The output value of g( -3 ) in the function g( a ) = 3a + 2 is -7.
What is the output value of g( -3 ) in the given function?A function is simply a relationship that maps one input to one output. For relation to qualify as a function, each x-value can only have one y-value.
Given the data in the question;
g( a ) = 3a + 2g( -3 ) = ?To determine the output value of g( -3 ), replace all the occurrence of 'a' with -3 in the function and simplify.
g( a ) = 3a + 2
g( -3 ) = 3( -3 ) + 2
Multiply 3 and -3
g( -3 ) = -9 + 2
Add -9 and 2
g( -3 ) = -7
Therefore, the output value is -7, this forms an ordered pair of (-3,-7).
Learn more about functions here: brainly.com/question/2541698
#SPJ1
Kwai bought `15` potage tamp for `\$8. 25`. All tamp cot the ame amount. How many tamp can Kwai purchae with $12
Lamp that can be bought with $12 is 21
What is an example of a unitary method?
A single or distinct unit is referred to by the word unitary. Therefore, the goal of this strategy is to establish values in reference to a single unit. The unitary technique, for instance, can be used to calculate how many kilometers a car will go on one litre of gas if it travels 44 km on two litres of fuel.
How is the unitary method divided?
This can be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees. In order to determine the value of one unit, we essentially divide the total value of a set of items by the number of units. The unitary approach is this.
Given that
Kwai bought 15 lamp for $8.25
$8.25 = 15 lamp
$1 = 15/8.25
$12 = (15/8.25)*12 = 21 approx.
Study up on the unitary technique.
brainly.com/question/24587372
#SPJ4
10. √961
how please help me
Answer: 31
Step-by-step explanation:
the prime factorization of 961 is 31×31 the value of the square root of 961 is 31.
Hope this helps! Have a good day! :)
what is the probability that at most eight of ten independently selected specimens have a hardness of less than 73.84?
The probability that at most eight of ten independently selected specimens have a hardness less than 73.84 is 0.2639.
Probability:
The chance that a particular event (or set of events) will occur is expressed on a linear scale from 0 (impossibility) to 1 (certainty), also expressed as a percentage between 0 and 100%. The analysis of events governed by probability is called statistics.
Here we have to find the probability:
The probability that each specimen has a hardness less than 73.84 is:
p =Ф( Z< 973.84 - 70)/ 3)
= Ф(Z<1.28 ) = 0.899
P(X<=8) = 1 - P(X=9) - P (X=10)
= 0.2639
So out of 10 specimens, the probability that 8 or fewer have a hardness less than 73.84 is 0.2639
To know more about the probability refer to the link given below:
https://brainly.com/question/13604758
#SPJ4
The parabolic path of a performer who is shot out of a cannon, where y is the height (in feet) and x is the horizontal distance traveled (in fleet), has a vertex of (60,50) and a y-intercept of (0,30). Write an equation of the parabola. The performer lands in a net 80 feet from the cannon. What is the height of the net?
[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\begin{cases} h=60\\ k=50 \end{cases}\implies y=a(x-60)^2+50\qquad \textit{we also know that} \begin{cases} x=0\\ y=30 \end{cases} \\\\\\ 30=a(0-60)^2 + 50\implies -20=a(-60)^2\implies -20=3600a \\\\\\ \cfrac{-20}{3600}=a\implies -\cfrac{1}{180}=a\hspace{5em}\boxed{y=-\cfrac{1}{180}(x-60)^2+50} \\\\\\ \textit{when x = 80, what is "y"?}\qquad y=-\cfrac{1}{180}(80-60)^2+50 \\\\\\ y=-\cfrac{20^2}{180}+50\implies y=-\cfrac{20}{9}+50\implies y=\cfrac{430}{9}\implies y=47\frac{7}{9}[/tex]
for a thin piece of 30 inches by 30 inches cardboard, square corners are cut out so that the sides can be folded up to make a box. what dimensions will yield a box of maximum volume? what is the maximum volume?
Dimensions 5in x 10in x 10in will yield a box with a max. volume of 500 cubic inches.
Volume = height x length x width
Considering 'x' as the length of the square corners that has been cut out from the cardboard and also, that is height of the cardboard box.
Square corners are cut out so that the sides can be folded up to make a box, cardboard sides would reduce by 2x
Therefore,
V = x (30-2x) (30-2x) --------------------------------- (1)
V=( 30x - 2x²) (30-2x)
V= 900x- 60x² - 60x² + 4x³
V= 4x³ - 120 x²+ 900x
Taking derivative with respect to x:
dV /dx = 12x² - 240 x +900
dV/dx = 4 (3x² - 60x +225)
For maximum dV/dx, make it equal zero
dV/dx = 0
⇒ 4 (3x² - 60x +225)=0
⇒ 3x² - 60x+225=0 (taking 3 common)
⇒ x² - 20x + 75 =0
Solving this quadratic equation, we get,
x² - 15x -5x + 75 =0
x(x-15) - 5(x-15) =0
Either (x-15)=0
x=15
Or, x-5=0
x = 5
If we substitute x = 15 in equation (1), volume becomes zero.
Therefore, x cannot be 15
When x= 5, putting in the equation (1)
V = 5 (30-2(5)) (30-2(5))
V= 5 (10) (10)
V= 500 cubic inches,
Therefore, Dimensions 5in x 10in x 10in will yield a box with a max. volume of 500 cubic inches
Learn more about Volume:
https://brainly.com/question/2416240
#SPJ4
my computer crashes on average once every 4 months. what is the probability that it will not crash in a period of 4 months.
The probability that a computer will not crash in a period of 4 months is 0.632.There is a 75% chance that the computer will not crash in a period of 4 months.
To solve this problem stepwise, first calculate the probability that the computer will crash in a given month. This can be done by using the Poisson distribution. The probability that the computer will crash in a given month is 0.0333.
Next, calculate the probability that the computer will not crash in a given month. This is simply 1 - 0.0333, or 0.9667.
Now, to calculate the probability that the computer will not crash in a period of 4 months, simply take the probability of not crashing in a given month and raise it to the 4th power. This gives us a probability of 0.632.
Learn more about probability: https://brainly.com/question/11234923
#SPJ4
Kayden just accepted a job at a new company where he will make an annual salary of
$48000. Kayden was told that for each year he stays with the company, he will be
given a salary raise of $4500. How much would Kayden make as a salary after 4 years
working for the company? What would be his salary after t years?
Salary after 4 years:
Salary after t years:
The salary of Kayden after 4 years will be $ 221,952.00
The annual salary is $48000
Salary rise is $4500
The rate of the this salary can be found out by [tex]\frac{48,000- 4500}{48000}[/tex]
= [tex]\frac{43,500}{48,000}[/tex] × 100
= 90.6 %
The time interval is 4 years
thus the prinicipal amount is given as $48000.
thus simple interest is P × R × T/ 100
which when calculated will give us
simple interest = $221,952.00
$221,952.00 is the total amount accrued from simple interest on a principal of $48,000.00 at a rate of 90.6% per year for 4 years. This includes both principal and interest.
To know more about simple interest or related problems you may visit the link which is mentioned below:
https://brainly.com/question/25845758
#SPJ13
Write the equation for the following relation. P = {(x, y): (1, 0), (2, 4), (3, 8), (4, 12), . . .}
The equation of the relation x and y is y = 4x - 4
How to represent linear equation?The relation follows a linear pattern. Therefore, the relationship is linear.
A linear relationship can be represented in different form such as slope intercept form and point slope form.
Let's represent the equation in slope intercept form.
y = mx + b
where
m = slopeb = y-interceptTherefore,
m = 4 - 0 / 2 - 1
m = 4 / 1
m = 4
Therefore, let's find the y-intercept using (1, 0)
y = 4x + b
0 = 4(1) + b
b = -4
Therefore, the equation is y = 4x - 4
learn more on equation here: https://brainly.com/question/6358267
#SPJ1
a researcher finds 200 women over 50 who exercise regularly, pairs each with a woman who has a similar medical history but does not exercise, then follows the subjects for 10 years to see which group develops more cancer. this is a ...
A researcher finds 200 women over 50 who exercise regularly, pairs each with a woman who has a similar medical history but does not exercise, then follows the subjects for 10 years to see which group develops more cancer. this is a prospective study.
Define prospective study.Individuals are tracked over time in prospective studies, and information is gathered about them as their characteristics or circumstances change. Prospective studies include things like birth cohort studies. In retrospective research, people are sampled, and details about their past are gathered. Always after a predetermined number of incidents, the analysis takes place. The fact that individuals were enrolled and baseline data was obtained before any subjects experienced an outcome of interest identifies a study as prospective.
Given,
A researcher finds 200 women over 50 who exercise regularly, pairs each with a woman who has a similar medical history but does not exercise, then follows the subjects for 10 years to see which group develops more cancer. this is a ...
Prospective study
To learn more about prospective study, visit:
https://brainly.com/question/28565073
#SPJ4
Huey lost 80 marbles. He was to find 45% of them. How many marbles did Huey find
Answer:
OK, so we know that 50% of the 80 marbles is 40, but we are supposed to find 45% of it, so basically it is 36 marbles he has found, I hope this is right!
Love from Ella
you and your friends go to joshua tree national park on december 13 to watch the peak of the geminid meteor shower. according to the griffith observatory website, the expected number of meteors you will see is 150150 per hour. what is the probability that you will see at least two meteors in the first minute?
The probability that we will see at least two meteors in the first minute is 1251.5.
What is probability?The probability is the likelihood that something will happen, to put it simply. When we don't know how something will turn out, we can talk about the possibility of one outcome or the likelihood of several. The study of events that fit into a probability distribution is known as statistics. Probability is a branch of mathematics that deals with numerical representations of the likelihood of an event occurring or of a proposition being true.So, the probability that we will see at least 2 meteors in the first minute:
The expected start we can see in 1 hour is 150150.Then, in 1 minute:
150150/60 = 2,502.5Rounding off: 2,503Now, at least 2 meteors in 1 minute:
Probability formula: P(E) = Favourable events/Total eventsSolve as follows:
P(E) = Favourable events/Total eventsP(E) =2/2,503P(E) = 7.99P(E) = 1251.5Therefore, there is a 1251.5 percent probability that we will observe two meteors or more in the first minute.
Know more about probability here:
https://brainly.com/question/28924396
#SPJ13
IM BEGGING FOR HELP !!! find the volume of each shape and then compare do not reduce your fractions.
Answer:
64/125 > 150/512
Step-by-step explanation:
4/5 *4/5 *4/5 = 64/125 (also equals 0.512)
5/8 * 6/8 * 5/8 = 150/512 (also equals 0.293)
Therefore: 0.512 > 0.293
1. Noah is running a portion of a marathon at a constant speed of 6 miles per hour.
Complete the table to predict how long it would take him to run different distances at that speed, and how far he would run in different time intervals.
time in hours
miles traveled at 6 miles per hour
1
6
1
2
3
1
1
3
8
1
1
2
9
4
1
2
Please help with this
Step-by-step explanation:
remember, the circumference of a circle is
2×pi×r
and that is for the full 360° of a circle.
how long will the arc length of 1° be ?
well,
2×pi×r / 360
and how long will the arc length of 78° be ?
well,
78 × 1° = 2×pi×r × 78/360
you see ? that is the whole trick ...
now we only need to enter the value for r (radius).
and that is GH = 9 units.
so, the length of the arc GJ is
2×pi×9 × 78/360 = 2×pi × 78/40 = pi × 78/20 =
= 12.25221135... ≈ 12.25 units
Which expression is equivalent to (8−2 • 35)−2?
100 points and brainliest
Answer: -64
Step-by-step explanation:
(8−2 • 35)−2
8-70-2
8-72
-64
Answer:
(8 - 2 • 35) - 2 = -64
Step-by-step explanation:
Given problem,
→ (8 - 2 • 35) - 2
Let's solve the problem,
→ (8 - 2 • 35) - 2
→ (8 - (2 × 35)) - 2
→ (8 - 70) - 2
→ -62 - 2
→ -64
Hence, the answer is -64.
A city doubles its size every 5 years. If the population is currently 469,900, what will the
population be in 20 years?
the population would be 7,518,400
469,900 • 2^20/5
* 20/5 is part of the exponent
Answer:
7518400
Step-by-step explanation:
Doubling time model:
[tex]P= P_o 2^{\frac{t}{D}}[/tex]
Here, P is the initial value, D is the time taken to double the quantity, t is the given period of time.
[tex]P_o = 469,900\\\\\\D = 5 \ years\\t = 20 \ years[/tex]
[tex]P = 469,900 * 2^\frac{20}{5}\\\\P = 469,900 * 2^4[/tex]
= 469,900 * 2 * 2 * 2 * 2
= 7518400
ce
4. Six foot tall pine trees were planted during the
school's observation of Earth Awareness Week in
1990. The trees have grown at an average rate of
3/4 foot per year. How tall would they be in 2010?
The height of the trees in the year 2010, given their average rate of growth will be 21 foot
How to find the height of the trees?The trees are said to grow at a rate of 3/4 foot per year. In decimals this is:
= 3 / 4
= 0.75
The number of years between 1990 and 2010 is:
= 2010 - 1990
= 20 years
The height of the trees in 2010 would be:
= Current height x ( Rate of growth x number of years)
= 6 x (0.75 x 20)
= 21 foot
Find out more on the height of trees at https://brainly.com/question/9655877
#SPJ1
Six trigonometric functions of the angle (20,21)
The exact values of the six trigonometric functions for the point (x, y) = (20, 21) are listed below:
sin θ = 21 / 29, cos θ = 20 / 29, tan θ = 21 / 20, cot θ = 20 / 21, sec θ = 29 / 20, csc θ = 29 / 21
How to determine the exact six trigonometric functions related to a point in rectangular format
Points in rectangular format are points of the form (x, y), where x and y represent the position of the point respect to the origin and along the respective orthogonal axis.
The line segment between the origin and that point represents the hypotenuse of a right triangle. Then, we can determine the six trigonometric functions by using the following formulae:
sin θ = y / √(x² + y²)
cos θ = x / √(x² + y²)
tan θ = y / x
cot θ = x / y
sec θ = √(x² + y²) / x
csc θ = √(x² + y²) / y
If we know that x = 20 and y = 21, then the exact values of the trigonometric functions are:
sin θ = 21 / √(20² + 21²)
sin θ = 21 / 29
cos θ = 20 / √(20² + 21²)
cos θ = 20 / 29
tan θ = 21 / 20
cot θ = 20 / 21
sec θ = √(20² + 21²) / 20
sec θ = 29 / 20
csc θ = √(20² + 21²) / 21
csc θ = 29 / 21
To learn more on trigonometric functions: https://brainly.com/question/14746686
#SPJ1
what do you add to 5 8/9 to make 7
what is 315.00 divided by 30.
Answer:
Step-by-step explanation:
Answer 10.5
8/5 + 7/3 Please put step by step
Answer:
59/15
Step-by-step explanation:
8/5 + 7/3 Multiply the numerator and denominator by the LCF of the denominator
(3/3) 8/5 + 7/3 (5/5) Multiply
24/15 + 35/15 Add the numerators
59/15
∠1 ​ and ∠2 are complementary. m∠1=x°m∠2=(3x 30)° what is the value of x? select from the drop-down menu to correctly answer the question.
The value of x is 15
If two angles sum to 90 degrees, they are said to be complimentary angles. In other terms, a right angle is created when two complementary angles are combined (90 degrees). If the sum of angles 1 and 2 equals 90 degrees (i.e., angle 1 plus angle 2 = 90°), then the angles are complementary and are referred to as one another's complements.
∠1 and ∠2 are complementary angles i.e the sum of ∠1 and ∠2 is 90° .
Thus
∠1 + ∠2 = 90°
x° + (3x+30)° = 90°
x + 3x + 30 = 90
4x = 90-30
4x = 60
x = 15
Therefore the value of x is 15.
Learn more about angles:
https://brainly.com/question/28451077
#SPJ4
PLEASE HEIP MEE
What sequence equation would represent this graph?
The equation would represents the graph is y = 20000 + 1750x and the graph has been plotted
From the table
The investment in 1 year = $20000
The investment in 2 year = $21750
The investment in 3 year = $23500
The investment in 4 year = $25250
The investment in 5 year = $27000
Then the equation will be
y = 20000 + 1750x
Where y is the investment in dollars
x is the number of years
Draw the graph as number of years in x axis and the amount of investment in y axis
Hence, the equation would represents the graph is y = 20000 + 1750x and the graph has been plotted
Learn more about equation here
brainly.com/question/11897796
#SPJ1
The wholesale cost for a purse in a department store is $12. 50. The store plans to mark up the purse by 140%. What will be the selling price of
the purse to the nearest cent?
Give me the right anwser
The selling price of the the purse in a department store is cents.
Define the term selling price?A product's or service's selling price is the seller's final price, or how much the buyer pays for anything. The trade can be for a certain proportion, quantity, or measure of a commodity or service.The price at which you sell anything must be sufficient to generate a profit. It must also establish a market position.For the given question-
A purse in such a department store costs $12.50 at wholesale.
The purse will be 140% more expensive at the store.
Then,
140% of 12.50 = 140 x 12.50 / 100
140% of 12.50 = 17.5
Selling price = percent increase + cost price
Selling price = 17.5 + 12.5
Selling price = $30.0
Selling price = 3000 cents
Thus, the selling price of the the purse in a department store is cents.
To know more about the selling price, here
https://brainly.com/question/1153322
#SPJ4
what is this asap
x=6+29
Answer:
x=35
Step-by-step explanation:
29+6=35
btw are you sure that you are in highschool???
Answer:
35
Step-by-step explanation:
29+6 is 35 u sure in high school?
Write an equation in point-slope form for the line that passes through the
point with the given slope.
(-6, -3), m = -1
Answer:
( y + 3 ) = - ( x + 6 )
Step-by-step explanation:
The Equation of Line in Point-Slope Form is
[tex](y-y_1)=m(x-x_1)\\where\ m \is \ the \ slope\ and \ (x_1 , y_1) \ is \ any \ point \ on \ the \ line[/tex]
So by Substitution by the Givens
( y - (-3) ) = -1( x - (-6) )
( y + 3 ) = - ( x + 6 )
Glad to Help
You are asked to write an equation for the line of best fit for the scatter plot shown at the right without the use of a graphing calculator. What should you do first? Explain
Answer:
Find the slope between the points (1,2) and (9,12).
Step-by-step explanation:
If I was going to draw the line of best fit without a calculator, I would draw it including these two points. Once I had these two points, I would find the slope using these points.
help meeeeeeeeeeee pleaseeeeeeeeeee rn rnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeee pleaseeeeeeeeeee rn rnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The Maximum and Minimum values of x is = (3,30)
The maximum of a quadratic function occurs at
x = − b/2a
If a is negative, the maximum value of the function is
f ( − b/2a).
f max x =ax^2+bx+c occurs at
x = −b/2a
Finding the value of
x = −b/2a
Substitute in the values of a and b.
x = − 18/2(3)
Simplify
x = -3
Replace the variable x with -3 in the expression
f (-3) = -3(-3)^2+18(-3)+3
f(-3) = - 27 +54 +3
f(-3) = -30
f(3) = 30
The maximum of -3x^2+18x+3 = (3,30)
Learn more about the maximum value here :
https://brainly.com/question/14316282
#SPJ1
Y-4=2/3(×+2) look like on line graph
The graph of the linear equation:
y - 4 = (2/3)*(x + 2)
Can be seen on the image at the end.
How to graph the linear equation?
Here we have the following linear equation:
y - 4 = (2/3)*(x + 2)
Isolating y, we get:
y = (2/3)*(x + 2) + 4
To graph the line, we just need to evaluate it in two different values of x so we get two points, once we get the points, we can graph them on a coordinate axis and then connect them with a line.
If we use x = 1 we get:
y = (2/3)*(1 + 2) + 4
y = (2/3)*3 + 4
y = 2 + 4 = 6
y = 6
Then we have the point (1, 6)
if x = 4 then:
y = (2/3)*(4 + 2) + 4
y = (2/3)*6 + 4
y = 4 + 4 = 8
So we have the point (4, 8)
Then the graph of the linear equation is the one you can see below:
Learn more about linear equations:
https://brainly.com/question/1884491
#SPJ1
i need help asap i need an awncer
3x=y-4z=-22
2x+3y+4z=32
x-y+2z=16
Answer:
3x + y - 4z = -222x + 3y + 4z = 32x - y + 2z = 16 Write and number each equation. Eq 1 3x+y-4z = 16. Eq 2 -222x+3y+4z = 16. Eq 3 32x-y+2z = 16
Step-by-step explanation:
Hope it helps you buddy(:
Answer: 16
You already got the answer- But whatever.
The values of [x], [y] and [z] are 2, 0 and 7.
What is the general equation of a Straight line?The general equation of a straight line is -
[y] = [m]x + [c]
where -
[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.
The equation of a straight line can be also written to express proportional relationship as -
y = kx {k is constant}
We have the following system of equation -
3x+y-4z=-22
2x+3y+4z=32
x-y+2z=16
We can write -
x - y + 2z = 16
x = 16 + y - 2z
So, we can write 3x + y - 4z = -22 as -
3(16 + y - 2z) + y - 4z = -22 ...eq[1]
and we can write 2x + 3y + 4z = 32 as -
2(16 + y - 2z) + 3y + 4z = 32 ...eq[2]
Plot eq[1] and eq[2], and find [y] and [z]. Refer to graph.
We get y = 0 and z = 7
So -
x = 16 + 0 - 14
x = 2
Therefore, the values of [x], [y] and [z] are 2, 0 and 7.
To solve more questions on system of equations, visit the link below-
https://brainly.com/question/20067450
#SPJ2
