Answer:
Step-by-step explanation:
We are given the equation [tex](x+1)^2-4(x+1)+2=0[/tex]. Consider the substitution u = (x+1). Then the equation turns out to be [tex]u^2-4u+2=0[/tex]
Recall that given a second degree polynomial of the form [tex]ax^2+bx+c =0[/tex] then its solutions are given by the expression
[tex] x = \frac{-b \pm \sqrt[]{b^2-4ac}}{2a}[/tex]
In our case, a = 1, b = -4 and c =2. Then the solutions are
[tex]u_1 = \frac{4+\sqrt[]{(-4)^2-4(2)}}{2} = 2 +\sqrt[]{2}[/tex]
[tex]u_2 = \frac{4-\sqrt[]{(-4)^2-4(2)}}{2} = 2 -\sqrt[]{2}[/tex]
We have that x = u-1. So the original solutions are
[tex]x_1 = 2 +\sqrt[]{2}-1 = 1 + \sqrt[]{2}[/tex]
[tex]x_2 =2 -\sqrt[]{2} -1 = 1 - \sqrt[]{2}[/tex]
Answer: x+4
Step-by-step explanation: part one- x+4
Part two- 3+sqrt21 over 2 +4 & 3- sqrt21 over 2 +4
Suppose that the genders of the three children of a certain family are soon to be revealed. Outcomes are thus triples of "girls" (g) and "boys" (b), which we write gbg, bbb, etc. For each outcome, let R be the random variable counting the number of girls in each outcome. For example, if the outcome is gbb, then R9gbb)=1. Suppose that the random variable X is defined in terms of R as follows: X=2R^2-4R-2. The values of X are thus:
Complete Question
The complete question is shown on the first uploaded image
Answer:
Value x of X -3 -7 -15
[tex]P_X (x)[/tex] [tex]\frac{1}{2}[/tex] [tex]\frac{3}{8}[/tex] [tex]\frac{1}{8}[/tex]
Step-by-step explanation:
From the question we are told that
The values of X are [tex]X = -3 , -7 , -15[/tex]
The total number of outcomes is n = 8
The probability distribution function of X is evaluated as follow
[tex]p(X = -3 ) = \frac{N_{-3}}{n}[/tex]
Where [tex]N{-3}[/tex] is the number of time X = -3 occurred and from the table the value is [tex]N _{-3} = 4[/tex]
Therefore
[tex]p(X = -3 ) = \frac{4}{8}[/tex]
[tex]p(X = -3 ) = \frac{1}{2}[/tex]
Now
[tex]p(X = -7 ) = \frac{N_{-7}}{n}[/tex]
Where [tex]N_{-7} = 3[/tex] from table
So
[tex]p(X = -7 ) = \frac{3}{8}[/tex]
Also
[tex]p(X = -15 ) = \frac{N_{-15}}{n}[/tex]
[tex]p(X = -15 ) = \frac{1}{8}[/tex]
The amounts of time per workout an athlete uses a stairclimber are normally distributed, with a mean of 24 minutes and a standard deviation of 7 minutes. Find the probability that a randomly selected athlete uses a stairclimber for
(a) less than 19 minutes,
(b) between 24 and 33 minutes, and
(c) more than 40 minutes.
Which event is unusual?
Answer:
(a) The probability that a randomly selected athlete uses a stairclimber for less than 19 minutes is 0.2388.
(b) The probability that a randomly selected athlete uses a stairclimber for between 24 and 33 minutes is 0.3997.
(c) The probability that a randomly selected athlete uses a stairclimber for more than 40 minutes is 0.0113.
Step-by-step explanation:
We are given that the amounts of time per workout an athlete uses a stairclimber are normally distributed, with a mean of 24 minutes and a standard deviation of 7 minutes.
Let X = amounts of time per workout an athlete uses a stairclimber
So, X ~ Normal([tex]\mu=24,\sigma^{2} =7^{2}[/tex])
The z-score probability distribution for the normal distribution is given by;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = mean time = 24 minutes
[tex]\sigma[/tex] = standard deviation = 7 minutes
(a) The probability that a randomly selected athlete uses a stairclimber for less than 19 minutes is given by P(X < 19 minutes)
P(X < 19 min) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{19-24}{7}[/tex] ) = P(Z < -0.71) = 1 - P(Z [tex]\leq[/tex] 0.71)
= 1 - 0.7612 = 0.2388
The above probability is calculated by looking at the value of x = 0.71 in the z table which has an area of 0.7612.
(b) The probability that a randomly selected athlete uses a stairclimber for between 24 and 33 minutes is given by = P(24 min < X < 33 min)
P(24 min < X < 33 min) = P(X < 33 min) - P(X [tex]\leq[/tex] 24 min)
P(X < 33 min) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{33-24}{7}[/tex] ) = P(Z < 1.28) = 0.8997
P(X [tex]\leq[/tex] 24 min) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\leq[/tex] [tex]\frac{24-24}{7}[/tex] ) = P(Z [tex]\leq[/tex] 0) = 0.50
The above probability is calculated by looking at the value of x = 1.28 and x = 0 in the z table which has an area of 0.8997 and 0.50 respectively.
Therefore, P(24 min < X < 33 min) = 0.8997 - 0.50 = 0.3997
(c) The probability that a randomly selected athlete uses a stairclimber for more than 40 minutes is given by P(X > 40 minutes)
P(X > 40 min) = P( [tex]\frac{X-\mu}{\sigma}[/tex] > [tex]\frac{40-24}{7}[/tex] ) = P(Z > 2.28) = 1 - P(Z [tex]\leq[/tex] 2.28)
= 1 - 0.9887 = 0.0113
The above probability is calculated by looking at the value of x = 2.28 in the z table which has an area of 0.9887.
The event of probability that a randomly selected athlete uses a stairclimber for more than 40 minutes is unusual because this probability is less than 5% and any even whose probability is less than 5% is said to be unusual.
Nicole has x beads. Together we have 56 beads. How many beads will I have if I lose 1/4 of my beads?
Answer:
(56 - x) * 3/4
Step-by-step explanation:
x + y = 56
y = 56 - x
y' = (56 - x) * 3/4
find the pattern then find the next term of the sequence. 5, 1, 7, 0, 9, -1, 11
Answer:
5, 1, 7, 0, 9, -1, 11, -2, 13
Step-by-step explanation:
5, 1, 7, 0, 9, -1, 11
Two series in one:
5, 7, 9, 11, 131, 0, -1, -2What is the most important difference between an experiment and an observational study? An experiment is conducted in a laboratory and an observational study is conducted outside. An experiment has a treated group and a control group while an observational study does not. In an experiment, the researcher applies a treatment to a randomly assigned group and studies the results, while an observational study just looks at things that have happened without intervention. In an experiment, the researcher studies the effects of medical treatments or other scientific results, while an observational study looks at subjects in the social science arena.
Answer:
In an observational study, we measure or survey members of a sample without trying to affect them. In a controlled experiment, we assign people or things to groups and apply some treatment to one of the groups, while the other group does not receive the treatment.
hope it helps :)
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In an experiment, the researcher applies a treatment to a randomly assigned group and studies the results, while an observational study just looks at things that have happened without intervention.
What is an experiment?An experiment is designed to test the effect of an intervention or treatment on a particular outcome, by comparing the results from a group that receives the intervention to a control group that does not receive the intervention. In this way, the experiment can establish cause-and-effect relationships and determine if the treatment has a significant effect.
On the other hand, an observational study does not involve any manipulation of the independent variable. It simply observes and records the relationship between variables. Observational studies cannot establish cause-and-effect relationships and the results may be subject to confounding variables, which can make it difficult to interpret the findings.
Hence, the correct answer would be an option (C).
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Brainliest to best answer!
Understanding proofs can be challenging for many students. What advice would you
give to a student struggling with these concepts?
Answer:
take your time and always ask for help when needed
Step-by-step explanation:
You've found yourself trapped in a desert, desperate for a drink of water. Amazingly, you come across a food cart right there and they have glasses of water available for just $1! You even have a dollar! You're all set. Except the cart vendor tells you He only sells 80z glasses of water, and he only have 6oz and 10oz glasses. "I'll pay a dollar for the 6oz!" you say. "No," he replies, "I won't be cheating you." How can you use the 6oz glass and the 10oz glass to measure out exactly 8oz?
If I'm understanding the problem correctly, the vendor sells water in exactly 8 oz increments, but only has glasses that can hold 6 oz or 10 oz.
Fill up the 10 oz glass, then (carefully) pour its contents into a 6 oz glass until it it is full. Then the 10 oz glass should contain 4 oz of water. Drink the 4 oz, repeat this process to get your 8 oz, and pay the man.
Find m
A) 110
B) 222
C) 28
D) 82
Answer:
As angel WVU = angel WVF + angel FVU
Therefore angel WVF =152 - 70
so, angel WVF = 82
Activity Question 1 When designing a truss, a truss builder might know the base angle measurement and the length of the tie beam needed. The next step is to compute the height of the king post. Let's take a look at some right triangles to see whether knowing the measure of an acute angle of a right triangle and the length of one of the sides is enough to find the lengths of the other two sides. Part A What is the measure of ∠BAC?
Answer:
36.87°
Step-by-step explanation:
Assume the triangles are as in the diagram below.
∠BAC includes ∠DAE.
The measure of ∠BAE is 36.87°.
Answer:
36.87°
Step-by-step explanation:
i just had this question on edmentum and it was right.
If x^6=60 and w^10=20, what is x^12×w^-10? A. 36, B. 60, C. 180 or D. 360
Answer:
[tex] x^{12} w^{-10}[/tex]
And we can find this rewriting the expression in terms of the info given and we got:
[tex]x^{12} w^{-10} = (x^6)^2 (w^{10})^{-1}[/tex]
And replacing we got:
[tex]x^{12} w^{-10} = (60)^2 (20)^{-1}= \frac{60^2}{20}= 180[/tex]
And the best option would be:
C. 180
Step-by-step explanation:
For this case we know that:
[tex] x^6, w^{10} = 20[/tex]
And we want to find the value for:
[tex] x^{12} w^{-10}[/tex]
And we can find this rewriting the expression in terms of the info given and we got:
[tex]x^{12} w^{-10} = (x^6)^2 (w^{10})^{-1}[/tex]
And replacing we got:
[tex]x^{12} w^{-10} = (60)^2 (20)^{-1}= \frac{60^2}{20}= 180[/tex]
And the best option would be:
C. 180
Two cyclists, 112 miles apart, start riding toward each other at the same time. One cycles 3 times as fast as the other, and they meet after 4 hours of riding.
a. Write an equation using the information as it is given above that can be solved to answer this problem. Use the variable r to represent the speed of the slower cyclist.
b. What are the speeds of the two cyclists? Put both values in the answerbox, separated with a comma, and select the appropriate units.
Answer:
Speed of a= 21 miles/hr
r = Speed of b= 7 miles/hr
Speed of a = 3r
Step-by-step explanation:
The cyclist are 112 miles apart
Time traveled by two = 4 hours
Speed of a = 3 * speed of b
If a cylcles 3 times More than b, then a will cover 3*distance of b
But speed = distance/time
Time = 4hours
Total distance=112
a = 3b
3b + b = 112
4b = 112
b = 112/4
b = 28 miles
a = 3b
a = 3*28
a = 84 Miles
They bought traveled 4 hours
Speed of a = 84miles/4 hours
Speed of a= 21 miles/hr
Speed of b = 28miles/4 hours
Speed of b = 7 miles/hr
what is the area of a circle with a diameter of 8
Step-by-step explanation:
Radius (R) =diameter /2 =8/2 =4
So area=
[tex]\pir {r}^{2} = \pi {4}^{2} = 50.27[/tex]
Hope this helps..
Type the expression that results from the following series of steps:
Start with t times by 5.
Answer:
t times 5 is t * 5 or 5t.
The National Cancer Institute estimates that 3.65% of women in their 60s get breast cancer. A mammogram can typically identify correctly 85% of cancer cases and 95% of cases without cancer. What is the probability that a woman in her 60s who has a positive test actually has breast cancer?
Answer:
39.17% probability that a woman in her 60s who has a positive test actually has breast cancer
Step-by-step explanation:
Bayes Theorem:
Two events, A and B.
[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)}[/tex]
In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.
In this question:
Event A: Positive test.
Event B: Having breast cancer.
3.65% of women in their 60s get breast cancer
This means that [tex]P(B) = 0.0365[/tex]
A mammogram can typically identify correctly 85% of cancer cases
This means that [tex]P(A|B) = 0.85[/tex]
Probability of a positive test.
85% of 3.65% and 100-95 = 5% of 100-3.65 = 96.35%. So
[tex]P(A) = 0.85*0.0365 + 0.05*0.9635 = 0.0792[/tex]
What is the probability that a woman in her 60s who has a positive test actually has breast cancer?
[tex]P(B|A) = \frac{0.0365*0.85}{0.0792} = 0.3917[/tex]
39.17% probability that a woman in her 60s who has a positive test actually has breast cancer
Choose an appropriate metric unit for the capacity of a bottle of ink.
During a trip, Amy had to take two different trains. Her first train traveled for 3 hours, and the second
train traveled for 4 hours. Combined, the trains traveled 625 miles.
If the equation 3m + 4n = 625 represents this situation, which statements are true regarding this
equation?
Select two that apply.
The variable m in the equation represents the speed of the first train.
The variable m in the equation represents the speed of the second train.
The variable n in the equation represents the speed of the second train.
The variable n in the equation represents the speed of the first train.
The variable m in the equation represents the number of hours Amy traveled on the
first train.
The variable n in the equation represents the number of hours Amy traveled on the
second train.
Answer:
Let's solve for m.
3m + 4n = 625
Step 1: Add -4n to both sides.
3m + 4n + −4n = 625 + −4n
3m = −4n + 625
Step 2: Divide both sides by 3.
3m/3 = 4n + 625/3
m = -4/3 n + 625/3
C) The variable m in the equation represents the number of hours Amy traveled on the
first train.
D) The variable n in the equation represents the number of hours Amy traveled on the
second train.
A parabola can be drawn given a focus of (5, 10) and a directrix of y= -2. what can be said about the parabola?
the parabola has a vertex at (_,_), has a low-value of _ and it opens __.
Answer:
(5, 4)4upwardStep-by-step explanation:
The directrix is a horizontal line (y=-2). The parabola will open in the direction the focus is from the directrix. Here, the y-coordinate of the focus is 10, so the focus is above the directrix and the parabola opens upward.
The vertex is halfway between the directrix and the focus, so has y-coordinate ...
(-2 +10)/2 = 4
Since the parabola opens upward, the vertex is a minimum (the "low value"). Its x-coordinate is the same as that of the focus, so the vertex is (5, 4).
The parabola has a vertex at (5, 4), has a low value of 4, and it opens upward.
Find the measure of an angle whose supplement measures five times its measure.
The angle measure ___ degrees.
Answer:
30°
Step-by-step explanation:
supplementary angles are two sets of angles whose sum form 180°
According to the problem, one set equals 5 times the other.
Let the other be x,
It means it's compliment is 5x;
It means therefore that ;
x + 5x = 180°
6x = 180°;
x = 180°/ 6 = 30°;
Therefore the angle measures 30° and it's supplement 150°.
BC =
Round your answer to the nearest hundredth.
B
35°
6
А
Using the cosine ratio, the length of BC to the nearest hundredth is: 4.91.
What is the Cosine Ratio?Cosine ratio is: cos ∅ = adjacent side/hypotenuse
Given the right triangle in the diagram above, thus:
∅ = 35°Adjacent = ? = BCHypotenuse = 6Thus:
cos 35 = BC/6
BC = cos 35 × 6
BC = 4.91
Thus, using the cosine ratio, the length of BC to the nearest hundredth is: 4.91.
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You are conducting a study to see if the proportion of men over the age of 50 who regularly have their prostate examined is significantly less than 0.37. A random sample of 780 men over the age of 50 found that 206 have their prostate regularly examined. Do the sample data provide convincing evidence to support the claim. Test the relevant hypotheses using a 10% level of significance. Give answers to at least 4 decimal places. What are the correct hypotheses?
Answer:
1. Yes, the sample data provides convincing evidence to support the claim that the proportion of men over the age of 50 who regularly have their prostate examined is significantly less than 0.37
2. The correct hypotheses are;
The null hypothesis is H₀: p ≥ p₀
The alternative hypothesis is Hₐ: p < p₀
Step-by-step explanation:
given
The null hypothesis is H₀: p ≥ p₀ where p₀ = 0.37
The alternative hypothesis is Hₐ: p < p₀
The formula for the z test is presented as follows;
[tex]z=\dfrac{\hat{p}-p_0}{\sqrt{\dfrac{p_0 (1 - p_0)}{n}}}[/tex]
Where:
[tex]\hat p[/tex] = Sample proportion = 206/780 = 0.264
p₀ = Population proportion = 0.37
n = Sample size = 780
α = Significance level = 10% = 0.01
Plugging in the values, we have;
[tex]z=\dfrac{0.264-0.37}{\sqrt{\dfrac{0.37 (1 - 0.37)}{780}}} = -6.13[/tex]
From the the z relation/computation, we have the p value = 0.000000000451
Since the p value which is 0.000000000451 is less than α, which is 0.01 we reject the null hypothesis and we fail to reject the alternative hypothesis, that is there is sufficient statistical evidence to suggest that the proportion of men over the age of 50 who regularly have their prostate examined is significantly less than 0.37.
Simplify the following expression.
(2x + 5) + (3x2 + 7x + 3)
Answer:
3x^2 + 9x + 8
Step-by-step explanation:
2x+5+3x^2+7x+3
2x+5+3x^2+7x+3
(3x^2)+(2x+7x)+ (5+3)
3x^2+9x+8
2. Find the measure of angle G. Round your answer to the nearest degree.
Answer:
G = 53 degrees
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
sin theta = opp/ hyp
sin G = 24/30
Take the inverse sin of each side
sin ^-1 sin G = sin ^-1 (24/30)
G =53.13010235
To the nearest degree
G = 53 degrees
Find the 17th term of the arithmetic sequence.
-6, 3, 12, 21, ...
The 17th term is
Answer:
nth term = dn + (a - d) Where d is the difference between the terms, a is the first term and n is the term number.
Step-by-step explanation:
9*17 + (-6- 9)= 138
First find the common difference.
This can be found by subtracting the second term minus the
first term which in this case us 3 - (-6) or 3 + (+6) which is 9.
So we add 9 to reach the next term in this sequence.
Since this sequence isn't too long, continuing adding 9
until you reach the 17th term in this arithmetic sequence.
-6 ⇒ 1st term
3 ⇒ 2nd term
12 ⇒ 3rd term
21 ⇒ 4th term
30 ⇒ 5th term
39 ⇒ 6th term
48 ⇒ 7th term
57 ⇒ 8th term
66 ⇒ 9th term
75 ⇒ 10th term
84 ⇒ 11th term
93 ⇒ 12th term
102 ⇒ 13th term
111 ⇒ 14th term
120 ⇒ 15th term
129 ⇒ 16th term
138 ⇒ 17th term
By manually doing this, we found that our 17th term is 138.
In circle O two secants,
ABP and CDP, are drawn to external point P. If mAC = 72°, and mBD = 34°, what is the measure of ∠P?
(1) 19° (3) 53°
(2) 38° (4) 106°
Answer:
(1)19°
Step-by-step explanation:
The diagram is drawn and attached below.
Let x=mAC = 72°; and
y=mBD = 34°
By the Angle-Arc relationship, the external angle is half the difference.
[tex]\angle P=\frac{1}{2}(x^\circ-y ^\circ)\\$Therefore:\\m\angle P=\frac{1}{2}(72^\circ-34 ^\circ)\\m\angle P=19^\circ[/tex]
What is the coefficient of the term x5y7 in the expansion of (x - y)12 ?
Answer:
12 and -12
Step-by-step explanation:
12x-12y is the expansion using the distributive property, so the coefficient of x is 12 and the coefficient of y is -12
11. Little Sally Walker has a choice between going to an in-state college where she would pay
$3,500 per year for tuition or an out of state college where she would pay $6,000 per year. The
cost of living at the in-state college is $700 per month in rent. The out of state college is $400
per month in rent. Assuming all the other factors are equal,
a. what is the yearly expense of the in-state college?
b. what is the yearly expense of the out-of-state college?
Answer:
Step-by-step explanation:
Lets calculate first for in state college
yearly tuition fees = $3,500
monthly living expense = $700
one year has 12 months so yearly living expense =$700 * 12 = $8,400
Yearly expense of the in state college = yearly tuition fees ($3,500 )+ yearly living expense($8,400) = $3,500 + $8,400 = $11,900
____________________________________________________
Lets calculate first for out of state college
yearly tuition fees = $6,000
monthly living expense = $400
one year has 12 months so yearly living expense =$400 * 12 = $4,800
Yearly expense of the out of state college = yearly tuition fees ($3,500 )+ yearly living expense($8,400) = $6,000 + $4,800 = $10,800
____________________________________________________
This question is rlly confusing
Answer: C.
Step-by-step explanation:
To find the discounted value off of a full price, you can multiply the full price by the discount percentage to find the discount:
250 * 0.20 = 50
The discount is 50 dollars.
The laptop costs $250, but with the discount of $50, it is now for sale for $200.
The correct answer is C.
arc
An 8 inch pie (diameter is 8) was sliced into 4 equal parts. How large is the 2 points
pie crust of one slice? *
Answer:
6.28 inches
Step-by-step explanation:
Given that the diameter of the pie=8 inch
Radius=Diameter/2
Therefore: Radius of the pie=8/2=4 Inch
Circumference of a circle [tex]=2\pi r[/tex]
Since the pie is sliced into 4 equal parts:
Length of the Pie crust of one slice[tex]=\dfrac{2\pi r}{4}[/tex]
Substituting the value of r, we obtain:
Length of the Pie crust of one slice[tex]=\dfrac{2*\pi *4}{4}\\=2\pi $ inches\\=6.28 inches (correct to 2 decimal places)[/tex]
Ashley mixes two types of soft drinks with different types of concentration: one soft drink has 20% sugar and the other drink has 45% sugar. Each can has 250 milliliters of soda. What is the sugar concentration of the mixed soft drink?
Answer:
Sugar concentration of the mixed soft drink will be 32.5%.
Step-by-step explanation:
Sugar concentration of first drink = 20%
Volume of first soda = 250 ml
Sugar in first soda = 20% of 250 ...... (1)
Sugar concentration of second drink = 45%
Volume of second soda = 250 ml
Sugar in second soda = 45% of 250 ...... (2)
Let [tex]x\%[/tex] be the sugar concentration in resultant mixture.
Volume of mixture = 250 + 250 = 500 ml
Sugar in mixture = [tex]x\%[/tex] of 500 ml ...... (3)
Total sugar concentration (Adding (1) and (2)) and equating it to equation (3):
20% of 250 + 45% of 250 = [tex]x\%[/tex] of 500
[tex]\Rightarrow \dfrac{20}{100} \times 250 + \dfrac{45}{100} \times 250 = \dfrac{x}{100} \times 500\\\Rightarrow 2 \times x = 65\\\Rightarrow x = 32.5\%[/tex]
Hence, Sugar concentration of the mixed soft drink will be 32.5%.
how and explain how to find the value of x . step by step I will give the most correct one the brainiest
Answer:
X=96
Step-by-step explanation:
180-134=46
180-130=50
SUM OF TWO INTERIOR ANGLES = EXTERIOR ANGLE
50 + 46=96
