She ran 15 miles at a quicker speed based on the information supplied. See explanation below. This is a distance time problem.
What is the justification for the above result?The distances between the two "half" of the race are our unknowns here. We must assign them to variables - Alicia ran x miles in the first half of the race and y miles in the second.
Since the race is 21 miles in total, x and y together must add up to 21.
Hence,
x + y = 21
The speeds at which she raced and the total time involved are then given; we can link this to the distances using the speed and distance equation
d = st, or t = d/s.
Because she completed in two hours, the hours spent running the first and second parts must sum up to two hours, or:
x/8 + y/12 = 2
Two equations are sufficient to solve for two unknowns. We can approach this by multiplying the second equation by the LCM, 24
3x + 2y = 48
And rearrange the first to get y = 21 - x, which we can plug into the above. This gives us:
3x + 2(21 - x) = 48
3x + 42 - 2x = 48
x = 6
Use y = 21 - x again:
y = 21 - (6) = 15.
Recall that the question asks how long she ran at the faster speed - this would be the second half of the race, which we've labeled y, so 15 miles. But first, let's make sure our solution works.
Obviously, 15 + 6 = 21, thus the overall distance is correct.
In terms of time, 6 miles at 8 mph takes
6/8 =.75 hours = 45 minutes, whereas
15 miles at 12 mph takes 15/12 = 1.25 hours = 75 minutes.
As stated in the question, the total time to complete would be.
75 + 1.25 = 2 hours.
As a result, this solution is correct, as Alicia ran 15 miles at a quicker rate.
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7/8 of a can of drink is water, the rest is syrup. What is the ratio of water to syrup?
Answer:
7 : 1.
Step-by-step explanation:
1 - 7/8 = 1/8 is syrup.
So, water to syrup
= 7/8 : 1/8
= 7 :1.
The ratio of water to syrup is 7:1
What is a ratio?The quantitative relation between two amounts showing the number of times one value contains or is contained within the other. for example-"the ratio of computers to students is now 2 to 1"
Given here, 7/8 of a can of drink is water, the rest is syrup thus the fraction for syrup is 1/8 of the can. Therefore the ratio of water and syrup is
7/8:1/8=7:1
Hence, The ratio of water to syrup is 7:1
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How can you find 40% of 150 using mental math? Explain.
Answer:
60
Step-by-step explanation:
rid of precentage and zeros, multiply the numbers you have left.
Under her cell phone plan, Nayeli pays a flat cost of $41.50 per month and $5 per gigabyte. She wants to keep her bill under $50 per month. Write and solve an inequality which can be used to determine g, the number of gigabytes Nayeli can use while staying within her budget.
The inequality which can be used to determine the number of gigabytes is 41.5 + 5x < 50 and the solution is x < 1.7
How to write and solve an equation which can be used to determine the number of gigabytes?The given parameters are
Flat cost = $41.50
Rate = $5 per gigabyte
Budget = Under $50
The equation is represented as:
Total cost = Flat cost + Rate * Number of gigabyte
So, we have
y = 41.5 + 5x
The budget is under 50
So, we have
41.5 + 5x < 50
Subtract 41.5 from both sides
5x < 8.5
Divide by 5
x < 1.7
Hence. the inequality which can be used to determine the number of gigabytes is 41.5 + 5x < 50 and the solution is x < 1.7
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Given that 2x+11y=119, work out the value of x and y. PLEASE HELP if possible add how to calculate it as well
anyone mind helping a girl out???
Hi!
Let's solve the equation for x!
[tex]\mid\bold{x-1\mid+5=2}[/tex]
Step 1:
Subtract 5 from both sides.[tex]\bold{\mid x-1\mid=-3}[/tex]
Now it's a little easier to solve! :')
Now, What does | | mean ?
Remember, It means "absolute value", and it's Always a positive number.
And this statement states: "take the absolute value of x-1, Whatever that happens to be, And it'll equal -3".
But that's impossible!
Therefore, this equation has no solutions.
I hope I helped you, have a wonderful day!
Good luck.- stargazing [tex]\tiny\pmb{0.2}[/tex]
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{|x - 1| + 5 = 2}[/tex]
[tex]\large\text{Add }\rm{-5}\large\text{ to both sides: }[/tex]
[tex]\mathsf{|x - 1| + 5 - 5 = 2 - 5}[/tex]
[tex]\large\text{Simplify it:}[/tex]
[tex]\mathsf{|x - 1| = 2 - 5}[/tex]
[tex]\mathsf{|x - 1| = -3}[/tex]
[tex]\large\text{Since, the absolute value is SMALLER than 0, we have no solutions}[/tex]
[tex]\huge\boxed{\text{Answer: }\mathsf{No\ solutions}}[/tex][tex]\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
A 'variable' is defined as when a characteristic of interest differs in kind or degree among various observations. True or false
True ,A 'variable' is defined as when a characteristic of interest differs in kind or degree among various observations.
How do nominal and ordinal differ?
Nominal: The information is only classifiable. Ordinal: The information is classifiable and rankable. Interval: The data can be equally spaced, categorized, and rated. Ratio: The data is evenly spaced, categorizable, rankable, and has a natural zero.What in statistics is a ratio variable?
Multiplicity of ratio variables (statistics) a variable with interval characteristics as well as meaningful ratios between any two of its values, which makes multiplication and division operations comprehensible.
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On the following number line, what number would you plot at point C?
A
+++
6
06.038
6.408
6.82
6.983
6.1
6.2 6.3
B
++++
6.4 6.5 6.6
6.7
C
D
++++
6.9
7
6.8
Answer:
Step-by-step explanation:
69420 hello my name is 69420
D
S
Ed
D
17k to 19.04k increase. What is the percent increase?
Need Answered ASAP
Answer:
4 %
Step-by-step explanation:
Select 3 collinear points.
r
A
B
D
s
N
C
What is the side length of a square with an area of 121 square centimeters?
In centimeters
The answer to this question is:
Size of a square's side = 11 cm
A Square is a flat geometric shape with four right angles and equal sides. The square's four sides are equal to one another or congruent. The square's opposing sides run parallel to one another. The square's diagonals form a 90° angle with one another. The two diagonals of the square are equivalent to one another. The square is made up of four vertices and four sides.
Area of square = ( Side )²
Given that:
Area of square = ( Side )² = 121 cm²
Dimensions of a square's side = √ Area
so, the length of the square's side = √ 121
= √ 11*11
= √ ( 11 )²
= 11
Thus, side of the square = 11 cm
Therefore, side length of square = 11cm
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Who is correct? (−3, 6), (−2, 4), (−3, −1), (−1, −6), (−4, −5), (−2, −7), (−5, −9), (−8, −9), (−12, −3), (2, 4), (3, 2) and (4, 1).
Regarding the quadrants, we have that:
Leila is correct, as most y-coordinates are also negative, meaning that most points are in quadrant 3.
What are the signals of the coordinates in each quadrant?There are four quadrants of points (x,y), and their signals are given as follows:
Quadrant 1: x > 0, y > 0.Quadrant 2: x < 0, y > 0.Quadrant 3: x < 0, y < 0.Quadrant 4: x > 0, y < 0.For this problem, we have that Leila is correct, as most y-coordinates are also negative, meaning that most points are in quadrant 3.
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There is enough information to prove that triangles tno and gcm are congruent. true false
False, there is not enough information provided to Prove that both the triangles are congruent.
What is the congruent triangle?
Triangles have three sides and three angles, as we discovered in pre-algebra. We also discovered that a triangle's total angle is 180 degrees.
Congruent triangles are two triangles that are the same size and shape. Two congruent triangles remain congruent even if we flip, turn, or rotate one of them.
Two triangles must have the same angles and, as a result, must be congruent if their sides are the same. If two triangles are congruent or not, we may determine this simply by looking at their sides.
These two triangles are also equivalent if we know that two sides of one triangle and the angle between them are congruent to two sides and the angle between them of another triangle.
If we know that two angles and the side between them in one triangle are congruent with two angles and the side between them in another triangle, then these two triangles are probably congruent.
When two angles and a non-included side in one triangle are congruent to the corresponding angles and side of another triangle, we are left with the final scenario that results in congruent triangles.
The given data doesn't satisfy any of the conditions.
Hence, there is not enough information provided to Prove that the two triangles are congruent.
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Answer:
tru but u gotta put a picture next time man
Step-by-step explanation:
How much will a person pay for 1.4 pounds of bananas at a price of $1.85 per pound?
1. Yu Yan competes in a sprint triathlon. The race consists of three parts: a 0.5-mile swim, a
12.4-mile bike ride, and a 3.1-mile run.
a. Yu Yan completes the swim portion of the sprint triathlon in 25 minutes. What is her average
swimming speed in miles per minute?
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
a farmer has feet of fenced area available to enclose a rectangular area bordering a river. if no fencing is required along the river, find the dimensions of the fenced area that will maximize the area. what is the maximum area?
The dimensions of the fence that will maximize the area are-
Length = 1350 ftWidth = 675 ftMaximum area = 911250 sq. ftWhat is rectangular area?Multiply the width by the height of a rectangle to find its area. If we know the lengths of two sides of a rectangle, we can calculate the height and width.
Now, as per the question;
Let 'L' be the length and,
'W' width of the rectangular
Also, let the river is running along L.
Perimeter to be covered by fence:
P = L + 2W
2700 = L + 2W
Thus, L= 2700 - 2W
Substitute the value of L in the area
Area, A= LW
A = (2700 - 2W)W
A = 2700W - 2W²
This is a quadratic equation;
Now, the vertex of the rectangular with the greatest area will have the greatest width.
(W,A), where W= -b/2a where b = 2700 and a = -2
Solve for W,
W = -2700/2×(-2)
= -2700/-4
W = 675 ft.
Substitute the value of W in L to find it.
L= 2700 - 2W
= 2700 - 2×675
L = 1350 ft
Thus, the maximum area will become;
Maximum area A = 1350 × 675
Maximum area A = 911250 sq. ft
Therefore, the maximum area is found to be 911250 sq. ft
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The complete question is-
A farmer has 2700 feet of fencing available to enclose a rectangular area bordering a river. if no fencing is required along the river, find the dimensions of the fence that will maximize the area. what is the maximum area
Someone pls help with this !! Tyyy
Answer:
a , b , e , f
Step-by-step explanation:
Factor.
1. 9a²-18a
2. 16a³b³ +32a¹b
3. x2+x^ + xử
4. 3x5 + 4x4 - 5x²
5. 2x³-X
Please Help
The below mentioned are the factors of given equations
Factorization:
In mathematics, factorization or factoring is the method of expressing a quantity or another numerical component as a product of many factors, typically small or easier components of the same kind.
In the case of integers, ancient Greek mathematicians were the first to consider factorization. They demonstrated the fundamental theorem of arithmetic, which states that any positive integer can be taken account into a prime number product , which cannot be factored into integers greater than 1. Furthermore, this factorization is unique until the order of the factors is changed.
1)[tex]9a^{2}-18a=9a(a-2)[/tex]
2)[tex]16a^{3}b^{3} +32ab=16ab((ab)^{2} +2)[/tex]
3) inappropriate question
4)[tex]3x^{5} +4x^{4} -5x^{2} =x^{2} (3x^{3} +4x^{2} -5)[/tex]
5)[tex]2x^{3} -x=2(x-1)(x+1)[/tex]
Therefore,The above mentioned are the factors of the given questions.
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If i have 608 employees and the total salary is $39,086,197.48; what is the average salary of employees?
Answer:
$64,286.51
Step-by-step explanation:
This is the arithmetic mean, and is calculated by adding a group of numbers and then dividing by the count of those numbers. In this case, you have the total number of employees and the total salary.
39,086,197.48 ÷ 608 = 64286.5090132
You would then round up.
Write and solve an equation to answer the question. The perimeter of the school crossing sing is 120 inches. What is the volume of s?
The value of the s for the school crossing sign is (s = 18).
What is defined as the perimeter?The total distance round the shape is described as its perimeter.
It is the length of every two-dimensional geometric shape's outline or boundary. Depending on the dimensions, the perimeters of differing results can be identical in size.The perimeter of a shape is the length covered by its boundary. As a result, the perimeter's units will be identical to the length's units. We can call perimeter one-dimensional. As a result, it can be measured in millimeters, kilometers, centimeters, and other units.The perimeter of school crossing board is 120 inches.
2s + s + s + ( s + 6 ) + ( s + 6 ) = 120 (perimeter)
6s + 12 = 120
6s = 120 – 12
6s = 108
s = 108/6
s = 18 units
Therefore, for the school crossing sign, the value of s is found as (s = 18) inches.
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The correct question is-
Write and solve an equation to answer the question. The perimeter of the school crossing sing is 120 inches. What is the value of s?
Opposite sides are congruent.
Diagonals are perpendicular.
Exactly one pair of opposite angles are
congruent.
Diagonals are congruent.
Diagonals bisect opposite interior angles.
Consecutive interior angles are
supplementary.
Answer:
Diagonals linse
Step-by-step explanation:
convert 574 inches to yards foot and inches
Answer:
Firstly, you need to divide by 36! That'll tells you how many yards there are. Then, divide the remainder by 12! That'll tells you how many feet are there. The final remainder tells you the number of inches!
In the year 2000, a company made $2.2 million in profit. for each consecutive year
after that, their profit increased by 13%. how much would the company's profit be in
the year 2003, to the nearest tenth of a million dollars?
The company's profit in the year 2003 is $3.1 million
Profit is defined as the amount of revenue generated after deduction of all the liabilities.
Given that in the year 2000 profit = $2.2 million
Each year increase in profit = 13% =0.13
Total number of year = 2003-2000=3 years
Profit is denoted by
[tex]profit=initial profit(1+each.year.increase)^{years}[/tex]
Substituting the values we get
profit=[tex]2.2(1+0.13)^3[/tex]
=[tex]2.2(1.13)^3=2.2*1.442897[/tex]
=3.174373
=3.1 million
Therefor , the company's profit in the year 2003 is $3.1 million
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A school has 1000 students. of these, 3/4 are boys. how many of the students are boys? how many of the students are girls?
Answer:
750 students are boys, 250 are girls.
Step-by-step explanation:
1/4 of 1000 is 250.
250 + 250 + 250 = 750 boys.
if 3/4 are boys, then 1/4 (the rest of the school population) are girls.
150 students are girls.
18 x 4/3 please help me. ☕
Answer:
24
Step-by-step explanation:
18/3 = 6
6*4 = 24
hi
18 = 6*3
so 18* 4/3 = 6*3*4 /3 = 24
a3 = 125 solve (Type integers or simplified fractions.)
Answer:
41.666 =~41.67
Step-by-step explanation:
3a=125
a=125÷3
a=41.67
Answer:
41.667
Step-by-step explanation:
3a=125
a= 125/3
a=41.667
|x+4|<9
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If f (x) = 3x - 1 and g (x) = x²+1, find the following.
a) f(-1) + g (4) =
b) g(2) - g (-3) =
Will give 5 star rating and Brainliest thank you.
which function below has the largest slope? f(x) x f(x) −3 −10 −1 −7 1 −4 g(x) equals one half x plus 3 h(x) lance gains 1 level each time he plays his favorite video game. he started at level 10. (2 points) f(x) g(x) h(x) the functions all have the same slope
The function with the largest slope would be f(x) = 1.5
What is the slope in math?
The inclination of a line with respect to the horizontal is measured numerically. The ratio of the vertical to the horizontal distance between any two points on a line, ray, or line segment is known as its slope in analytic geometry ("slope equals rise over run").For f(x), choose any two points say (-3,-10) and (-1,-7) where
x1 = -3 ; y1 = -10 ; x2 = -1 ; y2 = -7
Find the slope (m)
m=(y2 - y1) / (x2 - x1) = (-7 - -10)/ (-1 - -3) = 3/2 or 1.5
slope of f(x) = 1.5
g(x) = 1/2 x + 3
standard formula: y = mx + b where m is the slope.
slope of g(x) = 1/2 or 0.5
Since lance gains 1 level every time he plays,
slope = 1/1 = 1 so, slope of h(x) = 1
the function with the largest slope would be f(x) = 1.5
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1. Find the length of the indicated side.
Helpp i dont know what to do after finding the angle (39) pls explain
Using Trigonometric ratios, we can conclude the length of the indicated side is 12.70m.
It can be solved using Trigonometric ratios and Pythagoras theorem
Firstly using Trigonometric ratios
Using Sinθ,
Sinθ = perpendicular / hypotenuse(h)
Sin 39 = 8 / h
0.63 = 8 / h
h = 8 / 0.63
h = 12.70
∴ The length of indicated side is 12.70m
Secondly, using Pythagoras theorem,
(hypotenuse)² = (Altitude)² + (Base)²
⇒ (H)² = 8² + 10²
⇒ (H)² = 64 + 100
⇒ (H)² = 164
⇒ H = √164
⇒ H = 12.80
∴ The length of indicated side is 12.80m
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I need this asap pleasee!
Answer:
The answers are below
Step-by-step explanation:
The greater sign is > and the less then symbol is <
Using the red arrows on the number line, you can tell which one is bigger or less. The dot is colored in so it has to have a line under it. So for the first one (top, left), The red arrow is pointing to the right side meaning x is bigger than 3. Therefore x ≥ 3.
In the next one (top, right) the arrow is pointing to the negative side so that one must be less than 3. The dot is also colored in meaning it is: x ≤ 3
In the next one (bottom, left) the arrow is pointing to the right, the dot not colored in, so it has no line. Therefore it is x > 3
Last one (bottom right) the arrow is pointing left, dot is white meaning that the answer is x < 3
If you're wondering what the open dots and closed dots mean:
An open dot is used to show that the ray's endpoint is not a component of the solution when the inequality is "strict" ( < or >).
A closed dot is used to denote that the endpoint is a component of the solution for the other types of inequalities (≥ and ≤ ).
