The table shows the growth, in centimeters, of plants in two different soils after two weeks.



Which statement explains which soil tended to have a greater growth?

Soil A had greater growth because its data have a greater standard deviation.
Soil A had greater growth because its data have a greater mean.
Soil B had greater growth because its data have a greater interquartile range.
Soil B had greater growth because its data have a greater median.

Answer:

y = -4

Step-by-step explanation:

Assuming the problem is [tex]8^{2y+4}=16^{y+1}[/tex], it would be nice if we could convert both sides of this equation to the same base; that way, we could compare the exponents directly in an equation of their own. Fortunately, 8 and 16 are both powers of 2 -- [tex]2^3[/tex] and [tex]2^4[/tex], we can rewrite the original equation by substituting those in:

[tex](2^3)^{2y+4}=(2^4)^{y+1}[/tex]

When you have an exponent raised to another exponent, you multiply those exponents together, so we can simplify our equation by distributing a 3 in the left exponent and a 4 in the right:

[tex]2^{3\cdot(2y+4)}=2^{4\cdot(y+1)}\\2^{3\cdot2y+3\cdot4}=2^{4\cdot y+4\cdot1}\\2^{6y+12}=2^{4y+4}[/tex]

With both of our bases the same, we can now simply compare their exponents directly to solve for y:

[tex]6y+12=4y+4\\2y=-8\\y=-4[/tex]

Answer:

Step-by-step explanation:

c. The point (10,100) reprensents that after 10 business hours, it costs $100 for electricity

d. c=10h

Answer: C= 50.2652

Step-by-step explanation:

The circumference of a circle with an area of 201.06 square inches is approximately 50.24 inches, after calculating the radius from the area and applying it to the circumference formula.

To find the circumference of a circle when given the area, you'll want to perform a series of mathematical steps. The area of a circle is given by the formula A = πr², and the circumference is given by C = 2πr. You can rearrange the area formula to solve for the radius, r, and then substitute that into the circumference formula.

First, solve for the radius:
A = πr² → r = √(A/π) → r = √(201.06/π).

Once you have r, plug it into the circumference formula:

C = 2πr.

Using a calculator, you'll find the following values:

The circumference of a circle with an area of 201.06 square inches is approximately 50.24 inches.

Answer:

Option d. [tex]4y+2x\leq -1[/tex]

Step-by-step explanation:

we know that

If a ordered pair is a solution of an inequality, then the ordered pair must be satisfy the inequality

Verify each case

case a) [tex]y\geq2x+8[/tex]

we have

[tex]x=5, y=-3[/tex]

Substitute the value of x and the value of y in the inequality and then compare the results

[tex]-3\geq2(5)+8[/tex]

[tex]-3\geq18[/tex] -----> is not true

therefore

the ordered pair is not a solution

case b) [tex]-2y<3x-9[/tex]

we have

[tex]x=5, y=-3[/tex]

Substitute the value of x and the value of y in the inequality and then compare the results

[tex]-2(-3)<3(5)-9[/tex]

[tex]6<6[/tex] -----> is not true

therefore

the ordered pair is not a solution

case c) [tex]y-2x>5[/tex]

we have

[tex]x=5, y=-3[/tex]

Substitute the value of x and the value of y in the inequality and then compare the results

[tex]-3-2(5)>5[/tex]

[tex]-13>5[/tex] -----> is not true

therefore

the ordered pair is not a solution

case d) [tex]4y+2x\leq -1[/tex]

we have

[tex]x=5, y=-3[/tex]

Substitute the value of x and the value of y in the inequality and then compare the results

[tex]4(-3)+2(5)\leq -1[/tex]

[tex]-2\leq -1[/tex] -----> is  true

therefore

the ordered pair is a solution

d. 4y+2x≤−1

Step-by-step explanation:

Answer:

-4

Step-by-step explanation:

Okay so basically with functions you are gonna wanna substitute 7 where x is since x=7.

10-2(7) = ?

2 x 7 = 14

10-14=-4

Have a nice day hope this helps :)

:)

Answer:

Step-by-step explanation:

Just put 7 in the place of x

[tex]f(7)=10-2(7)\\f(7)=10-14\\f(7)=-4[/tex]

sqrt(4x) / 2x + 1 = 3

Set domain :

2x + 1 cannot equal 3

2x cannot equal 2 | :2

x cannot equal 1

sqrt(4x) = 3(2x + 1)

sqrt(4x) = 6x + 3

4x = 36x^2 + 9

36x^2 - 4x + 9 / f(x) = ax^2 + bx + c

16-4*36*9

16-1296 = - 1280

There's no solutions in Real Number set.

See the image for solution

Answer: A,B,C

Step-by-step explanation: I did it on Imagine Math :)

Answer:

g(x) is the image of f(x) after stretched horizontally

by scale factor = 5

Step-by-step explanation:

∵ f(x) = x² ⇒ quadratic function

∵ g(x) = (1/5 x)² ⇒ The image of f(x) after one transformation

* Stretches or compresses horizontally:

  It means stretches away from the y-axis

  or compresses toward the y-axis

* If f(x) = (ax)²  :

∵ |a| > 1 is a compression by factor of 1/a

∵ 0 < |a| < 1 is a stretch by factor of 1/a

∵ x-coordinate of f(x) multiplied by 1/5

∵ 0 < 1/5 < 1

∴ The transformation is ⇒ stretched horizontally

∴ g(x) is the image of f(x) after stretched horizontally

  by scale factor = 1 ÷ 1/5 = 5

Answer:

Pretty sure it's 2 strides

Step-by-step explanation:

To get from 7 to 5 you minus by 2, and look how many spaces there are. There are 2

Division and subtraction.

Associative property does not work for Subtraction and Division.

The associative property states that after grouping the expressions in different ways the outcome will not change.

(a + b) + c = a +(b + c)

So associative property is applicable for addition.

( a X b) X c = a X ( b X c) = abc

So associative property is applicable for multiplication

(a ÷ b) ÷ c ≠ a ÷ (b ÷ c)

So, the associative property is not applicable for  Division

(a-b) - c ≠ a - (b -c)

So,  the associative property is not applicable for Subtraction

So, we can say associative property does not work for Subtraction and division.

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Check the picture below.

namely, is the volume of the rectangular prism Paraffin, equals or less than the volume of the cone made from it?

[tex]\bf  \textit{volume of a rectangular prism}\\\\ V=Lwh~~ \begin{cases} L=length\\ w=width\\ h=height\\[-0.5em] \hrulefill\\ L=8\\ w=6\\ h=4 \end{cases}\implies V=8\cdot 6\cdot 4\implies \boxed{V=192} \\\\[-0.35em] ~\dotfill\\\\ \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=5\\ h=25 \end{cases}\implies V=\cfrac{\pi (5)^2(25)}{3}\implies \boxed{V\approx 654.5}[/tex]

well, clearly the cone has enough room to take the 192 cm³.

Is there supposed to be a picture

Answer:

[tex]2\frac{2}{3}[/tex]

Step-by-step explanation:

Given : BC is parallel to DE

To Find : What is the length of CE?

Solution :

AB = 3

BD = 2

AC = 4

Since BC || DE

So, [tex]\frac{AB}{BD}=\frac{AC}{CE}[/tex]

[tex]\frac{3}{2}=\frac{4}{CE}[/tex]

[tex]CE=\frac{4 \times 2}{3}[/tex]

[tex]CE=\frac{8}{3}[/tex]

[tex]CE=2\frac{2}{3}[/tex]

Hence the length of CE is [tex]2\frac{2}{3}[/tex]

Answer:

(x+1) meters

Step-by-step explanation:

Area is length times width so x^2-x-2 = L * (x-2)

factor and divide x-2 to get x+1

The equation would look like this: -3(x + 6) = 4. Then solve to find x.

-3x -18 = 4 → -3x = 22 → x = -7.3

You can substitute this number into the equation to check.

-3(-7.3 + 6) = 4 → 3.9 = 4. As you can see the number isn't exact becuase -7.3 is a repeating decimal.

Answer:

-7 1/3

Step-by-step explanation:

Let x= the distance that Jana lives from school. Then, x < 2/3

The answer 5 (1/4) because if you add 1 and a quarter to it then that would make it 6 and a half

Answer:

B, C,and E

Step-by-step explanation:

edge 2020

Answer:

The answer is (-3, 4).

Step-by-step explanation:

(3, 4) is located in Quadrant I, which is (+, +). Since you're reflecting the point across the x-axis, you'll be in Quadrant IV, which is (-, +). The point will now be (-3, 4).

I hope this helped! :-)

Answer:

x and see others below

Step-by-step explanation:

To find the equivalent expression, multiply the terms using exponent rules.

Exponent rules state to add the exponent of same bases being multiplied.

[tex]x^{\frac{1}{2}} *x^{\frac{1}{2}} =x^{\frac{1+1}{2}} =x^{\frac{2}{2}} = x^1 = x[/tex]

Each of the parts of the expression are equivalent. The simplified equivalent expression is x.

Answer:

Range:

{−7,−2,1,2}

Step-by-step explanation:

[tex] {x}^{2} - 2x - 24 \\ = {x}^{2} - 6x + 4x - 24 \\ = x(x - 6) + 4(x - 6) \\ = (x - 6)(x + 4)[/tex]

Answer:

I  -3/20

Step-by-step explanation:

-3       2

---- * -----

8       5

Multiply the numerators

-3*2 = -6

Multiply the denominators

8*5= 40

The fraction is

-6/40

Both the top and the bottom can be divided by 2

-6/2 = -3

40/2 =20

The fraction becomes

-3/20

The simplified expression is x + 46.

To simplify the expression, let's distribute and simplify each term:

4(-8x + 5) - (-33x - 26)

First, distribute 4 into -8x + 5:

= -32x + 20

Then, distribute -1 into -33x - 26:

= -32x + 20 + 33x + 26

Now, combine like terms:

= (-32x + 33x) + (20 + 26)

= 1x + 46

= x + 46

So, the simplified expression is x + 46.

∴(108+27) cubic feet = 135 cubic feet of concrete are required.

The dimension of lower step is 6 ft× 3 ft× 1.5 ft

and the dimension of upper step is 6 ft ×(9-3)ft × (1.5+1.5)ft = 6 ft × 6 ft ×3 ft

Therefore concrete are required to make lower step = (6×3×1.5) cubic feet

                                                                                      = 27 cubic feet

and concrete are required to make upper step = (6×6×3) cubic feet

                                                                              =108 cubic feet

∴(108+27) cubic feet = 135 cubic feet of concrete are required.

complete questions

Tony needs to create a platform shaped like the diagram with the labeled dimensions.

How many cubic feet of concrete are required?

A) 60 cubic feet

B) 81 cubic feet

C) 108 cubic feet

D) 135 cubic feet

Answer:

Use the simple interest formula: A = P(1 + rt) where P is the Principal amount of money to be invested at an Interest Rate R% per period for t Number of Time Periods.

First, converting R percent to r a decimal

r = R/100 = 5.5%/100 = 0.055 per year.

Solving our equation:

A = 30000(1 + (0.055 × 7)) = 41550  

A = $41,550.00

The total amount accrued, principal plus interest, from simple interest on a principal of $30,000.00 at a rate of 5.5% per year for 7 years is $41,550.00.

Step-by-step explanation:

Answer:

11550

Step-by-step explanation:

Formula for calculating simple interest is : Simple Interest=P x R x T/100

Step 1: Identify P,R,T

P: Principal amount-basic amount of the loan (30,000)

R: The interest rate of the loan (5.5%)

T: Time of payment of loan-in years (7 years)

Step 2: Substitute the values

Simple Interest= P x R x T/100

Simple Interest= 30,000 x 5.5 x7

                                     100

Simple Interest= 1155000

                                100

Simple Interest= 11550

Let's answer the first part of the question: "How much does he owe?"

Step 1: We have calculated simple interest which is 11550.

Step 2: The principal amount has to be paid with the simple interest.

Step 3: Formula- Total money owed= Principal amount + Simple Interest

Total money owed= 30,000 + 11550=41550

Now let's answer the second part of the question: "What is the monthly payment if he chooses the 7-year loan payment plan?"

Step 1: Calculate how many months are there in 7 years. Each year has 12 months therefore 7 years have (7 x 12) 84 months.

Step 2: Divide the total amount that has to be paid by the number of months it has to be paid in.

Monthly payment = Total money owed/ total number of months

Monthly payment = 41550/ 84

Monthly payment = 494.64

2)

P(4,-4) -->(-4, 7)

4 - 8 = -4           -------->left 8

-4 + 11 = 7         -------->up 11

Answer: left 8;  up 11

3)

C(3,-1) , left 4 up 1

3 - 4 = -1    -------->left 4

-1 + 1 = 0   -------->up 1

a)

(x , y) -->(x - 4 , y +1)

C(3, -1) -->C'(-1 , 0)

b)

(x , y) --> (x - 4, y + 1); (-1 , 0)

Answer:   [tex]\bold{\dfrac{2}{65}}[/tex], Dependent

Step-by-step explanation:

[tex]\dfrac{\text{\# of vowels}}{\text{total \# of letters}}[/tex]

1st draw  and   2nd draw

     [tex]\dfrac{5}{26}[/tex]        x           [tex]\dfrac{4}{25}[/tex]     =     [tex]\dfrac{20}{650}[/tex]

[tex]\dfrac{20}{650}\div\dfrac{10}{10}=\dfrac{2}{65}[/tex]

This is dependent because the number of vowels remaining for the 2nd draw is dependent on whether or not a vowel was chosen on the 1st draw.

The area of the tile is 9 square inches.

The area of the tile is given by a product of length and width.

Given

The length of the tile = 3 inches

The width of the tile = 3 inches

The area of the tile is defined as the length of the tile and width of the tile.

[tex]\rm Area \ of \ the \ tile=Length \times Width\\\\[/tex]

Substitute all the values in the formula;

Area of the tiles = length × width

Area of the tile = 3 × 3

Area of the tile = 9

Hence, the area of the tile is 9 square inches.

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The area of a square (side*side) tile with sides of 3 inches is 9 square inches.

The question is asking for the area of a square tile with a side length of 3 inches. In mathematics, the area of a square can be found using the formula Area = side².

So, in this case, the area would be 3² = 9.

This means that the area of the tile is 9 square inches.

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Answer:

[tex]\boxed{\bold{\left(3x-2\right)^2}}[/tex]

Step By Step Explanation:

[tex]\bold{\left(3x\right)^2-2\cdot \:3x\cdot \:2+2^2}[/tex]

[tex]\bold{\left(3x\right)^2-2\cdot \:3x\cdot \:2+2^2}[/tex]

[tex]\bold{\left(3x-2\right)^2}[/tex]

ANSWER

[tex]9 {x}^{2} - 12x + 4 = (3x - 2) ^{2} [/tex]

EXPLANATION

The given expression is

[tex]9 {x}^{2} - 12x + 4[/tex]

This is in the form

[tex]a {x}^{2} + bx + c[/tex]

[tex]a=9,b=-12 ,c=4[/tex]

[tex]ac=9 \times 4 = 36[/tex]

Split with -6x-6x

[tex]9 {x}^{2} - 6x - 6x + 4[/tex]

[tex] = 3x( 3x - 2) - 2(3x - 2)[/tex]

Factor further to obtain,

[tex] = (3x - 2)(3x - 2)[/tex]

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

Answer

So, Sam only asked 20 people in his entire middle school. That is a very small fraction of the amount of kids attending that school. He cannot say that video games is 75% of the entire school's favorite weekend activity if he only asked 20 people. To get a better, more valid result, he should ask around 100+ kids.

Step-by-step explanation:

Two lines y = -x + 3 and y = 2x - 5 are graphed to find their intersection, which gives the x and y values that satisfy both equations.

To find x and y values that satisfy both equations y = -x + 3 and y = 2x - 5, we need to graph these equations and look for their point of intersection.

The intersection represents the x and y values that make both original equations true simultaneously. Use the graph to identify the coordinates of this point for the exact solution.

Out of the choices provided, only [tex]$(-3,5)$[/tex] lies on the intersection of the two lines. Thus the answer is a. [tex]$(-3,5)$[/tex].

Here's a step-by-step solution to find the x and y values that satisfy both equations:

1. Graph the Equations:

    Take the first equation, y = -2/3x + 3. This equation is in slope-intercept form (y = mx + b), where m (slope) is -2/3 and b (y-intercept) is 3.

     -   Plot the y-intercept (3) on the y-axis.

      -  Since the slope is -2/3, remember "rise over run." So in this case for every 2 positions you move down (because it's negative), you move  3 positions to the right. Plot another point based on this movement.

       - Connect these two points with a straight line.

  -  Repeat the process for the second equation, y = 2x - 5. This equation is also in slope-intercept form with m (slope) as 2 and b (y-intercept) as -5.

       - Plot the y-intercept (-5) on the y-axis.

       - The slope is 2, so for every 2 positions you move up, you move 1 position to the right. Plot another point based on this movement.

       - Connect these two points with a straight line.

2. Find the Intersection Point:

   - Observe the graph. The point where the two lines intersect represents the solution where both equations are true simultaneously.

   - In this case, the lines intersect at the point (-3, 5).

Verification:

   - You can substitute x = -3 and y = 5 in both the original equations and see if they hold true.

      - For y = -2/3x + 3, substituting x = -3 gives you y = (-(2/3) [tex]\times[/tex] (-3)) + 3 = 2 + 3 = 5 (which is true).

      - For y = 2x - 5, substituting x = -3 gives you y = (2 [tex]\times[/tex] -3) - 5 = -6 - 5 = -11 (which is not true).

Therefore, the solution (x, y) that makes both equations true is (-3, 5). This is the point where the two lines intersect on the graph.

The graph is provided below.