Answer:
y = 10 between 0 and 1
AND
y=15x for x>=1
Step-by-step explanation:
This has 2 segments. One when 0 < x < 1 (y=$10), and one when x >= 1 (y=$15x)
So
y = 10 between 0 and 1
AND
y=15x for x>=1
What is the percent change from 75 to 14?
Answer:
the change is -81.33% (the 3 is repeating)
Q.5(b) The population {(P) in millions} of a country is estimated by the function, P=125e0.035t, t = time measured in years since 1990. (a) what is the population expected to equal in year 2000 (b) determine the expression for the instantaneous rate of change in the population (c) what is the instantaneous rate of change in the population expected to equal in year 2000.
Answer:
Hello,
Step-by-step explanation:
Q.5(b) The population {(P) in millions} of a country is estimated by the function, P=125e0.035t, t = time measured in years since 1990. (a) what is the population expected to equal in year 2000 (b) determine the expression for the instantaneous rate of change in the population (c) what is the instantaneous rate of change in the population expected to equal in year 2000.
[tex]P(t)=125*e^{0.035*t}\\a)\\P(2000)=125*e^{0.035*(2000-1990)}=177.38...\\\\b)\\P'(t)=125*0.035*e^{0.035*t}\\\\c)\\\\P'(2000)=125*0.035*e^{0.035*(2000-1990)}=6.2084...[/tex]
Graph the function f(x) = 2√x+2 .
All help is appreciated!
Answer:
Not sure which was your intended, but here are two options.
Step-by-step explanation:
Find the remainder when x^3-ax^2 +6x -a is divided by x-a
Answer:
When x^3 - ax^2 + 6x -a is divided by x-a
Remainder = 5a
Find the surface area of a
sphere with a diameter of
15 in.
Can someone please explain how?
Answer:
About 706.5 square inches.
Step-by-step explanation:
Surface area of a sphere is: [tex]SA=4\pi r^2[/tex]
The radius is half the diameter. So, the radius of the given sphere is 7.5 in.
15/2 = 7.5
Find the surface area:
I use 3.14 for pi.
[tex]SA=4*3.14*7.5^2\\\\SA=4*3.14*56.25\\\\SA=12.56*56.25\\\\\boxed{SA=706.5}[/tex]
The surface area is about 706.5 square inches.
Hope this helps.
Answer:
SA=706.86 in²
Step-by-step explanation:
surface area of a sphere = 4πr²
radius r=d/2=15/2=7.5
SA=4(π)(7.5)²
SA=706.86 in²
solve each equation type the answers in the boxes below a( 3x equals 12 B( -3x equals 9 c( 3 x equals 1/2 D( 1/2 x equals 12
Answer:
a) x = 4
b) x = -3
c) x = 1/6
d) x = 24
Step-by-step explanation:
Basic solve for x techniques
a) 3x = 4
Divide both sides by 4. This applies to all the questions.
what is the greatest common factor of 48,24,and 32
Answer:
8
Step-by-step explanation:
gcf
Members of a soccer team raised $1946.50 to go to a tournament. They rented a bus for $974.50 and budgeted $60.75 per player for meals. Write and solve an equation which can be used to determine pp, the number of players the team can bring to the tournament.
Answer:
16 players can be brought to the tournament. The equation is written within my step-by-step explanation.
Step-by-step explanation:
Variable p = number of players
Set up an equation:
974.50 + 60.75p = 1946.50
Isolate variable p:
60.75p = 972
Divide:
p = 16
Check your work:
974.50 + 60.75(16) = 1946.50
974.50 + 972 = 1946.50
1946.50 = 1946.50
Correct!
Answer:
Step-by-step explanation:
A police car is located 40 feet on a small straight road perpendicular to main highway. A red car is driving along a highway in the direction of an intersection with that small road and is 180 feet away from the intersection. The police radar reads that the distance between the police car and the red car (this distance is straight between them - not on either road) is decreasing at a rate of 100 feet per second. How fast is the red car actually traveling along the road
Answer:
the red car is traveling at 102.44 ft/s along the road
Step-by-step explanation:
From the given information:
Let consider p be how far the car is up the road and q be how far the police is off the road.
Also, suppose that r is the distance between the police and the car.
Then, we can have a right triangle in which we can use the Pythagorean Theorem to calculate the r (distance between the cop and the car)
NOW,
p² + q² = r²
r² = 40² + 180²
r² = 1600 + 32400
r² = 34000
r = [tex]\sqrt{34000}[/tex]
r = 184.39
If we consider q' to be how fast the car is traveling down the road.
And, p' be how fast the police is traveling toward the road.
r' be how fast the distance between the police and the car is changing.
then , the derivative of our equation, p² + q² = r² with respect to time can now be:
2p(p') +2q(q') = 2r(r')
p(p') +q(q') = r(r')
By replacing our values; we have:
40(0) +180(y') = [tex]\sqrt{34000} \times 100[/tex] (given that the police is not moving p' =0)
180(y') = [tex]\sqrt{34000} \times 100[/tex]
[tex](y') = \dfrac{\sqrt{34000} \times 100}{180}[/tex]
[tex](y') = \dfrac{184.39 \times 100}{180}[/tex]
[tex]\mathbf{(y') = 102.44 \ ft/s}[/tex]
the red car is traveling at 102.44 ft/s along the road
The table shows the steps for solving the given inequality 4-3(x-5)>6x-17
Step-by-step explanation:
(=) 1 ( x-5 ) > 6x-17
(=) x-5 > 6x -17
(=) -5x > -12
=> x < 12/5
he blood platelet counts of a group of women have a bell-shaped distribution with a mean of 247.3 and a standard deviation of 60.7. (All units are 1000 cells/μL.) Using the empirical rule, find each approximate percentage below. a. What is the approximate percentage of women with platelet counts within 3 standard deviations of the mean, or between 65.2 and 429.4
Answer:
The approximate percentage of women with platelet counts within 3 standard deviations of the mean is 99.7%.
Step-by-step explanation:
We are given that the blood platelet counts of a group of women have a bell-shaped distribution with a mean of 247.3 and a standard deviation of 60.7.
Let X = the blood platelet counts of a group of women
The z-score probability distribution for the normal distribution is given by;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean = 247.3
[tex]\sigma[/tex] = standard deviation = 60.7
Now, according to the empirical rule;
68% of the data values lie within one standard deviation of the mean.95% of the data values lie within two standard deviations of the mean.99.7% of the data values lie within three standard deviations of the mean.Since it is stated that we have to calculate the approximate percentage of women with platelet counts within 3 standard deviations of the mean, or between 65.2 and 429.4, i.e;
z-score for 65.2 = [tex]\frac{X-\mu}{\sigma}[/tex]
= [tex]\frac{65.2-247.3}{60.7}[/tex] = -3
z-score for 429.4 = [tex]\frac{X-\mu}{\sigma}[/tex]
= [tex]\frac{429.4-247.3}{60.7}[/tex] = 3
So, it means that the approximate percentage of women with platelet counts within 3 standard deviations of the mean is 99.7%.
3) Find f(3) for the function below.
f(x) = 2x² – 3x
Answer:
9
Step-by-step explanation:
f(x) = 2x² – 3x
Let x=3
f(3) = 2 * 3^2 - 3*3
= 2 *9 - 9
= 18-9
= 9
Answer:
f(3) = 9Step-by-step explanation:
[tex]f(x) = 2x^2 -3x\\ f(3) = ?\\\\ f(3) = 2(3)^2 -3(3)\\ f(3) = 2(9) - 9\\ f(3) = 18- 9\\ f(3) = 9[/tex]
Ajay is researching how the population of his hometown has changed over time. Specifically, he learns his hometown had a population of 20{,}00020,00020, comma, 000 in 199019901990, and that the population has since increased by about 8\%8%8, percent every 333 years.
Ajay predicts that his town can only support a population of 50{,}00050,00050, comma, 000. Ajay is relieved to see that population has not exceeded 50{,}00050,00050, comma, 000 ttt years after 199019901990.
Write an inequality in terms of ttt that models the situation.
Answer:
Could you Write the question more clearly?
Step-by-step explanation:
Darnell goes to the movies with his friends. The receipt on his phone
shows the cost of the tickets after a discount. What is the price of a ticket before the discount?
answer
8(+ - 0.75)=62.00
the price of the tickets before is 8.50
Step-by-step explanation:
8(+-.075)=62.00
+-0.75+0.23
+=8.50
Place the two large triangles around the square to form a triangle, a parallelogram ,and a trapezoid .Please answer it step by step
Answer:
Step-by-step explanation:
Suppose the radius of a circle is 2. What is its circumference?
Answer:
12.57
Step-by-step explanation:
The formula to solve the circumference of a circle is:
2 x PI x R (radius)
=> 2 x PI x 2
=> 4 PI or 12.57
Line R: 2x + 2y = 18 Line M: x + y = 9 Which statement is true about the solution to the set of equations?
Answer:
Step-by-step explanation:
2x + 2y = 18
-2x -2y = -18
0 = 0
infinite solution of equations
find the value of x
3+x/4=5
Step-by-step explanation:
it think it will help you
Answer:
the value of x = 8
Step-by-step explanation:
3+x/4 = 5
x/4 = 5 - 3
= 2
X = 2 ×4
=8
5^-4 over 5^3
simplify
A. 5^7
B. 5^-1
C. 1/5
D. 1/5^7
Answer:
D is the correct answer.
What Is the answer to it?
Answer:
2(x + 10)
Step-by-step explanation:
The sum of x and 10 is x + 10
The product of 2 and x + 10 means multiply them, thus
2 × (x + 10)
= 2(x + 10) ← parenthesis indicates x and 10 are added before being multiplied by 2
Each cat at the animal shelter gets
5/6 pound of food. Allie has 9 1/2
pounds of cat food. How many cats
can Allie feed?
A: 7
B:9
C: 11
D:13
Answer: C : 11
Step-by-step explanation:
A certain box has a width that is 2 inches more than its length and a height that is 5 inches less than its length. If each of the two smallest faces of the box has an area of 36 square inches, what is the volume if the box?
Answer:
V = 396 cubic inches
Step-by-step explanation:
width = w; length = l; height = h; volume = V; area of smallest face = a
base units are inches
w = 2 + l
h = l - 5
Height is smallest and length is second smallest (h = l -, l = l, w = l +), so a is for h and l.
a = h × l = (l - 5) × l
36 = l^2 - 5l ==> l^2 - 5l - 36 = 0
Factor ==> (l - 9) × (l + 4) = 0
l = 9 and l = -4
Since length cannot be negative, 9 is the only Real answer.
l = 9
h = l - 5 = 9 - 5 = 4
w = 2 + l = 2 + 9 = 11
Volume of rectangular prism/box is length times width times height.
V = l × w × h = 9 × 11 × 4 = 396
The volume of the box with the given dimensions is;
Volume = 396 in³
Let us denote the properties of the box as follows;
Length of box = l
Width of box = w
Height of box = h
Area of the smallest face of box = a
We are told that the width is 2 inches more than the length. Thus;
w = 2 + l
We are told that the height is 5 inches less than its length. Thus;
h = l - 5
Since length is smaller than width but bigger than height, the height and length are the 2 smallest faces
Thus,
a = h × l
plugging in the relevant values gives;
a = (l - 5) × l
a = l² - 5l
We are told that the area of the two smallest faces is 36 in². Thus;
l² - 5l = 36
l² - 5l - 36 = 0
Using online quadratic equation solver, we have; l = 9 inches
Plugging in 9 for h in; h = l - 5
h = 9 - 5
h = 4
Also, plugging in 9 for l into; w = 2 + l, we have;
w = 2 + 9
w = 11
Volume of box is given by;
Volume = length × width × height
Volume = 9 × 11 × 4
Volume = 396 in³
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A piece of blue yarn is 5/ 3/7 yards long. A piece of pink yarn is 5 times as long as the blue yarn. How much longer is the pink yarn than the blue yarn?
Answer:
27 1/7
Step-by-step explanation:
Multiply 5×5=25 and afterwards multiply 3/7×5=2 1/7
What is the perimeter of a square which has the same area as a circle with circumfrence of 4π
Answer:
Perimeter square = 8 sqrt(pi)
Step-by-step explanation:
The perimeter of a square is 4*s
The area of a circle is Area = pi * r^2
The circumference of a circle is C = 2*pi * r
C = 4 pi
4pi = 2*pi * r
r = 2
So the area of the circle is pi * r^2 = pi * 2^2 = 4pi
The square has the same area
Area = 4*pi
Square = 4*pi
s^2 = 4*pi
s = sqrt(4*pi)
s = 2*sqrt(pi)
The perimeter = 4 * 2 * sqrt(pi)
The perimeter = 8 * sqrt(pi)
ans of this
fast to get 10 pts
Answer:
2.equivalent sets is answer.This equation shows how the total number of necklaces Denise owns is related to the amount of money she spends on additional necklaces.
n = d + 74
The variable d represents the amount of money she spends on additional necklaces, and the variable n represents the total number of necklaces she owns. With $16 to spend on new necklaces, how many total necklaces can Denise own?
the volume of a cube is 125cm cubed. The area of a square is 64cm squared. How does the length of one edge of the cube compare to the length of one side of the square? Explain
Answer:
One edge of the cube is 5 cm, one edge of the square is 8 cm, so the edge of the cube is 3 cm shorter than the edge of the square.
Step-by-step explanation:
The volume of the cube is found by the formula
V = s³,
where s is the side length (called the edge in this problem)
Since V = 125 cm³, we can take the cube root of 125 to find the edge length.
The cube root of 125 is 5, ( 5³ = 125)
So the edge of the cube is 5 cm
The are of a square is found by the formula
A = s² ,
where s is the side length (called the edge in this problem)
Since A = 64 cm², we can take the square root of 64 to find the edge length.
The square root of 64 is 8 (8² = 84)
So the edge of the square is 8cm
Comparing the two edges tells us that the edge of the cube is 3cm shorter than the edge of the square.
How do you simplify the square root of 64a^6
Answer:
it's (2a)^6
Step-by-step explanation:
so first you need to write 64a^6 in exponential form simplifying it to 2^6a^6
then multiply the bases which gives you (2a)^6
sorry if I didn't explain it very well but I hope I helped!
Answer:
[tex]\sqrt{64a^{6} } = 8a^{3}[/tex]
8*8 = 64
a^3*a63 = a^6
Step-by-step explanation:
31. Which inequality is represented by
this graph?
Answer:
A. x/5 - 6 > -4
Step-by-step explanation:
The graph shows that x > 10. We need to solve each of the inequalities. After we do, we see that A is the answer.
A. x/5 - 6 > -4
x/5 > 2
x > 10
Find the area of triangle ABC to the nearest tenth if AB = 11 ft, ∠BCA = 67 , and ∠CAB = 28 .
Answer:
30.7
Step-by-step explanation:
Assuming the angled are degrees and not radian.
side BC= (11÷sin67)•sin28= 5.6
angle ABC= 180-67-28=85°
A= 11•5.6•sin85÷2≈30.68