The function h is defined by h(x)=x^2 +2.
Find h(3y).
PLS Help While on a strenuous hike, Tara recorded her distance from the peak of the mountain at two different time intervals. The table shows the two pieces of data she collected.
Answer:
Step-by-step explanation:
Equation of a line representing the relation between distance from the peak of the mountain and time is,
h = mt + b
Here, m = Slope of the line
b = y-intercept
Since, slope of the line passing through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given by,
m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
From the table attached,
Slope of the line passing through (2, 2600) and (5, 950) will be,
m = [tex]\frac{2600-950}{2-5}[/tex]
= -550
Therefore, equation of the line will be,
h = -550t + b
Since, point (2, 2600) lies on this line,
2600 = -550(2) + b
b = 2600 + 1100
b = 3700
So, equation of the line will be,
h = -550t + 3700
Input - output values for this line,
t 2 4 6
h 2600 1500 400
Now we can plot these points and get the graph of the line.
[IMAGE ATTACHED]
PLEASE HELP ME WITH 9 (and 7a./7b. If you can) :)
Answer:
y = (1/4) 2^x
Step-by-step explanation:
Remark
y = a * x^n is the general equation. Let's see what that means.
Solution
Solve for x
t_12 = a x^12
1024 = a x^12
t_8 = a x^8
64 = a x^8
Now divide the two equations.
1024/64 = a x^12/a x^8 Cancel out the as
1024 / 64 = x^12 / x^8
16 = x^(12 - 8)
16 = x^4 Take the 4th root of both sides.
[tex]\sqrt[4]{x^4}[/tex] = [tex]\sqrt[4]{16}[/tex]
x = 2
Go back and solve for a
y_12 = a x^12
1024 = a 2^12
1024 = a 4096 Divide by 4096
1024 / 4096 = a
a = 1/4
Problem 7
a) First of negative numbers are probably not a good idea. It means that the population is going to decrease. That's not what will happen if you take care of the fruit flies.
So for the domain, 0 is a good starting point.
That will give you 100 flies on day 0. That's how many you bought.
I'm not a biologist so I have no idea in the world how long a fruit fly will live even with the best of care. I'm going to try 60 days and see what happens.
y = 100 * 1.05 ^60
y = 100 * 18.68
y = 1868
Is this number reasonable? Even with the biggest olive jar you can find, and the best care, I don't think that number is realistic. It's too large. Eventually all will die of disease because they are living in their own waste. So Let's try 20 days
y = 100 * 1.05^20
y = 100 * 2.65
y = 265
That's a lot more reasonable. So for convenience sake let us say that 265 flies could live for 20 days
So to answer the question
The domain would be 0 to 20
The range would be 100 to 265
b)
2 weeks = 2*7 days
2 weeks = 14 days
y = 100 * 1.05^14
y = 100 * 1.98
y = 198 fruit flies.
Evaluate (–6)^2 – 7^2.
A) 85
B) 169
C) –85
D) –13
7+9 x (3+8) Order of operations. Please explain.
Answer:
Not sure if that is "9x" or "9 times" but I will do both. I have attached a picture of me solving and explaining the steps. Hope this helps, thank you !!
Plsss help me!!!Mei graphed the locations of several places in her town on the coordinate plane shown below. There is also
an ice cream shop halfway between the school and hospital.
At what coordinates should Mei graph the ice cream shop?
Answer:
(6, -4)? is this on khan academy or smth
Step-by-step explanation:
Ms. Gonzalez buys folders for her office. She buys 4 small folders for every 1 large
folder. She buys 15 folders in all. Small folders cost $0.75, and large folders cost
$1.25. How much more money does Ms. Gonzalez spend on small folders than
large folders? Show your work.
Answer:
Step-by-step explanation:
The amount of money that Ms. Gonzalez spends on small folders than large folders will be $12.75.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
Ms. Gonzalez buys folders for her office. She buys 4 small folders for every 1 large folder. She buys 15 folders in all. Small folders cost $0.75, and large folders cost $1.25.
Let 'x' be the number of small folders and 'y' be the large folders. Then the equations are given as,
x + y = 15 ...1
y = 4x ...2
From equations 1 and 2, then we have
x + 4x = 15
5x = 15
x = 3
Then the value of 'y' is given as,
3 + y = 15
y = 12
The cost of the small folder is given as,
⇒ $0.75 × 3
⇒ $2.25
The cost of the large folder is given as,
⇒ $1.25 × 12
⇒ $15
The difference is given as,
⇒ $15 - $2.25
⇒ $12.75
The amount of money that Ms. Gonzalez spends on small folders than large folders will be $12.75.
More about the solution of the equation link is given below.
https://brainly.com/question/545403
#SPJ5
help with geometry please !
A computer laboratory manager was in charge of purchasing new battery packs for her lab of laptop computers. She narrowed her choices to two models that were available for her machines. Since the models cost about the same, she was interested in determining whether there was a difference in the average time the battery packs would function before needing to be recharged. She took two independent samples and computed the following summary information: Battery Pack Model 1 Battery Pack Model 2Sample Size 9 9Sample Mean 5 hours 5.5 hoursStandard Deviation 1.5 hours 1.3 hoursUsing the null and alternate hypothesis:H0:mu1-mu2=0 vs. Ha: mu1-mu2 not equal 0Calculate the test statistic for this test.
Answer:
-0.756
Step-by-step explanation:
N1 = 9
N2 = 9
Sd1 = 1.5 hours
Sd2 = 1.3 hours
X1 = 5 hours
X2 = 5.5 hours
Hypothesis
H0: mu1 - mu2 = 0
H1 : mu1 - mu2 not equal to 0
Test statistic
t = (x1 - x2)/SE
SE is the standard error, which is unknown
SE = √sd1²/n1 + sd2²/n2
= √1.5²/9 + 1.3²/9
= √0.25+0.1878
= √0.4378
= 0.66166
t statistics = (5-5.5)/0.66166
= -0.5/0.66166
= -0.756
Write out the form of the partial fraction decomposition of the function (as in this example). Do not determine the numerical values of the coefficients. (a) x − 20 x2 + x − 20 Incorrect: Your answer is incorrect. (b) x2 x2 + x + 20 Incorrect: Your answer is incorrect.
Answer:
[tex]\frac{x - 20}{ x^2 + x - 20} = \frac{5}{9(x-4)}+\frac{4}{(x+5)}[/tex]
Step-by-step explanation:
Given
[tex]\frac{x - 20}{ x^2 + x - 20}[/tex]
Required
Decompose into partial fraction
Start by factorizing the denominator:
[tex]x^2 + x - 20 =x^2 + 5x -4x- 20[/tex]
[tex]x^2 + x - 20 =x(x + 5)-4(x+5)[/tex]
[tex]x^2 + x - 20 =(x-4)(x+5)[/tex]
So, we have:
[tex]\frac{x - 20}{ x^2 + x - 20} = \frac{A}{x-4}+\frac{B}{x+5}[/tex]
Take LCM
[tex]\frac{x - 20}{ x^2 + x - 20} = \frac{A(x+5)+B(x-4)}{(x-4)(x+5)}[/tex]
Cancel out the denominator
[tex]x - 20 = A(x+5)+B(x-4)}[/tex]
Open brackets
[tex]x - 20 = Ax+5A+Bx-4B[/tex]
Collect Like Terms
[tex]x - 20 = Ax+Bx+5A-4B[/tex]
[tex]x - 20 = (A+B)x+5A-4B[/tex]
By comparison;
[tex](A +B)x = x[/tex] ==>[tex]A + B = 1[/tex]
[tex]5A - 4B = 1[/tex]
Make A the subject in [tex]A + B = 1[/tex]
[tex]A = 1 - B[/tex]
Substitute 1 - B for A in [tex]5A - 4B = 1[/tex]
[tex]5(1-B) -4B = 1[/tex]
[tex]5-5B -4B = 1[/tex]
[tex]5-9B = 1[/tex]
Collect Like Terms
[tex]-9B = 1 - 5[/tex]
[tex]-9B = - 4[/tex]
[tex]B = \frac{4}{9}[/tex]
[tex]A = 1 - B[/tex]
[tex]A = 1 - \frac{4}{9}[/tex]
[tex]A = \frac{9-4}{9}[/tex]
[tex]A = \frac{5}{9}[/tex]
So:
[tex]\frac{x - 20}{ x^2 + x - 20} = \frac{A}{x-4}+\frac{B}{x+5}[/tex]
[tex]\frac{x - 20}{ x^2 + x - 20} = \frac{5}{9(x-4)}+\frac{4}{(x+5)}[/tex]
Select the correct answer.
What is the complete factorization of x2 + 2x - 63?
A. (x+ 21)(x-3)
B.
(x-9)(x+7)
C.
(x + 9)(x-7)
D.
(x-21)(x + 3)
Reset
Answer:
the answer of this question is
c
Pls help due in 10 minutes
Answer:
Boy I'm really boutta get to yo pickle chin ahh boy, egg head like collard greens head a//ss boy, oh hell nah boy yo dirt ahh boy stank ahh boy afro head ahh, lip gloss chin ahh boy ugly ahh boi
Step-by-step explanation:
Aawdadakdaw da awdwa dadeefdcdcs
Find an equation of a line parallel to the line y = 1/2x-3that contains the point (6,4).
Write the equation in slope-intercept form.
#First find the gradient first, remember that the formula of equation of the line is y = mx + c and gradient's symbol is m
y = ½x - 3
#so the gradient is ½, now u can find the equation of the lime.
y - y1 = m(x - x1)
y - 4 = ½(x - 6)
y - 4 = ½x - 3
y = ½x - 3 + 4
y = ½x + 1
Answer : y = ½x + 1если x=6 то y=
если y=-4 то x=
Step-by-step explanation:
ssshzvecucsussddyz wksoav
Answer:
X=6 To y=-6
y=-4 TO X = 4
꧁꧁꧁꧁꧂꧂꧂꧂
꧂꧂꧂꧂꧂
four times a number increased by 8 is 54?
Answer:
4x+8=54 this is the correct answer
To keep in shape, Vincent exercises at a track near his home. He requires 40 minutes to do 4 laps running and 7 laps walking. In contrast, he requires 18 minutes to do 2 laps running and 3 laps walking. Assuming he maintains a consistent pace while running and while walking, how long does Vincent take to complete a lap at each pace?
Answer:
He completes a lap running in 3 minutes, and walking in 4 minutes.
Step-by-step explanation:
This question can be solved by a system of equations.
I am going to say that:
x is the time needed to complete a lap running.
y is the time needed to complete a lap walking.
He requires 40 minutes to do 4 laps running and 7 laps walking.
This means that:
[tex]4x + 7y = 40[/tex]
[tex]4x = 40 - 7y[/tex]
He requires 18 minutes to do 2 laps running and 3 laps walking.
This means that
[tex]2x + 3y = 18[/tex]
Multipluing everything by 2
[tex]4x + 6y = 36[/tex]
Since [tex]4x = 40 - 7y[/tex]
[tex]40 - 7y + 6y = 36[/tex]
[tex]y = 4[/tex]
And
[tex]4x = 40 - 7y[/tex]
[tex]4x = 40 - 7*4[/tex]
[tex]4x = 12[/tex]
[tex]x = \frac{12}{4}[/tex]
[tex]x = 3[/tex]
He completes a lap running in 3 minutes, and walking in 4 minutes.
Evaluate
ifr=9 and s = 2.
S
Answer:
(4 × 9) / 2 = 36/2 = 18 gitu yaaa
Answer:
18
Step-by-step explanation:
plug in r and s
4(9)/2
36/2
18
solve for x 0°<x<360
3cos2x +sinx=1
Step-by-step explanation:
3cos2x +sinx=1
3(1-2sin²x)+sinx=1
3-6sin²x+sinx=1
sinx(-6sinx+1)=1
either
sinx=1
sinx=sin(90)
:.x=90
or
-6sinx+1=1
-6sinx=1-1
sinx=0/-6
sinx=sin0,sin180
:.x=0,180and90
origanal price $60 sale price $45
Answer:
di ko po alam ehh
Step-by-step explanation:
sorry po
Answer:
Step-by-step explanation:
What is the question?
Price reduced by $15
Percentage reduction = 15/60 = 0.25 = 25%
7x= -42
What is the solution to this equation?
Answer:
X= -6
Step-by-step explanation:
7x = -42
(÷7) (÷7)
X = -6
If a sprinkler waters 1/20 of a lawn in 1/5 of an hour how much time will it take to water the entire lawn?
• 3/20 hour
• 1/4 hour
• 4 hours
• 5 hours
Answer:
4 hours
Step-by-step explanation:
12 more than the square of a number is the same as 7 times the number.
Answer: Sorry I don't know
Step-by-step explanation:
The ratio of girls to boys on a soccer team is 2 to 3. If there are 15 boys on the team, how many are girls? Let g = the number of girls on the team. Set up a proportion for this word problem.
Answer:
3X=15
X=5
2X5= 10
G=10
Step-by-step explanation:
if the force acting on a body of mass 4kg accelerates it at a constant rate of 4m/s. what would be the acceleration of the mass is doubled?
Answer:
4kg=4m/s
8kg=?
3m/s
Step-by-step explanation:
12kgm/s/4kg
1 over blank = 2 over 10 = blank over 100
Answer:
[tex]\frac{1}{5}[/tex] = [tex]\frac{2}{10}[/tex] = [tex]\frac{20}{100}[/tex]
Step-by-step explanation:
It's all about equivalent fractions.
[tex]\frac{1}{5}[/tex]
[tex]\frac{2}{10}[/tex]
[tex]\frac{20}{100}[/tex]
[tex]\frac{1}{5}[/tex] 1 × 2 = 2. 5 × 2 = 10. That is what makes [tex]\frac{2}{10}[/tex].
[tex]\frac{2}{10}[/tex] 2 × 10 = 20. 10 × 10 = 100. That is what makes [tex]\frac{20}{100}[/tex].
To test the effectiveness of a drug proposed to relieve symptoms of depression, psychiatrists recruited volunteers for clinical tests. All of the volunteers were diagnosed with symptoms of depression. The psychiatrists provided the drug to first group and a sugar pill to the second group. In the description of the above situation, determine the control group.
Answer:
The control group is the group that takes the sugar pill
Step-by-step explanation:
In drug testing, to determine the efficacy of a drug, different groups of experimental subjects are recruited, one group is given the drug to be tested (treatment group) while another group is given a placebo.
A placebo is a fake version of the drug to be tested that does not have any therapeutic effect on the test subjects that receive it. In this case, the control group receives the placebo which is the sugar pill. They serve as the baseline of measurement when the outcome of the effect of the drug testing is done. The groups that received the actual drugs are compared against the groups that received the hoax treatment, and any change occuring in the test subjects become the changes occuring as a result of the test drug used, when the observations on the control group has been ruled out.
Need Trig Help plz Picture attached
PLEASE HELP!!! WILL GIVE BRAINLIEST!!!
Instructions
Search your home for a rectangular prism. Some examples are a cereal box, a CD case, or a coffee table. Measure your prism using appropriate units, such as inches, centimeters, or feet.
Complete the following. Show all work for calculations.
List the dimensions of your box. Be sure to include the units (in, cm, ft, etc.).
Length: 6 inches
Width: 2 and a half inches
Height: 12 inches (1 foot)
Describe the shape of the cross section when the box is cut parallel to the base.
What is the surface area of the box?
What is the surface area of the box if it is scaled up by a factor of 10?
What is the volume of the box?
What is the volume of the box if it is scaled down by a factor of 1/10?
Answer:
I chose a box of cereal-------> rectangular prism
see the attached figure
Part 1)List the dimensions of your box. Be sure to include the units (in, cm, ft, etc.).
Length: 20 cm
Width: 8 cm
Height: 32 cm
Part 2).
Describe the shape of the cross-section when the box is cut parallel to the base
the shape of the cross-section would be a rectangle of dimensions
20 cm x 8 cm
Part 3)
What is the surface area of the box?
surface area=2*area of the base+perimeter of the base*height
area of the base=20*8=160 cm²
perimeter of the base=2*[20+8]-----> 56 cm
height=32 cm
surface area=2*160+56*32------> 2,112 cm²
the answer part 3) is
2,112 cm²
Part 4)
What is the surface area of the box if it is scaled up by a factor of 10?
we know that
surface area of the larger box=[scale factor]²*surface area original box
scale factor=10
surface area original box=2,112 cm²
so
surface area of the larger box=10²*2,112-----> 211,200 cm²
the answer part 4) is
211,200 cm²
Part 5)
What is the volume of the box?
volume of the box=L*W*H-----> 20*8*32------> 5,120 cm³
the answer Part 5) is
5,120 cm³
Part 6)
What is the volume of the box if it is scaled down by a factor of 1/10
we know that
volume of the smaller box=[scale factor]³*volume original box
scale factor=1/10
volume original box=5,120 cm³
so
volume of the smaller box=[1/10]³*5,120-----> 5.12 cm³
the answer part 6) is
5.12 cm³
Step-by-step explanation:
Answer:
541/2 square
Step-by-step explanation:
we know that
the volume of the smaller box=[scale factor]³*volume original box
scale factor=1/10
volume original box=5,120 cm³
so
volume of the smaller box=[1/10]³*5,120-----> 5.12 cm³
the answer part 6) is 541/2 square
what is 3333 x 33 x 23 - 908
Answer:
2528839
Step-by-step explanation:
your welcome
The 2010 U.S. Census asked every household to report information on each person living there. Suppose for a sample of 30 households selected, the number of persons living in each was reported as follows. 2 3 1 2 6 4 2 1 5 3 2 3 1 2 2 1 3 1 2 2 4 2 1 2 9 3 2 1 1 3 Compute the mean, median, mode, range, lower and upper quartiles, and interquartile range for these data. (Round the mean to 2 decimal places.) Mean
Answer:
[tex]\bar x =2.53[/tex] -- Mean
[tex]Median= 2[/tex]
[tex]Mode = 2[/tex]
[tex]Range = 8[/tex]
[tex]Q_1 = 1[/tex]
[tex]Q_3 = 3[/tex]
[tex]IQR = 2[/tex]
Step-by-step explanation:
Given
n = 30
Data: 2 3 1 2 6 4 2 1 5 3 2 3 1 2 2 1 3 1 2 2 4 2 1 2 9 3 2 1 1 3
Solving (a): The mean
This is calculated as:
[tex]\bar x =\frac{\sum x}{n}[/tex]
[tex]\bar x =\frac{2 +3 +1 +2 +6 +4 +2 +1 +5 +3 +2 +3+ 1+ 2 +2 +1 +3 +1 +2 +2 +4 +2 +1 +2 +9 +3 +2 +1 +1 +3}{30}[/tex]
[tex]\bar x =\frac{76}{30}[/tex]
[tex]\bar x =2.53[/tex]
Solving (b): The median
First arrange the given data
Arranged: 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 4 4 5 6 9
[tex]Median =\frac{1}{2}(n+1)[/tex]
[tex]Median =\frac{1}{2}(30+1)[/tex]
[tex]Median =\frac{1}{2}(31)[/tex]
[tex]Median = 15.5th[/tex]
This implies that the median is the average of the 15th and 16th item
[tex]Median = \frac{2+2}{2}[/tex]
[tex]Median = \frac{4}{2}[/tex]
[tex]Median= 2[/tex]
Solving (c): The mode
From the given data; 2 has the highest frequency of 11.
So,
[tex]Mode = 2[/tex]
Solving (d): The Range
[tex]Range = Highest\ Data - Lowest\ Data[/tex]
The highest is 9 and the lowest is 1,
So:
[tex]Range = 9 - 1[/tex]
[tex]Range = 8[/tex]
Solving (e): Lower (Q1) and Upper (Q3) quartile.
Q1 is calculated as:
[tex]Q_1 = \frac{1}{4}(n+1)th[/tex]
[tex]Q_1 = \frac{1}{4}(30+1)th[/tex]
[tex]Q_1 = \frac{1}{4}(31)th[/tex]
[tex]Q_1 = 7.75th[/tex]
[tex]Q_1 = 8th\ item[/tex]
[tex]Q_1 = 1[/tex] -- from the arranged data
Q3 is calculated as:
[tex]Q_3 = \frac{3}{4}(n+1)th[/tex]
[tex]Q_3 = \frac{3}{4}(30+1)th[/tex]
[tex]Q_3 = \frac{3}{4}(31)th[/tex]
[tex]Q_3 = 23.25th[/tex]
[tex]Q_3 = 23rd\ item[/tex]
[tex]Q_3 = 3[/tex] -- from the arranged data
Solving (f): The interquartile range (IQR)
[tex]IQR = Q_3 - Q_1[/tex]
[tex]IQR = 3-1[/tex]
[tex]IQR = 2[/tex]