Katie has a collection of nickels dimes and quarters with a total value of $4.60. there are 6 more dimes than nickels and 8 more quarters than nickels. How many of each coins does she have?

Answer:

A) [tex]\int\frac{2x^2}{3}dx=\frac{2x^3}{9}+C[/tex]

B) [tex]\int(5-x)^{23}dx=-\frac{(5-x)^{24}}{24}+C[/tex]

Step-by-step explanation:

A)

So we have the integral:

[tex]\int\frac{2x^2}{3}dx[/tex]

First, remove the constant multiple:

[tex]=\frac{2}{3}\int x^2\dx[/tex]

Use the power rule, where:

[tex]\int x^ndx=\frac{x^{n+1}}{x+1}[/tex]

Therefore:

[tex]\frac{2}{3}\int x^2\dx\\=\frac{2}{3}(\frac{x^{2+1}}{2+1})[/tex]

Simplify:

[tex]=\frac{2}{3}(\frac{x^{3}}{3})[/tex]

And multiply:

[tex]=\frac{2x^3}{9}[/tex]

And, finally, plus C:

[tex]=\frac{2x^3}{9}+C[/tex]

B)

We have the integral:

[tex]\int(5-x)^{23}dx[/tex]

To solve, we can use u-substitute.

Let u equal 5-x. Then:

[tex]u=5-x\\du=-1dx[/tex]

So:

[tex]\int(5-x)^{23}dx\\=\int-u^{23}du[/tex]

Move the negative outside:

[tex]=-\int u^{23}du[/tex]

Power rule:

[tex]=-(\frac{u^{23+1}}{23+1})[/tex]

Add:

[tex]=-(\frac{u^{24}}{24})[/tex]

Substitute back 5-x:

[tex]=-(\frac{(5-x)^{24}}{24})[/tex]

Constant of integration:

[tex]=-\frac{(5-x)^{24}}{24}+C[/tex]

And we're done!

Answer:

2 points

Step-by-step explanation:

0+3-4-2+5=2 points

Answer:

107.33 inches

Step-by-step explanation:

Area of the square more = length ^2

Area of the square mirror = 720 square inches

Area of the square more = length ^2

720 = length^2

Find the square root of both sides

√720 = √lenght^2

Length = √720

Length = 26.83281573 inches

Each length of the wood = 26.83281573 inches

There are 4 equal sides on the square mirror

Total length of the wood = 26.83281573 × 4

= 107.33126292 inches

Length of wood trim is needed to go around the entire mirror to the nearest hundredth = 107.33 inches

Answer:

The measure of the angles:

24°  and   66°

Step-by-step explanation:

Complementary angles sum 90°

then:

(3x + 3) + (10x-4) = 90

3x + 10x + 3 - 4 = 90

13x - 1 = 90

13x = 90+1

13x = 91

x = 91/13

x = 7°

then:

3x+3 = 3*7 + 3 = 21+3 = 24°

10x - 4 = 10*7  - 4 = 70 - 4 = 66°

Check:

66° + 24° = 90°

Answer:

The yellow polygon is the scaled version of the red one (scaled by 3×), so the variable w = 9

Answer:

9

Step-by-step explanation:

The similarity ratio is 4/x = z/9 = 2/6 = 3/w = y/15

2/6 = 3/w cross multiply expressions 2w = 18 and w = 9

Answer:

16

Step-by-step explanation:

Let x be the number of chocolates obtained by each student

Since the number of chocolates obtained by each student = the number of students in the class, then, number of students in the class = x

256/x = x

Multiply both sides by x

256 = x × x ( x squared)

Multipy powers raised on both sides by 1/2

X = 16

Both planes have the same normal vector:

[tex]6x-y-z=6\implies\mathbf n=\langle6,-1,-1\rangle[/tex]

The plane we want must contain the point (4, -3, -1), so its equation would be

[tex]\mathbf n\cdot\langle x-4,y+3,z+1\rangle=0[/tex]

[tex]\implies 6(x-4)-(y+3)-(z+1)=0[/tex]

[tex]\implies\boxed{6x-y-z=28}[/tex]

Answer:

Step-by-step explanation:

Since x is used a lot as a variable in algebra, I would use another symbol for multiplication. Though if your teacher requires you to use x as a multiplication symbol, then keep it as is. I use the asterisk symbol

Example: 2 times 3 = 2*3

------------------------------------------

For problem 2, you have the parenthesis in the wrong spots. Saying "the sum of four plus five" means we have 4+5 as you'd expect. Then you multiply that group with 2. So you'd really have (4+5)*2

How is this different from 4+5*2 back in problem 1? It comes down to how the order of operations handles things. To evaluate 4+5*2, we multiply first, then add. So we have 4+5*2 = 4+10 = 14

With the other expression, we add first because it is in the parenthesis block. Afterward we multiply the values to get (4+5)*2 = 9*2 = 18

Answer:

[tex]FH=22[/tex]

Step-by-step explanation:

FH is the combined lengths of FG and GH.

In an equation, this is:

[tex]FH=FG+GH[/tex]

We already know that FG is 8 and that GH is 14. Thus:

[tex]FH=8+14[/tex]

Add:

[tex]FH=22[/tex]

So, the length of FH is 22.

And we're done!

step 1

(x - 4) • (x + 5) = 0

STEP

:

A product of several terms equals zero.

When a product of two or more terms equals zero, then at least one of the terms must be zero.

We shall now solve each term = 0 separately

Solving a Single Variable Equation:

2.2 Solve : x-4 = 0

Add 4 to both sides of the equation :

x = 4

Solving a Single Variable Equation:

2.3 Solve : x+5 = 0

Subtract 5 from both sides of the equation :

x = -5

.

Answer:

A) [tex]\huge\boxed{\sf x^2 + x - 20 = 0}[/tex]

B) [tex]\huge\boxed{\sf x = - 5 \ \ \ \ OR \ \ \ \ x = 4}[/tex]

Step-by-step explanation:

[tex]\sf (x+5)(x-4) = 0[/tex]

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

Expanding:

Expanding Brackets

[tex]\sf x^2 -4x+5x-20 = 0[/tex]

Adding / Subtracting Like terms

[tex]\sf x^2 + x - 20 = 0[/tex]

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

Solving:

Given the equation:

(x+5)(x-4) = 0

Using zero Method

Either,

x + 5 = 0   OR      x - 4 = 0

x = - 5       OR       x = 4

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

Answer:

yes

Step-by-step explanation:

Answer:

(√2 + √6)/4.

Step-by-step explanation:

Use the addition formula

sin (A+ B) = sinAcosB + cosAsinB

sin (7pi/12) =  sin( 3pi/12 + 4pi/12)

= sin(pi/4 + pi/3) =  sin pi/4 cos pi/3 + cos pi/4 sin pi/3

= 1/√2 * 1/2 + 1/√2 * √3/2     (using the 45-45-90 and 30-60-90 triangles)

= 1 / 2√2 + √3/2√2

=   √2/4 + √6/4

= (√2 + √6)/4

Answer:

$1.5 unit

Step-by-step explanation:

According to the given situation, the calculation of the unit rate is shown below:-

Candy bars = 6

Amount of candy bars = $9:00

Unit rate

[tex]= \frac{Amount\ of\ candy\ bars}{Number\ of\ candy\ bars}[/tex]

Now we will put the values into the above formula

[tex]= \frac{\$9:00}{6}[/tex]

Which gives result

= $1.5 unit

Therefore for computing the unit rate we simply divide the amount of candy bars by the number of candy bars.

Answer:

-3/2

Step-by-step explanation:

Take two points from the table and use the slope formula

m= (y2-y1)/(x2-x1)

   = ( 19 - 13)/ ( -4 - 0)

   = 6/-4

   = -3/2

Since there is 28 cards, the chance of drawing 1 card will be [tex]\frac{1}{28}[/tex]

Therefore, [tex]P(13)=\frac{1}{28}[/tex].

There are 13 numbers less than 14 and greater than 0.

Therefore [tex]P(>14)=\frac{13}{28}[/tex]

There are 26 numbers that are not 2 or 17.

Therefore [tex]P(\neq 2,17)=\frac{26}{28}=\frac{13}{14}[/tex]

Hope this helps.

頑張って!

Probability of

Option (1). P(13) =[tex]\frac{1}{28}[/tex]

Option (2). P(less than 14) = [tex]\frac{13}{28}[/tex]

Option (3). P(not 2 or 17) =[tex]\frac{13}{14}[/tex]

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur

Given,

Total number of card = 28

Probability = Number of favorable outcome / Number of total outcome

Probability of picking 13 = [tex]\frac{1}{28}[/tex]

Probability of picking a card less then 14 = [tex]\frac{13}{28}[/tex]

Probability of not picking 2 or 17 = [tex]\frac{26}{28}=\frac{13}{14}[/tex]

Hence, the probability of

Option (1). P(13) =[tex]\frac{1}{28}[/tex]

Option (2). P(less than 14) = [tex]\frac{13}{28}[/tex]

Option (3). P(not 2 or 17) =[tex]\frac{13}{14}[/tex]

Learn more about Probability here

https://brainly.com/question/11234923

#SPJ2

(f+g)(x) = f(x) + g(x)

= 4x - 4 + 2[tex]x^{2}[/tex] - 3x

= 2[tex]x^{2}[/tex] + x - 4

Answer:42.55

Step-by-step explanation:

Les get the big boi out of the way first. We see that it is 3.5 by 9 and if we multiply we get 31.5. Next left triangle 2 by 2 so four but divided by 2 is 2. God so many  2's. So total is 33.5 so far. Next triangle is 2 by 5 soo  10 divided by 2 is 5. total is 38.5. Last dude in the middle. We know one side is two so we have to subtract here from the triangles which gets u the other side of 2 so 4. Total is 42.5

The Area of the Shape Shown is 42.5 square units.

The area of Rectangle is length times of width.

The area of the rectangle in the given figure is

Area of rectangle=3.5×9

=31.5 square units.

The area of left side triangle is

Area of triangle=1/2×2×2

=2 square units

The area of right side triangle 1/2×5×2

=5 square units

Now the area of square =2²

=4 square units.

Now total area of figure is 31.5+2+5+4 is 42.5 square units.

Hence, the Area of the shape Shown is 42.5 square units.

To learn more on Area of Rectangle click:

https://brainly.com/question/20693059

#SPJ2

Answer:

y = 2  when x = 150

Step-by-step explanation:

Inverse variation is

xy = k

5*60 = k

300 = k

xy = 300

150y = 300

Divide by 150

150y/150 = 300/150

y = 2

Answer:

Absolute value equation is; |x - 25| ≤ 3

Minimum number of bolts is 22 while Maximum number of bolts is 28

Step-by-step explanation:

We are told that;

Each bag should have 25 bolts in it but 22 or 28 is acceptable.

Since 22 or 28 is acceptable, it means the allowable error is ±3.

Thus, if x is the number of bolts in the bag, the absolute value equation would be;

|x - 25| ≤ 3

Minimum number of bolts is 22 while maximum is 28

Answer: the number of devices expected to fail during the second month is 24

Step-by-step explanation:

Given that

The device has a constant failure rate with MTTF of 2 months.

As the device has constant failure rate so it has exponential failure distribution

f(t) = λe^-λt

Here MTTF = 1/ λ

so  λ = 1/2 Months⁻¹ = 0.5 Months⁻¹ and from the question,  Number of devices = 100

E( 1 < x < 2) = E ( x < 2) - E (x < 1)

so E(x < X) can be calculated with λ  = 0.5 Months⁻¹ will be calculated as the failure function

f(x) = λ exp ( - λ×t) for t > 0

F (x>0) = 1 - exp( - λx)

so E ( 1 < x < 2) = E ( x < 2) - E (x < 1)

E ( x < 2) = 1 - exp(-0.5 × 2) = 0.6321 ; E (x<1) = 1 - exp(-0.5 × 2) = 1 - exp( -0.5) = 0.3934

so E ( 1 < x < 2) = 0.6321 - 0.3934 = 0.2387

so the number of devices expected to fail during the second month is;

100 × 0.2387 = 23.87 ≈ 24

Answer:

17/20

Step-by-step explanation:

Total no. of beads = 6 + 3 + 11 = 20

We need RED or GREEN bead .

So no. of beads needed = 6 + 11 = 17

So probability of getting GREEN or RED beads = 17/20

Answer:

3 to 12

Step-by-step explanation:

3 months (January, June, July) and 12 monthes

Answer: the answer is 3 to 12

Step-by-step explanation: hope this will help

Answer:

1/2 meter long

Step-by-step explanation:

To answer this question use the equation 1 1/3 - 5/6

Next make 1 1/3 an improper fraction

To do this multiply the integer and the denominator and then add all of that plus the numerator

This means that 1 1/3 is 4/3

4/3 - 5/6

Next make the denominators the same

This means finding the LCM which is 6

8/6 - 5/6 = 3/6 (1/2)

Heidis hair is 1/2 meters long

Answer:

8

Step-by-step explanation:

Answer:

0 - 1 - 2 + 3 - 4 + 5 - 6 +7 - 8 + 9 = 3

Step-by-step explanation:

Answer:

x = 3

Step-by-step explanation:

mid point means it bisects the segment into two equals halfs meaning

ST = TU

8x + 11 = 12x - 1

8x + 12 = 12x

12 = 4x

3 = x

Answer:  [tex]l=\dfrac{P}{2}-b[/tex]

Step-by-step explanation:

P = 2(l + b)

Divide both sides by 2:

[tex]\dfrac{P}{2}=l+b[/tex]

Subtract b from both sides:

[tex]\dfrac{P}{2}-b=l[/tex]

Note: You can also multiply b by  [tex]\frac{2}{2}[/tex] if you want the left side to be one fraction.

[tex]\dfrac{P}{2}-\bigg(\dfrac{2}{2}\bigg)b=l\\\\\\\dfrac{P-2b}{2}=l[/tex]

Answer:

-5.8<2.9

Step-by-step explanation:

Answer:

bold

Step-by-step explanation:

hshsjjsududidididiidododododokdodkdjdndndnjdudududuididjdjdjd

A plane is a two dimensional figure.

Answer:

147 toys

Step-by-step explanation:

for 1 person, 28toys/8hours = 3.5toys/ 1hour

for 42 people, 42 * 3.5toys/ 1hour = 147 toys/hour

~Hope it Helps!~