Answer:
We conclude that the rate of smoking among those with four years of college is less than the 27% rate for the general population.
Step-by-step explanation:
We are given that a survey showed that among 785 randomly selected subjects who completed four years of college, 144 of them are smokers.
Let p = population proportion of smokers among those with four years of college
So, Null Hypothesis, [tex]H_0[/tex] : p [tex]\geq[/tex] 27% {means that the rate of smoking among those with four years of college is more than or equal to the 27% rate for the general population}
Alternate Hypothesis, [tex]H_A[/tex] : p < 27% {means that the rate of smoking among those with four years of college is less than the 27% rate for the general population}
The test statistics that will be used here is One-sample z-test for proportions;
T.S. = [tex]\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n} } }[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = sample proportion of smokers = [tex]\frac{144}{785}[/tex] = 0.18
n = sample of subjects = 785
So, the test statistics = [tex]\frac{0.18-0.27}{\sqrt{\frac{0.27(1-0.27)}{785} } }[/tex]
= -5.68
The value of z-test statistics is -5.68.
Also, the P-value of the test statistics is given by;P-value = P(Z < -5.68) = Less than 0.0001
Now, at a 0.01 level of significance, the z table gives a critical value of -2.3262 for the left-tailed test.
Since the value of our test statistics is less than the critical value of z, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.
Therefore, we conclude that the rate of smoking among those with four years of college is less than the 27% rate for the general population.
General solution of equation sin x + sin 5x = sin 2x + sin 4x is
Answer:
x=nπ3, n∈I
Step-by-step explanation:
sin x + sin 5x = sin 2x + sin 4x
⇒⇒ 2 sin 3x cos 2x = 2 sin 3x cos x
⇒⇒ 2 sin 3x(cos 2x - cos x) = 0
⇒ sin 3x=0 ⇒ 3x=nπ ⇒ x=nπ3⇒ sin 3x=0 ⇒ 3x=nπ ⇒ x=nπ3 , n∈I, n∈I
or cos 2x−cos x=0 ⇒ cos 2x=cos xcos 2x-cos x=0 ⇒ cos 2x=cos x
⇒ 2x=2nπ±x ⇒ x=2nπ, 2nπ3⇒ 2x=2nπ±x ⇒ x=2nπ, 2nπ3 , n∈I, n∈I
But solutions obtained by x=2nπx=2nπ , n∈I, n∈I or x=2nπ3x=2nπ3 , n∈I, n∈I are all involved in x=nπ3x=nπ3 , n∈I
Olcquations
Week 5 Assignment: Mixture Problems and Systems of Equations
Due Sunday by 11:59pm
Points 10
Submitting an external tool
Solve interest applications using a system of equations
Question
Matthew invested $3,000 into two accounts. One account paid 3% interest and the other paid 8% interest. He earned 4%
interest on the total investment. How much money did he put in each account?
Sorry, that's incorrect. Try again?
3% amount: S 600
8% amount: S 2400
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Answer:
$600 at 8%$2400 at 3%Step-by-step explanation:
You have the right numbers, but the wrong accounts.
__
Let x represent the amount invested at 8% (the highest rate). Then the total interest is ...
.08x +.03(3000 -x) = .04(3000)
.05x = .01(3000) . . . . subtract .03(3000)
x = 3000/5 = 600
Matthew invested $600 at 8%, $2400 at 3%.
_____
Comment on checking your answer
You may notice that the overall interest rate is 4%, closer to 3% than to 8%. That means more of the money must be invested at 3% than at 8%.
Anand needs to hire a plumber. He's considering a plumber that charges an initia
hourly rate of $28. The plumber only charges for a whole number of hours. Anar
more than $250, and he wonders how many hours of work he can afford.
Let H represent the whole number of hours that the plumber works.
1) Which inequality describes this scenario?
Choose 1 answer:
28 - 65H <250
Complete question :
Anand needs to hire a plumber. He's considering a plumber that charges an initial fee of $65 along with an
hourly rate of $28. The plumber only charges for a whole number of hours. Anand would like to spend no more than $250, and he wonders how many hours of work he can afford.
Let H represent the whole number of hours that the plumber works.
1) Which inequality describes this scenario?
Choose 1 answer:
A. 28 + 65H < 250
B. 28 + 65H > 250
C. 65 + 28H < 250
D. 65 +28H > 250
2) What is the largest whole number of hours that Anand can afford?
Answer:
65 + 28H < 250
Number of hours Anand can afford = 6 hours
Step-by-step explanation:
Given the following information :
Initial hourly rate = $65
Hourly rate = $28
Number of hours worked (whole number) = H
Maximum budgeted amount to spend = $250
Therefore ;
(Initial charge + total charge in hours) should not be more than $250
$65 + ($28*H) < $250
65 + 28H < 250
Number of hours Anand can afford :
65 + 28H < 250
28H < 250 - 65
28H < 185
H < (185 / 28)
H < 6.61
Sinve H is a whole number, the number of hours he can afford is 6 hours
Answer:
65 + 28H < 250
6
Step-by-step explanation:
tried it, it worked.
the other answer is correct but hard to understand so give them thanks and 4 star :)
Evaluate
1+5.3
2
please answer quickly
Answer:
1+5.3=6.3
Step-by-step explanation:
not sure what your asking for with the 2
explain what your looking for with the 2 and maybe we can help you further
(I have to do it the way I did it because the 2 in the question is confusing)
Answer:
For expression 1 + 5.32: 6.32
For expression 1 + 5.3 × 2: 11.6
Step-by-step explanation:
If the expression is 1 + 5.32:
Add 1 to 5.32: 1 + 5.32 = 6.32If the expression is 1 + 5.3 × 2:
5.3 × 2 = 10.6Plug in 10.6: 1 + 10.61 + 10.6 = 11.6
Evaluate the expresión 6c-d when c=2 and d=10 I need help?
Answer:
the answer is 18
Step-by-step explanation:
8 is the answer
In a triangle ABC two points D,E are taken on BC so that angle BAD=angle DAE=angleCAE. Determine AE if AB=5,BC=10 angle BAC=90. PLEASE HELP I NEED HELP WITHIN TEN MINS PLEASE
Answer:
AE = 7.5
Step-by-step explanation:
Since <BAC = [tex]90^{0}[/tex], then;
<BAD = <DAE = <CAE = [tex]30^{0}[/tex] (complementary angles)
From ΔABC, applying the Pythagoras theorem to determine the length of side AC;
[tex]/BC/^{2}[/tex] = [tex]/AC/^{2}[/tex] + [tex]/AB/^{2}[/tex]
[tex]/10/^{2}[/tex] = [tex]/AC/^{2}[/tex] + [tex]/5/^{2}[/tex]
100 = [tex]/AC/^{2}[/tex] + 25
[tex]/AC/^{2}[/tex] = 100 - 25
[tex]/AC/^{2}[/tex] = 75
AC = [tex]\sqrt{75}[/tex]
Applying trigonometric function to ΔCAE,
Cos [tex]30^{0}[/tex] = [tex]\frac{AE}{\sqrt{75} }[/tex]
AE = [tex]\sqrt{75}[/tex] × Cos [tex]30^{0}[/tex]
= 7.5
Therefore, AE = 7.5
Select the correct answer. If , which statement is true? if g(x) = f(1/3x)
A. The graph of function f is stretched vertically by a scale factor of 3 to create the graph of function g.
B. The graph of function f is stretched horizontally by a scale factor of 3 to create the graph of function g.
C. The graph of function f is compressed horizontally by a scale factor of to create the graph of function g.
D. The graph of function f is compressed vertically by a scale factor of to create the graph of function g.
Answer:
B. The graph of function f is stretched horizontally by a scale factor of 3 to create the graph of function g.
Step-by-step explanation:
The rules for linear transformations are that
g(x) = a·f(b·(x-c)) +d
stretches the graph vertically by a factor of "a" (before the shift)
compresses the graph horizontally by a factor of "b" (before the shift)
shifts it to the right by amount "c"
shifts it up by amount "d".
Your equation has b=1/3, so the graph is compressed by a factor of 1/3, which is equivalent to a stretch by a factor of 3.
The appropriate choice of description is ...
b) the graph of g(x) is horizontally stretched by a factor of 3
Answer:
B
Step-by-step explanation:
Correct on Plato
the city of James town is 2 meters below sea level. Takoradi, a city in western region, is 7 meters below sea level . How much higher is James town than Takoradi
Answer:
James town is 5 meters higher than Takoradi .
Step-by-step explanation:
Given:
Height of James town = 2 meters below sea level
Height of Takoradi town = 7 meters below sea level
To find:
How much higher is James town that Takoradi = ?
Solution:
As we can see the standard of height is how much the town is below the sea level.
So, the height of town having lesser value will be at a higher level.
Value of Height of James town is lesser than that of Takoradi town.
Therefore, James town is at a higher level.
Difference of height = 7 meters - 2 meters = 5 meters
So, the answer is:
James town is 5 meters higher than Takoradi.
Please help soon as possible! This is urgent! Match each expression with the correct description.
Answer:
Hey there!
q is 1, and n=-2.
q-n=1-(-2), which is 3.
n-q=-2=1, which is -3.
q is 1.
Thus, the least value is n-q, and the greatest value is q-n. Closest to zero would be q.
Let me know if this helps :)
Answer:
Least: n-q
Greatest: q-n
Closest to zero: q
Little bit more math hw
Answer:
[tex]x=-2[/tex]
Step-by-step explanation:
For these kind of problems, simply take the denominator and compare it to zero. Then solve the equation.
[tex]x+2=0\\\\\Rightarrow x=-2[/tex] By subtracting 2 from both sides!
Best Regards!
Show all work to solve 3x2 − x − 2 = 0.
Answer:
x=-2/3 and 1
Step-by-step explanation:
3x^2-x-2=0
(3x+2)(x-1)
3x=-2
x=-2/3
x=1
PLEASE HELP Weekly wages at a certain factory are
normally distributed with a mean of
$400 and a standard deviation of $50.
Find the probability that a worker
selected at random makes betweenh
$250 and $300.
Answer: 0.0215 .
Step-by-step explanation:
Let X denotes the weekly wages at a certain factory .
It is normally distributed , such that
[tex]X\sim N(\mu=400,\ \sigma= 50)[/tex]
Then, the probability that a worker selected at random makes between
$250 and $300:
[tex]P(250<X<300)=P(\dfrac{250-400}{50}<\dfrac{x-\mu}{\sigma}<\dfrac{300-400}{50})\\\\=P(\dfrac{-150}{50}<z<\dfrac{-100}{50})\ \ [z=\dfrac{x-\mu}{\sigma}]\\\\=P(-3<z<-2)\\\\=P(z<-2)-P(z<-3)\\\\=1-P(z<2)-(1-P(z<3))\\\\=P(z<3)-P(z<2)\\\\=0.9987-0.9772\\\\=0.0215[/tex]
Hence,the required probability = 0.0215 .
solve 3/4x+5=-9 please
Answer:
exact form: x=-56/3
mixed number form: -18 2/3
Solve for x by simplifying both sides of the equation, then isolating the variable.
F
19) The points (6,5), (7,2), (9,6), and (10,3) are vertices of an inscribed square.
A)(x - 8)2-(y - 4)2 = 5
B) (x – 8)2 + (y - 4)2 = 15
C) (X + 8)2 + (y + 4)2 = 5
D) (x - 8)2 + (y - 4)2 = 5
Find an equation for the circle
Answer:
The equation of circle is [tex](x-8)^2+(y-4)^2=5[/tex]
(D) is correct option.
Step-by-step explanation:
Given that,
Points (6,5), (7,2), (9,6) and (10,3) are vertices of an inscribed square.
We need to calculate the distance between (7,2) and (9,6)
Using formula of distance
[tex]d=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}[/tex]
Put the value into the formula
[tex]d^2=(9-7)^2+(6-2)^2[/tex]
[tex]d^2=20\ m[/tex]
The radius will be
[tex]r^2=\dfrac{20}{4}[/tex]
[tex]r^2=5[/tex]
We need to calculate the center of the point (7,2) and (9,6)
Using formula of center point
For x axis,
[tex]h=\dfrac{x_{2}+x_{1}}{2}[/tex]
Put the value into the formula
[tex]h=\dfrac{9+7}{2}[/tex]
[tex]h=\dfrac{16}{2}[/tex]
[tex]h=8[/tex]
For y axis,
[tex]k=\dfrac{y_{2}+y_{1}}{2}[/tex]
Put the value into the formula
[tex]k=\dfrac{6+2}{2}[/tex]
[tex]k=\dfrac{8}{2}[/tex]
[tex]k=4[/tex]
We need to find the equation for the circle
Using formula of equation of circle
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Put the value into the formula
[tex](x-8)^2+(y-4)^2=5[/tex]
Hence, The equation of circle is [tex](x-8)^2+(y-4)^2=5[/tex]
(D) is correct option.
Please answer this correctly without making mistakes
Answer:
10 9/20
Step-by-step explanation:
Hey there!
If Hillsboro to Campbell is 16 2/20 and Hillsboro to Oxford is 5 13/20,
we’ll do
16 2/20 - 5 13/20
Imrpoper form
322/20 - 113/20
322 - 113
209/20
10 9/20 miles from Oxford to Campbell.
Hope this helps :)
PLZ HELP 55 POINTS Two quantities, x and y, are related proportionally such that 3x=2y . Which equation shows the same proportional relationship? A x/y=3/2 B x/2=y/3 C x/3=y/2 D x/2=3/y
Answer:
B
Step-by-step explanation:
3x = 2y
One way to solve this is to simply plug in values. If we say the following:
x = 2
y = 3
Then, we can start testing.
A: [tex]x/y = 3/2[/tex]
by plugging 2 and 3 in, we see that A doesn't work.
B: x/2 = y/3
This works! First we should look at the other equations.
C: x/3 = y/2
Nope.
D: x/2 = 3/y
This also works, but only with certain numbers. If we were to make x = 4, and y = 6, this wouldn't work.
You could also find out all of this using algebra. so, our anwser is B.
in the diagram, POS and UOR are straight lines. OQ is the bisector of angle POR . angle POU and angle UOT are complementary angles.Find the values ofx abd y.
Answer:
x = 34° and y = 62°
Step-by-step explanation:
Complementary angles sum to 90°, therefore 90 = 56 + x which means that x = 34°. The angles formed by an angle bisector are congruent and so are vertical angles; this means that ∠SOR = ∠POU = 56° and ∠POQ = ∠QOR = y. Since POS is a straight line, straight lines have a measure of 180° and because ∠POS = ∠POQ + ∠QOR + ∠SOR, we know that 180 = y + y + 56 → 180 = 2y + 56 → 180 → 2y = 124 → y = 62°.
Laura is bowling 5 games. Her first 4 scores were 135, 144, 116, and 132.
To end up with an average score of at least 136.8, what is the lowest score Laura will need in the fifth game?
Answer:
157
Step-by-step explanation:
135+144+116+132=527
527+136.8=762.8
762.8÷5= 157
I need help with this!
Answer:
i) [tex]\frac38\pi[/tex]
ii) n = 33
Step-by-step explanation:
For this question you can actually focus on the sine, and forget about the e power. The x-coordinates of the extremes of the curve will be the same as for y=sin(4x)
i) equivalent to solving sin(4x) = -1, so 4x = 3/2 pi, x=3/8 pi
ii) The Tn values are at x = (n·π - π/2)/4
solving (n·π - π/2)/4 > 25 gives:
n > 1/2 + 100/π, so n > 32.331, but n must be integer, so we get n=33
A football field has the shape of a rectangle with dimensions of 300 feet long and 160 feet wide. If a fan was to run diagonally from one end zone to the opposite end zone, how far would she run to the nearest foot? Enter only the number.
Answer:
340 feet
Step-by-step explanation:
we use Pythagora
d² = l² + w²
d = √300ft)² + 160ft)²
= √90000ft² + 25600ft²
= √115600ft²
= √(2⁴ₓ5²ₓ17²)ft²
= √(2²ₓ5ₓ17)ftₓ(2²ₓ5ₓ17)ft
= √340ftₓ340ft
= 340 feet
Log 1/10 how do you convert this without a calculator
Answer:
log(1/10) = -1
Step-by-step explanation:
Use the law of exponents and the meaning of logarithm.
1/10 = 10^-1
log(10^x) = x
So, you have ...
log(1/10) = log(10^-1)
log(1/10) = -1
Calculate the surface area of this composite shape.
Answer:
1284 m^2
Step-by-step explanation:
Front face and back face:
2 * [28 m * 5 m + (22 m - 5 m) * 6 m] = 484 m^2
Left face and right face:
2 * 22 m * 8 m = 352 m^2
Bottom face and top face:
2 * 28 m * 8 m = 448 m^2
total surface area = 484 m^2 + 352 m^2 + 448 m^2 = 1284 m^2
Find the length S of the spiral (t cos(t), t sin(t)) for 0 ≤ t ≤ 3π. (Round your answer to three decimal places.) S =
The arc length is
[tex]S=\displaystyle\int_C\mathrm ds[/tex]
where C is the given curve and ds is the line element. C is defined on 0 ≤ t ≤ 3π by the vector function,
[tex]\mathbf r(t)=(t\cos t,t\sin t)[/tex]
so the line element is
[tex]\mathrm ds=\left\|\dfrac{\mathrm d\mathbf r(t)}{\mathrm dt}\right\|\,\mathrm dt[/tex]
[tex]\mathrm ds=\sqrt{\left(\dfrac{\mathrm d(t\cos t)}{\mathrm dt}\right)^2+\left(\dfrac{\mathrm d(t\sin t)}{\mathrm dt}\right)^2}\,\mathrm dt[/tex]
[tex]\mathrm ds=\sqrt{1+t^2}\,\mathrm dt[/tex]
So we have
[tex]S=\displaystyle\int_0^{3\pi}\sqrt{1+t^2}\,\mathrm dt\approx46.132[/tex]
If f(x)=4x-6 and g(x) vx+2 what is (f*g)(7)
Answer: The value of (f*g)(7) is 66.
Step-by-step explanation:
Given functions: [tex]f(x)= 4x-6\text{ and } g(x)=\sqrt{x+2}[/tex]
Since, product of two functions: [tex](u*v)(x)=u(x)\times v(x)[/tex]
[tex](f*g)(x)=f(x)\times g(x)\\\\=4x-6\times \sqrt{x+2}\\\\\Rightarrow\ (f*g)(x)=(4x-6) \sqrt{x+2}[/tex]
[tex](f*g)(7)=(4(7)-6)\sqrt{7+2}\\\\=(28-6)\sqrt{9}\\\\=22\times 3=66[/tex]
Hence, the value of (f*g)(7) is 66.
Find the sum of the first 12 terms of the sequence 512, 256, 128, … This is infinite series notation, the answer is NOT 896...
Answer:
1023.75
Step-by-step explanation:
The sum of a geometric sequence is
sum = a( 1 - r^n) / (1-r)
where a is the first term r is the common ratio and r^n is the nth term
We need to find the common ratio
r = 256/512 = 1/2
sum = 512 ( 1 - 1/2^12) / ( 1-1/2)
=512( 1-.000244141) / (.5)
=512(.999755859) /.5
=1023.75
Answer:
1023.75
Step-by-step explanation:
sum = a( 1 - r^n) / (1-r)
a1 = 512
n = 12
r = 256 / 512 = 1/2
512 (1 - 1/2¹²)
therefore.. sum = ------------------ = 1023.75
1 - 1/2
What is the number of square units in the area of the triangle whose vertices are points A(2,0), B(6,0), and C(8,5)?
10 units squared. Hope this helped.
The area of the triangle is 10 square units.
The given coordinates are A(2,0), B(6,0), and C(8,5).
What is the formula to find the area of a triangle?The formula of area of triangle formula in coordinate geometry is the area of the triangle in the coordinate geometry is: [tex]A=\frac{1}{2} |x_{1} (y_{2}-y_{3})+x_{2} (y_{3}-y_{1})+x_{3} (y_{1}-y_{2})|[/tex]
Now, Area=1/2|2(0-5)+6(5-0)+8(0-0)|=0.5|20|
=10 square units
Therefore, the area of the triangle is 10 square units.
To learn more about the area of the triangle visit:
https://brainly.com/question/11952845.
#SPJ2
Find the degree, leading coefficient, and the constant term of the polynomial.
[tex] \LARGE{ \boxed{ \purple{ \rm{Answers;)}}}}[/tex]
☃️ Degree of the polynomial- The highest degree of any term in a polynomial. Here the highest degree is 5.
⇛ 4x⁴ + 5 + 6x⁵ - 2x(° of polynomial = 5)
☃️ Leading coefficient- The coefficient of the term having the highest degree of the polynomial. Here, the highest degree is 5 and the term is 6x⁵
⇛ 4x⁴ + 5 + 6x⁵ - 2x (Leading coeff. = 6)
☃️ Constant term- It is the term having no coefficients, only a fixed real number. This remains constant in any value of polynomial.
⇛ 4x⁴ + 5 + 6x⁵ - 2x (Constant term = 5)
━━━━━━━━━━━━━━━━━━━━
How many adults must be randomly selected to estimate the mean FICO (credit rating) score of working adults in a country? We want % confidence that the sample mean is within points of the population mean, and the population standard deviation is .
Answer: hello below is the complete question
How many adults must be randomly selected to estimate the mean FICO (credit rating) score of working adults in a country? We want 90% confidence that the sample mean is within 4 points of the population mean, and the population standard deviation is 66. Round up to the nearest whole number
answer : 737 adults
Step-by-step explanation:
confidence interval = 90% = 0.9
( E ) = 4
standard deviation = 66
first we have to calculate the value of a
a = 1 - confidence interval
= 1 - 0.9 = 0.10 hence a / 2 = 0.05
next find the value of Z a/2 from table
Z[tex]_{0.05}[/tex] = 1.645
The number of Adults selected can be determined using this relation
N = [tex](Z_{a/2} * (s/E))^2[/tex]
= [tex](Z_{0.05} * ( 66/4))^2[/tex]
= 737
The Brooklyn Burn is a small company that makes and sells hot sauces. The profit that The
Brooklyn Burn makes in a month from its “Buckingham Burn" hot sauce can be measured using
the following function:
y=6x - 200
where x is the number of bottles of "Buckingham Burn" hot
sauce sold, and y is the profit in dollars for the month.
Using this function and its context involving sales of hot
sauce), describe the meaning of the numbers shown in the
table at the right.
150
700
Answer:
I know the answer
Step-by-step explanation:
If we use 150 the answer would be 6(150) - 200 = 700. The answer is 200.
Brooklyn Burn sold 150 bottles of hot sauce every month, 700 is the profit they make eachmonth.
The miss Petra psychic hotline charges 5$ For the first minute and 2$ for each additional minute. Give an equation the describes the situation
Answer:
y=2(x-1)+5
Step-by-step explanation:
We know that it is 5 dollars for the first minute so we know the equation will start off with +5.
Than for the rest of the minutes, we have to make sure to subtract one from them, because the first number is worth 3 dollars more. Which is why it is x-1.
Then we multiply the new value times 2, because each additional minute is 2 dollars more.
