A manufacturer uses 34 yard of fabric in each skirt.
How many yards of fabric will the manufacturer use in 4 skirts? in 7 skirts? in 9 skirts?

Answer:

B.

Step-by-step explanation:

Recall the properties of logs and once you find the value of x, substitute it into the equation.

Option C ([tex]\frac{10}{27}[/tex]) is the correct alternative.

Given expression is:

→ [tex]3^x = 10[/tex]

By taking log both sides, we get

→ [tex]ln \ 3^x = ln \ 10[/tex]

 [tex]x \ ln \ 3= ln \ 10[/tex]

         [tex]x = \frac{ln \ 10}{ln \ 3}[/tex]

By substituting the value of "x" in "[tex]3^{x-3}[/tex]", we get

→ [tex]3^{x-3}[/tex] = [tex]3^{\frac{ln \ 10}{ln \ 3} -3}[/tex]

          = [tex]\frac{10}{27}[/tex]  

So the above is the right solution.

Learn more:

https://brainly.com/question/47626

Answer:

Directional derivative = 1/√2

Step-by-step explanation:

We are given f(x, y) = y cos(xy)

Now, we know that;

∇f(x, y) = ycos xy

Thus, applying that to the question, we have;

∇f(x, y) = [-y² sin xy, cos (xy) - xy sin xy]

At coordinates (0,1),we now have;

∇f(0, 1) = [-1²•sin0, (cos 0) - 0]

∇f(0, 1) = [0, 1]

Now, unit vector indicated by the angle θ is given as; u = [cos θ, sin θ]

From the question, since θ = π/4, thus

u = [cos π/4, sin π/4]

Cos π/4 in surd form is; 1/√2

Also, sin π/4 in surd form is; 1/√2

So, u = [1/√2, 1/√2]

Directional derivative = [∇f(0, 1)] • u

= [0, 1] × [1/√2, 1/√2] = 0 + 1/√2 = 1/√2

Step-by-step explanation:

Meters measures length, hectares measures area.

1 hectare = 10,000 m²

Answer Meters measures length, hectares measures area.

1 hectare = 10,000 m²

Step-by-step explanation:

Answer: C. 84

Step-by-step explanation:

In triangles ABD y BCD:

- AD=CD

- Angle BAD = angle BCD

- BD common side

THEN the triangles are equal because they have two sides and the angle opposite the longest side respectively equal.

CBD = ABD = 42 because the triangles ABD y BCD are equal

ABC = CBD+ABD = 42+42= 84

Answer:

C. 84 degrees

Step-by-step explanation:

Answer:

x = 40

Step-by-step explanation:

The angles are vertical angles.  We know that vertical angles are equal

120 = 3x

Divide each side by 3

120/3 = 3x/3

40 =x

Answer:

40

Step-by-step explanation:

I forgot what you would call this, but basically 3x = 120. both of the angles are the same. So divide both sides of the equation by 3. 3x/3 = 120/3 and your answer is 40.

It's a bad explanation but I hope it helps!

Answer:

Domain: [10, ∞)

Step-by-step explanation:

Domain is the set of x-values that can be inputted into function f(x).

Step 1: Write equation

f(x) = √(x - 10)

We know that if we get negatives under the square root, we would get imaginary numbers.

Our domain to include all x-values would have to be bigger than 10:

f(10) = √(10 - 10) = √0 = 0

If the number is smaller than 10, we get: f(9) = √(9 - 10) = √-1 = i

Therefore, our real numbers domain would be [10, ∞) or x ≥ 10.

Answer:

82 1/3

Step-by-step explanation:

89 - 6 2/3

Borrow 1 from the 89 in the form of 3/3

88 + 3/3 - 6 2/3

88 3/3 - 6 2/3

Subtract the whole numbers

88-6 =82

Subtract the fractions

3/3 - 2/3 = 1/3

82 1/3

Answer and Step-by-step explanation:

The matching of the vocabulary word with its corresponding example is shown below:-

a. Data - The list of answers that the 85 Americans give.

Data refers the information that is to be collected.

b. Variable - The answer "Strongly Agree" or "Agree" or "Disagree" or "Strongly disagree".

Variable refers the changes of the expression according to the context.

c. Parameter - The proportion of all Americans who strongly agree that prisoners with life sentences who has Alzheimer's should be released.

A parameter is a quantity that affects a mathematical object's production or behavior, but is considered constant

d. Statistics - The proportion of 85 Americans surveyed who strongly agree that prisoners with life sentences who has Alzheimer's should be released.

Statistics is a field of mathematics involved in data collection, organisation and analysis.

e. Sample - The 85 Americans who participated in the survey.

A sample is the result of an experiment on randomly.

f. Population - All Americans

Population refers to the number of the public.

Answer:

a. Data - The list of answers that the 85 Americans give.

Data refers the information that is to be collected.

b. Variable - The answer "Strongly Agree" or "Agree" or "Disagree" or "Strongly disagree".

Variable refers the changes of the expression according to the context.

c. Parameter - The proportion of all Americans who strongly agree that prisoners with life sentences who has Alzheimer's should be released.

A parameter is a quantity that affects a mathematical object's production or behavior, but is considered constant

d. Statistics - The proportion of 85 Americans surveyed who strongly agree that prisoners with life sentences who has Alzheimer's should be released.

Statistics is a field of mathematics involved in data collection, organisation and analysis.

e. Sample - The 85 Americans who participated in the survey.

A sample is the result of an experiment on randomly.

f. Population - All Americans

Population refers to the number of the public.

Step-by-step explanation:

Answer:

5/4   5 ft

Step-by-step explanation:

We are going from 12 to 15

We need to multiply by

15 = k *12

Divide each side by 12

15/12 = k

5/4 = k

The scale factor is 5/4

1 in = 4 ft

Multiply the 4 ft by the scale factor

1 in = 4 * 5/4 = 5 ft

1 in = 5 ft

Answer:

Raphael saw a square patio that was 12-feet long on each side. He wants to build a patio that will be 15-feet long on each side.

The change in the scale factor is  

✔ 4/5

.

The change of scale means that 1 inch represented  4 feet, but now 1 inch represents  

✔ 5

feet.

Answer:

27%

Step-by-step explanation:

6/10*45/100=270/1000 which is 27/100 which is 27%

Step-by-step explanation:

-3(7 + 5) + 9(2)

-3(12) + 18

-36 + 18

= - 18

In my opinion this should be the answer

Answer:

14

Step-by-step explanation:

Your welcome!

Answer: 39 minutes 51 seconds

Step-by-step explanation:

Nt=N0 * 2^n

N0=Initial population

n=number of times bacteria divide

700=320*2^n

log2(700/320)=1.129283017=n

45/1.129283017=39.84829252 minutes

0.84829252*60=50.89755135≈51seconds

so the answer is

39minutes and 51seconds

Answer:

The translation corresponds to : [tex]g(x)=\sqrt[3]{x-4}[/tex]

which is the first option in your list of possible answers

Step-by-step explanation:

Notice that this new function's graph responds to a horizontal translation to the right of the original graph of [tex]f(x)=\sqrt[3]{x}[/tex]. Notice that the crossing of the x-axis, which for f(x) is at the origin (0, 0), has now moved to the point (4,0), which means a translation to the right in exactly 4 units.

Recall that horizontal translations are performed by subtracting from the independent variable  (x) , the number of units you move (in this case 4)

Therefore the new function should look like:

[tex]g(x)=\sqrt[3]{x-4}[/tex]

The answer is A.

did the test

9514 1404 393

Answer:

  B, D

Step-by-step explanation:

The volume is the product of the dimensions. For dimensions 9 ft, 9 ft, 10 ft, the volume is found by multiplying (9 ft) × (9 ft) × (10 ft) = 810 ft³.

To fill the volume with boxes of volume 1 ft³ would require 810 boxes.

Answer:

[tex] \boxed{D. \: 40\degree} [/tex]

Step-by-step explanation:

Angle sum property of triangle states that the sum of interior angles of a triangle is 180°

So,

[tex] = > 2y \degree + (y + 10)\degree + 50\degree = 180\degree \\ \\ = > 2y\degree + y\degree + 10\degree + 50\degree = 180\degree \\ \\ = > 3y\degree + 60\degree = 180\degree \\ \\ = > 3y\degree = 180\degree - 60\degree \\ \\ = > 3y\degree = 120\degree \\ \\ = > y = \frac{120\degree}{3\degree} \\ \\ = > y = 40\degree [/tex]

Answer:

x = -4 and x = 6

Step-by-step explanation:

Factor using AC method.

1 × -24 = -24

Factors of -24 that add up to -2 are +4 and -6.

P(x) = (x + 4) (x − 6)

Therefore, zeroes of P(x) are x = -4 and 6.

Answer:

To get your answer, you need to fix the typos, but the answer is gonna be the closest thing to 13/42 if that is the real value

Step-by-step explanation:

none of these answers are anywhere near to 13/42

Answer:

h= 1+3d

Step-by-step explanation:

total amount of hairbands equals the 1 hairband she has + 3 times how ever many more she decides to buy

Answer:

$157.60

Step-by-step explanation:

77 shares + 120 shares = 197 total shares

197/10 = 19.7

19.7 x 8 = 157.60

Answer:

b on edge hope this helps :)

Step-by-step explanation:

Answer:

[tex]\dfrac{1}{5} $ square foot.[/tex]

Step-by-step explanation:

Area of the Poster =1 sq.ft.

The collage will cover a part of the poster that is [tex]\dfrac{1}{3} ft.$ wide and \dfrac{3}{5} ft.$ long.[/tex]

Area of the Photo Collage Section

=Length X Width

[tex]=\dfrac{1}{3} X \dfrac{3}{5} \\\\=\dfrac{1}{5} $ square foot.[/tex]

[tex]\text{Therefore, the photo collage will cover }\dfrac{1}{5} $ of a square foot.[/tex]

Answer:

a. P(X ≤ 5) = 0.999

b. P(X > λ+λ) = P(X > 2) = 0.080

Step-by-step explanation:

We model this randome variable with a Poisson distribution, with parameter λ=1.

We have to calculate, using this distribution, P(X ≤ 5).

The probability of k pipeline failures can be calculated with the following equation:

[tex]P(k)=\lambda^{k} \cdot e^{-\lambda}/k!=1^{k} \cdot e^{-1}/k!=e^{-1}/k![/tex]

Then, we can calculate P(X ≤ 5) as:

[tex]P(X\leq5)=P(0)+P(1)+P(2)+P(4)+P(5)\\\\\\P(0)=1^{0} \cdot e^{-1}/0!=1*0.3679/1=0.368\\\\P(1)=1^{1} \cdot e^{-1}/1!=1*0.3679/1=0.368\\\\P(2)=1^{2} \cdot e^{-1}/2!=1*0.3679/2=0.184\\\\P(3)=1^{3} \cdot e^{-1}/3!=1*0.3679/6=0.061\\\\P(4)=1^{4} \cdot e^{-1}/4!=1*0.3679/24=0.015\\\\P(5)=1^{5} \cdot e^{-1}/5!=1*0.3679/120=0.003\\\\\\P(X\leq5)=0.368+0.368+0.184+0.061+0.015+0.003=0.999[/tex]

The standard deviation of the Poisson deistribution is equal to its parameter λ=1, so the probability that X exceeds its mean value by more than one standard deviation (X>1+1=2) can be calculated as:

[tex]P(X>2)=1-(P(0)+P(1)+P(2))\\\\\\P(0)=1^{0} \cdot e^{-1}/0!=1*0.3679/1=0.368\\\\P(1)=1^{1} \cdot e^{-1}/1!=1*0.3679/1=0.368\\\\P(2)=1^{2} \cdot e^{-1}/2!=1*0.3679/2=0.184\\\\\\P(X>2)=1-(0.368+0.368+0.184)=1-0.920=0.080[/tex]

Answer:

B

Step-by-step explanation:

JK = LM (equidistant from centre)

3x+19=6x+7

19-7=6x-3x

12 = 3x

Dividing both sides by 3

x = 4

JK = 3(4)+19

JK = 12+19

JK = 31

Answer:

31

Step-by-step explanation:

JK = LM (since they are equidistant from centre)

3x + 19 = 6x + 7

- 3x = - 12

x = 4

JK = 3 * (4) + 19

= 12 + 19

= 31

Hope this helps!

Answer:

p = x² − 6x + 10

Step-by-step explanation:

Complex roots come in conjugate pairs.  So if 3−i is a root, then 3+i is also a root.

p = (x − (3−i)) (x − (3+i))

p = x² − (3+i)x − (3−i)x + (3−i)(3+i)

p = x² − 3x − ix − 3x + ix + (9 − i²)

p = x² − 6x + 10

You can check your answer using the quadratic formula.

x = [ -b ± √(b² − 4ac) ] / 2a

x = [ 6 ± √(36 − 40) ] / 2

x = (6 ± 2i) / 2

x = 3 ± i

Answer:

≈103.67cm

Step-by-step explanation:

Shape: Circle

Solved for circumference

Diameter: 33cm

Formula: C=πd

Answer: ≈103.67cm

Hope this helps.

Answer:

C = 33 pi

Step-by-step explanation:

The circumference of a circle is given by

C = pi *d

C = 33 pi

We can approximate pi by 3.14

C = 33*3.14 =103.62

or by using the pi button

C =103.6725576

Answer:

x=3

Step-by-step explanation:

2x-6=0

2x=0+6

2x=6

2x/2=6/2

x=3

SEE BELOW FOR THE CORRECT FORMAT OF THE QUESTION

Answer:

(a) [tex]\mathbf{C_{(t)} =\dfrac{I}{F} [ 1- e \dfrac{-Ft}{v}+ C_oe \dfrac{-Ft}{v} ]}[/tex]

(b) [tex]\mathbf{\lim_{t \to \infty} C_t = \dfrac{I}{F}[1-0+ 0 ] \ = \dfrac{I}{F}}[/tex]

(c) T = 6.02619 years

(d) T = 431.593 years

Step-by-step explanation:

(a)

[tex]\dfrac{dC}{dt} = -\dfrac{F}{v}C + \dfrac{I}{v} \\ \\ \\ \dfrac{dC}{dt} + \dfrac{F}{v}C = \dfrac{I}{v}[/tex]

By integrating the factor of this linear differential equation ; we have :

[tex]= e \int\limits \dfrac{F}{v}t \\ \\ \\ = e \dfrac{Ft}{v}[/tex]

[tex]C* e \frac{Ft}{v}= \int\limits \dfrac{I}{v}*e \dfrac{Ft}{v} dt[/tex]

[tex]C* e \frac{Ft}{v}= \dfrac{I}{v}* \dfrac{e \frac{Ft}{v} }{F/v}+ K[/tex]

[tex]C* e \frac{Ft}{v}= \dfrac{I}{v}* \dfrac{V}{F} e \dfrac{Ft}{v} + K[/tex]

[tex]Ce \dfrac{Ft}{v} = \dfrac{I}{F} \ * \ e \dfrac{Ft}{v} + k \ \ \ \ (at \ t = 0 \ ; C = C_o)[/tex]

[tex]C_o = \dfrac{I}{F} e^o + K[/tex]

[tex]K = C_o - \dfrac{I}{F}[/tex]

[tex]C_{(t)} = [ \dfrac{I}{F}e \dfrac{Ft}{v}+ C_o - \dfrac{I}{F}] e\dfrac{-Ft}{v}[/tex]

[tex]C_{(t)} =\dfrac{I}{F} [ e \dfrac{Ft}{v} * e \dfrac{-Ft}{v}+ C_oe \dfrac{-Ft}{v} - 1* e \dfrac{-Ft}{v}][/tex]

[tex]\mathbf{C_{(t)} =\dfrac{I}{F} [ 1- e \dfrac{-Ft}{v}+ C_oe \dfrac{-Ft}{v} ]}[/tex]

(b)

[tex]\lim_{t \to \infty} C_t = \dfrac{I}{F}[1-e^{- \infty} + C_o e^{- \infty} ][/tex]

since  [tex](e^{- \infty} = 0)[/tex]

[tex]\mathbf{\lim_{t \to \infty} C_t = \dfrac{I}{F}[1-0+ 0 ] \ = \dfrac{I}{F}}[/tex]

(c)

V = 458 km³   and F = 175 km³  , I = 0

[tex]\dfrac{dC}{dt} = - \dfrac{-175}{458}C[/tex]

[tex]= \int\limits \ \dfrac{dC}{C} = - \dfrac{175}{458}\int\limits dt[/tex]

[tex]In (C_{(t)}) = - \dfrac{175}{458} t + K[/tex]

[tex]C_{(t)} = e \dfrac{-175}{458}t + K[/tex]

Let at time t = 0 [tex]C_{(t)}} = C_o \to C_o = e^{0+k} = e^K[/tex]

[tex]C_{(t)} = e \dfrac{-175}{458}t[/tex]

Now at time t = T ; [tex]C_{9t)} = \dfrac{C_o}{10}[/tex]

[tex]\dfrac{C_o}{10} = C_o e \dfrac{-175}{458}T \to \dfrac{1}{10} = e \dfrac{-175}{458}T[/tex]

[tex]In ( \dfrac{1}{10}) = \dfrac{-175}{459}T[/tex]

[tex]- In (10) = \dfrac{175}{458}T[/tex]

[tex]T = \dfrac{458}{175} In (10)[/tex]

T = 6.02619 years

(d) V = 12221 km³

F = 65.2 km³/ year

[tex]\mathbf{T = \dfrac{v}{F}In (10)}[/tex]

[tex]T = \dfrac{12221}{65.2}In (10)[/tex]

T = 431.593 years

Answer:

The standard cost of Bramble's product is $69.5 per unit.

Step-by-step explanation:

We can calculate the standard cost per unit of Bramble's product as the sum of the material cost, direct labor cost and overhead cost.

Each unit of product uses 2 pounds of materials, that cost $6 per pound. So the material cost is:

[tex]MC=2\,lb/u\cdot6\,\$/lb=12\,\$/u[/tex]

Each unit needs 2.5 direct labor hours, and they have a cost of $11 per hour, so the direct labor cost is:

[tex]LC=2.5\,h/u\cdot11\,\$/h=27.5\,\$/u[/tex]

The overhead costs are calculated in this case as $12 per direct labor hour. As 2.5 labor hours are needed per unit, we have:

[tex]OC=2.5\,h/u\cdot 12\,\$/h=30\,\$/u[/tex]

The standard cost is then:

[tex]C=MC+LC+OC=12+27.5+30=69.5\,\$/u[/tex]

Answer:

-3

Step-by-step explanation:

We can see that the line passes through (0,3) and (1,0)

So using rise over run we have

-3/1

or

-3