What is the quotient of 7.14 x 10^7 and 4.2 x 10^3 expressed in scientific notation?

Answer:

196

Step-by-step explanation:

Using the z-distribution, as we are working with a proportion, it is found that 1016 constituents are required.

A confidence interval of proportions is given by:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which:

The margin of error is given by:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

The estimate is of [tex]\pi = 0.61[/tex], while the margin of error is of M = 0.03, hence solving for n we find the minimum sample size.

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.03 = 1.96\sqrt{\frac{0.61(0.39)}{n}}[/tex]

[tex]0.03\sqrt{n} = 1.96\sqrt{0.61(0.39)}[/tex]

[tex]\sqrt{n} = \frac{1.96\sqrt{0.61(0.39)}}{0.03}[/tex]

[tex](\sqrt{n})^2 = \left(\frac{1.96\sqrt{0.61(0.39)}}{0.03}\right)^2[/tex]

[tex]n = 1015.5[/tex]

Rounding up, 1016 constituents are required.

More can be learned about the z-distribution at https://brainly.com/question/25890103

Answer:

Point form=(-6,-2)

Equation Form= x=-6, y=-2

Step-by-step explanation:

Step-by-step explanation:

Step by Step Solution



STEP1:Equation at the end of step 1

STEP2:

22b5 Simplify ———— 9b

Dividing exponential expressions :

 2.1    b5 divided by b1 = b(5 - 1) = b4

Final result :

4b4 ——— 9

Answer:
Hope this helps <3

Step-by-step explanation:

(I color coded them and named them for you so that you wouldn’t have trouble with finding the points <3)

Answer:

15 and -26.

Step-by-step explanation:

Answer:

15 and -26

Step-by-step explanation:

just bc

Check the picture below.

well, is an isosceles trapezoid, namely the slanted sides are equal, so the diagonals, in red, are also equal, so let's just find the length of the solid line diagona, since the dashed one will be the same length anyway.

[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-5}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{1})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[2 - (-5)]^2 + [1 - (-1)]^2}\implies d=\sqrt{(2+5)^2+(1+1)^2} \\\\\\ d=\sqrt{7^2+2^2}\implies d=\sqrt{53}\implies d\approx 7.28[/tex]

Answer:

1/21

Step-by-step explanation:

We start with 7 cards. The probability of picking a 4 is 1/7. Since the first card is not put back, there are 6 cards left. Of these 6 cards, there are two which have divisors of 63: 3 and 7. So the probability of picking a divisor of 63 is 2/6, which reduces to 1/3. Multiplying these probabilities gives 1/21.

Answer:

157.08 ft

Step-by-step explanation:

R = 20+5 = 25

Circumfrence = 2*pi*r = 2*pi*25 = 157.079 ft

Answer:

Deductible

Step-by-step explanation:

you pay the first $1,000 of covered services yourself

$1000 represents the deductible amount.

In the case of an accident, the policyholder must pay a deductible as the first amount; the insurance company will only cover any expenses (losses) incurred after the deductible has been paid by the policyholder.

The consumer can first set his deductible while purchasing insurance.

Smaller deductibles often result in higher rates, and larger deductibles frequently result in lower premium payments.

The insurance company has asked Manny to pay the first $1000 in an instance when he was involved in an accident and incurred charges totaling $11,500. The $1,000 deductible amount.

Hence, the answer is deductible amount.

Learn more about deductible amount here:

https://brainly.com/question/30098276

#SPJ6

Answer: $ 27.27

Step-by-step explanation:

Answer:

62.59

Step-by-step explanation:

Answer:

6x3=18 pieces

6/18 = 1/3

=

18 pieces

72 inches

Answer:

d

Step-by-step explanation:

The answer must be a multiple of 4, because 4q⁵rs⁴ is divisible by 4. Only option d has this condition.

Answer:

-3(x-2)×2+17=0

1. Area of sector is 14.14 sq.m

2. Length of the missing side is 10 cm

Using formula:

Where,

Substituting the required values:

→ Area = 45°/360° × 22/7 × (6)²

→ Area = 0.125 × 22 × 36/7

→ Area = 2.75 × 36/7

→ Area = 99/7

→ Area = 14.14 sq.m

In given right angled traingle:

Using Pythagoras theorem,

where,

Substituting the required values:

→ (Hypotenuse)² = (8)² + (6)²

→ (Hypotenuse)² = 64 + 36

→ (Hypotenuse)² = 100

→ Hypotenuse = √100

→ Hypotenuse = 10 cm

Hence,

Answer:

C.80

Step-by-step explanation:

37.9% of 192.3

=37.9/100 × 192.3

=0.379×192.3

=72.8817

≈80 (possible answer)

Answer:

32+4x(16x)-12=

32+64x-12=

64x-12+32=64x+20

64×÷64÷=20÷64=

x=0.3125

Answer:

Step-by-step explanation:

7) 2ab + 4ac = 2*a*b + 2 *2 *a*c

                     = 2a(b + 2c)

[tex]\dfrac{2ab^{2}c}{2ab+4ac}=\dfrac{2*a* b^{2}*c}{2a(b+2c)}\\\\\\\text{2a in the denominator and numerator get cancelled}\\\\ = \dfrac{b^{2}c}{b+2c}[/tex]

8) ac - a²c² = c( a - a²c)

bc - abc     = c(b - ab)

[tex]\dfrac{ac - a^{2}c^{2}}{bc-abc^{2}}=\dfrac{c(a-a^{2}c)}{c(b-ab)}\\\\[/tex]

               [tex]=\dfrac{a-a^{2}c}{b-abc}[/tex]

9) b²+ 4b - 5 = b² + 5b - 1b - 5

                    = b(b + 5) - 1(b + 5)

                    = (b +5)(b - 1)

b² + 8b  + 15 = b² + 5b + 3b + 15

                    = b(b + 5) + 3(b + 5)

                    = (b + 5 )(b + 3)

[tex]\dfrac{b^{2}+4b-5}{b^{2}+8b+15}=\dfrac{(b+5)(b-1)}{(b+5)(b+3)}\\\\\\[/tex]

                     [tex]=\dfrac{b-1}{b+3}[/tex]

Answer:

50

Step-by-step explanation:

add

9 + 1 = 10

multiply

10 * 5 = 50

Answer: 50

Answer: 666.22 m^3

Step-by-step explanation:

The formula for the volume of a right circular cone is: V = π*r^2*(h/

3)

Therefore, plugging in 14.1 for "r" and 3.2 for "h" yields 666.22

Answer:

(x - 2)(x - 1)(x + 1)(x + 2)

Step-by-step explanation:

[tex] {x}^{4} - 5 {x}^{2} + 4 \\ \\ = {x}^{4} - 4 {x}^{2} - {x}^{2} + 4 \\ \\ = {x}^{2} ( {x}^{2} - 4) - 1( {x}^{2} - 4) \\ \\ = ( {x}^{2} - 4)( {x}^{2} - 1) \\ \\ = (x + 2)(x - 2)(x + 1)(x - 1) \\ \\ = (x - 2)(x - 1)(x + 1)(x + 2)[/tex]

Answer:

[tex](x+1)(x-1)(x+2)(x-2)[/tex]

Step-by-step explanation:

To factorise  [tex]x^4-5x^2+4[/tex] :

Let [tex]x^2=u[/tex]

[tex]\implies x^4-5x^2+4=u^2-5u+4[/tex]

Now factorise  [tex]u^2-5u+4[/tex]

[tex]\textsf{for} \ ax^2+bx+c \ \textsf{find} \ v, w \ \textsf{such that} \ v \cdot w=a \cdot c \ \textsf{and} \ v+w=b[/tex]

[tex]\textsf{and group into} \ (ax^2+vx)+(wx+c)[/tex]

[tex]\implies v=-1, w=-4[/tex]

[tex]\implies u^2-u-4u+4[/tex]

Break into groups

[tex]\implies (u^2-u)+(-4u+4)[/tex]

Factor each parentheses:

[tex]\implies u(u-1)-4(u-1)[/tex]

Factor out common term [tex](u-1)[/tex]:

[tex]\implies (u-1)(u-4)[/tex]

Substitute back [tex]u=x^2[/tex] :

[tex]\implies (x^2-1)(x^2-4)[/tex]

Factor both parentheses using the Difference of Two Squares: [tex]a^2-b^2=(a+b)(a-b)[/tex]

[tex]\implies (x+1)(x-1)(x+2)(x-2)[/tex]

Therefore, the factorisation of [tex]x^4-5x^2+4[/tex] is

[tex](x+1)(x-1)(x+2)(x-2)[/tex]

Answer:

20+2C

Step-by-step explanation:

sum means addition

if Craig's age is c than twice his age is 2xC, also expressed as 2C

20+2C

Answer:

8.7kilos

Step-by-step explanation:

70.22 divided by 8

hope this helps!

[tex]\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2 \qquad \begin{cases} c=\stackrel{hypotenuse}{11 + x}\\ a=\stackrel{adjacent}{x}\\ b=\stackrel{opposite}{17}\\ \end{cases}\implies (11+x)^2=x^2+17^2 \\\\\\ (11+x)(11+x)=x^2+17^2\implies \stackrel{F~O~I~L}{121+22x+x^2}~~ = ~~x^2+289 \\\\\\ 121+22x=289\implies 22x=168\implies x=\cfrac{168}{22}\implies x=\cfrac{84}{11}\implies x=7\frac{7}{11}[/tex]

Answer:

x ≈ 5.8 degrees

Step-by-step explanation:

the sum of all exterior of any polygon is 180 degrees

so:  7x+4 + 5x+4 + 4x+9 + 9x-6 + 4x+1 =  180

combine 'like terms':

29x + 12 = 180

29x = 168

x ≈ 5.8

Answer:

Brand B is better

Step-by-step explanation:

Brand A's unit price is $0.24

Brand B's unit price is $0.21

Answer:

$120

Step-by-step explanation:

Total Parts = 3+2+5 = 10

400 / 10 = $40 per part

Amy = 40 x 3 = 120