Answer:
[tex]x= +2\sqrt{5} or -2\sqrt{5}[/tex]
Step-by-step explanation:
for the given equation,
[tex]4 - x^{2} = -16[/tex]
using rules of equation and inverse operations as isolating x on one side of equation,
interchanging sides of equation we get,
[tex]x^{2} =20[/tex]
[tex]x= +\sqrt{20} or x= -\sqrt{20}[/tex]
[tex]x= +2\sqrt{5} or x= -2\sqrt{5}[/tex]
A mixture of 5 pounds of fertilizer A, 13 pounds of fertilizer B, and 4 pounds of fertilizer C provides the optimal nutrients for a plant. Commercial brand X contains equal parts of fertilizer B and fertilizer C. Commercial brand Y contains one part of fertilizer A and two parts of fertilizer B. Commercial brand Z contains two parts of fertilizer A, five parts of fertilizer B, and two parts of fertilizer C. How much of each fertilizer brand is needed to obtain the desired mixture?
The optimal mixture to compose the desired fertilizer can be obtained using 17 lbs of Brand X, 6 lbs of Brand Y, and 8 lbs of Brand Z.
Explanation:To solve this problem, let us denote X as the amount of brand X, Y as the amount of brand Y, and Z as the amount of brand Z. Since brand X contains equal parts of fertilizers B and C, and the optimal nutrients contain 13 lbs of B and 4 lbs of C, we can say that X = 13 lbs + 4 lbs = 17 lbs.
Brand Y contains one part of A and two parts of B. As we know from the problem that we need 5 lbs of A and 13 lbs of B, we get the equation Y = 5/3 lbs + 13/3 lbs = 6 lbs of Y. This equation is derived from the fact that for every 3 lbs of Y, you get 1.lb of A and 2 lbs of B.
Lastly, brand Z contains two parts of A, five parts of B, and four parts of C. So, Z could be calculated by the combined remainder of A, B and C i.e. (5 - 5/3 lbs) of A, (13 - 13 lbs) of B, and (4 - 4 lbs) of C which will get you approximately 8 lbs of brand Z.
So, you would need roughly 17 lbs of brand X, 6 lbs of brand Y, and 8 lbs of brand Z to create the desired fertilizer mixture.
https://brainly.com/question/30233543
#SPJ12
All questions answer help me! I need it right now! Step by step explain please!
Answer:
C
Step-by-step explanation:
Just by looking at the chart the answer concludes the correct equation for the graph hope this helps CORRECT ME IF I'M WRONG
ps: is that you on your profile picture?
Answer:
A
Step-by-step explanation:
1.9
A
ABC is reflected across x = 1 and y = -3. What are the coordinates of the reflection image of A after both reflections?
(-2, -7) (-2, 7) (7, -2) (7, 2)
Answer:
option C) (7, -2)
Step-by-step explanation:
By the graph, the initial coordinates of point A are ( -5, -4)
first reflection along the line x=1, only the x coordinate will change.
the new x coordinate is = x = 7
thus the point becomes (7, -4)
similarly, reflection along y= -3, only the y coordinate will change.
the new y coordinate is = y = -2
thus the final coordinates are (7, -2)
Need help with this I am not good in Geometry
Answer:
Step-by-step explanation:
Lines p and line r are parallel. This actually means that they will extend continuously without meeting at a point.
Let us assign an alphabet to an angle to make it easy for reference. The diagram is shown in the attached photo
From the photo,
Angle T is equal to 34 degrees. This is because angle T and 34 degrees are corresponding angles.
Angle G = angle T. This is because angle T is vertically opposite to angle G. Therefore
G = 34 degrees
An investment of d dollars at k percent simple annual interest yields $600 interest over a 2-year period. In terms of d, what dollar amount invested at the same rate will yield $2,400 interest over a 3-year period?A. (2d)/3
B. (3d)/4
C. (4d)/3
D. (3d)/2
E. (8d)/3
Answer:
easey
Step-by-step explanation:
Traci collects donations for a dance marathon. One group of sponsors will donate a total of $15 for each hour she dances. Another group of sponsors will donate $110 no matter how long she dances. What number of hours should Traci dance if she wants to raise at least $500?
Answer:
she will need to dance for 26 hours
Step-by-step explanation:
500=15(26)+110
Answer:
26 hours
Step-by-step explanation:
One group will donate $15 per hour, while the other is offering a flat sum of $110. She wants $500, so we can set up the equation
15x + 110 = 500 (with x being the number of hours Traci dances). You subtract 110 from 500 to isolate the variable with its coefficient, resulting in
15x = 390 . Then, dividing 390 by 15 to get x by itself, the answer of 26 hours is found.
It has been observed that some persons who suffer acute heartburn, again suffer acute heartburn within one year of the first episode. This is due, in part, to damage from the first episode. The performance of a new drug designed to prevent a second episode is to be tested for its effectiveness in preventing a second episode. In order to do this two groups of people suffering a first episode are selected. There are 55 people in the first group and this group will be administered the new drug. There are 45 people in the second group and this group will be administered a placebo. After one year, 11% of the first group has a second episode and 9% of the second group has a second episode. Conduct a hypothesis test to determine, at the significance level 0.1, whether there is reason to believe that the true percentage of those in the first group who suffer a second episode is different from the true percentage of those in the second group who suffer a second episode? Select the [Rejection Region, Decision to Reject (RH0) or Failure to Reject (FRH0)]
A. [ z < -1.65, RHo]
B. [ z < -1.65 and z > 1.65, FRHo
C. [z > 1.65, FRHo]
D. [z < -1.65 and z > 1.65, FRHo]
E. [z > -1.65 and z < 1.65, RHo]
F. None of the above
help me find the equation pls!!
Answer:
y(x) = e^(-2x +3)
Step-by-step explanation:
The graphed line has a "y-intercept" of 3 and a slope of -2, so its equation is ...
ln(y) = -2x +3
Taking antilogs, we get ...
y(x) = e^(-2x +3)
According to Harper's Index, 55% of all federal inmates are serving time for drug dealing. A random sample of 16 federal inmates is selected.
(a) What is the probability that 11 or more are serving time for drug dealing? (Round your answer to three decimal places.)
(b) What is the probability that 2 or fewer are serving time for drug dealing? (Round your answer to three decimal places.)
(c) What is the expected number of inmates serving time for drug dealing? (Round your answer to one decimal place.)
Answer:
a)[tex]P(X\geq 11) = 0.198[/tex]
b)[tex]P(X\leq 2) = 0.000565[/tex]
c) Mean = 8.8
Step-by-step explanation:
1) Previous concepts
Binomial Distribution is a "discrete probability distribution which is used to calculate the probabilities for the independent trials and for each trial there is only two outcomes success or failure and probability for each success remains constant throughout each trial".
The Binomial distribution is a type of Bernoulli experiment with following properties:
a)There are two possible outcomes; success or failure.
b) Outcomes are independent on preceding result of a trial.
c) The probability of success remains constant throughout the experiment.
d)The number of successes are fixed.
The probability mass function for the Binomial distribution is given by:
[tex]P(X=a)=(nCa)(p)^x (1-p)^{n-x}[/tex]
Where [tex]p[/tex] is the probability of success, n the number of trials and x the number of successes that we want on the n trials.
[tex]X[/tex] represent the number federal inmates that are serving time for drug dealing
[tex]p=0.55[/tex] represent the proportion of federal inmates that are serving time for drug dealing
[tex]n=16[/tex] random sample selected
2) Part a
The random variable X follows this distribution [tex]X \sim Binom(n,p)[/tex]
On this case we want the following probability, and since says greater or equal than 11 we can express like this:
[tex]P(X \geq 11)=P(X=11)+P(x=12)+P(x=13)+P(x=14)+P(x=15)+P(x=16)[/tex]
[tex]P(X=11)=(16C11)(0.55)^{11} (1-0.55)^{5} =0.112[/tex]
[tex]P(X=12)=(16C12)(0.55)^{12} (1-0.55)^{4} =0.0572[/tex]
[tex]P(X=13)=(16C13)(0.55)^{13} (1-0.55)^{3} =0.0215[/tex]
[tex]P(X=14)=(16C14)(0.55)^{14} (1-0.55)^{2} =0.00563[/tex]
[tex]P(X=15)=(16C15)(0.55)^{15} (1-0.55)^{1} =0.000918[/tex]
[tex]P(X=16)=(16C16)(0.55)^{16} (1-0.55)^{0} =0.00007011[/tex]
[tex]P(X \geq 11)=0.112+0.0572+0.0215+0.00563+0.000918+0.00007011=0.198[/tex]
3) Part b
[tex]P(X \leq 2)=P(X=0)+P(x=1)+P(x=2)[/tex]
[tex]P(X=0)=(16C0)(0.55)^{0} (1-0.55)^{16} =0.00000283[/tex]
[tex]P(X=1)=(16C1)(0.55)^{1} (1-0.55)^{15} =0.0000552[/tex]
[tex]P(X=2)=(16C2)(0.55)^{2} (1-0.55)^{14} =0.000507[/tex]
[tex]P(X \leq 2)=0.00000283+0.0000552+0.000507=0.000565[/tex]
4) Part c
The expected value for the binomial distribution is given by the following formula:
[tex] E(X)=np=16*0.55=8.8[/tex]
So then the average number of federal inmates that are serving time for drug dealing on a sample of 16 is approximately 9.
Mrs. Andretti is having new drapes made for her living room. The cost of the fabric is $15 per yard. The fee to make and hang the drapes is $250. She uses the expression 15x + 250 to calculate the total cost of the drapes. Mrs. Andretti states that x represents the total cost of the fabric. Is she correct?
Answer: No
Step-by-step explanation:
X does not represent the cost of fabric. X represents the number of yards of fabric used.
15x + 250
Could be read as ($15 × # of yards) + $250
So she has to pay $15 per yard of fabric plus an additional $250 base amount for having them made and hung in the first place.
She could use an additional variable to represent the cost of fabric.
Example: Y
Y= 15x
Cost of fabric is equal to $15 per yard × # of yards.
The equation for the total cost depending on the number of students in Emma's Extreme Sports classes is C = 50 + 20x.
C = 50 + 20x
Where C represents the total cost, 50 is the fee per class, and 20 is the cost per student.
A pick-up truck with two passengers weighs about 14100 N. In good driving conditions around a curve, the maximum friction with the road is equal to the truck's weight. What is the minimum safe curve radius that the truck could negotiate at 26.2 m/s?
Answer:
r=68.64 m
Step-by-step explanation:
Given that
Weight ,wt= 14100 N
mass m = 1410 kg ( g = 10 m/s²)
Friction force = Weight
Fr= 14100 N
v= 26.2 m/s
Lets take radius of the curve = r
To balance the truck ,radial force should be equal to the friction force
[tex]\dfrac{mv^2}{r}=Fr[/tex]
mv² = Fr x r
1410 x 26.2² = 14100 x r
r=68.64 m
Therefore radius of the curve will be 68.64 m
Answer - r=68.64 m
The minimum safe curve radius that the truck could negotiate at 26.2 m/s in good driving conditions is approximately 78.94 meters. This relies on the principles of centripetal force and friction, and requires converting the weight of the truck into its mass. The resulting radius ensures that the centripetal force, provided by the friction between the tires and the road, is enough to keep the truck on its path.
Explanation:The subject of this question is related to Centripetal Force and Friction in physics. Centripetal force is the net force on an object moving in a circular path and it points towards the center of the circular path. This force keeps the object moving along this path and is provided by the frictional force between the truck's tires and the road.
In this case, if friction equates to the weight of the truck (14100 N), it will be the centripetal force. The equation for centripetal force is given by:
Fc = mv²/rwhere Fc is the centripetal force, m is the mass of the object, v is the velocity of the object and r is the radius of the circular path. We can arrange this formula to calculate the safe curve radius(r) the truck can negotiate:
r = mv²/FcHowever, in this case, the mass of the truck is given as a force (Weight = 14100 N). So first we need to convert this weight into mass. We can do this by using the formula: Weight = mass (m) × acceleration due to gravity (g). Here, g = 9.8 m/s²:
m = Weight / g = 14100 N / 9.8 m/s² = 1438.78 kgNow we can substitute m = 1438.78 kg, v = 26.2 m/s and Fc = 14100 N into our radius equation to find the minimum safe curve radius for the truck:
r = (1438.78 kg × (26.2 m/s)²) / 14100 N = 78.94 mSo, the minimum safe curve radius that the truck could negotiate at 26.2 m/s in good driving conditions is approximately 78.94 meters.
Learn more about Centripetal Force and Friction here:https://brainly.com/question/32206643
#SPJ11
Which point lies on the graph of the line? (5, 8) (1, 6) (–3, 3) (–4, 2)
Answer:
the answer is (-4,2)
Step-by-step explanation:
Answer:
Step-by-step explanation:
the answer is (-4,2)
The students want to make care packages for unhoused people for winter season. They would like to put 5 boxes of tissues into each care package. If they have 450 boxes pack, how many tissue boxes will they need to complete the boxes?
Answer: 50 tissue boxes
Step-by-step explanation:
The students want to make care packages for unhoused people for winter season.
They would like to put 5 boxes of tissues into each care package.
If they have 450 boxes pack, to determine how many tissue boxes that they need to complete the boxes, we will divide the total number of boxes pack that they have by the number of tissues that will go into one pack. It becomes
450/9 = 50
Enter the equation of the parabola in vertex form that has its vertex at (4,–13) and passes through the point (6,–5).
Answer:
Step-by-step explanation:
If you plot the vertex and the point that it goes through, the point it goes through is above the vertex, so the vertex is a positive one that opens upwards. The general vertex form of a parabola of this type is
[tex]y=a(x-h)^2+k[/tex]
We have the x, y, h, and k. We will plug all those in and solve for a. That looks like this:
[tex]-5=a(6-4)^2-13[/tex] which simplifies to
-5 = 4a - 13 and
8 = 4a so
a = 2
That means that the paraobola in vertex form is
[tex]y=2(x-4)^2-13[/tex]
The total surface of the cuboid is 112cm2 find the value of x bottom length 10cm side bottom length 2cm, id prefer just an answer as im about to get an hour detention, thank you
Answer:
The value of x is 3 cm.
Step-by-step explanation:
Given,
Total surface area of cuboid = 112 cm^2
Height of cuboid = 10 cm
Breadth of cuboid = 2 cm
Length of cuboid = x cm
Solution,
Formula for total surface of cuboid = [tex]2\times(length\times breadth +breadth\times height+height\times length)[/tex]
∴[tex]112=2(x\times2+2\times10+10\times x)\\112=2(2x+20+10x)\\112=2(12x+20)\\12x+20=\frac{112}{2}\\12x+20=56\\12x=56-20\\12x=36\\x=\frac{36}{12}=3[/tex]
Thus the length of cuboid is 3 cm.
A municipality wanting to use integrated waste management methodologies for its citizens would do all of the following EXCEPT: A. pay for each individual's tipping fees at landfills with taxes B. offer curbside recycling to its residents C. attract businesses that utilize source reduction in their manufacturing processes D. offer mulch to its residents at no cost E. maintain a hazardous waste collection site for its residents
Answer:
A. pay for each individuals tipping fee at landfills with taxes
Step-by-step explanation:
Because it is a recyclic methodology .It is a service provide to household for dispose of the waste and recycled it. So as a municipality wanting to waste management so Curbside recycling can be used.
Municipal should attract business that utilize source reduction in their manufacturing.
They should offer much to its resident.
They maintain a hazardous waste collection site for its residents as well.
Please show ALL WORK
WILL MARK BRAINLIEST
Which inequality is graphed below?
y ≥ -2|x - 1| + 3
y ≤ -2|x - 1| + 3
y ≤ -2|x + 1| - 3
y ≥ -2|x + 1| + 3
Answer
The answer
it is y ≥ -2|x + 1| + 3
since the -2 or A controls the negative or positive of an absolute value graph its negative so it's down.
| x+1| if it's like that then you must reverse the sign so it is -1
and for the +3 that controls your vertical line meaning up or down. & in this case it went up so its +3
ASAP PLZ!!! Select the correct answer. Which equation cannot be solved by factoring? A. x2 + 5x − 4 = 0 B. x2 + 6x + 9 = 0 C. x2 + 3x − 4 = 0 D. x2 − x − 6 = 0
Answer:
Step-by-step explanation:
We have four equations here. Let's actually solve them, using factoring if possible and some other method if factoring is not possible.
A) x^2 + 5x + 4 factors into (x + 1)(x + 4), but x^2 + 5x - 4 does not.
B) x^2 + 6x + 9 factors into (x + 3)^2.
C) x^2 + 3x - 4 factors into (x + 4)(x - 1).
D) x^2 - x - 6 factors into (x - 3)(x + 2)
x^2 + 5x - 4 = 0 can be solved, but not by factoring.
In a recent month, 88% of automobile drivers filled their vehicles with regular gasoline, 2% purchased midgrade gas, and 10% bought premium gas. Given that a driver bought regular gas, 28% paid with a credit card; given that they bought midgrade and premium gas, 34% and 42% respectively, paid with a credit card. Suppose we select a customer at random.
a. Draw a tree diagram to represent this situation.
b. What is the probability that an automobile driver filled with regular gasoline AND paid with a credit card?
c. What is the probability that an automobile driver filled with premium gasoline AND did NOT pay with a credit card?
d. What’s the probability that the customer paid with a credit card?
Answer:
b) 0.2464
c) 0.0580
d) 0.2952
Step-by-step explanation:
Probability of those that purchased regular gas = 88% = 0.88
2% purchased mid grade gas
10% purchased premium gad
Given that a driver bought regular gas, 28% paid with credit card
Given that a driver bought mid grade gas, 34% paid with credit card
Given that a driver bought premium gas, 42% paid with credit card
Let R represent drivers that bought regular gas
Let M represent drivers that bought mid grade gas
Let P represent drivers that bought premium gas
Let C represent credit card payment
Let NC represent non-credit card payment
Pr(R) = 88% = 0.88
Pr(M) = 2% = 0.02
Pr(P) = 10% = 0.10
Pr(C|R) = 28%= 0.28
Pr(C|M) = 34%= 0.34
Pr(C|P) = 42%= 0.42
Pr(NC|R) = 1 - 0.28= 0.72
Pr(NC|M) = 1 - 0.34 = 0.66
Pr(NC|P) = 1 - 0.42 = 0.58
Using multiplication rule
Pr(AnB) = Pr(A) * Pr(B|A) = Pr(B) * Pr(A|B)
Using conditional probability,
P(B|A) = Pr(AnB) / Pr(A)
Pr(CnR) = Pr(R) * Pr(C|R)
= 0.88*0.28
= 0.2464
Pr(CnM) = Pr(M) * Pr(C|M)
= 0.02*0.34
= 0.0068
Pr(CnP) = Pr(P) * Pr(C|P)
= 0.10*0.42
= 0.0420
b) the probability that an automobile driver filled with regular gasoline AND paid with a credit card =
Pr(CnR)
= 0.2464
c) the probability that an automobile driver filled with premium gasoline AND did NOT pay with a credit card = Pr(P n NC) = Pr(NC|P) * Pr(P)
= 0.58 * 0.10
= 0.0580
d) The probability of those that paid with credit card is given as
Pr(CnR) + Pr(CnM) + Pr(CnP)
= 0.2464 + 0.0068 + 0.042
= 0.2952
This problem involves calculating different probabilities pertaining to customers' selection of gas type and payment method. These probabilities are found by multiplying corresponding probabilities together for intersecting events, and adding different possibilities together for compound events.
Explanation:The subject of this question is probability, used in Mathematics. Let's solve each part step-by-step:
a. Drawing a tree diagram is a bit tricky in text form, however, it would start with a broad branch representing the initial choice of gas type. This would split into three branches for regular, midgrade, and premium. From each of these, two branches would sprout for the methods of payment: credit card or not credit card. b. The probability that an automobile driver filled with regular gasoline AND paid with a credit card is found by multiplying the probability of each event. So, 0.88 (probability filling with regular gas) * 0.28 (probability of paying with a credit card given that they bought regular gas) = 0.2464 or 24.64%. c. Similarly, the probability that an automobile driver filled with premium gasoline AND did NOT pay with a credit card is calculated as 0.10 (probability filling with premium gas) * 0.58 (probability of not paying with a credit card given that they bought premium gas) = 0.058 or 5.8%. d. The probability a random customer paid with a credit card can be found by adding up the possibilities for each gas type: (0.88 * 0.28) + (0.02 * 0.34) + (0.10 * 0.42) = 0.2464 + 0.0068 + 0.042 = 0.2952 or 29.52%. Learn more about Probability here:https://brainly.com/question/32117953
#SPJ3
A certain company has 255 employees. If an employee is to be selected at random from the company's employees, is the the probability less than 1/2 that the employee selected will be a woman who has a college degree?
(1) 130 of the company's employees do not have a college degree
(2) 125 of the company's employees are men
Answer:
a) 125 < 128
b) The maximum probability that all 130 women are with college degree is 130 < 128 (this is not possible)
The minimum probability that none of the 130 women are college holders = 0 < 128 (this is possible)
Step-by-step explanation:
Total number of employees = 255
If the probability is less than 1/2 that the employee selected will be a woman who has college degree, we have
Women with college degree < 255/2
< 128
a) if 130 of the company employee do not have college degree, we consider that all the college degree holders are women.
The women with college degree = 255 - 130
= 125
Therefore; 125 < 128 ( this is possible)
b) If 125 of the company employees are men, the number of women = 250 -125
= 130 women
The maximum probability that all 130 women are with college degree is 130 < 128 (this is not possible)
The minimum probability that none of the 130 women are college holders = 0 < 128 (this is possible)
A random number generator is used to create a list of 300 single-digit numbers. Of those 300 numbers, 146 are odd and 154 are even. The number 8 was generated 22 times. What is the experimental probability of an even number other than 8 being generated
Answer:
0.44
Step-by-step explanation:
The total numbers drawn = 300
Out those 146 are odd and 154 are even.
The number 8 was drawn = 22 times
So, the number of times an even number other than 8 = 154 -22 = 132
The experimental probability = The number of favorable outcomes ÷ The number of possible outcomes.
The experimental probability of an even number other than 8 being generated = [tex]\frac{132}{300}[/tex]
Simplify the above fraction to decimal, we get
= 0.44
Therefore, the answer is 0.44
The angle measurements in the diagram are represented by the following expressions.
Solve for X then find the measurement of ∠A:
∠A = ∠B
6x + 12 = 3x + 63
6x - 3x = 63 - 12
3x = 51
x = 51 ÷ 3
x = 17
6(17) + 12
102 + 12
∠A = 114°
Answer:
114
Step-by-step explanation:
Kyle says 3/5 is equal to 60%. Which statement explains Kyle is correct?
A) Kyle is correct because 3/5 is equivalent to 10/6 .
B) Kyle is correct because 3/5 is equivalent to 60/100 .
C) Kyle is incorrect because 3/5 is less than 1 and 60% is greater than 1.
D) Kyle is incorrect because 3/5 is not a whole number and 60 is a whole number.
Kyle is correct in saying that 3/5 is equal to 60% because 3/5 is equivalent to 60/100.
Explanation:Kyle says that 3/5 is equal to 60%. This statement can be explained by saying that 3/5 is equivalent to 60/100. To convert a fraction to a percentage, you multiply the top number (numerator) by 100 and then divide by the bottom number (denominator). In this case, multiplying 3 by 100 gives you 300, and when you divide 300 by 5, it equals 60. Hence, 3/5 is indeed equivalent to 60%, which makes Kyle's statement correct.
Learn more about Fraction to Percentage Conversion here:https://brainly.com/question/37435567
#SPJ3
Are triangles △ABCtriangle, A, B, C and △DEFtriangle, D, E, F similar? To answer, try to map △ABCtriangle, A, B, C onto △DEFtriangle, D, E, F using the interactive widget.
Answer:
From three condition the it is proved that Δ ABC and Δ DEF are similar Triangles .
Step-by-step explanation:
Given as :
To Proof : Triangle Δ ABC and Triangle Δ DEF are similar
There are three methods for two Triangles to be similar
A ) SAS i.e side angle side
B ) AA i.e angle angle
C ) SSS i.e side side side
Now,
A) If two triangle have a pair of equal corresponding angles and sides are proportional then triangle are similar
So, If in Δ ABC and Δ DEF
∠ B = ∠ E
and , [tex]\dfrac{AB}{DE}[/tex] = [tex]\dfrac{BC}{EF}[/tex]
Then Δ ABC [tex]\sim[/tex] Δ DEF
I.e SAS similarity
B ) If two triangles have equal corresponding angles , then triangles are similar .
So, If in Δ ABC and Δ DEF
∠ B = ∠ E and ∠ A = ∠ D
Then Δ ABC [tex]\sim[/tex] Δ DEF
I.e AA similarity
C ) If two triangles have three pairs of corresponding sides proportional then triangles are similar .
So, If in Δ ABC and Δ DEF
[tex]\dfrac{AB}{DE}[/tex] = [tex]\dfrac{BC}{EF}[/tex] = [tex]\dfrac{AC}{DF}[/tex]
Then Δ ABC [tex]\sim[/tex] Δ DEF
I.e SSS similarity
Hence From three condition the it is proved that Δ ABC and Δ DEF are similar Triangles . answer
Answer: Neither
Step-by-step explanation:
Got it wrong bc of the person it top of me but yea
answer correctly / explain a lil.
Which relation could be rewritten using FUNCTION notation?
A) x = 3
B) x + y = 3
C) x + y2 = 3
D) x2 + y2 = 3
Answer:
B) x + y = 3
Step-by-step explanation:
This is a specific way to give details without a detailed written explanation of the function. There will be NO exponents when trying to find out information about something:
[tex]\displaystyle x + y = 3 → y = -x + 3[/tex]
I am joyous to assist you anytime.
I love sharks! In fact, before I became a statistician, I wanted to be a marine biologist specializing in shark research (I even went to school for it for a little while). Of particular interest to me were hammerheads and great whites.
Great white sharks are big and hungry. The lengths of 44 great white sharks tagged near False Bay, South Africa had a mean of 15.6 ft with standard deviation 2.5 feet. Based on this sample, is there evidence that the mean length of great white sharks near False Bay are greater than 15 feet? Use a significance level, α = 0.10.
State the null hypothesis.
Answer:
Null hypothesis: [tex]\mu \leq 15[/tex]
Alternative Hypothesis: [tex]\mu >15[/tex]
We have enough evidence to reject the null hypothesis at 10% level of significance.
Step-by-step explanation:
1) Data given
n =44, representing the sample size
[tex]\bar X=15.6ft[/tex] represent the sample mean for the length of great white sharks
[tex]s=2.5ft[/tex] represent the sample standard deviation for the length of great white sharks
[tex]\alpha =0.1[/tex] significance level for the test
2) Formulas to use
On this case we are intereste on the sample mean for the length of great white sharks, and based on the paragraph the hypothesis are given by:
Null hypothesis: [tex]\mu \leq 15[/tex]
Alternative Hypothesis: [tex]\mu >15[/tex]
since we have n>30 but we don't know the population deviation [tex]\sigma[/tex] so we will can use the t approximation. The sample mean have the following distribution
[tex]\bar X \sim N(\mu,\frac{\sigma}{\sqrt{n}})[/tex]
Based on this the statistic to check the hypothesis would be given by:
[tex]t=\frac{\bar X-\mu}{\frac{s}{\sqrt{n}}}[/tex]
Replacing the values given we have:
[tex]t_{calc}=\frac{15.6-15}{\frac{2.5}{\sqrt{44}}}=1.592[/tex]
We can calculate the degrees of freedom with:
[tex]df=n-1=44-1=43[/tex]
With [tex]\alpha[/tex] and the degrees of freedom we can calculate the critical value, since [tex]\alpha=0.1[/tex] we need a value from the t distribution with 43 degrees of freedom that accumulates 0.1 of the area on the right or 0.9 of the area on the left.
We can use excel, a calculator or a table for this, calculating this value we got:
[tex]t_{(43,critc)}=1.302[/tex]
Since our calculatesd value was [tex]t_{calc}=1.592>t_{crit}[/tex], we can reject the null hypothesis at 0.1 level of significance.
Other way in order to have a criterion for reject or don't reject the null hypothesis is calculating the p value, on this case based on the alternative hypothesis the p value would be given by:
[tex]p_v=P(t_{(43)}>1.592)=0.0594[/tex]
So then [tex]p_v <\alpha[/tex] so we have enough evidence to reject the null hypothesis at 10% level of significance.
An investor has $80,000 to invest in a CD and a mutual fund. The CD yields 8% and the mutual fund yields 6%. The mutual fund requires a minimum investment of $9,000, and the investor requires that at least twice as much should be invested in CDs as in the mutual fund. How much should be invested in CDs and how much in the mutual fund to maximize the return? What is the maximum return?
Answer:
mutual fund: $9000CDs: $71000return: $6220, an average of 7.775%Step-by-step explanation:
Since the mutual fund is the lower yield vehicle, only the minimum should be invested there.
The investments and returns should be ...
mutual fund: $9000, return = 6% × $9000 = $540
CD: $71000, return = 8% × $71000 = $5680
The maximum return is ...
$540 +5680 = $6220
To maximize the return, we need to find the amount to be invested in CDs and the mutual fund. The amount to be invested in CDs is $53,333.33 and the amount to be invested in the mutual fund is $26,666.67. The maximum return is $5,333.33.
Explanation:To maximize the return, we need to find the amount to be invested in CDs and the mutual fund. Let's assume the amount invested in the mutual fund is x dollars. Since the investor requires at least twice as much to be invested in CDs, the amount invested in CDs will be 2x dollars. The total investment amount is $80,000, so we can write the equation: x + 2x = $80,000. Simplifying the equation, we have 3x = $80,000. Dividing both sides by 3, we get x = $26,666.67 (rounded to two decimal places).
The amount to be invested in CDs is 2 times x, which is $53,333.33 (rounded to two decimal places). Therefore, the maximum return can be calculated by multiplying the amount invested in CDs and the mutual fund by their respective interest rates and adding them. The return from the CDs would be 8% of $53,333.33 and the return from the mutual fund would be 6% of $26,666.67. Calculating the returns and adding them, we get the maximum return as $5,333.33 (rounded to two decimal places).
Learn more about investment here:https://brainly.com/question/34489138
#SPJ3
Calvin thinks a certain potato chip maker is putting less product in their personal-sized bags of chips. In the past, these bags contained one ounce of product. Calvin conducted a test of H0:μ=1vs. HA:μ<1. From a random sample of 23 bags of potato chips he calculated a p - value of 0.086 for the sample.
(a) At a 5% level of significance, is there evidence that Calvin is correct? (Type Yes or No):
(b) At a 10% level of significance, is there evidence that he is correct? (Type Yes or No):
Answer:
a) There are no evidence that Calvin is correct.
b) There are evidence that Calvin is correct.
Step-by-step explanation:
We are given the following in the question:
Population mean, μ = 1 ounce
Sample size, n = 23
First, we design the null and the alternate hypothesis
[tex]H_{0}: \mu = 1\text{ ounce}\\H_A: \mu < 1\text{ ounce}[/tex]
P-value = 0.086
a) Significance level = 5% = 0.05
Since
P-value > Significance level
We fail to reject the null hypothesis and accept it. Thus, the chips bag contain one ounce of product. Thus, there are no evidence that Calvin is correct.
b) Significance level = 10% = 0.10
Since
P-value < Significance level
We reject the null hypothesis and accept the alternate hypothesis. Thus, the chips bag contain less than one ounce of product. Thus, there are evidence that Calvin is correct.
A rectangle is drawn so that the width is 3 feet shorter than the length. The area of the rectangle is 28 square feet. Find the length of the rectangle.
Answer:
7 feet
Step-by-step explanation:
Assuming the dimensions are integers, we can look at the factors of 28:
28 = 1·28 = 2·14 = 4·7
The last pair differs by 3, so can be the solution to the problem.
The length of the rectangle is 7 feet.
If the length of a rectangle is given by the expression 2 153 and the width is given by 4 68 , which radical expression represents the perimeter of the rectangle? A) 6 34 B) 14 17 C) 28 17 D) 32 17
Answer:
C) 28√17
Step-by-step explanation:
The perimeter is twice the sum of the two given side lengths, so is ...
P = 2(L +W) = 2(2√153 +4√68)
= 2(6√17 +8√17) = 2(14√17)
P = 28√17 . . . . . matches choice C
_____
This is about simplifying radicals. The applicable rules are ...
√(ab) = (√a)(√b)
√(a²) = |a|
__
153 = 9×17, so √153 = (√9)(√17) = 3√17
68 = 4×17, so √68 = (√4)(√17) = 2√17
_____
Comment on the problem presentation
It would help if there were actually radicals in the radical expressions. We had to guess based on the spacing and the answer choices.
In any event, this problem can be worked with a calculator. Find the perimeter (≈115.45) and see which answer matches that. (That's what I did in order to verify my understanding of what the radical expressions were.)