Answer:
A ratio in words compares a whole to a part. For example, the ratio of apples to oranges in a basket is "three to one." This can also be written as "3:1" or "3/1."
Another example: is the ratio of students to teachers in a class is "twenty to one." This can also be written as "20:1" or "20/1."
Step-by-step explanation:
A colony of 100 bacteria doubles in size every 60 hours what will the population be 189 hours from now
By evaluating an exponential equation, we will see that the population after 189 hours will be 888 bacteria.
What will be the population in 189 hours from now?We know that initially we have a total of 100 bacteria, and it doubles in size every 60 hours, then the population can be modeled with the exponential equation.
p(x) = 100*(2)^x
Where x is groups of 60 hours, we can rewrite:
x = t/60h
Where t is the amount of hours, and rewrite the equation as:
p(t) = 100*(2)^(t/60h)
The population in 189 hours from now willbe:
p(189 h) = 100*(2)^(198 h/60h) = 887.7
The population is 888 (where we rounded the value)
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Name the true solution(s) to the equation. name the extraneous solution(s) to the equation.
The true solution to the equation [tex]\(x + 5 - \sqrt{x} = 3\)[/tex] is [tex]\(x = \frac{4}{9}\)[/tex], and there are no extraneous solutions.
To find the true solution(s) to the equation, we need to solve for x and check if the obtained solutions satisfy the original equation. The extraneous solution(s), if any, will be the solutions that do not satisfy the original equation.
To solve the equation, we can start by isolating one of the square root terms. Rearranging the equation, we have:
[tex]\sqrt{x + 5} = 3 + \sqrt{x}[/tex].
The equation can be evaluated as:
[tex]\sqrt{x + 5} - \sqrt{x} &= 3 \\(\sqrt{x + 5})^2 &= (3 + \sqrt{x})^2 \\x + 5 &= 9 + 6\sqrt{x} + x \\6\sqrt{x} &= -4 \\\sqrt{x} &= \frac{-2}{3} \\x &= \frac{4}{9}\end{align*}[/tex]
Therefore, the true solution to the equation [tex]\(x + 5 - \sqrt{x} = 3\)[/tex] is [tex]\(x = \frac{4}{9}\)[/tex], and there are no extraneous solutions.
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The complete question:
Solve the following equation and identify the true solution(s) as well as the extraneous solution(s):
[tex]\sqrt{x + 5} - \sqrt{x} = 3[/tex].
determine the dimensions of a rectangular solid (with a square base) of maximum volume if its surface area is 150 square inches.
The rectangular solid with the maximum volume would be a cube.
The surface area of a cube = 6A,
where A = the area of any one side
hence, the area of one side = 150/6 = 25 sq in.
The length of one face,
L = 25^0.5 = 5 in.
The volume, V of a cube = L^3.
Surface area
Surface area is the amount of space covering the outside of a three-dimensional shape.
volume
Volume is a three-dimensional quantity that is used to measure the capacity of a solid shape. It means the amount of three-dimensional space a closed figure can occupy is measured by its volume.
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A survey asked a random sample students if they estimated they spent more or less than an hour a day on social media.
According to 43% of eighth graders, they spend more than an hour a day on social media.
What do you meant by Percentage ?A ratio stated as a fraction of 100 is what is meant by the term %. Students were asked in a poll if they thought they spent more or less time per day on social media.more less , 7th 12 14 , 8th 20 ,26 . The number of students who responded "more" must be divided by the total number of 8th graders polled in order to arrive at the %, which must then be multiplied by 100.
This percentage is the proportion of 8th graders who believe they spend more than an hour each day on social media.Twenty of the forty-six students (20+26) responded "more," or roughly 43.48 percent. As a result, 43% of eighth graders claim to spend more than an hour every day on social media.
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At a sale this week, a desk is being sold for $272. This is 80% of the original price.
What is the original price?
Answer:
$340
Step-by-step explanation:
You want to know the original price of a desk priced such that $272 is 80% of its original price.
Original priceWe can write the relation as an equation. If p represents the original price, then we have ...
$272 = 80% × p
p = $272/0.80 = $340 . . . . . . . divide by the coefficient of p
The original price is $340.
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Is the relation shown in the arrow diagram a function? (0,-2) (0,1) (1,2) (2,1) (3,4)
Answer: no, not a function
Step-by-step explanation: 0 is in the input twice, and if it were a function, it would only be there once. every input can only have one output
Need help 7-10 asap I’m stuck on these
7. To show that VRHK is a square, one can observe that the opposite sides of the quadrilateral, VR and HK, are equal in length and the two adjacent sides, RH and VK, are also equal in length.
8. For VRHK to be a square, z must equal √2, so that VC = 6√2 and
VR = 12.
9. The length of RK is 12√2
10. The length of VK is 12√2
Give difference between sides and diagonal of square?A square is a two-dimensional, regular geometric shape with four sides of equal length and four angles of 90 degrees. The sides of a square are the four straight lines that make up the shape. The length of each side is the same as the length of the other three sides.The diagonal of a square is a line segment that connects two opposite corners of the square. The diagonal is not a side of the square, as it does not run along the same line as the other sides. The diagonal of a square is always the same length, which is the square root of the sum of the squares of the sides. This is known as the Pythagorean Theorem.The sides of a square are all equal, while the diagonal of a square is not equal to any of the sides. The length of the sides of a square is always the same, regardless of the size of the square, while the length of the diagonal of a square varies with the size of the square. The diagonal of a square is always longer than any of the sides, since it is the hypotenuse of a right triangle.Solution:
8. We can solve this problem by using the Pythagorean Theorem. We know that the sides of a square are equal, so we can set up an equation using the theorem. VC = 6z, VR = 12, and we want the hypotenuse, VRHK, to be a square. VH² = VR² + RH² = 12√2.
VC = 6z = VH/2 = 12√2/2 = 6√2
6z = 6√2
z = √2
9. The length of RK' = s√2 =12√2
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a six foot man standing 200 feet from a tower observes the angle of elevation to the top of the tower to be 67 degrees. how high is the tower?
So, the height of the tower is approximately 363.6 feet.
You can use trigonometry to solve this problem.
If we call the height of the tower "h" and the distance between the man and the base of the tower "d", then the angle of elevation is defined as the angle between the line of sight from the observer to the top of the tower and the horizontal line.
We can use the tangent function to relate the angle of elevation to the height and distance.
tan(67) = h/d
We know that the distance between the man and the tower is 200 feet. We can use this information to find the height of the tower.
h = d * tan(67)
h = 200 * tan(67)
The height of the tower is approximately 363.6 feet.
Please note that due to the approximation of the trigonometric functions, the answer may not be exactly as calculated.
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Write an expression that only uses multiplication and that is equivalent to x reduced by 1/8 of x
The expression that only uses multiplication and that is equivalent to x reduced by 1/8 of x is: x * (1 - 1/8).
An expression in mathematics is a combination of numbers, variables, and operations that represent a value or set of values.
The expression calculates the reduction of x by 1/8 of x by subtracting 1/8 of x from x, which is x * 1/8. By subtracting this from x, the expression calculates x reduced by 1/8 of x. The expression that only uses multiplication and that is equivalent to x reduced by 1/8 of x is:
x * (1 - 1/8).
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What is the relations between
[tex] \leqslant [/tex]
AXE and
[tex] \leqslant [/tex]
EXD this figure
The m∠EXD and m∠AXE are the supplementary angles.
The two angles will be linear pairs if the sum is 180° therefore, linear pair of 62° is 118°. The value of x in the figure is 113°
An angle is a geometry in plane geometry that is created by 2 rays or lines that have an identical terminus.
The identical endpoint of the two rays—known as the vertex—is referenced as an angle's sides.
01)
Two angles will be linear pairs if their sum is 180°.
If the first angle is 62° then the second will be 180° - 62° = 118°
Hence "The two angles will be linear pairs if the sum is 180° therefore, linear pair of 62° is 118°".
02)
The angle x is in the same line with supplementary angle 67° so
x = 180 - 67 = 113°.
Hence "The value of x in the figure is 113°".
03)
In the figure, AXD is a straight line, therefore,
m∠EXD + m∠AXE = 180°
Since the sum of two angles is 180° then they are called supplementary angles.
Hence "The m∠EXD and m∠AXE are the supplementary angles".
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What blood types can someone with type A blood donate to? (select all that
apply)
Blood types A and AB are receivers from someone with type A blood donors.
What is blood type?
There are four major blood groups determined by the presence or absence of two antigens, A and B, on the surface of red blood cells. In addition to the A and B antigens, there is a protein called the Rh factor, which can be either present (+) or absent (–), creating the 8 most common blood types (A+, A-, B+, B-, O+, O-, AB+, AB-).
Someone with blood type A can donate blood to individuals with blood types A and AB.
This is because type A blood has the A antigen on the red blood cells and type AB has both A and B antigens.
While type A blood doesn't have the B antigen which is present in type B and AB blood, so it cannot be donated to those with type B or type B.
It's important to note that there are also positive and negative blood types, which are determined by the presence or absence of the Rh (Rhesus) antigen on the red blood cells.
So, someone with type A negative blood can only donate to individuals with type A negative or type AB negative blood.
Therefore, for A type blood donors can donate to A and AB blood type.
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Find a value for a that makes each statement true.
1. a ÷ 6 is greater than 1
Type a value in the box below [ ] ÷ 6 > 1
2. a ÷ 6 is equal to 1
Type a value in the box below [ ] ÷ 6 = 1
3. a ÷ 6 is less than 1
Type a value in the box below [ ] ÷ 6 < 1
4. Find a value for a that makes this statement true a ÷ 6 is equal to a whole number
Type the answer in the box below
| |
| |
| |
| |
| |________________________|
Answer:
1. a > 6
2. a = 6
3. 0 < a < 6
4. a is divisible by 6
Answer:
1. a>6 the answer could be, 7, 8, 9, 10 and it keeps going on.
2. the answer is 6
3. a<6 the answer is anything below 6 so 5, 4, 3, 2, 1, and more.
4. anything that is a multiple of 6 is true. like 6, 12, 18, 24, 30, 36, and it keeps going.
In ΔRST, r = 79 inches, t = 70 inches and ∠T=58°. Find all possible values of ∠R, to the nearest 10th of a degree
In ΔRST, the measure of angle R is 73.1°
Let us assume that r represents the opposite side of ∠R, and 't' represents the opposite side of ∠T
i.e., r = side ST and t = side RS
We know that the law of sine for triangle states that the ratio of the side length of a triangle to the sine of the opposite angle, which is the same for all three sides.
i.e., for triangle ABC,
[tex]\frac{sin~A}{a} =\frac{sin~B}{b} =\frac{sin~C}{c}[/tex]
Using sine law for ΔRST,
[tex]\frac{sin~R}{r} = \frac{sin~S}{s} =\frac{sin~T}{t}[/tex]
Consider equation,
[tex]\frac{sin~R}{r} =\frac{sin~T}{t} \\\\\frac{sin~R}{79} = \frac{sin~(58)}{70}[/tex]
79 × 0.8481 = sin(R) × 70
sin(R) = 66.99 / 70
sin(R) = 0.9571
∠R = arcsin(0.9571)
∠R = 73.1°
Thus, measure of angle R = 73.1°
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The table shows ordered pairs that belong to quadratic function H. What is the range of H?
For the quadratic equation -2x²+12x-13, the range is option D: All real numbers less than or equal to 5.
What is a quadratic function?
A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of second degree.
The values for x and h(x) are given in the table.
Real numbers can be said to be all continuous values of quantity, which can be negative or positive values.
The range of h, h(x), in the table given are all real numbers.
The quadratic equation from the points in the table can be deduced as -2x²+12x-13.
The maximum of the graph is at (3,5).
For a parabola ax²+bx+c with Vertex (xv,yv) -
If a<0, then the range is f(x) ≤ yv.
If a>0, then the range is f(x) ≥ yv.
Since, a = -2, then f(x)≤ 5.
Therefore, the range values of h is f(x)≤ 5.
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Priya thinks the answers to these two questions will be different. This month, a website had a 12% decrease in traffic. If there were 250 visitors last month, how many visitors were there this month? This month, another website had a 12% increase in traffic. If there were 250 visitors this month, how many visitors were there last month?
The number of customers are not exactly same in two cases.
What is percentage?In mathematics →
a percentage is a number or ratio expressed as a fraction of 100.it is often denoted using the percent sign "%".Given is the -
This month, a website had a 12% decrease in traffic. There were 250 visitors last month.This month, another website had a 12% increase in traffic. There were 250 visitors this month.( 1 ) -Number of customers this month -
{x} = 250 - {12% of 250}
{x} = 250 - {12/100 x 250}
{x} = 250 - 12 x 2.5
{x} = 250 - 30
{x} = 220
( 2 ) -Number of customers last month -
250 = {x} + {12% of x}
250 = {x} + (12/100){x}
250 = {x} (1 + 3/25)
250 = {x} (28/25)
{x} = (250 x 25/28)
{x} = 223 {approx.}
Therefore, the number of customers are not exactly same in two cases.
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The roof shingles are arranged so that each row has 7 fewer shingles than the row below it. If the first row has 75 shingles, how many shingles are in the 6th row?
Answer:110
Step-by-step explanation: Add 7 shingles every row you go up.
Row 1=75
2=82
3=89
4=96
5=103
6=110
Answer:
33
Step-by-step explanation:
it starts with 75 and decreases by 7 for each row. on the 6th row youll be at 33!
STARTS AT 75
row one: 68
row two: 61
row three:54
row four: 47
row five: 40
row six: 33
NEED HELP ASAP!!
When Lisa runs, she takes 80 steps in 100 meters. How far has Lisa run when she has taken 2500 steps. Round to kilometers
Answer 0.000032 km
Step-by-step explanation: divide
Find the missing variables in the triangle below. Leave your answer in simplest radical form.
the value of x, y, and z are 2√14, √74, and √252.
What is the right-angle triangle?A triangle is said to be right-angled if one of its angles is exactly 90 degrees. The total of the other two angles is 90 degrees. Perpendicular and the triangle's base are the sides that make up the right angle. The longest of the three sides, the third side is known as the hypotenuse.
Given, the right triangle that has two other right triangles inside it:
From the Pythagorean theorem:
Hyppotaneus ² = height ² + base²
from the Bigger triangle:
H = 14 + 4 = 18
b = y
h = x
Thus,
y² + z² = 18*18
y² + z² = 324.....(1)
from the triangle with a height of 14,
z² = x² + 14²
z² = x² + 196....(2)
From the triangle with the base of 4:
y² = x² + 16...(3)
For equations 2 and 3 substitute the value in equation 1
2x² + 212 = 324
2x² = 112
x² = 56; x = 2√14
Thus,
y² = 56 +16
y² = 74; y = √74
z² = 56 + 196
z² = 252; z = √252
Therefore, the value of x, y, and z are 2√14, √74, and √252.
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Finally, Jorge does inventory on the amount of cheese in the restaurant. He starts with Friday. That evening, 12 customers ordered cheeseburgers. Each cheeseburger uses 3/4 of a pound of cheese. The same night, 2 waiters each dropped 1.2 pounds of cheese on the ground and had to throw it away.Jorge wants to know how many pounds of cheese were used that night. He solves an equation and so does his assistant chef, Matty. Who is correct? Jorge: 12x 0.75+ 2x 1.2=13.2. Matty: (12x 0.75) + (2x 1.2 =11.4
The person who is correct is Matty: (12x 0.75) + (2x 1.2 =11.4 (second option)
Who is correct?The total pound of cheese is the total amount of of cheese used for cheeseburgers and the total amount of cheese wasted.
Total pounds of cheese = total pounds used for cheeseburgers + total cheese wasted
= (pounds of cheese needed for one cheeseburger x number of cheeseburger) + (number of waiters x pounds of cheese dropped)
= (12 x 3/4) + (1.2 x 2)
= 9 + 2.4
= 11.4 pounds
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1. In parallelogram ABCD, what is the relationship between angle a° and angle b°?
a° = b°
a° - b° = 180°
a° = -b°
a° + b° = 180°
2. In rectangle FGHK, FC = CH = 8. 5 cm. What is the area of rectangle FGHK?
8. 5cm
120cm
125. 5cm
15cm
3. In rectangle FGHK, FC = CH = 8. 5 cm. What is the length of GK?
8 cm
8. 5 cm
15. 5 cm
17 cm
4. In parallelogram EFGH, what is the relationship between angle e and angle g?
e° – g° = 180°
e° = -g°
e° = g°
e° + g° = 180°
1. In parallelogram ABCD, the sum of ∠a and ∠b is 180 degree. So the option d "a° + b° = 180°" is correct.
2. In rectangle FGHK, FC = CH = 8. 5 cm, then the area of rectangle FGHK is 120 square cm. So the option b is correct.
3. The length of GK is 17 cm because the length of all diagonal is same in rectangle. So the option d is correct.
4. In parallelogram EFGH, the sum of ∠e and ∠f is 180 degree. So the option d "a° + b° = 180°" is correct.
1. In parallelogram ABCD, ∠a and ∠b are adjacent to each other.
So, AB║DC.
Then we get ∠a and ∠b as subsequent interior angles, both of which need to be added.
So the sum of ∠a and ∠b is 180 degree.
a° + b° = 180°
2. In rectangle FGHK, FC = CH = 8. 5 cm.
From the diagram, FG = 8 cm
FH = FC + CH
FH = 8.5 + 8.5
FH = 17 cm
Using Pythagorean Theorem to find the value of GH.
FH^2 = FG^2 + GH^2
(17)^2 = (8)^2 + GH^2
289 = 64 + GH^2
Subtract 64 on both side, we get
GH^2 = 225
Taking square root on both side, we get
GH = 15 cm
The area of rectangle = FG × GH
The area of rectangle = 8 × 15
The area of rectangle = 120 square cm
3. In rectangle FGHK, FC = CH = 8. 5 cm.
So FH = FC + CH
FH = 8.5 + 8.5
FH = 17 cm
As, a rectangle is split into two congruent right triangles by a diagonal. The length of the rectangle's diagonals are all the same.
So GK = FH = 17 cm
4. In parallelogram EFGH, ∠e and ∠f are adjacent to each other.
So, EF║HG.
Then we get ∠e and ∠f as subsequent interior angles, both of which need to be added.
So the sum of ∠e and ∠f is 180 degree.
e° + f° = 180°
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a room has dimensions of 9.15 meters by 9.4 meters by 3.68 meters. what is the volume of the room in cm^3?
The room with the given dimensions has a volume of 316, 516, 800 cm^3.
The volume of a room is a measure of the amount of space inside it, and it is calculated by multiplying the length, width, and height of the room.
In this case, the room has dimensions of 9.15 meters by 9.4 meters by 3.68 meters.
To find the volume of the room in cm^3, we first need to convert the dimensions of the room from meters to centimeters.
1 meter is equal to 100 centimeters, so
9.15 meters is equivalent to 915 centimeters,
9.4 meters is equivalent to 940 centimeters,
and 3.68 meters is equivalent to 368 centimeters.
Once we have the dimensions in centimeters, we can calculate the volume by multiplying the length, width, and height:
915 cm x 940 cm x 368 cm = 316, 516, 800 cm^3.
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A woman wants to measure the height of a nearby tower. She places a 7ft pole in the shadow of the tower so that the shadow of the pole is exactly covered by the shadow of the tower. The total length of the tower's shadow is 182ft, and the pole casts a shadow that is 4.75ft long. How tall is the tower? Round your answer to the nearest .
What is the distance between the Library and Post Office?
5
5
3
2
In a City
Library
1
Restaurant
O6 units
O 4 units
O 5 units
3 units
Park
Complex
0 1 2 3 4 5 6 7
Museum
Post Office
Answer: The answer is 5 units
Step-by-step explanation:
If you plot it on a graph and what not it comes out to 5 units, going diagonally.
In a city, the distance between the library and the post office is three units. This may be calculated by counting the gaps between the two points on the grid illustrated above. The Library is in position 1 and the Post Office is in position 4, therefore the distance between them is three units.
What is distance?The amount of space between two locations is defined as distance. It is commonly measured in meters, kilometers, miles, or feet. Distance is used to compute the length of a journey, the time required to go a specific distance, and the speed of an item moving a specific distance. It may also be used to determine the dimensions of an item. In trigonometry, distance is also used to measure angles, such as the angle between two points on a circle. Distance may be present in practically every facet of our daily lives, from city distances to item sizes. Distance is an important term to grasp in both physics and mathematics.
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A circle has a circumference of
452.16
452.16452, point, 16 units.
What is the radius of the circle?
The radius of the circle is approximately =71.96 units
What is circle ?Circles can be defined by their radii and all points on the circumference of a circle are equidistant from the center. Circles are widely used in mathematics, science and engineering for various applications, including modeling and solving problems in geometry.
The formula for the circumference of a circle is 2 * pi * r, where r is the radius.
Given the circumference, we can solve for the radius:
452.16 = 2 * pi * r
r = 452.16 / (2 * pi)
The radius of the circle is approximately 71.96 units.
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Lin wrote this number sentence to solve a problem: 35+7-5 Which problem was Lin MOST LIKELY trying to solve?
There are 35 students in Mr. Ken's class. There are 7 students in his class who are sick today. How many students in his
class are not sick?
There are 35 students in Mr. Ken's class. During class, 7 more students join the class to watch a movie. How many
students are there in all?
There are 35 students in Mr. Ken's class. There are 7 classes in the school, each with the same number of students. How
many students are in the school?
There are 35 students in Mr. Ken's class. He made 7 groups for reading. He put an equal number of students in each
group. How many students are in each group?
Answer:
Step-by-step explanation:
You need to buy ome chicken for dinner tonight. You found an ad howing that the tore acro town ha it on ale for $3.09 a pound, which i cheaper than your uual neighborhood tore, which ell it for $3.19 a pound. I it worth the extra drive?
How much chicken will you be buying? 3 pound
How much far are the two tore? My neighborhood tore i 2.3 mile away, and take about 8 minute. The tore acro town i 8.7 mile away, and take about 25 minute.
How kind of mileage doe your car get? It average about 19 mile per gallon in the city.
How many gallon doe your car hold? About 13 gallon
How much i ga? About $3.62/gallon right now.
Yes, it is worth the extra drive to going the far store for buying the chicken. The difference between the both store worth is about $1.24.
We have to buy some chicken for dinner tonight. We found an ad showing that the store across town has it on sale for $3.09 a pound, which is cheaper than our usual neighborhood store, which sells it for $3.19 a pound.
Let's compare chicken costs: We need 3 pounds of chicken so, we would pay$3.09 ×3 = $19.14 (far store)
$3.19 × 3 = $20.34 (near store)
Let's see at how much it costs to travel in our car:For the neighbourhood store :
Distance = 2.3 mile
Multiply by 2 because we not only have to drive there, but also back home for the round trip: so, total distance = 2.3 miles × 2 = 4.6 miles
As car average is 19 miles per gallon
= 4.6 mile/ 19 miles per gallon
= 0.24 gallon < 13 gallons
Now, costs to travel to each store from the gas used. Cost of gas is $3.62/gallon,
total cost = 0.2421 gallons×$3.62 /gallons = $0.88
Similarly for far store : distance from home to store = 8.7 miles but take double of it we get, 8.7 miles × 2 = 17.4 miles
As car average is 19 miles per gallon
= 17.4 miles /19 miles per gallons
= 0.915 gallons < 13 gallons
The cost of gas for the respective trip = 0.915 gallons × $3.62 /gallons = $3.32
Now, let's add the gas and chicken costs together to get total worth
$19.14 + $3.32 = $22.46 to the far store
$20.34+ $0.88 = $21.22 to the near store
Hence, the worth in travelling far store is greater than neighbourhoid store.
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Complete question:
You need to buy some chicken for dinner tonight. You found an ad showing that the store across town has it on sale for $3.09 a pound, which is cheaper than your usual neighborhood store, which sells it for $3.19 a pound. Is it worth the extra drive? First, determine what information you need to answer this question, then click here to display that info (along with other info).
How much chicken will you be buying? 3 pounds
How far apart are the two stores? My neighborhood store is 2.3 miles away, and takes about 8 minutes. The store across town is 8.7 miles away, and takes about 25 minutes.
How kind of mileage does your car get? It averages about 19 miles per gallon in the city.
How many gallons does your car hold? About 13 gallons
How much is gas? About $3.62/gallon right now.
Yes, it is worth the extra drive to the far store to get the chicken. The value of the two stores varied by around $1.24.
To make chicken for dinner tonight, we must purchase some. We discovered an advertisement indicating that the supermarket across town is selling it for $3.09 per pound, which is less expensive than our typical neighborhood grocery, which charges $3.19 per pound.
Compare the prices of chicken: We would pay for the 3 pounds of chicken that we require.
$3.09 ×3 = $19.14 (far store)
$3.19 × 3 = $20.34 (near store)
Let's look at the expense of driving in our car:
For the local retailer: = 2.3 miles away
Because we need to travel both ways, we must double the distance by two, making the total distance 2.3 miles x 2 = 4.6 miles.
Since the average automobile gets 19 mpg
19 miles per gallon/4.6 miles = 13 gallons x 0.24 gallons
Now, add the cost of gas used to drive to each store. Gas costs $3.62 per gallon.
Total cost = 0.2421 gallons at a cost of $0.88 per gallon.
The same goes for a far store:
the distance from home to the store is 8.7 miles, but if we double that by two, we get 17.4 miles.
Since the average automobile gets 19 mpg = 17.4 miles per gallon /19 miles per mile
13 gallons equals 0.915 gallons.
The gas price for the relevant journey is 0.915 gallons times $3.62 a gallon, or $3.32.
To determine the overall cost,
let's now combine the costs of the chicken and petrol.
$22.46 to the far store from $19.14 plus $3.32
$20.34 plus $0.88 equals $21.22 for the nearby retailer.
Therefore, a far store is more valuable than a nearby store. The difference is $1.24
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Solve the inequality + 6 > -3.
A x < -2
B x > -2
C x < 12
D x > 12
The solution to the inequality is (b) x > -2
How to determine the solution to the inequalityFrom the question, we have the following parameters that can be used in our computation:
4.5x + 6 > -3
Collect the like terms
So, we have the following representation
4.5x > - 3 - 6
Evaluate the like terms
This gives
4.5x > -9
Divide both sides by 4.5
x > -2
Hence, the solution is (b) x > -2
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How much larger is the digit 3 in 903.7 than the value of the digit 3 in 4.31?
Answer:
10 times larger.
The 3 in 903.7 is in the ones place, and the 3 in 4.31 is in the tenths place, which is to the left of the decimal one time.
If you were to move the 3 in 4.31 to the right of the decimal like where the 3 is in 903.7, then you would be increasing the 3s value by 10.
Step-by-step explanation:
Hope it helps! =D
there were x quarts of liquid in a con-tainer. first, 3 4 of the liquid in the container was removed. then another 1 2 quart was poured into the container. write an expression in terms of x for the number of quarts of liquid in the container at the end. then write another equivalent expres-sion.explain
The another equivalent expression of total liquid is (x+2)/4.
Expressions that perform similarly but differ in appearance are said to be equivalent expressions. When the same value for the variable is entered, two algebraic expressions that are equivalent will have the same result.
x quarts liquid in the container 3/4 part of liquid is removed
Then remaining liquid in container = X - [tex]\frac{3}{4}X[/tex]
Then remaining liquid in container = x/4quarts
Another 1/2 quart is poured into container
Then total liquid = [tex]X-\frac{3}{4}X+\frac{1}{2}[/tex] quarts
total liquid = [tex]\frac{X+2}{4}[/tex] quarts
So, then the another equivalent expression of total liquid is (x+2)/4.
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BRO MY MATH TEACHER IS ON TO ME SOMEONE HELP A family camping in a national forest builds a temporary shelter with a tarp and a 6-foot pole. The bottom of the pole is even with the ground, and one corner is staked 10 feet from the bottom of the pole. What is the slope of the tarp from that corner to the top of the pole?
To find the slope of the tarp, we can use the concept of rise over run, which is the ratio of the vertical change (the rise) to the horizontal change (the run). In this case, the rise is the distance from the corner of the tarp to the top of the pole, and the run is the distance from the corner of the tarp to the bottom of the pole.
We can use the Pythagorean theorem to find the length of the hypotenuse of the right-angled triangle formed by the corner of the tarp, the bottom of the pole and the top of the pole.
The length of the hypotenuse is the distance from the corner of the tarp to the top of the pole and the length of the adjacent side is the distance from the corner of the tarp to the bottom of the pole.
We know that:
adjacent side = 10 ft
Hypotenuse = h
Applying the Pythagorean theorem:
h^2 = 10^2 + 6^2
h = √(10^2 + 6^2)
h = √(100 + 36) = √136 = 11.66 ft
Now we can calculate the slope:
slope = rise/run = (h-10) / 6
slope = (11.66-10) / 6 = 1.66/6 = 0.277
So the slope of the tarp from the corner to the top of the pole is 0.277 or approximately 0.28.