Find the total amount
$20,700 at 9% compounded
semiannually for 4 years

Step-by-step explanation:

the original side length is x.

the volume of a block is length × width × height.

so, for a cube with all sides being equal, the volume in our case is x³ (x × x × x).

now, with the same formula but with every side shortened by 1 cm we get

(x-1)(x-1)(x-1) = x³ - 91 (the original volume minus 91)

now, we have to do the multiplications.

(x-1)(x-1) = x² - 2x + 1

(x²-2x+1)(x-1) = x³ - x² - 2x² + 2x + x - 1 = x³ -3x² + 3x -1

x³ - 3x² + 3x - 1 = x³ - 91

-3x² + 3x = -90

-x² + x = -30

x² - x = 30

x² - x - 30 = 0

the general solution to such a squared equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

a = 1

b = -1

c = -30

x = (1 ± sqrt((-1)² - 4×1×-30))/(2×1) =

= (1 ± sqrt(1 + 120))/2 = (1 ± sqrt(121))/2 =

= (1 ± 11)/2

x1 = (1 + 11)/2 = 12/2 = 6

x2 = (1 - 11)/2 = -10/2 = -5

a negative number does not make any sense for a side length, so our solution is x = 6 cm.

the original side length of the cube is 6 cm.

to check :

6³ = 216

(6-1)³ = 5³ = 125

216 - 125 = 91

perfect.

Answer: $ 27.27

Step-by-step explanation:

Answer:

62.59

Step-by-step explanation:

Answer:

32+4x(16x)-12=

32+64x-12=

64x-12+32=64x+20

64×÷64÷=20÷64=

x=0.3125

Answer:

157.08 ft

Step-by-step explanation:

R = 20+5 = 25

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

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

I know you're looking for an answer but i'm doing a challenge where i have to answer 10 questions by the end of today, I'm sorry! :(

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:

$120

Step-by-step explanation:

Total Parts = 3+2+5 = 10

400 / 10 = $40 per part

Amy = 40 x 3 = 120

Answer:

8.7kilos

Step-by-step explanation:

70.22 divided by 8

hope this helps!

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:

Point form=(-6,-2)

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

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

a^2 + b^2 = c^2

in this case 24 is a and 30 is c

24^2 = 576

30^2 = 900

900 - 576 = 324

the square root of 324 is 18

Answer:

3.0625[tex]\pi[/tex] ft^2

Step-by-step explanation:

A=[tex]\pi[/tex]r^2

A=[tex]\pi[/tex]1.75^2

A=3.0625[tex]\pi[/tex]

3.0625[tex]\pi[/tex] ft^2

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:

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:

6x3=18 pieces

6/18 = 1/3

=

18 pieces

72 inches

Answer:

-3(x-2)×2+17=0

Answer: A)72.8067226km/hr (final asnwer)
b) volume of a cube= a^3 (sides^3) =4.5^3= 91.125 cm^3 (final asnwer)

c) 1 day cost= $(35.9 +11.55 + 35) =$82.45
therefore for 5 days= $82.45 * (multiplied) by 5 = $412.25 (final asnwer)

Step-by-step explanation:

Answer:

(a)≈72.8 kilometer per hour

(b)91.125 cm^3

(c)272.25$

Step-by-step explanation:

(a)speed=mile/hour

=371mile/8.2hours

=371×1.609kilometers/8.2hours

≈72.8 kilometer per hour

(b)the vol: of cube= a^3 (a=side)

=(4.5)^3

=91.125cm^3

(c) for 5 days, (35.9×5)+(11.55×5)+35 ($35 is ofor one-off charge so there is no need to multiply with 5)

=272.25$

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:

nothing

Step-by-step explanation:

2cups= orange juice

1 cup= cranberry juice

nothing the orange and juice was used to make the mixture of juice

Answer:

its nothing??

Step-by-step explanation:

you gave it to mags so its nothing

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:

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:

[tex]\huge\boxed{\sf x = 10}[/tex]

Step-by-step explanation:

Since the two angles are complementary angles, the measures of these angles add up to 90 degrees.

5x + 25 + x + 5 = 90

5x + x + 25 + 5 = 90

6x + 30 = 90

Subtract 30 to both sides

6x = 90 - 30

6x = 60

Divide 6 to both sides

x = 60 / 6

x = 10

[tex]\rule[225]{225}{2}[/tex]

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

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:

The answer would be B. c ÷ 158.14

Step-by-step explanation:

i just took this test :) the question was:

The space shuttle carries c pounds of cargo, and each piece of cargo weighs 158.14 pounds. Which of the following expressions represents the number of pieces of cargo The space shuttle carries c pounds of cargo, and each piece of cargo weighs 158.14 pounds? Which of the following expressions represents the number of pieces of cargo?

A. c × 158.14

B. c ÷ 158.14

C. c - 158.14

D. c + 158.14

Answer: 1/3

Step-by-step explanation: 50, and 90, 2/6 reduces to 1/3.................2 pp ignore the 2 and p I'm in mobile

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