Answer:
[tex]\boxed {\boxed {\sf \$15.06 \ billion }}[/tex]
Step-by-step explanation:
We are given the function f(x). This is the value of diamond production for the year in billions.
[tex]f(x)= 0.21x+13.8[/tex]
We want to find the value of the diamond production in 2006.
We know that x is the number of years after 2000. The year 2006 was 6 years after 2000 because 2006 - 2000 = 6. Therefore, x (years after 2000) is equal to 6. We can substitute 6 in for x.
[tex]f(6)= 0.21(6)+ 13.8[/tex]
Solve according to PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction).
Multiply 0.21 and 6.
[tex]f(6)= 1.26+13.8[/tex]
Add 1.26 and 13.8
[tex]f(6)=15.06[/tex]
Remember the answer is in billions of dollars.
[tex]f(6)= \$ 15.06 \ billion[/tex]
Diamond production in 2006 is expected to be worth 15.06 billion dollars.
Statesville's population in 2010 was about 24,500, and was growing by about 1% each year. continues, what will Statesville's population be in 2019? [Round to the nearest person.]
Answer:
26,795 people
Step-by-step explanation:
P(x) = 24,500 × (1 + 0.01)^(2019-2010)
= 24,500 × (1.01)^9
= 24,500 × 1.0937
= 26,795 people
The required population of Statesville in the year 2019 will be 26,795.
Statesville's population in 2010 was about 24,500, growing by about 1% each year. Statesville's population be in 2019 to be determined.
The function which is in format f(x) = a^x where, a is constant and x is variable, the domain of this exponential function lies ( -∞, ∞ ).
Let Statesville's population in 2019 = x
Statesville's population in 2010 = 24500
Population growing by about 1% = 1/100
= 0.01
Difference in year n = 2019 - 2010
n = 9
Population in 2019,
x = 24500 * ( 1 + 0.01 )^9
x = 24500 * ( 1.01 )^9
x = 26, 795.295
To the nearest people x = 26,759
the population of Statesville in the year 2019 = 26,759
Thus, the required population of Statesville in the year 2019 will be 26,795.
Learn more about exponential function here:
brainly.com/question/15352175
#SPJ2
The scale on a map indicates that 1 inch corresponds to an actual distance of 75 miles. Two cities are 5.5 inches apart on the map. What is the actual distance between the two cities?
Answer:
412.5
Step-by-step explanation:
Answer:
[tex]412.5[/tex] miles
Step-by-step explanation:
Since 1 inch=75 miles you just multiply [tex]75*5.5[/tex] to get how many miles 5.5 inches is.
The amount of tax on a chair was $3.60. The tax rate was 5%. Find the original price of the chair.
Bianca solved the problem below. Find Bianca’s error.
0.05(3.60) = Original price
The original price is $0.18.
9514 1404 393
Answer:
$72.00
Step-by-step explanation:
The relationship between price and tax is ...
tax amount = (tax rate) × (price)
Then the price can be found by dividing by the tax rate:
price = (tax amount)/(tax rate)
price = $3.60 / 0.05 = $72.00
The original price of the chair was $72.00.
__
Bianca apparently did not pay any attention to the way tax is computed. Nor did she check her work. The original price is not a small fraction of the tax. It is the other way around. Bianca used a wrong relationship between tax and price.
Question 1 of 10
The triangles shown below may not be congruent.
66V
100
100
00
2017
A. True
B. False
SUBMIT
Answer:
A. TRUE
Step-by-step explanation:
To determine if two triangles are congruent, we need to establish the facts that the three angles and three side lengths of one is congruent to corresponding angles and side lengths of the other triangle.
The diagram given only tells us the angle measure of the two triangles which are congruent to each other. The side length wasn't given. Therefore, the triangles may not be congruent.
Which functions have a range of {y e R | -
Answer:
The range of a function is the complete set of all possible resulting values of the dependent variable (y, usually), after we have substituted the domain. In plain English, the definition means: The range is the resulting y-values we get after substituting all the possible x-values.
Step-by-step explanation:
idontknow
Sketch the graph of each line.
7) 2x - y = -4
Answer:
check the attachment
Step-by-step explanation:
2x - y = - 4
- y = - 4 - 2x
y = 2x + 4
slope of the line = 2 with y - intercept 4
Caffeine: Following are the number of grams of carbohydrates in 12-ounce espresso beverages offered at a coffee shop. 44 29 11 61 15 38 20 41 42 25 26 10 30 12 18 40 21 24 43 6 46 55 34 35 Send data to Excel Part: 0 / 40 of 4 Parts Complete Part 1 of 4 Your Answer is incorrect (a) Find the first and third quartiles of these data. The first quartile of these data is . The third quartile of these data is
Answer:
[tex]Q_1 = 19[/tex] --- first quartile
[tex]Q_3 = 41.5[/tex] --- third quartile
Step-by-step explanation:
Required:
The first and the third quartile
First, we order the dataset in ascending order[tex]Sorted: 6, 10, 11, 12, 15, 18, 20, 21, 24, 25, 26, 29, 30, 34, 35, 38, 40, 41, 42, 43, 44, 46, 55, 61[/tex]
The count of the dataset is:
[tex]n = 24[/tex]
Calculate the median position
[tex]Median=\frac{n+1}{2}[/tex]
[tex]Median=\frac{24+1}{2}[/tex]
[tex]Median=\frac{25}{2}[/tex]
[tex]Median=12.5th[/tex]
This means that the median is between the 12th and the 13th item
Next;
Split the dataset to two parts: 1 to 12 and 13 to 24
[tex]First: 6, 10, 11, 12, 15, 18, 20, 21, 24, 25, 26, 29[/tex]
[tex]Second: 30, 34, 35, 38, 40, 41, 42, 43, 44, 46, 55, 61[/tex]
The median position is:
[tex]Median = \frac{n + 1}{2}[/tex]
In this case; n = 12
So:
[tex]Median = \frac{12 + 1}{2}[/tex]
[tex]Median = \frac{13}{2}[/tex]
[tex]Median = 6.5th[/tex]
This means that the median is the average of the 6th and 7th item of the sorted dataset
So, we have:
[tex]Q_1 = \frac{18 + 20}{2}[/tex]
[tex]Q_1 = \frac{38}{2}[/tex]
[tex]Q_1 = 19[/tex] --- first quartile
[tex]Q_3 = \frac{41+42}{2}[/tex]
[tex]Q_3 = \frac{83}{2}[/tex]
[tex]Q_3 = 41.5[/tex] --- third quartile
1 red marble 4 blue marbles 3 green marbles probability of drawing 2 blue marbles
Answer:
3/14
Step-by-step explanation:
Assuming you draw one after the other without replacement, you have a 1/2 chance of drawing blue the first time, and after one is taken out, you have 7 left. In order to draw 2 blues you would have to have a blue the first time, so there would be 3 blue left. Multiplying the 2 probabilities gets 1/2*3/7= 3/14. Double check that though.
Solve using the substitution method
16x – 4y = 16
4x - 4 = y
Answer:
y = 4 x − 4
Step-by-step explanation:
What is the volume of a cone with a height of 27 cm
and a radius of 13 cm? Round your answer to the
nearest tenth.
Use the button on your calculator to complete this
problem.
V=
cm3
Answer:4778.3 cm^3
Step-by-step explanation: The formula for volume of a cone is V=1/3h pi r^2. By plugging in the height and the radius we get our answer.
Answer:
4778.4 :)
Step-by-step explanation:
Find the L. C. M in division method of the following
a) 18,27
b) 21,38
Answer:
hope it will be helpful to you.....
HELP!!!!!! I need an answer fasttttt
Answer:
see the attachment
Step-by-step explanation:
Hope it helps you
Let v=-9i+j and w=-i-6j find 8v-6w
Answer:
78i+52j
Step-by-step explanation:
8(9i+2j)-6(-i-6j)
72i+16j+6i+36j
=78i+52j
an oil tank, which is a shape of a cylinder, is 3m high and has a diameter of 6m. the oil tank is two-thirds full. find the number of cubic meters of oil in the tank. use 3.14 for pi
Answer:
Step-by-step explanation:
The key is to find out the entire volume the tank can hold when it is full, then take 2/3 of that amount. The volume of a cylinder is
[tex]V=\pi r^2h[/tex] and filling in:
[tex]V=3.14(3)^2(3)[/tex] (if the diameter is 6 m, the radius is 3) so
V = 84.78 m³ when it is full all the way. If we need the amount that makes up 2/3 of that:
[tex]\frac{2}{3}(84.78)=56.52m^3[/tex]
Exam V Psych 2317 Name: _____________________________
Attention: Read carefully each sentence and choose the best answer (2 points each)
1) While comparing a sample to a population, which design is appropriate?
A) One sample t test B) Related samples t-test C) Independent samples t-test D) ANOVA
2) While comparing two samples of different individuals, which research design is appropriate?
A) One sample t test B) Related samples t-test C) Independent samples t-test D) ANOVA
3) While comparing the same individuals two times, which research design is appropriate?
A) One sample t test B) Related samples t-test C) Independent samples t-test D) ANOVA
4) While comparing three samples of different individuals with an interest in one variable, which design is appropriate?
What are the domain and range of the function f(x) = 3^x + 5?
a. domain: (negative infinity, infinity); range: (0, infinity)
b. domain: (negative infinity, infinity); range: (5, infinity)
c. domain:(0, infinity); range: (negative infinity, infinity)
d. domain: (5, infinity); range: (negative infinity, infinity)
PLEASE RESPOND QUICKKK THANK YOUU
Answer:
b. domain: (negative infinity, infinity); range: (5, infinity)
Step-by-step explanation:
Answer:
B. Domain: (negative infinity, infinity);
Range: (5, infinity)
You are making a committee from the class and need to have 6 students on it. There are 32 students in the class.
answer in permutations
Answer:
32P6
Step-by-step explanation:
nPr
n=32
r=6
What is y=-2(x+3)^2+2
Answer:
y = -2(x + 3)² + 2
y = 2{ -(x + 3)²+ 1}
y = 2{ -(x² + 6x + 9) + 1}
y = 2{ -x² - 6x - 9 + 1}
y = 2{ -x² - 6x - 8 }
y = -2 { x² + 6x + 8}
OR
y = -2{(x + 4)(x + 2)}
SCALCET8 3.8.001.MI. A population of protozoa develops with a constant relative growth rate of 0.6137 per member per day. On day zero the population consists of two members. Find the population size after seven days. (Round your answer to the nearest whole number.) P(7)
Answer:
A population of protozoa develops with a constant relative growth rate of 0.6137 per member per day. On day zero the population · Q: For this discussion, you will work in groups to find the area and answer questions.
Step-by-step explanation:
Question:
which is a y-intercept of the graphed function?
Answers:
A. (-9,0)
B. (-3,0)
C. (0,-9)
D. (0,-3)
Answer:
(0, -9)
Step-by-step explanation:
The y intercept is the y value when x =0
(0, -9)
4
920
26°
?
74°
find the missing angle.
9514 1404 393
Answer:
44°
Step-by-step explanation:
The sum of the marked angles on the right is equal to the sum of the marked angles on the left:
? + 74 = 92 + 26
? = 92 +26 -74 = 44
The missing angle is 44°.
_____
Additional comment
The vertical angles in the center of the figure are v = 62°, the measure required to bring the total to 180° in each triangle. We have shortcut the equation(s) ...
? + 74 + v = 180 = 92 + 26 + v
by subtracting v from both sides, giving ...
? +74 = 92 +26
When two parallel lines are cut by a transversal, argles A and B are alternate Interior angles that each measure 105°. What is the measure of
each of the other alternate interior angles
Answer:
The angle for the other interior angel is 75°, all you have to do is subtract 180, from the 105
Step-by-step explanation:
Josephine left home traveling at 25 mph. One hour later her friend, Steve, leaves from the same place and travels the same road traveling at 50 mph. How many hours will it take Steve to catch up to Josephine?
Answer:
1 hour
Step-by-step explanation:
J = 50 mph by 2 hours
S = 50 mph by 1 hour
2-1 = 1
Alex thinks of a number. he squares it, then takes away five .Next multiplies it by 4 ,takes away seven, divides it by three ,and finally adds six his answer is nine what number did he start with
Answer:
3
Step-by-step explanation:
start with the ending answer and go backwards
Answer:
3.
Step-by-step explanation:
.
evaluate expression when a=5 b= -3
6a-b
The x intercepts of the function f(x) = 2x(x-5)^2(x+4)^3
are…
Answer:
[tex]\boxed{\sf x- intercepts = 0 , 5 \ and \ -4}[/tex]
Step-by-step explanation:
A function is given to us and we need to find the x Intercepts of the graph of the given function . The function is ,
[tex]\sf \implies f(x) = 2x( x - 5 ) ^2(x+4)^3 [/tex]
For finding the x intercept , equate the given function with 0, we have ;
[tex]\sf \implies 2x ( x - 5 )^2(x+4)^3= 0 [/tex]
Equate each factor with 0 ,
[tex]\sf \implies 2x = 0[/tex]
Divide both sides by 2 ,
[tex]\sf \implies\bf x = 0[/tex]
Again ,
[tex]\sf \implies ( x - 5)^2=0 [/tex]
Taking squareroot on both sides,
[tex]\sf \implies x - 5 = 0 [/tex]
Add 5 to both sides,
[tex]\sf \implies \bf x = 5[/tex]
Similarly ,
[tex]\sf \implies \bf x = -4 [/tex]
Hence the x Intercepts are -4 , 0 and 5 .
{ See attachment also for graph } .
Can someone solve this for me and a couple more questions ?
Answer:
C. -4
Step-by-step explanation:
Answer:
(c) - 4
is your right answer
Suppose that the IQ of a randomly selected student from a university is normal with mean 115 and standard deviation 25. Determine the interval of values that is centered at the mean and for which 50% of the students have IQ's in that interval.
Answer:
The interval is [98,132]
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Normal with mean 115 and standard deviation 25.
This means that [tex]\mu = 115, \sigma = 25[/tex]
Determine the interval of values that is centered at the mean and for which 50% of the students have IQ's in that interval.
Between the 50 - (50/2) = 25th percentile and the 50 + (50/2) = 75th percentile.
25th percentile:
X when Z has a p-value of 0.25, so X when Z = -0.675.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.675 = \frac{X - 115}{25}[/tex]
[tex]X - 115 = -0.675*25[/tex]
[tex]X = 98[/tex]
75th percentile:
X when Z has a p-value of 0.75, so X when Z = 0.675.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.675 = \frac{X - 115}{25}[/tex]
[tex]X - 115 = 0.675*25[/tex]
[tex]X = 132[/tex]
The interval is [98,132]
Rohit thinks of a 4 digit number. The digit in the one’s place is 3 more than the digit in the ten’s place, but 5 less than the digit in the thousand’s place. The value of the hundred’s place is 600. The digit in thousand’s place is the greatest odd number. What is the number Rohit is thinking of?
Answer:
9614
Step-by-step explanation:
Generic number with 4 digit
1000t + 100h + 10y + x
x = 3 + y
x = m - 5
h = 6
m = 9
if we substitute the value we have:
x = 9 - 5 = 4
4 = 3 + y
y = 1
Final number
9614
An office manager buys 2 office chairs and 4 file cabinets for $380. Next year she buys 4 office chairs and 6 file cabinets for $660. What is the cost of each office chair, c? What is the cost of each file cabinet, f? Explain how you fond the cost of each chair and file cabinet.
Answer:
16.5
Step-by-step explanation:
Answer:
file cabinet = 50
chair = 90
Step-by-step explanation:
x = chair
y = file cabinet
1st year, solve for x
2x+4y = 380
2x = 380 - 4y
x = 190 - 2y
2nd year
Now substitute x = 190 - 2y in your 2nd year formula
4x+6y = 660
4(190-2y)+6y = 660
760 - 8y + 6y = 660
-2y = -100
y = 50
The cost of the filling cabinet is 50 each
Now use the value for y (50) in your first formula to get x
2x+4y=380
2x+4*50=380
2x=380-200
2x=180
x=90
