Answer:
B
Step-by-step explanation:
10 + 6 ÷ 2 =
2(5) - 7 =
36 - (4 +8) ÷ 4 =
(2 x 5) -4 =
Write an expression involving integers for each statement a) moving 4 steps left, then moving 9 steps right b) on 3 separate occasions, Shari lost 2 pencils
Answer:
a) x-4+9
b) x-2
For part b, I am not 100% sure about my answer, but I am sure about part a.
Peter is buying office supplies. He is able to buy 3 packages of paper and 4 staplers for $40, or he is able to buy 5 packages of paper and 6 staplers for $62. How much does a package of paper cost? How much does a stapler cost?
Answer:
paper = $4 and stapler = $7
Step-by-step explanation:
let p represent paper and s represent stapler, then
3p + 4s = 40 → (1)
5p + 6s = 62 → (2)
Multiplying (1) by 5 and (2) by - 3 and adding will eliminate p
15p + 20s = 200 → (3)
- 15p - 18s = - 186 → (4)
Add (3) and (4) term by term to eliminate p
2s = 14 ( divide both sides by 2 )
s = 7
Substitute s = 7 into either of the 2 equations and evaluate for p
Substituting into (1)
3p + 4(7) = 40
3p + 28 = 40 ( subtract 28 from both sides )
3p = 12 ( divide both sides by 3 )
p = 4
Thus package of paper costs $4 and stapler costs $7
The owner of a car wash wants to see if the arrival rate of cars follows a Poisson distribution. In order to test the assumption of a Poisson distribution, a random sample of 150 ten-minute intervals was taken. You are given the following observed frequencies: Number of Cars Arriving in a 10-Minute Interval Frequency 0 3 1 10 2 15 3 23 4 30 5 24 6 20 7 13 8 8 9 or more 4 150 Calculate mean and use Poisson probabilities. The expected frequency of exactly 3 cars arriving in a 10-minute interval is a. .1533. b. 26.145. c. .1743. d. 23.
Answer: c. 0.1743
Step-by-step explanation: Poisson Probability or Poisson Distribution is a discrete distribution that models the number of events ocurring in a given period of time.
The mean, or expected value, of the observed frequencies is:
E(X) = ∑xP(x)
E(X) = 0*3/150 + 1*(10/150) + 2*(15/150) + 3*(23/150) + 4*(30/150) + 5*(24/150) + 6*(20/150) + 7*(13/150) + 8*(8/150) + 9*(4/150)
E(X) = 4.399
The Poisson distribution is calculated by:
P(X = k) = [tex]\frac{mean^{k}.e^{-mean}}{k!}[/tex]
The question asks for the expected frequency of exactly 3 cars:
P(X = 3) = [tex]\frac{4.399^{3}.e^{-4.399}}{3!}[/tex]
P(X = 3) = [tex]\frac{4.399^{3}.e^{-4.399}}{3.2.1}[/tex]
P(X = 3) = 0.1743
The expected frequency of exactly 3 cars is 0.1743
www.g A bag contains 3 white counters, 10 black counters, and 4 green counters. What is the probability of drawing (a) a white counter or a green counter
Answer:
41.18% probability of drawing a white counter or a green counter
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
In this question:
There are 3+10+4 = 17 counters.
Of those, 3+4 = 7 are white or green
7/17 = 0.4118
41.18% probability of drawing a white counter or a green counter
You wish to accumulate $14,580 in 6 years. Payments are made at the end of every six-month period into an account earning 7.2% compounded semi-annually. Find the required payment amount to accomplish your goal.
At 95% confidence, how large a sample should be taken to obtain a margin of error of 0.05 for the estimation of a population proportion
Answer:
A sample of 385 is needed.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
How large a sample:
We need a sample of n.
n is found when M = 0.05.
We dont know the true proportion, so we work with the worst case scenario, which is [tex]\pi = 0.5[/tex]
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.05 = 1.96\sqrt{\frac{0.5*0.5}{n}}[/tex]
[tex]0.05\sqrt{n} = 1.96*0.5[/tex]
[tex]\sqrt{n} = \frac{1.96*0.5}{0.05}[/tex]
[tex](\sqrt{n})^{2} = (\frac{1.96*0.5}{0.05})^{2}[/tex]
[tex]n = 384.16[/tex]
Rounding up
A sample of 385 is needed.
Graph the equation y = 1/8x-7
Answer:
[tex]slope:1/8y-intercept:-7\\COORDINATES(x,-7)\\\\(56,0)[/tex]
Step-by-step explanation:
The correlation matrix obtained for the variables bp (y) (blood pressure), age (x1) (age), smk (x2) (smoke) and WET(X3) (Weight), is given by:
BP AGE SMK WET
BP 1 0.64 0.72 0.48
AGE 1 0.32 0.78
SMK 1 0.40
WET 1
Based on this matrix please calculate the partial correlation.
a. 0.53
b. 0.48
c. 0.62
d. 0.32
Answer:
c) 0.62
Step-by-step explanation:
In this case, we are required to find the partial correlation, [tex] r_Y_X_1_|_X_2[/tex].
To find the partial correlation, use the formula:
[tex] r_Y_X_1_|_X_2 = \frac{r_Y_X_1 - r_Y_X_2 * r_X_1_X_2}{\sqrt{1 - r_X_1_X_2}^2 - \sqrt{1 - r_Y_X_2}^2} [/tex]
[tex] r_Y_X_1_|_X_2 = \frac{0.64 - 0.72 * 0.32}{\sqrt{1 - 0.32}^2 - \sqrt{1 - 0.72}^2} [/tex]
[tex] = \frac{0.410}{0.657}[/tex]
[tex] r_Y_X_1_|_X_2 = 0.62 [/tex]
The partial correlation is 0.62.
Option C
You just purchased two coins at a price of $1,030 each. Because one of the coins is more collectible, you believe that its value will increase at a rate of 7.7 percent per year, while you believe the second coin will only increase at 7.1 percent per year. If you are correct, how much more will the first coin be worth in 20 years
Answer:4541(Rounded) 4541.99779(Unrounded)
Step-by-step explanation:
A= P(1 + r)^T
A= answer
P=principle(amount of money)
r=Rate(percent / 100)
T=Time(Annually)
1030(1 + .077)^20
Brainliest would be appericiated!
A rectangle measures 18 cm by 3 cm what is its area
Answer:
54 cm²
Step-by-step explanation:
Area of a Rectangle Formula: A = lw
We are given 18 as l and 3 as w, so simply plug it into the formula:
A = 18(3)
A = 54
Inga is solving 2x2 + 12x – 3 = 0. Which steps could she use to solve the quadratic equation?
Which linear inequality is represented by the graph?
HELPPPP!!!
Answer:
b
Step-by-step explanation:
Solve for y: |6y - 3| + 8 = 35 Select one: a. y = -5 b. y = 5 or y = -4 c. =5=−203 y = 5 o r y = − 20 3 d. y = 5
Answer:
y=5 or y=-4
Step-by-step explanation:
6y - 3| + 8 = 35
|6y-3|=35-8
|6y-3|=27
either 6y-3=-27 then 6y=27+3
y=30/6=5
or 6y-3=-27
6y=-27+3
y=-24/6
y=-4
Find the product.
(3b + 6at)(b - at)
Answer:
3bat + 3b² - 6a²t²
Step-by-step explanation:
First you have to expand it to get;
3b(b - at) + 6at(b - at)
Then you can now multiply.
3b² - 3bat + 6bat - 6at²
Group like terms
6bat - 3bat + 3b² -6at²
3bat + 3b² - 6a²t²
okay the answer is attached. i was the first to answer, but brainly decided to delete it >:(
Use ¬, →, ∧ and ∨ to express the following declarative sentences in propositional logic; in each case state what your respective propositional atoms p, q, etc. a) If interest rates go up, share prices go down. b) If Smith has installed central heating, then he has sold his car or he has not paid his mortgage. c) Today it will rain or shine, but not both. d) If Sam met Jane yesterday, they had a cup of coffee together, or they took a walk in the park. e) My sister wants a black and white cat.
Answer:
a) If interest rates go up, share prices go down : this will be assigned p→q
b) If Smith has installed central heating, then he has sold his car or he has not paid his mortgage. P → (q∨¬r)
c) Today it will rain or shine, but not both:(p∨q) ∨ ¬(p∧q)
d) If Sam met Jane yesterday, they had a cup of coffee together, or they took a walk in the park. P → (q∨r)
e) My sister wants a black and white cat. p∧q
Step-by-step explanation:
A statement is said to be propositionally logical if the statement that can be assigned either true or false.
∧and
∨or
¬not
→implies
a) If interest rates go up, share prices go down : this will be assigned p→q implies because the occurrence of event (share prices go down) depends on the possibility of the other event happening.
b) If Smith has installed central heating, then he has sold his car or he has not paid his mortgage. P → (q∨¬r) : either of the two of the other events (i.e. he has sold his car or he has not paid his mortgage ) can only occur if the first event occur
c) Today it will rain or shine, but not both:(p∨q) ∨ ¬(p∧q) : either of the events can occur but not both i.e. they are mutually exclusive
d) If Sam met Jane yesterday, they had a cup of coffee together, or they took a walk in the park. P → (q∨r) either of the two of the other events (i.e. they had a cup of coffee together or they took a walk in the park ) can only occur if the first event (Sam met Jane yesterday) occur
e) My sister wants a black and white cat. p∧q : both events can only occur together
While the Pareto distributions are continuous, they tend to be used to model discrete data in humanities and actuarial sciences. Moreover, with its roots in power functions, Pareto distributions may be used in the growing popularity of the studies of networks. The probability density function (PDF) for a Pareto distribution is
Answer:
Step-by-step explanation:
While the pareto distributions are continuous in nature, they are sometimes used to model discrete data in fields such as Social Sciences, Humanities, Geophysics, and Actuarial Sciences.
The Pareto Distribution is a power-law probability distribution used in studies of observable phenomena.
The probability density function (PDF) for a Pareto Distribution is:
Xn = 1
for various Alpha levels
Where Xn is the probability value of X
As Alpha tends to infinity, the pareto distribution tends to ¶ [X-Xn]
Where ¶ is the Dirac Delta function.
No one is helping me :( Can someone please give me a hand? :(
Which statement best describes the graph of x^3 – 3x^2
- X + 3?
A.It starts down on the left and goes up on the right
and intersects the x-axis at x = -1, 2, and 3.
B.It starts down on the left and goes up on the right
and intersects the x-axis at x = -1, 1, and 3.
C.It starts up on the left and goes down on the right
and intersects the x-axis at x = -1, 2, and 3.
D.It starts up on the left and goes down on the right
and intersects the x-axis at x = -1, 1, and 3.
Given that (0,0) is on the graph of f(x), find the
corresponding point for the function
f(x) – 5.
Answer:
(0, -5)
Step-by-step explanation:
You have (x, f(x)) = (0, 0) and you want (x, f(x) -5).
That would be ...
(x, f(x) -5) = (0, 0 -5) = (0, -5)
Solve the equation. dx/dt =3/xet +9x An implicit solution in the form F(t.x)C, where C is an arbitrary constant.
Answer:
[tex]\text{The implicit solution:} \frac{1}{81} e^{9x}(9x - 1) + \frac{3}{e^t} = C[/tex]
Step-by-step explanation:
It is given that there is arbitrary constant C and we have to find the implicit solution. Therefore, first separate the variable that is given in equation and then use integration to find the implicit solution. Here, below is the calculation.
The given equation is:
[tex]\frac{dx}{dt} = \frac{3}{xe^{t-9x}}[/tex]
Now, if we use separation of variable.
[tex]\frac{dx}{dt} = \frac{3}{xe^{t-9x}} \\\frac{dx}{dt} = \frac{3}{xe^{9x}e^{t}} \\xe^{9x}dx = \frac{3}{e^{t}}dt \\[/tex]
Now integrate both side:
[tex]\int xe^{9x} dx = \int \frac{3}{e^{t}} dt \\\frac{e^{9x}}{9}(x) - \int \left [ \frac{e^{9x}}{9} \right]dx = -3e^{-t} + C \\[/tex]
[tex]\frac{xe^{9x}}{9} - \frac{e^{9x}}{81} = -3e^{-t} + C \\\frac{1}{81} e^{9x}(9x - 1) + \frac{3}{e^t} = C \\[/tex]
Thus, the implicit solution is:
[tex]\frac{1}{81} e^{9x}(9x - 1) + \frac{3}{e^t} = C[/tex]
can someone help me asap pls?
[tex]\mathfrak{\huge{\pink{\underline{\underline{AnSwEr:-}}}}}[/tex]
Actually Welcome to the Concept of the Trigonometry.
so here, we gonna use the cosine ratios.
so here, we also use the Pythagoras Theorem.
[tex] {h}^{2} + {k}^{2} = {r}^{2} [/tex]
so we here, we get
h= 1 ,
[tex]h = 1 \: r = 2 \: k = \sqrt{3} \: \\ \alpha = 60 \: \beta = 30[/tex]
Evaluate
[tex]lim \: f(x) \: as \: x \: approaches \: 0[/tex]
knowing that
[tex] \frac{1}{2} - {x}^{2} \leqslant 1 - f(x) \leqslant \frac{1}{2} [/tex]
for all instances of x
Answer:
f(0) = 1/2
Step-by-step explanation:
At x=0, the inequality tells you ...
1/2 ≤ 1 -f(0) ≤ 1/2
That is, ...
1 - f(0) = 1/2
f(0) = 1/2
[tex]\boxed{\lim\limits_{x\to 0}{f(x)}=\dfrac{1}{2}}[/tex]
identify which graphs are functions and which graphs are not.
Answer:
Step-by-step explanation:
We will apply the vertical line test in the given graphs to test them for a function.
Option (1) [First in top row]
If we draw a vertical line from any point, none other point of the graph passes through it.
Therefore, Graph (1) is a function.
Option (2) [2nd in the top row]
When we draw a vertical line through (2, 1), another point (2, -1) will pass through this line.
Therefore, Graph (2) is not a function.
Option (3) [1st in the second row]
In this option when a vertical line is drawn from (2, 1) two more points (2, 2) and (2, 3) pass through this line.
Therefore, graph (4) is not a function.
Option (4). [2nd in the 2nd row]
In this graph only one point lie on the vertical lines drawn.
Therefore, Graph (4) is a function.
Mary Jo spends $2,690 to buy stock in two companies. She pays $24 a share to one of the companies and $25 a share to the other. If she ends up with a total of 110 shares, how many shares did she buy at $24 a share and how many did she buy at $25 a share?
Answer:
60 of 24 dollars each and 50 of 25 dollars
Step-by-step explanation:
x= 24 dollars
110 shares, total x at 24 dollars each
110-x at 25 dollars each
24x+25 (110-x)=2690
24x+ 2750 - 25x= 2690
-1x= -60
x= 60
24 multiplied by 60 =1440
2690-1440 =1250
1250 / 25 = 50
can u vote me as brainliest ?
Find the slope of the function when x=4
y=
2x+1/x2
Select one:
a. 386
b. 0.56 X
C. -0.16
d. 1/4
e. -0.125
Answer:
Option C.
Step-by-step explanation:
The given function is
[tex]y=\dfrac{2x+1}{x^2}[/tex]
We need to find the slope of the function when x=4.
Differentiate the given function w.r.t. x.
[tex]\dfrac{dy}{dx}=\dfrac{x^2\dfrac{d}{dx}(2x+1)-(2x+1)\dfrac{d}{dx}x^2}{(x^2)^2}[/tex] (Using quotient rule)
[tex]\dfrac{dy}{dx}=\dfrac{x^2(2+0)-(2x+1)(2x)}{x^4}[/tex]
[tex]\dfrac{dy}{dx}=\dfrac{2x^2-4x^2-2x}{x^4}[/tex]
[tex]\dfrac{dy}{dx}=\dfrac{-2x^2-2x}{x^4}[/tex]
[tex]\dfrac{dy}{dx}=\dfrac{-2x(x+1)}{x^4}[/tex]
[tex]\dfrac{dy}{dx}=\dfrac{-2(x+1)}{x^3}[/tex]
Now substitute x=4 in the above equation.
[tex]\dfrac{dy}{dx}_{x=4}=\dfrac{-2(4+1)}{4^3}[/tex]
[tex]\dfrac{dy}{dx}_{x=4}=\dfrac{-2(5)}{64}[/tex]
[tex]\dfrac{dy}{dx}_{x=4}=\dfrac{-10}{64}[/tex]
[tex]\dfrac{dy}{dx}_{x=4}=-0.15625[/tex]
[tex]\dfrac{dy}{dx}_{x=4}\approx -0.16[/tex]
Therefore, the correct option is C.
there are 480 students in a class. the ratio of boys to girls is 1:3 how many students in the class are boys
Answer:
120
Step-by-step explanation:
480/(1+3)
480/4
= 120
1 × 120 : 3 × 120
120 : 360
Boys to girls are in the ratio 120:360.
There are 120 boys.
The mean weight of an adult is 6767 kilograms with a variance of 121121. If 164164 adults are randomly selected, what is the probability that the sample mean would be greater than 64.864.8 kilograms
Answer:
99.48% probability that the sample mean would be greater than 64.8 kilograms.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation(which is the square root of the variance) [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question:
[tex]\mu = 67, \sigma = \sqrt{121} = 11, n = 164, s = \frac{11}{\sqrt{164}} = 0.86[/tex]
What is the probability that the sample mean would be greater than 64.8 kilograms?
This is 1 subtracted by the pvalue of Z when X = 64.8.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{64.8 - 67}{0.86}[/tex]
[tex]Z = -2.56[/tex]
[tex]Z = -2.56[/tex] has a pvalue of 0.0052
1 - 0.0052 = 0.9948
99.48% probability that the sample mean would be greater than 64.8 kilograms.
Simple linear equations
Check Whether the value given in the brackets is the root of the given equation or not (nessessary steps is needed)
a) 4x = -4 [x=-1]
b) 2(x-3) =-12 [x=3]
c) 8x - 4x = 24 [x = 1/2]
d) 9x - 4x = 24 [x=18]
Answer: Evaluate the Function, right?
Hello!
~~~~~~~~~~~~~~~~~~
A) 4x = -4 [x=-1] =
4x = -4 =
x = -1 = x = -1
( The steps : Substitute the given value into the function and evaluate.)
B) 2(x-3) =-12 [x=3] =
2 ( x - 3) = -12 = x = -3
x = 3 = x = 3
( The steps : Substitute the given value into the function and evaluate.)
C) 8x - 4x = 24 [x = 1/2] =
8x - 4x = 24 = x = 6
x = 1/2 = x = 1/2
( The steps : Substitute the given value into the function and evaluate.)
D) 9x - 4x = 24 [x=18] =
9x - 4x = 24 = x = 24/5
x = 18 = x = 18
( The steps : Substitute the given value into the function and evaluate.)
~~~~~~~~~~~~~~~~~~
Step-by-step explanation: All the steps are the same. Substitute the given value into the function and evaluate.
Hope this helped you!
Complete the square to rewrite y = x2 - 6x + 16 in vertex form. Then state
whether the vertex is a maximum or minimum and give its coordinates.
Answer:
y = x² + 6x + 16
= (x² + 6x + 9) - 9 + 16
= (x + 3)² + 7 ← vertex form
Therefore, vertex is (-3, 7) and since the coefficient of (x + 3)² is positive the vertex is a minimum.
Answer:
minimum (3,7)
Step-by-step explanation:
I NEED HELP PLEASE THANKS!
An airplane is taking off headed due north with an air speed of 173 miles per hour at an angle of 18° relative to the horizontal. The wind is blowing with a velocity of 42 miles per hour at an angle of S47°E. Find a vector that represents the resultant velocity of the plane relative to the point of takeoff. Let i point east, j point north, and k point up.
(Show work)
Answer:
30.7i + 135.9j + 53.4k
Step-by-step explanation:
The ' horizontal ' may act as the x - axis in this case, the airplane taking off at an angle of 173 cos 18 respective to this x - axis. Respectively it travels restricted to an angle of 173 sin 18 from the y - axis. The following shows this angle at vector( s ) j and k relative to the air -
j - ( 173 cos 18 ),
k - ( 173 sin 18 )
Thus, one can assume such -
[tex]0i + ( 173 cos 18 )j + ( 173 sin 18 )k[/tex]
Knowing that, this second bit here should be similar to the first bit above, given that the wind is now blowing with a velocity of 42 miles per hour at an angle of 47 degrees. Therefore, j = 42 cos 47, i = 42 sin 47 -
[tex]( 42 sin 47 )i + ( 42 cos 47 )j + 0k[/tex]
Adding the two we should get the following -
[tex]30.7i +135.9j + 53.4k[/tex]
Answer:
30.72i+ 135.89j +53.46k
Step-by-step explanation:
If we measure angle φ up from the horizontal and angle θ CCW from east, the direction vector of the airplane at take-off is ...
(ρ, θ, φ) = (173 mph, 90°, 18°)
The rectangular expression of this vector will be ...
(ρ·cos(θ)·cos(φ), ρ·sin(θ)·cos(φ), ρ·sin(φ)) = (0, 164.53, 53.46) . . . mph
__
The wind vector is ...
(ρ, θ, φ) = (42, -43°, 0°) ⇒ (30.72, -28.64, 0) . . . mph
And the rectangular coordinate sum of these vectors is ...
(0, 164.53, 53.46) +(30.72, -28.64, 0) = (30.72, 135.89, 53.46)
The resultant velocity vector of the airplane is ...
30.72i+ 135.89j +53.46k