Hello
We have two equations and need to find x and y
(1) 6x+7y=-46
(2) 3x-2y=32
multiply (2) by 2 it gives
(2') 6x-4y=64
(1) - (2') gives
6x+7y-6x+4y=-46-64 = -110
so 11y = -110
y = -10
replace in (2) it gives
3x+20=32
3x=12
x = 12/3 = 4
the solution is (4,-10)
do not hesitate if you need further explanation
if you like my answer, tag it as the brainliest :-)
Provide three logically possible directions of causality, indicating for each direction whether it is a reasonable explanation for the correlation based on the variables involved. Explain why?
Answer:
Step-by-step explanation:
Ari thinks the perfect milkshake has
3
33 ounces of caramel for every
5
55 scoops of ice cream. Freeze Zone makes batches of milkshakes with
6
66 ounces of caramel and
8
88 scoops of ice cream.
What will Ari think about Freeze Zone's milkshakes?
Answer:
too much caramel
Step-by-step explanation:
3 ounces : 5 scoops = 3·2 ounces : 5·2 scoops = 6 ounces : 10 scoops
If the Freeze Zone shakes have 6 ounces : 8 scoops, then Ari will think they need more ice cream (2 scoops per shake) or less caramel.
As is, the ratio of caramel to ice cream is too high.
If you are offered one slice from a round pizza (in other words, a sector of a circle) and the slice must have a perimeter of 32 inches, what diameter pizza will reward you with the largest slice
Answer:
A 16 inches diameter will reward you with the largest slice of pizza.
Step-by-step explanation:
Let r be the radius and [tex]\theta[/tex] be the angle of a circle.
According with the graph, the area of the sector is given by
[tex]A=\frac{1}{2}r^2\theta[/tex]
The arc length of a circle with radius r and angle [tex]\theta[/tex] is r [tex]\theta[/tex]
The perimeter of the pizza slice is composed of two straight pieces, each of length r inches, and an arc of the circle which you know has length s = rθ inches. Thus the perimeter has length
The perimeter of the pizza slice is composed of two straight pieces, each of length r inches, and an arc of the circle which you know has length s = rθ inches.
Thus the perimeter has length
[tex]2r+r\theta=32 \:in[/tex]
We need to express the area as a function of one variable, to do this we use the above equation and we solve for [tex]\theta[/tex]
[tex]2r+r\theta=32\\\\r\theta=32-2r\\\\\theta=\frac{32-2r}{r}[/tex]
Next, we substitute this equation into the area equation
[tex]A=\frac{1}{2}r^2(\frac{32-2r}{r})\\\\A=\frac{1}{2}r(32-2r)\\\\A=16r-r^2[/tex]
The domain of the area is
[tex]0<r<12[/tex]
To find the diameter of pizza that will reward you with the largest slice you need to find the derivative of the area and set it equal to zero to find the critical points.
[tex]\frac{d}{dr} A=\frac{d}{dr}(16r-r^2)\\\\A'(r)=\frac{d}{dr}(16r)-\frac{d}{dr}(r^2)\\\\A'(r)=16-2r16-2r=0\\\\-2r=-16\\\\\frac{-2r}{-2}=\frac{-16}{-2}\\\\r=8[/tex]
To check if r=8 is a maximum we use the Second Derivative test
if [tex]f'(c)=0[/tex] and [tex]f''(c)<0[/tex] , then f(x) has a local maximum at x = c.
The second derivative is
[tex]\frac{d}{dr} A'(r)=\frac{d}{dr} (16-2r)\\\\A''(r)=-2[/tex]
Because [tex]A''(r)=-2 <0[/tex] the largest slice is when r = 8 in.
The diameter of the pizza is given by
[tex]D=2r=2\cdot 8=16 \:in[/tex]
A 16 inches diameter will reward you with the largest slice of pizza.
Find the general solution to y′′+6y′+13y=0. Give your answer as y=.... In your answer, use c1 and c2 to denote arbitrary constants and x the independent variable. Enter c1 as c1 and c2 as c2.
Answer:
[tex]y(x)=c_1e^{-3x} cos(2x)+c_2e^{-3x} sin(2x)[/tex]
Step-by-step explanation:
In order to find the general solution of a homogeneous second order differential equation, we need to solve the characteristic equation. This is basically as easy as solving a quadratic.
For a second order differential equation of type:
[tex]ay''+by'+cy=0[/tex]
Has characteristic equation:
[tex]a r^{2} +br+c=0[/tex]
Whose solutions [tex]r_1 , r_2 ,.., r_n[/tex] are the roots from which the general solution can be formed. There are three cases:
Real roots:
[tex]y(x)=c_1e^{r_1 x} +c_2e^{r_2 x}[/tex]
Repeated roots:
[tex]y(x)=c_1e^{r x} +c_1 xe^{r x}[/tex]
Complex roots:
[tex]y(x)=c_1e^{\lambda x}cos(\mu x) +c_2e^{\lambda x}sin(\mu x)\\\\Where:\\\\r_1_,_2=\lambda \pm \mu i[/tex]
Therefore:
The characteristic equation for:
[tex]y''+6y'+13y=0[/tex]
Is:
[tex]r^{2} +6r+13=0[/tex]
Solving for [tex]r[/tex] :
[tex]r_1_,_2= -3 \pm 2i[/tex]
So:
[tex]\mu = 2\\\\and\\\\\lambda=-3[/tex]
Hence, the general solution of the differential equation will be given by:
[tex]y(x)=c_1e^{-3x} cos(2x)+c_2e^{-3x} sin(2x)[/tex]
A soup can has a diameter of 8 centimeters and a height of 15 centimeters how much soup does the can hold?
Answer:
V = 240 pi
Step-by-step explanation:
We want the volume of a cylinder
V = pi r^2 h
We have the diameter and want the radius
r = d/2 = 8/2 = 4
V = pi ( 4)^2 * 15
V = pi * 16* 15
V = 240 pi
Let pi = 3.14
V =753.6 cm^3
Let pi be the pi button
V =753.9822369 cm^3
Answer:
240 pi
Step-by-step explanation:
found the answer online so now work (don't delete my answer)
(x-5)(x+1)=x-5 3(x+1) 3 For what values of x are the two expressions equal ?
Answer:
x=-77+5√ 231 x=-77-5√231
I got this answer for x and the both equations are equal
A triangle has two sides of length 10 and 19. What is the smallest possible whole-number length for the third side?
Answer:
answer for the question is 130 length
what the product of the reciprocals of 2/3, 1/8, and 5
Answer:
12/5
Step-by-step explanation:
Reciprocal of 2/3 is 3/2
Reciprocal of 1/8 is 8/1
Reciprocal of 5 is 1/5
[tex]\frac{3}{2} \times \frac{8}{1} \times\frac{1}{5} = \frac{24}{10} \\[/tex]
Can be simplified to
[tex]\frac{12}{5}[/tex]
x/2 = -5 solve for x
Answer:
[tex]x=-10[/tex]
Step-by-step explanation:
[tex]\frac{x}{2}=-5\\\mathrm{Multiply\:both\:sides\:by\:}2\\\frac{2x}{2}=2\left(-5\right)\\Simplify\\x=-10[/tex]
Peter, Gordon and Gavin share £36 in a ratio 2:1:1. How much money does each person get?
Answer:
Peter gets 18£
Gordon and Gavin each get 9£
Answer:
peter = 18 Gordon = 9 Gavin = 9
Step-by-step explanation:
2+1+1 = 4
36 div 4 = 9
2 times 9 = 18
1 times 9 = 9
Which values for h and k are used to write the function f(x) = x2 + 12x + 6 in vertex form?
h=6, k=36
h=-6, k=-36
h=6, k=30
h=-6, k=-30
Answer: The answer is h=-6, k=-30
Step-by-step explanation:
d on edg
There are 10 balls in a bag, 4 red balls and 6 black balls. If you pick one red ball, you will take it without replacement. If you pick one black ball, you will return it into the bag. Now you pick two times and each time you can only take one ball. What is the probability that you will pick two red balls
Answer:
The probability of selecting two red balls is 0.132.
Step-by-step explanation:
In a bag there are 10 balls in a bag, 4 red balls and 6 black balls.
The conditions of selecting a ball are:
If you pick one red ball, you will take it without replacement. If you pick one black ball, you will return it into the bag.It is also provided that only one ball can be picked at a time.
Now, it is given that two balls are picked.
The number of ways to select a red ball in the first draw is: [tex]{4\choose 1}=4\ \text{ways}[/tex]
Compute the probability of selecting a red ball in the first draw as follows:
[tex]P(\text{First ball is Red})=\frac{{4\choose 1}}{{10\choose 1}}=\frac{4}{10}=0.40[/tex]
Now as a red ball is selected it will not be replaced.
So, there are 9 balls in the bag now.
The number of ways to select a red ball in the second draw is: [tex]{3\choose 1}=3\ \text{ways}[/tex]
Compute the probability of selecting a red ball in the second draw as follows:
[tex]P(\text{Second ball is Red})=\frac{{3\choose 1}}{{9\choose 1}}=\frac{3}{9}=0.33[/tex]
Compute the probability of selecting two red balls as follows:
[tex]P(\text{Two Red balls})=P(\text{First ball is Red})\times P(\text{Second ball is Red})[/tex]
[tex]=0.40\times 0.33\\\\=0.132[/tex]
Thus, the probability of selecting two red balls is 0.132.
find ∠AEC in the figure below.
Answer:
C. 105°
Step-by-step explanation:
Angles BED and CED are supplementary, so ...
(2y +x) +(-2y +3x) = 180
4x = 180
2x = 90
Substituting this into the expression for angle AEB, we have ...
Angle AEB = (90 -15)° = 75°
Angle AEC is the supplement to that, so is ...
∠AEC = 180° -75° = 105° . . . . . matches choice C
Answer: C. 105
Step-by-step explanation:
Adding BED and DEC for being adjacent angles we obtain:
[tex]2y+x +-2y+3x = 180\\4x = 180\\x=45\\[/tex]
Substituting x in BEA
[tex]BEA=2(45)-15=75[/tex]
Adding BEA and AEC for being adjacent angles we obtain:
[tex]BEA+AEC=180\\AEC=180-BEA\\AEC=180-75\\AEC=105[/tex]
A: What are the solutions to the quadratic equation x2+9=0? B: What is the factored form of the quadratic expression x2+9? Select one answer for question A, and select one answer for question B. B: (x+3)(x−3) B: (x+3i)(x−3i) B: (x−3i)(x−3i) B: (x+3)(x+3) A: x=3 or x=−3 A: x=3i or x=−3i A: x=3 A: x=−3i
Answer:
A. The solutions are [tex]x=3i,\:x=-3i[/tex].
B. The factored form of the quadratic expression [tex]x^2+9=(x-3i)(x+3i)[/tex]
Step-by-step explanation:
A. To find the solutions to the quadratic equation [tex]x^2+9=0[/tex] you must:
[tex]\mathrm{Subtract\:}9\mathrm{\:from\:both\:sides}\\\\x^2+9-9=0-9\\\\\mathrm{Simplify}\\\\x^2=-9\\\\\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}\\\\x=\sqrt{-9},\:x=-\sqrt{-9}[/tex]
[tex]x=\sqrt{-9} = \sqrt{-1}\sqrt{9}=\sqrt{9}i=3i\\\\x=-\sqrt{-9}=-\sqrt{-1}\sqrt{9}=-\sqrt{9}i=-3i[/tex]
The solutions are:
[tex]x=3i,\:x=-3i[/tex]
B. Two expressions are equivalent to each other if they represent the same value no matter which values we choose for the variables.
To factor [tex]x^2+9[/tex]:
First, multiply the constant in the polynomial by [tex]i^2[/tex] where [tex]i^2[/tex] is equal to -1.
[tex]x^2+9i^2[/tex]
Since both terms are perfect squares, factor using the difference of squares formula
[tex]a^2-i^2=(a+i)(a-i)[/tex]
[tex]x^2+9=x^2+9i^2=\left(-3i+x\right)\left(3i+x\right)[/tex]
While conducting experiments, a marine biologist selects water depths from a uniformly distributed collection that vary between 2.00 m and 7.00 m. What is the probability that a randomly selected depth is between 2.25 m and 5.00 m?
Answer:
55% probability that a randomly selected depth is between 2.25 m and 5.00 m
Step-by-step explanation:
An uniform probability is a case of probability in which each outcome is equally as likely.
For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.
The probability that we find a value X between c and d is given by the following formula.
[tex]P(c \leq X \leq d) = \frac{d - c}{b - a}[/tex]
While conducting experiments, a marine biologist selects water depths from a uniformly distributed collection that vary between 2.00 m and 7.00 m.
This means that [tex]a = 2, b = 7[/tex]
What is the probability that a randomly selected depth is between 2.25 m and 5.00 m?
[tex]P(2.25 \leq X \leq 5) = \frac{5 - 2.25}{7 - 2} = 0.55[/tex]
55% probability that a randomly selected depth is between 2.25 m and 5.00 m
what is 2/3 of 460? Just a little easy one for points
Answer:
2/3 * 460 = 306 and 2/3
Multiply 460 by 2/3 by first multiplying 460 by 2, then divide that by 3:
460 x 2 = 920
920 /3 = 306 2/3
The answer is 306 2/3
which quadrilateral will always have four reflection symmetry
Step-by-step explanation:
a rectangle has reflectional symmetry when reflected over the line through the midpoints of its opposite sides
Answer: A square always has a four reflection symmetry no matter the size.
The lengths of a professor's classes has a continuous uniform distribution between 50.0 min and 52.0 min. If one such class is randomly selected, find the probability that the class length is between 50.1 and 51.1 min. P(50.1 < X < 51.1) =
Answer:
P(50.1 < X < 51.1) = 0.5
Step-by-step explanation:
An uniform probability is a case of probability in which each outcome is equally as likely.
For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.
The probability that we find a value X between c and d is given by the following formula:
[tex]P(c < X < d) = \frac{d - c}{b - a}[/tex]
The lengths of a professor's classes has a continuous uniform distribution between 50.0 min and 52.0 min.
This means that [tex]a = 50, b = 52[/tex]
So
[tex]P(50.1 < X < 51.1) = \frac{51.1 - 50.1}{52 - 50} = 0.5[/tex]
how to find a local minimum of a function?
Answer:
Find the places where the derivative is zero and the second derivative is positive.
Step-by-step explanation:
By definition, a function has a minimum where the first derivative is zero and the second derivative is positive.
That will be a "local" minimum if there are other points on the function graph that have values less than that. It will be a "global" minimum if there are no other function values less than that. A global minimum is also a local minimum.
__
On a graph, a local minimum is the bottom of the "U" where the graph changes from negative slope to positive slope.
Sander bought 5 bags of nuts. Each bag costs $5.69.
How much did Sander spend for the nuts?
Enter your answer in the box.
Answer:
28.45.
Step-by-step explanation:
5 x 5.69
Using propositional logic to prove that each argument is valid.If Jose took the jewelry or Mrs. Krasov lied, then a crime was committed. Mr. Kraso was not in town. If a crime was committed, then Mr. Krasov was in town. Therefore Jose did not take the jewerly. Use letters J, L, C, T.So for this question, I am very confused and would appreciate any help offerd.
Answer:
Step-by-step explanation:
We will first translate the situation to propositional logic. First, some notation is needed: [tex]\lor[/tex] is the or logical operation and [tex]\implies[/tex] is the symbol for logical implication. Define the following events:
J: Jose took the jewelry. L: Mrs Krasov lied, C: a crime was committed. T: Mr Krasov was in town.
We will symbol the propositions in logical symbols. Recall that [tex]\neg[/tex] means negation
If Jose took the jewelry or Mrs. Krasov lied, then a crime was committed: [tex]J\lor L \implies C[/tex]
Mr. Krasov was not in town: [tex]\neg T[/tex]
If a crime was committed, then Mr. Krasov was in town: [tex]C\implies T[/tex]
We want to check if the conclusion Jose did not take the jewerly: [tex]\neg J[/tex] can be deduced from the premises.
First, recall the following:
- if [tex] a\implies b[/tex] and a is true, then b is true.
- [tex] a\implies b[/tex] is logically equivalent to [tex]\neg b \implies a[/tex]
Coming back to the problem, we have the following premises
[tex]J\lor L \implies C, \neg T, \neg T \implies \neg C, \neg C \implies \neg(J\lor L)[/tex]
where the equivalence for the logical implication was applied. REcall that the negation of an or statement is g iven by
[tex] \neg( a \lor b ) = \neg a \land \neg b [/tex] where [tex] \land[/tex] is the and logical operator.
USing this, we get the premises
[tex]J\lor L \implies C, \neg T, \neg T \implies \neg C, \neg C \implies \neg J\land \neg L[/tex]
Since [tex]\neg T[/tex], by having [tex]\neg T \implies \neg C[/tex], then it must be true that [tex]\neg C[/tex]. Since [tex]\neg C \implies \neg J\land \neg L[/tex], then it must be true that [tex] \neg J\land \neg L[/tex]. This final conclusion implies that it is true that [tex]\neg J[/tex] which is the statement that Jose did not take the jewelry.
In 1970, 59% of college freshmen thought that capital punishment should be abolished; by 2005, the percentage had dropped to 35%. Is the difference real, or can it be explained by chance
Answer:
there is significant distinction in opinion regarding abolition of capital punishment.
Step-by-step explanation:
Compute the p cost of 2-proportion for estimating difference. The Minitab output pronounces the p valu eto be 0.000. This is less than the assumed importance degree of alpha = 0.05. Therefore, reject null hypothesis to finish that there is significant distinction in opinion regarding abolition of capital punishment.
p(x) is a polynomial with integer coefficients and p(-3) = 0. Which statements must be true? Choose all that apply. x - 3 is a factor of the polynomial. -3 is the constant term of the polynomial. p( x) can have at most 3 linear factors. x + 3 is a factor of the polynomial.
Answer:
yes all that apply to this q9
I need help again♀️,
Answer:
The second choice.
Step-by-step explanation:
Answer:
2nd graph down
Step-by-step explanation:
3a+11 > 5
Subtract 11 from each side
3a+11-11 > 5-11
3a > -6
Divide each side by 3
3a/3 > -6/3
a >-2
Open circle at 02
line going to the right
you need 418 yards of blue silk to make one bridesmaid’s dress and 358 yards of the same fabric to make another. How many yards of blue silk do you need to make both dresses?
Answer: you would need 776 yards to make both dresses
Step-by-step explanation:
You would need to find the sum of the amount if yards needed for both dresses.
The first dress needs 418 yards
The seconds dress needs 358 yards
418 + 358 = 776
Therefore you would need 776 yards to be able to make both of the dresses
What’s the correct answer for this?
Answer:
D.
Step-by-step explanation:
If we rotate the 3-D figure around y-axis, we'll obtain a cylinder with a radius of 1 unit.
A polygraph (lie detector) is an instrument used to determine if the individual is telling the truth. These tests are considered to be 86% reliable. In other words, if an individual lies, there is a 0.86 probability that the test will detect a lie. Let there also be a 0.070 probability that the test erroneously detects a lie even when the individual is actually telling the truth. Consider the null hypothesis, "the individual is telling the truth," to answer the following questions.
a. What is the probability of Type I error? (Round your answer to 3 decimal places.)
Probability
b. What is the probability of Type II error? (Round your answer to 2 decimal places.)
Probability
Answer:
Step-by-step explanation:
a) The probability of a Type I error in a lie detection test would be the probability that the lie detection machine incorrectly detected lie for the truth tellers. This is already given in the problem as 0.07.
Therefore,
[tex]P(Type-I) = 0.07[/tex]
Therefore 0.07 is the required probability here.
b) The probability of a Type II error in a lie detection test would be the probability that the lie detection machine incorrectly detected truth for the the people who are actually liars. This is thus 1 - reliability.
[tex]P(Type-II) = 1 - Reliability = 1- 0.86 = 0.14[/tex]
Therefore 0.14 is the required probability here.
Answer:
a) 0.070
b) 0.14
Step-by-step explanation:
Given that the tests are 86% reliable, i.e a probability of 0.86 a lie would be detected.
Probability of error = 0.070
a) For type I error, we have:
The probability of a type I error in this lie detector is the probability that the test erroneously detects a lie even when the individual is actually telling the truth, i.e
P(type I error) = P(rejecting true null)
= 0.070
b) The probability of a Type II error this lie detectot is the probability that the test erroneously detected truth insteax of lie.
i.e = 1 - reliability
P (Type II error) = P(Failing to reject false Null)
= P(Not detecting a lie)
= 1-0.86
= 0.14
Solve the equation A = bh for b.
b = Ah
b = A/h
b = h/A
b = h – A
Answer:
A/h = b
Step-by-step explanation:
A = bh
Divide each side by h
A/h = bh/h
A/h = b
Answer:
[tex]b=\frac{A}{h}[/tex]
Step-by-step explanation:
→To get "b," by itself, all you need to do is divide both sides by "h," like so:
[tex]A=bh[/tex]
[tex]\frac{A}{h} =\frac{bh}{h}[/tex]
[tex]\frac{A}{h} = b[/tex]
Moise Moliere
Mrs. Johnson has 159 chickens that she puts in shelters at night to keep safe. She places 12 chickens in a shelter
and continues putting this number of chickens in each shelter until she comes to the last one. How many chickens
will Mrs. Johnson put in the last shelter?
3
4
13
11
6
7
8 9 10
14
Back
2 3 4 5
9:3
INTL
Answer: she putz 9 in the last shelter
Step-by-step explanation:
The percent, X, of shrinkage on drying for a certain type of plastic clay has an average shrinkage percentage :, where parameter : is unknown. A random sample of 45 specimens from this clay showed an average shrinking percentage of 18.4 and a standard deviation of 2.2. est at 5% level of significance whether the true average shrinkage percentage : is greater than 17.5 and write your conclusion. Report the p-value.
Answer:
[tex]t=\frac{18.4-17.5}{\frac{2.2}{\sqrt{45}}}=2.744[/tex]
The degrees of freedom are given by:
[tex]df=n-1=45-1=44[/tex]
The critical value for this case is [tex]t_{\alpha}=1.68[/tex] since the calculated value is higher than the critical we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly higher than 18.4
[tex]p_v =P(t_{(44)}>2.744)=0.0044[/tex]
We see that the p value is lower than the significance level so then we can reject the null hypothesis in favor of the alternative.
Step-by-step explanation:
Information given
[tex]\bar X=18.4[/tex] represent the sample mean
[tex]s=2.2[/tex] represent the sample standard deviation
[tex]n=45[/tex] sample size
[tex]\mu_o =17.5[/tex] represent the value to verify
[tex]\alpha=0.05[/tex] represent the significance level
t would represent the statistic
[tex]p_v[/tex] represent the p value
We want to test if the true mean is higher than 17.5, the system of hypothesis would be:
Null hypothesis:[tex]\mu \leq 17.5[/tex]
Alternative hypothesis:[tex]\mu > 17.5[/tex]
The statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
And replacing we got:
[tex]t=\frac{18.4-17.5}{\frac{2.2}{\sqrt{45}}}=2.744[/tex]
The degrees of freedom are given by:
[tex]df=n-1=45-1=44[/tex]
The critical value for this case is [tex]t_{\alpha}=1.68[/tex] since the calculated value is higher than the critical we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly higher than 18.4
The p value would be given by:
[tex]p_v =P(t_{(44)}>2.744)=0.0044[/tex]
We see that the p value is lower than the significance level so then we can reject the null hypothesis in favor of the alternative.