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Answer:

the smaller is 9 while the digger is 18

Answer:

f(x) = 60(2)ˣ

Step-by-step explanation:

f(x) = a(b)ˣ

After one month:

120 = a(b)¹

After four months:

960 = a(b)⁴

Divide the second equation by the first:

8 = b³

b = 2

Plug into either equation and find a.

120 = a(2)¹

a = 60

Therefore, f(x) = 60(2)ˣ.

Answer:   (-5, 5)

Step-by-step explanation:

J = (-3, 1)    K = (-8, 11)          ratio 2 : 3    --> 2 + 3  = 5 segments

x-distance from J to K: -8 - (-3) = -5 units

y-distance from J to K: 11 - 1 = 10 units

Divide those distance into 5 segments:

x = -5/5  = -1 unit per segment

y = 10/5 = 2 units per segment

The partition is 2 segments from J:

x = -3 +2(-1)  = -5

y = 1 + 2(2)   = 5

The partition is located at (-5, 5)

Answer:

5

Step-by-step explanation:

Answer:se

Step-by-step explanation:

Answer:

867.44 ft²

Step-by-step explanation:

The area of the shaded region is A = 196π + 252.

We have the dimensions of the unshaded region are 14ft x 18ft.

We have to find the area of shaded region.

The area of a rectangle is -

A(R) = Length x Breadth = L x B

and the area of Circle is -

A(C) = [tex]\pi r^{2}[/tex]

According to the question -

Dimensions of the unshaded region -

L = 18ft

B = 14ft

Area of the shaded region (A) = Total Area - Area of Rectangle

Total Area = Area of 2 semicircles of radius (7 + 7) 14ft + Area of rectangle of length 18ft and breadth 28ft.

Total Area = ( [tex]2\times \frac{1}{2}\times \pi \times14 \times 14[/tex] ) + ( 18 x 28)

Total Area = 196π + 504

Area of the shaded region (A) = 196π + 504 - 252 = 196π + 252

Hence, the area of the shaded region is A = 196π + 252.

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Answer:

Please check if the answer is a = 4 or not

Answer:

200,000

Step-by-step explanation:

The current population: 50,000

Doubling time:70

Population after 280 years=?

280/70=4

50,000*4=200,000

Hope this helps ;) ❤❤❤

Answer: 800,000

Step-by-step explanation: 50,000x2=100,000. That is after 70 years. 100,000x2=200,000. This is after 140 years. 200,000x2=400,000. This is after 210 years. 400,000x2=800,000. This is after 280 years.

Answer: :o I FINALLY MADE IT

(5, 2)

x = 5

y = 2

Step-by-step explanation:

First, I graphed both equations.  They meet at the points (5,2) and (2,5).  Because y < 5, the solution is (5, 2)

Hope it helps <3

Answer:

[tex]x=5\\y=2[/tex]

Step-by-step explanation:

[tex]x^2 +y^2 =29[/tex]

[tex]x+y=7[/tex]

Solve for x in the second equation.

[tex]x+y=7[/tex]

[tex]x+y-y=7-y[/tex]

[tex]x=7-y[/tex]

Plug in the value for x in the first equation and solve for y.

[tex](7-y)^2 +y^2 =29[/tex]

[tex]y^2-14y+49+y^2 =29[/tex]

[tex]2y^2-14y+20=0[/tex]

[tex]2(y-2)(y-5)=0[/tex]

[tex]2(y-2)=0\\y-2=0\\y=2[/tex]

[tex]y-5=0\\y=5[/tex]

[tex]y<4[/tex]

[tex]y=2[/tex]

[tex]y\neq 5[/tex]

Plug y as 2 in the second equation and solve for x.

[tex]x+y=7[/tex]

[tex]x=7-y[/tex]

[tex]x=7-2[/tex]

[tex]x=5[/tex]

Answer:  see below

Step-by-step explanation:

[tex]P(x)=\dfrac{2}{3x-1}\qquad \qquad Q(x)=\dfrac{6}{-3x+2}\\[/tex]

P(x) ÷ Q(x)

[tex]\dfrac{2}{3x-1}\div \dfrac{6}{-3x+2}\\\\\\=\dfrac{2}{3x-1}\times \dfrac{-3x+2}{6}\\\\\\=\large\boxed{\dfrac{-3x+2}{3(3x-1)}}[/tex]

P(x) + Q(x)

[tex]\dfrac{2}{3x-1}+ \dfrac{6}{-3x+2}\\\\\\=\dfrac{2}{3x-1}\bigg(\dfrac{-3x+2}{-3x+2}\bigg)+ \dfrac{6}{-3x+2}\bigg(\dfrac{3x-1}{3x-1}\bigg)\\\\\\=\dfrac{2(-3x+2)+6(3x-1)}{(3x-1)(-3x+2)}\\\\\\=\dfrac{-6x+4+18x-6}{(3x-1)(-3x+2)}\\\\\\=\dfrac{12x-2}{(3x-1)(-3x+2)}\\\\\\=\large\boxed{\dfrac{2(6x-1)}{(3x-1)(-3x+2)}}[/tex]

P(x) - Q(x)

[tex]\dfrac{2}{3x-1}- \dfrac{6}{-3x+2}\\\\\\=\dfrac{2}{3x-1}\bigg(\dfrac{-3x+2}{-3x+2}\bigg)- \dfrac{6}{-3x+2}\bigg(\dfrac{3x-1}{3x-1}\bigg)\\\\\\=\dfrac{2(-3x+2)-6(3x-1)}{(3x-1)(-3x+2)}\\\\\\=\dfrac{-6x+4-18x+6}{(3x-1)(-3x+2)}\\\\\\=\dfrac{-24x+10}{(3x-1)(-3x+2)}\\\\\\=\large\boxed{\dfrac{-2(12x-5)}{(3x-1)(-3x+2)}}[/tex]

P(x) · Q(x)

[tex]\dfrac{2}{3x-1}\times \dfrac{6}{-3x+2}\\\\\\=\large\boxed{\dfrac{12}{(3x-1)(-3x+2)}}[/tex]

Answer:  width = 2.4 in, length = 5

Step-by-step explanation:

The max area of a right triangle is half the area of the original triangle.

Area of the triangle = (6 x 8)/2  = 24

--> area of rectangle = 24 ÷ 2 = 12

Next, let's find the dimensions.

The length is adjacent to the hypotenuse. Since we know the area is half, we should also know that the length will be half of the hypotenuse.

length = 10 ÷ 2 = 5

Use the area formula to find the width:

A = length x width

12 = 5 w

12/5 = w

2.4 = w

The dimensions of the rectangle with greatest area is length is 3 inch and the width is 4 inch.

Let the length and width of the rectangle be x and y.

Then Area of the rectangle = xy

Now, from the triangle we can conclude that

[tex]\frac{6-x}{y} =\frac{6}{8} \\y=8(\frac{6-x}{6} ).[/tex]

Put the value of y in Area we get

[tex]A(x)=x\frac{8}{6} (6-x)\\A(x)=\frac{8}{6}(6x-x^{2} )\\[/tex]

Differentiating it w.r.t x we get

[tex]A'(x)=\frac{8}{6}(6-2x )\\A''(x)=\frac{8}{6}(0-2 )\\A''(x)=\frac{-8}{3}[/tex]

Put A'(x)=0 for maximum /minimum value

[tex]A'(x)=0\\\frac{8}{6}(6-2x)=0\\x=3[/tex]

Now, [tex]A''(3)=-\frac{8}{3} &lt;0[/tex]

Therefore the area of the rectangle is maximum for x=3 inch

Now,

[tex]y=\frac{8}{6} (6-3)\\y=4[/tex]

Thus the dimensions of the rectangle with greatest area is 3 inch by 4 inch.

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Answer:

The  class width is  [tex]C_w \approx 13[/tex]

Step-by-step explanation:

From the question we are told that

 The  upper class limits is [tex]max = 121[/tex]

  The  lower class limits is  [tex]min = 14[/tex]

   The number of classes is  [tex]n = 8 \ classes[/tex]

The class width is mathematically represented as  

       [tex]C_w = \frac{max - min}{n }[/tex]

substituting values

       [tex]C_w = \frac{121 - 14}{8 }[/tex]

       [tex]C_w = 13.38[/tex]

      [tex]C_w \approx 13[/tex]

Since

Answer:

The value of  annuity is  [tex]P_v = \$ 7929.9[/tex]

Step-by-step explanation:

From the question we are told that

    The periodic payment is  [tex]P = \$ 250[/tex]

     The  interest rate  is   [tex]r = 5\% = 0.05[/tex]

     Frequency at which it occurs in a year is  n = 4 (quarterly )

      The number of years is  [tex]t = 10 \ years[/tex]

The  value of the annuity is mathematically represented as

             [tex]P_v = P * [1 - (1 + \frac{r}{n} )^{-t * n} ] * [\frac{(1 + \frac{r}{n} )}{ \frac{r}{n} } ][/tex] (reference EDUCBA website)

 substituting values

             [tex]P_v = 250 * [1 - (1 + \frac{0.05}{4} )^{-10 * 4} ] * [\frac{(1 + \frac{0.05}{4} )}{ \frac{0.08}{4} } ][/tex]

             [tex]P_v = 250 * [1 - (1.0125 )^{-40} ] * [\frac{(1.0125 )}{0.0125} ][/tex]

             [tex]P_v = 250 * [0.3916 ] * [\frac{(1.0125)}{0.0125} ][/tex]

            [tex]P_v = \$ 7929.9[/tex]

Answer:

4 plants

Step-by-step explanation:

If betty has $33 dollars and each plant is $8, than 33/8 ≈ 4

(8 * 4 is 32)

She will have one dollar left but she can't buy another plant since that's not enough.

Answer:

4 plants

Step-by-step explanation:

Take the amount of money she has and divide by the cost per plant

33/8

The amount is 4 with 1 dollar left over

4 plants

Answer:

(28/33+28 ) *100

Step-by-step explanation:

(28/33+28 ) *100

(28/61)*100

Answer:

it's 2

Step-by-step explanation:

I did it before

You did not give any options but i will try to answer.

y < -lxl basically means that the value of y is less than the absolute value of x time - 1.

So if x = 2, then y is any number less than -2.

And if x is -3. then y is any number less than -3.

Happy to help!

Answer:

The probability that the sample mean of IQ scores will not differ from the population mean by more than 2 points is 0.67

Step-by-step explanation:

Please check attachment for complete solution and step by step explanation

Answer:

In 10 years she'll have approximately $21865.4 in her account.

Step-by-step explanation:

When an amount is compounded continuously its value over time is given by the following expression:

[tex]v(t) = v(0)*e^{rt}[/tex]

Applying data from the problem gives us:

[tex]v(10) = 12000*e^{(0.06*10)}\\v(10) = 12000*e^{0.6}\\v(10) = 21865.4[/tex]

In 10 years she'll have approximately $21865.4 in her account.

Answer:

21,865.43

previous answer left out the last digit

Step-by-step explanation:

Answer:

x = 5

Step-by-step explanation:

x = 8 - 3

Thus, x = 5

ANSWER :

6i - (1-i)

Step - by - step explanation:

( 4 + 2i ) - ( 1 - i )

( 4 + 2 × i) - ( 1 - i )

( 6× i ) - ( 1 - i )

= 6i- (1-i)

Hope this helps and pls mark as brainliest :)

Answer:

There are 23 people in line at 6:00 A.M

Step-by-step explanation:

When you plug in h=1, we get 23 people

h corresponds with the time 6:00 am, as a result there are 23 people in line

The equation represents how many people will come as the hour increases.

23 represents the initial amount of people in line.

(got this from Khan academy too:))

Answer:

D. The statement is false. Double blinding is used to decrease the placebo effect.

Step-by-step explanation:

In a double blind study, neither researchers nor the participants know which group is receiving the placebo. If the researchers do not know which group took the medication, they cannot influence the behavior of this group, knowingly or nor, by suggesting how they should behave.

Therefore, a​ double-blind experiment is used to decrease the placebo effect.

Answer:

160 adults and 80 students

Step-by-step explanation:

With the information from the exercise we have the following system of equations:

Let x = number of students; y = number of adults

I want to maximize the following:

z = 3 * x + 6 * y

But with the following constraints

x + y = 240

y / 2 <= x

As the value is higher for adults, it is best to sell as much as possible for adults.

So let's solve the system of equations like this:

y / 2 + y = 240

3/2 * y = 240

y = 240 * 2/3

y = 160

Which means that the maximum profit is obtained when there are 160 adults and 80 students, so it is true that added to 240 and or every two adults, there must be at least one student.

Answer:

See below

Step-by-step explanation:

Proof:

Statements                                    |  Reasons

AD ≅ BC                                         | Given

AD ║ BC                                         | Given

AC ≅ AC                                         |  Reflexive Property

∠DAC ≅ ∠ACB                               | If 2 || lines are cut by a trans., the                                                                       |  alternate interior ∠s are congruent.

ΔADC ≅ ΔBCA                               | S.A.S  Postulate

BA ≅ DC                                         | Corresponding sides of congruent Δs

So, quad. ABCD is a ║gm             | If a quad. has its opposite sides

                                                       | congruent, the quad. is a parallelogram.

It is prove that given quadrilateral is a parallelogram.

            AD ≅ BC      and AD ║ BC              

            AC ≅ AC            

       So that,   ∠DAC ≅ ∠ACB                              

            ΔADC ≅ ΔBCA    

        So that, BA ≅ DC                                        

Hence, opposite sides of given quadrilateral are equal. Therefore, given quadrilateral are parallelogram.

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Answer:

after 6 half lives: 210(1/2)^6= 3.28125

Step-by-step explanation:

isotope to be reduced to half its initial mass at first:

210(1/2)=105 half it is original weight

after second life: 210(1/2)^2=105(1/2)=52.5

after third : 210(1/2)^3=52.5/2=26.25

after fourth : 26.25/2=12.125

after fifth : 13.125/2

after 6 half lives: 210(1/2)^6= 3.28125

Answer:

13, 21

Step-by-step explanation:

Add 8 to the next number from the left to the right.

Answer:

The next three numbers in the sequence are: 13, 21, 29.

Step-by-step explanation:

Common Pattern: +8

-27 +8 = -19

-19 + 8 = -11

-3 + 8 = 5

5 + 8 = 13

13 + 8 = 21

21 + 8 = 29

Answer:

x = 8 ± 2i[tex]\sqrt{2}[/tex]

Step-by-step explanation:

Given

x² - 16x + 60 = - 12 ( subtract 60 from both sides )

x² - 16x = - 72

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(- 8)x + 64 = - 72 + 64, thus

(x - 8)² = - 8 ( take the square root of both sides )

x - 8 = ± [tex]\sqrt{-8}[/tex] = ± 2i[tex]\sqrt{2}[/tex] ( add 8 to both sides )

x = 8 ± 2i[tex]\sqrt{2}[/tex]

The solution of the given expression is ±2√2i+8

An equation is an expression that shows the relationship between two or more numbers and variables.

Given that

x² - 16x + 60 = - 12

Then subtract 60 from both sides;

x² - 16x = - 72

To complete the square then add ( half the coefficient of the x- term )² to both sides

x² + 2(- 8)x + 64 = - 72 + 64,

(x - 8)² = - 8 ( take the square root of both sides )

x =  ±2√2i+8

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Answer:

Blue paint=21 ounces

Step-by-step explanation:

3/4 cup=6 ounces

1 cup=8 ounces

3/4 cup of blue paint=6 ounces of blue paint

1 cup of white paint= 8 ounces of white paint

Ava has 28 ounces of white paint

Find the required blue paint

Let the required blue paint=x

Blue paint ratio white paint

6:8=x:28

6/8=x/28

Cross product

6(28)=x(8)

168=8x

x=168/8

x=21 ounces

Answer:

the length of DF = 3/4 AC

see below for explanation

Step-by-step explanation:

ABC is said to be approximately equal to DEF

The scale factor from ABC to DEF = 3/4

From the question, we can tell the original and new shape is a triangle because the lettering to indicate the vertices for both are 3.

We can deduce from the question, ΔABC was dilated to form ΔDEF

In dilation, the length of each of the corresponding side of the new figure is equal to the multiplication of each of the corresponding sides of the old figure and thee scale factor.

In the absence of cordinates for each vertices and length of each sides, ΔABC has 3 sides :

AB, BC and AC

ΔDEF has 3 sides : DE, EF and DF

If AB corresponds to DE

BC corresponds to EF

AC corresponds to DF

Then:

length DE = scale factor × AB = 3/4 AB

length EF = scale factor × BC = 3/4 BC

length DF = scale factor × AC = 3/4 AC

Therefore, the length of DF = 3/4 AC

Answer:

$57

Since $71.25 was paid for working 7.5 hours.

That means he was being paid $9.5 per hour.

Which is 71.25÷7.5.

And on tuesday that's 9.5×6 which is $57