Answer:
the expression of the information in terms of function f is:
13 = f(40)
The town of Tola has a population of 5000 persons and produces 2 tons of garbage each week.
Step-by-step explanation:
suppose G and p are the two unknowns variables.
where;
G is measured in tons per week and:
p is measured in thousands of people.
∴
The relation between the amount of garbage produced by a city with population p can be expressed as:
G = f(p)
However;
The town of Tola has a population of 40,000 and produces 13 tons of garbage each week.
The objective is to express the information in terms of the function f.
So, if there is a population of 40,000 person in the town,
since p is measured in person per thousand and the value of garbage produced is 13 tons per week.
∴ the expression of the information in terms of function f is:
13 = f(40)
Explain the meaning of the statement f(5) = 2.
The given statement implies that
P which is measured in thousand people = 5
and the value of the garbage produced is 2.
SO , we can say that;
The town of Tola has a population of 5000 persons and produces 2 tons of garbage each week.
f (x) = √2X-6
What is f(5)?
Answer:
f(5) = 2
Step-by-step explanation:
Given:
Function f(x) = [tex]\sqrt{2x - 6}[/tex]For x=5 :
f(5) = [tex]\sqrt{2*5 - 6}[/tex] = [tex]\sqrt{4}[/tex] = 2iven h (t) = t squared + t + 12 andk (t) = StartRoot t minus 1 EndRoot, evaluate (k compose h) (10)
Answer:
11Step-by-step explanation:
Given h(t) = t²+t+ 12 and k(t) = √t-1, we are to find k(k.h)(10)
k{h(t)} = k{ t²+t+ 12}
Since k(t)= √t-1, we will replace the variable t in the function with t²+t+ 12
k(h(t)) = √{(t²+t+ 12)-1}
k(h(t)) = √t²+t+12-1
k(h(t)) = √t²+t+11
Substituting t = 10 into the resulting function;
k(h(10)) = √(10)²+(10)+11
k(h(10)) = √100+10+11
k(h(10)) = √121
k(h(10))= 11
hence the value of (k compose h) (10) is 11
The expression 0.09x+(x−30) models the final price of a bicycle with an instant rebate in a state that charges a sales tax. The tax is on the original price. Which expression represents the amount of tax that is paid on the bicycle?
A. x−30
B. 0.09x
C. 1.09x
D. 0.09x−30
Answer:
B. 0.09x
Step-by-step explanation:
x is the initial price.
0.09x is the 9% sales tax.
-30 is the instant rebate.
carol had 3/4 yard of ribbon .she wanted decorate two picture frames if she uses half the ribbon on each frame how many feet will she use for one frame
Answer:
1.125 feet
Step-by-step explanation:
1 yard = 3 feet
3/4 yard = 2.25 feet
2.25 feet / 2 = 1.125 feet per frame
i hope this helps!
-TheBusinessMan
one third divided by eight
Answer:
1/24
Step-by-step explanation:
1/3÷ 8
Copy dot flip
1/3 * 1/8
1/24
Answer:
1/24
Step-by-step explanation:
Alex buys a car for $19500 and later sells it at a profit of 5%. At what price did he sell the car?
Answer:
$20,475
Step-by-step explanation:
you multiply 19,500 by 0.05 (19500*0.05) to get $20,475
Hope this helps :)
Simplify the expression below.
Answer:
c or b
Step-by-step explanation:
Use the number line below, where RS=7y+2, ST=5y+7, and RT=14y−3. a. What is the value of y? b. Find RS, ST, and RT.
Answer:
j
Step-by-step explanation:
find the first principle f(x)=1/x
Answer:
see explanation
Step-by-step explanation:
Assuming you require the derivative of f(x) from first principles, then
f' (x) = [tex]lim_{h>0}[/tex] [tex]\frac{f(x+h)-f(x)}{h}[/tex]
= [tex]lim_{h>0}[/tex] [tex]\frac{\frac{1}{(x+h)}-\frac{1}{x} }{h}[/tex]
= [tex]lim_{h>0}[/tex] [tex]\frac{\frac{x-(x+h)}{x(x+h)} }{h}[/tex]
= [tex]lim_{h>0}[/tex] [tex]\frac{\frac{x-x-h}{x(x+h)} }{h}[/tex]
= [tex]lim_{h>0}[/tex] [tex]\frac{-h}{hx(x+h)}[/tex] ← cancel h on numerator/ denominator
= - [tex]\frac{1}{x^2}[/tex]
An instructor of a biology class believes the average final exam score for his biology class was more than 75. Suppose a sample of 25 was taken and the sample mean he observed was 78.48 and a standard deviation of 5 points. What is the value of the test statistic?Report your answer to 2 decimal places.
Answer:
The value for the test statistics = 3.48
Step-by-step explanation:
Given that:
population mean [tex]\mu[/tex] = 75
sample size n = 25
sample mean [tex]\overline x[/tex]= 78.48
standard deviation = 5
The value for the test statistics can be computed by using the formula:
[tex]z = \dfrac{\overline x- \mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \dfrac{78.48- 75}{\dfrac{5}{\sqrt{25}}}[/tex]
[tex]z = \dfrac{3.48}{\dfrac{5}{5}}[/tex]
z = 3.48
The value for the test statistics = 3.48
Is a − b equal to b − a?
Answer:
a is a 1 and then you subtraction the b is equal 0
(3xy2x2y−3)2(9xy−3x3y2)−1.
Answer:
-18x square y -+36xy square + 54 xy - 1
Step-by-step explanation:
collect the terms, calculate the product, collect the terms, then distribute
A man walks along a straight path at a speed of 3 ft/s. A searchlight is located on the ground 4 ft from the path and is kept focused on the man. At what rate is the searchlight rotating when the man is 3 ft from the point on the path closest to the searchlight
Answer: 0.48 rad/sec
Step-by-step explanation:
dx/dt = 3ft
to find d∅/dt when x = 3
Using the right angled triangle
ΔABC
Now perpendicular (BC) = X FT
Base ( AC) 4 ft
so Hypotenuse(AB) = √ (BC² + AC²) = √ ( x² + 4²) = √ ( x² + 16)
and x/4 = tan∅ ; x = 4tan∅
now we differentiate each side
dx/dt = d/dt(4tan∅) = d/d∅(4tan∅) d∅/dt
⇒ dx/dt = (4sec²∅) d∅/dt = ( 1/4 cos²∅) dx/dt
⇒ d∅/dt = cos²∅/4 × 3 = 3/4 cos²∅
now when x = 3, the length of the beam is
{from our initial equation (AB) = √ (BC² + AC²)}
AB = √(3² + 4²) = √(9 + 16) = 5ft
therefore cos∅ = 4/5
so we substitute in (d∅/dt = ( 1/4 cos²∅) dx/dt)
d∅/dt = 1/4 ( 4/5)² × 3
d∅/dt = 12/15 = 0.48 rad/sec
Manolo has a toy in the shape of a triangle pyramid If x=6" y=8" and z=10", what is the volume of the toy
Answer:480
Step-by-step explanation:
To find volume u need to multiply height * width * length
If you were to open an account that will pay you 3.5% interest with a deposit of $150 so find the following ending amount for each period at the end of 2 years
Answer:
FV= $160.68
Step-by-step explanation:
Giving the following information:
Initial investment= $150
Interest rate= 3.5% compounded annually
Number of periods= 2
To calculate the future value, we need to use the following formula:
FV= PV*(1+i)^n
PV= present value
i= interest rate
n= number of periods
FV= 150*(1.035^2)
FV= $160.68
Points P, Q, and R are shown on the number line. What is the distance between point P and point R?
Answer:
5
Step-by-step explanation:
2.75-(-2.25)=
2.75+2.25=
5
Which decimals are less than 2.312? Select all that apply. A. 2.311 B. 2.4 C. 2.32 D. 2.3 E. 2.31 F. 2.313
Answer:
a c d
Step-by-step explanation:
Mark this question Select the following statement that describes non-overlapping events.
A. Jon needs to roll an even number to win. When it's his turn, he rolls a two.
B. Jon wants a face card so he can have a winning hand, and he receives the eight of clubs.
C. Receiving the King of Hearts fulfills Jon's need of getting both a face card and a heart.
D. To win, Jon needs a red card. He receives a Queen of Diamonds.
Answer:
B. Jon wants a face card so he can have a winning hand, and he receives the eight of clubs.
Step-by-step explanation:
non overlapping events are mutually exclusive events meaning that they do not occur together, one occurs and the other doesn't and vice versa. From the example, Jon wants a face card but got eight of clubs, he cannot have a face card and eight of clubs together, one occurs while the other is absent. So if Jon got a face card, he would not have eight of clubs
Jon wants a face card so he can have a winning hand, and he receives the eight of clubs.
Given,
Statements .
Here,
Non overlapping events are mutually exclusive events meaning that they do not occur together, one occurs and the other doesn't and vice versa.
For instance,
Jon wants a face card but got eight of clubs, he cannot have a face card and eight of clubs together, one occurs while the other is absent.
So if Jon got a face card, he would not have eight of clubs .
Thus option B is correct statement .
Know more about mutually exclusive events,
https://brainly.com/question/28565577
#SPJ6
Two adjacent sides of a parallelogram are 6mm and 10mm respectively, and they form an angle measuring 60. Find the area of the parallelogram.
Answer:
51.96 mm² approximately
Step-by-step explanation:
the first thing you should know is that the area of a rectangle is base*height sin of (
the included angle i.e
Arectangle= bh sin90° since all angles of a rectangle are equal then the included angle is 90°
Arectangle= bh sin90° since sin90 is 1 we simply use the equation bh because multiplying bh by one is bh. bearing this in mind , the area of the parallelogram can be calculated as:
Aparallelogram= bh sin of sin of the included angle
Aparallelogram= bh sin of sin of the included angle Aparallelogram=6mm*10mm sin 60°
Aparallelogram= bh sin of sin of the included angle Aparallelogram=6mm*10mm sin 60°Aparallelogram=60mm² * 0.866
Aparallelogram= bh sin of sin of the included angle Aparallelogram=6mm*10mm sin 60°Aparallelogram=60mm² * 0.866Aparallelogram=51.96 mm² approximately
solve for n+4 + n/6=16
Answer:
n = 10.286 aprox.
Step-by-step explanation:
n+4 + n/6 = 16
n/6 = 16 - 4 - n
n = 6(12-n)
n = 6*12 + 6*-n
n = 72 - 6n
n + 6n = 72
7n = 72
n = 72/7
n = 10.286 aprox.
verify:
10.286 + 4 + (10.286/6) = 16
14.286 + 1.714 = 16
The CEO of a large corporation asks his Human Resource (HR) director to study absenteeism among its executive-level managers at its head office during the year. A random sample of 30 executive level managers reveals the following: Absenteeism: Sample mean = 7.3 days, Sample standard deviation=6.2 days 18 mid-level managers out of the 30 randomly selected mid-level managers, cite stress as a cause of absence. (a) Construct a 90% confidence intervalestimate for the mean number of absences for mid- level managers during the year.(b) Construct a 98% confidence intervalestimate for the population proportion of mid-level managers who cite stress as a cause of absence. (c) What sample size is needed to have 95% confidence in estimating the population mean absenteeism to within 1.5 days if the population standard deviation is estimated to be 8 days? (d) How many mid-level managers need to be selected to have 99% confidence in estimating population proportion of mid-level managers who cite stress as a cause of absence to within +0.075 if no previous estimate is available?
Answer:
Following are the answer to this question:
Step-by-step explanation:
Given:
n = 30 is the sample size.
The mean [tex]\bar X[/tex] = 7.3 days.
The standard deviation = 6.2 days.
df = n-1
[tex]= 30-1 \\ =29[/tex]
The importance level is [tex]\alpha[/tex] = 0.10
The table value is calculated with a function excel 2010:
[tex]= tinv (\ probility, \ freedom \ level) \\= tinv (0.10,29) \\ =1.699127\\ = t_{al(2x-1)}= 1.699127[/tex]
The method for calculating the trust interval of 90 percent for the true population means is:
Formula:
[tex]\bar X - t_{al 2,x-1} \frac{S}{\sqrt{n}} \leq \mu \leq \bar X+ t_{al 2,x-1} \frac{S}{\sqrt{n}}[/tex]
[tex]=\bar X - t_{0.5, 29} \frac{6.2}{\sqrt{30}} \leq \mu \leq \bar X+ t_{0.5, 29} \frac{6.2}{\sqrt{30}}\\\\=7.3 -1.699127 \frac{6.2}{\sqrt{30}}\leq \mu \leq7.3 +1.699127 \frac{6.2}{\sqrt{30}}\\\\=7.3 -1.699127 (1.13196)\leq \mu \leq7.3 +1.699127 (1.13196) \\\\=5.37 \leq \mu \leq 9.22 \\[/tex]
It can rest assured that the true people needs that middle managers are unavailable from 5,37 to 9,23 during the years.
Divide. Give the quotient and remainder.
746+21
Answer:
well you put a plus sign, but im letting you know I did the division.
Step-by-step explanation:
The answer is 35 remainder 11.
Hope this helped
To draw a gragh for y = 2x +5, a person can draw a point at x of 0 and y of _, a second point by going over 1 and ip _, and then draw a line through the points.
Answer: A person can draw a point of x of 0 and y of 5, a second point by going over 1 and up 2, and then draw a line through the points.
Step-by-step explanation:
if x is equal to 0 then y will equal to 5 which in this case will represent the y intercept. And after plotting the point (0,5) you can use the slope and move over or left by 1 and move up by 2 to find the next point.
Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule to approximate the given integral with the specified value of n.
x3 sin(x) dx, n = 8
1) The Trapezoidal Rule
2) The Midpoint Rule
3) Simpson's Rule
Answer:
-1392.09-1744.43-1636.41Step-by-step explanation:
using the given integral
calculate: Δx = (12-0) / 8 = 3/2
Xo = 0, f(x) = [tex]x^3sin(x)[/tex]
X1 = 3/2 , X2 = 3, X3 = 9/2, X4 = 6, X5 = 15/2, X6 = 9, X7 = 21/2, X8 = 12
Inputting the given values into the Trapezoid rule, midpoint rule and Simpson's rule to approximate the given integral with the specified value of n = 8
Evaluate n/6+2when n=12
can someone PLEASE help me with these two ill mark them as brainliest!!!!!
Answer:
20
Step-by-step explanation:
A=1/2bh
A=1/2(8×5)
A=1/2(40)
A=20
A spherical bowl of radius r cm is a quarter full when 6 liters of water is poured into it.calculate correct to three significant figures, the diameter of the bowl.
Answer:
The bowl's diameter is 35.8 cm
Step-by-step explanation:
Recall that 1 liter = 1000 cubic cm ad have in mind that in order to get a diameter in cm, we would need to write the volume of the bowl in cubic cm.
if 6 liters is 1/4 of the bowl, then 4 times 6 liters must fill the bowl. That is: the volume of the sphere is 24 liters.
24 liters in cubic cm is: 24000 cubic cm
now, we need to use the formula for the volume of a sphere of radius R:
[tex]Vol=\frac{4}{3} \pi\,R^3\\24000=\frac{4}{3} \pi\,R^3\\R^3=\frac{24000\,(3)}{4\,\pi} \\R=\sqrt[3]{\frac{24000\,(3)}{4\,\pi} } \\R\approx 17.894\,\,cm[/tex]
therefore, the diameter of the bowl is twice this radius value:
[tex]Diameter\approx 17.894\,* 2=35.788\,\,cm[/tex]
this value rounded to 3 significant figures is: 35.8 cm
What is 1000 words in 5 minutes rate as a unit rate.
Answer:
200 words per minute
Step-by-step explanation:
1000:5
1000/5 reduced will give you your unit rate.
200 words/minute
If 1000 words were read in 5 minutes, each minute would be 1000 divided by 5 which is 200.
Select all the correct answers.
Which expressions are equivalent to the given expression.
y^-8y^3x^0x^-2
Answer:
[tex]x^{-2}y^{-5}[/tex]
Step-by-step explanation:
The options are not given; however, the question can still be solved
Given
[tex]y^{-8}y^3x^0x^-2[/tex]
Required
Simplify
Start by rewriting the expression
[tex]y^{-8} * y^3 * x^0 * x^{-2}[/tex]
Apply the following laws of indices: [tex]a^x * a^y = a^{x+y}[/tex]
This gives:
[tex]y^{-8+3} * x^{0-2}[/tex]
Evaluate the exponents
[tex]y^{-5} * x^{-2}[/tex]
[tex]x^{-2}y^{-5}[/tex]
Hence, [tex]x^{-2}y^{-5}[/tex] is equivalent to [tex]y^{-8}y^3x^0x^-2[/tex]
Answer:
The answer is- (Drumroll)
Step-by-step explanation:
The answers are [tex]x^-2y^-5[/tex], and [tex]1/x^2y^5[/tex]
Can someone help explain how i would solve this using the pascals triangle? Like how to convert it into (x + 4)^3 = ax^b+cx^d+ex^f+g
Pascal's triangle is a way of organizing the coefficients in the binomial expansion, [tex](a+b)^n[/tex]:
n = 0 => 1
n = 1 => 1 1
n = 2 => 1 2 1
n = 3 => 1 3 3 1
n = 4 => 1 4 6 4 1
and so on, where each row starts and ends with a 1, and the numbers in the middle are obtained by adding together the two numbers directly above and to the left. These coefficients are then mulitplied by descending powers of a and descending powers of b (or vice versa, because the pattern is symmetric), starting with 0 and going up to n.
In this case, we have
[tex](x+4)^3=1\cdot x^3\cdot4^0+3\cdot x^2\cdot4^1+3\cdot x^1\cdot4^2+1\cdot x^0\cdot4^3[/tex]
Notice how the powers of x and 4 always sum to n = 3.
Simplifying, we get
[tex](x+4)^3=x^3+12x^2+48x+64[/tex]
so that
a = 1
b = 3
c = 12
d = 2
e = 48
f = 1
g = 64