Food and clothing are shipped to victims of a natural disaster. Each carton of food will feed 13 ​people, while each carton of clothing will help 6 people. Each 20​-cubic-foot box of food weighs 40 pounds and each 5​-cubic-foot box of clothing weighs 25 pounds. The commercial carriers transporting food and clothing are bound by the following​ constraints:- The total weight per carrier cannot exceed 21 000 pounds.- The total volume must be no more than 7000 cubic feet.How many cartons of food and clothing should be sent with each plane shipment to maximize the number of people who can be helped?

Answer:

Option 2: (x-4)^2 + (x-5)^2 = 4

Step-by-step explanation:

The given circle's center is: (4,5)

And the radius is 4 units.

We are told in the question that the center will remain same only the radius will be changed.

The center is denoted by (h,k) = (4,5) and radius is 2

Standard equation of circle is:

(x-h)^2 + (y-k)^2 = r^2

So the equation of another circle with same center and radius of 2 units will be:

(x-4)^2 + (x-5)^2 = 2^2

(x-4)^2 + (x-5)^2 = 4  

Hence option 2 is correct ..

Answer:

264 transistors.

Step-by-step explanation:

By proportion the total number made if  16 are faulty is (35/2) * 16

=  280.

The number of good ones is 280 - 16

= 264 transistors.

Answer:

264 good ones

Step-by-step explanation:

2 in 35 are faulty = in a batch of 35, 2 will be faulty = there are 33 good for every 2 faulty ones there are

16 faulty have been made - to figure out how many batches there have been do 16/2=8

8 batches of 35, 8 × 35 = 280 total

280 total - 16 faulty = 264 good

OR do 8 batches × 33 good per batch = 264 good

at least thats how i interpreted it!

Answer:

  5y = 5

Step-by-step explanation:

When the second equation is multiplied by -2, it becomes ...

  -2(x -2y) = -2(-1)

  -2x +4y = 2

Adding this to the first equation gives ...

  (2x +y) +(-2x +4y) = (3) +(2)

  2x +y -2x +4y = 5 . . . . . . . . . eliminate parentheses

  5y = 5 . . . . . . . . . . . . . . . . . . .collect terms

Answer:

  3

Step-by-step explanation:

Segment BC corresponds to segment DF. The length of BC is the distance between coordinates (0, 2) and (3, 2). These points are on the same horizontal line (y=2), so the distance between them is the difference of their x-coordinates: 3 - 0 = 3.

Answer:

DF = 3

Step-by-step explanation:

If ABC is equivalent to EDF, then DF is equivalent to BC, which form the following ordered pairs:

D = (0,2)

F = (3,2)

It can be seen that both pairs have the same value of "y" or second value, that is 2.

As a rule, when the points are located on the y-axis (of the ordinates) or on a line parallel to this axis, the distance between the points corresponds to the absolute value of the difference of their ordinates.

So,

DF = D(x) + F(x) = 0 + 3 = 3

If we apply the equation of the distance between two points we get the same result,

[tex]DF=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}   }=\sqrt{(3-0)^{2}+(2-2)^{2}   }=\sqrt{(3)^{2}+(0)^{2}   }=\sqrt{9+0   }=\sqrt{9}=3[/tex]

Hope this helps!

6x + y = 28.  The standard form of the equation that is parallel to y = -6x + 5 and goes through point (4, 4) is 6x + y = 28.

The equation is written in the slope-intercept form y = mx +b. So:

y = -6x + 5

The slope m = -6

Since the slopes of parallel lines are the same, we are looking for a slope line m = -6 and goes through point (4, 4).

With the slope-intercept form:

y = mx + b

Introducing the slope m = -6:

y = -6x + b

Introducing the point (4, 4):

4 = -6(4) + b

b = 4 + 6(4)

b= 24 + 4

b = 28

Then

y = -6x + 28

write the equation in standard form ax + by = c:

y = -6x + 28

6x + y = 28

Answer:

  POLYNOMIAL is a 10-letter word

Step-by-step explanation:

A polynomial is such an expression.

Virtually any kind of algebraic expression is made by adding or subtracting terms, grouping them, applying functions to them, or dividing them. (A term is already a product; increasing the number factors doesn't change that.)

A polynomial is a special kind of sum-of-terms expression involving terms that are non-negative integer powers of a variable.

Answer:

Step-by-step explanation:

The dot product is the sum of products of the corresponding coordinate values:

[tex]\text{\bf{a}$\cdot$\bf{b}}=a_{x}b_{x}+a_{y}b_{y}[/tex]

The value of this can also be written in terms of the magnitudes of the vectors and the angle θ between them:

  |a|·|b|·cos(θ)

But the angle between the vectors is the same as the difference of their individual angles, θ = α - β, so this can also be written as ...

  |a|·|b|·cos(α-β)

And the trig identity for the cosine of the difference of angles lets us write the above as ...

  = |a|·|b|·(cos(α)cos(β) +sin(α)sin(β))

Answer:

  remaining zeros: negative i comma 5 minus i

Step-by-step explanation:

The remaining two zeros are the conjugates of the two zeros given. That brings the total number to 4 zeros, consistent with the number of zeros expected for a 4th-degree polynomial.

The conjugate of a complex number has the same real part and the opposite imaginary part.

Answer:

-i, 5-i

Step-by-step explanation:

Given that a function f(x) has only real coefficients and also of degree 4.

Since any polynomial with real roots have imaginary roots only with conjugate pairs, we can find other two roots easily

Degree of polynomial = 4

No of roots = 4

GIven roots are i, 5+i

Conjugate of the given roots are -i, 5-i

Hence remaining zeroes of f are -i, 5-i

Option A & B are true about trapezoids and rhombuses.

What are trapezoids and Rhombuses?

A trapezoid is a polygon that has only one pair of parallel sides. These parallel sides are also called parallel bases of trapezoid. The other two sides of trapezoids are non-parallel and called legs of trapezoids.

A rhombus is a special case of a parallelogram. In a rhombus, opposite sides are parallel and the opposite angles are equal. Moreover, all the sides of a rhombus are equal in length, and the diagonals bisect each other at right angles. The rhombus is also called a diamond or rhombus diamond.

Now determine which statement is true about trapezoid and rhombuses

We have given,

Option A: Both shapes are 2-dimensional figures.

This option is true because both trapezoid and rhombuses are a type of quadrilateral and we know quadrilaterals are 2 dimensional figures.

Option B: The first shape has the same number of angles as the second shape.

Yes,this option is true because both the shapes  are quadrilateral type  and a quadrilateral is a closed polygon containing 4 sides and 4 vertices enclosing 4 angles.

Option C: Both shapes have all sides of equal length.

No,this is not true as rhombus has all sides of equal length but trapezoid has all sides of different length.

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Answer:

A = 13.5 cm²

Step-by-step explanation:

* Lets explain how to find the area of the parallelogram

- In any parallelogram each two opposite sides are parallel

- In any parallelogram each two opposite sides are equal in length

- Each two opposite sides have height perpendicular on them

- So the parallelogram has 2 different bases and 2 different heights

- The area of the parallelogram = base × the height of this base

* Lets solve the problem

- The lengths of the two bases of the parallelogram are 4.5 cm , 5 cm

- The height of the base which length is 4.5 is 3 cm

- We will calculate the area of the parallelogram from this base

∵ The base of the parallelogram = 4.5 cm

∵ The height of this base = 3 cm

∵ Area of parallelogram = base × its height

∴ Area of parallelogram = 4.5 × 3 = 13.5 cm²

* The area of the following parallelogram is 13.5 cm²

Answer:

13.5 cm²

Step-by-step explanation:

The area (A) of a parallelogram is calculated as

A = bh ( b is the base and h the perpendicular height )

here b = 4.5 and h = 3, so

A = 4.5 × 3 = 13.5 cm²

Answer:

I think its 21.6 or 22 (Mostly 21.6 though) Sorry if its not right but i'm mostly sure of it like this!

Answer:

Area=14.22π

Step-by-step explanation:

Area=πr²(C/360)

C  is the central angle in degrees

r  is the radius of the circle of which the sector is part.

Area = π(8)²(80/360)

Area=π(64)(0.2222)

Area=π(14.22)

Area=14.22π....

Answer:

For [tex]3,604\ books[/tex] the cost for both methods will be the same

Step-by-step explanation:

Let

y ------> the production cost

x ------> the number of books

we know that

First production Method

[tex]y=19.25x+22,427[/tex] -------> equation A

Second production Method

[tex]y=10.50x+53,962[/tex] -------> equation B

Solve the system of equations

Equate equation A and equation B and solve for x

[tex]19.25x+22,427=10.50x+53,962[/tex]

[tex]19.25x-10.50x=53,962-22,427[/tex]

[tex]8.75x=31,535[/tex]

[tex]x=3,604\ books[/tex]

Answer:

y<-3x+8

Step-by-step explanation:

We are given 3x+y<8. There is exactly one step to put this in slope-intercept form, y=mx+b form where the equal sign can be an inequality sign. Our goal is to isolate y.

To do in 3x+y<8, we will just need to subtract 3x on both sides giving us y<-3x+8.

Answer:

y<-3x + 8

Step-by-step explanation:

y=mx+b form

Answer:

  A = √29

Step-by-step explanation:

The short of it is that ...

  A² = 2² + 5² = 29

  A = √29

_____

Amplitude

If you expand the second form using the sum-of-angles formula, you get ...

  Asin(ωt +φ) = Asin(ωt)cos(φ) +Acos(ωt)sin(φ)

Comparing this to the first form, you find ...

  c₂ = 2 = Acos(φ)

  c₁ = 5 = Asin(φ)

The Pythagorean identity can be invoked to simplify the sum of squares:

  (Asin(φ))² + (Acos(φ))² = A²(sin(φ)² +cos(φ)²) = A²·1 = A²

In terms of c₁ and c₂, this is ...

  (c₁)² +(c₂)² = A²

  A = √((c₁)² +(c₂)²) . . . . . . . formula for amplitude

_____

Phase Shift

We know that tan(φ) = sin(φ)/cos(φ) = (Asin(φ))/(Acos(φ)) = 5/2, so ...

  φ = arctan(c₁/c₂) . . . . . . . formula for phase shift*

  φ = arctan(5/2) ≈ 1.19029 radians

___

* remember that c₁ is the coefficient of the cosine term, and c₂ is the coefficient of the sine term.

In this mathematics problem, to rewrite in the appropriate form, the amplitude, A, has to be first determined using the given values and the Pythagorean identity. This gives the formula as A=sqrt( + ), where A is the calculated amplitude.

To rewrite in the form, we first need to find the amplitude A. Given values and, if we use the Pythagorean identity, we can solve for A. According to the Pythagorean identity, the sum of the squares of the values equals the square of the amplitude. In mathematical terms, A=sqrt( + ). The result will give you the correct amplitude. Therefore, the given value can be rewritten in the form Acos(ωt+ϕ).

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Answer:

  A ≈ 32°

Step-by-step explanation:

You are given two sides and the angle between them, so the law of cosines applies. The measure of side b can be found to be ...

  b² = a² + c² -2ac·cos(B)

  b² = 2² +3² -2·2·3·cos(95°) ≈ 14.0459

  b ≈ 3.74778

Then the law of sines can help you find angle A, the angle opposite the shortest side.

  sin(A)/a = sin(B)/b

  A = arcsin(a/b·sin(B)) = arcsin(2/3.74778·sin(95°)) ≈ 32.11°

  A ≈ 32°

The smallest angle is about 32°.

Answer:

1/11

Step-by-step explanation:

if you solve for the expression, you get .0909090909

if you divide 1 by 11, you get the same answer of .0909090909

There are 511 positive integers whose digits strictly increase from left to right.

To determine how many positive integers have digits that strictly increase from left to right, we need to consider combinations of digits. Since the digits must strictly increase, we cannot repeat any digit, and we can only use digits from 1 to 9.

Each number can be considered a unique combination of these digits, where the order of digits matters. For example, the digits {1, 2, 3} can only form the number 123. The total number of such combinations is given by the binomial coefficient C(9, k), where k is the number of digits.

Answer:

c

Step-by-step explanation:

Answer:

answer would be The mean must have a mean of 0 and a standard deviation of 1. hope this helps

Step-by-step explanation:

Answer:

It would take Tom 8 hours alone

Step-by-step explanation:

We are looking at this basic equation:

Tom + Shirley = 8 hours

Tom takes x hours to cut the grass; this means that 1/x of the job gets done in 1 hour

It takes Shirley 3 times as long as Tom, so it takes her 3x hours to cut the grass; this means that 1/3x of the job gets done in 1 hour

If the total number of hours it takes them to do the job is 6 hours; this means that 1/6  of the job gets done in 1 hour

Looking back at the original basic equation, we will fill in our info:

[tex]\frac{1}{x}+\frac{1}{3x}=\frac{1}{6}[/tex]

We can solve for x by first finding the LCD and eliminating the denominators.  The LCD is 6x, since all the denominators go into 6x evenly.

We will multiply the rational equation through by the LCD:

[tex]6x[\frac{1}{x}+\frac{1}{3x}=\frac{1}{6}][/tex]

Dividing each denominator into the LCD gives us:

6 + 2 = x so

x = 8

This means that it takes Tom 8 hours to do the job alone.  It would take Shirley 24 hours alone.  Ugh.

The time it would take Tom to mow the lawn alone is 3 hours

From the information given;

Let Tom's working hours be x.

Let Shirley's working hours be y.

We have  that;

Shirley and Tom work 6 hours together, this is expressed as;

x + y = 6

Given that Shirley work 3 hours alone, we have;

y = 3

Substitute the value of y as 3 in the equation

x + 3 = 6

x = 6 - 3

x = 3

Thus, the time it would take Tom  to mow the lawn alone is 3 hours

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Answer:

Step-by-step explanation:

For principal amount P, the future value of the simple interest account will be ...

  P(1 + rt) = P(1 + .026·20) = 1.52P

The future value of the compound interest account will be ...

  P(1 +r)^t = P(1.026^20) ≈ 1.6708875P

The value of the compound interest account is about 10% greater after 20 years.

I would choose the compound interest account because it has a higher rate of return.

Answer:

428.7 mm²

Step-by-step explanation:

The area (A) of the sector is calculated as

A = area of circle × fraction of circle

   = πr² × [tex]\frac{170}{360}[/tex]

   = π × 17² × [tex]\frac{17}{36}[/tex]

   = 289π × [tex]\frac{17}{36}[/tex]

   = [tex]\frac{289(17)\pi }{36}[/tex] ≈ 428.7 mm²

The area of a sector with a central angle of 170° and a radius of 17 mm is calculated using the sector area formula, resulting in approximately 428.7 mm², rounded to the nearest tenth.

To find the area of the sector, we use the formula [tex]\( \text{Area} = \frac{\text{Central Angle}}{360\°} \times \pi \times \text{Radius}^2 \)[/tex]. Substituting the given values, we get [tex]\( \text{Area} = \frac{170\°}{360\°} \times \pi \times 17^2 \)[/tex]. Simplifying, we have [tex]\( \text{Area} = \frac{17^2}{2} \times \pi \)[/tex]. Evaluating this expression, we find [tex]\( \text{Area} \approx 428.7 \)[/tex] mm². Therefore, the area of the sector, rounded to the nearest tenth, is approximately 428.7 mm². This calculation represents the portion of the circle enclosed by the given central angle and radius, providing the area of the sector.

[tex]\bf ~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$1000\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ t=years\dotfill &10 \end{cases} \\\\\\ A=1000e^{0.08\cdot 10}\implies A=1000e^{0.8}\implies A=2225.54~\hfill \stackrel{interest = A - P}{1225.54}[/tex]

btw, we could have used the compound formula just the same, by simply using a compounding cycle of 365, namely daily, assuming a year has 365 days.

The expression that shows the total attendance is 7 x 40 + 7 x 2.

An algebraic expression is consists of variables, numbers with various mathematical operations,

Given that,

Total number of rows = 8.

Number of seats in each row = 42.

Total number of seats = 42 x 8 = 336.

Since, an act needs to keep first row empty, but rest of the seats sold.

So the remaining seats = 336 - 42 = 294.

So, the expression for the total attendance can be given as,

7 x 40 + 7 x 2 = 280 + 14 = 294.

The required expression is 7 x 40 + 7 x 2.

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Answer:

[tex] x=2 \pm \sqrt{7} [/tex]

Step-by-step explanation:

Given this form ax^2+bx=k, here are my steps for completing the square while answer your question:

First step: Divide both sides by what is in front of x^2.  You want the coefficient of x^2 to be 1.  To do this for your question, divided both sides by 3.

This gives us x^2-4x  = 3.

Second step:  We are ready to begin the completing the square process at this step.  We are going to add (b/2)^2 on both sides.  For this question b=-4.

So we will be adding (-4/2)^2 on both sides.

This gives us x^2-4x+(-4/2)^2=3+(-4/2)^2.

Third step:  I like to simplified the things inside the square and I do not actually apply the square at this step.  It makes a later step easier in my opinion.

So this step gives us  x^2-4x+(-2)^2=3+(-2)^2.

Fourth step:  I'm actually going to write the left hand side as a square.  Just drag the things that are inside the squares down into ( )^2.

This is what I mean x^2-4x+(-2)^2=(x-2)^2.

So at the end of this step we have (x-2)^2=3+(-2)^2.

Fifth step: I'm going to simplify the right hand side.

This step gives us (x-2)^2=7

Sixth step:  We are ready to square root both sides.  

This gives us [tex] x-2=\pm \sqrt{7} [/tex]

Seveth step:  Get x by itself like you normally would with a linear equation.  My step here is just to add 2 on both sides.

Final answer:  [tex] x=2 \pm \sqrt{7} [/tex]

[tex]3x^2-12x=9\\x^2-4x=3\\x^2-4x+4=7\\(x-2)^2=7\\x-2=\sqrt7 \vee x-2=-\sqrt7\\x=2+\sqrt7\vee x=2-\sqrt7[/tex]

Answer:

Explanation:

1) Set the algebraigic expression that represents the combinations of sofa and pillow orders:

2) Predict the graph of the inequality x + 2y ≥ 4

        x = 0 ⇒ 2y = 4 ⇒ y =4/2 ⇒ y = 2 ⇒ point (0,2)

        y = 0 ⇒ x = 4 ⇒ point (4,0)

        Then the lines goes through (0,2) and (4,0) ... [the four graphs meet this]

3) Conclusion:

That means that the correct graph is the last one: solid line, shaded area over the line y = 2 - x/2.

Note: a more detailed graph would include the fact that the items cannot be negative, i.e. x ≥ 0 and y ≥ 0, which would result in that the shaded area would be on the first quadrant.

Answer: D

Step-by-step explanation:

Answer:

The probability that the card drawn is a club is 0.25.

The probability that card drawn is a club, when it is given that the card is black is 0.5.

Step-by-step explanation:

In a standard​ deck of cards:

Total number of cards = 52

Total number of cards of each suit (club, spade,heart, diamond) = 13

The probability that the card drawn is a club is

[tex]P=\frac{\text{Favorable outcomes}}{\text{Total outcomes}}[/tex]

[tex]P=\frac{^{13}C_1}{^{52}C_1}=\frac{13}{52}=0.25[/tex]

Therefore the probability that the card drawn is a club is 0.25.

Let A and B represents the following events:

A : Card is black

B : Card is a club

Total number of black cards = 26

[tex]P(A)=\frac{26}{52}=\frac{1}{2}=0.5[/tex]

From the above parts

[tex]P(B)=0.25[/tex]

Total number of black club cards = 13

[tex]P(A\cap B)=\frac{13}{52}=\frac{1}{4}=0.25[/tex]

We need to find the probability that card drawn is a club, when it is given that the card is black.

[tex]P(\frac{B}{A})=\frac{P(A\cap B)}{P(A)}[/tex]

[tex]P(\frac{B}{A})=\frac{0.25}{0.5}=0.5[/tex]

Therefore the probability that card drawn is a club, when it is given that the card is black is 0.5.

Answer:

B

Step-by-step explanation:

We are given f(x) is height in cm while x is days old.

We are also given f(60)=210.

If you compare f(60) to f(x) you should see that x is 60 so we have the sunflower is 60 days old.  Since f(60)=210, then you have the height of the sunflower is 210 cm tall.

Answer:

B.) The height of the sunflower plant is 210 cm when it is 60 days old.

Step-by-step explanation:

Answer:

quarters = 6+x

dimes = x

Total value = 325

Dime value = 10

Quarter value = 25

Step-by-step explanation:

25x+150+10x=325 (simplify)

35x=175

x=5  

6+5 = 11  

Hence Zoe has 5 dimes and 11 quarters.

Hope this helps!!❤

Step-by-step explanation:

the e standard form of parabola with vertex (h,k) is

y=a(x-h)²+k

here (h,k)=(-3,6)

so the answer to your question is

y=-3(x-(-3))²+6

y=-3(x+3)²+6

Answer:

Option D is correct.

Step-by-step explanation:

The vertex is (-3,6)

We will check which equation satisfies the given vertex.

A) y = -3(x-3)^2 - 6

if x = -3 then value of y should be 6

Checking:

y = -3(-3-3)^2 - 6

y = -3(-6)^2 - 6

y = -3(36) -6

y = -114

if x= -3, y ≠ 6

B) y = -3(x+3)^2 - 6

if x = -3 then value of y should be 6

Checking:

y = -3(-3+3)^2 - 6

y = -3(0)-6

y = -6

if x= -3, y ≠ 6

C) y = -3(x-3)^2 + 6

if x = -3 then value of y should be 6

Checking:

y = -3(-3-3)^2 + 6

y = -3(-6)^2 + 6

y = -3(36) + 6

y = -102

if x= -3, y ≠ 6

D) y = -3(x+3)^2 + 6

if x = -3 then value of y should be 6

Checking:

y = -3(-3+3)^2 + 6

y = -3(0)^2 + 6

y = 6

So, if x= -3, y =6 so, if the vertex of parabola is at (-3,6) the equation will be

y = -3(x+3)^2 + 6

So. Option D is correct.