By using the natural logarithm, we will see that the value of a is 0.33
How to get the value of a?
We know that:
h(x) = x^a
And we know that:
h(27x) = 3h(x).
We can rewrite this as:
(27x)^a = 3*(x)^a
And remember that we can distribute exponents, so the left side can be rewritten as:
(27*x)^a = (27^a)*(x^a)
Then we have:
(27^a)*(x^a) = 3*(x)^a
This means that:
27^a = 3
Now remember the rule:
ln(x^n) = n*ln(x)
If we apply the natural logarithm to both sides, we get:
ln(27^a) = ln(3)
a*ln(27) = ln(3)
a = ln(3)/ln(27) = 0.33
If you want to learn more about the natural logarithm, you can read:
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3. Find the area of a trapezoid with bases 20 cm and 14 cm and height 5 cm.
Given :
Base = 20 cm and 14 cm.Height = 5 cm.To find :
Area of trapezoid.Solution :
We know,
[tex]{\qquad \dashrightarrow{ \bf{Area_{(Trapezoid)}= \dfrac{1}{2 } \times (b_{1} + b_{2}) \times h} }}[/tex]
Now, Substituting the values :
[tex]{\qquad \dashrightarrow{ \bf{Area_{(Trapezoid)}= \dfrac{1}{2 } \times (20 + 14) \times 5} }}[/tex]
[tex]{\qquad \dashrightarrow{ \bf{Area_{(Trapezoid)}= \dfrac{5}{2 } \times 34} }}[/tex]
[tex]{\qquad \dashrightarrow{ \bf{Area_{(Trapezoid)}= \dfrac{5}{ \cancel2 } \times \cancel{34}} }}[/tex]
[tex]{\qquad \dashrightarrow{ \bf{Area_{(Trapezoid)}=5 \times 17} }}[/tex]
[tex]{\qquad \dashrightarrow{ \bf{Area_{(Trapezoid)}=85} }}[/tex]
Therefore,
The area of the trapezoid is 85 cm² .Answer:
85cm²
Step-by-step explanation:
Here we are given a trapezium with base = 20cm and 14cm and height = 5cm . And we are interested in finding the area of the trapezium .
Figure :-
[tex]\setlength{\unitlength}{1.5cm}\begin{picture}\thicklines\qbezier(0,0)(0,0)(1,2.2)\qbezier(0,0)(0,0)(4,0)\qbezier(3,2.2)(4,0)(4,0)\qbezier(1.5,2.2)(0,2.2)(3,2.2)\put(0.8,2.4){$\bf A $}\put(3,2.4){$\bf D $}\put(-0.3,-0.3){$\bf B$}\put(4,-0.3){$\bf C$}\put(4.4,0){\vector(0,0){2.2}}\put( 4.4, 0){\vector(0,-1){0.1}}\put(4.6,1){$\bf 5\ cm$}\put(0, -0.5){\vector(1,0){4}}\put(0, -0.5){\vector( - 1, 0){0.1}}\put(1.7, - 0.9){$\bf 20\ cm $}\put(0.8, 2.8){\vector(1,0){2.5}}\put(0.8, 2.8){\vector( - 1, 0){0.1}}\put(1.7, 3){$\bf 14\ cm $}\end{picture} [/tex]
As we know that the area of trapezium is given by ,
[tex]\longrightarrow\rm Area =\dfrac{1}{2}(sum \ of \ || \ sides)\times height [/tex]
Here 20cm and 14cm are parallel sides .Substitute the respective values in stated formula,
[tex]\longrightarrow\rm Area =\dfrac{1}{2}(20cm +14cm)5cm \\[/tex]
Solve the parenthesis ,
[tex]\longrightarrow\rm Area =\dfrac{1}{2}\times (34cm)(5cm)[/tex]
Simplify by multiplying ,
[tex]\longrightarrow\rm \underline{\underline{\red{{Area = 85\ cm^2}}}}[/tex]
And we are done !
[tex]\rule{200}4[/tex]
Asap! I’ll mark you brainlest
What does How many kilometers did Jon run?
Add
Subtract
Divide
Multiply
What is the distance between each pair of numbers? 0 and a
Answer:
a units
i do rsm and its right
answer: its a because ITS A
If UV=p+13 and RT=p–1, what is the value of p?
Answer: 15
Step-by-step explanation:
Luke tried to use Cavalieri's principle to show that the two figures have the same volume. The base areas are the same. Therefore, corresponding cross-sections have the same area. The prisms have the same height. So the volumes must be the same. What is the first mistake Luke made?
The error Luke made when trying to use Cavalieri's principle to show that the two figrues have the same volume is stating that: "corresponding cross-sections have the same area" which is NOT TRUE.
What is the Cavalieri's Principle?The Cavalieri's principle was named after Bonaventura Cavalieri. The Cavalieri's principle states the volume of two figures are the same if they have the same height and teh same cross-sectional area at every point along the height.
Thus, the two figures have entirely different cross-sectons. Their areas would be diffrent.
Therefore, the error Luke made when trying to use Cavalieri's principle to show that the two figrues have the same volume is stating that: "corresponding cross-sections have the same area" which is NOT TRUE.
Learn more about Cavalieri's principle on:
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Answer:
the height
Step-by-step explanation:
Answer from cadencewest69. thanks cadencewest69!!! :)
HELP ASAP!! BRAINLIEST!!
Answer:
i) 2.3× 10⁻¹²
ii)2.3× 10¹⁰
iii)2.3× 10¹³
iv)2.3× 10⁻¹¹
Step-by-step explanation:
The degree and power depends on the position of the decimal. The degree of 10 is negative when the decimal is before 23 and is positive when it's after 23.
Mr. Robert is a real estate agent, he earns 5% commission of his total sales. If he sold a property for $135,000. How much commission did he receive?
Answer:
ok if I did this right the answer should be 675. sorry if it's wrong. I hope it's right.
Which is true of a geometric point?
Answer:
It has no size i.e. no width, no length and no depth. A point is shown by a dot. A line is defined as a line of points that extends infinitely in two directions. It has one dimension, length.
Step-by-step explanation:
Hope it helps :)
Have a good day/night
Brainliest pls?
A Buffalo school district randomly tests its employees to determine how many have gotten the flu shot this season. Their sample shows that 15 of them have gotten it, and 27 have not. Estimate the true proportion of employees in the district who have gotten a flu shot, with a 90% confidence level. Check conditions to see if you can use normal sampling distribution for sample proportion
Using the z-distribution, as we are working with a proportion, the 90% confidence level estimate for the true proportion of employees in the district who have gotten a flu shot is (0.2355, 0.4784).
What is a confidence interval of proportions?As long as there are 10 successes and 10 failures in the sample, that is, [tex]n\pi \geq 10[/tex] and [tex]n(1 - \pi) \geq 10[/tex], a confidence interval of proportions is given by:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which:
[tex]\pi[/tex] is the sample proportion.z is the critical value.n is the sample size.In this problem, the parameters are:
[tex]n = 42, \pi = \frac{15}{42} = 0.3571, z = 1.645[/tex]
We have the [tex]n\pi = 15, n(1 - \pi) = 27[/tex], hence you can find the interval.
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3571 - 1.645\sqrt{\frac{0.3571(0.6429)}{42}} = 0.2355[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3571 + 1.645\sqrt{\frac{0.3571(0.6429)}{42}} = 0.4787[/tex]
The 90% confidence level estimate for the true proportion of employees in the district who have gotten a flu shot is (0.2355, 0.4784).
More can be learned about the z-distribution at https://brainly.com/question/25890103
Stefan said that the y-intercept for the graph of the function f(x)=3log(x−7)+1 is 1. He also said that as x approaches positive infinity, the graph of f(x) approaches positive infinity. Describe which of Stefan's statements, if any, are incorrect, and, if so, correct the statements.
Answer:
see below
Step-by-step explanation:
f(x)=3log(x−7)+1
There is no y intercept
log (x) does not intercept the y axis. This shifts the function 7 units to the right so the graph will not intercept the y axis
Answers:
His first statement is incorrect
His second statement is correct.
======================================
Explanation:
The first statement is incorrect because plugging x = 0 into f(x) leads to
f(x) = 3*log(x-7)+1
f(0) = 3*log(0-7)+1
f(0) = 3*log(-7)+1
We stop here because we cannot take the log of a negative number (unless you want a complex number but that's for another time). This means that x = 0 is not in the domain. The domain is x > 7 to ensure that x-7 > 0. That way we avoid taking the log of a negative number, and taking the log of zero as well.
The vertical asymptote is at x = 7 and the log curve is entirely to the right of it, so there's no way it's reaching the y axis.
Simply put: there is no y intercept for this function.
---------------------
The second statement is correct.
The function y = log(x) has y go off to infinity when x does.
The same applies to y = 3log(x) and y = 3log(x-7) and y = 3log(x-7)+1
We can say it "rises to the right" as another way of describing part of the end behavior.
A graph can confirm this as shown below.
an article is bought and sold with a profit of 25% of selling price.find the profit percent
Answer:
Profit on cost will be = 33.33%
8.
Use the graph to
write an equation of the
and interpret the slope.
Answer:
cant really solve for it i think
Step-by-step explanation:
to find the slope use the equation
y 2 y- 1 / x2 - x1
300 - 180 / 3 - 5
120 / -2
-60
y = -60x + b
now to find the y-intercept you need another point so umm... you may need to ask your teacher
A 3.45
B 43.3
C 50
D 61.2
Answer: B
Step-by-step explanation:
Work out 81.19 % of 283.84 cm Give your answer rounded to 2 DP.
Answer:
230.45
Step-by-step explanation:
81.19% × 283.84
= 0.8119 × 283.84
= 230.45
Answer:
230.45Step-by-step explanation:
Solving steps81.19 % of 283.84
Step 1: Find the percentage value
=> [tex] \frac{283.84}{1} \times \frac{81.19}{100}\\ [/tex]
=> [tex] \frac{23,044.9696}{100}\\ [/tex]
=> 230.449696Step 2: Round to 2 dp(decimal points)
=> 230.449696=> 230.45
x y 3 9 6 18 9 27 12 36 The table shows a proportional relationship between x and y. What is the unit rate of y per x? A) 1 B) 3 C) 6 D) 9
Answer:yes
Step-by-step explanation:
It does show a proportion relationship because it has an upward growth of approximately 5.99999483838and 6x so if you do that together in your calc then you can get that answer please vote 5 stars.
bob made 41/4 pounds of fruit salad he added 10 ounces of pineapple how many 6 ounce servings did bob make
Identify the percent increase in total sales and the percent increase in sales of trench coats. then find which percent of increase is greater and by how much greater it is than the other. (round your answer to the nearest tenth.) a. sales of trench coats increased 0.7 percentage points faster than total coat sales. b. sales of trench coats increased 8.3 percentage points faster than total coat sales. c. total coat sales increased 2.5 percentage points faster than sales of trench coats. d. total coat sales increased 10.7 percentage points faster than sales of trench coats.
Answer:
0.7×8.3×2.5÷100×10.7
Step-by-step explanation:
0.7×8.3 =
10.7×2.5
all divided by 100
Answer:
it's B. 8.3
Step-by-step explanation:
Find the volume of a right circular cone that has a height of 3.2 in and a base with a
diameter of 5.8 in. Round your answer to the nearest tenth of a cubic inch
Answer:
28.18, rounding it, it would be 28.2 cubic inches
Step-by-step explanation:
V=Pir^2(h/3)
What is 6/8 minus 1/4? Answer as a decimal and reduce the answer.
Answer:
0.5 or 1/2
Step-by-step explanation:
so we make 6/8 have the same denominator as 1/4 (but if you want to make it harder sure make 1/4 have the same denominator loll)
6/8 = 3/4
3/4 - 1/4 = 2/4 = 1/2
Answer:
0.5 or 1/2
Step-by-step explanation:
hope this he's you
The temperature in a room at midnight is 20 degrees Celsius. Over the next 24 hours, the temperature changes at a rate modeled by the differentiable function H, where H(t) is measured in degrees Celsius per hour and time t is measured in hours since midnight. Which of the following is the best interpretation of 0 6 H(t) dt?
(A) The temperature of the room, in degrees Celsius, at 6:00 A.M.
(B) The average temperature of the room, in degrees Celsius, between midnight and 6:00 A.M.
(C) The change in the temperature of the room, in degrees Celsius, between midnight and 6
(D) The rate at which the temperature in the room is changing, in degrees Celsius per hour, at 6:00 A.M.
It will represent the change in temperature between midnight and 6, the correct option is C.
Which is the best interpretation of ∫H(t)*dt?
H(t) is the rate at which the temperature changes. So, if we integrate H(t), we will get the change of temperature.
In this case, we have:
[tex]\int\limits^6_0 {H(t)} \, dt[/tex]
This will give the change in temperature between 6:00 AM (represented by the 6) and midnight (represented with the 0).
So the correct option is C.
If you want to learn more about integration, you can read:
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The questions are below! Best answer get brainliest! 50+ points!!
Poop answers get reported!!!
Be clear when answering!!!
1. 54
2. 4
3. 2
4. 60
5.46
Answer:
1. 54
2. 4
3. 2
4. 60
5.46
Pls answer i will mark u brainlist
Answer:
35000
Step-by-step explanation:
Convert 25m to cm
25m = 2500cm
2500 x 7 = 17500cm
Convert 17500cm to m
17500cm = 175m^2
Now take 175m^2 x 200
35000
PLS HELP ASAP THANKS ILL GIVE BRAINLKEST PLS THANKS PLS
Answer:
(9, -8)
step-by-step explanation:
original coordinates of B: (-9, -8)if reflected over y-axis, use the formula: (x, y) → (-x, y)
new coordinates: (-(-9), -8) → (9, -8)HELPP PLEASE FOR BRZINLEST!!!
In a certain town there were 171 robberies last year. This year the number of robberies has gone down 39%. How many robberies were there this year, to the nearest whole number?
Answer:
104 robberies
Step-by-step explanation:
No of robberies last year = 171
Robberies for this year reduced by 39%
Percentage robberies of this year reduced to 39%
39% * 171
= 39/100 * 171
= 66.09
That is to say that this year robberies reduced by 66.09
Therefore this year robberies = 171 - 66.09
= 104.31
= 104 to the nearest
whole number
NOTE: don't forget to put the approximation sign in the final answer
The change, in yards, in a football team’s position on the field in the last 4 plays is -4, 8, -3, 2 Which list correctly compares the changes, in yards, in the football team’s position on the field?
Answer:
you must changed 4 8 and 3 2
A car leaving a stop sign accelerates constantly from a speed of 0 feet per second to reach a speed of 44 feet per second. The distance of the car from the stop sign, d, in feet, at time t, in seconds, can be found using the equation d=1.1t2.
What is the average speed of the car, in feet per second, between t=2 and t=5?
5.5
6.6
7.7
8.5
Answer:
7.7
Step-by-step explanation:
Answer:
7:7
Step-by-step explanation:
5 2/3 / 3/3
please help it’s due at 11:59 and it’s 10:17 and last day to turn in missing work
Answer:
34/9 or 3 7/9
Step-by-step explanation:
to do this u must turn 5 2/3 into an improper fraction first
5 2/3 is also 17/3
to divide you can multiply the first number by the second numbers reciprocal or flipped numbers
17/3 * 2/3
you flipped 3/2 to make it 2/3
for 17/3 * 2/3 just multiply across
34/9
then you can make that a mixed number
3 7/9
that is your answer
Answer:
the answer is 3 7/9
Step-by-step explanation:
in order to find the answer to this you need to change the mixed fraction into a improper fraction then do the reciprocal on 3/2 would would change to 2/3. Then, since you cant divide fractions you need to multiply 17/3×2/3 which would give you 34/9. But since 34/9 is improper, you need to change it to a mixed fraction and simplify if you can. So that means your final answer should be 3 7/9
♡--------------------------------------------------♡
An algebra tile configuration. only the product spot is shown. 9 tiles are in the product spot in 5 columns with 5 rows. first row: 1 x squared, 4 x. below the x squared tile are 4 x tiles. which value is needed in the expression below to create a perfect square trinomial? x2 8x ______ 4 8 16 64
We need 16 in the given expression to create a perfect square trinomial.
Let us say the given expression is:
[tex]x^{2} +8x +k^2[/tex]...............(1)
We can rewrite the above expression as:
[tex]x^{2} +2*x*4 +k^2[/tex].........(2)
What is (a+b) squared?The square of a+b is a²+2ab+b².
If we compare (2) with [tex]a^{2} +2ab+ b^{2}[/tex]
We get, a =x, b = 4 and k²=b²
Since b=4
So, k² =4²
k² =16
Put the value of k² in (1)
We get the expression [tex]x^{2} +8x +16[/tex]
Therefore, We need 16 in the expression [tex]x^{2} +8x+....[/tex]to create a perfect square trinomial.
To get more about polynomials visit:
https://brainly.com/question/2833285
Answer: OPTION C aka 16
Step-by-step explanation:
-6n - 2n= 16
Show answer
Answer:
n= -2
Step-by-step explanation: