Answer:14
Step-by-step explanation:
As we know motorcycle started from rest so it was initially at rest than vi=0 and vf=?
From 1st equation of motion vf=vi+at
Putting values
vf=0+(7)*(2)
vf=0+14
vf= 14m/s
Remember m/s is the unit of velocity so it is included with velocity
One positive number is 2 more than twice another. Their product is 180.
Step 2 of 2 : Find the numbers by solving the equation.
Answer:
9 and 20
Step-by-step explanation:
x = one number
y = 2x+2 = other number
xy = 190
x(2x+2) = 180
2x^2 +2x = 180
2x^2 +2x- 180 = 0
Factor out 2
x^2 +x -90 = 0
(x+10)(x-9) =0
Using the zero product property
x+10 = 0 x-9=0
x= -10 x=9
But they have to be positive
x = 9
y = 2x+2 = 2(9)+2 = 18+2 = 20
Instructions: Find the measure of the indicated angle to the nearest degree.
Answer:
? = 13.6
Step-by-step explanation:
Let the unknown angle be y
so
tan y= p/b
tan y =8/33
y = tan‐¹(8/33)
y = 13.62699486
y = 13.6
If(a²-1) x²+(a-1)x+a²-4a+3=0 is an identity in x, then find the value of a
Answer:
Step-by-step explanation:
[tex](a^2-1)x^2+(a-1)x+a^2-4a+3=0\\\\Calculate\ and\ identify\ the\ polynomials\\\\\Longleftrightarrow\ a^2x^2-x^2+ax-x+a^2-4a+3=0\\\\\Longleftrightarrow\ a^2x^2+ax+a^2-4a+3=x^2+x+0\\\\\Longleftrightarrow\ \left\{\begin{array}{ccc}a^2&=&1\\a&=&1\\a^2-4a+3&=&0\\\end{array} \right.\\\\\Longleftrightarrow\ \left\{\begin{array}{ccc}(a-1)(a+1)&=&0\\a-1&=&0\\(a-1)(a-3)&=&0\\\end{array} \right.\\\\\\We\ must\ exclude\ a=-1\ and\ a=3\ (not\ solution)\\\Longrightarrow\ a=1\\[/tex]
Let h(x)=20e^kx where k ɛ R (Picture attached. Thank you so much!)
Answer:
A)
[tex]k=0[/tex]
B)
[tex]\displaystyle \begin{aligned} 2k + 1& = 2\ln 20 + 1 \\ &\approx 2.3863\end{aligned}[/tex]
C)
[tex]\displaystyle \begin{aligned} k - 3&= \ln \frac{1}{2} - 3 \\ &\approx-3.6931 \end{aligned}[/tex]
Step-by-step explanation:
We are given the function:
[tex]\displaystyle h(x) = 20e^{kx} \text{ where } k \in \mathbb{R}[/tex]
A)
Given that h(1) = 20, we want to find k.
h(1) = 20 means that h(x) = 20 when x = 1. Substitute:
[tex]\displaystyle (20) = 20e^{k(1)}[/tex]
Simplify:
[tex]1= e^k[/tex]
Anything raised to zero (except for zero) is one. Therefore:
[tex]k=0[/tex]
B)
Given that h(1) = 40, we want to find 2k + 1.
Likewise, this means that h(x) = 40 when x = 1. Substitute:
[tex]\displaystyle (40) = 20e^{k(1)}[/tex]
Simplify:
[tex]\displaystyle 2 = e^{k}[/tex]
We can take the natural log of both sides:
[tex]\displaystyle \ln 2 = \underbrace{k\ln e}_{\ln a^b = b\ln a}[/tex]
By definition, ln(e) = 1. Hence:
[tex]\displaystyle k = \ln 2[/tex]
Therefore:
[tex]2k+1 = 2\ln 2+ 1 \approx 2.3863[/tex]
C)
Given that h(1) = 10, we want to find k - 3.
Again, this meas that h(x) = 10 when x = 1. Substitute:
[tex]\displaystyle (10) = 20e^{k(1)}[/tex]
Simplfy:
[tex]\displaystyle \frac{1}{2} = e^k[/tex]
Take the natural log of both sides:
[tex]\displaystyle \ln \frac{1}{2} = k\ln e[/tex]
Therefore:
[tex]\displaystyle k = \ln \frac{1}{2}[/tex]
Therefore:
[tex]\displaystyle k - 3 = \ln\frac{1}{2} - 3\approx-3.6931[/tex]
When f(x) =-3 what is x?
Answer:
D or -1
Step-by-step explanation:
It says that f(x) is equal to -3.
f(x) is the same as y-values, and x is the same as the x-values on a coordinate grid because x is the independent variable, meaning y is the dependent variable, where f(x) depends on the value of x to find y.
So if y is -3, it can be found on the graph on the 4th line, so x = -1 when y = -3
Tính tích phân sau bằng cách dùng tọa độ cực I=∫∫ [tex]\frac{1}{\sqrt{x^{2} +y^{2} } }[/tex]dxdy R là miền nằm trọg góc phần tư thứ nhất thỏa mãn 4[tex]\leq x^{2} +y^{2} \leq 9[/tex]
It sounds like R is the region (in polar coordinates)
R = {(r, θ) : 2 ≤ r ≤ 3 and 0 ≤ θ ≤ π/2}
Then the integral is
[tex]\displaystyle \iint_R\frac{\mathrm dx\,\mathrm dy}{\sqrt{x^2+y^2}} = \int_0^{\pi/2}\int_2^3 \frac{r\,\mathrm dr\,\mathrm d\theta}{\sqrt{r^2}} \\\\ = \int_0^{\pi/2}\int_2^3 \mathrm dr\,\mathrm d\theta \\\\ = \frac\pi2\int_2^3 \mathrm dr \\\\ = \frac\pi2r\bigg|_2^3 = \frac\pi2 (3-2) = \boxed{\frac\pi2}[/tex]
Abigail buys two cartons of strawberries. One carton has 191919 berries and the other carton has 262626 berries. She wants to divide the berries into bags so there are exactly 666 berries in each bag.
How many bags will have 666 berries?
Answer:
682
Step-by-step explanation:
191,919 + 262,626
454545 ÷ 666 = 682.5
Thus meaning 682 bags will have 666 berries and one bag will have 333 berries.
Polymer composite materials have gained popularity because they have high strength to weight ratios and are relatively easy and inexpensive to manufacture. However, their nondegradable nature has prompted development of environmentally friendly composites using natural materials. The article "Properties of Waste Silk Shod Fiber/Cellulose Green Composite Films" (. of Composite Materials, 2012: 123-127) reported that for a sample of 10 specimens with 2% fiber content, the sample mean tensile strength (MPa) was 51.3 and the sample standard deviation was 1.2. Suppose the true average strength for 0% fibers (pure cellulose) is known to be 48 MPa. Does the data provide compelling evidence for concluding that true average strength for the WSF/cellulose composite exceeds this value?
Complete Question
Polymer composite materials have gained popularity because they have high strength to weight ratios and are relatively easy and inexpensive to manufacture. However, their nondegradable nature has prompted development of environmentally friendly composites using natural materials. An article reported that for a sample of 10 specimens with 2% fiber content, the sample mean tensile strength (MPa) was 51.1 and the sample standard deviation was 1.2. Suppose the true average strength for 0% fibers (pure cellulose) is known to be 48 MPa. Does the data provide compelling evidence for concluding that true average strength for the WSF/cellulose composite exceeds this value? (Use α = 0.05.)
t=8.169
P-value= ?
Answer:
a) [tex]P-value=0[/tex]
b) Hence,We FAil to reject the alternative hypothesis and accept that the true average strength for the WSF/ cellulose composite exceeds 48 MPa.
Step-by-step explanation:
From the question we are told that:
Sample size [tex]n=10[/tex]
Mean [tex]\=x= 51.3[/tex]
Standard deviation [tex]\sigma=1.2[/tex]
Significance level is taken as [tex]\alpha=0.05[/tex]
t test statistics
[tex]t=8.169[/tex]
Therefore
[tex]P-Value=P(t>8.169)[/tex]
Critical point
[tex]t_{\alpha,df}[/tex]
[tex]\alpha=0.05[/tex]
[tex]df=10-1=>9[/tex]
Therefore
P-value from T distribution table
[tex]P-value=0[/tex]
Conclusion
[tex]P-value (0)< \alpha(0.05)[/tex]
We Reject the Null Hypothesis [tex]H_0[/tex]
Hence,We FAil to reject the alternative hypothesis and accept that the true average strength for the WSF/ cellulose composite exceeds 48 MPa.
when 18 is subtracted from six times a certain number the result is 96 what is the number
Let the number be x
ATQ
[tex]\\ \sf\twoheadrightarrow 6x-18=96[/tex]
[tex]\\ \sf\twoheadrightarrow 6x=96+18[/tex]
[tex]\\ \sf\twoheadrightarrow 6x=112[/tex]
[tex]\\ \sf\twoheadrightarrow x=\dfrac{112}{6}[/tex]
[tex]\\ \sf\twoheadrightarrow x=7[/tex]
A canoeist paddled down a river a distance of 2 miles in 45 minutes. Paddling up-stream on his return, it took him 90 minutes. Find the rate of the canoe in still water.
There are 768 beds in a hospital.
Each floor has 64 beds.
How many floors are there?
Answer:
12 floors
Step-by-step explanation:
768 ÷ 64 = 12.
Answer:
12
Step-by-step explanation:
768 divided by 64 =12
(7/8*9)*3/4*(9/3*5)=
Answer:
2835/32 or 88 19/32Step-by-step explanation:
(7/8 × 9) × 3/4 × (9/3 × 5)= 63/8 × 3/4 × (3 × 5)= 63/8 × 3/4 × 15= 2835/32 or 88 19/32[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]
Answer:
[tex]88 \frac{19}{32} [/tex]
How to find the inverse of this matrix
[tex]\left[\begin{array}{ccc}1&0\\0&3\\\end{array}\right][/tex]
Answer:
Here we have the matrix:
[tex]M = \left[\begin{array}{ccc}1&0\\0&3\end{array}\right][/tex]
And we want to find its inverse.
The inverse of a 2x2 matrix A is:
(1/det(A))*adj(A)
where det(A) is the determinant of the matrix.
Such that for a matrix:
[tex]A = \left[\begin{array}{ccc}a_{11}&a_{12}\\a_{21}&a_{22}\end{array}\right][/tex]
The determinant is:
det(A) = a₁₁*a₂₂ - a₁₂*a₂₁
in the case of our matrix M, the determinant is:
det(M) = 1*3 - 0*0 = 3
and adj(A) is a transposition along the diagonal, and for the other elements, we just change its sign.
Then for our matrix A we would have:
[tex]adj(A) = \left[\begin{array}{ccc}a_{22}&-a_{12}\\-a_{21}&a_{11}\end{array}\right][/tex]
Then for our matrix M, we have:
[tex]adj(M) = \left[\begin{array}{ccc}3&-0\\-0&1\end{array}\right][/tex]
Then the inverse of the matrix M is:
[tex]M^{-1} = \frac{1}{det(M)} *adj(M) = \frac{1}{3}\left[\begin{array}{ccc}3&0\\0&1\end{array}\right] = \left[\begin{array}{ccc}1&0\\0&1/3\end{array}\right][/tex]
create a graph of 4.95 + 3.99
Answer:
????
Step-by-step explanation:
as in y = 4.95 + 3.99 or points? if so just draw a horizontal line at 8.94
Aaron Lloyd what is a?
Answer:
Rugby lawyer
Step-by-step explanation:
Aaron is a partner in the firm’s dispute resolution division. He advises clients on a range of litigious and risk related matters, with particular expertise in the areas of corporate misconduct, white collar criminal and regulatory affairs, sports law and employment law. Aaron leads our sports law practice, and is a member of the firm’s health and safety, public law, and organisational integrity teams.
Well regarded by clients for his ability to analyse and strategise complex situations, Aaron is internationally recognised for his ability to implement pragmatic and commercial strategies to minimise risk and create opportunity. This ability has resulted in clients avoiding significant litigation and commercial consequences.
Aaron is an experienced advocate, having argued cases in the District Court, High Court, Employment Court, the Court of Appeal and Supreme Court of New Zealand, along with numerous tribunals.
He is recognised by international legal directories including by Chambers & Partners (Asia Pacific), Who’s Who Legal, Expert Guides, Best Lawyers and Doyles.
Before joining MinterEllisonRuddWatts Aaron practiced as a barrister with Paul Davison QC, and has lectured at the University of Auckland.
The length of the hypotenuse of a 30 -60 -90 triangle is 32. What are the lengths of the legs?
Answer:
16, 16(sqrt3)
Step-by-step explanation:
30-60-90 triangles follow a rule where the hypotenuse is 2 times the shortest leg, and the longer leg is sqrt3 times the shorter leg.
So, the sides are x, 2x, and (sqrt3)x.
If 2x = 32, then x = 16.
Therefore the two legs are 16 and 16(sqrt3)
you can search up 30-60-90 triangle for more information
51.Tandin Dorji was married to five women. First woman had three
daughters and five sons and the youngest wife had two sons. Two
of the remaining wives had one son each. If the ratio of children of
5th wife was 1:3 with the children of other wives. How many
children does Tandin have
Answer:
Tandin has 16 children.
Step-by-step explanation:
Total of children:
3+5 = 8(first woman)
2(youngest wife)
1 + 1 = 2(two of the remaining wives)
So
8 + 2 + 2 = 12
If the ratio of children of 5th wife was 1:3 with the children of other wives.
Thus the 5th wife has 12/3 = 4 children.
How many children does Tandin have?
12 + 4 = 16
Tandin has 16 children.
Find the lengths the missing side
Answer:
Short leg = x
Longer leg = 12
Hypotenuse = y
Short leg = 4√3
longer leg = 12
Hypotenuse = 8√3
Answered by GAUTHMATH
Fill in the blanks.
(3b^3)^2 = _b^_
We can seperate (3b³) into two different parts, the constant and the variable.
The constant (3) and the variable (b) can both be squared and multiplied to get the correct answer, so:
3² = 9
(b³)² = [tex]b^{6}[/tex]
So, [tex](3b^{3})^{2} = 9b^{6}[/tex]
Describe what is the most difficult part of solving equations, for you personally.
What do you personaly feel like is most dificult.
For me its rembering minus signs
Which is a perfect square?
6’1
6’2
6’3
6’5
Answer:
6'2
Step-by-step explanation:
Can someone help me? I am struggling and I would be so happy if any of you helped me. Thank you for your help!
Answer:
Mean = 52
Standard Deviation = 13.64
Step-by-step explanation:
mean = 260/5
= 52
Standard Deviation = [tex]\sqrt{\frac{930}{5} }[/tex] = 13.64
I wasn't sure about my answer so used the Gauthmath app
help giving brainilest, heart, and 5 stars
Answer:
4 = 6
5 = -17
Step-by-step explanation:
4. a² - b / b² - c
a² = 2² = 4
b = -2
4 - (-2) = 4 + 2 = 6
6 / b² - c = 6/4 - 3 = 6/1 = 6
4 = 6
5. -3x² + 2xy + 7
-3x² = -3 * -2² = -3 * 4 = -12
2xy = 2 * -2 * 3 = -4 * 3 = -12
-12 + -12 + 7 = -24 + 7 = -17
5 = -17
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
(PLEASE HELP ITS THE LAST QUESTION)
Find the measure of angle L.
A) 21.6°
B) 43.8°
C) 33.4°
D) 21.9°
Answer:
A
Step-by-step explanation:
lemme meh knw if it was helpful..
Dividing integers
7. (-154) ➗ (-14) =
11. (-40) ➗10=
15. 90 ➗ (-15)=
16. 108 ➗ (-9)=
17. (-48) ➗ (-6)=
18. (-105) ➗ 7=
first we shall learn the rules.when numbers with same sign are divided it gives pisitive sign but, when numbers of different signs are divided it gives negetive sign.
here,
7. (-154) ➗ (-14) =11
11. (-40) ➗10=-4
15. 90 ➗ (-15)=-6
16. 108 ➗ (-9)=-12
17. (-48) ➗ (-6)=8
18. (-105) ➗ 7=-15
hope it helps you......
If f(x) is an exponential function where f(-1.5) 26 and
f(5.5) = 7, then find the value of f(10), to the nearest hundredth.
Answer:
[tex]f(10) = 1147.25[/tex]
Step-by-step explanation:
Given
[tex]f(-1.5) = 26[/tex]
[tex]f(5.5) = 7[/tex]
Required
f(10)
An exponential function is represented as:
[tex]f(x) = ab^x[/tex]
[tex]f(-1.5) = 26[/tex] impleies that:
[tex]26 = ab^{-1.5}[/tex] --- (1)
[tex]f(5.5) = 7[/tex] implies that
[tex]7 = ab^{5.5}[/tex] --- (2)
Divide (2) by (1)
[tex]26/7 = ab^{-1.5}/ab^{5.5}[/tex]
[tex]3.71429 = b^{-1.5+5.5}[/tex]
[tex]3.71429 = b^{4}[/tex]
Take 4th root
[tex]b = 1.39[/tex]
Substitute [tex]b = 1.39[/tex] in [tex]26 = ab^{-1.5}[/tex]
[tex]26 = a * 1.39^{-1.5}[/tex]
[tex]26 = a * 0.6102[/tex]
Solve for (a)
[tex]a = 26/0.6102[/tex]
[tex]a = 42.61[/tex]
f(10) is calculated as:
[tex]f(10) = ab^{10}[/tex]
[tex]f(10) = 42.61 * 1.39^{10}[/tex]
[tex]f(10) = 1147.25[/tex]
True or False. A rational number can be expressed as the quotient a/b where b ≠ 0
Answer:
true. A rational number can be expressed as the quotient a/b where b ≠ 0
Given: 3x+11=y, solve for x if y = 29
answer is 6
Step-by-step explanation:
3x+11=y
y=29
3x+11=29
3x=29-11
3x=18
x=18÷3
x=6
Answer:6
Step-by-step explanation:
3x+11=29
3x=29-11
3x=18
X=18/3
X=6
A manufacturer claims that its drug test will detect steroid use (that is, show positive for an athlete who uses steroids) 95% of the time. Further, 15% of all steroid-free individuals also test positive. 10% of the rugby team members use steroids. Your friend on the rugby team has just tested positive. The correct probability tree looks like
Answer:
The probability tree is;
0.95 [tex](+)[/tex]
[tex](S)[/tex]
0.1 0.05 [tex](-)[/tex]
[ P ]
0.9 0.15 [tex](+)[/tex]
[tex](S_{no})[/tex]
0.85 [tex](-)[/tex]
Step-by-step explanation:
Given the data in the question;
10% of the rugby team members use steroids
so Probability of using steroid; P( use steroid ) = 10% = 0.10
Probability of not using steroid; P( no steroid use ) = 1 - 0.10 = 0.90
Since the test show positive for an athlete who uses steroids, 95% of the time.
Probability of using steroids and testing positive = 95% = 0.95
Probability of using steroids and testing Negative = 1 - 0.95 = 0.05
Also from the test, 15% of all steroid-free individuals also test positive.
so
Probability of not using steroids and testing positive = 15% = 0.15
Probability of not using steroids and testing negative = 1 - 0.15 = 0.85
To set up the probability tree, Let;
[tex](S)[/tex] represent steroid use
[tex](S_{no})[/tex] represent no steroid use
[tex](+)[/tex] represent test positive
[tex](-)[/tex] represent test negative
so we have;
0.95 [tex](+)[/tex]
[tex](S)[/tex]
0.1 0.05 [tex](-)[/tex]
[ P ]
0.9 0.15 [tex](+)[/tex]
[tex](S_{no})[/tex]
0.85 [tex](-)[/tex]
a2 - ab + 8b + b2 - 1
Answer:
а²-ab+8b+b²-1=a(a-b)+b(8+b)-1
