Exponential functions

Quadratic equation :The maximum height reached by Alonzo's ball will be 9m.

What is a quadratic equation?

The equation whose highest degree of the variable used in the equation is 2 and has 2 roots, is called quadratic equation.

Here the quadratic equation of the path of Chase's ball is given by y = - 4x²+ 5x+ 7
To compare the height of both paths followed by the ball
we have to first calculate the height of the path of Chase's ball.
the path of Chase's ball is f(x)=-4x²+ 5x+ 7
The function will have the highest value when f'(x) will be 0.
f'(x)=-8x+5
f'(x)=0
⇒-8x+5=0
⇒-8x=-5
⇒x=5/8
at x=5/8, function value is
f(x)=-4x²+ 5x+ 7
=-4(5/8)²+ 5(5/8)+ 7
=-4(25/64)+(25/8)+7
=(-25/16)+25/8+7
=8.5625
There maximum value of f(x) is 8.5625.
The maximum height reached by Chase's ball will be 8.5625m.
From the graph of the path of Alonzo's ball, it is clear that
The maximum height reached by Alonzo's ball will be 9m.
As 8.5625m < 9m
Alonzo's baseball will reach greater height.

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Complete Question:
Chase and Alonzo stand next to each other and throw baseballs in the air. The path of Chase's ball is described by the equation y = - 4x²+ 5x+ 7. The path of Alonzo's ball is shown by the graph. In each function, x is the horizontal distance the ball travels in meters, and y represents its height. Whose baseball reaches a greater height?
A. Both baseballs reach the same height.
B. Chase's baseball
C. Alonzo's baseball
D) Non of these

Answer:

Alonzo's baseball

whompwhompwhompwhopwhompwhompwhompwhompwhompwhompwhompwhompwhompwhompwhomp

Step-by-step explanation:

The expression fraction with negative 4 times the quantity 2 minus the cube root of 8 times 6 end quantity as the numerator and 5 is simplified to give 8

The fraction: negative 4 times the quantity 2 minus the cube root of 8 times 6 end quantity as the numerator and 5 is written in words

Rewriting the fraction

-4( (2 - ∛8 * 6) / 5)

The equation is simplified as

= -4( (2 - ∛8 * 6) / 5)

= -4( (2 - 2 * 6) / 5)

= -4( (2 - 12) / 5)

= -4( (-10) / 5)

= -4( -2)

= 8

Option C, 8 is the correct answer

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Answer:

NO

FALSE

Step-by-step explanation:

The diameter divides the circle into two equal part called semi– circles( the image on white)

A sector is the plane figure enclosed by two radii of a circle or ellipse and the arc between them.

( the image that is dark)

i hope this helped

Answer: No, the diameter of a circle divides the circle into two equal halves called semi circle.

Step-by-step explanation:

The line that splits a circle into two identical halves is its diameter. The widest chord that divides the circle in half exactly is called the diameter. Each component is known as a semicircle.

Answer:

6 days

Step-by-step explanation:

total is 445

first day charge is 145

so, 445-145 = 300

second day onwards its 60.

so, 300/60 = 5 days

so total 5+1 = 6 days.

I hope I helped you

Answer: 9.7

Step-by-step explanation: 97 divided by 10 is 9.7

The total miles that Laney walked is 11 2/3 miles.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

In this situation, Laney walks 2 1/3 miles to school from her house and rides the bus home and she attended school five days last week.

The total miles that Laney walked will be:

= 2 1/3 × 5

= 7/3 × 5

= 35/3

= 11 2/3 miles

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Step-by-step explanation:

y = 2/3x + 7

Multiply both sides by 3 to get rid of the fraction 2/3

3y = 2x +21

subtract 2x from both sides

3y - 2x = 21

Answer ofc is 3x - 2y = 21

Please rate if you get the answer right.

For 8% p-value cutoff , Melissa should use 92% confidence interval

A confidence interval calculated for a treatment effect measure shows the range in which the true treatment effect is likely to fall.

A smaller sample size or higher variability will result in a wider confidence interval with a larger margin of error. The interval width is also influenced by the level of confidence. If you want a higher level of certainty, the interval should be wider.

The width of the confidence interval and the size of the p value are related.

The narrower the interval, the smaller the p value. The confidence interval, on the other hand, provides useful information about the likely magnitude of the effect under consideration as well as the accuracy of the estimate.

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AE(X) = $23,333.33  could John expect to collect in yearly leases for the whole building in a given year.

What is  probability ?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a proposition is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

The given table is:

Number of Lease Offices :  0           1         2       3        4         5

Probability                         : 5/18     1/4     1/9    1/18     2/9      1/12

The expected probability is

Expected probability [tex]$=\sum_{i=0}^5 x_i p\left(x_i\right)$[/tex]

Expected probability [tex]$=0 p(0)+1 P(1)+2 P(2)+3 P(3)+4 P(4)+5 P(5)$[/tex]

Expected probability [tex]$=0 \cdot\left(\frac{5}{18}\right)+1 \cdot\left(\frac{1}{4}\right)+2 \cdot\left(\frac{1}{9}\right)+3 \cdot\left(\frac{1}{18}\right)+4 \cdot\left(\frac{2}{9}\right)+5 \cdot\left(\frac{1}{12}\right)=\frac{35}{18}$[/tex]

It is given that the yearly lease [tex]$=\$ 12,000$[/tex].

The yearly leases for the whole building in a given year is

Yearly leases [tex]$=\frac{35}{18} \times 12000=23333.3333333 \approx 23333.33$[/tex]

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Answer:

Step-by-step explanation:

-1

Answer:

-11

Step-by-step explanation:

Equation:

5+x=-6

The image after a dilation with scale factor k=3, then the vertices of triangle X'Y'Z' are X'(-9, 6), Y'(6, 9) and Z'(3, -3).

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).

The basic formula to find the scale factor of a figure is expressed as,

Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape.

Given that, the triangle with vertices X(−3, 2), Y(2, 3), and Z(1,−1) and scale factor k=3.

Now, X(-3, 2)→3(-3, 2)→X'(-9, 6)

Y(2, 3)→3(2, 3)→Y'(6, 9)

Z(1,-1)→3(1, -1)→Z'(3, -3)

Vertices of X'Y'Z' are X'(-9, 6), Y'(6, 9) and Z'(3, -3).

Therefore, the image after a dilation with scale factor k=3, then the vertices of triangle X'Y'Z' are X'(-9, 6), Y'(6, 9) and Z'(3, -3).

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Answer:

The runners will be in a straight line after 1/2 seconds.

To solve this problem, we can set the y-coordinates of each runner equal to each other and solve for t. The y-coordinate represents the lane number, and if the lane numbers are equal, the runners are on a straight line.

Jon: y = 1

Laura: y = 2

Ellis: y = 4

Jon: 3t = 1

Laura: 4t = 2

Ellis: 6t = 4

Solving these equations simultaneously, we find that t = 1/2 seconds. This means that after 1/2 seconds, the runners will be in a straight line.

Answer:

Step-by-step explanation:

(2, 0), (4, -6)

(-6 -0)/(4 - 2)= -6/2= -3

y - 0 = -3(x - 2)

y = -3x + 6

or

f(x) = -3x + 6

Answer:

Step-by-step explanation:y= -3x + 6

The simplified form of the given expression, [tex]\frac{4x \times 1}{x^{-5} \times x^{-3} }[/tex] is equal to [tex]4x^{9}[/tex]

What are Exponents?

What is the Product of Powers rule?

In this question, the expression is  [tex]\frac{4x \times 1}{x^{-5} \times x^{-3} }[/tex]  ------(1)

Multiplying the values in the numerator, we get

[tex]\frac{4x \times 1}{x^{-5} \times x^{-3} }=\frac{4x}{x^{-5} \times x^{-3} }[/tex]

Now, the values in the denominator can be simplified using the Product of Powers rule.

The formula for the Product of Powers rule is given as, [tex]x^{m} \times x^{n} =x^{m+n}[/tex]

Simplifying the given expression using the Product of Powers rule, we get

[tex]\frac{4x \times 1}{x^{-5} \times x^{-3} }=\frac{4x}{x^{-5+(-3)} }\\\implies \frac{4x \times 1}{x^{-5} \times x^{-3} }=\frac{4x}{x^{-8} }[/tex]     -----(2)

The formula for the Quotient of Powers rule is given as, [tex]\frac{x^{m} }{x^{n} } =x^{m-n}[/tex]

Simplifying the expression in (2) using the Quotient of Powers rule, we get

[tex]\frac{4x \times 1}{x^{-5} \times x^{-3} }=4x^{1-(-8)} \\\implies \frac{4x \times 1}{x^{-5} \times x^{-3} }=4x^{9}[/tex]

Therefore, the simplified form of the given expression is [tex]4x^{9}[/tex]

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The best buy is pack  of 30 .

A cost function is a mathematical formula used to chart how production expenses will change at different output levels.

The general form of the cost function formula is C(x)=F+V(x) C ( x ) = F + V ( x ) , where F is the total fixed costs, V is the variable cost, x is the number of units, and C(x) is the total production cost.

Division is the opposite of multiplication.

A division is a process of splitting a specific amount into equal parts.

Pack A has 30 pencils

sells for $7.50.

pack of 30:

7.97/30 = 0.27 per pencil

Pack B has 12 pencils

costs of $4.25.

pack of 12:

4.77/12 = 0.40 per pencil

The best buy is pack  of 30 because:

0.27 < 0.40

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(b) System B is likely to experience a smaller increase in the average time in queue.

As utilization increases, the length of time in line grows more quickly. So a 5% increase in utilization has a larger effect from 90% to 95% than from 80% to 85%.

When you use something, you use it, whether it's a tool—like when you write something down with a pen—or a talent or skill—like the speed you use when you run a race. Utilization is the act of using something, such as using your voice to sing a song. It may be necessary for a team to use a gym for practices until the rain stops.

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Answer:

The average rate of change of f(x)= 4x^2 + 3x on the interval [1,5] is 18.

The equation for the line we want to get is:

y = -x + 3

A general linear equation is written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

Two lines are perpendicular of the product between the slopes of the two lines is -1.

Here we want to find a line perpendicular to the one that passes through  the line with Y(1,3) and Z(-3,-1), the slope of that line is:

a = (-1 - 3)/(-3 - 1) = 1

Then the slope of a perpendicular line, a', is:

a'*1 = -1

a' = -1

Then our line is like:

y = -1*x + b

To find the value of b, we use the fact that this line passes through (1, -4), then we will get:

-4 = -1*1 + b

-4 + 1 = b

-3 = b

So the linear equation is:

y = -x + 3

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1. Reason: Since QA divides ∠PQR into two different parts so it is a bisector∠PQA≅∠RQA.

2. The line which divides an angle into two different angles is known as a bisector.

4. ∠QXA≅∠QYA and they are situated opposites to each other so we can say that right angles are conjugate.

5. Given, Both are situated in the same plan so QA≅QA

6.ΔQXA≅ΔQYA, by the AAS Postulate.

8. Definition of equidistant. XA=XY.

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Answer:

Step-by-step explanation:

a) the opposite angles of a quadrilateral inscribed in a circle are supplementary

70 + angle D = 180

angle D = 180 - 70

angle D = 110 degrees

b) DAB is a semicircle, so angle A and angle C are two circumference angles whose sides passes through the extremes of the diameter.

The centre angle of a semicircle is 180 degrees and its circumference angle is half that measure, so its value is 90 degrees

A = 90 degrees

C = 90 degrees

The probability that at least one of ten random numbers drawn from a standard normal distribution will exceed 2.66 is 0.045.

This can be calculated using the complementary probability formula, which is 1 - P(x ≤ 2.66), where P(x ≤ 2.66) is the probability that all ten numbers are less than or equal to 2.66.

The probability that all ten numbers are less than or equal to 2.66 can be calculated using the normal distribution function, which gives the probability that a random variable x follows a normal distribution with mean μ and standard deviation σ. For a standard normal distribution, the mean is 0 and the standard deviation is 1, so the probability that all ten numbers are less than or equal to 2.66 can be calculated as:

where Φ(x) is the normal distribution function.

Substituting this value into the complementary probability formula, we get:

Thus, the probability that at least one of ten random numbers drawn from a standard normal distribution will exceed 2.66 is 0.045.

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Answer:

Here is your answer,

Step-by-step explanation:

(c)

x + y = 31 ------ (i)

x - y = 5 ------ (ii)

We have subtract eqn (ii) from eqn (i). Here we get the equation as,

2y = 26

y = 13 ------(iii)

Put eqn (iii) in eqn (i), we get -

=> x + y = 31

=> x = 31 - 13

=> x = 18

Therefore, their present ages of younger brother & older brother is 13 yrs & 18 yrs respectively.

In mile there are 63360 inches.

The number of inches in a mile is equal to the number of inches in a foot times the number of feet in a mile

We multiply 528 by 12 and add one zero to the right of the result.

Use vertical form to perform the multiplication.

So. 12 × 5280=63360

  ∴ 5280/6336

  = 1056

The number of inches in a mile = 12 × 5280

We multiply 528 by 12 and add one zero to the right of the result.

Use vertical form to perform the multiplication:

  528 × 12 = 1056

1056 + 5280 = 6336

So, 12 × 5280 = 63360 miles

Therefore, in mile there are 63360 inches.

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Answer:

x = 20

Step-by-step explanation:

x + 2x + 6x = 9x / 180

x=20

triangles = 180

angle 1 = ?

angle 2 = 160?

angle 3 = 20

Answer:  -45x + 111 or -3(15x-37)

Step-by-step explanation:

Instead of :6 (8-3x )− 3 (9x−1 )+ 60

54 - 18x = −27x − 3 + 60

54 - 18x = −27x + 57

-18x = -27x + 3

9x = 3

x= 1/3

Corrected :

6 (8-3x )− 3 (9x−1 )+ 60

First Simplify : 54 - 18x -27x - 3 + 60

Combine Like terms Like 54, - 3, and 60 : 111 - 18x -27x

Combine Like Terms Like -18x and -27x : 111 -45x

Rearrange It So The Variable Is First : -45x + 111

So, the answer is -45x + 111 or if you want you can still simplify it by finding the common factor which you will get -3(15x-37)

Corrections : The friend is wrong because he turned the equation into an inequality instead of simplifying it. He turned the equation into an inequality by adding an equal sign in the middle then he tried to solve it like how you solve inequalities.

P.S : So, correct me if I am wrong but i will try my best to answer. Hope it helps.

The value of x in quadrilateral JKLM is 29

A quadrilateral is a closed shape and a type of polygon that has four sides, four vertices and four angles. It is formed by joining four non-collinear points. The sum of interior angles of quadrilaterals is always equal to 360 degrees.

The sum of the interior angles in a quadrilateral is 360°

∠J + ∠K + ∠L + ∠M = 360

3X + 90 + 2X + 8 + 4X + 1 = 360

9x + 99 = 360

9x = 360 - 99

9x = 261

x = 261/9

x = 29

In conclusion 29 is the value of x in the quadrilateral.

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The random variable Y does not have a binomial distribution, therefore this is not a binomial experiment

Here, a computer is used to randomly dial a telephone number

Then the  operator asks the answering person whether she has time to answer some questions.

Y is the number of calls made until the first person replies that she is willing to answer the questions

There is no independent variable the affect the value of the Y. here the number of trial are not fixed, so there wont be any binomial distribution

Therefore, this is not a binomial experiment, because y does not have a binomial distribution

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The angle should it have to go straight to its destination is 66° east of north. The correct option is D.

Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions. There are numerous distinctive trigonometric identities that relate to a triangle's side length and angle.

Given that a ship's destination is 30 miles north and 12 miles east. The angle will be calculated as,

tanθ = 30 / 12

θ = tan⁻¹ ( 30 / 12)

θ = 66°

The angle is θ = 66°

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Answer: the answers should be B and D

Step-by-step explanation:

so basically, this is just simplifying

B is the correct answer because the numerator 12, when divided by 4 is 3, and the denominator 32, when also diving by 4, is eight. This makes the two fractions equivalent.

Same goes for D, for if you diving the numerator and denominator by 2, you get answer choice D

it’s kind of a trial and error type problem and you have to test out all possibilities

hope this helps!

Answer:

B and D

Step-by-step explanation:

12/32 (if you divide them both by three) does not equal 4/10

12/32 fully simplified is 3/8

12/32 - subtracting is not simplifying, therefore, 10/30 is not correct

12/32 - both divided by two, a common factor, is 6/16, therefore, this answer is correct

12/32 - both of them divided by three equals 4/10.7 (rounded up to the nearest tenth), therefore, 4/9 is not a correct answer

12/32 - both divided by six equals 2/5.3 (rounded down to the nearest tenth), therefore, 2/6 is not a correct answer

Answer: His work shows that the answer is an F. E. Which means a False Equation.

Step-by-step explanation:

This happens when an equation cannot be solved. Here is an example of a false equation answer:

Let's say that 3=6, in the equation or expression, all the letters like "x, y, z..." have been undone.

Therefore we can no longer undo, so the answer to your question is a False Equation.