Yesterday, Lily withdrew $25 from her savings account to buy a birthday gift for her grandfather.
What integer represents the change in Lily's account balance?

Part A: equate the expressions 6x - 8 = 3x - 5

collect the like terms 6x -3x = -5 + 8

Divide by the coefficient x = 1

Part B: The values are (1, -3)

To determine the value of the variables,  we need to consider the equations.

From the information given, we have the equations given as;

y = 3x − 5

y = 6x − 8

Now, equate the expressions, we get;

6x - 8 = 3x - 5

collect the like terms, we have;

6x - 3x = -5 + 8

add or subtract the like terms

3x = 3

Divide by the coefficient

x = 1

Substitute the value

y= 6(1) - 9

expand the bracket

y = 6 - 9 = -3

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1. The function representing the population of bacteria after t minutes is P(t) = 4900× [tex]e^{(0.08(t/60)}[/tex]

2. The percentage rate of change per minute is approximately 0.13%.

The general form of an exponential growth function ⇒ P(t) = P0 ×[tex]e^{(rt)}[/tex]

P(t) is the population at time t,

P0 is the initial population,⇒4900

r is the growth rate  ⇒ 8%

t is the time.

Therefore, our function in terms of hours (t) becomes:

P(t) = 4900 × [tex]e^{(0.08t)}[/tex]

To find per minute, there are 60 minutes in an hour,

∴ t becomes  t/60

P(t) = 4900× [tex]e^{(0.08(t/60))}[/tex]

We know the rate of change per hour is 8%, so the rate of change per minute will be 8% divided by 60, which is

[tex]e^{(0.08/60)-1}[/tex] × 100 = 0.13%.

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Area of shape 1:

Area of triangle = 1/2 × b × h

Area of triangle = 1/2 × 6 × 8

Area of triangle = 24 cm²

Area of shape 2:

Area of Semicircle = πr²/2

Radius of Semicircle = Diameter / 2

Radius of Semicircle = 3 cm

Then,

Area of semicircle = π(3)²

Area of semicircle = 9π cm²

Total Area = Area of semicircle + Area of triangle

Total Area  = (24 + 9π) cm²

Total Area = 52.27 cm² .

Hence Total area of the figure combining triangle and semicircle is 52.27 cm².

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The total invoice is $788.80, we find this by find the cost of each item.

To find the invoice total, we need to calculate the total cost of each item.

For the tablecloth:

Quantity: 16

Unit Price: $35.00

Total Cost = Quantity × Unit Price = 16 × $35.00 = $560.00

For the rings:

Quantity: 8

Unit Price: $6.50

Total Cost = Quantity × Unit Price = 8 × $6.50 = $52.00

For the cups (cases):

Quantity: 4 cases

Unit Price: $25.30

Total Cost = Quantity × Unit Price = 4 × $25.30 = $101.20

For the bowls:

Quantity: 12

Unit Price: $6.30

Total Cost = Quantity × Unit Price = 12 × $6.30 = $75.60

Now, let's calculate the invoice total by adding up the total costs of each item:

Invoice Total = $560.00 + $52.00 + $101.20 + $75.60

= $788.80

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The increase in certain individuals leads to:

An increase in certain individuals within a bacterial population can lead to:

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Answer:

measure of angle 7 + measure of angle 8 = 180°.

Answer:

B). No two lines are parallel

Step-by-step explanation:

In spherical geometry, there are no parallel lines. This is because any two lines on a sphere will eventually intersect.

The length of the cement post's statue is 6.25 feet.

We shall use Mathematical operators to compute the length of the cement post's statue.

(Height of the statue) / (Length of the shadow) = (Height of the cement post's statue) / (Height of the cement post)

Given:

Height of the statue = 25 feet

Length of the shadow = 16 feet

Height of the cement post = 4 feet

Let x =  length of the cement post's statue

25 feet / 16 feet = x / 4 feet

To find x, we cross-multiply:

25 * 4 = 16 * x

100 = 16 * x

To isolate x, we divide both sides of the equation by 16 feet:

100 / 16 = x

x ≈ 6.25 feet

Therefore, the length of the cement post's statue is 6.25 feet.

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The equation of the circle is (x + 4)² + (y - 1)² = 81

Given is an equation of a circle we need to convert it in standard form,

x² + y² + 8x - 2y = 64,

To convert the equation of a circle to standard form, you need to complete the square for both the x and y variables.

The standard form of a circle equation is:

(x - h)² + (y - k)² = r²

where (h, k) represents the center of the circle, and r represents the radius.

Let's convert the given equation to standard form step by step:

x² + y² + 8x - 2y = 64

Rearrange the equation to group the x-terms and y-terms:

x² + 8x + y² - 2y = 64

Now, complete the square for the x-terms.

Take half of the coefficient of x (which is 8 in this case), square it, and add it to both sides of the equation:

x² + 8x + 16 + y² - 2y = 64 + 16

Simplify:

(x + 4)² + y² - 2y = 80

Complete the square for the y-terms.

Take half of the coefficient of y (which is -2 in this case), square it, and add it to both sides of the equation:

(x + 4)² + y² - 2y + 1 = 80 + 1

Simplify:

(x + 4)² + (y - 1)² = 81

Now, the equation is in standard form, with the center at (-4, 1) and a radius of √81 = 9.

Hence the equation of the circle is (x + 4)² + (y - 1)² = 81

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Answer:

3.14 seconds

Step-by-step explanation:

Answer:

x = 6
JN = 10

Step-by-step explanation:

if the values of SN and SP are the same, so are the corresponding sides next to the right angles.
which means:
if SP = SN, then JK = LM.
Use the reverse version of the function for calculating LM (3x + 2).
-2 * 1/3
Now apply that function to 20.
(20-2)/3
= 18/3
= 6.
x = 6
Now JK is a chord.
and Radius SQ intersects JK at a perpendicular right angle (at point N).
So JN would be half the length of JK.
20/2 = 10.
JN = 10

The required median is 110- 120 and the upper quartile of the scores is 110-120.

Given that, the data from the histogram is

CI                 |             f

80-90          |            5

90-100,        |            3

100-110,        |            4

110-120,        |            4

120-130,       |             3

130-140,       |             3

140-150,       |             2

150-160        |             2

To find the median and upper quartile of the given scores, make the cumulative frequency table.

The cumulative frequency table is given below.

CI                 |             f               |             cf            

80-90          |            5               |             5

90-100,        |            3               |             8

100-110,        |            4               |            12

110-120,        |            4               |             16

120-130,       |             3               |             19

130-140,       |             3               |             22

140-150,       |             2               |             24

150-160        |             2               |             26

N = 26.

The median is the N/2 th score when N is even.

Median  = 13th score = 110-120 scores

To find the upper quartile, the product of (3/4 and N )th score gives the upper quartile.

Upper quartile = (3/4 x 26)th score.

Upper quartile = 19.5th  score.

The upper quartile score range is 110 - 120.

Therefore,the required median is 110- 120 and the upper quartile of the scores is 110-120.

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Using the trigonometric ratios:

(1). sinA = 5/13, cosA = 12/13 and tanA = 5/13. And by Pythagoras rule:

(2). x = √116

(3). x = 90

The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.

The basic trigonometric ratios includes;

sine, cosine and tangent.

(1). sinA = 5/13 {opposite/hypotenuse}

cosA = 12/13 {adjacent/hypotenuse}

tanA = 5/13 {opposite/adjacent}

By Pythagoras rule

(2). x = √(4² + 10²)

x = √(16 + 100)

x = √116

(3). 106² = x² + 56²

x² = 106² - 56²

x = √(11236 - 3136)

x = √8100

x = 90

Therefore, using trigonometric ratios:

(1). sinA = 5/13, cosA = 12/13 and tanA = 5/13. And by Pythagoras rule;

(2). x = √116

(3). x = 90

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Answer: The length of the rectangle is given as "2 feet more than 3 times its width."

Let's break it down step by step:

The formula for the area of a rectangle is length multiplied by width. So, in terms of n, the area of the rectangle would be:

Area = Length × Width

= (3n + 2) × n

= 3n^2 + 2n

Therefore, the area of the rectangle, in terms of n, is 3n^2 + 2n.

The notation which is the most appropriate notation when calculating conditional probabilities is option B.

The appropriate notation for calculating conditional probabilities is often denoted using the vertical bar symbol "|". This symbol represents "given" or "conditional on."

In a mathematical expression, the conditional probability of event A given event B is written as P(A | B), where "P" stands for probability. This notation indicates that the probability of event A occurring is being calculated assuming that event B has already occurred.

Thus option B is correct.

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Hello!:

24/12 - 8

= 2 - 8

= -6

The 77th term of the given Sequence is 244.

The given sequence is an arithmetic progression with a common difference of 3. To find the 77th term of the sequence, we can use the formula for the nth term of an arithmetic progression.

The formula for the nth term of an arithmetic progression is:

_ = _1 + ( − 1),

where _ is the nth term, _1 is the first term, is the position of the term in the sequence, and is the common difference.

In this case, _1 = 16 and = 3. Plugging in these values into the formula, we get:

_77 = 16 + (77 − 1) × 3.

_77 = 16 + 76 × 3.

_77 = 16 + 228.

_77 = 244.

Therefore, the 77th term of the given sequence is 244.

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This one's a special case of a right angled triangle with sides (3, 4, and 5 units)

[tex]\qquad\displaystyle \tt \dashrightarrow \: 5 \sin \bigg( \frac{ \pi}{3} x \bigg) = 3[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: \sin \bigg( \frac{ \pi}{3} x \bigg) = \frac{3}{5} [/tex]

Now, check the triangle, sin 37° = 3/5

therefore,

[tex]\qquad\displaystyle \tt \dashrightarrow \: \sin \bigg( \frac{ \pi}{3} x \bigg) = \sin(37 \degree) [/tex]

[ convert degrees on right side to radians ]

[tex]\qquad\displaystyle \tt \dashrightarrow \: \sin \bigg( \frac{ \pi}{3} x \bigg) = \sin \bigg(37 \degree \times \frac{ \pi}{180 \degree} \bigg ) [/tex]

There are three more possible values as :

[tex]\qquad\displaystyle \tt \dashrightarrow \: \sin( \theta) = \sin(\pi - \theta) [/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: sin( \theta) = \sin \bigg( { 2\pi}{} + \theta \bigg) [/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: sin( \theta) = \sin \bigg( \frac{ 3\pi}{} - \theta\bigg) [/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: \frac{ \pi}{3} x = 37 \times \frac{ \pi}{180} [/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: x = 37 \times \frac{ \cancel \pi}{180} \times \frac{3}{ \cancel \pi} [/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: x = \frac{37}{60} [/tex]

or in decimals :

[tex]\qquad\displaystyle \tt \dashrightarrow \: x = 0.616666... = 0.6167[/tex]

[ 6 repeats at third place after decimal, till four decimal places it would be 0.6167 after rounding off ]

similarly,

[tex]\qquad\displaystyle \tt \dashrightarrow \: \pi - \frac{ \pi}{3} x = 37 \times \frac{ \pi}{180} [/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: \pi \bigg(1 - \frac{x}{3} \bigg ) = 37 \times \frac{ \pi}{180} [/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: 1 - \frac{x}{3} = \frac{37}{180} [/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: - \frac{x}{3} = 0.205 - 1[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: \frac{x}{3} = 0.795[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: x = 3 \times 0.795[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: x = 2.385[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: 2\pi + \frac{ \pi}{3} x = 37 \times \frac{ \pi}{180} [/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: \pi \bigg(2 + \frac{x}{3} \bigg ) = 37 \times \frac{ \pi}{180} [/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: 2 + \frac{x}{3} = \frac{37}{180} [/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: \frac{x}{3} = 0.205 - 2[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: \frac{x}{3} = - 1.795[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: x = 3 \times -1 .795[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: x = -5.385[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: 3 \pi - \frac{ \pi}{3} x = 37 \times \frac{ \pi}{180} [/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: \pi \bigg(3 - \frac{x}{3} \bigg ) = 37 \times \frac{ \pi}{180} [/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: 3 - \frac{x}{3} = \frac{37}{180} [/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: - \frac{x}{3} = 0.205 - 3[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: \frac{x}{3} = 2.795[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: x = 3 \times 2.795[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: x = 8.385[/tex]

" x can have infinite number of values here with the same result, here are the four values as you requested "

I hope it was helpful ~

The surface area of the rectangular prism is 318 square mm

From the question, we have the following parameters that can be used in our computation:

9 mm by 6 mm by 7 mm

The surface area of the rectangular prism is calculated as

Surface area = 2 * (Length * Width + Length * Height + Width * Height)

Substitute the known values in the above equation, so, we have the following representation

Area = 2 * (9 * 6 + 9 * 7 + 6 *7)

Evaluate

Area = 318

Hence, the area is 318 square mm

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Question

The net of a rectangular prism and its dimensions are given as 9 mm 6 mm 7 mm. What is the total surface area of the rectangular prism in square inches?

The greatest common factor of -x^2 + 6x - 19 is 1.

To find the greatest common factor (GCF) of the polynomial [tex]-x^2 + 6x - 19,[/tex] we need to factorize the polynomial and identify the common factors among its terms.

First, let's examine the polynomial and see if we can factor it further:

[tex]-x^2 + 6x - 19[/tex]

The polynomial does not appear to have any common factors among its terms.

It cannot be factored using simple integer factors.

In this case, we can say that the GCF of the given polynomial is 1.

It is important to note that the GCF represents the highest degree of common factors that can be factored out from all terms of a polynomial. In this particular case, the polynomial does not possess any common factors that can be factored out.

It's worth mentioning that this polynomial is already in its simplest form and cannot be factored further.

However, if the polynomial had common factors that could be factored out, such as common binomial factors or other mathematical patterns, the GCF would differ from 1.

But in this case, the polynomial does not exhibit any common factors beyond 1.

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While direct answers to iReady tasks are not provided, guidance for tackling problems involving unit rates and ratios with fractions was presented. The concept to calculate the unit rate involves dividing the first quantity by the second quantity. One should work towards solving these problems independently to reinforce the learning.

I'm sorry, but I cannot provide direct answers to your iReady task; it would not be fair or beneficial to your learning. However, I can guide you in how to tackle problems involving unit rates and ratios with fractions. With a unit rate, you're finding a ratio that compares a quantity to one unit of another quantity. The method typically involves dividing the first quantity by the second one.

For example, if you have a problem that says '6 cookies cost $1.50, what is the unit rate?', you would solve it by dividing 1.50 (the cost) by 6 (the number of cookies) to find the unit cost of a single cookie. This gives you a unit rate of $0.25 per cookie. If your questions on iReady involve complex fractions or operations, follow the same concept but use the relevant operation (multiplication, division, etc.). Practice moving toward solving these problems independently to improve your understanding of the concept.

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The exponential regression equation is y = 11.37 * 3.87ˣ

From the question, we have the following parameters that can be used in our computation:

(-4,0.05), (-3, 0.20), (-2, 0.75)

To calculate the exponential regression equation that best fits the data shown, we use a graphing tool

An exponential function is represented as

y = abˣ

From the graphing tool, we have

a = 11.37

b = 3.87

substitute the known values in the above equation, so, we have the following representation

y = 11.37 * 3.87ˣ

Hence, the exponential regression equation is y = 11.37 * 3.87ˣ

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Answer:

friend with this information you cannot know the answer you have to say everything says about that mathematical problem

According to the synthetic division below, the true statements are as follows:

B. The number 4 is a root of F(x) = 3x2-13x+4.

D. (3x2 - 13x+4) - (x - 4) = (3x - 1)

F. (x-4) is a factor of 3x2.13x+ 4.​

Synthetic divisions are the manual ways of bypassing long divisions while performing the Euclidean dividion of polynomials. For the given expressions, we can determine the true statements in this way:

1. F(x) = 3x² - 13x +4.

(x-4) (3x-1)

So, x = 4 or 1/3

4 is an actual root of the function.

2. (3x² - 13x + 4) ÷ (x - 4) = (3x - 1)

3. 3x² - 13x + 4 = (x-4) (3x-1)

So, since all these expressions are true, they meet the requirements for the synthetic division.

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Complete Question:

According to the synthetic division below, which of the following statements are true? Check all that apply. 4 4)3 -13 12 3 0 O A. The number -4 is a root of F(x) = 3x2.13x + 4. B. The number 4 is a root of F(x) = 3x2-13x+4. O C. (3x2 - 13x + 4) - (x + 4) = (3x - 1) D. (3x2 - 13x+4) - (x - 4) = (3x - 1) O E. (x + 4) is a factor of 3x2 - 13x + 4. IF (x-4) is a factor of 3x2.13x+ 4.​

Step-by-step explanation:

5(2x – 3) = x – 15 + 9x

10x - 15 = x - 15 + 9x

10x - 9x - x = -15 + 15

0 = 0

Answer = A) Infinity many solutions

The volume of the largest piece is 10, 597. 5 cm³

The largest part of the cone takes the shape of a cylinder.

Now, the formula for calculating the volume of a cylinder is expressed as;

V = πr²h

The parameters of the formula are enumerated as;

Now, substitute the values, we get;

Diameter = 2 radius

Radius = 30/2

Radius = 15cm

Height = 15cm

Now, substitute the values, we get;

Volume = 3.14 × 15² ×15

Find the square value and substitute, we have;

Volume = 10, 597. 5 cm³

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Answer:

2

Step-by-step explanation:

Ujeli had 11 pencils and she kept 3 so 11-3 = 8

so that means that the remaining pencil were dived by 4 (8÷2) = 2

Answer:

The surface area of the hexagonal pyramid is 313.13 square inches.

Step-by-step explanation:

Hexagonal pyramid,

Surface Area = Area of hexagon base + areas of six triangles

b = 6

h = 12.2 (height of the triangle)

A = [tex]\frac{3\sqrt{3} }{2}b + 6(\frac{1}{2} bh)[/tex]

A = [tex]\frac{3\sqrt{3} }{2}b +3bh[/tex]

A = [tex]\frac{3\sqrt{3} }{2}6 +3*6*12.2\[/tex]

A = 93.53 + 219.6

A = 313.13 square inches