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3 years ago

Question 7 of 10

Mathematics

1 answer:

Mama L [17]3 years ago

8 0

Answer:

Step-by-step explanation:

Given a quadratic equation in standard form

ax² + bx + c = 0 ( a ≠ 0 )

Then the discriminant is

Δ = b² - 4ac

• If b² - 4ac > 0 then 2 real irrational roots

• If b² - 4ac > 0 and a perfect square then 2 real rational roots

• If b² - 4ac = 0 then 1 real double root

• If b² - 4ac < 0 then 2 complex roots

Given

x² + 3x - 7 = 0 ← in standard form

with a = 1, b = 3, c = - 7 , then

b² - 4ac

= 3² - (4 × 1 × - 7) = 9 + 28 = 37

Since b² - 4ac > 0 then 2 real irrational roots

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P and q are on a number line. If p has a coordinate -5 and pq =7 , what could the coordinate of p be

liraira [26]

2 and -12 are the coordinates of p

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4 years ago

A survey reported in Time magazine included the question ‘‘Do you favor a federal law requiring a day waiting period to purchase

il63 [147K]

Answer:

The 90% confidence interval for the difference between proportions is (-0.260, -0.165).

Step-by-step explanation:

The question is incomplete. The complete question is:

"A survey reported in Time magazine included the question ‘‘Do you favor a federal law requiring a 15 day waiting period to purchase a gun?” Results from a random sample of US citizens showed that 318 of the 520 men who were surveyed supported this proposed law while 379 of the 460 women sampled said ‘‘yes”. Use this information to find a 90% confidence interval for the difference in the two proportions, pm - pw. Subscript pm is the proportion of men who support the proposed law and pw is the proportion of women who support the proposed law. (Round answers to 3 decimal places.)"

We want to calculate the bounds of a 90% confidence interval.

For a 90% CI, the critical value for z is z=1.645.

The sample of men, of size nm=-0.26 has a proportion of pm=0.612.

$p_m=X_m/n_m=318/520=0.612$

The sample 2, of size nw= has a proportion of pw=0.824.

$p_w=X_w/n_w=379/460=0.824$

The difference between proportions is (pm-pw)=-0.212.

$p_d=p_m-p_w=0.612-0.824=-0.212$

The pooled proportion, needed to calculate the standard error, is:

$p=\dfrac{X_m+X_w}{n_m+n_w}=\dfrac{318+379}{520+460}=\dfrac{697}{980}=0.711$

The estimated standard error of the difference between means is computed using the formula:

$s_{pm-pw}=\sqrt{\dfrac{p(1-p)}{n_m}+\dfrac{p(1-p)}{n_w}}=\sqrt{\dfrac{0.711*0.289}{520}+\dfrac{0.711*0.289}{460}}\\\\\\s_{pm-pw}=\sqrt{0.00039+0.00045}=\sqrt{0.001}=0.029$

Then, the margin of error is:

$MOE=z \cdot s_{pm-pw}=1.645\cdot 0.029=0.0477$

Then, the lower and upper bounds of the confidence interval are:

$LL=(p_1-p_2)-z\cdot s_{p1-p2} = -0.212-0.0477=-0.260\\\\UL=(p_1-p_2)+z\cdot s_{p1-p2}= -0.212+0.0477=-0.165$

The 90% confidence interval for the difference between proportions is (-0.260, -0.165).

6 0

3 years ago

If I have a line that starts at the origin (0,0), and goes 13 meters at an angle of π/6 in the standard position (ie. 30° north

Klio2033 [76]

Line goes 11.2583303 meters in the x direction (east) and 7.5 meters in the y direction (north) .

Step-by-step explanation:

Here we have , If I have a line that starts at the origin (0,0), and goes 13 meters at an angle of π/6 in the standard position (i.e. 30° north of east) . We need yo find how far does it go in the y direction (north), and how far does it go in the x direction (east). Let's find out:

According to question we have a right angle triangle as :

$Hypotenuse =13m\\x=\frac{\pi}{6} =30$

x direction (east)

We know that ,

⇒ $cosx = \frac{Base}{Hypotenuse}$

⇒ $cos30 = \frac{Base}{13}$

⇒ $\frac{\sqrt{3} }{2} = \frac{Base}{13}$

⇒ $Base=\frac{\sqrt{3}(13) }{2} m$

⇒ $Base=11.2583303m$

y direction (North )

We know that ,

⇒ $sinx = \frac{Perpendicular}{Hypotenuse}$

⇒ $sin30 = \frac{Perpendicular}{13}$

⇒ $\frac{1}{2} = \frac{Perpendicular}{13}$

⇒ $Perpendicular=7.5m$

Therefore , Line goes 11.2583303 meters in the x direction (east) and 7.5 meters in the y direction (north) .

8 0

4 years ago

PLEASE HELP ME!?!?!?!?!

melisa1 [442]

Part 1:

A. Like terms must have the same variable and exponent.

B. Give an example of two terms that cannot be combined: 7c and 4b

C. Write one complete sentence to explain why the two terms you wrote cannot be combined: 7c and 4b cannot be combined because they have different variables, and are therefore not like terms.

D. Use distributive property: 2(-4 + 6.1) + 3(5 - x)

2 * -4 = -8

2 * 6.1 = 12.2

-8 + 12.2 + 3(5 - x)

3 * 5 = 15

3 * x = 3x

-8 + 12.2 + 15 -3x

-8 + 12.2 = 4.2

4.2 + 15 = 19.2

19.2 - 3x is the simplest version.

Part 2:

A. Thor is wrong because, in step 4, he subtracted to isolate the variable when he should have divided.

B. 4x + 9 = 6

Step 1: 4x + 9 - 9 = 6 - 9

Step 2: 4x = -3

Step 3: 4x/4 = -3/4

Step 4: x = -0.75

6 0

3 years ago

Plz solve for the area, questions 10,11,and 12 plz

marishachu [46]

Answer:

10-52.85ft squared 11-144.84centimeters squared 12-304meters squared

Step-by-step explanation:

A-bh/2 10-7*15.1=105.7/2=52.85ft squared

A-bh 11-10.2*14.2=144.84cenitmeters squared

A-bh 20*15.2=304meters squared

4 0

3 years ago