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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7, 13, 9, 15, 11, 7, 11. Find the Interquartile range of this data set
What is the volume of the rectangular prism?
4 GET EVE ⠀ Directions:
Answer:
not a solution.. simple not needed to explain too
Which function has a vertex at the origin?
f(x) = (x + 4)²
f(x) = x(x-4)
f(x) = -x²
f(x) = (x-4)(x+4)
Answer:
[tex]f(x)=-x^2[/tex]
Step-by-step explanation:
Vertex form of a quadratic function:
[tex]f(x)=a(x-h)^2+k[/tex]
where:
(h, k) is the vertexa is some constantIf the vertex is at the origin, then (h, k) = (0, 0)
[tex]\implies f(x)=a(x-0)^2+0[/tex]
[tex]\implies f(x)=ax^2[/tex]
Comparing this with the answer options suggests that the function with a vertex at the origin is [tex]f(x)=-x^2[/tex]
If f(x) = x + 1 and g(x) = 2x – 7, which expression is equivalent to [f o g](3)? (3 + 1)(2(3) –7) 2(3)2 – 6 2(3 + 1) – 7 (2(3) – 7) + 1
Answer:
Solution
-1
f
x=
1
-X+
2
Step-by-step explanation:
f(x=2x-7
Solving Steps
y=2x-7
Interchange the variables
x=2y-7
Swap the sides
2y-7=X
Move the constant to the right
2y=X+7
Divide both sides
1
y=
>+*.
7
2
Solution
-1
f
x=
1
-X+
2
Phyllis invested 800 dollars into two different accounts, a portion earning a yearly interest rate of
4
percent per year compounded monthly and the rest earning a rate of
6
percent per year compounded quarterly
After 12 years the investments were worth $1579.05. How much money did she invest at each rate
The amount of money that Phyllis invested at each given rate of 4 and 6 percent is = $394.57 and $591.86 respectively.
Calculation of the total capital investedThe time the investment lasted= 12 years.
Simple interest = 1579.05 - 800= $779.05
The principal capital= $800
Rate of the both capital invested;
= SI × 100/P ×T
= 779.05 × 100/800 × 12
= 77,905/9600
= 8.11%
To find the amount of money that Phyllis invested at each given rate,
Rate 1 = 4/8.11× 800
= 3200/8.11
= $394.57
Rate 2 = 6/8.11× 800
= 4800/8.11
= $591.86
The amount of money that Phyllis invested at each given rate of 4 and 6 percent is = $394.57 and $591.86 respectively.
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Help for college scholarships! Must be a paragraph.
How has your family background affected the way you see the world?
Family background refers to the culture and tradition of the family into which a person is born.
What is family background?Family background refers to the culture and tradition of the family into which a person is born. it is worthy of note that most of this family traditions are unspoken yet are firmly entrenched in the psyche of individual as he/she grows.
My family is strictly conservative having had a Southern Baptist orientation. My dad believes deeply in religion and a moralist and perfectionist.
As a result of this, I find myself always grappling with the unfortunate disorder in the world; always trying to bring order to my world as much as I can.
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The brick will be painted. Which measure will help the painter know how much paint to buy?
Step-by-step explanation:
B) Surface Area
C) Volume
Find the value of each variable
Answer:
x = 10[tex]\sqrt{2}[/tex] , y = 10[tex]\sqrt{6}[/tex]
Step-by-step explanation:
using the sine and cosine ratios in the right triangle and the exact values
cos60° = [tex]\frac{1}{2}[/tex] , sin60° = [tex]\frac{\sqrt{3} }{2}[/tex] , then
cos60° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{20\sqrt{2} }[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )
2x = 20[tex]\sqrt{2}[/tex] ( divide both sides by 2 )
x = 10[tex]\sqrt{2}[/tex]
and
sin60° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{y}{20\sqrt{2} }[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )
2y = 20[tex]\sqrt{2}[/tex] × [tex]\sqrt{3}[/tex] = 20[tex]\sqrt{6}[/tex] ( divide both sides by 2 )
y = 10[tex]\sqrt{6}[/tex]
I NEED HELP NOWWWW PLSSS
From this data, how many male, female, adult, and baby moose do you predict are in the park?
Elk Mountain Goat Deer Moose
Male 105 71 42 52
Female 120 93 63 34
Adult 173 103 72 58
Baby 52 61 33 28
The data shows that the number of male, female, adult, and baby moose that are in the park will be 52, 34, 58, and 28 respectively.
What is data?It should be noted that data simply means the facts and statistics that are given which are used for analysis.
In this case, the data shows that the number of male, female, adult, and baby moose that are in the park will be 52, 34, 58, and 28 respectively. This can be seen from the information in the table.
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Question 32 of 40
The ratio
opposite
hypotenuse
describes which function?
The ratio [tex]\frac{Opposite}{Hypotenuse }[/tex] describes the Sine function . The correct option is C. Sine
TrigonometryFrom the question, we are to determine the function that the ratio of opposite to hypotenuse describes
By SOH CAH TOA
We have that
[tex]Sine = \frac{Opposite}{Hypotenuse }[/tex]
[tex]Cosine = \frac{Adjacent}{Hypotenuse }[/tex]
and
[tex]Tangent = \frac{Opposite}{Adjacent}[/tex]
Hence, the ratio [tex]\frac{Opposite}{Hypotenuse }[/tex] describes the Sine function . The correct option is C. Sine
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Can someone help me? I’ll give brainliest to whoever gets it right first
Answer:
108°
Step-by-step explanation:
From the diagram,
Angle X + Angle CXD = 180°
Angle X + 72° = 180°
Angle X = 180° - 72° = 108°
Of the following fractions: 1/4, 7/9, 7/12, and 9/16, which is the largest?
Answer:
1/4, 7/8, 7/12, 9/16
LCM of 4,8,12,16 = 48
1/4= 1×12/4×12= 12/48
7/8= 7×6/8×6= 42/48
7/12= 7×4/12×4= 28/48
9/16= 9×3/16×3= 27/48
hence, 7/8 is the largest fraction. I hope it helps ya!!
The largest fraction is 7/8.
What is Least Common Multiple?Least Common Multiple is defined as the smallest number that is a multiple of two or more numbers.
Given fractions,
1/4, 7/8, 7/12, 9/16
LCM of 4,8,12,16 = 48
1/4= 1×12/4×12= 12/48
7/8= 7×6/8×6= 42/48
7/12= 7×4/12×4= 28/48
9/16= 9×3/16×3= 27/48
Since the largest will be the fraction
NUMERATOR > DENOMINATOR
Hence, the largest fraction is 7/8.
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Using horizontal strip, determine the area of the region bounded by curves x² + 4y - 8 = 0 and x =
2y
The Area of the region bounded by curves = 9 sq.units.
What is Area ?Area is the space occupied by a two dimensional figure on a two dimensional space coordinate.
The two curves given are
x² + 4y - 8 = 0 and x =2y
Convert the two equation so ‘x’ is the dependent variable.
y = -(1/4) x² +2 and y = (1/2)x
Find the limit by the intersection point of both the graph
so (-4, 2) and (2, 1)
The x-values of the line are greater so subtract the parabola:
A = ∫ (1/2)x - (-(1/4) x² +2 ) in the limits of (-4 and 1)
The Area = 9 sq.units.
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in a circle H with m angle GKJ=27 find the m angle GHJ
In a circle H with a measure of angle ∠GKJ = 27°. Then the measure of angle ∠GHJ will be 54°
What is a circle?It is the center of a line drawn from the center to an equidistant location. The space between the center and the periphery of a circle is measured in radius.
In a circle H with a measure of angle ∠GKJ = 27°.
Then the measure of angle ∠GHJ will be
We know that a chord's slope in the center is double that of the chord's slope at the perimeter.
Then we have
∠GHJ = 2 x ∠GKJ
∠GHJ = 2 x 27°
∠GHJ = 54°
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solve u^2 = -4, where u is a real number. Simplify your answer as much as possible.
will mark brainliest if correct
Answer:
2i and -2i
Step-by-step explanation:
I'll change u to x to be easier to understand.
x^2 = -4
sqrt(x^2) = sqrt(-4)
sqrt(-4) = 2i, or -2i
if the absolute terms in the expansion of (x2+k )12 is 495 find the value of k
x
Answer:
if the absolute terms in the expansion of (x2+k )12 is 495 find the value of k
x
Step-by-step explanation:
Kevin sold a house and receives a 6 1/2% commission he gave the listing broker 30% or 3,575 what was the price of the house
Answer:
12 just because I need the free credit things sorry this ain't gonna be helpful lol
(2x4 +7) + (5x4 - 4)
simpfly
Step-by-step explanation:
(2x4 +7) + (5x4 - 4)
=(8+7) + (20-4)
=15+16
= 31
Hope it helps
Answer: Heyaa! ~
Your Answer is... 31!
Step-by-step explanation:
(2x4 +7) + (5x4 - 4) = 31/ 7x⁴+3
Hopefully this helps you ! ^^
Please show how you solved
Answer:
x = 7 degrees
Step-by-step explanation:
The unlabelled angle at M PLUS 12x + 24 = 180
then the unlabelled interior angle is 180 - (12x+24)
The sum of the interior angles then = 180
80 + 4x + 180-(12x+24) = 180
236 -8x = 180
x = 7
pls help it’s the last day of school
Answer:
12.56ftcube
Step-by-step explanation:
if V=(3.14×1^2)×4= 3.14 ×4=12.56
What is the solution to the system of equations graphed below?
realmente no lo se bro per necesito completar este paso
Identify some exterior angles in the figure. Select the two correct answers.
O c
O e
O a
O d
O b
I WILL GIVE YOU BRAINLIEST!!
a pet store has 8 empty fish tanks that each hold 5544 cubic inches of water one goldfish requires a minimum of 1386 cubic inches of water.
What is the greatest number of goldfish that the pet store can have given the volume of water needed for one goldfish?
Answer:
32 goldfish
Step-by-step explanation:
Given:
Number of fish tanks = 8Volume of water per fish tank = 5,544 in³Water required by 1 goldfish = min 1,386 in³Number of fish per tank = water per tank ÷ water per goldfish
= 5544 ÷ 1386
= 4
Therefore, each tank can hold a maximum of 4 goldfish.
Greatest number of goldfish = number of tanks × fish per tank
= 8 × 4
= 32
TYPES OF CARS WORKED ON German cars 25% Other 10% American 50% Japanese 15% These are the types of cars worked on in the auto service.
6) What is the probability that the next car worked on will be Japanese or German?
7) If the mechanics work on 6,000 cars next year, how many cars would probably be Japanese?
I really would appreciate help on this! Thank you
Answer:
6) 40%7) 900 carsStep-by-step explanation:
German 25%
Other 10%
American 50%
Japanese 15%
……………………………………………
6) the probability that the next car worked on
will be Japanese or German :
p(J∪G) = p(J) + p(G) = 15% + 25% = 40%.
…………………………………………………………
7) the probable number of Japanese cars :
[tex]6000\times \frac{15}{100} = 900[/tex]
For a computer company, the cost to produce one PC is $1410 plus a one-time cost of $125,000 for research and development. The revenue from selling one PC is $1984. How many PCs must they sell to make a profit?
The temperature at 10:00 AM is 260 c. if temperature rises 4 degrees more each hour. What will be temperature at 1:00 pm in the Afternoon?
Answer:
272 c
Step-by-step explanation:
Roses by 4 every hour
10 to 1 can be represented in 24 hour time as 10 to 13
13 subtract 10 is 3
3 multiplied by 4 is 12
260 add 12 is 272 c
Which image below is an acute triangle?
Triangle A has angles measuring ninety five degrees, forty five degrees, and thirty degrees. Triangle B has angles measuring one hundred degrees, twenty five degrees, and twenty five degrees. Triangle C has angles measuring fifty degrees, sixty five degrees, and sixty five degrees. Triangle D has angles measuring thirty degrees, one hundred ten degrees, and twenty degrees.
Answer:
The answer is Triangle C
Step-by-step explanation:
6230000 in standard form
Answer:
6.23*10^6
Step-by-step explanation:
in standard form, it should be written as x*10^n, and x is only allowed from 1-9, so
1) write the first number and add a decimal point(.) and copy down the numbers behind the first number (DO NOT WRITE 0):
6.23
2) check how many numbers are they behind the first number
6230000
~~~~~~
in here, it's 6numbers, so 10^6
3) all in all, your answer is
6.23*10^6
For the following trapezoid, h = 5 ft, b = 7.9 ft, and B = 14.6 ft. What is the area?
Answer:
The area of the trapezoid is 56.25² feet.
Step-by-step explanation:
The formula for the area of a trapezoid is [tex]A=\frac{b+B}{2} h[/tex]
A = area (of the trapezoid)b = base of the trapezoidB = (other) base of the trapezoidh = height of the trapezoid*Note: Trapezoids have 2 bases that are parallel to one another, but are not always the same length.
Using the information given to us, we can simply plug in numbers into the equation. By doing so, we'd get [tex]A=\frac{7.9+14.6}{2} 5[/tex]. By plugging this into a calculator, you'd get [tex]A=56.25[/tex].