Lindsey is a member of the swim team at a local university. She has been working hard to perfect her dive for an upcoming swim meet. Lindsey's dive can be modeled by the quadratic equation y = – 16x2 + 33x + 45, where x is time in seconds, and y is Lindsey's height in the air in feet.

1. At what time will Lindsey be 30 feet in the air?

2. How high is the diving board? Explain your thinking.

Interest on interest, or compound interest, is the adding of interest to the principal sum of a loan or deposit. Mike's account balance after 21 years is $69,131.44.

Interest on interest, or compound interest, is the adding of interest to the principal sum of a loan or deposit. It's the outcome of reinvesting interest rather than paying it out so that interest is received on the principal plus previously collected interest in the next quarter.,

[tex]A = P(1+ \dfrac{r}{n})^{nt}[/tex]

where A is the final amount

P is the principal amount

r is the rate of interest

n is the number of times interest is charged in a year

t is the number of years

The principal amount that Mike invested is $29,000. The rate of interest is 7.24% compounded daily, for 21 years. Therefore, the account balance after 21 years is

[tex]\text{Account Balance after 21 years} = 29,000(1+\dfrac{0.0724}{365})^{(365 \times 21)}[/tex]

                                                     = $69,131.44

Hence, Mike's account balance after 21 years is $69,131.44.

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Equations are separated by an equal sign. The value of x is given as -6/5

Given the equations below;

5(3x + 4) = 2

Expand

5(3x) + 5(4) = 2

15x +20 = 2

Subtract 2 from both sides

15x = 2 - 20

15x = -18

x = -18/15

x = -6/5

Hence the value of x is given as -6/5

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Answer:

x = 37

Step-by-step explanation:

Answer:

14.3%

Step-by-step explanation:

5 students got an A out of 35 total students. This means that the probability of students getting an A is 5/35 = 0.1428

Answer:if we start with 26 letters in the English/Latin alphabet: 26*25*24*23*

and modern Arabic numerals 0–9,

10*9 do the math by multiplying all

Number of dispositions of 4 letters without repetitions of the alphabet (26 letters): 26*25*24*23=358800. 2-digit numbers without repetitions:10*9=90. Number of passwords with 4 letters and 2-digit number without repetitions:

a) if the 2-digit numbers must be in one single position (examples:….XB73DY……..GZ57FE): 358800*90 = 32,292,000.

b) if the 2-digit numbers can be in each of the 5 possible positions (ex.:…73XBDY…X73BDY..XB73DY..XBD73Y..XBDY73…) 5*358800*90=161,460,000.

c) if both digits can be in (C6;2) = 6*5/2= 15 positions (ex.: 7XB3DY…X73BDY…..) 15*358800*90=484,380,000.26*25*24*23*10*9 = 32,292,000

Step-by-step explanation:

Multiply -1/4 by -7/9 ((To do this, multiply the numerator by the numerator and the denominator by the denominator.)

[tex]\bf{\dfrac{-1(-7)}{4\times9)} \ \ \to \ \ \ Multiply }[/tex]

Do the multiplications in the fraction -1(-7) / 4 x 9.

[tex]\bf{\dfrac{7}{36} \ \ \Rightarrow \ \ \ Answer }[/tex]

Answer:

1274

it is 1274

Step-by-step explanation:

mark as brainlest for the answer thankyou

Answer:

c=6p

Step-by-step explanation:

you multiply

6 dollars per pound by p pounds

pounds cancel out and you are left with dollars

that is the cost

Step-by-step explanation:

im sorry but im not sure about this question

Answer:

334.488 miles

Step-by-step explanation:

You don't have a specific request on what I should answer, if it was distance then here's your answer

The steps of student B are in the correct order but the steps of student A are in the incorrect order.

Lines that intersect at a right angle are named perpendicular lines. Lines that are always the same distance apart from each other are known as parallel lines and the lines that never intersect are known as parallel lines.

We have:

You are given AB and point C. Construct a line parallel to AB that passes through point C

The correct way to draw a parallel line to AB that passes through point C is:

The steps of student B are in the correct order but the steps of student A are in the incorrect order.

Thus, the steps of student B are in the correct order but the steps of student A are in the incorrect order.

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Answer: Table 1: Answer = 1. 404

Table 3 Answer = 1.66

Step-by-step explanation: i hope it's right if not, tell me

The more appropriate measure of center is mean.

The more appropriate measure of spread is standard deviation.

Mean is a measure of central tendency that determines the average of a set of numbers. Standard deviation is used to determine the spread of a dataset. It does this by determining the square root of the average of the squared differences of the numbers from the mean of the data set.

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The standard equation of user will be y = 625x²+1250x+5000

A function in mathematics from a set X to a set Y allocates precisely one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two changing quantities.

A connection or statement involving one or more variables is called a function.

From the graph we can find following equation:

(0,5000) ----------- 5000 = [tex]\frac{1}{4(f-k)}(0-h)^2 +k[/tex]

(2,10000) ---------- 10000 = [tex]\frac{1}{4(f-k)}(2-h)^2 +k[/tex]

(4,20000) --------- 20000 = [tex]\frac{1}{4(f-k)}(4-h)^2 +k[/tex]

Solving the above three equations we will get following values:

h = -1

k = 4375

f = 10937501/2500

Hence the standard equation of user will be y = 625x²+1250x+5000

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Answer: c

Step-by-step explanation:

It has been given that the point (3,1) is on the graph.

And in order for the point (3,1) to lie on the graph, of all the given options the closest we can get is when we have Option C

Answer:

Step-by-step explanation:

số nữ là 65- 35= 30

vậy tỷ lệ số tv nữ trên tổng số thành viên của phòng tập là 30/65 = 6/13

The best estimate to the nearest one percent of the fraction; 7/15 is; 47%.

From the task content, it follows that the fraction given whose estimate is to be determined is; 7/15.

The fraction expressed as a percentage is;

(7/15) × 100 %

= 46.667%.

Hence, when rounded to the nearest one percent; = 47%.

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cos and sec can be found

The requried simplified expression is 1 / cosØ, which is equivalent to secØ. The correct option is secØ.

Let's simplify the given expression and see which of the provided options match:

We are given the expression √(1 + tan²Ø).

Now, recall the trigonometric identity: tan²Ø = sin²Ø / cos²Ø.

Substitute this identity into the expression:

√(1 + sin²Ø / cos²Ø)

Next, find a common denominator for the fraction inside the square root:

√((cos²Ø + sin²Ø) / cos²Ø)

Since cos²Ø + sin²Ø = 1 (as per the Pythagorean trigonometric identity), the expression becomes:

√(1 / cos²Ø)

Now, we can take the square root of 1 and cos²Ø separately:

√1 / √cos²Ø

Simplify:

1 / cosØ

The simplified expression is 1 / cosØ, which is equivalent to secØ.

Therefore, the correct option is: secØ.

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[tex] \sf \blue{True✅}[/tex]

Given,

[tex]f(x) = - x + 8 \: and \: f( - 4)[/tex]

Solution:

[tex] f( x) = - ( - 4) + 8 \\ \\ = 4 + 8 \\ \\ = 12[/tex]

Answer:8.8 pounds a day

Step-by-step explanation:

7 days in a week

28/7=4 kg a day

2.2*4=8.8

8.8 pounds

Answer:

x = 3

y = -1

z = 2

Step-by-step explanation:

if x+y = 2, and x+y-z = 0, then we can substitute 2 for x+y. this means 2-z=0, meaning z=2.  if y-z=-3, then y-2=-3, and y=-1. x+y=2 which means x-1=2 so x=3. plug in the values to check your answer.

If the function is f(x) = √(7x – 21). Then the inverse function of the function will be f⁻¹(x) = (1/7) x² + 3.

Let the function will be

f: X → Y

Then the inverse function will be

f⁻¹: Y → X

The function is given below.

f(x) = √(7x – 21)

Then the inverse function will be

x = √[7{f⁻¹(x)} – 21]

x² = 7f⁻¹(x) – 21

7f⁻¹(x) = x² + 21

f⁻¹(x) = (1/7) x² + 3

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Answer:

im not too sure about that sorry!

Step-by-step explanation:

uiwgorihvncjkdnskv

It takes 15 seconds for the first cyclist to overtake the second cyclist.

First, identify the two phases of the first cyclist's motion.

Phase 1: The cyclist accelerates from rest to a constant speed of 8 m/s.

Phase 2: The cyclist travels at a constant speed of 8 m/s.

Find the equations of the two straight-line sections of the graph.

The equations of the two straight-line sections of the graph are as follows:

Phase 1:

s = [tex]2t^2[/tex]

Phase 2:

s = 8t

where s is the distance traveled by the cyclist and t is the time

Set the two equations equal to each other to find the time it takes the first cyclist to overtake the second cyclist

The first cyclist overtakes the second cyclist when the first cyclist has traveled a distance of 8 m more than the second cyclist.

Let t be the time it takes the first cyclist to overtake the second cyclist.

The distance traveled by the first cyclist is then 8t, and the distance traveled by the second cyclist is 8(t - 5).

Setting these two expressions equal to each other, we get:

8t = 8(t - 5)

Solving for t, we get:

t = 15

Therefore, it takes 15 seconds for the first cyclist to overtake the second cyclist

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Answer:

x = -5

Step-by-step explanation:

9x - 7 = -52

we want to single out x,

add 7 to both sides to be one step closer to getting x alone

9x - 7 + 7 = -52 + 7

9x = -45

divided both sides by 9 to get x alone

9x / 9 = -45 / 9

x = -5

Let me know if you need any clarification!

[tex] 9x - 7 = - 52[/tex]

Firstly rearrange the variable on the left side of the equation...

[tex]9x = - 52 + 7[/tex]

Calculate the sum or differences

[tex]9x = - 45[/tex]

[tex]x = - \frac{45}{9} \\ [/tex]

[tex]x = - 5[/tex]

:)

..

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Answer:  [tex]\textsf{y - 2 = -6/5(x - 0)}[/tex]

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Given:  [tex]\textsf{Slope = -6/5, Goes through (0, 2)}[/tex]

Find:  [tex]\textsf{The equation in point-slope form}[/tex]

Solution: We need to take the values that were given to us and plug them into the point-slope form.  It doesn't seem like the problem is asking for anything more than that so we will leave it at that.

Plug in the values

Since the problem is just asking for the equation in point-slope form the final expression would be y - 2 = -6/5(x - 0).

Answer:

[tex]\sf y - 2 = -\dfrac{6}{5}(x - 0)[/tex]

Step-by-step explanation:

[tex]\sf \large \underline{\textsf{Given:}}\ \textsf{a line with a slope of $-\dfrac{6}{5}$, and a y-intercept of $2$}[/tex]

We're given a y-intercept of 2, but using the slope-intercept form, we can immediately determine that x = 0. Hence, the given point is (0, 2).

Then, we substitute these values into the Point-Slope Form to find the equation.

Here are both forms for future reference:

⇒ Slope-Intercept Form: y = mx + b

[ Where: m is the slope, and b is the y-intercept (when x = 0). ]

⇒ Point-Slope Form: y - y₁ = m(x - x₁)

[ Where: m is the slope, and (x₁, y₁) is a given point. ]

Substitute the values into the Point-Slope Form:

[tex]\sf\\\implies y - y_1 = m(x - x_1)\\\\\implies y - 2 = -\dfrac{6}{5}(x - 0)[/tex]

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By definition of linear functions and the comparison with the attached figure, the function that represents the graph is y = (7/15) · x + 4, - 6 ≤ x ≤ 9.

Graphically speaking, linear functions represent lines and we see that the line seen in the figure presents two bounds, the points (- 6, 0) and (9, 7). Linear functions are characterized by slope and intercept:

y = m · x + b     (1)

Slope

m = (7 - 0)/[9 - (- 6)]

m = 7/15

Intercept

b = 4

By definition of linear functions and the comparison with the attached figure, the function that represents the graph is y = (7/15) · x + 4, - 6 ≤ x ≤ 9.

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Answer:

A=30

B=35

C=44

Step-by-step explanation:

The degrees of freedom in testing for differences between the means of two dependent populations where the variance of the differences is unknown are: df = n - 1

In statistics, degrees of freedom refers to the number of distinct values that can change in an evaluation without exceeding any constraints.

The degree of freedom is crucial and necessary when attempting to comprehend the significance of a test statistic and the validity of the null hypothesis.

In testing for differences between the means of two dependent populations where the variance of the differences is unknown, the degrees of freedom are: df = n - 1

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