A new species of fish is released into a lake, and the fish multiply quickly. The growth of their population is modeled by the exponential function P(t) = 7bt, where t is the time in weeks after the release and b is a positive unknown base. After observing the population growth over a few weeks, the exponential function P(t) = 7(2)t is used to model the growth. Interpret the significance of 2 in the function as it applies to the situation.

Answer: He bought 2.89 pounds of cameo apples.

Step-by-step explanation:

Since we have given that

Total number of pounds of apples he bought = 4.08

Number of gala apples = 1.19 pounds

So, the rest are cameo apples.

As we know to get the remaining value we always use the subtraction operation,

Now,

[tex]4.08-1.19=2.89[/tex]

So, 2089 pounds of apple are cameo apples.

Final answer:

To find out how many pounds of cameo apples Jake bought, subtract the pounds of gala apples (1.19 pounds) from the total pounds of apples (4.08 pounds), resulting in 2.89 pounds of cameo apples.

Explanation:

Jake bought 4.08 pounds of apples. He knows that 1.19 pounds are gala apples and needs to find out how many pounds of cameo apples he bought. To find the weight of the cameo apples, we subtract the weight of the gala apples from the total weight of apples purchased.

So, the calculation will be as follows:
Total weight of apples - Weight of gala apples = Weight of cameo apples.

4.08 pounds - 1.19 pounds = 2.89 pounds.

Thus, Jake bought 2.89 pounds of cameo apples.

We know that 4 cans of coffee cost $1.60. So, if we divide that number by 4, we get

[tex] 4\text{ cans of coffee} = 1.60 \iff \dfrac{4\text{ cans of coffee}}{4} = \dfrac{1.60}{4} \iff 1 \text{ can of coffee} = 0.4 [/tex]

Now we can simply repeat this process again: if we divide both sides by 4, we get

[tex] 1 \text{ can of coffee} = 0.4 \iff \dfrac{1 \text{ can of coffee}}{4} = \dfrac{0.4}{4} \iff \dfrac{1}{4}\text{ cans of coffee} = 0.1 [/tex]

(0, 0) → t = 0, w = 0 → w = 0 · 0

(1, 4) → t = 1, w = 4 → w = 1 · 4

(2, 8) → t = 2, w = 8 → w = 2 · 4

(3, 12) → t = 3, w = 12 → w = 3 · 4

See the attached picture for the steps:

Answer:

Step-by-step explanation:

The line has a slope (m) of 1 and a y-intercept (b) of -7. Thus the equation in slope-intercept form is

... y = mx + b

... y = x - 7

For a linear function such as this, the size of the domain is equal to the size of the range (because the slope is 1). Thus when one increases, so does the other.

_____

Comments on the problem

It appears the first answer choice is a result of mixing up slope and intercept in the equation of the line. A slope (x-coefficient) of -7 is a pretty steep line going downward from left to right. The graph does not have that characteristic.

It is a bit unusual to talk about domain and range increasing or decreasing. The domain is the region over which the function is defined, so is generally fixed. The range is the corresponding set of values of the function, fixed once the domain is determined. Here, since the function is linear, if one were to define it over a larger region, the range of values produced by the function would also get larger.

ANSWER

EXPLANATION

We want to solve

[tex]0.5(7d+4)=7-1.5d[/tex]

Let us first multiply through by [tex]10[/tex] to clear the decimal.

[tex]10\times 0.5(7d+4)=7\times 10 -1.5d\times 10[/tex]

This implies that;

[tex]5(7d+4)=70 -15d[/tex]

We now expand to obtain;

[tex]35d+20=70 -15d[/tex]

We group like terms to obtain;

[tex]35d+15d=70 -20[/tex]

[tex]50d=50[/tex]

Dividing through by 50 gives;

[tex]d=1[/tex]

Answer:

The value of the equation for d is 1.

Step-by-step explanation:

Consider the provide equation.

[tex]0.5(7d+4)=7-1.5d[/tex]

We need to solve the equation for d.

Open the parentheses.

[tex]3.5d+2=7-1.5d[/tex]

Add 1.5d both sides.

[tex]3.5d+1.5d+2=7-1.5d+1.5d[/tex]

[tex]5d+2=7[/tex]

Subtract 2 from both sides.

[tex]5d+2-2=7-2[/tex]

[tex]5d=5[/tex]

Divide both the sides by 5.

[tex]d=1[/tex]

Hence, the value of the equation for d is 1.

x + 4x = 150

5x = 150  

x = 30

John has x = 30 coins

Mary has 4x = 4*30 = 120 coins.Let the number of coins John has be "x".

The the number of coins Mary has is "4x"

John has 40 coin and Mary has 160 coins because 40 times 4 equals 160 and 160 plus 40 equals 200 so Mary has 160 and John has 40

We could use the standard form of subtraction.

We put 71.120 on top and we put 2.359 at the bottom.

Then, we subtract the thousandths place. It involves a carry-over.

Then, we subtract and the answer is:

68.761

The subtraction of 71.120 and 2.359 equals 68.761.

This question is asking for the subtraction of two decimal numbers, the first being 71.120 and the second being 2.359. To do this, you would stack the numbers on top of each other, aligning the decimal points, and subtract as you would with whole numbers.

So, your subtraction would look like this:

So, 71.120-2.359 equals 68.761.

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The equation of a direct variation: y = kx

Therefore your answer is [tex]D)\ y=\dfrac{2}{3}x[/tex]

Answer: [tex]x = \frac{2}{3}i , -\frac{2}{3}i[/tex]

Step-by-step explanation:

9x² + 4 = 0

       -4   -4

9x²       = -4

   [tex]\frac{9x^{2} }{9} = \frac{-4}{9}[/tex]

    x² = [tex]\frac{-4}{9}[/tex]

   [tex]\sqrt{x^{2} } = \sqrt{-\frac{4}{9} }[/tex]

    [tex]x = +/- \frac{2}{3}i[/tex]

The area of a square is calculated suing the formula x^2, where x is a side length of the square. This is just like length times width because a square has equal side lengths.

Take the left side and add the two lengths together because they form one side length of the square. A side length of the square is x + 4.

To find the area using the side length x + 4, you would square the side length. Your answer is (x + 4)^2.

35 Centimeters Less than Triple the width:

190 cm.   The Perimeter of the box:

W       =      Width of Box

L         =        Length of Box

Length      =     3c    -     35

2W       +    2L        =    190

Just solve to get your answer

Hope that helps!!!!                           : )

a. 500 X 12 =

b. 20,000

Solution:

This problem is a permutation because the order matters here. This means that choosing A as King, B as Knight, C as Bishop and D as Rook results in a different arrangement from B as King, A as Knight, D as Bishop and C as Rook. We would count them both because in the first case A is King, but in the second case A is Knight.

Therefore, the possible number of ways are given below:

[tex]19P4=\frac{19!}{(19-4)!} =\frac{19 \times 18 \times 17 \times 16 \times 15!}{15!} =19 \times 18 \times 17 \times 16 =93024[/tex]

Hence there will be 93024 ways 19 members of a chess club fill the offices of King, Knight, Bishop, and Rook.

There are 19 members in the chess club, and they can fill the offices of King, Knight, Bishop, and Rook in 38760 ways.

In how many ways can the 19 members of a chess club fill the offices of​ King, Knight,​ Bishop, and​ Rook.

To determine the number of ways to fill the offices, we use the concept of permutations. Since each office must be filled by a different member, the number of ways is calculated as 19P4 = 19! / (19-4)! = 38760 ways.

Answer:

Step-by-step explanation:

Given equation is,

y=-0.5x-2

when x=-2 , y=-0.5(-2)-2=1-2=-1

when x=0 , y=-0.5(0)-2=0-2=-2

when x=2 , y=-0.5(2)-2=-1-2=-3

So, we get the points (-2,-1) , (0,-2) , (2,-3)

Now, using the points on the graph and adding them, we will get the graph of given line.

Please check image for the graph.

Now for the second part- we have to find values of x , for which y is positive.

That means, y will be above the x-axis.

From the graph we can see that-  when x<-4,

then the graph is above the x-axis.

So, for all values of x, which are less than  -4,

we will get the positive graph.

x-intercept → y = 0

substitute to 4x - 3y = -24:

4x - 3(0) = -24

4x - 0 = -24

4x = -24   |divide both sides by 4

x = -6

The first one  is your answer because if you plug into the cal it shows the x and y table and it shows that the first one is correct.

The correct ordered pairs for the equation y = -4x + 5 are (-1, 9) and (1, 1).

The correct ordered pairs for the equation y = -4x + 5 are (-1, 9) and (1, 1).

To determine if an ordered pair is a solution to the equation, substitute the x and y values into the equation and check if the equation holds true. For example, for the ordered pair (-1, 9):

y = -4x + 5

9 = -4(-1) + 5

9 = 4 + 5

9 = 9

Since the equation is true, (-1, 9) is a solution to the equation.

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Answer: The two estimates of quotient is 522 and 523 .

Step-by-step explanation:

Compatible numbers are numbers which are close in value to the given numbers, and  make it easy to calculate the answer for any given arithmetic problem .

To find two estimates that the quotient is between in 1045÷2

We now that 1045 is greater than 1044 and less than 1046 i.e.1044<1045<1046

Dividing 2 from all sides ,we get

1044÷2<1045÷2<1046÷2

⇒522<1045÷2<523

As the quotient of 1045÷2 is lying between 522 and 523.

Therefore, the two estimates of quotient is 522 and 523

To estimate the quotient of 1045 divided by 2 using compatible numbers, one can use 1040 (which gives an estimate of 520) and 1050 (which gives an estimate of 525) as they are easily divisible by 2. Hence, the quotient should fall between 520 and 525.

The student is asked to find two estimates that the quotient 1045 ÷ 2 falls between using compatible numbers. To estimate, we look for numbers that are easy to divide. Compatible numbers to 1045 that are close to it and divisible by 2 could be 1040 and 1050. So our two estimates for 1045 ÷ 2 are:

Therefore, the quotient of 1045 ÷ 2 should be between 520 and 525.

I think the answer to your problem is 69

The value of CD = AB = 6.5 cm. Angle CDA = 0 degrees.

To find the value of CD, we can use the fact that the opposite sides of a Trapezium properties are parallel and equal in length.

So, CD = AB = 6.5 cm.

Next, to find the size of angle CDA, we can use the fact that angles formed between perpendicular lines and the base of a trapezium are complementary.

Since BM is perpendicular to AD, angle CDA + angle BDM = 90 degrees.

We are given that angle BDM is 90 degrees, so angle CDA must be 0 degrees.

Learn more about Trapezium properties here:

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The probable question may be:

ABCD is  a trapezium

B draws a perpendicular line on segment AD  as BM is 90 degree

AB=6.5 cm, AD=23 cm, BC=9 cm , BM is 6 cm

Find the value of CD. Work out the size of angle CDA

Complete solution is given in attachment below.

5.51181 in feet. Hope this helps

A) the growth is 56% per week. The 1.56 is multiplying the weight of the pumpkin now by the 56% to get the total weight after the 56% increase.

B) Replace P with 80 and solve for n:

80 = 25(1.56)^n

Divide each side by 25:

80/25 = 1.56^n / 25

3.2 = 1.56^n

Take the natural logarithm of both sides:

ln(3.2) = ln(1.56^n)

Remove the exponent:

ln(3.2) = n(ln(1.56)

Divide both sides by ln(1.56)

n = ln(3.2) / ln(1.56)

n = 2.6 weeks, round to 3 weeks.

C)  Change 1.56 to 1.32 and redo the same calculation from B.

80 = 25(1.32)^n

80/25 = 1.32^n /25

3.2 = 1.32^n

ln(3.2) = ln(1.32^n)

ln(3.2) = n(ln(1.32)

n = ln(3.2) / ln(132)

n = 4.2, round to 4 weeks.

To expand the expression (y + 2)(2y^2 + y + 4), use the distributive property and multiply each term. Combine like terms to simplify the expression.

The given expression is (y + 2)(2y^2 + y + 4). To expand this expression, we can use the distributive property. We multiply each term in the first expression (y + 2) by each term in the second expression (2y^2 + y + 4).

Using the distributive property, we get:

(y + 2)(2y^2 + y + 4) = y * 2y^2 + y * y + y * 4 + 2 * 2y^2 + 2 * y + 2 * 4

Simplifying this expression, we get:

2y^3 + y^2 + 4y + 4y^2 + 2y + 8

Combining like terms, we have:

2y^3 + 5y^2 + 6y + 8

I think the answer would be 6?

6x-1=4x+6

subtracting  4x from each side

2x-1=6

adding 1 to each side

2x=7

divide by 2

x=7/2 or 3.5

check:  6(7/2) -1 =4(7/2)+6

           21-1 =14+6

20=20  correct

The length of a side of the square can be found using the Pythagorean theorem. In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Therefore, we find the length of a side of the square to be the square root of half of the square of the hypotenuse.

To find the length of the side of the square, we are going to use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as: a² + b² = c².

Consider a square with a hypotenuse labeled as 's'. If we bisect this square diagonally, we form two right triangles. Since the sides of the square are equal, we can denote the other two sides of the right triangle as 'D' and 'L'. So, the Pythagorean theorem becomes: D² + D² = s², since D = L. Solving this, we find that s² = 2D².

Therefore, the length of a side of the square 'D'= √(s²/2).

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Answer:

A) y - 2 = 3(x+4)

Step-by-step explanation:

Given that the equation is a line with slope =m=3 and

a point on it (x1,y1) = (-4,2)

Any line having slope m and passing through (x1,y1) has equation in point slope form as

y-y1 = m(x-x1)

We are given here x1 =-4, y1 =2 and m =3

y-y1 = y-2 and x-x1 = x-(-4) = x+4

So equation is y-2 = 3(x+4)

Verify:

The line is y = 3x+12+2 = 3x+14

Hence slope =3 is verified

Substitute the point x =-4 and y =2

2 =3(-4)+14 = 2 is true

Thus verified

Answer:

A is correct option. Equation of line: y-2=3(x+4)

Step-by-step explanation:

Slope of line is 3 and passing point (-4,2).

If slope and passing point given then we have an equation of line

[tex]y-y_1=m(x-x_1)[/tex]

where,

[tex](x_1,y_1)\rightarrow (-4,2)[/tex]

Slope (m)=3

Equation of line:

y-2=3(x+4)

This equation match with option A

Thus. option A is correct.