The required real-world situation has been written in the solution part which could be modeled by the expression Y equals 1/20 XP.
A real-world situation that could be modeled by the expression Y = 1/20XP is the relationship between the distance a person runs and the number of calories they burn.
In this situation, Y represents the number of calories burned and X represents the distance run in miles. The constant 1/20 represents the rate at which calories are burned per mile.
For example, if a person runs 5 miles, we can substitute 5 for X in the expression to find the number of calories they burn:
Y = 1/20 × 5X
Y = 1/4
Thus, the person burns 1/4 calorie for every mile they run.
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Which rule defines S, for an = 3(0.7)n?
Sn=7(0.7n)
Sn = 2.1(0.7n)
Sn= 7(1-0.7n)
Sn= 2.1(1-0.7n)
Answer: C
Sn= 7(1-0.7n)
Step-by-step explanation:
The rule that defines S for [tex]a_n = 3(0.7)^n[/tex] is:
[tex]S_n = 7(1 - 0.7^n)[/tex]
The rule of S means that we calculate the rule that defines the sum of n terms of the geometric progression.
Given that:
[tex]a_n = 3(0.7)^n[/tex]
Rewrite as:
[tex]a_n = 3 (0.7)^n \times 1[/tex]
Replace 1 with 0.7/0.7
[tex]a_n = 3 (0.7)^n \times \frac{0.7}{0.7}[/tex]
Rewrite as:
[tex]a_n = 3 *0.7 \times \frac{(0.7)^n}{0.7}[/tex]
Apply law of indices
[tex]a_n = 3 \times 0.7 \times (0.7)^{n-1}[/tex]
[tex]a_n = 2.1 \times (0.7)^{n-1}[/tex]
The n term of a geometric progression is:
[tex]a_n = ar^{n-1}[/tex]
Compare [tex]a_n = ar^{n-1}[/tex] to [tex]a_n = 2.1 \times (0.7)^{n-1}[/tex]
[tex]a = 2.1[/tex] --- the first term
[tex]r = 0.7[/tex]
The sum of n terms of a geometric progression is:
[tex]S_n = \frac{a(1 - r^n)}{1 -r}[/tex]
This gives:
[tex]S_n = \frac{2.1(1 - 0.7^n)}{1 -0.7}[/tex]
[tex]S_n = \frac{2.1(1 - 0.7^n)}{0.3}[/tex]
[tex]S_n = 7(1 - 0.7^n)[/tex]
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6. Mrs. Sam buys pencils for $15 per one hundred packs.
a. If she sells them to her students for 10 cents each, what is her profit/loss?
b. If she sells them to her students for 25 cents each, what is her profit/loss?
c. What price should she sell them at to not make or lose any money?
Answer:
a.) her loss is 5 dollars
b.) her profit is 10 dollars
c.) she should sell them for $0.15
State if the three numbers can be the measures of the sides of a triangle.
5, 12, 10
Yes or No
Answer:
yes
Step-by-step explanation:
write the expression in standard form
2x-(5+4x)
Answer:
- 2x - 5
Step-by-step explanation:
2x - (5 + 4x)
2x - 5 - 4x
- 2x - 5
Answer: The answer is -2x - 5
Step-by-step explanation:
-5x - 5 > 15 solve this inequality
Answer:
-5×-5>15
+5 +5
-5×>20
÷-5 ÷-5
x<-4
whe you divide by a negativr you flip the sign
In ΔQRS, the measure of ∠S=90°, QR = 7.7 feet, and SQ = 6.5 feet. Find the measure of ∠R to the nearest tenth of a degree.
Answer:
57.6°
Step-by-step explanation:
It is always helpful to draw a picture. Also, you need to memorize all the definitions of the trig functions. For example,
sine of an angle = opposite side/hypotenuse
In your case, SQ is opposite side to angle R and QR is the hypotenuse
Therefore, sin R = 6.5/7.7
m∠R = arcsin (6.5/7.7) = 57.6°
Melissa works at Best Buy and gets paid $250 a week plus
commission. She earns $15 for every cell phone she sales.
Which function can be used to find t, the amount of money
Melissa will receive on her weekly paycheck for selling n
number of cell phones?
A.
t=250x + 15
C. t = 15x
B.
t = 15x + 250
D. Not Here
Answer:
option b is correct
I hope it helps
Confused!! The picture below shows the question.
Answer:
25
Step-by-step explanation:
Easy questions just a bit of help no rush 100 points to do this
Is this a test or do you need help
Sin(x)=sqrt3/2 solutions of
Answer:
pi/3+2pin, 2pi/3+2pi(n)
Answer:
the next one is c - pi/2
Step-by-step explanation:
Spider Rock is located in Canyon de Chelly National Park in Arizona. A surveyor stands 370 feet from the base of Spider Rock. From a point 5.5 feet above the ground, he measures the angle of elevation to the top of Spider Rock to be 65°. According to the surveyor's measurements, what is the height of Spider Rock? Round your answer to the nearest tenth. A. 178.0 ft. B. 340.8 ft. C. 413.7 ft. D. 799.0 ft.
Answer:
799 feet
Step-by-step explanation:
We solve using the Trigonometric function of Tangent.
tan theta = Opposite /Adjacent
From the above question, we have the height of the surveyor = 5.5 feet
theta = Angle of elevation = 65°
Adjacent = 370 feet
Let Opposite = height + height of spider rock
tan 65° = h - 5.5 /370 feet
Cross Multiply
tan 65° × 370 feet = h - 5.5
793.46756059 feet = h - 5.5
h = 793.46756059 feet + 5.5
h = 798.96756059 feet
Approximately = 799 feet
The height of the Spider rock = 799 feet
can someone help me with my perfect square homework? thank you.
Answer:
Any better explanation
Answer:
49
Step-by-step explanation:
Given
v² - 14v
To complete the square
add ( half the coefficient of the v- term )² to v² - 14v
v² - 14v + (- 7)²
= v² - 14v + 49
= (v - 7)² ← a perfect square
One pair of parallel sides proves a quadrilateral to be a parallelogram
True
False
A rectangle swimming pool is measured up to 15 meters long and 7 1 fourth meters wide what is the area of this swiming pool
Answer:
108.75 m^2
Step-by-step explanation:
Area of a rectangle = length x breadth
15 x 7 1/4
15 x 29 / 4 = 108.75 m^2 or 108 3/4 m^2
A street light is 21 feet high and casts a 40-foot shadow. At the same time, a cell-phone
tower next to the street light casts a 57-foot shadow. Which proportion can be used to find
the height, H, of the cell-phone tower?
Answer:
21/H = 40/57
Step-by-step explanation:
Which of the following points are located 3 units from (-4,-2) ?
The lines graphed below are perpendicular. The slope of the red line is 4.
What is the slope of the green line?
Answer: -1/4
Step-by-step explanation:
so lets just eliminate some of the choices here.
4 and -4 are 4/1 or -4/-1 and it doesnt go up or down 4 here so those can be ruled out. If we look at which way the green line is facing, positive goes up on the graph, but green line is going down so we can rule out 1/4. So all that is left is -1/4, so there's your slope.
A and b are positive integers and a-b=2. Evaluate the following:
27^1/3b/9^1/2a
thank you very much
Answer:
Answer: 1/9
Step-by-step explanation:
(27^1/3 = 3
9^1/2 = 3
3^b
====
3^a
3^(b - a)
3^-2 = 1/9
1/9
What is the probability that the spinner will not land on a 5 or 8? 5 points
Answer:
3/4
Step-by-step explanation:
Based on the spinner attached :
Faces are in equal divisions ; number of faces = 8
Probability the spinner will not land on a certain number = 1 - P(spinner lands on that number)
P(spinner lands on 5) = 1 /8
P(spinner will not land on 5) = 1 - 1/8 = 7/8
P(spinner lands on 8) = 1/8
P(spinner will not land on 8) = 1 - 1/8 = 7/8
Hence,
P(spinner will not land on 5 or 8)
Required outcome = (1, 2, 3, 4, 6, 7) = 6
Total possible outcomes = (1.2, 3, 4, 5, 6, 7, 8) = 8
P(spinner will not land on 5 or 8). = 6/8 = 3/4
if f (x) = 8 (5x - 2) find f (x)
Answer:
f-1(x) = (x - 16)/40
B
Step-by-step explanation:
Call f(x) = y
Interchange x and y
x = (5y + 2)*8 Remove the brackets
x = 40y + 16 Subtract 16 from both sides
x - 16 = 40y Interchange the left and right sides
40y = x - 16 Divide by 40
y = (x - 16)/40
f-1(x) = (x - 16)/40
PLEASE HELP ME!! I WILL GIVE BRAINLIEST. ITS DUE IN AN HOUR
Answer:
p-3=8.25
p=11.25
Answer:
p - 3 = 8.25 and 11.25
Step-by-step explanation:
hi there!
the question is asking us to first find out which equation we can use to solve this wordy problem.
its not going to be answers 1 or 3 since they are adding/ multiplying more on to our wooden plank, when the question is stating that we are subtracting 3 inches off.
knowing that now, our answer is p - 3 = 8.25 or 4 !
now all we have to do is add 3 to 8.25 to get our answer of how long the plank was before we cut it
3 + 8.25
= 11.25
p = 11.25 <---------------- our final answer!
i hope this helped you! i hope you have a good rest of your day :)
( im sorry if this this late!! )
Need help asap!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The measures of three of the interior angles of a quadrilateral are 60o, 110o, and 90o What is the measure of the fourth angle of this quadrilateral?
Answer:
100 degrees
Step-by-step explanation:
sum of angles in a quadrilateral = 360
missing angle = 360 - (60 + 110 + 90) = 100
Can you guys help me find the missing parts where the letters are
Answer:
I’m going in the order form up to down
1) Total cost is $15.60 (you multiply the unit rate by the quantity to find the total cost)
2) Unit rate is $13.20 (You divide the total by the quantity to find the unit rate)
3) Quantity is 6 (You divide the total by the unit rate to find the amount of things or quantity)
4) 12 percent tax rate (We can make an eqaution to find out how much you multiply thr total to find the tax rate by doing 82.5x=9.9. THe result would be 0.12 or 12 percent)
Please help me out I’ll mark brainliesttttt
Answer:
x = 4
Step-by-step explanation:
Since the triangle is 45-90-45, x = 4.
Answer:
4 is the answer
Step-by-step explanation:
By Pythagorean theorem
hypotenuse^2=base^2+altitude^2
(4sqrt2)^2=(4)^2+x^2
32=16+x^2
32-16=x^2
16=x^2
taking square root on both sides
x=4
What is the slope of the line?
2
-2
1/2
1
Answer:
the answer to the question is 1
Order these numbers from least to greatest. 7.63, 7.6032, 7.6,
Answer:
7.6032,7.63,7.6
Sorry if I am wrong.
Step-by-step explanation:
Calculate the product below and give your answer in scientific notation.
(1.3 x 10-^2) (0.05) = ?
Answer:
1 Simplify 1.3\times 101.3×10 to 1313.
(13-2)\times 0.05
(13−2)×0.05
2 Simplify 13-213−2 to 1111.
11\times 0.05
11×0.05
3 Simplify.
0.55
0.55
The product of (1.3 x 10⁻²) and (0.05) is 0.065x 10⁻²
What is Equation?Two or more expressions with an Equal sign is called as Equation.
We need to find the product of (1.3 x 10⁻²) and (0.05)
Multiplication is a method of finding the product of two or more numbers
First multiply as if there is no decimal.
Next, count the number of digits after the decimal in each factor.
Finally, put the same number of digits behind the decimal in the product.
1.3×0.05=0.065
So 0.065x 10⁻² is the value of product (1.3 x 10⁻²) and (0.05)
Hence, the product of (1.3 x 10⁻²) and (0.05) is 0.065x 10⁻²
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A man wants to build around water fountain with diameter, d = 11.28 feet. The man is trying to put up a fence around the build with some wire. What is the length of the wire that the man needs to complete the task?
Answer:
35.44
Step-by-step explanation:
2 times pi times radius.
What is the area of the triangle?
5
3
units?