Let Q(t) = t^2. find a formula for the slope of the secant line over the interval [3,t]. (express numbers in exact form. use symbolic notation and fractions where needed.)

The student will need to save approximately 488.33 dollars per month in order to pay off the remaining cost at the end of 12 months.

First, let's calculate the amount that the student's grandparent will pay: 19,700 / 2 = 9,850

Next, let's subtract the amount of the athletic scholarship: 19,700 - 9,850 - 5,000 = 5,850

Finally, to find the minimum amount that the student will need to save every month, we can divide the remaining cost by the number of months (12): 5,850 / 12 = 488.33

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Rounding to the nearest tenth, the area of the playground is 176.7 square feet.

As per the data given in the question,

We have,

The shape of the playground = circular

So, for finding the area of a circle, we can use the formula of finding the area of a circle:

So, the value of the area will be: A = πr^2,

where A is the area and r is the radius.

Since the fence is 47.1 feet long,

we can assume that it is the circumference of the circle and divide it by 2π to find the radius:

47.1 feet / 2π

= 47.1 / (2 * 3.14)

= 7.5 feet

So the radius is 7.5 feet and the area of the playground is:

A = π * 7.5^2

A= 3.14 * 56.25

= 176.71 square feet

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Answer:

1). 3a^4c^3 or D

2). -1/25 or C

3). -z/y^7 or D

4). 3 or A

5). -4^-4 or A

Step-by-step explanation:

I took the quick check already so enjoy your 100% :)

Answer:

C

Step-by-step explanation:

create two inequalities:

3 < x + 3   and  x + 3 < 6

0 < x         and  x < 3

The simplification are as follows:

Simplification in mathematics refers to the process of making an expression, equation, or mathematical problem easier to understand, solve, or manipulate by reducing its complexity. This can be achieved by combining like terms, cancelling out common factors, reducing fractions, or using the properties of arithmetic operations.

The goal of simplification is to transform a complex expression into a simpler form that can be more easily understood or used in further mathematical analysis.

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The probability of selecting a spade and then selecting a heart is 0.0625, and the correct answer is option A.

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.

Given that the cards are selected with replacement.

The probability of selecting a spade card is:

P(S) =13/52

Now, a heart card is selected.

Since, the previous card is replaced in the deck the total number of cards is 52.

The probability of selecting a heart card is:

P(H) = 13/ 52

The probability of selecting a spade and then selecting a heart is:

P = 13 / 52 × 13/52

P = 0.0625

Hence, the probability of selecting a spade and then selecting a heart is 0.0625, and the correct answer is option A.

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If the line "r" written as y = 1/2x + 8. is perpendicular to Line "s" which includes the point (2,-7) , then the equation of line"s" is  y = -2x -3 .

The Equation of Line perpendicular to another line can be found by interchanging the x and y variables and negating the slope sign .

The equation of line r is :  y = 1/2x + 8, and the slope of line r is 1/2.

The slope of a line perpendicular to line r will be the negative reciprocal of 1/2 that is  -2.

So the equation of line s, which is perpendicular to line r and passes through the point (2, -7), can be written as follows:

⇒ y -(-7) = -2(x - 2)

Expanding and simplifying, we get:

⇒ y + 7 = -2x + 4   ⇒ y = -2x -3

Therefore ,  the equation of line s is ⇒ y = -2x -3 .

The given question is incomplete , the complete question is

The equation for line r can be written as y = 1/2x + 8. Line "s" which is perpendicular to line r, includes the point (2,-7). What is the equation of line s ?

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Answer:

Step-by-step explanation:

Part A:

To find the value of the remaining angles, we can use the fact that the sum of the angles in a triangle is 180°.

First, let's find the value of <1. We have:

<4 + <1 + <2 = 180°

4 + <1 + (180° - 5 - 4) = 180°

4 + <1 + 171° = 180°

<1 = 5°

Next, let's find the value of <7. We have:

<7 + <5 + <6 = 180°

<7 + 135° + (180° - 10 - 5) = 180°

<7 + 135° + 165° = 180°

<7 = 0°

Finally, let's find the value of <9. We have:

<9 + <10 + <11 = 180°

<9 + 11° + (180° - 10 - 11) = 180°

<9 + 11° + 159° = 180°

<9 = 0°

Part B:

The angle <4 is supplementary to angle <1, meaning they add up to 180°.

The angle <7 is congruent to angle <5, meaning they have the same measure.

The angle <9 is congruent to angle <10, meaning they have the same measure.

The number of cupcakes that the customer can buy as inequality will be 3.5C + 2 < 44.

When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relationship between variables and the numbers.

Given that Rebecca sells cupcakes for $3.50 each and charges customers an automatic $2 charge for a cupcake box as well. A customer walks in with $44 dollars.

The inequality can be written as:-

3.5C + 2 < 44.

Where C is the number of cupcakes and $2 is the charge for the box. Which should be lesser than the total amount.

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The inequality equation is x ≤ 8 , where x is the number of cupcakes

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the number of cupcakes be represented as A

Now , the equation will be

The cost of each cupcake = $ 3.50

The cost per box of cupcake = $ 2.00

So , the total cost of x cupcakes = x ( 3.50 + 2.00 )

The total cost of x cupcakes = 5.50x

Now , The amount of money with Rebecca = $ 44

So , the maximum number of cupcakes she can buy is

total cost of x cupcakes < amount of money with Rebecca

Substituting the values in the equation , we get

5.50 x ≤ 44

Divide by 5.50 on both sides of the equation , we get

x ≤ 44/5.50

x ≤ 8 cupcakes

Hence , the inequality equation is x ≤ 8

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You and your friend are approximately 181.23 meters apart at that point in time.

To find the distance between you and your friend, we can use the Pythagorean theorem. Let's call the distance between you two "d".

d² = 250² + 195² - 2 X 250 X 195 X cos(18)

d = √(250² + 195² - 2 X 250 × 195 X cos(18))

d ≈ 181.23 m

So you and your friend are approximately 181.23 meters apart.

The answer was determined using the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two smaller sides equals the square of the length of the largest side (the hypotenuse).

In this case, the two smaller sides represent the distances covered by you and your friend, and the hypotenuse represents the distance between you both.

We can use the theorem to calculate the distance "d" between you and your friend by rearranging the equation to isolate "d". We know the lengths of the two smaller sides (250 m and 195 m), and we also know the angle between them (18 degrees).

We can use the cosine formula to find the cosine of 18 degrees, and plug in all the values into the equation to find "d".

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Answer:

Below

Step-by-step explanation:

5 out of 8 are NOT blue     5/8=.625

The sum of compound interest on a sum of money is (principal ) Rs 2000.

CI = P*(1+R/100) is the formula for compound interest, which is computed by multiplying the starting principle amount by one and  annual interest rate multiplied by the number of compound periods minus one (T)

CI = A – P

Periodic compounding formula is another name for this formula. In this case, A stands for the updated principle amount or the entire sum of money after the compounding period. P stands for the first or original quantity.

now we have :-

time (annual)=2

time (semi-annual)=4

rate  (annual)= 20

rate (semi-annual=10

difference compound interest =   482

CI(semi-annual)-CI(annual) =482

P*(1+10/100)^(4)  - P*(1+20/100)^(2)=482

P{ (14641/10000) - (36/25)}= 482

P(241/10000)=482

P=(482*10000)/241

P= 20000.

So, sum of money is (principal ) Rs 2000.

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the probability of rolling an odd number or rolling a 2 is 2/3

The probability of rolling an even number or a 4 is 2/3

Probability is a mathematical concept that measures the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 means an event is impossible and 1 means an event is certain to occur. The probability of an event can also be expressed as a percentage or as a fraction.

If you roll a six-sided die. The probability of rolling 1, 2, 3, 4, 5 and 6 are as follows:

P (1) = 1/6

P (2) = 1/6

P (3) = 1/6

P (4) = 1/6

P (5) = 1/6

P (6) = 1/6

a. Since there are three odd numbers, P(odd) = 3/6 = 1/2

Thus, the probability of rolling an odd number or rolling a 2 will be:

P(odd or 2) = P(odd) + P(2)

                  = 1/2 + 1/6 = 2/3

b. Since there are three even numbers, P(even) = 3/6 = 1/2

Thus, the probability of rolling an even number or a 4 will be:

P(even or 4) = P(even) + P(4)

                  = 1/2 + 1/6 = 2/3

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A month does not have four weeks, nor does a year have 52 weeks.

The ISO week-numbering year, however, has 52 or 53 weeks.

That translates to 364 or 371 days rather than the typical 365 or 366 days.

Since every month has at least 28 days, every month has 4 full weeks.

There are extra days in some months.

1 week = 7 days.

For the months of January, March, May, July, August, October, and December, a month has 4 weeks and 3 days.

A month in April, June, September, and November has 4 weeks and 2 days.

February in a leap year has 4 weeks and 1 day in a month.

There are around 29 days more than a calendar year.

Which means 4 weeks plus some days.

From 12 month: 4 × 12 = 48 weeks.

Form 29 extra days: 4 weeks and 1 days.

Total weeks: 52 weeks in a year.

Total days: 52 × 7 + 1 = 365 days in a year.

In a leap year, the month of February has 4 weeks and 1 day.

366 days make up a leap year.

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a) Dilation 1 has a scale factor of 3 units.

b) Dilation 2 has a scale factor of 4 units.

c) Dilation 3 has a scale factor of 0 units.

What is a scale factor?

A scale factor is a number used to multiply the dimensions of a shape to enlarge or reduce its size. In geometry, the scale factor is used to create similar figures by preserving their shape while changing their size. If a figure is scaled up by a scale factor of 'k', its dimensions are increased by a factor of 'k'. If a figure is scaled down, its dimensions are reduced by a factor of 'k'.

For the triangle, the scale factor would be 3 units.

For the square, the scale factor would be 4 units.

For the line, the scale factor would be 0 units.

Hence,

a) Dilation 1 has a scale factor of 3 units.

b) Dilation 2 has a scale factor of 4 units.

c) Dilation 3 has a scale factor of 0 units.

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The expression when evaluated is 72 and the expression is 6 * (5 + 7)

The greatest common factor (GCF) of 30 and 42 is 6. We can write each number as a product of 6 and another factor:

30 = 6 * 5

42 = 6 * 7

Now we can use the distributive property to find the sum:

30 + 42 = 6 * 5 + 6 * 7

= 6 * (5 + 7)

= 6 * 12

= 72

So, the sum of 30 and 42 is 72.

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The slope-intercept equation of the line that best fits the data, with a slope of 5.3333 and a y-intercept of 9.6666.

What is the slope?

The slope of a line represents the change in the dependent variable (y) for a unit change in the independent variable (x). In this case, the slope of the line of best fit represents the average change in the test grade for a one hour increase in studying. To find the slope, you can use the formula:

m = (Σxy - (Σx)(Σy)/n) / (Σx² - (Σx)²/n)

To find the slope-intercept equation of the trend line using the first and last data points, we'll first find the slope (m) of the line. The slope can be found using the formula:

m = (y₂ - y₁) / (x₂ - x₁)

where x₁ and y₁ are the values for the first data point, and x₂ and y₂ are the values for the last data point. In this case, the first data point is (1, 15) and the last data point is (7, 47):

m = (47 - 15) / (7 - 1) = 32 / 6 = 5.3333

Next, we'll use the slope and the first data point to find the y-intercept (b) using the formula:

b = y₁ - m * x₁

b = 15 - 5.3333 * 1 = 15 - 5.3333 = 9.6666

Finally, we'll use the slope and y-intercept to write the slope-intercept equation of the line:

y = mx + b

y = 5.3333x + 9.6666

Hence, the slope-intercept equation of the line that best fits the data, with a slope of 5.3333 and a y-intercept of 9.6666.

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Answer:

[tex]y=\dfrac{16}{3}x+\dfrac{29}{3}[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{8cm}\underline{Slope Formula}\\\\Slope $(m)=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line.\\\end{minipage}}[/tex]

The first and last data points of the given table are:

Substitute the data points into the slope formula to find the slope of the trend line:

[tex]\text{Slope}\;(m)=\dfrac{47-15}{7-1}=\dfrac{32}{6}=\dfrac{16}{3}[/tex]

[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]

Substitute the found slope and the first data point into the slope-intercept formula and solve for b:

[tex]\implies 15=\dfrac{16}{3}(1)+b[/tex]

[tex]\implies 15=\dfrac{16}{3}+b[/tex]

[tex]\implies b=15-\dfrac{16}{3}[/tex]

[tex]\implies b=\dfrac{45}{3}-\dfrac{16}{3}[/tex]

[tex]\implies b=\dfrac{45-16}{3}[/tex]

[tex]\implies b=\dfrac{29}{3}[/tex]

Therefore, the equation of the trend line in slope-intercept form is:

[tex]y=\dfrac{16}{3}x+\dfrac{29}{3}[/tex]

According to the concept of fraction the value of the quantity at any time t is -4.

A fraction is a mathematical representation of division of two numbers. In this case, we will be using fractions to solve an initial value problem.

The initial value problem is ′=−2,(0)=−4.

This means that the rate of change of the quantity is -2 and its starting value at time 0 is -4.

To solve this problem, we need to find the value of the quantity at some other time.

Here the first step is to find the general solution to the differential equation ′=−2.

This can be done by integrating both sides, which gives us

=> −2.

Integrating, we get

=> −2 + C, where C is an arbitrary constant.

Next, we use the initial value to find the value of C.

We know that when t=0, the value of the quantity is -4, so we can substitute these values into the general solution to get

=> -4 = -2 + C.

Solving for C, we get C = -2.

Finally, we substitute C into the general solution to get

=> -2 -2 = -4.

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The person incurred a loss of: ₹8 in the bargain.

The person purchased 10 eggs for ₹4 each, so the total cost of the eggs is:

This is the money they spent on buying the eggs.

They then sold 8 eggs for ₹4 each,

so the revenue from the sale is:

This is the money they received from selling the eggs.

To calculate the profit or loss in the transaction, we subtract the cost from the revenue:

A negative result indicates a loss. So, in this case, the person incurred a loss of ₹8 in the bargain. This means they received less money from selling the eggs than what they spent on buying them.

Complete Question:

"A person purchased 10 eggs for ₹4 and sold 8 eggs for ₹4. The profit or loss in the bargain will be?"

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The height of the tree that casts a shadow is 28.45 meters will be 12.68 meters.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

The ratio of the matching sides will remain constant if two triangles are comparable to one another.

Ethan is 1.85 meters tall. At 10 a.m., he measures the length of a tree's shadow to be 28.45 meters. He stands 24.3 meters away from the tree.

Then the height of the tree is given as,

h / 1.85 = 28.45 / (28.45 - 24.3)

h / 1.85 = 28.45 / 4.15

h = 1.85 x 28.45 / 4.15

h = 12.68 meters

The height of the tree that casts a shadow is 28.45 meters will be 12.68 meters.

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The height of the chimney is 357 feet according to mentioned dimensions of the chimney and observer.

The ratio of base and height according to angled of elevation will be -

tan theta = perpendicular ÷ base. The same will be for chimney. Hence, equating the ratio of both to find the height of chimney.

The formula will be -

Perpendicular ÷ base of observer = perpendicular ÷ base of chimney

6/4 = height/238

Rewriting the equation according to height of chimney

Height = (6 × 238)/4

Performing multiplication on Right Hand Side of the equation

Height = 1428/4

Performing division on Right Hand Side of the equation

Height = 357

Thus, chimney is 357 feet tall.

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Answer:

Below

Step-by-step explanation:

Interest for a WHOLE 12 months would be   14 000 * .025 = 350

but Jane had the account for   9 out of 12 months

9/12  * 350 = 262.50 dollars

The choice that  is equivalent to the product given is 2√10

What are surds ?

Surds in mathematics are the square root values that can't be further condensed into whole numbers or integers. Numbers with surds are illogical.

Surds are the square roots of numbers ( √) that are not able to be divided into whole or rational numbers. It cannot be precisely described by a fraction. A surd, then, is a root of a whole number with an irrational value.

√8 •√5

= √(8*5) = √40

= √(10*4)

= √4  * √10

= 2√10

The choice that  is equivalent to the product given is 2√10

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The peak to peak value of a sine wave is twice the peak value. Therefore, total number of the peak to peak value of this waveform is 2 x 80 VAC = 160 VAC.

The peak to peak value of a sine wave is an important measure of the waveform's amplitude. It is calculated by multiplying the peak value of the waveform by two. The peak value of this particular waveform is 80 VAC, so the peak to peak value of the waveform is 2 x 80 VAC = 160 VAC. This peak to peak value is a measure of the total number voltage swing of the waveform, from its lowest point to its highest point. The peak to peak value of this waveform is a useful parameter for understanding the waveform's strength and potential for causing electrical damage. As such, it is important to measure and understand the peak to peak value of any sine wave in order to successfully manage its power and potential for causing harm.

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The size of the input is doubled, the time taken to execute the loop will also double.

The time complexity of this pseudocode is O(n). This can be determined by analyzing the number of times the loop is executed. The loop is entered once and is then executed n times, where n is the number of times the loop is executed. This can be expressed mathematically as T(n) = 1 + n. Since the loop is executed a constant number of times, regardless of the size of the input, the time complexity of the pseudocode is O(n). This means that the execution time of the loop grows linearly with the size of the input. Thus, if the size of the input is doubled, the time taken to execute the loop will also double.

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y = tan(x) - (π/2 + πn)

This equation represents a tangent function with a domain of all real numbers, except for multiples of pi/2 plus pi.

The equation y = tan(x) - (π/2 + πn) represents a tangent function with a domain of all real numbers except for multiples of pi/2 plus pi. This equation is useful for finding the tangent value of any given x-value, as long as it is not equal to a multiple of pi/2 plus pi. The equation works by subtracting the multiple of pi/2 plus pi from the x-value, and then finding the tangent of the new value. This allows the tangent of the x-value to be found, regardless of whether or not it is equal to a multiple of pi/2 plus pi.

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54.10Answer:

Step-by-step explanation:

Answer:

The answer should be 20 days.

Step-by-step explanation:

The way that I solved it: 1/4 times 5.

James and Sandra drank the most soda from their cup.

The information that was given gave specific amount that each person drank from their soda, but James and Sandra were not given a specific amount, so one can only assume they drank the most since their own percentage of drink is not disclose.

Percentage is a way to express a number as a fraction of 100. It's often denoted using the symbol "%". For example, 50% means 50 per 100, or one half

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