The output value of g( 3b ) in the function g( x ) = x² - x is 9b² - 3b.
What is the value of g( 3b ) in the function?A function is simply a relationship that maps one input to one output, that is, each x-value can only have one y-value.
Given the data in the question;
g( x ) = x² - xg( 3b ) = ?To determine the output value of g( 3b ), replace all the occurrence of x with 3b in the function and simplify.
g( x ) = x² - x
g( 3b ) = (3b)² - 3b
Apply product rule
g( 3b ) = 3²b² - 3b
Raise 3 to the power of 2
g( 3b ) = 9b² - 3b
Therefore, the output value of g( 3b ) is 9b² - 3b.
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You toss a coin and roll a number cube. Find P(heads and an even number)
1- 1
2- 1/12
3- 1/6
4- 1/4
The probability of a head and an even number is 1/4.
What is probability?Probability is the occurrence of a certain event out of the total events than can occur in a given context.
Given event is a coin is tossed and then a die is rolled.
∴ The sample space (S) is = (H,1), (T,1), (H,2), (T,2), (H,3),(T,3), (H,4), (T,4), (H,5), (T,5), (H,6), (T,6).
So, the number of sample spaces N(S) = 12.
The number of heads and an even number N(H,E) = 3.
∴ The probability of a head and an even number is = N(H,E)/N(S).
= 3/12.
= 1/4.
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A company prices its tornado insurance using the following assumptions:
• In any calendar year, there can be at most one tornado.
• In any calendar year, the probability of a tornado is 0.04.
• The number of tornadoes in any calendar year is independent of the number of tornados in any other calendar year.
Using the company's assumptions, calculate the probability that there are fewer than 2 tornadoes in a 14-year period.Round your answer to 4 decimals.
The correct answer is 0.4834
There can only be one tornado every year on the calendar. This indicates that there are only two conceivable outcomes of the event: either there will be one tornado or none at all.
The likelihood of a tornado in any given year is 0.14. This indicates that an event's chance of occurring is fixed. p = 0.14
The frequency of tornadoes in one year is unrelated to the quantity in other years. This indicates that the incidents are unrelated to one another.
The likelihood that there won't be more than two tornadoes in a 12-year period has to be calculated. This indicates that the number of trials, n, is set at 12.
p = 0.14
q = 1 - p = 1 - 0.14 = 0.86
n = 12
x = 2
We need to find: P( x < 2)
Fewer than 2 tornadoes means either 1 or 0 tornado. So,
P(x < 2) = P(x=0) + P(x=1)
the likelihood of less than two tornadoes occurring in a 12-year period is 0.4834
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Louises saving change by -9 dollars each time she goes bowling in all a change by -$99 during the summer how many times did she go bowling in the summer
Answer:
11 times
Step-by-step explanation:
-99/-9=11
Find the circumference of each circle round answer to the nearest tenth
Answer: ask your teacher
Step-by-step explanation:u have to multiply
classify as =1 , <1 , >1 . for n>1.
|1.1n|
a. <1
b. >1
c. =1
The value of the absolute value expression given; | 1.1n | for n > 1 as required in the task content can be classified as; Choice B; >1.
What is the best classification of the expression | 1.1n | for n > 1?It follows from the task content that the best classification of the expression | 1.1n | for n > 1 be determined.
Since the domain of variable n is such that n > 1, it follows that 1.1 × n > 1.1.
There, it follows that; 1.1n > 1.1 > 1.
By definition; The absolute value |n| of any real number n is the non-negative value of x irrespective of its sign. For instance, the absolute value of 15 is 15, and also the absolute value of −15 is also 5.
Hence, the absolute value sign; | 1.1n | indicates positive values.
Ultimately, the correct classification of.the expression is; Choice B; > 1.
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Jenny wants to buy a new dress for her first school dance. She borrows $25.63 from her sister to help pay for the dress. Then Jenny earns $16.33 helping her dad organize his home office. If she gives all the earnings to her sister, Jenny will still owe her sister $ .
Answer:
Jenny owes her sister 9.3 dollars.
Step-by-step explanation:
23.63 - 16.33 = 9.3
You run $2\frac{1}{2}$ miles as a part of an exercise routine. you run $\frac{1}{3}$ of that distance on a hill. you run down a slope for the last $\frac{1}{2}$ of the hill. on how many miles of your run do you run down the slope?
Given,
Total distance [tex]=2\frac{1}{2}[/tex] miles
You run 1/3 of that distance on a hill.
Distance on a hill[tex]=\frac{1}{3} * 2\frac{1}{2}[/tex] miles
You run down a slope for the last 1/2 of the hill=[tex]\frac{1}{3} * 2\frac{1}{2}*\frac{1}{2}[/tex] miles[tex]=\frac{5}{12}[/tex] miles
Distance you run down the slope [tex]=\frac{5}{12}[/tex] miles
A father and a son go hunting. The father kills an average of 2 animals every 5 shots and the son kills one animal every 2 shots. If the two fired at the same animal at the same time, what is the probability that they will obtain kill?
The probability that the father and son will obtain a kill if they both fired at an animal the same time is 0.9
What is the probability of an event?The probability of an event is the likelihood of the occurrence of event.
The average number of animals the father kills every 5 shots he takes = 2
The average number of animals the son kills every 2 shots he takes = 1
[tex]Probability = \dfrac{Number \ of \ required \ items}{Number \ of \ possible \ outcomes}[/tex]
Which gives:
The probability that the father kills an animal = [tex]P(F) = \dfrac{2}{5} = 0.4[/tex]
The probability that the son kills an animal is; [tex]P(s) = \dfrac{1}{2} =0.5[/tex]
The probability that if the father and the son fires at the same animal, the probability that they will obtain a kill, which is the probability that the animal is killed , P(A) = The probability that the father kills the animal + The probability that the son kills the animal
P(A) = P(F) + P(s) = P(F) ∪ P(s)Which gives: P(A) = 0.4 + 0.5 = 0.9
The probability that the animal will be killed is approximately 0.9
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What is the length of side AC of the triangle? A=6x + 7 B= 5x + 5 C = 7x - 1
ok it literally shows on the figure the length of the side AC is 6x + 7.
Answer:
AC = 25 units
Step-by-step explanation:
since ∠ A and ∠ C are congruent then the 2 legs BC and AB are congruent
BC = AB ( substitute values )
7x - 1 = 5x + 5 ( subtract 5x from both sides )
2x - 1 = 5 ( add 1 to both sides )
2x = 6 ( divide both sides by 2 )
x = 3
Then
AC = 6x + 7 = 6(3) + 7 = 18 + 7 = 25
Solve it please
Iwhdhehehdhdh
Hello!
To evaluate h(3)
==> must plug '3' into x's position in the equation:
[tex]h(3)=3^2-4(3)+5\\h(3)=9-12+5=2[/tex]
Hope that helps!
Answer:
2
Step-by-step explanation:
substitute 3 for the x
3²-4(3)+5
9-12+5
2
[23+4x(2+5)<15-5x(8-7)]2^5
Answer:
[tex]23+4x(2+5)<15-5x(8-7)]2^5[/tex]
You have 8 nickels, 5 dimes, 6 quarters and 4 pennies. How much money do you
have?
$2.49
$2.44
$2.54
$2.59
Expand & simplify
(
x
+
3
)
2
(
2
x
−
5
)
Answer:
4x²+2x-30
Step-by-step explanation:
(x+3) 2(2x-5)
(x+3) (4x-10)
4x²-10x+12x-30
4x²+2x-30
1/2x+1/2+1/2x+1/2?
PLEASE HELP!
Answer:
X+1
Step-by-step explanation:
x+1
What is an equation in point-slope form for the line perpendicular to y =-5x - 14 that contains (10, -4)?
keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above
[tex]y = \stackrel{\stackrel{m}{\downarrow }}{-5}x-14\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {-5\implies \stackrel{slope}{\cfrac{-5}{1}} ~\hfill \stackrel{reciprocal}{\cfrac{1}{-5}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{1}{-5}\implies \cfrac{1}{5}}}[/tex]
so we're really looking for the equation of a line whose slope is 1/5 and it passes through (10, -4)
[tex](\stackrel{x_1}{10}~,~\stackrel{y_1}{-4})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{5} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-4)}=\stackrel{m}{ \cfrac{1}{5}}(x-\stackrel{x_1}{10}) \implies {\large \begin{array}{llll} y +4= \cfrac{1}{5} (x -10) \end{array}}[/tex]
(8d+4)⁰
(6d+8)°
3. Find d. Show a picture of your work.
d =
pic goes here (or ok to type your steps)
Answer:
d=12
Step-by-step explanation:
8d+4+6d+8 = 180 (Straight angle = 180)
14d+12=180
14d=168
d=12
:]
Answer:
D =12
Step-by-step explanation:
8d+4+6d+8 =180 (being a linear pair)
14d+12=180
14d=180-12
14d=168
d= 168/14
d=12#
Suppose the sequence 28, 14, ... is geometric.
a)Determine the common ratio.
b) List the next 3 terms in the sequence. Explain your reasoning.
please help me!!
Answer:
see explanation
Step-by-step explanation:
(a)
common ratio r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{14}{28}[/tex] = [tex]\frac{1}{2}[/tex] = 0.5
(b)
to find the next term, multiply the previous term by r = 0.5
14 × 0.5 = 7
7 × 0.5 = 3.5
3.5 × 0.5 = 1.75
the next 3 terms in the sequence are 7 , 3.5 , 1.75
⇒In a geometric sequence to find the common ratio(r) we use the formula
[tex]r=\frac{T_{2} }{T_{1} }[/tex]
But in general we use the formula is [tex]r=\frac{T_{n+1} }{T_{n} }[/tex]
In this case we are going to use
[tex]r=\frac{14}{28} \\r=\frac{1}{2}[/tex]
⇒The common ratio of the sequence is [tex]\frac{1}{2}[/tex], to get the 3 consecutive terms you are going to multiply the current term by the common ratio which in this case is [tex]\frac{1}{2}[/tex]
[tex]T_{3} =T_{2} * r\\\\T_{3}=14(\frac{1}{2} )\\T_{3} =7[/tex]
[tex]T_{4} =T_{3} *r\\T_{4}=7(\frac{1}{2} )\\T_{4}=\frac{7}{2}[/tex]
[tex]T_{5}=T_{4} *r\\T_{5}=\frac{7}{2} *\frac{1}{2} \\T_{5}=\frac{7}{4}[/tex]
If you have any questions ask me as soon as possible.
GOODLUCK!!
What is 955 divided by 36 rounded to the nearest tenth?
How would i solve for X?
Please help!
Answer: 49 degrees
Step-by-step explanation:
130+99=229
229-180=49
49 degrees
180 degrees is a straight line
It takes 0.5 gallon of cream to make 1 pound of butter.
How much butter could you make with 0.25 gallons of cream?
How much cream would you need to make 2.5 pounds of butter?
Pleasehelp Name the reciprocal
Answer:
x = 12
Step-by-step explanation:
3/4x = 9
x = 9/1(4/3)
x = 12
Tommy deposited $2,000 into a savings account that earns 5% interest per year. What
equation would be used to determine how much money Tommy has after x number of years?
Answer:
7A, 8D
Step-by-step explanation:
The compound interest formula is as followed
[tex]A = P(1+\frac{r}{n} )^{nt}\\[/tex]
A = accumulated amount
P = principle
r = interest rate
n = compounding
t = time
The accumulated amount is represented by f(x).
The principle is the amount of money you start with. In this case Tommy starts with 2000 dollars. P = 2000
The interest rate is 5%. This needs to be converted into a decimal.
5% = 0.05 = r
The money is compounded annually, thus n = 1.
The time is represented by x. x = t.
thus
[tex]f(x) = 2000(1+0.05)^{x}[/tex]
After six years, you simply find f(6), or substitute 6 into x.
f(6) = 2000(1.05)^6 = $2,680.19
Question 8
g Principal (p) = 1500, Rate (r) = 7%, Time (t)
= 8 years. Calculate the Interest.
n
et A.
C.
$840
$2,340
B.
D.
$1200
$660
[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$1500\\ r=rate\to 7\%\to \frac{7}{100}\dotfill &0.07\\ t=years\dotfill &8 \end{cases} \\\\\\ I = (1500)(0.07)(8) \implies I = 840[/tex]
In Salt Lake City, it is 8˚ colder than it is in Houston. What's the temperature in Salt Lake City? the Houston degree is 8
The temperature in salt lake city will be 0° Celsius.
What is temperature?
Temperature tells us about the degree of hotness or coldness of a body. According to the thermodynamics, temperature is a measure of the average kinetic energy of the atoms or molecules in the system.
Given is Salt Lake City where it is 8˚ colder than it is in Houston.
The degree of coldness on Celsius scale increase as the temperature tends to negative values and degree of hotness on Celsius scale increase as the temperature tends to positive values. The temperature in Houston is 8° Celsius. Since, the temperature is 8 degrees colder, we will subtract 8° from the temperature value in Houston. Therefore, temperature in salt lake city will be -
T[S] = + 8 - 8 = 0° Celsius
Therefore, the temperature in salt lake city will be 0° Celsius.
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(X-3)^2=5 to 3 significant figures
The solution to the equation is x = 5.24
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to evaluate the expression?The equation is given as
(x - 3)^2 = 5
Take the square root of both sides
So, we have
x - 3 = 2.24
Add 3 to all sides of the equation
So, we have
x = 5.24
Hence, the solution is x = 5.24
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A department store is selling 3 pairs of socks for $5. Mrs. Wagner want to buy a dozen pairs. How much will this cost?
The answer to x/-2+1>4
Answer: x < -6
Step-by-step explanation:
1) Bring 1 to the other side
x/-2 > 3
2) Bring -2 to the other side. The sign flips when the number multiplied or divided is negative
x < -6
how much time has elapsed 2:20 pm to 5:57 pm
Answer:
2:20 pm to 5:57 pm is 3 hours and 37 minutes.
Answer:
3 hours and 37 minutes.
Step-by-step explanation:
5:57
-2:20
= 3:37
The first three terms of an arithmetic sequence are as follows.-26, -19, -12Find the next two terms of this sequence.-26, – 19, -12,
1) Given that we were told that the first three terms of this Sequence. Let's find the common difference:
[tex]\begin{gathered} -26+7=-19 \\ -19+7=-12 \\ d=7 \end{gathered}[/tex]2) Based on that, we can do the following to find the next two terms:
[tex]\begin{gathered} -26+7=-19 \\ -19+7=-12 \\ -12+7=-5 \\ -5+7=2 \\ \\ -19,-12,-5,2 \\ Or \\ \\ a_4=a_1+d(n-1) \\ a_4=-26+7(4-1) \\ a_4=-26+21 \\ a_4=-5 \\ \\ a_5=-26+7(5-1) \\ a_5=-26+7(4) \\ a_5=-26+28 \\ a_5=2 \end{gathered}[/tex]Thus, the next terms are -5 and 2
a school Liberian ordered new books for the library of the new books covered 1/3 are science 2/5 are biography,and the rest of the books are friction. what fraction of the books ordered are fiction?
Given that of the new books the new books the new liberian ordered;
-1/3 are science
-2/5 are biography
Let s, b and f represent the fraction of science, biography and fiction of the new book.
[tex]s+b+f=1[/tex]substituting the values of s and b given;
[tex]undefined[/tex]