Suppose you have entered 97-mile biathlon that consists of a run and a bicycle race. During your run, your average velocity is 8 miles per hour, and during your bicycle race, your average velocity is 27 miles per hour. You finish the race in 5 hours. What is the distance of the run? What is the distance of the bicycle race?
The distance of the run Will be 16miles and the Distance of the bicycle race will be 81 miles.
What is speed?Speed is defined as the ratio of the time distance travelled by the body to the time taken by the body to cover the distance.
Distance = average velocity × time
Let the time and distance of the run, respectively, be t₁ and.d₁
Let those of the bicycle race be t₂ and d₂
From the question,
t₁ + t₂ = 5
d₁ = 8t₁
d₂ = 27t₂
Total distance = 97
8t₁ + 27t₂ = 97
8 ( 5 - t₂ ) + 27t₂ = 97
40 - 8t₂ + 27t₂ = 97
40 + 19 t₂ = 97
19t₂ = 57
t₂ = 3 hours
t₁ + t ₂ = 5
t₁ = 5 - t₂
t₁ = 5 - 3 = 2 hours
Now the distances are calculated as:-
d₁ = 8t₁ = 8 x 2 = 16 miles
d₂ = 27t₂ = 27 x 3 = 81 miles
Therefore the distance of the run Will be 16miles and the Distance of the bicycle race will be 81 miles.
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please help me. i’m very stressed.
[tex]\sqrt[n]{a^n}=a[/tex], therefore [tex]\sqrt[4]{5^4}=5[/tex].
Answer:
It is 5
Key solutions:
[tex]\left(\sqrt[n]{a}\right)^n=a[/tex]Step-by-step explanation:
Isolate the exponents and remove the square, giving you 5
[tex]\left(\sqrt[4]{5}\right)^4\\=5[/tex]
If you rolled two dice, what is the probability
that you would roll a sum of 3?
second
1
first
2 3
5
4
6
1
[?]
1,1 1,2 1,3 1,4 1,5 1,6
2 2,1 2,2 2,3 2,4 2,5 2,6
3 3,1 3,2 3,3 3,4 3,5 3,6
4,1 4,2 4,3 4,4 4,5 4,6
5 5,1 5,2 5,3 5,4 5,5 5,6
6,1 6,2 6,3 6,4 6,5 6,6
6
Probability =
Desired Outcome
All Outcomes
Simplify your fraction, then enter the numerator AND DENOMINATOR.
Thank youuuu
Answer:
2 / 36 = 1/18
Step-by-step explanation:
there are 2 ways to get 3
1 then 2 or 2 then 1 , 2 out of a possible 36 outcomes
This is super easy. Explanation, please!
The proposition given by definition of function "division" is false as [tex]\frac{f}{g} \ne {(1, 2)}[/tex] for the former function f = (9, 5) and the latter function g = (9, 0).
How to analyse a operation between two functions by propositional approach
In this question we have a definition of division between two functions, consisting in dividing each component of the ordered pair of the former function (f) by the component of the ordered pair of the latter function (g) such that resulting ordered pair is (1, 2).
We must check if the proposition is true for every ordered pair. Let analyze each case:
Case I
[tex]\frac{f}{g} = \left(\frac{1}{1}, \frac{6}{3} \right) = (1, 2)[/tex]
Case II
[tex]\frac{f}{g} = \left(\frac{9}{9}, \frac{5}{0} \right) = (1, NaN)[/tex]
Thus, the proposition is false.
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draw a point that belongs to the solution region of this system of inequalities. y>1.5^x + 4 y< 2/3x + 6
The point (1,6) belongs to the solution region of the system of inequalities.
How to determine the point in the solution region?The system of inequalities is given as:
y>1.5^x + 4
y< 2/3x + 6
Next, we plot both inequalities on a graph (see attachment)
From the attached graph, the point (1,6) is on the solution region of the inequalities
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Fahari kicks a ball on the ground into the air. One
second after being kicked, the ball reaches its
maximum height of 16 feet above the ground, and
2 seconds after being kicked, the ball is back on the
ground. A quadratic function models the height h(t) ,
in feet, of the ball t seconds after Fahari kicks it.
Which equation defines this relationship?
The equation that defines the relationship between the height and the time and models the position of the ball in time is the quadratic function y = - 8 · t² + 24 · t.
How to derive a quadratic function for the height of a ball
Quadratic functions are polynomials of grade 2 of the form y = a · t² + b · t + c, where t and y are the time and the height of the ball, in seconds and feet, respectively. To determine the value of the three coefficients we need to know three different points of the form (t, y).
If we know that (t₁, y₁) = (0 s, 0 ft), (t₂, y₂) = (1 s, 16 ft) and (t₃, y₃) = (3 s, 0 ft), then the quadratic function is:
a · 0² + b · 0 + c = 0 (1)
a · 1² + b · 1 + c = 16 (2)
a · 3² + b · 3 + c = 0 (3)
The solution to this system is a = - 8, b = 24, c = 0.
The equation that defines the relationship between the height and the time and models the position of the ball in time is the quadratic function y = - 8 · t² + 24 · t.
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Directions: Name each polygon and tell if it is regular or irregular.
Answer:
regular pentagon. 2 irregular. 3 irregular. 4 regular octagon. 5 regular nonagon. remember that regular polygon is a polygon that
Which of the following is a complex number?
OA. -8√-3/1/2
OB. 3√/+√√
9
5
OC. 9-17
OD. 5-2V7
2√7
4
Answer:
[tex]B)~ 3\sqrt{\dfrac 75} + \sqrt{- \dfrac 95 }[/tex]
Step-by-step explanation:
[tex]3\sqrt{\dfrac 75} + \sqrt{- \dfrac 95 }\\\\\\= 3\sqrt{\dfrac 75} + i\sqrt{\dfrac 95 }\\\\\text{It is now in the standard form of a complex number (a+bi).}[/tex]
Rose bought a bag of potatoes for $6.00 and some granola bars for $5.25 per package. Her total bill was $74.25. How many packages of granola bars did she buy? Enter your answer in the box.
Answer:
Rose bought 14 packages of granola bars.
Step-by-step explanation:
Total bill = 1 bag of potatoes + x amount of packages of granola bars
Total bill = $74.25
1 bag of potatoes = $6.00
1 package of granola bar = 5.25
We set the equation to:
74.25 = 6.00 + 5.25x
Subtract 6.00 from both sides:
68.25 = 5.25x
Divide both sides by 5.25 to leave x by itself
68.25/5.25 = 5.25x/5.25
13 = x
This means Rose bought 13 packages of granola bars.
Let's recheck our work by inputting x = 13 into the equation:
74.25 = 6.00 + 5.25(13)
74.25 = 6.00 + 68.25
74.25 = 74.25
15
5. At the Redbridge School, of pupils have a pet dog, & have a cat and have a
The rest have no pets.
A)What fraction of the children has no pet? Write this in its simplest form.
B)There are 250 pupils at the School. How many children have no pets?
C)At the Bluebell School, 23% have no pets. What percentage increase of pupils at
the Bluebell School have no pets compared to the Redbridge School?
A percentage is a way to describe a part of a whole. The number of people who don't have pets is 50 people.
What are Percentages?A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.
To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.
Given at the Red bridge School, 1/3 of pupils have a pet dog 2/5 have cat and 1/15 have a hamster.
A.) Number of people who don't have pets = 1 - 1/3 - 2/5 - 1/15
= (15-5-6-1)/15
= 3/15
= 1/5
B.) Given there are 25 people at the school. Therefore, the number of people who don't have a pet is,
Number of people who don't have pets = (1/5) × 250 = 50
C.) The percentage increase of pupils at the Bluebell School that has no pets compared to the Red bridge School is,
Percentage increase = (23%-20%)/20% × 100% = 15%
Hence, the number of people who don't have pets is 50 people.
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Find the length of the arc in terms of pi
Answer:
[tex]9\pi[/tex]
Step-by-step explanation:
[tex]\text{Arc length,}~ s = r\theta\\\\~~~~~~~~~~~~~~~~~~=12 \times \left( \dfrac{135\pi}{180} \right)\\\\~~~~~~~~~~~~~~~~~~=9\pi[/tex]
If you were charged $151 in taxes on a $3,020 purchase, you were charged Blank 1 % on the purchase.
Answer:
5 %
Step-by-step explanation:
3020 * x = 151 x is the percentage in decimal form
x = 151 / 3020 = .05 which is 5 %
WHAT IS THIS HELP
if u put a bad answer i'll report
Answer:
C
Step-by-step explanation:
Two negatives cancel out and turn into a positive.
In the expression 11 - ( -3 5/8 ) there are two negative signs. If the parenthesis are removed, the two negative signs cancel out and turn into a positive and we are left with 11 +3 5/8
So the answer is C
3(5z-7) - 2 (9z-11) = 4 (8z-13) - 17
how to find the area of a trapezium
A chef randomly pulls cupcakes from a box containing 6 cupcakes of the same shape and size. There is 1 cupcake with vanilla frosting, 3 cupcakes with chocolate frosting, and 2 cupcakes with pink frosting. He draws 1 cupcake and then draws out another cupcake without replacing the first one. Find the probability of picking 1 cupcake with chocolate frosting followed by another cupcake with chocolate frosting, and show the equation used, and solve it.
Answer:
To pull our the first chocolate, it would be a probability of 1/2.
To pull the second chocolate out, it would be a probability of 2/5.
Hope that helps, you just use ratios, the first cupcake needs to be chocolate, and there are 3 chocolate cupcakes out of the 6. Make that into a fraction 3/6, and simplify into 1/2.
The same goes for the second cupcake.
Graph the function and identify the domain and range.
y=-3x^2
Answer:
Domain:
X is all the real numbers
or
[tex] - \infty < x < \infty [/tex]
Range:
[tex]y \leqslant 0[/tex]
or
[tex] - \infty < y \leqslant 0[/tex]
Step-by-step explanation:
This is the graph.
A circular disc has circumference 250 cm.
Calculate the radius of the disc.
[tex]\textit{circumference of a circle}\\\\ C=2\pi r ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ C=250 \end{cases}\implies 250=2\pi r\implies \cfrac{250}{2\pi }=r\implies \stackrel{cm}{39.79}\approx r[/tex]
If the property tax on a $250,000 home is $1200, what is the tax on a $120,000 home?
Answer:
well i mean it all depends were you live at
Step-by-step explanation:
in new york it will be $36,198. but in California it would be about $31,682 and Your average tax rate is 16.51% and your marginal tax rate is 24%.
This figure is a square, with side lengths as shown.
415 mm
What are the perimeter and the area of the square?
80
200
400
8√5 16√5
32√5
The perimeter of the square is,
The area of the square is_
millimeters.
square millimeters
The perimeter and area of the square are 16√5 mm and 80 mm²
How to find perimeter and area of a square?Perimeter of a square = 4L
where
l = lengthTherefore,
Perimeter of a square = 4 × 4√5
Perimeter of a square = 16√5 mm
Area of a square = l²
Area of a square = (4√5)²
Area of a square = 16 × 5
Area of a square = 80 mm²
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A flower bed is in the shape of a rectangle. It measures 7 yards long and 3 yards wide. David wants to use mulch to cover the flower bed. The mulch is sold by the square foot. Find the area of the flower bed in square feet.
The area of the rectangle is equal to 216ft^2.
We have given that,
A flower bed is in the shape of a rectangle.
It measures 7 yards long and 3 yards wide. David wants to use a mulch to cover the flower bed.
The mulch is sold by the square foot.
A yard is equal to 3 feet.
7 yards = 7(3) = 24 feet
3 yards = 3(3) = 9 feet
What is the formula for the area of the rectangle?
Area of the rectangle= Lw
Area of the rectangle= 24(9)
Area of the rectangle= 216 ft^2
Therefore the area of the rectangle is equal to 216ft^2.
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whate is answer of 36-[100÷5{60-32(8÷4-1)}]
Answer:
[tex]67\frac{23}{28}[/tex]
Step-by-step explanation:
[tex]36-\left[100\div \:560-32\left(8\div \:4-1\right)\right]\\\\100\div \:560-32\left(8\div \:4-1\right)\\\\=100\div \:560-32\cdot \:1\\\\=\frac{100}{560}-32\cdot \:1\\\\=\frac{100}{560}-32\\\\=-\frac{891}{28}\\\\\\=36-\left(-\frac{891}{28}\right)\\\\36-\left(-\frac{891}{28}\right)\\\\=36+\frac{891}{28}\\\\\frac{36\cdot \:28}{28}+\frac{891}{28}\\\\\frac{36\cdot \:28+891}{28}\\\\=\frac{1899}{28}\\\\\\\frac{1899}{28}(1899\div28)=67\frac{23}{28}[/tex]
Please solve with explanation (high points)
So, we know that:
[tex]A=\dfrac{1}{2}ab\\P=a+b+c\\a^2+b^2=c^2[/tex]
We also know that [tex](a+b)^2=a^2+2ab+b^2[/tex]. We will use that fact to find [tex]c[/tex] in terms of [tex]A[/tex] and [tex]P[/tex].
[tex]A=\dfrac{1}{2}ab\Rightarrow 2ab=4A\\P=a+b+c\Rightarrow a+b=P-c[/tex]
Therefore:
[tex](P-c)^2=c^2+4A\\P^2-2cP+c^2=c^2+4a\\2cP=P^2-4A\\c=\dfrac{P^2-4A}{2P}[/tex]
A sum of Rs. 12,500 amounts to Rs. 16,500 in 4 years at the rate of simple interest. What is the rate of interest?
Answer:
100
Step-by-step explanation:
Answer:
The rate of interest is6.4 %
Step-by-step explanation:
Given : Principal (P) = Rs12500
Total amount (A) = Rs16500.
The time period (t) =5 years
To find : Rate of interest (R) = ?
Solution :
It is given that Principal (P) = Rs. 12500
Total amount (A) = Rs. 16500
The time period (t) =5 years
We have to find rate of interest (R).
We know the formula for simple interest as,
S.I. = A-P
= 16500±12500
= Rs. 4000
Now, to find rate of interest, use the formula for simple interest as
S.I. =
∴
∴ *R
∴
∴
∴R=6.4 %
∴ The rate of interest is6.4 %.
In which number does the digit 3 have a value that is ten times greater than the value of the digit 3 in the number 145,317?
A number where the digit 3 has a value ten times greater than the 3 in 145,317 can be 143,417.
How to work with place values?
In any number, the place value refers to the "place" that a digit has on a number. The first one is the units place, the second is the tens place, and so on.
As more in the left is the place value, the largest value it represents.
Particularly, in 145,317
The 3 is on the third place, so it represents the value 300.
For example, in 143,417
The 3 is more in the left than before, this time on the fourth place, this time the value of the 3 is 3,000.
Then, a number where the digit 3 has a value ten times greater than the 3 in 145,317 can be 143,417.
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A baker bakes 48 dozen doughnuts each morning. She sells 18 dozen
in her store and fills orders with the rest. Write a fraction to show the
portion of doughnuts the baker sells in her store. Be sure to simplify.
Answer:
30/48
Step-by-step explanation:
The mean temperature for the first 7 days in January was 4 °C. The temperature on the 8th day was -1 °C. What is the mean temperature for the first 8 days in January?
Answer:
3.375 °C
Step-by-step explanation:
Mean temperature for first 7 days = 4 °C
⇒ Total temperature over first 7 days = 4 °C × 7 = 28 °C
Temperature on 8th day = -1 °C
[tex]\sf mean=\dfrac{\textsf{sum of all the numbers}}{\textsf{amount of numbers}}[/tex]
Therefore, mean temperature for first 8 days:
= [28 - 1] ÷ 8
= 27 ÷ 8
= 3.375 °C
graph linear equation 6x - 2y = 12
The graph of the linear equation 6x - 2y = 12 would be option C .
What is a linear equation?Linear equation is equation in which each term has at max one degree. Linear equation in variable x and y can be written in the form y = mx + c
Linear equation with two variables, when graphed on the cartesian plane with axes of those variables, give a straight line.
Subtract both sides from 6x, leaving you with the equation:
-2y = -6x + 12
Now, you divide all of the sides by -2,
y = 3x - 6
The graph of the linear equation 6x - 2y = 12 would be option C .
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Conor’s monthly costs are £695 he wants to go on holiday and needs to save £680 how much does he need to save each month if he saves for 5 months
The amount of money Conor should save each month for 5 months is £136.
How much should he save each month?Division is the mathematical operation that is used to determine the quotient of a number. It involves grouping a number into equal parts using another number.
The amount of money Conor should save each month = total amount needed / number of month
£680 / 5 = £136
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The graph of y=kcos(8x)
The x coordinate of point A that is shown on the graph is 3π/16.
How to explain the graph?From the information given, y = kcos(8x). Also, the axis of symmetry is given as kx.
Therefore, the x coordinate will be:
= π/8 + π/16
The LCM of 8 as 16 is 16.
= 2π/16 + π/16
= 3π/16
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