 30 minute television show, 12 minute of airtime are spent on commercials
Answers
The percentage of the 30 minute television show's air time that is spent on commercials.
Given that 12 minutes out of 30 minutes are commercials. This indicates that the fraction would be
[tex]\frac{12}{30}[/tex]
This fraction can be converted into percentage as follows:
Use division to convert the fraction to a decimal:
[tex]\frac{12}{30} = 12 \div 30 = 0.4\\[/tex]
Multiply by 100 to get percent value:
[tex]0.4 \times 100 = 40\%[/tex]
What is percentage?A value or ratio that may be stated as a fraction of 100 is referred to as a percentage. Divide the number by the total and multiply by 100 to find the percent of a given number. So, a part per hundred is what the percentage refers to. Per 100 is what the word percent means. The sign "%" is used to indicate .
How to calculate percentage?Finding the fraction of a whole in terms of 100 in refers to calculating percentage. A percentage can be found in one of two ways:
a) use the unitary approach.
b) by changing the fraction's denominator to 100.
It should be noted that when the denominator is not a factor of 100, the second technique of percentage calculation is not applied. In these situations, we employ the unitary approach.
The percentage of the 30 minute television show's air time that is spent on commercials.
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Help asp before 11:59 pm please thank you if you helped
Answers
The function has been shifted down by 8 units.
What is transformation of a function?The curve representing the graph "moves to the left/right/up/down" or "expands or compresses" or "reflects" when functions are transformed.Transformations are classified into three types: translations, reflections, and dilations. When a function is transformed, it can be vertical (affecting the y-values) or horizontal (affecting the x-values) (affects the x-values).Here given the function,
y = x
Required that,
Find the transformation that results in: y = x - 8
When a function f(x) is shifted by b units, the new function g(x) is defined as g(x) = f(x) - b.
In this instance:
y = x
b = 8
As a result, the new function is:
y = x - b
8 should be substituted for b.
y = x - 8
Hence, the function is shifted 8 units downward,
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By first rounding both numbers to 1
significant figure, estimate the answer to
12 x 478
Answers
Answer:
Step-by-step explanation:
Rounding to 1 sig fig:
12 becomes 10
478 becomes 500 (that hurts)
Multiply
10 x 500 = 5000
[Actual value of 12 x 478 is 5736. The reason the estimated value is lower is due to the fact that going from 12 to 10 was a reduction of 17%, while going from 478 to 500 was an increase of only 5%]
A cyclist rides 8 miles in 30 minutes.
What is the speed of the cyclist in miles per hour? Round to the nearest mile per hour.
WHAT IS THE ANSWER
Answers
The speed of the cyclist in miles per hour is 16 miles per hour
What is the definition of speed?The speed of an object is the rate of change of the object's distance over time
What is the speed of the cyclist in miles per hour?From the question, we have the following parameters that can be used in our computation:
A cyclist rides 8 miles in 30 minutes.
The parameters in the above statement can be further expressed as
Distance = 8 miles
Time = 30 minutes
This means that the distance is 8 miles and the time taken to cover the distance is 30 minutes
Convert the minutes to hour
So, we have
Time = 0.5 hour
The speed of the cyclist in miles per hour is then calculated as
speed = 8 miles/0.5 hour
Evaluate the quotient
speed = 16 miles/hour
Hence, the cyclist' speed is 16 miles/hour
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find the slope of the line that contains the points (4,3)and(-6,27)
Answers
slope = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are two points on the line.
To find the slope of the line that contains the points (4,3) and (-6,27), we can substitute the coordinates of the points into the formula:
slope = (27 - 3) / (-6 - 4)
Solving this equation, we find that the slope of the line is:
slope = 24 / -10
Simplifying the fraction, we get:
slope = -12/5
Therefore, the slope of the line that contains the points (4,3) and (-6,27) is -12/5.
4x + 3 = 2x + 14 solve each equations
Answers
4x - 2x = 14 - 3
2x = 11
x = 11/2 or x = 5.5
A music website charges x dollars for individual songs and y dollars for entire albums. Person A pays $25.92 to download 6 individual songs and 2 albums. Person B pays $33.93 to download 4 individual songs and 3 albums. Write a system of linear equations that represents this situation. How much does the website charge to download a song? an entire album???
Answers
Answer:
1/ y= -3x + 12.96
2/ $9.99 for an entire album & $0.99 for a song
Step-by-step explanation:
We know that the
The amount charged for downloading individual songs = x dollars
And the amount charged for downloading an entire album = y dollars
Let's write a function for person A first
6x + 2y = 25.92
Solve, and we will get
y = -3x + 12.96
Now to person B
4x + 3y = 33.93
Putting the value of y from the first equation in the second
4x + 3(12.96 - 3x) = 33.93
- 5x = - 4.95
x = $0.99
Then we take
y = 12.96 - 3x
= 12.96 - 2.97
= $9.99
help me with this plssssssss
Answers
Answer: Its 130 degrees
*PLEASE ANSWER* NEED HELP!
Answers
Answer:
Step-by-step explanation:
1/5 (1/3) + 1/15 = 1/15 + 1/15
= 2/15
Are -1/3(-3m+6-12+15m) and 2(1-2m) equivalent
Answers
Algebraic expressions -1/3(-3m+6-12+15m) and 2(1-2m) are equivalent as they give same expression of simplifying.
What are equivalent algebraic expressions?
Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.
According the given question:
The given algebraic expressions in variable m are -1/3(-3m + 6- 12 + 15m) and 2(1 - 2m)
Simplifying 1st expression
-1/3(-3m + 6- 12 + 15m)
-1/3(-3m) -1/3(6) -1/3(-12) -1/3(15m)
m - 2 + 4 - 5m
-4m + 2 is the simplified form
Similarly simplifying 2nd expression
2(1 - 2m)
2 - 4m
Clearly both the algebraic expressions are same when simplified.
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A 5 inch x 7 inch photograph is placed inside a picture frame. Both the length and width of the frame are 2x
inches larger than the width and length of the photograph. Which expression represents the perimeter of the
frame?
O 4x + 12
O 8x + 24
O 2x² +24
O 4x²+24x+35
Mark this and return
Save and Exit
Next
Submit
Answers
The expression that represents the perimeter of the frame is (8x+24) inches. Option C
How to find the perimeter of a rectangle?From the question, we are given that dimensions of the photograph is 5 inch × 7 inchIt is given that the dimensions of the frame are 2x inches larger than the dimensions of the photograph. Thus, the dimensions of the frame is (2x+5) inches × (2x+7) inches.
Since, the frame is in rectangular shape. Perimeter of a rectangle = 2(Length + Width)
= 2(2x+5+2x+7)
= 2(4x+12)
= 8x+24 inches.
Thus, the perimeter of the frame is represented by the expression (8x+24) inches.
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The value of n is a distance of 1.5 units from -2 on a number line.
Answers
Answer: -3.5
Step-by-step explanation:
Can someone help!?!?!
Answers
24 fluid ounces of juice in number cups is 3 cups.
Given that, Shen drank 24 fluid ounces of juice.
What is metric conversion?Metric Conversion refers to the conversion of the given units to desired units for any quantity to be measured.
From table, 1 cup = 8 fluid ounce
So, 24/8
= 3 cups
Therefore, 24 fluid ounces of juice in number cups is 3 cups.
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10x-22 3x+7 find x and the converse
Answers
The value of the x for the given condition will be 4.14.
What are vertically opposite angles?It is defined as the angles when two lines intersect each other and at the intersecting point, some pair of angles are formed which we call vertically opposite angles, as the name describes that they have vertically opposite angles.
It is given that, ∠1 =10x-22, ∠2=3x+7
Since they are vertically opposite angles they are equal.
∠1 = ∠2
10x-22 = 3x+7
10x-3x=7+22
7x=29
x=29/7
x=4.14°
Thus, the value of the x for the given condition will be 4.14.
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The value of x is 15, for the given pair of parallel lines.
What is angle?An angle is the formed when two straight lines meet at one point, it is denoted by θ.
Given that,
Lines y and z are parallel,
And angles are (10x-22)° and 3x+7)°
The supplementary angle of (10x-22)° is 180° - (10x-22)°.
Since, lines y and z are parallel, therefore,
angle 180° - (10x-22)° and (3x+7)° will be equal.
180° - (10x-22)° = (3x+7)°
180° = 3x+7 + 10x - 22
180 = 13x - 15
195 = 13x
x = 15
The required value of x is 15.
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An aquarium can be modeled as a right rectangular prism and it can hold 540 cubic inches of water when it is full. Its width is 6 in and height is 5 in. Find the length of the aquarium in inches. Round your answer to the nearest tenth if necessary.
Answers
The required length of the right rectangular prism is 18 in whose volume is 540 cu. in
What is a rectangular prism?Having six faces, a rectangular prism is a three-dimensional shape (two at the top and bottom and four are lateral faces). The prism's faces are all rectangular in form. There are three sets of identical faces as a result. A rectangular prism is often referred to as a cuboid because of its form. A rectangular prism may be found in everyday objects like a geometry box, notebooks, diaries, and rooms.
Rectangular prism characteristics
There are 6 faces, 12 edges, and 8 vertices on a rectangular prism.The rectangular prism's top and bottom are always rectangles.It has three dimensions, or length, breadth, and height, much like a cuboid.opposing face pairs are identical or coincidentThe lateral sides of a right rectangular prism are rectangle-shaped.The lateral faces of an oblique rectangular prim are parallelograms.Its cross-section is rectangular in shape.It has a perfect cuboid appearance.There are two categories into which rectangular prisms can be divided. These are:
Right Rectangular PrismOblique Rectangular PrismA rectangular prism is a prism with rectangular bases. A right rectangular prism is a prism with six rectangle-shaped faces with angles that are all right angles.
Vertices of a rectangular prism = 8
Edges of a rectangular prism = 12
Faces of a rectangular prism= 6 (including bases)
total volume of the prism = 540 cubic inches.
Width = 6 in
Height = 5 in
We know volume is length * breadth* height
⇒ 540 = 5*6* length
⇒length = 18 in
The required length of the right rectangular prism is 18 in.
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For which situations is it appropriate to use a sample? Select three options.
What percentage of pick-up truck drivers want their next vehicle purchase to be another pick-up truck?
What is the average number of rainbows each year in Honolulu?
How many pedestrians would use a walkway built over a busy road?
How many police cars are equipped with computers?
What is the most popular car color in the teachers’ parking lot?
Answers
Options B, C and D are the situations it is appropriate to use a sample.
What is a simple sample technique?Simple random sampling is a sampling technique in which each member of a population has an equal chance of being chosen, through the use of an unbiased selection method. The sample is chosen by a random method as every subject in the sample is assigned a number.
Sampling saves money by granting researchers to gather the same answers from a sample that they would receive from the population. Non-random sampling is significantly cheaper than random sampling because it lowers the cost associated with searching people and collecting data from them.
Therefore, options B, C and D are the situations it is appropriate to use a sample.
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Answer:
B,C,D
Step-by-step explanation:
Solve the nonlinear system of equations for real solutions. Y=x^2-3;6x-y=11
Answers
The required solution of the nonlinear equation is (4, 13) and (2, 1).
Given that,
To solve the nonlinear system of equations for real solutions. y =x²-3, 6x-y=11.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
y =x²-3 - - - - - [1]
6x-y=11
From equation 1,
6x -x² + 3 = 11
x² - 6x + 8 = 0
x = 4, and 2
Substitute this x's in equation 1
That gives for the above x's,
y = 13 and 1
Thus, The required solution of the nonlinear equation is (4, 13) and (2, 1).
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-x+6y= 5
2x - 12y = -10
Answers
Answer:
Step-by-step explanation:
-x+6y= 5 ----1
2x - 12y = -10 ----2
6y = x + 5
y = (x + 5)/6
2x -12(x + 5)/6 = -10
2x - 2x + 5 = -10
0 = -15
so, x and y have no value
Peter rode her bike 1 km
before topping. Lauren
rode 602 m before
topping. A) How many
metre farther did Peter ride
than Lauren?
Answers
The distance that Peter rode more than Lauren is 398 m .
In the question ,
it is given that ,
before stopping the distance that Peter rode is = 1km = 1000 m .
the distance that Lauren rode is = 602 m .
the difference in the distance can be calculated using the formula ,
So , the difference in the distance is = (distance rode by Peter) - (distance rode by Lauren) .
Substituting the values from above ,
we get ,
= 1000 - 602
on further simplification,
we get ,
= 398 m
Therefore , Peter rode 398m farther than Lauren .
The given question is incomplete , the complete question is
Peter rode her bike 1 km before stopping. Lauren rode 602 m before stopping. How many meter farther did Peter ride than Lauren ?
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Diego has a skateboard, scooter, bike, and go-cart. He wants to know which vehicle is the fastest. A friend records how far Diego travels on each vehicle in 5 seconds. For each vehicle, Diego travels as fast as he can along a straight, level path.
What is the distance each vehicle traveled in centimeters?
Skateboard:
cm
Scooter:
cm
Bike:
cm
Go-Cart:
Answers
The required, bike is the fastest among all the vehicles.
What is unit conversion?Unit conversion is defined as the conversion of units of the same identity through various methods such as, meters in kilometers and centimeters in kilometers.
1.
In 5 seconds skateboard traveled 90 feet.
SInce 1 feet = 30.48 centimeter
90 feet = 2743.2 centimeter
2.
In 5 seconds scooter traveled 1,020 inches
Since 1 inch = 2.54 centimeter,
1020 inches = 2590.8 centimeter
3.
In 5 seconds bike traveled 4800 centimeters
4.
In 5 seconds go-kart traveled 0.03 kilometers
Since, 1 kilometers = 100000 centimeter
0.03 kilometers = 3000 centimeter
Now compare all the distances which one has the higher distance will be the fastest,
Bike > go-kart > skateboard > scooter.
Thus, Bike is the fastest vehicle.
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como se escribe 621,000 en notación científica
Answers
Answer:
La notación científica es una forma de escribir números muy grandes o muy pequeños de manera más compacta y legible. En la notación científica, se mueve el punto decimal de un número hasta que tenga una sola cifra a la izquierda del punto y luego se multiplica el número resultante por 10 elevado a una potencia de 10.
Por ejemplo, para escribir 621,000 en notación científica, podemos mover el punto decimal tres lugares a la derecha para obtener el número 6.21. Luego, podemos multiplicar este número por 10 elevado a la potencia de 3 (10^3), lo que da 6.21 x 10^3 = 6.21 x 1000 = 621,000.
Entonces, en notación científica, 621,000 se escribe como 6.21 x 10^3.
When Earth and Mars are farthest from each other they are about 4.01 x 100,000,000 kilometers apart. Sarah says "To right this number in standard form, I can move the decimal point 9 digits to the right because there are 9 digits in the 100,000,000." Explain and correct Sarah's answer.
Answers
To correct Sarah's answer, the standard form of the given value would be = 4.01 × 10^⁹ km.
What is a standard form?Standard form is defined as the simplified method of representation of large numericals using decimal number, between 1.0 and 10.0, which is then multiplied by a power of 10.
The distance between the earth and Mars = 4.01 x 100,000,000 kilometers.
There are 9 digits in 100,000,000,
Therefore to write the standard form of the given distance of 4.01 x 100,000,000 kilometers would be;
4.01 × 10^⁹ km.
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Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.
Will and his good buddy Owen are both mechanics at a shop that does oil changes. They are in a friendly competition to see who can complete the most oil changes in one day. Will has already finished 4 oil changes today, and can complete more at a rate of 2 oil changes per hour. Owen just came on shift, and can finish 3 oil changes every hour. Sometime during the day, the friends will be tied, with the same number of oil changes completed. How many oil changes will Will and Owen each have done? How long will that take?
Answers
The number of oil changes that Will and Owen would each have done is 6 oil changes respectively.
The number of hours it would take both Will and Owen is equal to 4 hours.
How to write a system of equations?In order to write a system of equations to describe this situation, we would assign variables to the number of hours per oil change and number of oil changes respectively, and then translate the word problem into algebraic equation as follows:
Let the variable x represent the number of hours.Let the variable y represent the number of oil changes.Since Will has already finished 4 oil changes today, and can complete more at a rate of 2 oil changes per hour, we have;
y = 2x + 4 .....equation 1.
Since Owen just came on shift, and can finish 3 oil changes every hour, we have;
y = 3x .....equation 2.
Next, we would determine the number of hours per oil changes they both would have each completed by equating equation 1 and equation 2 as follows;
3x = 2x + 4
3x - 2x = 4
x = 4 hours.
For the number of oil changes for Will, we have;
y = 2(4) + 4
y = 12 oil changes.
For the number of oil changes for Owen, we have;
y = 3(4)
y = 12 oil changes.
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If point C divides segment AB with a ratio 2:3 , what are the coordinates of point C?
Answers
The coordinates of points C are (4,1).
The coordinates of the points D are (3, 2) respectively.
What is coordinates forumla?y = mx + c. Conversely,is the formula of coordinate that help to find satisfy to the equation y = mx + c is always lie on the line with the gradient m and y-intercept of c.
If the point C is divides AB in the ratio 2:3, then the coordinates of C are;
Xc=2(1)+3(6)/2+3
Xc=2+18/5
Xc=20/5 = 4
Yc=2(4)+3(-1)/2+3
Yc=8-3/5
Yc=5/5 = 1
The coordinates of points C are (4,1).
If the point D divides the AC in the ratio 3:2, then the coordinates of D are-
Xc= 3(1)+2(6)/3+2
Xc=3+12/5
Xc=15/5 = 3
Yc=3(4)+2(-1)/3+2
Yc=12-2/5
Yc=10/5=2
The coordinates of the point D are (3, 2).
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Perform the following operation. Write the answer in standard form.
(x-1)(x+3)(x+2)
Answers
n: 1/2 as 6:1
n = ?
Answers
Answer:
N=3. you get this by using the proportion 6/N=1/1/2.
what value of t makes the equation true 4t
Answers
Answer:
Step-by-step explanation:
so first 48+9e
then add 34
take away
Ayuda porfavor es para hoy, quien responda mal y por los puntos es gaY
Answers
Las soluciones de las ecuaciones lineales por propiedades algebraicas se listan a continuación:
7) x = 7
8) x = 16 / 7
9) x = - 1 / 4
10) x = 1 / 5
¿Cómo despejar una variable asociada a una ecuación lineal?
En este caso tenemos cuatro casos de ecuaciones lineales, cuya variable x debe ser despejada mediante propiedades algebraicas. A continuación, se procede a determinar las soluciones correspondientes a cada expresión:
Caso 7:
2 · (x - 1) - 5 = 14 - x
2 · x - 2 - 5 = 14 - x
2 · x - 7 = 14 - x
3 · x = 21
x = 7
Caso 8:
15 · x + 10 = 6 · x - 2 · (x - 7) + 3 · (1 - x)
15 · x + 10 = 6 · x - 2 · x + 14 + 3 - 3 · x
15 · x + 10 = x + 17
14 · x = 32
x = 32 / 14
x = 16 / 7
Caso 9:
x + 3 · (x - 1) = 6 - 4 · (2 · x + 3)
x + 3 · x - 3 = 6 - 8 · x - 12
4 · x - 3 = - 6 - 8 · x
12 · x = - 3
x = - 1 / 4
Caso 10:
6 - 3 · (x + 1) = 4 · x + 2 · (1 - x)
6 - 3 · x - 3 = 4 · x + 2 - 2 · x
3 - 3 · x = 2 · x + 2
- 5 · x = - 1
x = 1 / 5
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