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3 years ago

Solve: 2/3 - 4x + 7/2 = -9x + 5/6

Mathematics

2 answers:

sesenic [268]3 years ago

5 0

Standard form:
5x + 10/3

= 0
Factorization:
5/3

(3x + 2) = 0
Solutions:
x = −20/
30
≈ −0.666667

umka2103 [35]3 years ago

3 0

Solve by simplifying both sides of the equation, then isolating the variable.
x=-2/3

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What is 380 increased by 18%

Triss [41]

First you divide 380 by 100 to get what 1% is, (3.8) and then you multiply by 18 to give you 18%. The answer is 68.4, so add that to 380 and you'll have the final answer of 448.4.

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4 years ago

(a) A poll of 2,298 likely voters was conducted on the president’s performance. Approximately what margin of error would the app

SashulF [63]

Answer:

a.d= 0.0204

b.[0.4728;0.5072]

c.A.Yes, the confidence interval contains .50.

Step-by-step explanation:

Hello!

you have a sample of 2298 voters and the sample proportion of voters that agree with the president's performance is 49%, which means that the sample proportion of voters that oppose the president will be 51%.

a) The margin of error for a 95% CI to estimate the proportion of voters that approve the president.

The formula for the CI for the proportion is:

^ρ± $Z_{1-\alpha/2}$ *√(^ρ(1-^ρ))/n

The margin of error "d" is half the amplitude of the interval (or, to put it simply, is what you subtract and add to the sample proportion)

d= $Z_{0.975}$ *√(^ρ(1-^ρ))/n

d= 1.96*√(0.49(1-0.49))/2298

d= 0.0204

b) Construct a 90% CI for the true proportion

[^ρ± $Z_{1-\alpha/2}$ *√(^ρ(1-^ρ))/n]

[0.49±1.648*√(0.49(1-0.49))/2298]

[0.4728;0.5072]

c) The CI interval I've made in b. is for the voters that agree with that president, but since you want to see if the proportion of people on favor/opposing is 0.50 whether the interval is made with the information of the people who agree or oppose doesn't change the answer.

The interval contains 0.50 if you were to make the hypothesis that the proportion of people who agree with the president H₀:ρ=0.50, at complementary confidence level α: 0.10, you can say that the proportion of people who agree with the president is 50%. Then you can also say that the proportion of opposition voters is 50%.

I hope you have a SUPER day!

8 0

4 years ago

50 POINTS 10 QUESTIONS! Solve each quadratic equation using factoring PLEASE HELP!!

Tanzania [10]

Answer:

Quadratic Equation | Factoring

Solve each quadratic equation using factoring.

1) v² + 5v + 6 = 0

doing middle term factorisation

v²+(3+2)v+6=0

v²+3v+2v+6=0

v(v+3)+2(v+3)=0

(v+3)(v+2)=0

either

v=-3

or

v=-2

2) g² - 3g = 4

keeping all terms in one side

g²-3g-4=0

doing middle term factorisation

g²-(4-1)g-4=0

g²-4g+g-4=0

g(g-4)+1(g-4)=0

(g-4)(g+1)=0

either

g=4

or

g=-1

3)w² + 4w = 0

w(w+4)=0

either

w=0

or

w=-4

4) s² - 8s + 12 = 0

doing middle term factorisation

s²-(6+2)+12=0

s²-6s-2s+12=0

s(s-6)-2(s-6)=0

(s-6)(s-2)=0

either

s=6

or

s=2

5) x ²+ 2x - 35 = 0

doing middle term factorisation

x²+(7-5)x-35=0

x²+7x-5x-35=0

x(x+7)-5(x+7)=0

(x+7)(x-5)=0

either

x=-7

or

x=5

6) r(r + 2) = 99

opening bracket

r²+2r=99

keeping all terms in one side

r²+2r-99=0

r²+(11-9)r-99=0

r²+11r-9r-99=0

r(r+11)-9(r+11)=0

(r+11)(r-9)=0

either

r=-11

or

r=9

7)k(k-4)=-3

opening bracket

k²-4k=-3

keeping all terms in one side

k²-4k+3=0

k²-(3+1)k+3=0

k²-3k-k+3=0

k(k-3)-1(k-3)=0

(k-3)(k-1)=0

either

k=3

k=1

8)t²+ 3t + 2 = 0

doing middle term factorisation

t²+(2+1)t+2=0

t²+2t+t+2=0

t(t+2)+1(t+2)=0

(t+2)(t+1)=0

either

t=-2

or

t=-1

9)m ^ 2 - 81 = 0

m²=81

doing square root in both side

$\sqrt{m²}=\sqrt{9²}$

m=±9

either

m=9

or

m=-9

10) h²- 17h + 70 = 0

doing middle term factorisation

h²-(10+7)h+70=0

h²-10h-7h+70=0

h(h-10)-7(h-10)=0

(h-10)(h-7)=0

either

h=10

or

h=7

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3 years ago

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Answer:

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