The question is incomplete! Complete question along with answer and step by step explanation is provided below.
Question:
If (x + 1), 3x and (4x + 2) are in A.S. then the value of x is ?
Answer:
x = 3
Therefore, the value of x is 3.
Step-by-step explanation:
We are given the first three terms of an arithmetic sequence.
(x + 1), 3x, (4x + 2)
The common difference (d) is the difference between two consective terms.
d = (4x + 2) - 3x
d = 4x - 3x + 2
d = x + 2
Also,
d = 3x - (x + 1)
d = 3x - x - 1
d = 2x - 1
Since the common difference must be equal so,
x + 2 = 2x - 1
Combine the like terms
2x - x = 2 + 1
x = 3
Therefore, the value of x is 3.
The values of terms are
x + 1 = 3 + 1 = 4
3x = 3(3) = 9
(4x + 2) = 4(3) + 2 = 12 + 2 = 14
4, 9, 14
As you can notice, the difference between these terms is constant.
14 - 9 = 5
9 - 4 = 5
Let S be a sample space and E and F be events associated with S. Suppose that Pr (Upper E )equals 0.6, Pr (Upper F )equals 0.2 and Pr (Upper E intersect Upper F )equals 0.1. Calculate the following probabilities. (a) Pr (E|F )(b) Pr (F|E )(c) Pr (E| Upper F prime )(d) Pr (Upper E prime | Upper F prime )
Answer:
(a)0.5
(b)0.17
(c)0.625
(b)0.375
Step-by-step explanation:
Pr(E)=0.6
Pr(F)=0.2
[tex]Pr(E\cap F)=0.1.[/tex]
(a)Pr (E|F )
[tex]Pr (E|F )=\dfrac{Pr(E \cap F)}{Pr(F)} \\=\dfrac{0.1}{0.2}\\\\=0.5[/tex]
(b)Pr (F|E )
[tex]Pr (F|E )=\dfrac{Pr(E \cap F)}{Pr(E)} \\=\dfrac{0.1}{0.6}\\\\=0.17[/tex]
(c)Pr (E|F')
Pr(F')=1-P(F)
=1-0.2=0.8
[tex]Pr(E \cap F')=P(E)-P(E\cap F)\\=0.6-0.1\\=0.5[/tex]
Therefore:
[tex]Pr (E|F' )=\dfrac{Pr(E \cap F')}{Pr(F')} \\=\dfrac{0.5}{0.8}\\\\=0.625[/tex]
(d)Pr(E'|F')
[tex]P(E'\cap F')=P(E \cup F)'\\=1-P(E \cup F)\\=1-[P(E)+P(F)-P(E\cap F)]\\=1-[0.6+0.2-0.1]\\=1-0.7\\=0.3[/tex]
Therefore:
[tex]Pr (E'|F' )=\dfrac{Pr(E' \cap F')}{Pr(F')} \\=\dfrac{0.3}{0.8}\\\\=0.375[/tex]
Want Brainliest? Get this correct Which of the following is the quotient of the rational expressions shown below?
Answer:
[tex]\dfrac{4x^2+12x+5}{6x^2-3x}[/tex]
Step-by-step explanation:
Invert the denominator and multiply.
[tex]\dfrac{2x+5}{3x}\div\dfrac{2x-1}{2x+1}=\dfrac{2x+5}{3x}\cdot\dfrac{2x+1}{2x-1}\\\\=\dfrac{(2x+5)(2x+1)}{(3x)(2x-1)}=\boxed{\dfrac{4x^2+12x+5}{6x^2-3x}}\qquad\text{matches choice A}[/tex]
Answer:
[tex]\frac{4x^2+12x+5}{6x^2-3x}[/tex]
Step-by-step explanation:
After using the reciprocal of the second term, the denominator will multiply out to be [tex]6x^2-3x[/tex]. There is only one option with that as the denominator so it must be the correct answer.
A person has a bag containing dimes and nickels. There are a total of 120 coins in the bag, and the total value of the coins is $9.25. Determine how many dimes and nickels are in the bag. There are _____dimes. There are _____ nickels.
Answer:
There are 65 dimes. There are 55 nickels.
Step-by-step explanation:
This question can be solved using a system of equations.
I am going to say that:
x is the number of dimes
y is the number of nickels.
There are a total of 120 coins in the bag
This means that x + y = 120.
The total value of the coins is $9.25.
The dime is worth $0.10 and the nickel is worth $0.05. So
0.1x + 0.05y = 9.25
System:
[tex]x + y = 120[/tex]
[tex]0.1x + 0.05y = 9.25[/tex]
From the first equation:
[tex]y = 120 - x[/tex]
Replacing in the second:
[tex]0.1x + 0.05y = 9.25[/tex]
[tex]0.1x + 0.05(120 - x) = 9.25[/tex]
[tex]0.1x + 6 - 0.05x = 9.25[/tex]
[tex]0.05x = 3.25[/tex]
[tex]x = \frac{3.25}{0.05}[/tex]
[tex]x = 65[/tex]
[tex]y = 120 - x = 120 - 65 = 55[/tex]
There are 65 dimes. There are 55 nickels.
what is tan 11 pie/6
A student writes an incorrect step while checking if the sum of the measures of the two remote interior angles of triangle ABC below is equal to the measure of the exterior angle. A triangle ABC is shown. The base of the triangle extends into a straight line. The angle formed between this straight line and the edge of the triangle is marked as p. The angle adjacent to p is marked as o, and the other two angles inside the triangle are marked as m and n. Step 1: m∠m + m∠n + m∠p = 180 degrees (sum of angles of a triangle) Step 2: m∠p + m∠o = 180 degrees (adjacent supplementary angles) Step 3: Therefore, m∠m + m∠n + m∠o = m∠o + m∠p Step 4: So, m∠m + m∠n = m∠p In which step did the student first make a mistake and how can it be corrected? Step 1; it should be m∠m + m∠n + m∠o = 180 degrees (sum of angles in a triangle) Step 1; it should be m∠m + m∠n + m∠o = 90 degrees (adjacent angles) Step 2; it should be m∠o + m∠p = 180 degrees (alternate exterior angles) Step 2; m∠p − m∠o = 90 degrees (alternate interior angles)
Answer:
(A)Step 1; it should be m∠m + m∠n + m∠o = 180 degrees (sum of angles in a triangle)
Step-by-step explanation:
In the triangle, the exterior angle = pThe adjacent interior angle =oThe two opposite angles are marked m and nThe steps followed by the student are:
Step 1: m∠m + m∠n + m∠p = 180 degrees (sum of angles of a triangle)
Step 2: m∠p + m∠o = 180 degrees (adjacent supplementary angles)
Step 3: Therefore, m∠m + m∠n + m∠o = m∠o + m∠p
Step 4: So, m∠m + m∠n = m∠p
We observe that the student made a mistake in Step 1, it should be m∠m + m∠n + m∠o = 180 degrees (sum of angles in a triangle).
p is outside the triangle, therefore it cannot form one of the angles in the triangle.
Write a two column proof Given: AB || DC; BC || AE Prove: BC/EA = BD/EB
Answer:
AB || DC Given
∠ABE ≅ ∠CDB Alternate interior angles are congruent
BC || AE Given
∠CBD ≅ ∠BEA Alternate interior angles are congruent
ΔAEB is similar to ΔCBD AA Similarity Postulate
BC / EA = BD / EB Similar sides are proportional
A half marathon is 13.1 miles long. Leah is running a half marathon and has completed 7.75 miles. How many miles to
the finish line?
Answer:
5.35 more miles
Answer:
5.35 miles to the finish line
Step-by-step explanation:
Step one
13.1-7.75=
5.35
Which of these numbers are irrational?
Answer:
The answer is option B.
√5
Hope this helps you
Answer:
B. [tex]\sqrt{5}[/tex]
Step-by-step explanation:
Irrational numbers cannot be expressed as simple fractions.
3/5 is a fraction.
[tex]\sqrt{5}[/tex] cannot be expressed as a fraction.
-3.5 can be written as -7/2.
3.555... can be written as 32/9.
Determine whether the point (–3,–6) is in the solution set of the system of inequalities below. x ≤ –3 y < 5∕3x + 2
Answer:
The point (–3,–6) is not in the solution set of the system of inequalities below.
x ≤ –3 y < 5∕3x + 2
Step-by-step explanation:
Given point (-3, -6)
inequality
x ≤ –3
It means that value of x should be less than or equal to -3
since in point (-3,-6) , -3 is point for representing x which is equal to -3 and hence satisfy the criteria for valid value of x,
thus, -3 lie in the solution set of inequality x ≤ –3
lets now see for y = -6
to do that we will put x = -3 in the given below inequality
y < 5∕3x + 2
y < 5∕3*-6 + 2
y < -10 + 2
y < - 8
Thus, inequality suggests that value of y should be less than -8.
but here y is -6, if we see number line -6 is greater than -8 and hence does not belong to the solution set y < 5∕3x + 2 when x = -3
Thus, the point (–3,–6) is not in the solution set of the system of inequalities below. x ≤ –3 y < 5∕3x + 2
What is the solution to the system of linear equations below?
x+4y=22
2x+y=9
Answer:
[tex]\boxed{\sf \ \ \ x = 2 \ \ and \ \ y = 5 \ \ \ }[/tex]
Step-by-step explanation:
hello, we have two equation
(1) x + 4y = 22
(2) 2x + y = 9
let's multiply (1) by 2 and subtract (2)
2x + 8y - (2x + y) = 2*22 - 9 = 44 - 9 = 35
<=> 2x + 8y -2x -y = 35
<=> 7y = 35
<=> y = 35/7 = 5
we replace this value in (1) and it comes
x + 4*5 = 22
<=> x = 22 - 20 = 2
so the solution is
x = 2 and y = 5
hope this helps
Two cities whose longitudes are 10E and 20W on the equator are apart
Step-by-step explanation:
to be honest I'm not sure how to do
A tank contains 3,000 L of brine with 16 kg of dissolved salt. Pure water enters the tank at a rate of 30 L/min. The solution is kept thoroughly mixed and drains from the tank at the same rate. (a) How much salt is in the tank after t minutes
Answer:
The amount of salt in the tank after t minutes is
y= 16e^(t/100)kg
Step- by-step Explanation
The tank contain 3000L of the brine
The rate is 30L/ min
The solution is mixed thoroughly, therefore, the rate in= rate out
dy/dt= rate in to the tank= rate out of the tank
CHECK THE ATTACHMENT FOR DETAILED EXPLANATION
A rectangular playground is to be fenced off and divided in two by another fence parallel to one side of the playground. Three hundred feet of fencing is used
dimensions of the playground that maximize the total enclosed area. What is the maximum area?
The smaller dimension is
feet
Answer:
50 ft by 75 ft3750 square feetStep-by-step explanation:
Let x represent the length of the side not parallel to the partition. Then the length of the side parallel to the partition is ...
y = (300 -2x)/3
And the enclosed area is ...
A = xy = x(300 -2x)/3 = (2/3)(x)(150 -x)
This is the equation of a parabola with x-intercepts at x=0 and x=150. The line of symmetry, hence the vertex, is located halfway between these values, at x=75.
The maximum area is enclosed when the dimensions are ...
50 ft by 75 ft
That maximum area is 3750 square feet.
_____
Comment on the solution
The generic solution to problems of this sort is that half the fence (cost) is used in each of the orthogonal directions. Here, half the fence is 150 ft, so the long side measures 150'/2 = 75', and the short side measures 150'/3 = 50'. This remains true regardless of the number of partitions, and regardless if part or all of one side is missing (e.g. bounded by a barn or river).
The total number of hamburgers sold by a national fast-food chain is growing exponentially. If 3 billion had been sold by 2003 and 9 billion had been sold by 2010, how many will have been sold by 2013
Answer:
F(10) = 14.41 Billion
The total number of hamburgers that will have been sold by 2013 is 14.41 billion.
Step-by-step explanation:
The exponential function representing the total number of hamburgers sold by a national fast-food chain which grows exponentially can be expressed as;
f(t) = p(a)^t
In 2003, t = 0 and f(0) = 3 Billion
f(0) = p = 3 billion
The initial value p = 3 billion
In 2010, t = (2010-2003) = 7
f(7) = p(a)^7 = 9 billion
3(a)^7 = 9
a^7 = 9/3 = 3
a = 3^(1/7)
Therefore, the function f(t) is;
f(t) = 3(3)^(t/7) .......2
In 2013, t = (2013 - 2003) = 10
Substituting t = 10 into equation 2;
f(10) = 3(3)^(10/7)
F(10) = 14.41195997001 Billion
F(10) = 14.41 Billion
The total number of hamburgers that will have been sold by 2013 is 14.41 billion.
The initial population of a town in the year 2010 was 20 000. By 2014, the population had grown exponentially to 32 500 people. Write an equation to represent the population of the town (P) over time in years (n).
Answer:
P = 20000×1.625^(n/4)
Step-by-step explanation:
An exponential equation can be written using the given data:
value = (initial value)×(growth factor in period)^(n/(period))
Here, the growth is by a factor of 32500/20000 = 1.625, and the period is 4 years. Then your exponential equation is ...
P = 20000×1.625^(n/4)
Please need help Please
Answer: 14/11
Step-by-step explanation:
When 14/11 is multiplied by 1/4, you get a repeating decimal. All repeating decimals are rational.
Hope it helps <3
What is the length of Line segment A C? Round to the nearest tenth.
Step-by-step explanation:
To find AC we use tan
tan ∅ = opposite / adjacent
From the question
15 is the opposite
AC is the adjacent
tan 55 = 15 / AC
AC = 15 / tan 55
AC = 10.503
AC is 11 to the nearest tenthHope this helps you
Answer:
A: 10.5 m
Step-by-step explanation:
it's what i think it is, i may be wrong! hope this helps!!~
m∠1=28°, m∠6=65°, m∠5=65°. Find m∠MAX
Answer:
<MAX = 93
Step-by-step explanation:
Since <MAX is technically <1 + <5, we know that <1 is 28 and <5 is 65. We can add both of these angles up to solve for <MAX, which is 28 + 65 = 93.
The angle of MAX is 93 degrees.
What is addition?The addition is one of the mathematical operations. The addition of two numbers results in the total amount of the combined value.
Since m∠MAX = m∠1 + m∠5,
we know that m∠1 = 28 and m∠5 = 65.
To solve for m∠MAX, which is 28 + 65 = 93.
Thus, the angle of MAX is 93 degrees.
Learn more about angles here:
https://brainly.com/question/27458498
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the quotient of F and the product of r,s, and T
Behold the quotient of F and the product of r,s, and T: F / (r·s·T)
The numerical of the statement the quotient of F and the product of r,s, and T is F/(r×s×T).
What are quotient, remainder, divisor, and dividend?The number which is being divided is the dividend.
The number with which we are dividing is the divisor.
The result when a dividend is divided by the divisor is the quotient.
A remainder is the extra portion of a number when it isn't completely divisible.
Given, Are some variables F, r, s, and t.
Now, The product of r,s, and T is,
= r×s×T and the complete statement the quotient of F and the product of r,s, and T can be written as,
F/(r×s×T).
learn more about quotients here :
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I was having trouble solving #25 of this packet. Can you help?
Answer:
On Monday the temperature was 35 - 4 = 31°. On Tuesday, it was 31 + 2 = 33° and on Wednesday it was 33 - 5 = 28° F.
answer if u love cats & dogs
Answer:
(7, 5.25) lies on the graph.
Step-by-step explanation:
We are given the following values
x = 4, 6, 8, 12 and corresponding y values are:
y = 3, 4.5, 6, 9
Let us consider two points (4, 6) and (6, 4.5) and try to find out the equation of line.
Equation of a line passing through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given as:
[tex]y=mx+c[/tex]
where m is the slope.
(x,y) are the coordinates from where the line passes.
c is the y intercept.
Here,
[tex]x_{1} = 4\\x_{2} = 6\\y_{1} = 3\\y_{2} = 4.5[/tex]
Formula for slope is:
[tex]m = \dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]m = \dfrac{4.5-3}{6-4}\\\Rightarrow m = \dfrac{1.5}{2}\\\Rightarrow m = \dfrac{3}{4}[/tex]
Now, the equation of line becomes:
[tex]y=\dfrac{3}{4}x+c[/tex]
Putting the point (4,3) in the above equation to find c:
[tex]3=\dfrac{3}{4}\times 4+c\\\Rightarrow 3=3+c\\\Rightarrow c =0[/tex]
So, final equation of given function is:
[tex]y=\dfrac{3}{4}x[/tex]
OR
[tex]4y=3x[/tex]
As per the given options, the point (7, 5.25) satisfies the equation.
So correct answer is [tex](7, 5.25)[/tex].
If a linear function passes through two points (x1, y1) and (x2, y2), what is the average value of the function on the interval from x1 to x2
Answer:
(y1+y2)/2
Step-by-step explanation:
adding and dividing by the total is the way to calculate the average
Ms. Walker's science class is doing an egg drop experiment from the balcony of their school. Each egg is protected by a contraption that the students collectively designed. The height of the egg, in feet, after x seconds is given by the expression below. What do the zeros of the expression represent? A. the maximum height of the egg B. the time at which the egg reaches its maximum height C. the horizontal distance traveled by the egg D. the time at which the egg reaches the ground
Answer:
An object balances itself when a perpendicular line drawn through its Centre of Gravity (CG), passes through its base.
See the picture of a popular toy given below. The horse, the rider and the ball are all joined together as one single unit. This entire unit is balanced on the thin black rod shown. At which of the indicated positions, could the Centre of Gravity (CG) of the horse, rider and ball unit be?
July 10 book Science up55 down8
AA BB
CC DD
Step-by-step explanation:
Find the missing side. Round your answer to the nearest tenth.
Answer:
answer is a 107 hope it halp u
Answer:
24.9
Step-by-step explanation:
To do this, we set cos(58) to 15/x.
Using a calculator and some math, we get x is about 24.9.
Here is why we do that:
Since cosine is adjacent over hypotenuse, and we have the adjacent but not the hypotenuse, we can use that to create an equation.
Hope this helped!
What is the range of this function?
Answer:
Step-by-step explanation:
The answer is 2,4,3 and -9
The range is the y value
Terry has a collection of 50 coins. There are only quarters and dimes in the collection. The total value of the coins is $8.00. How many dimes does he have?
Answer:
30 dimes and 20 quarters
30×.10=$3.00
20×.25=$5.00
30+20=50
$3+$5=$8
What is the sign of f
Answer:
The sign of f is used to symbolize many things. In physics it is commonly used to mean frequency and in music it is used to symbolize forte, which means loud.
Legal descriptions tend to prefer neat straight lines from point to point, regardless of describing a square, rectangle, triangle or even a smooth circle. When might a property boundary end up being a squiggly line?
Answer:
When describing a property line drawn down the center of a creek bed
A publisher reports that 31% of their readers own a particular make of car. A marketing executive wants to test the claim that the percentage is actually different from the reported percentage. A random sample of 100 found that 21% of the readers owned a particular make of car. Determine the P-value of the test statistic. Round your answer to four decimal places.
Answer:
[tex]z=\frac{0.21 -0.31}{\sqrt{\frac{0.31(1-0.31)}{100}}}=-2.162[/tex]
Since is a bilateral test the p value would be:
[tex]p_v =2*P(z<-2.162)=0.0306[/tex]
Step-by-step explanation:
Information given
n=100 represent the random sample taken
[tex]\hat p=0.21[/tex] estimated proportion of the readers owned a particular make of car
[tex]p_o=0.31[/tex] is the value that we want to test
z would represent the statistic
[tex]p_v[/tex] represent the p value
Hypothesis to test
We need to conduct a hypothesis in order to test if the true proportion is 0.31 or no.:
Null hypothesis:[tex]p=0.31[/tex]
Alternative hypothesis:[tex]p \neq 0.31[/tex]
The statistic is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
And replacing we got:
[tex]z=\frac{0.21 -0.31}{\sqrt{\frac{0.31(1-0.31)}{100}}}=-2.162[/tex]
Since is a bilateral test the p value would be:
[tex]p_v =2*P(z<-2.162)=0.0306[/tex]
A survey of 61,647 people included several questions about office relationships. Of the respondents, 26% reported that bosses scream at employees. Use a 0.05 significance level to test the claim that more than ¼ of people say that bosses scream at employees.
Step-by-step explanation:
n = 61,647, p = 0.26, q = 0.74
μ = p = 0.26
σ = √(pq/n) = 0.00177
At 0.05 significance, z = 1.96.
0.26 ± 1.96 × 0.00177
(0.257, 0.263)
0.25 is outside of the confidence interval, so we can conclude with 95% confidence that the proportion is greater than 0.25.