A seed sprouted and grew
2
3
of a foot in 3 months. What was its rate of growth?
Simplify your answer and write it as a proper fraction, mixed number, or whole number.
feet per month

The sum of (8a + 2b - 4) and (3b - 5) is (8a + 5b - 9). We can find it in the following manner.

To find the sum of (8a + 2b - 4) and (3b - 5), we can simply add the corresponding coefficients of the variables a and b, as well as any constant terms.

So we have:

(8a + 2b - 4) + (3b - 5)

= 8a + 2b + 3b - 4 - 5 (grouping like terms)

= 8a + 5b - 9

Therefore, the sum of (8a + 2b - 4) and (3b - 5) is (8a + 5b - 9).

We can also explain this process by using the distributive property of addition over subtraction. This property states that the sum of two numbers with the same sign (positive or negative) can be found by adding their absolute values and keeping the common sign.

In this case, we can think of the expression (8a + 2b - 4) as the sum of three terms: 8a, 2b, and -4. Similarly, we can think of the expression (3b - 5) as the sum of two terms: 3b and -5.

Using the distributive property, we can add the terms with the same variable together:

(8a + 2b - 4) + (3b - 5)

= 8a + (2b + 3b) - (4 + 5)

= 8a + 5b - 9

Thus, we obtain the same result.

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[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{47.5\% of 1600}}{\left( \cfrac{47.5}{100} \right)1600}\implies 760~\hfill \underset{ females }{\stackrel{1600~~ - ~~760 }{\text{\LARGE 840}}}[/tex]

Step-by-step explanation:

Patel could use the Quadratic Formula to solve it    

   or

    he could 'complete the square' to solve it after dividing thru by 8                          or he could solve it graphically  

{   or he could use factoring to solve it   (difficult)  }

Answer:

a. m(arc) CD = 65°

b. m(arc) AE = 120°

c. m(arc) BC = 55°

d. m(arc) AC = 115°

e. m(arc) ADC = 245°

f. m(arc) AED = 180°

g. m(arc) CE = 125°

h. m(arc) BAD = 240°

Step-by-step explanation:

a.

m<CPD = 180 - 55 - 60 = 65

m(arc) CD = 65°

b.

m<APB = 60°

m<APE = 180° - 60° = 120°

m(arc) AE = 120°

c.

m(arc) BC = 55°

d.

m(arc) AC = 60° + 55° = 115°

e.

m(arc) ADC = 120° + 60° + 65 = 245°

f.

m(arc) AED = 180°

g.

m(arc) CE = 60° + 65° = 125°

h.

m(arc) BAD = 60° + 120° + 60° = 240°

If the distribution of values is normal with a mean of 93.2 and a standard deviation of 87.4. the score separating the bottom 81% from the top 19% is 168.24.

 The value of p81, which is the score separating the bottom 81% from the top 19%, can be calculated as follows:

 The given, Mean = μ = 93.2

                    Standard deviation = σ = 87.4

      We are supposed to find the score separating the bottom 81% from the top 19% which is nothing but the 81st percentile.

       Let X be a random variable with a normal distribution, then the z-score of the 81st percentile is calculated as follows:

               z = InvNorm(0.81)

               z ≈ 0.8 (by standard normal distribution tables)

    The 81st percentile in terms of X is given by:

              p81 = μ + zσp81

                     = 93.2 + 0.8(87.4)p81

              p81 = 168.24

   Thus, the score separating the bottom 81% from the top 19% is 168.24.

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Answer:28 and 16 cams

Step-by-step explanation: let the two parts be x cms and 44 -x cms.

So side of squares will be x/4 and (44-x)/4 resp

Area will be (x/4)^2 and ((44-x)/4)^2 resp

Equation is(x/4)^2  + ((44-x)/4)^2 = 65

(X-28)(x-16) = 0

X =28 or x = 16 cms

The wheel having 3feet diameter and travelling a distance of 45 feet is rotated about 30.00 radians.

A circle's circumference is equivalent to π times its diameter.

We can use the circumference formula to determine the circumference of the wheel

C = πd= π(3) = 9.42 feet where d is the diameter.

The wheel has traveled a distance of 45 feet.

We can determine the number of full rotations made by dividing the distance traveled by the circumference of the wheel.

Number of full rotations = distance traveled / circumference of the wheel= 45 / 9.42 = 4.77 full rotations

It is said that the wheel rolled without slipping, therefore the wheel must have turned 4.77 full rotations. The angle in radians through which it rotated is therefore

Angle in radians = number of full rotations x 2π= 4.77 x 2π= 30.00 radians

Therefore, the wheel rotated through a radian angle of 30.00.

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Answer:

The hypotenuse.

Step-by-step explanation:

The cost of the concrete used to make the cylinder was approximately $6,776.89.

The problem is asking us to find the cost of the concrete used to make a cylindrical pillar, given its dimensions and the cost per cubic meter of concrete. We first need to calculate the volume of the cylinder using the formula for the volume of a cylinder:

[tex]V=pir^2h[/tex]

where V is the volume, r is the radius, h is the height, and π is the constant pi (approximately 3.14159).

In the problem, the diameter of the cylinder is given as 4 meters, which means the radius is half of that, or 2 meters. The height of the cylinder is given as 5 meters.

Substituting these values into the formula, we get:

[tex]V = \pi r^2h = \pi (2)^2(5) = 20\pi cubic meters[/tex]

Next, we need to find the cost of the concrete used to make the cylinder, given that the cost per cubic meter of concrete is $107. We can do this by multiplying the volume of the cylinder by the cost per cubic meter of concrete:

20π × $107 = $6,776.89

Rounding to the nearest cent, we get that the cost of the concrete used to make the cylinder was approximately $6,776.89.

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200 m/s  is the wave speed of a wave that has a frequency .

What do you name a wave?

There are two different types of waves: longitudinal and transverse. Longitudinal waves are similar to those of sound in that they alternate between compressions and rarefactions in a medium, much like transverse waves in that the surface of the medium rises and falls.

                             The pattern of disruption brought about by the movement of energy through a medium (such as air, water, or any other liquid or solid matter) as it spreads away from the source of the sound is known as a sound wave.

The wave speed (v) of a wave can be calculated by multiplying its frequency (f) by its wavelength (λ). Mathematically, we can express this as

v = f x λ

Substituting the given values of frequency and wavelength into this formula, we get:

v = 500 Hz x 0.40 m

Multiplying these values, we get:

v = 200 m/s

Therefore, the wave speed of a wave that has a frequency of 500 Hz and a wavelength of 0.40 m is 200 m/s.

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607 students must there be to guarantee that there are two students with the same professor who earned the same fnal examination score

We use Pigenhole principle to solve this problem.

We know the Pigenjole principle states that if y number of items are put into z number of containers, with y > z, then it means that that at least one container must definitely contain more than one item.

Here, the possible scores are from 0 to 100 with both inclusive.

So, the number of possible scores = 101.

Now,  there are two students with the same professor who earned the same final examination score.

The number of students would be = 101 + 1

                                                     = 102

For each student there are 6 professors.

so the possible combination for a score would  be = 6

So, the number of students must there be to guarantee that there are two students with the same professor who earned the same fnal examination score: (6 × 101) + 1 = 607

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The correct answer is option C, Negative 1/3, which means that the container has lost 1/3 of its original yogurt.

When it comes to representing a decrease in the amount of something, the easiest way is to use negative values.

In this case, option C, Negative 1/3 is the correct choice.

The fraction 1/6 means that the container has 1 part of the original 6 parts of the yogurt left.

However, this shows the remaining amount of yogurt in the container, not the decrease.

Therefore, we can say that the fraction 1/6 is not the correct choice in this context.

Similarly, options B and D are not correct choices for the same reason.

The correct answer is option C, Negative 1/3, which means that the container has lost 1/3 of its original yogurt.

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QR has a length of 2√3. According to the given question

HOW TO CALCULATE THE SIDE OF THE SQUARE ?

In order to solve for QR, we need to use the information given to us in the problem and apply some basic geometry concepts.

First, we know that the diagonals of a square are perpendicular bisectors of each other, meaning they intersect at a 90-degree angle and divide each other in half. This tells us that the length of the diagonal is equal to the square root of two times the length of one of the sides of the square, or d = s√2.

Next, we are given that the midpoint of one of the diagonals is point U, and that US has a length of 3. Because U is the midpoint of the diagonal, we know that SU and UR are equal in length. Let's call this length x.

Now we can use the Pythagorean theorem to solve for x:

(US)²+ (UR)² = (SR)²

3²+  x= (s√2)²

9 + x² = 2s²

We also know that SU and UR are each equal to x, so:

2x² = s²

We can substitute 2x² for s² in the previous equation:

9 + x² = 2(2x²)

9 + x²= 4x²

3x² = 9

x² = 3

x = √3

Now we can use x to solve for the length of QR:

QR = 2x = 2√3

Therefore, QR has a length of 2√3.

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Answer: 0.000012

Step-by-step explanation: The exponent is -5, making it 10 to the power of negative 5. When an exponent is negative, the solution is a number less than the origin or base number. To find our answer, we move the decimal to the left 5 times

1.2 -> 0.000012

Therefore, the minimum acceptable settlement on the case is $103,000.

Percentage is a way of expressing a number as a fraction of 100. It is often denoted by the symbol "%". For example, 50% means 50 out of 100 or 50/100, which is equivalent to the fraction 1/2 or the decimal 0.5.

Percentages are commonly used to express proportions, rates, or changes. They are used in many different fields, such as finance, statistics, science, and everyday life. For instance, we might use percentages to describe the rate of interest on a loan, the percentage of people who have received a vaccine, or the percentage increase or decrease in the stock market.

by the question.

First, we need to calculate the total fee the attorney will earn based on the hourly rate and the percentage of the settlement.

The attorney's fee is the sum of the hourly fee and the percentage of the settlement:

hourly fee = 110 hours x $175 per hour = $19,250

percentage of the settlement = 25% of the settlement

total fee = hourly fee + percentage of the settlement

We know that the total fee must be greater than or equal to $45,000, so we can set up an equation to solve for the minimum acceptable settlement:

$19,250 + 0.25S ≥ $45,000

where S is the settlement amount.

Subtracting $19,250 from both sides, we get:

0.25S ≥ $25,750

Dividing both sides by 0.25, we get:

S ≥ $103,000

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Answer:

The 98% confidence interval for this data is (3.5, 4.4). This confidence interval tells us that 98% of the time, the average rating of all college students in the state for the course will fall between 3.5 and 4.4.

Answer:

Step-by-step explanation:

Step 1: Find the TV price:

£1200×(100%+20%)= £1440

Step 2: Find the final price Harry have to pay:

since he deposited £300 so the ammout he have to pay is:

£1440 - £300 = £1140

Step 3: Find the monthly payment

in this case he pays equally every month so we take the ammount he has to pay devided by 10 months

£1140÷10=£114

Conclusion: He has to pay £114 every month

Three pοints οn the line are: (0,0), (1,30), and (2,60)

When yοu knοw the slοpe οf the line tο be investigated and the given pοint is alsο the y intercept, yοu can utilise the slοpe intercept fοrmula, y = mx + b. (0, b). The y value οf the y intercept pοint is denοted by the symbοl b in the fοrmula.

Tο sοlve the prοblem, we can start by using the fοrmula fοr the equatiοn οf a line in slοpe-intercept fοrm:

y = mx + b

We can use the given infοrmatiοn tο find the slοpe:

m = tοtal distance / number οf days = 150 miles / 5 days = 30 miles/day

b = 0 miles

Therefοre, the equatiοn οf the line representing the tοtal distance Ms. Ibrahim travels fοr wοrk in x days is:

y = 30x

When x = 0 (i.e., when Ms. Ibrahim dοes nοt wοrk), y = 0.

When x = 1 (i.e., οn the first day), y = 30 miles.

When x = 2 (i.e., οn the secοnd day), y = 60 miles.

Sο, three pοints οn the line are: (0,0), (1,30), and (2,60)

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Thus, to order the 700 business cards, Mrs. Latham will spend the amount of $43.

In a linear equation, a first-degree polynomial is defined as the sum of a group of terms, where each term is the product of a constant as well as the initial power of a variable.

The linear equation using the slope intercept form is -

Y = mX + b,

where, Y - number of cards

Slope = (y2 - y1)/(x2 - x1),

y2=500 cards, y1=200 cards, x2=$35, and x1=$23.

m = (500-200)/(35-23) = 300/12

m = 25.

Now,  slope m = 25, apply slope-intercept formula to find y when x=0.

Y = mX + b,

25 = (200 - y)/(23-x),

At,  x=0,

25 = (200-y)/23

200 - y = 25*23

575 = 200 - y

y = -375 (y - intercept)

The linear equation :

Y = 25X -375.

Y = 700. Find X

700 = 25X - 375

25X = 325

X = $43

Thus, to order the 700 business cards, Mrs. Latham will spend the amount of $43.

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Answer:

6436

Step-by-step explanation:

78 x 82

= (80-2) * (80+2)

= (80^2 - 2^2)  

= 6436

Cameron will have to pay amount $242 for the coat, including taxes.

If the coat costs amount $220 and there is a 10% tax on it, Cameron will have to pay an additional:

10% of $220 = 0.1 x $220 = $22

So the total cost of the coat including taxes will be:

$220 + $22 = $242

Therefore, Cameron will have to pay $242 for the coat, including taxes.

When purchasing goods or services, it's important to be aware of any additional costs such as taxes. In this scenario, Cameron wants to buy a coat that costs $220. However, there is a 10% tax on it, which means he will have to pay an extra $22 in taxes. The total cost of the coat, including taxes, will be $242. It's important to note that tax rates may vary depending on the location and type of item being purchased. Being aware of these additional costs can help individuals better budget and make informed purchasing decisions.

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The point (11,10) lies on the circle with center (5,2).

The equation of the circle with center (5,2) and point (11,10) is given by [tex](x-5)^2 + (y-2)^2 = (x-11)^2 + (y-10)^2.[/tex]

Substitute the coordinates of the center and point in the equation and simplify, we get

[tex](x-5)^2 + (y-2)^2 = (x-11)^2 + (y-10)^2= (x-5)^2 + (y-2)^2 = (x-11)^2 + (y-10)^2= x^2 - 10x + 25 + y^2 - 4y + 4 = x^2 - 22x + 121 + y^2 - 20y + 100= -10x + 25 - 4y + 4 = -22x + 121 - 20y + 100= -10x - 22x = 121 - 25 - 20y + 4y=-32x = 96= x = 3[/tex]

Substitute this value of x in [tex](x-5)^2 + (y-2)^2 = (x-11)^2 + (y-10)^2[/tex] and simplify, we get

[tex](3-5)^2 + (y-2)^2 = (3-11)^2 + (y-10)^2= (-2)^2 + (y-2)^2 = (-8)^2 + (y-10)^2= 4 + y^2 - 4y + 4 = 64 + y^2 - 20y + 100= -4y + 8 = -20y + 96= 16 = 16[/tex]

Hence, the point (11,10) lies on the circle with center (5,2).

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complete question

Explain with formula and calculation how a circle with center (5,2) contains the point (11,10).

Explanation

Add up the frequencies:

7+6+12+19+19 = 63

Out of those 63 total spins, 6 of them landed on blue.

The empirical (aka experimental) probability of landing on blue is therefore 6/63 = 2/21

Answer:

7 seconds

Step-by-step explanation:

d is 1225, and we need to find t.

plug in 1225 for d:

1225/25 = t^2

49 = t^2

t = 7

Therefore, the equation in slope-intercept form that has a y-intercept at (0, -3) and also contains the point (4, 5) is y = 2x - 3.

In mathematics, an equation is a statement that asserts the equality of two expressions. It consists of variables, constants, and mathematical operators such as addition, subtraction, multiplication, and division. An equation is usually written with an equal sign (=) between the two expressions. Equations are used to represent mathematical relationships between quantities, to solve problems, and to model real-world situations. They can be used to find unknown values, to predict outcomes, and to test hypotheses. There are many types of equations, including linear equations, quadratic equations, polynomial equations, trigonometric equations, and differential equations. Each type of equation has its own rules and methods for solving it.

Here,

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept. We are given that the y-intercept is (0, -3), so b = -3. To find the slope, we can use the two given points (0, -3) and (4, 5).

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

= (5 - (-3))/(4 - 0)

= 8/4

= 2

Now that we know the slope and the y-intercept, we can write the equation in slope-intercept form:

y = 2x - 3

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Answer:

5 hours

Step-by-step explanation:

Since Shen drove at the same rate for both distances, we can use a proportion to solve for the time it would take him to drive 335 miles:

[tex]\frac{d_{1} }{t_{1} }=\frac{d_{2} }{t_{2} }[/tex]

where d1 is 603 miles, t1 is 9 hours, d2 is 335, and t2 is the unknown value.

Thus, we can simply plug in everything to the equation and solve for t2:

[tex]\frac{603}{9}=\frac{335}{t_{2} }\\ 67=\frac{335}{t_{2} }\\ 67t_{2}=335\\ t_{2}=5[/tex]

(*Note that 9 divides evenly into 603 and becomes 67, which is why I didn't cross-multiply first with he 603 and t2 and the 335 and 9, although you'd still get the same result for t2)

Thus, it would take Shen 5 hours to drive 335 miles.

You can check by finding the rate for both equations since we know that distance is equal to the product of rate and time (d = rt):

First equation:  603 miles = 9 hours * r mph

67 mph = r

603 = 67 * 9

Second equation: 335 miles = 5 hr * r mph

67 mph = r

335 = 67 * 5

The hypotenuse's length could therefore be between 9.03 and 10.70 units based on these estimates.

The term "right triangle" refers to a triangle with an internal angle of 90 degrees. The hypotenuse, the side that faces the right angle and is also the side with the longest side in a right triangle, and the height and base are the two limbs of the right angle.

Based on the information provided, it is reasonable to infer that we have a right-angled triangle with two sides that are y and 7, and we need to determine the length of the hypotenuse.

The hypotenuse's square length is equal to the total of the squares of the lengths of the other two sides, according to the Pythagorean theorem.

The result is:

y² + 7² = hypotenuse²

hypotenuse² = y² + 49

we can determine the length of the hypotenuse by assuming that y is somewhere between 5.7 and 8.1.

If y is 5.7, then:

hypotenuse² = 5.7² + 49

hypotenuse² = 81.49

hypotenuse ≈ 9.03

If  y is 8.1, then:

hypotenuse² = 8.1² + 49

hypotenuse² = 114.61

hypotenuse ≈ 10.70

So, based on these estimations, the length of the hypotenuse could be around 9.03 or 10.70 units.

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Complete question

Estimate the length of the hypotenuse, If the length of the two sides is y and 7 respectively

1) If y= 5.7

2) If y= 8.1

-1

To use regrouping to solve, we need to add and subtract the numbers in the expression, taking care to keep track of any negative signs.

10 - 1 - 1 - 6 - ² - 2

= 10 - (1 + 1) - 6 - ² - 2 [Group the first two numbers together and add them]

= 10 - 2 - 6 - ² - 2 [Simplify the first three terms]

= (10 - 2) - 6 - ² - 2 [Group the first two terms together and subtract them]

= 8 - 6 - ² - 2 [Simplify the first two terms]

= 2 - ² - 2 [Simplify the first two terms]

= -1 [Simplify the expression by subtracting ² and 2 from -1]

Therefore, the final answer is -1.

Answer:

Step-by-step explanation:

the answer is 785.51