Answer:
see below
Step-by-step explanation:
4x + 10 = 2(2x + 5)
Distribute
4x+10 = 4x+10
Since the left side is identical to the right side, there are infinite solutions
4x - 5 = 4x + 10
Subtract 4x from each side
-5 = 10
This is never true, so there are no solutions
4x-5 = -5
Add 5 to each side
4x = 0
x=0
There is one solutions
-4-(-1) answer the question
Answer:
-3
Step-by-step explanation:
Since you are subtracting a negative, it turns positive so it will be.
-4+1
-3
Answer:
-3
Step-by-step explanation:
-4-(-1) = -4 + 1 = -3
The radius of a right circular cylinder is increasing at the rate of 7 in./sec, while the height is decreasing at the rate of 6 in./sec. At what rate is the volume of the cylinder changing when the radius is 20 in. and the height is 16 in.
Answer:
[tex]\approx \bold{6544\ in^3/sec}[/tex]
Step-by-step explanation:
Given:
Rate of change of radius of cylinder:
[tex]\dfrac{dr}{dt} = +7\ in/sec[/tex]
(This is increasing rate so positive)
Rate of change of height of cylinder:
[tex]\dfrac{dh}{dt} = -6\ in/sec[/tex]
(This is decreasing rate so negative)
To find:
Rate of change of volume when r = 20 inches and h = 16 inches.
Solution:
First of all, let us have a look at the formula for Volume:
[tex]V = \pi r^2h[/tex]
Differentiating it w.r.to 't':
[tex]\dfrac{dV}{dt} = \dfrac{d}{dt}(\pi r^2h)[/tex]
Let us have a look at the formula:
[tex]1.\ \dfrac{d}{dx} (C.f(x)) = C\dfrac{d(f(x))}{dx} \ \ \ (\text{C is a constant})\\2.\ \dfrac{d}{dx} (f(x).g(x)) = f(x)\dfrac{d}{dx} (g(x))+g(x)\dfrac{d}{dx} (f(x))[/tex]
[tex]3.\ \dfrac{dx^n}{dx} = nx^{n-1}[/tex]
Applying the two formula for the above differentiation:
[tex]\Rightarrow \dfrac{dV}{dt} = \pi\dfrac{d}{dt}( r^2h)\\\Rightarrow \dfrac{dV}{dt} = \pi h\dfrac{d }{dt}( r^2)+\pi r^2\dfrac{dh }{dt}\\\Rightarrow \dfrac{dV}{dt} = \pi h\times 2r \dfrac{dr }{dt}+\pi r^2\dfrac{dh }{dt}[/tex]
Now, putting the values:
[tex]\Rightarrow \dfrac{dV}{dt} = \pi \times 16\times 2\times 20 \times 7+\pi\times 20^2\times (-6)\\\Rightarrow \dfrac{dV}{dt} = 22 \times 16\times 2\times 20 +3.14\times 400\times (-6)\\\Rightarrow \dfrac{dV}{dt} = 14080 -7536\\\Rightarrow \dfrac{dV}{dt} \approx \bold{6544\ in^3/sec}[/tex]
So, the answer is: [tex]\approx \bold{6544\ in^3/sec}[/tex]
Need Help
Please Show Work
Answer:
18 - 8 * n = -6 * n
The number is 9
Step-by-step explanation:
Let n equal the number
Look for key words such as is which means equals
minus is subtract
18 - 8 * n = -6 * n
18 -8n = -6n
Add 8n to each side
18-8n +8n = -6n+8n
18 =2n
Divide each side by 2
18/2 = 2n/2
9 =n
The number is 9
━━━━━━━☆☆━━━━━━━
▹ Answer
n = 9
▹ Step-by-Step Explanation
18 - 8 * n = -6 * n
Simple numerical terms are written last:
-8n + 18 = -6n
Group all variable terms on one side and all constant terms on the other side:
(-8n + 18) + 8n = -6n + 8n
n = 9
Hope this helps!
CloutAnswers ❁
━━━━━━━☆☆━━━━━━━
Two charged particles, Q1, and Q2, are a distance r apart with Q2 = 5Q1 Compare the forces they exert on one another when F1 is the force Q2 exerts on Q1and F2 is the force Q1 exerts on Q2.
a) F2 = 5F1.
b) F2 =-5F1.
c) F2 = F1.
d) F2 = -F1.
e) 5F2 = F1.
Answer:
d) F2 = -F1.
Step-by-step explanation:
According to Coulomb's law of forces on electrostatic charges, the force of attraction is proportional to the product of their charges, and inversely proportional to the square of their distance apart.
What this law means is that both particles will experience an equal amount of force on them, due to the presence of the other particle. This force is not just as a result of their individual charges, but as a result of the product of their charges. Also, the force is a vector quantity that must have a direction alongside its magnitude, and the force on the two particles will always act in opposite direction, be it repulsive or attractive.
a) which function has the graph with the greatest y intercept?
b) which functions have graphs with slopes less than -3
c) which functions graph is the least steep?
Answer:
a =4,b=2, c=3
Step-by-step explanation:
Evaluate −x^2−5 y^3 when x = 4 and y = 1
Answer:
Simplify:
[tex]-4^2-5(1^3)[/tex]
So you get:
[tex]-21\\[/tex]
Answer:
[tex]\huge\boxed{-21}[/tex]
Step-by-step explanation:
-x²-5y³
Given that x = 4, y = 1
[tex]-(4)^2-5(1)^3[/tex]
[tex]-16-5(1)\\-16-5\\-21[/tex]
[tex]4x - 2x = [/tex]
Answer:
2x
Step-by-step explanation:
These are like terms so we can combine them
4x-2x
2x
Answer:
2x
Explanation:
Since both terms in this equation are common, we can simply subtract them.
4x - 2x = ?
4x - 2x = 2x
Therefore, the correct answer should be 2x.
What is the name of a geometric figure that looks an orange
A. Cube
B. Sphere
C. Cylinder
D. Cone
Answer:
b . sphere
Step-by-step explanation:
A manufacturer claims that the calling range (in feet) of its 900-MHz cordless telephone is greater than that of its leading competitor. A sample of 19 phones from the manufacturer had a mean range of 1160 feet with a standard deviation of 32 feet. A sample of 11 similar phones from its competitor had a mean range of 1130 feet with a standard deviation of 30 feet.
Required:
Do the results support the manufacturer's claim?
Complete question is;
A manufacturer claims that the calling range (in feet) of its 900-MHz cordless telephone is greater than that of its leading competitor. A sample of 19 phones from the manufacturer had a mean range of 1160 feet with a standard deviation of 32 feet. A sample of 11 similar phones from its competitor had a mean range of 1130 feet with a standard deviation of 30 feet. Required:
Do the results support the manufacturer's claim?
Let μ1 be the true mean range of the manufacturer's cordless telephone and μ2 be the true mean range of the competitor's cordless telephone. Use a significance level of α = 0.01 for the test. Assume that the population variances are equal and that the two populations are normally distributed
Answer:
We will fail to reject the null hypothesis as there is no sufficient evidence to support the manufacturers claim.
Step-by-step explanation:
For the first sample, we have;
Mean; x'1 = 1160 ft
standard deviation; σ1 = 32 feet
Sample size; n1 = 19
For the second sample, we have;
Mean; x'2 = 1130 ft
Standard deviation; σ2 = 30 ft
Sample size; n2 = 11
The hypotheses are;
Null Hypothesis; H0; μ1 = μ2
Alternative hypothesis; Ha; μ1 > μ2
The test statistic formula for this is;
z = (x'1 - x'2)/√[(σ1)²/n1) + (σ2)²/n2)]
Plugging in the relevant values, we have;
z = (1160 - 1130)/√[(32)²/19) + (30)²/11)]
z = 2.58
From the z-table attached, we have a p-value = 0.99506
This p-value is more than the significance value of 0.01,thus,we will fail to reject the null hypothesis as there is no sufficient evidence to support the manufacturers claim.
Find the first three nonzero terms in the power series expansion for the product f(x)g(x).
f(x) = e^2x = [infinity]∑n=0 1/n! (2x)^n
g(x) = sin 5x = [infinity]∑k=0 (-1)^k/(2k+1)! (5x)^2k+1
The power series approximation of fx)g(x) to three nonzero terms is __________
(Type an expression that includes all terms up to order 3.)
Answer:
∑(-1)^k/(2k+1)! (5x)^2k+1
From k = 1 to 3.
= -196.5
Step-by-step explanation:
Given
∑(-1)^k/(2k+1)! (5x)^2k+1
From k = 0 to infinity
The expression that includes all terms up to order 3 is:
∑(-1)^k/(2k+1)! (5x)^2k+1
From k = 0 to 3.
= 0 + (-1/2 × 5³) + (1/6 × 10^5) + (-1/5040 × 15^5)
= -125/2 + 100000/6 - 759375/5040
= -62.5 + 16.67 - 150.67
= - 196.5
A cube has an edge of 2 feet. The edge is increasing at the rate of 5 feet per minute. Express the volume of the cube as a function of m, the number of minutes elapsed.
Answer:
[tex]V(m) = (2 + 5m)^3[/tex]
Step-by-step explanation:
Given
Solid Shape = Cube
Edge = 2 feet
Increment = 5 feet per minute
Required
Determine volume as a function of minute
From the question, we have that the edge of the cube increases in a minute by 5 feet
This implies that,the edge will increase by 5m feet in m minutes;
Hence,
[tex]New\ Edge = 2 + 5m[/tex]
Volume of a cube is calculated as thus;
[tex]Volume = Edge^3[/tex]
Substitute 2 + 5m for Edge
[tex]Volume = (2 + 5m)^3[/tex]
Represent Volume as a function of m
[tex]V(m) = (2 + 5m)^3[/tex]
Find an equation in slope-intercept form of the line that has slope –9 and passes through point A(-9,-1)
Answer:
y = -9x - 82
Step-by-step explanation:
Line with slope m=-9 passing through A(x1, y1) =A(-9,-1)
y-y1 = m(x-x1)
Substitute values
y-(-1) = -9(x-(-9)
y+1 = -9x -81
y = -9x - 82
In 2018, the population of a district was 25,000. With a continuous annual growth rate of approximately 4%, what will the
population be in 2033 according to the exponential growth function?
Round the answer to the nearest whole number.
Answer:
40,000 populationsStep-by-step explanation:
Initial population in 2018 = 25,000
Annual growth rate (in %) = 4%
Yearly Increment in population = 4% of 25000
= 4/100 * 25000
= 250*4
= 1000
This means that the population increases by 1000 on yearly basis.
To determine what the population will be in 2033, we need to first know the amount of years we have between 2018 and 2033.
Amount of years we have between 2018 and 2033 = 2033-2018
= 15 years
After 15 years, the population will have increased by 15*1000 i.e 15,000 more than the initial population.
Hence the population in 2033 will be Initial population + Increment after 15years = 25,000+15000 = 40,000 population.
The distribution of baby weights at birth is left-skewed because of premies (premature babies) who have particularly low birth weights. However, within a close range of gestation times, birth weights are approximately Normally distributed. For babies born at full term (37 to 39 completed weeks of gestation), for instance, the distribution of birth weight (in grams) is approximately N(3350,440).N(3350, 440).10 Low-birth-weight babies (weighing less than 2500 grams, or about 5 pounds 8 ounces) are at an increased risk of serious health problems. Among those, very-low-birth-weight babies (weighing less than 1500 grams, or about 3 pounds 4 ounces) have the highest risk of experiencing health problems.
A. What proportion of babies born full term are low-birth-weight babies?
B. What proportion of babies born full term are very-low-birth-weight babies?
Answer:
a
[tex]P(X < 2500) = 0.02668[/tex]
b
[tex]P(X < 1500) = 0.00001[/tex]
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 3350[/tex]
The standard deviation is [tex]\sigma = 440[/tex]
We also told in the question that the birth weight is approximately Normally distributed
i.e [tex]X \ \~ \ N(\mu , \sigma )[/tex]
Given that Low-birth-weight babies weighing less than 2500 grams,then the proportion of babies born full term are low-birth-weight babies is mathematically represented as
[tex]P(X < 2500) = P(\frac{ X - \mu }{\sigma } < \frac{2500 - \mu}{\sigma } )[/tex]
Generally
[tex]\frac{X - \mu}{ \sigma } = Z (The \ standardized \ value \ of \ X )[/tex]
So
[tex]P(X < 2500) = P(Z < \frac{2500 - \mu}{\sigma } )[/tex]
substituting values
[tex]P(X < 2500) = P(Z < \frac{2500 - 3350}{440 } )[/tex]
[tex]P(X < 2500) = P(Z <-1.932 )[/tex]
Now from the standardized normal distribution table(These value can also be obtained from Calculator dot com) the value of
[tex]P(Z <-1.932 ) = 0.02668[/tex]
=> [tex]P(X < 2500) = 0.02668[/tex]
Given that very-low-birth-weight babies (weighing less than 1500 grams,then the proportion of babies born full term are very-low-birth-weight babies is mathematically represented as
[tex]P(X < 1500) = P(\frac{ X - \mu }{\sigma } < \frac{1500 - \mu}{\sigma } )[/tex]
[tex]P(X < 1500) = P(Z < \frac{1500 - \mu}{\sigma } )[/tex]
substituting values
[tex]P(X < 1500) = P(Z < \frac{1500 - 3350}{440 } )[/tex]
[tex]P(X < 1500) = P(Z <-4.205 )[/tex]
Now from the standardized normal distribution table(These value can also be obtained from calculator dot com) the value of
[tex]P(Z <-1.932 ) = 0.00001[/tex]
[tex]P(X < 1500) = 0.00001[/tex]
how to write this in number form The difference of 9 and the square of a number
Answer:
9-x^2
Step-by-step explanation:
The difference of means subtracting. the first number is 9 and the second is x^2, so you get 9-x^2
Will Give Brainliest Please Answer Quick
Answer:
Option (2)
Step-by-step explanation:
If a perpendicular is drawn from the center of a circle to a chord, perpendicular divides the chord in two equal segments.
By using this property,
Segment MN passing through the center Q will be perpendicular to chords HI ans GJ.
By applying Pythagoras theorem in right triangle KNJ,
(KJ)² = (KN)² + (NJ)²
(33)² = (6√10)² + (NJ)²
NJ = [tex]\sqrt{1089-360}[/tex]
NJ = [tex]\sqrt{729}[/tex]
= 27 units
Since, GJ = 2(NJ)
GJ = 2 × 27
GJ = 54 units
Option (2) will be the answer.
Last Sunday, the average temperature was 8\%8%8, percent higher than the average temperature two Sundays ago. The average temperature two Sundays ago was TTT degrees Celsius. Which of the following expressions could represent the average temperature last Sunday?
Work Shown:
T = average Celsius temperature two Sundays ago
8% = 8/100 = 0.08
8% of T = 0.08T
L = average Celsius temperature last sunday
L = 8% higher than T
L = T + (8% of T)
L = T + 0.08T
L = 1.00T + 0.08T
L = (1.00 + 0.08)T
L = 1.08T
The 1.08 refers to the idea that L is 108% of T
Answer:
b and d
Step-by-step explanation:
khan
What is the value of x to the nearest tenth?
Answer:
x=9.6
Step-by-step explanation:
The dot in the middle represents the center of the circle, so therefore, the line that is represented by 16 is the radius. Since that is the radius, the side that is the hypotenuse of the small triangle is also 16, since they have the same distance.
The line represented by 25.6 with x as its bisector shows that when we divide it by 2, the other side of the triangle besides the hypotenuse is 12.8.
Now that we have the two sides of the triangle, we can find the last side (represented by x). Use pythagorean theorem:
[tex]a^2 +b^2=c^2\\x^2+(12.8)^2=16^2\\x^2+163.84=256\\x^2=92.16\\x=9.6[/tex]
A waiter earns $11.00 an hour and approximately 10% of what he serves in a shift. If he works a 6 hour shift and takes $425 in orders, his total earnings for the six hours would be:
Answer:
108.50
Step-by-step explanation:
First find the wages
11* 6 = 66 dollars
Then figure the commission
10% of 425
.10 * 425
42.5
Add the two amounts together
42.5+66
108.50
For the following graph, state the polar coordinate with a positive r and positive q (in radians). Explain your steps as to how you determined the coordinate (in your own words). I'm looking for answers that involve π, not degrees for your angles. State the polar coordinate with (r, -q). Explain how you found the new angle. State the polar coordinate with (-r, q). Explain how you found the new angle. State the polar coordinate with (-r, -q). Explain how you found the new angle.
Answer:
Points : ( 8, - 2π/3 ), ( - 8, π/3 ), ( - 8, - 5π/3 )
Step-by-step explanation:
For the first two cases, ( r, θ ) r would be > 0, where r is the directed distance from the pole, and theta is the directed angle from the positive x - axis.
So when r is positive, we can tell that this point is 8 units from the pole, so r is going to be 8 in either case,
( 8, 240° ) - because r is positive, theta would have to be an angle with which it's terminal side passes through this point. As you can see that would be 2 / 3rd of 90 degrees more than a 180 degree angle,or 60 + 180 = 240 degrees.
( 8, - 120° ) - now theta will be the negative side of 360 - 240, or in other words - 120
Now let's consider the second two cases, where r is < 0. Of course the point will still be 8 units from the pole. Again for r < 0 the point will lay on the ray pointing in the opposite direction of the terminal side of theta.
( - 8, 60° ) - theta will now be 2 / 3rd of 90 degrees, or 60 degrees, for - r. Respectively the remaining degrees will be negative, 360 - 60 = 300, - 300. Thus our second point for - r will be ( - 8, - 300° )
_________________________________
So we have the points ( 8, 240° ), ( 8, - 120° ), ( - 8, 60° ), and ( - 8, - 300° ). However we only want 3 cases, so we have points ( 8, - 120° ), ( - 8, 60° ), and ( - 8, - 300° ). Let's convert the degrees into radians,
Points : ( 8, - 2π/3 ), ( - 8, π/3 ), ( - 8, - 5π/3 )
Find the area of the surface generated by revolving x=t + sqrt 2, y= (t^2)/2 + sqrt 2t+1, -sqrt 2 <= t <= sqrt about the y axis
The area is given by the integral
[tex]\displaystyle A=2\pi\int_Cx(t)\,\mathrm ds[/tex]
where C is the curve and [tex]dS[/tex] is the line element,
[tex]\mathrm ds=\sqrt{\left(\dfrac{\mathrm dx}{\mathrm dt}\right)^2+\left(\dfrac{\mathrm dy}{\mathrm dt}\right)^2}\,\mathrm dt[/tex]
We have
[tex]x(t)=t+\sqrt 2\implies\dfrac{\mathrm dx}{\mathrm dt}=1[/tex]
[tex]y(t)=\dfrac{t^2}2+\sqrt 2\,t+1\implies\dfrac{\mathrm dy}{\mathrm dt}=t+\sqrt 2[/tex]
[tex]\implies\mathrm ds=\sqrt{1^2+(t+\sqrt2)^2}\,\mathrm dt=\sqrt{t^2+2\sqrt2\,t+3}\,\mathrm dt[/tex]
So the area is
[tex]\displaystyle A=2\pi\int_{-\sqrt2}^{\sqrt2}(t+\sqrt 2)\sqrt{t^2+2\sqrt 2\,t+3}\,\mathrm dt[/tex]
Substitute [tex]u=t^2+2\sqrt2\,t+3[/tex] and [tex]\mathrm du=(2t+2\sqrt 2)\,\mathrm dt[/tex]:
[tex]\displaystyle A=\pi\int_1^9\sqrt u\,\mathrm du=\frac{2\pi}3u^{3/2}\bigg|_1^9=\frac{52\pi}3[/tex]
If vectors i+j+2k, i+pj+5k and 5i+3j+4k are linearly dependent, the value of p is what?
Answer:
[tex]p = 2[/tex] if given vectors must be linearly independent.
Step-by-step explanation:
A linear combination is linearly dependent if and only if there is at least one coefficient equal to zero. If [tex]\vec u = (1,1,2)[/tex], [tex]\vec v = (1,p,5)[/tex] and [tex]\vec w = (5,3,4)[/tex], the linear combination is:
[tex]\alpha_{1}\cdot (1,1,2)+\alpha_{2}\cdot (1,p,5)+\alpha_{3}\cdot (5,3,4) =(0,0,0)[/tex]
In other words, the following system of equations must be satisfied:
[tex]\alpha_{1}+\alpha_{2}+5\cdot \alpha_{3}=0[/tex] (Eq. 1)
[tex]\alpha_{1}+p\cdot \alpha_{2}+3\cdot \alpha_{3}=0[/tex] (Eq. 2)
[tex]2\cdot \alpha_{1}+5\cdot \alpha_{2}+4\cdot \alpha_{3}=0[/tex] (Eq. 3)
By Eq. 1:
[tex]\alpha_{1} = -\alpha_{2}-5\cdot \alpha_{3}[/tex]
Eq. 1 in Eqs. 2-3:
[tex]-\alpha_{2}-5\cdot \alpha_{3}+p\cdot \alpha_{2}+3\cdot \alpha_{3}=0[/tex]
[tex]-2\cdot \alpha_{2}-10\cdot \alpha_{3}+5\cdot \alpha_{2}+4\cdot \alpha_{3}=0[/tex]
[tex](p-1)\cdot \alpha_{2}-2\cdot \alpha_{3}=0[/tex] (Eq. 2b)
[tex]3\cdot \alpha_{2}-6\cdot \alpha_{3} = 0[/tex] (Eq. 3b)
By Eq. 3b:
[tex]\alpha_{3} = \frac{1}{2}\cdot \alpha_{2}[/tex]
Eq. 3b in Eq. 2b:
[tex](p-2)\cdot \alpha_{2} = 0[/tex]
If [tex]p = 2[/tex] if given vectors must be linearly independent.
You are starting a sock company. You must determine your costs to manufacture your product. The start-up cost is $2000 (which helps you purchase sewing machines). Material and labor is $2.50 per pair of socks.
a. Write an equation to model your company’s cost for manufacturing the socks. (i.e. y=mx+b)
b. Which variable represents the domain? Explain your answer.
c. What is the domain for this situation?
d. Which variable represents the range? Explain your answer.
e. What is the range for this situation?
f. Using your equation, what would be the cost of manufacturing 25 pairs of socks?
g. How many socks could you make with $2500?
h. Create a coordinate graph on a sheet of paper to represent this situation. Describe the graph. Include the dimensions you would use for the x and y axes.
PLS HELP ASAP!
a. y = 2.5x + 2000
b. The variable x represents the domain because the domain is the range of the possible x values.
c. x ≥ 0
d. The variable y represents the range because the range is the range of the possible y values.
e. y ≥ 2000
f. y = 2.5(25) + 2000
y = 62.5 + 2000
y = $2062.50
g. 2500 = 2.5x + 2000
2.5x = 500
x = 200
h. I am sorry I cannot make the graph but hopefully you can figure out how to make it using the info I have given in the above parts of the problem :)
Sarah has $30,000 in her bank account today. Her grand-father has opened this account for her 15 years ago when she was born. Calculate the money that was deposited in the account 15 years ago if money has earned 3.5% p.a. compounded monthly through all these years.
Answer:
Deposit value(P) = $17,760 (Approx)
Step-by-step explanation:
Given:
Future value (F) = $30,000
Number of Year (n) = 15 year = 15 × 12 = 180 month
rate of interest (r) = 3.5% = 0.035 / 12 = 0.0029167
Find:
Deposit value(P)
Computation:
[tex]A = P(1+r)^n\\\\ 30000 = P(1+0.0029167)^{180} \\\\ 30000 = P(1.68917) \\\\ P = 17760.2018[/tex]
Deposit value(P) = $17,760 (Approx)
0 = -12 + 4y - 3x whats the slope
Answer:
3/4 is the slope
Step-by-step explanation:
We want to put this in slope intercept form
y = mx+b where m is the slope and b is the y intercept
0 = -12 + 4y - 3x
Subtract 4y from each side
-4y = -3x-12
Divide each side by -4
-4y/-4 = -3x/-4 -12/-4
y = 3/4 x +3
Answer:
Slope=3/4
Step-by-step explanation:
0=-12+4y-3x (Add 12 on the other side)
12=4y-3x (Add 3x on the other side)
3x+12=4y (Divide by 4)
y=3/4+3
Evan’s dog weighs 15 3/8 pounds. What is this weight written as a decimal? A. 15.125 Ib B. 15.375 Ib C. 15.385 Ib D. 15.625 Ib Please include ALL work!
Answer:
ok as we know 15 is a whole number by itself and 3/8 is the decimal part
so we know it is 15. something
that something is 3/8 to find decimal you do 3/8
3/8 is = .375
so 15.375 is the answer
hope it helps
brainliest give me pls
Step 1: Subtract 3 from both sides of the inequality
Step 2
Step 3: Divide both sides of the inequality by the
coefficient of x.
What is the missing step in solving the inequality 5 -
8x < 2x + 3?
O Add 2x to both sides of the inequality
O Subtract 8x from both sides of the inequality
O Subtract 2x from both sides of the inequality
Add 8x to both sides of the inequality.
Mark this and return
Save and Exit
Intext
Submit
Answer:
add 8x to both sides
Step-by-step explanation:
5-8x<2x+3
first step, subtract 3 from both sides:
2-8x<2x
second step,?
2<?x
so you need to add 8x first
Suppose a 99% confidence interval for the mean salary of college graduates in a town in Mississippi is given by [$34,393, $47,207]. The population standard deviation used for the analysis is known to be $14,900.
Required:
a. What is the point estimate of the mean salary for all college graduates in this town?
b. Determine the sample size used for the analysis.
Answer: a. $40,800 b. 36
Step-by-step explanation:
Given : a 99% confidence interval for the mean salary of college graduates in a town in Mississippi is given by [$34,393, $47,207].
[tex]\sigma= \$14,900[/tex]
a. Since Point estimate of of the mean = Average of upper limit and lower limit of the interval.
Therefore , the point estimate of the mean salary for all college graduates in this town = [tex]\dfrac{34393+47207}{2}=\dfrac{81600}{2}[/tex]
= 40,800
hence, the point estimate of the mean salary for all college graduates in this town = $40,800
b. Since lower limit = Point estimate - margin of error, where Margin of error is the half of the difference between upper limit and lower limit.
Margin of error[tex]=\dfrac{47207-34393}{2}=6407[/tex]
Also, margin of error = [tex]z\times\dfrac{\sigma}{\sqrt{n}}[/tex], where z= critical z-value for confidence level and n is the sample size.
z-value for 99% confidence level = 2.576
So,
[tex]6407=2.576\times\dfrac{14900}{\sqrt{n}}\\\\\Rightarrow\ \sqrt{n}=2.576\times\dfrac{14900}{6407}=5.99\\\\\Rightarrow\ n=(5.99)^2=35.8801\approx 36[/tex]
The sample size used for the analysis =36
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Answer:
The unknown integer that solves the equation is 6.
Step-by-step explanation:
In order to find the missing number, we can set up an equation as if we are solving for x.
x + (-8) = -2
Add 8 on both sides of the equation.
x = 6
So, the unknown integer is 6.
Answer:
6
Step-by-step explanation:
6 plus -8 is -2
You are an assistant director of the alumni association at a local university. You attend a presentation given by the university’s research director and one of the topics discussed is what undergraduates do after they matriculate. More specifically, you learn that in the year 2018, a random sample of 216 undergraduates was surveyed and 54 of them (25%) decided to continue school to pursue another degree, and that was up two percentage points from the prior year. The Dean of the College of Business asks the research director if that is a statistically significant increase. The research director says she isn’t sure, but she will have her analyst follow up. You notice in the footnotes of the presentation the sample size in the year of 2017 was 200 undergraduates, and that 46 of them continued their education to pursue another degree.
There is a short break in the meeting. Take this opportunity to answer the dean’s question using a confidence interval for the difference between the proportions of students who continued their education in 2018 and 2017. (Use 95% confidence level and note that the university has about 10,000 undergraduate students).
Answer:
(0.102, -0.062)
Step-by-step explanation:
sample size in 2018 = n1 = 216
sample size in 2017 = n2 = 200
number of people who went for another degree in 2018 = x1 = 54
number of people who went for another degree in 2017 = x2 = 46
p1 = x1/n1 = 0.25
p2 = x2/n2 = 0.23
At 95% confidence level, z critical = 1.96
now we have to solve for the confidence interval =
[tex]p1 -p2 ± z*\sqrt{((1-p1)*p1)/n1 + ((1-p2)*p2/n2}[/tex][tex]0.25 -0.23 ± 1.96*\sqrt{((1 - 0.25) * 0.25)/216 + ((1 - 0.23) *0.23/200}[/tex]
= 0.02 ± 1.96 * 0.042
= 0.02 + 0.082 = 0.102
= 0.02 - 0.082 = -0.062
There is 95% confidence that there is a difference that lies between - 0.062 and 0.102 on the proportion of students who continued their education in the years, 2017 and 2018.
There is no significant difference between the two.
