Answer:
Step-by-step explanation:
11.04 = 10(1.02)^n
1.104 = 1.02^n
ln 1.104 = ln 1.02^n
ln 1.104 = n ln 1.02
n = ln 1.104/ ln 1.02
n = 4.99630409516
4.99 can be rounded to 5.
So a reasonable domain would be 0 ≤ x < 5
PART B)
f(0) = 10(1.02)^0
f(0) = 10(1)
f(0) = 10
The y-intercept represents the height of the plant when they began the experiment.
f(1) = 10(1.02)^1
f(1) = 10(1.02)
f(1) = 10.2
(1, 10.2)
f(5) = 10(1.02)^5
f(5) = 10(1.1040808)
f(5) = 11.040808
f(1)=10(1.02)^1
f(1)=10.2
Average rate= (fn2-fn1)/(n2-n1)
=11.04-10.2/(5-1)
=0.22
the average rate of change of the function f(n) from n = 1 to n = 5 is 0.22.
Answer:
Part A
The domain should be 0 ≤n≤5
Part B
f(n) = 10(1.02)^n
The function is in the form y =a b^x where a is the y intercept
The y intercept is 10. This is the value when n =0 days.
Part C
The average rate of growth over the 4 days is .21 cm per day
Step-by-step explanation:
f(n) = 10(1.02)^n
Part A
Let f(n) = 11.04
11.04 = 10 * 1.02 ^n
Divide each side by 10
11.04/10 = 1.02^n
1.104 = 1.02^n
Taking the log of each side
log 1.104 = log 1.02^n
We know log a^b = b log a
log 1.104 = n log 1.02
log 1.104 / log 1.02 = n
4.99630=n
Rounding n to 5
The domain should be 0 ≤n≤5
Part B
f(n) = 10(1.02)^n
The function is in the form y =a b^x where a is the y intercept
The y intercept is 10. This is the value when n =0 days.
Part C
To find the average rate of change
f(5) - f(1)
-----------
5-1
f(5) = 11.04
f(1) = 10 *1.02 =10.2
11.04 - 10.2
-----------
5-1
.84
-----
4
.21 cm per day
The average rate of growth over the 4 days is .21 cm per day
You survey 300 students at the highschool. Of the 300 students, 103 of them said that pizza is their
favorite food. If 751 students attend the high school, about how many students would choose pizza as
their favorite food?
Answer:
258
Step-by-step explanation:
Sally wants to make a chocolate crunchy cake.
The recipe uses 16 biscuits and 22 squares of chocolate.
13
Sally wants to make her cake with 24 biscuits.
How many squares of chocolate will she need?
Answer:
33 squares of chocolate need
Answer:
33 Biscuits
Step-by-step explanation:
Uni method
How much biscuits do we need for 1 square of chocolate?
22/16 = 1.3
For 1 square of chocolate she needs 1.3 Biscuits.
So for 24 biscuits,
24 * 1.3
=33 biscuits
Find the product with the exponent in simplest
form. Then, identify the values of x and y.
6
X
- 64
.
6
X
y =
DONE
Answer:
[tex]\displaystyle 8^\bigg{\frac{8}{3}}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Exponential Rule [Powering]: [tex]\displaystyle (b^m)^n = b^{m \cdot n}[/tex]Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle \bigg(8^\bigg{\frac{2}{3}} \bigg)^4[/tex]
Step 2: Simplify
Exponential Rule [Powering]: [tex]\displaystyle 8^\bigg{\frac{2}{3} \cdot 4}[/tex]Multiply: [tex]\displaystyle 8^\bigg{\frac{8}{3}}[/tex]The length of a rectangle is 3 cm more than its breadth. If the perimeter of the
rectangle is 46 cm, find the length and the breadth.
Answer:
breadth = 10 cm
length = 13 cm
Step-by-step explanation:
so,
perimeter = 46cm
2(l+b) = 46cm
or, 2(3+b+b) = 46cm ( because l = 3+b)
or, 2(3+2b) = 46cm
or, 6 + 4b = 46cm
or, 4b = 46cm - 6
or, 4b = 40cm
or, b = 40/4 cm
so, b = 10 cm
now,
l = 3cm + b
l = 3 cm + 10cm
= 13cm
Answer:
Let us assume the breadth of the rectangle be 'b' cm.
So length of the rectangle will be b+3 cm.
Now
Perimeter =46
[tex] \large \mid\orange {2(l + b) = 46}[/tex]
[tex] \large \mid\orange {2(b+3+b)=46}[/tex]
[tex] \large\mid \orange {2(2b+3) = 46}[/tex]
[tex] \large\mid \orange {4b + 6 = 46}[/tex]
[tex] \large \mid \orange{4b = 46 - 6}[/tex]
[tex] \large\mid \orange {4b = 40}[/tex]
[tex] \large \mid \orange{b = \frac{40}{4} }[/tex]
[tex] \large\mid \orange {b = 10}[/tex]
[tex] \large \orange{l=b+3= \:10 + 3 = 13 cm }[/tex]
Length = 13cm
Breadth = 10cm
the second difference 4;x;8;y;20;.... is 2
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Answer:
x = 5y = 13Step-by-step explanation:
First differences are ...
x -4, 8 -x, y -8, 20 -y
Then second differences are ...
(8 -x) -(x -4)
(y -8) -(8 -x)
(20 -y) -(y -8)
Each of these is said to be 2, so we have ...
12 -2x = 2 ⇒ x = 5
28 -2y = 2 ⇒ y = 13
And an equation we can use to check:
x +y -16 = 2 ⇒ 5 +13 -16 = 2 . . . . true
_____
The explicit formula for the sequence is ...
an = n^2 -2n +5
If two line segments have the same length, which of the following must be
true?
• A. They share an endpoint.
C
B. a They form a right angle.k
•
C. They
are congruent.
D. They are equal.
Step-by-step explanation:
oprion C is the answer. The two line are congruent
A ball is thrown vertically upward from the top of a building. The height (in meters) of the ball after t seconds is given by the function
s(t) = -(t-3)^2+ 14. Find the instantaneous velocity of the ball at t= 4 seconds by considering the average velocities over the intervals [3.5, 4],
[3.7.4]. [3.9,4]. [3.99, 4], [4, 4.01], [4, 4.1], [4, 4.3], and [4,4.5).
ОА.
1.50 m/sec.
OB.
2.00 m/sec.
Ос.
-2.00 m/sec.
OD. -1.50 m/sec.
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Answer:
C. -2.00 m/sec
Step-by-step explanation:
The average velocity on the interval [a, b] is found by ...
m = (s(b) -s(a))/(b -a)
One end of the interval remains constant here, so we can define 'd' so that the interval is [4, 4+d]. Then the average velocity is ...
m = (s(4 +d) -s(4))/((4 +d) -4)
m = (s(4+d) -s(4))/d
The attached table shows the average velocity values on the intervals required by the problem statement. Respectively, they are ...
-1.5 m/s, -1.7 m/s, -1.9 m/s, -1.99 m/s, 2.01 m/s, 2.1 m/s, 2.3 m/s, 2.5 m/s
We expect the instantaneous velocity at d=0 to be the average of the values at d=-0.01 and d=+0.01. We estimate the instantaneous velocity at t=4 seconds to be -2.00 m/s.
According to this diagram, what is tan 74°?
74°
25
7
16
90°
24
O A.
7
24
B. 24
C.
D. 24
O E. 25
F.
Option B is correct, the value of tan 74° is 24/7
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
We have to find the value of tan74°
The tan function is ratio of opposite side and adjacent side.
We have to find the opposite side of angle 74°,
The opposite side has length 24
Now let us find the adjacent side of angle 74 which is 7
tan 74° = 24/7
Hence, option B is correct, the value of tan 74° is 24/7.
To learn more on trigonometry click:
https://brainly.com/question/25122835
#SPJ5
Classify the graph as a linear function, nonlinear function, or relation (non-
function)
Answer: Nonlinear function
Step-by-step explanation:
Need help ASAP hshehebsbeb
Answer:
I thing option A. all real numbers.
but IAM not exactly sure....
Answer:
all real numbers is correct answer
Graph the image of trapezoid PQRS after a translation 9 units right and 10 units up.
Tính I = tích phân ( x^2 - 3xy) dx + ( x-y) dy với đường cung định hướng AB là ve tẻ nối điểm A ( 2,3 ) và B ( 1 , 1 )
what is the answer?
(2a³b⁴)⁴=
Answer:
16a^12 b^16
Step-by-step explanation:
that's the answer. just multiply out the powers
Answer:
16*(a^12)*(b^16)
Step-by-step explanation:
In order to solve this problem, we can split these term into three separate terms.
[tex]{(2 {a}^{3} {b}^{4})}^{4} = {2}^{4} \times {( {a}^{3}) }^{4} \times {( {b}^{4} )}^{4} [/tex]
2 to the power of 4 is 16.
[tex] {2}^{4} = 16[/tex]
As for the terms a and b, the two exponents can multiply with each other.
[tex] {( {a}^{3} )}^{4} = {a}^{(3 \times 4)} = {a}^{12} [/tex]
[tex] {( {b}^{4} )}^{4} = {b}^{(4 \times 4)} = {b}^{16} [/tex]
Now, we can directly multiply the values together by combining into one term.
Hence, the final answer is
[tex]16 {a}^{12} {b}^{16} [/tex]
What number must be added to both the numerator and denominator of the fraction 2/5 to get 7/8?
a) 13
b) 15
c) 17
d) 19
Mary wants to buy candies with an amount of money she has in her pocket.  we know that if she had $3.20 more money she could buy 120 candies. While if she had $2.40 less money she could buy 85 candies. What is the price per candy?
Answer:
the price per candy is $0.16
and she has $16.00 in her pocket.
Step-by-step explanation:
x = the money in her pocket.
y = the price per candy
x + 3.2 = 120×y
x - 2.4 = 85×y
y = (x - 2.4)/85
=>
x + 3.2 = 120×(x - 2.4)/85 = (24x - 57.6)/17
=>
(17x + 17×3.2)/17 = (24x - 57.6)/17
17x + 54.4 = 24x - 57.6
54.4 = 7x - 57.6
112 = 7x
x = 16
y = (16 - 2.4)/85 = 13.6/85 = 0.16
Jim is the quarterback on his football team.
He was sacked 3 times during the game.
Each time he was sacked, the team lost 7
yards. What was the total number of yards
lost from the sacks?
Answer: 21 yards
Step-by-step explanation:
Multiply 3 by 7 to find the number of years lost from the sacks because he was sacked 3 times and each time he lost 7 yards.
He lost 7 yards per sack , so in three sacks he will lose 21 yards.
3* 7 = 21
The Punjab Highway department is studying traffic pattern on G.T. Road near Lahore. As part of previous study, population standard deviation is 680 number of vehicles per day. A random sample of 64 days gives mean of 5410 cars. Find a 90 percent confidence interval for population Mean (the average number of vehicles per day).
Answer:
for this we need 90 percent 5410
so we multiply 5410*0.9=4869
Hope This Helps!!!
Which phrase describes the linear relationship between the values of x and y shown in the table?
-- --
X|Y
12|8
13|9
14|10
-- --
A. y is 4 less than x
B. y is 4 more than x
C. y is 2/3 of x
D. x is 4 less than y
Answer:
the answer is C...i guess?
Answer: its a
explanation: trust me, i did this question just now and got it right.
also.... BRAINLIEST PLEASE
A sample of students at a university took a test that diagnosed their learning styles as active or reflective and also as visual or verbal. Each student received a numerical score on the active/reflective style and also a numerical score on the visual/verbal style. The sample size was 39, and the sample correlation coefficient turned out to equal .273.a. State the hypotheses for testing whether there is a positive correlation between these variables in the population of all students at this university.b. Calculate the value of the test statistic.c. Determine the p-value as accurately as possible.d. State the test decision for the α= .10 and α= .05 significance levels, and summarize your conclusion in context.e. If the sample size was much larger, and the value of the sample correlation coefficient stayed the same, describe the impact on your test statistic, p-value, and conclusion.
Answer:
Kindly check explanation
Step-by-step explanation:
Given that :
Sample size, n = 39
Correlation Coefficient, r = 0.273
The hypothesis test to examine if there is a positive correlation :
H0 : ρ = 0
If there is a positive correlation, then ρ greater than 1
H0 : ρ > 1
The test statistic :
T = r / √(1 - r²)/(n - 2)
T = 0.273 / √(1 - 0.273²)/(39 - 2)
T = 0.273 / 0.1581541
T = 1.726
The Pvalue using a Pvalue calculator can be be obtained using df = n - 2, df = 39 - 2 = 37
The Pvalue = 0.0463
α= .10 and α= .05
At α= .10
Pvalue < α ; Hence, we reject H0 and conclude that a positive correlation exists
At α= 0.05 ;
Pvalue < α ; Hence, we reject H0 and conclude that a positive correlation exists
Which statement is true about the function f(x)= sqrt of x?
Someone help please!!
Answer:
9 (a) [tex]d = \frac{\sqrt{e}}{\sqrt{3}}[/tex]
9 (b) [tex]d = \frac{\sqrt{7k}}{\sqrt{2}}[/tex]
Step-by-step explanation:
Hope this helped!
PLEASE HELP!! I WILL GIVE BRAINLIEST AND POINTS!!
The safety inspector notes that Ray also needs to plan for a vertical ladder through the center of the coaster's parabolic shape for access to the coaster to perform safety repairs. Find the vertex and the equation for the axis of symmetry of the parabola, showing your work, so Ray can include it in his coaster plan.
f(x) = -x2 - 6x
Answer:
Rewrite in vertex form and use this form to find the vertex
Rewrite in vertex form and use this form to find the vertex
(h,k).(−3,9)
Step-by-step explanation:
George bought a shirt and a pair of pants at a clothing store. The pants cost $5.33 more than the shirt, and he used a $10 off coupon to purchase the shirt. The equation below is used to determine the cost of the shirt before the coupon, s.
Answer:
15.99
Step-by-step explanation:
5.33+5.33+5.33
HELPPPPPPPPPP
Which of the following is equivalent to the expression below ?
square root 8 minus square root 72 plus square root 50 ?
A. 13 square root 2
B. 7 square root 2
C. 3 square root 2
D. Square root 2
Answer:
a13 square root
..cv
..
..
If AABC= A DEF, which congruences are true by CPCTC? Check all that
apply.
APEC correct answer is:
AB =DE
AC= DF
See photo.
Answer:
Options A, B and D
Step-by-step explanation:
If the two triangles are congruent, their corresponding parts will be congruent.
If ΔABC ≅ ΔDEF
By the property of CPCTC,
AB ≅ DE
AC ≅ DF
BC ≅ EF
∠A ≅ ∠D
∠C ≅ ∠F
∠B ≅ ∠E
Therefore, Options A, B and D are the correct options.
A student measured the lead content of a paint sample 4 times. The standard deviation of the measurements was found to be 0.76% of the average. Calculate the confidence interval at the 90% confidence level.
Answer:
[tex]CI =0.894%[/tex]
Step-by-step explanation:
From the question we are told that:
Sample size [tex]n=4[/tex]
Standard deviation [tex]\sigma=0.76\% of \=x[/tex]
Confidence level [tex]\mu =90\%=0.90[/tex]
Degree of Freedom [tex]Df=n-1=3[/tex]
Therefore
Test T from table is given
[tex]t=2.353[/tex]
Generally the equation for Confidence interval CI is mathematically given by
[tex]CI =t*\frac{\sigma}{\sqrt{n}}[/tex]
[tex]CI =2.353*\frac{0.76}{\sqrt{4}}[/tex]
[tex]CI =0.894%[/tex]
PLS HELP ASAP
Graph x+3y=6x
Answer:
Not sure what more you need, but here is an example of the graph on Desmos.
Answer:
Your graph should look like the one on the pic...
☆•☆•☆•☆•☆•☆
Hope it helps. .
Have a great day!!
The frequency n of vibration of a stretched string is a function of its tension F, the length l and the mass per unit length m. From the knowledge of dimensions, prove that, n∝1/l √f/m
Pls fast
Answer:
n ∝ (1/l) (√F/m)
Step-by-step explanation:
Since frequency, n of vibration of a stretched string is a function of its tension F, the length l and the mass per unit length m, and has dimensions [T]⁻¹ where T = time, its dimension must be equal to that of the combination of F, L and m
Since n = f(F,L,m)
n = kFᵃLᵇmˣ
dimension of n = (dimension of F)ᵃ × (dimension of L)ᵇ × (dimension of m)ˣ
Since n = frequency, dimension of n = [T]⁻¹
F = Force, dimension of F = [M][L][T]⁻²
Also, L = length, dimension of L = [L] and
m = mass per unit length, dimension of m = [M][L]⁻¹
So, n = FᵃLᵇmˣ
[T]⁻¹ = ([M][L][T]⁻²)ᵃ( [L] )ᵇ([M][L]⁻¹)ˣ
[T]⁻¹ = ([M]ᵃ[L]ᵃ[T]⁻²ᵃ[L]ᵇ([M]ˣ[L]⁻ˣ
[M]⁰[L]⁰[T]⁻¹ = ([M]ᵃ ⁺ˣ)([L]ᵃ ⁺ ᵇ ⁻ˣ)([T]⁻²ᵃ)
equating the exponents on both sides, we have
a + x = 0 (1 )⇒ x = -a
a + b - x = 0 (2) ⇒
-2a = -1 (3) ⇒ a = 1/2
Substituting x into 2, we have
a + b -(-a) = 0
a + b + a = 0
2a + b = 0
b = -2a
b = -2 (1/2)
b = -1
x = -a = -1/2
So, substituting the variables into n, we have
n = kFᵃLᵇmˣ
n = kFᵃLᵇmˣ
[tex]n = kF^{\frac{1}{2} }L^{-1}m^{-\frac{1}{2} }[/tex]
n = k/l(√F/m)
n ∝ (1/l) (√F/m)
A person must enter a 4 digit code to gain access to his cell phone. He will enter codes until he is successful, however he cannot try more than 3 times or the phone will lock him out. Let S denote a successful attempt and F denote a failed attempt. What is the sample space for this random experiment
Answer:
(S, FS, FFS, FFF)
Step-by-step explanation:
According to the Question,
Given, A person must enter a 4 digit code to gain access to his cell phone. He will enter codes until he is successful.however, he cannot try more than 3 times or the phone will lock him out.Let, S denote a successful attempt and F denote a failed attempt.So, the sample space for this random experiment is
{S, FS, FFS, FFF}
The person stops trying when he successfully enters the code or when he has failed at all 3 attempts .
What are the coordinates of the vertices of the triangle under the translation (x, y) -> (x + 2, y + 3)?
(−4, 5), (3, 4), (0, 0)
(6, −5), (5, 2), (1, −1)
(5, −4). (4, 3), (−1, 2)
(−5, 6), (2, 5), (−1, 1)
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Answer:
(d) (−5, 6), (2, 5), (−1, 1)
Step-by-step explanation:
No answer choices have any points in common, so we only need to find one translated point to determine the correct answer choice.
For the point on the y-axis, (0, 2), the translation is ...
(x, y) ⇒ (x +2, y+3)
(0, 2) ⇒ (0 +2, 2 +3) = (2, 5) . . . . matches choice D