Mariana baked 14 cakes. She gave 1/7 of them to her family before she took the rest to a party. How many cakes did Mariana give to her family?

Answer:

c.

0.1824

Step-by-step explanation:

The computation of the decay factor is as follows;

= (1 - decrease percentage) × (1 - decrease percentage) × (1 - decrease percentage)

= (1 - 0.2) × (1 - 0.4) × (1 - 0.62)

= (0.8) × (0.6) × (0.38)

= 0.1824

hence, the decay factor is 0.1824

Therefore the option c is correct

Answer:

[tex]-\frac{3 \cdot cos^2x}{(1+sinx)^3}[/tex]

Step-by-step explanation:

[tex]y = (\frac{cosx}{1+sinx})^3\\\\\frac{dy}{dx} = 3 \cdot (\frac{cosx}{1+sinx})^2 \cdot \frac{dy}{dx}(\frac{cosx}{1+sinx})[/tex]                        [tex][ y = x^n\ \ \ => \ \ \ \frac{dy}{dx} = b \cdot x^{n-1} \ ][/tex]

    [tex]= 3 \cdot (\frac{cosx}{1+sinx})^2 \cdot \frac{(1+sin x(-sinx) - cosx(cosx)}{(1+sinx)^2}\\\\[/tex]     [tex][\ \frac{u}{v} = \frac{v \dcot u'- u \cdot v'}{v^2}\ ][/tex]

    [tex]= 3 \cdot (\frac{cosx}{1+sinx})^2 \cdot \frac{-sin x-sin^2x- cos^2x}{(1+sinx)^2}\\\\= 3 \cdot (\frac{cosx}{1+sinx})^2 \cdot \frac{-sin x- (sin^2x+ cos^2x)}{(1+sinx)^2}\\\\= 3 \cdot (\frac{cosx}{1+sinx})^2 \cdot \frac{-sin x-1}{(1+sinx)^2}\\\\= 3 \cdot (\frac{cosx}{1+sinx})^2 \cdot \frac{-1 \cdot(sin x+1)}{(1+sinx)^2}\\\\= 3 \cdot (\frac{cosx}{1+sinx})^2 \cdot \frac{-1}{(1+sinx)}\\\\[/tex]

   [tex]= -3 \cdot \frac{cos^2x}{(1+sinx)^3}[/tex]

Answer:

C(min) = 0.5*V  +  √V/1.256  $

Step-by-step explanation:

The volume of a circular cylinder is: V(c)  = π*r²*h    where r is the radius of the circumference of the base and h is the height

The cost of the can is = the cost of (base and top) + lateral cost

Base surface = top surface =  π*r²

Then cost of ( base + top ) is = (2* π*r² )*0,1

Lateral surface is  = 2*π*r*h

Then cost of lateral surface is:  (2*π*r*h)*0,5

Total cost C(t) = (2* π*r² )*0,1  +  (2*π*r*h)*0,5

V = π*r²*h

Total cost  as a function of (V >0 a parameter) and r then

h  =  V / π*r²

C(V,r)  =  (2* π*r² )*0,1  +  π*r*(V / π*r²)

C(V,r)  =  0.2*π*r²  + V*/r

Taking derivatives on both sides of the equation we get:

C´(V,r)  =  2*0.2*π*r  -  V/r²

C´(V,r)  =  0             0.4*π*r  - V/r  = 0

Solving for r

0.4*π*r² - V = 0      ⇒  1.256*r²  = V          r = √ V/ 1.256    cm

and  h  =  V /π *  (√ V/ 1.256)²

h =  1/ 1.256*π

h  =  0.254 cm

C(V,r)  =  0.2*π*r²  + V*/r

C(min) = 0.2*π* (√ V/ 1.256)²   +  V/ √ V/ 1.256

C(min) =  0.2*π*V/1.256  +   V/ √ V/ 1.256

C(min) = 0.5*V  +  √V/1.256  $

Answer:

120 [tex]{ft}^{3}[/tex]

Step-by-step explanation:

To find the volume of a rectangular prism, multiply the lengths of all of the sides

3 x 5 x 8 = Ans --> 3 x 40 = Ans -->120 = Ans

Therefore, the volume of the rectangular prism is 120 [tex]{ft}^{3}[/tex]

Answer:

ASA

Step-by-step explanation:

Both triangles contains two angles which indicate that it can only be the top 2 options.

Answer:

D

Step-by-step explanation:

because in standard form the first number is only up to 10 and above 10 it is decimal places e.g.6.12×10^5

hope this helps u understand :)

Answer:

x=16.53cm

Step-by-step explanation:

1 liter = 1000 cm^3

The volume of water in the rectangular prism will be 11*11*x = 2000

121x=2000

x=2000/121

x=16.53cm

Answer:

the answer is 2. (6 and 4)

Step-by-step explanation:

6 + 4 = 10

Answer:

fraction is 75/100

decimal is 0.75

Step-by-step explanation:

because there are 75 of them that are shaded out if 100 so 75/100 and to find out in decimal 75÷100=0.75.

hope this helps u understand:)

Answer:

i believe the pre-tax subtotal would be 1890.69

Step-by-step explanation:

the 2,033 represents 100%. to remove that 7% you would do

.93 • 2,033 which gives you 1890.69

Answer:

35

Step-by-step explanation:

the whole line is 49 and line DB is 30.

minus 16 from 30 so 30-16=14

then you minus line CB from EB so 49-14=35

that makes line EC 35

Answer:

19 - 28/n

n=7

19 - 28/7

19 - 4

=15

Answer:

V≈733.88cm³

Step-by-step explanation:

Thank you

9514 1404 393

Answer:

  D.  reals ≥ -4

Step-by-step explanation:

The range is the vertical extent of the graph. Here the graph goes down to -4 and includes all numbers greater than that. The range is ...

  All real numbers greater than or equal to -4

Answer:

equiangular equilateral

all sides are equal  

Answer:

[tex]q = 8[/tex]

[tex]r = 3[/tex]

Step-by-step explanation:

Given

[tex]n = dq + r[/tex]

[tex]0 \le r < d[/tex]

[tex]n = 67[/tex] --- not -67

[tex]d = 8[/tex]

Required

Find q and r

Substitute values for d and b

[tex]n = dq + r[/tex]

[tex]67 = 8 * q + r[/tex]

[tex]67 = 8q + r[/tex]

Make q the subject

[tex]q = \frac{67 - r}{8}[/tex]

[tex]0 \le r < d[/tex] means that r is less than 8 but greater than or equal to 0

And r and q are integers.

Let [tex]r = 3[/tex]

[tex]q = \frac{67 - 3}{8}[/tex]

[tex]q = \frac{64}{8}[/tex]

[tex]q = 8[/tex]

No other true values of r and q can be gotten.

Answer:

a) The 98% Confidence Interval for the proportion of all students that prefer ebooks is (0.55, 0.65).

b) The margin of error is of 0.05.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

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

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

The margin of error is of:

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

In a sample of 400 students, 60% of them prefer eBooks.

This means that [tex]n = 400, \pi = 0.6[/tex]

98% confidence level

So [tex]\alpha = 0.02[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.02}{2} = 0.99[/tex], so [tex]Z = 2.054[/tex].

Margin of error -> Question b:

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

[tex]M = 2.054\sqrt{0.6*0.4}{400}}[/tex]

[tex]M = 0.05[/tex]

The margin of error is of 0.05.

A.Find 98% Confidence Interval for the proportion of all students that prefer ebooksb.

Sample proportion plus/minus the margin of error.

0.6 - 0.05 = 0.55

0.6 + 0.05 = 0.65

The 98% Confidence Interval for the proportion of all students that prefer ebooks is (0.55, 0.65).

Answer:

The expected total amount of time in minutes the operator will spend on the calls each day is of 210 minutes.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

n-values of a normal variable:

For the sum of a sample of n values, the mean is of [tex]M = n\mu[/tex] and the standard deviation is of [tex]s = \sigma\sqrt{n}[/tex]

Average 2.8 minutes

This means that [tex]\mu = 2.8[/tex]

75 calls each day.

This means that [tex]n = 75[/tex]

What is the expected total amount of time in minutes the operator will spend on the calls each day?

[tex]M = n\mu = 75(2.8) = 210[/tex]

The expected total amount of time in minutes the operator will spend on the calls each day is of 210 minutes.

Answer:

as the sample size increases, the margin of error decreases

Answer:i actually dunno

Step-by-step explanation:

wat

Answer:

18 in

Step-by-step explanation:

Area of rectangle = 3 times the area of the square

Area of square = a² ; a = side length

a = 12 in

Area of square = 12² = 144 in²

Area of rectangle = 3 * 144 = 432 in²

Length of rectangle = 24 in

Width = x

Area of rectangle = length * width

432 = 24 * x

x = 432 / 24

x = 18 in

Answer:

5x + 3(10) = 140

Step-by-step explanation:

Step-by-step explanation:

2*10+((4+10)x8)/2

=20+14*8/2

=76 sq meters

Answer:

[tex]a_5 = 120[/tex]

Step-by-step explanation:

Given

[tex]a_1 = 1[/tex]

[tex]a_n = n(a_{n-1})[/tex]

Required

[tex]a_5[/tex]

This is calculated as:

[tex]a_5 = 5(a_{5-1})[/tex]

[tex]a_5 = 5*a_4[/tex]

Calculate [tex]a_4[/tex]

[tex]a_4 =4(a_{4-1})[/tex]

[tex]a_4 =4*a_3[/tex]

Calculate [tex]a_3[/tex]

[tex]a_3 =3*a_2[/tex]

Calculate [tex]a_2[/tex]

[tex]a_2 = 2 * a_1[/tex]

[tex]a_2 = 2 * 1[/tex]

[tex]a_2 = 2[/tex]

So:

[tex]a_3 =3*a_2[/tex]

[tex]a_3 = 3 * 2 = 6[/tex]

So:

[tex]a_4 =4*a_3[/tex]

[tex]a_4 = 4 * 6 =24[/tex]

Lastly;

[tex]a_5 = 5*a_4[/tex]

[tex]a_5 = 5 * 24[/tex]

[tex]a_5 = 120[/tex]

Answer:

The three sides are 27 feet, 15 feet, 13 feet

Step-by-step explanation:

Let second side of a triangle be = a

Let one side be 12 feet shorter than the second side = (a - 12)

Let the third side be 2 feet shorter than the second side= (a - 12) - 2 =(a - 14)

Perimeter of triangle = Sum of length of all 3 sides

55 = a + (a - 12) + (a - 14)

55 = a + a + a - 12 - 14

55 = 3a - 26

55 + 26 = 3a

81 = 3a

a = 27

Length of one side, a - 12 = 27 - 12 = 15 feet

Length of second side, a = 27 feet

Length of third side, a - 14 = 27 - 14 = 13 feet

The answer is attached. I hope this helps answer your question!

Use the following property below:

[tex] \large \boxed{ \sqrt[n]{a} \times \sqrt[n]{a} \times \sqrt[n]{a} = { (\sqrt[n]{a}) }^{3} }[/tex]

Therefore,

[tex] \large{ \sqrt[7]{x} \times \sqrt[7]{x} \times \sqrt[7]{x} = { (\sqrt[7]{x}) }^{3} }[/tex]

Then we use next property.

[tex] \large{ \sqrt[n]{ {a}^{m} } = {a}^{ \frac{m}{n} } }[/tex]

Hence,

[tex] \large{ \sqrt[7]{ {x}^{3} } = {x}^{ \frac{3}{7} } }[/tex]

Answer

Answer:

sis

Step-by-step explanation:

Answer:

Irony

Explanation:

I just took the test

9514 1404 393

Answer:

  about 0.299 kg/m³

Step-by-step explanation:

Density is the ratio of mass to volume.

  ρ = M/V

  ρ = (10 kg)/(4/3π(2 m)³) = 15/(16π) kg/m³ ≈ 0.299 kg/m³