as part of a science experiment, Carson designs and creates a cushioned egg carrier. he puts an egg inside it and then drops it from a window to see whether his design can safely cushion the egg and keep it from breaking. the egg's height in feet x seconds after being dropped is given by 27 - 16x^2. after how many seconds will the egg hit the ground?

The slope-intercept form of the equation of the line through the given point with the given slope is y=-4x+1.

The given coordinate point is (-1, 5) and slope=-4.

The slope intercept form of a straight line is one of the most common forms used to represent the equation of a line. The slope intercept formula can be used to find the equation of a line when given the slope of the straight line and the y-intercept.

The standard form of the slope intercept form is y=mx+c.

Substitute (x, y)=(-1, 5) and m=-4 in standard form of the slope intercept form, we get

5=-4×(-1)+c

⇒ c=5-4

⇒ c=1

Substitute m=-4 and c=1 in y=mx+c, we get

y=-4x+1

Therefore, the slope-intercept form of the equation of the line through the given point with the given slope is y=-4x+1.

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The solution of the fraction is 6 11/35.

Covert mixed numbers to improper fractions:

[tex]2\frac{5}{7}g=\frac{19}{7}g[/tex]

[tex]3\frac{3}{5}g=\frac{18}{5}g[/tex]

factor out common term g:

=[tex]g(\frac{19}{7} +\frac{18}{5})\\g(\frac{221}{35})[/tex]

Convert improper fractions to mixed numbers:

[tex]=\frac{221}{35}g \\\\=6\frac{11}{35} g[/tex]

Hence, The solution of the fraction is 6 11/35.

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The amount of interest he will pay on this loan is $12,400.

Principal = $10,000

Rate = 8%

Time = 36 months, 1 year - 12 months

36 months - 36/12= 3 years

S.I. = PRT/100

10,000*8*3/100

240,000/100 = $2,400

A = P+I = 10,000+2,400= $12,400

The amount of interest he will pay on this loan $12,400.

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Therefore the solution to this question is expression a=3/5 & expression b=6/5  3a+b=3 , and  10a+5b=6+6=12 .

Probability is the study of how likely it is for an event to occur or for a statement to be true, with numerical explanations of probability being a key component. An event's probability is represented by a number between 0 and 1, where, broadly speaking, 0 indicates that the event is impossible and 1 indicates that it is certain to occur.

Here,

Naturally, the total probability for x∉[0,1] is 0 and since the total probability must be 1, we have

∫01a+bx2dx=1

The left-hand side is

[ax+b[tex]x^{3}[/tex]/3] x=1 & x=0 => a+b3

3a+b=3

In general, for continuous probability distributions we have

E(x)=∫P(x)xdx

(If you have a sufficiently advanced version of integration, the restriction to continuous distributions may be lifted.)

In this case, it's

E(x)=[a[tex]x^{2}[/tex]/2+b[tex]x^{4}[/tex]/4]x=1 & x=0 => a/2+b/4

So,

a/2+b/4=3/5

10a+5b=12

Being shrewd with matrix inversion or anything of the sort is pointless. Just get rid of b:

15a+5b=15

5a=3

a=3/5

b=3(1−a)=6/5

and indeed  3a+b=3 , and  10a+5b=6+6=12 .

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Answer:

it is B

Eplanation:

180-155=75 (straight line add up 180 degrees)

75+55+x=180

130+x=180(angles in triangle also add up 180 degrees)

x=180-130(rearranging formula)

x=50, which is option letter B

Following values can be filled in the table:

(0,-3), (-1,0), (1,-8), (-2,1), (2,-15)

It can be solved using the concept of graph plotting and function.

What is graph?

When a set of points are connected together to form a strcture then the structure is known as graph. The set of ponts is known as ordered pair.

Consider the eqution.

[tex]y=-(x+2)^2+1[/tex]

Substitute the simplest value x = 0 and find the value of y.

[tex]y=-(0+2)^2+1\\=-3\\[/tex]

Now, substitute x = -1 and find the value of y.

[tex]y=-(-1+2)^2+1\\=0\\[/tex]

Now, substitute x = 1 and find the value of y.

[tex]y=-(1+2)^2+1\\=-8\\[/tex]

Now, substitute x = -2 and find the value of y.

[tex]y=-(-2+2)^2+1\\=1\\[/tex]

Now, substitute x = 2 and find the value of y.

[tex]y=-(2+2)^2+1\\=-15\\[/tex]

Hence, following values can be filled in the table:

(0,-3), (-1,0), (1,-8), (-2,1), (2,-15)

It can be solved using the concept of graph plotting.

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Answer:

∠ABC = 98°

Step-by-step explanation:

an isosceles triangles base angles have the same angle measures

so both are 71

add them and then subtract that from 180 to find ∠ABD

180 - (71 + 71)

180 - 142 = 38

that is ∠ABD

to find ∠ABC you must add ∠DBC to ∠ABD

all angles of an equilateral triangle are equivalent

they are also 60 degrees

so add 60 to 38

38 + 60 = 98

that is your answer

The composition of translations for the first image is (x+1, y+5) and for the second image is (x-4, y).

What is a translation?

A transformation that moves a figure through its points using a given ruler—a translation vector—is referred to as a translation. Without altering the original geometry, this process moves each point in a picture both horizontally and vertically.

Given a graph of translation

The first image is translated as 1 unit upward and 5 units right side.

Then, translation (x,y) → (x+1, y+5)

And,

The second image is translated as 4 units downward only.

Then, translation (x,y) → (x-4, y)

Hence, the above is the required composition of translations.

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The null hypothesis is a typical statistical theory which suggests that no statistical relationship and significance exists in a set of given single observed variable, between two sets of observed data and measured phenomena.

The required details for null hypothesis in given paragraph

The null hypothesis and alternative hypothesis in this case would be:

H₀: The distribution of hockey players' birth months is uniformly distributed.

H₁: The distribution of hockey players' birth months is not uniformly distributed.

The expected counts for each birth month can be calculated as follows:

Expected Count = (Total Number of Players) * (Proportion of Total Players for Each Birth Month)

Since there are 4 birth months and the distribution is assumed to be uniform, the proportion of total players for each birth month is 1/4 = 0.25. Therefore, the expected count for each birth month is:

Expected Count = 188 * 0.25 = 47

To test the null hypothesis, we can then calculate the chi-square statistic using the following formula:

χ² = ∑((O - E)² / E)

where O is the observed count, E is the expected count, and the sum is taken over all birth months.

Plugging in the observed and expected counts, we get:

χ² = ((66 - 47)² / 47) + ((59 - 47)² / 47) + ((34 - 47)² / 47) + ((29 - 47)² / 47)

= 3.87 + 2.04 + 3.87 + 5.57

= 15.35

In this case, df = 3.

Looking up the critical value in the chi-square table with df = 3 and a = 0.05, we find that the critical value is 7.815. Since the chi-square statistic (15.35) is greater than the critical value, we reject the null hypothesis and conclude that there is evidence to suggest that the distribution of hockey players' birth months is not uniformly distributed.

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There are 3457440 ways combination in which this dance committee can be formed.

What is permutation and combination?

A set of items can be divided into subsets in two different ways: combination and permutation. The subset's components can be listed in any order when combined. The components of the subset are arranged in a particular order in a permutation.

2 freshmen out of 7 freshmen can be chosen in ⁷C₂ ways.

3 sophomores out of  9 sophomores can be chosen in ⁹C₃  ways.

4 juniors out of 7 juniors can be chosen in ⁷C₄ ways.

5 seniors out of 8 seniors can be chosen in ⁸C₅ ways.

⁷C₂ × ⁹C₃ × ⁷C₄ ×  ⁸C₅  ways, the dance committee of 2 freshmen, 3 sophomores, 4 juniors, and 5 seniors can be chosen.

= 7!/(7-2)!2! × 9!/(9-3)!3! × 7!/(7-4)!4! × 8!/(8-5)!5!

= 7!/5!2! × 9!/6!3! × 7!/3!4! × 8!/3!5!

= 21×84×35×56.

= 3457440 ways.

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Answer:

1.32x10^-3

Step-by-step explanation:

hope it helps

Answer:

y = 2.5x

Step-by-step explanation:

When the relationship is proportional you can find the slope (or unit rate) by taking any point in the form y/x

20/8 = 2.5

30/12 = 2.5

This will work of every point n the line.

Step-by-step explanation:

Let x = cost of cheese pizza

Let y = cost of pepperoni pizza

x + 6y = 136

2x + 2y = 49

Solve the system:

x = $14

y = $15

It would cost a family of 5 $132.35 more to get the jets game than a Lions game

Given that:

The average ticket price for Jets game = $105.66

The average ticket price for Lions game = $79.19

Jets game for a family of 5 will be:

Jet game cost = 5× $105.66 = $528.3

Lions game for a family of 5 will be:

Lions game cost = 5× $79.19 = $395.95

Difference = $528.3 - $395.95 = $132.35

Therefore, it would cost a family of 5 $132.35 more to get the jets game

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The x-intercepts of the parabola are (x₁, y₁) = (6.67, 0) and (x₂, y₂) = (5.33, 0).

What is the equation of a parabola?

The general equation of a parabola is given by y = a(x – h)2 + k or x = a(y – k)2 +h. Here (h, k) denotes the vertex.

To write the equation of the given parabola in the desired form, we can complete the square.

The equation of a parabola with vertex at (h, k) and axis of symmetry x = h is given by:

y = a(x - h)^2 + k

where a is a nonzero constant.

In this case, the vertex is (6, -5) and the y-intercept is (0, 175), so the equation of the parabola is of the form:

y = a(x - 6)^2 - 5

Substituting the y-intercept, we have:

175 = a(0 - 6)^2 - 5

Solving for a, we find that a = 15/4.

Thus, the equation of the parabola is:

y = 15/4(x - 6)^2 - 5

To find the x-intercepts, we need to find the values of x such that y = 0. Substituting y = 0 into the equation of the parabola, we have:

0 = 15/4(x - 6)^2 - 5

Adding 5 to both sides, we have:

5 = 15/4(x - 6)^2

Dividing both sides by 15/4, we have:

4/15 = (x - 6)^2

Taking the square root of both sides, we have:

x - 6 = +/- 2/3

Thus, the x-intercepts are at x = 6 +/- 2/3.

Therefore, the x-intercepts of the parabola are (x₁, y₁) = (6 + 2/3, 0) and (x₂, y₂) = (6 - 2/3, 0).

Rounded to the nearest hundredth, the x-intercepts are (x₁, y₁) = (6.67, 0) and (x₂, y₂) = (5.33, 0).

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The system of equation that describes the relation between the total cost (Y) and the number of tickets purchased (X) in a single visit to the park is Y = 3X + 20 i.e, option (C)

Define System of Equation

A set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.

Given,

Cost of theme park is = $20

Tickets for each ride and attraction are = $3 a piece

Number of tickets purchased = X

So, total cost of tickets is = 3 * X

Total cost of visit to the theme park is = Y

So, the equation we get

Y = 3X + 20

Hence, the system of equation that describes the relation between the total cost (Y) and the number of tickets purchased (X) in a single visit to the park is Y = 3X + 20 i.e, option (C).

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Natural numbers and irrational numbers are two pairs of sets that have the same cardinality.

It is sufficient to demonstrate the existence of a bijection between the set of real numbers R and the set of irrational numbers RQ in order to demonstrate that both have the same cardinality:

For each positive integer n, map n to 2n to produce a countable number of holes in R. Be aware that these countable holes are located at all irrational locations (2n-1), as well. R should be mapped to itself. R should be mapped to itself. Feel free to use your preferred irrational number in the above in place of [tex]\pi[/tex].

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By simplifying and solving, Tamala is not in class while she is at school is 0.5 hour.

Algebraic simplification is the process of rewriting an algebraic expression in a simpler form, without changing its value.

Algebra is a branch of mathematics that involves the use of letters and symbols to represent unknown quantities, known as variables, in equations and formulas.

Tamala is in class for 6 * (7/6) = 7 hours.

Tamala is not in class for 7(1/2) - 7 = 1/2 hours.

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You owe $31000 on student loans at an interest rate of 3.35% compounded monthly.

Generally, To calculate the monthly payment amount, you can use the following formula:

monthly payment = (interest rate / 12) x (loan balance / (1 - (1 + (interest rate / 12)) ^ (-term in months)))

Plugging in the values given in the question, the monthly payment would be:

monthly payment = (3.35% / 12) x ($31000 / (1 - (1 + (3.35% / 12)) ^ (-8 years x 12 months/year)))

= (0.00335) x ($31000 / (1 - (1 + 0.00335) ^ (-96)))

= $318.54

So the monthly payment would be $318.54.

To calculate the total interest paid over the course of the loan, you can use the following formula:

total interest = (monthly payment x term in months) - loan balance

Plugging in the values given in the question, the total interest paid would be:

total interest = ($318.54 x 96 months) - $31000

= $30,443.84 - $31,000

= $-556.16

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The equation is accurate. A line's slope and y-intercept are expressed in the form y is mx + c, where m is the slope and c is the y-intercept.

A line's slope and y-intercept are expressed in the form y = mx + c, where m is the slope and c is the y-intercept.

y = (3/2)x + 1 is the given equation for the line.

Add x = 0 to the above equation, y = (3/2)(0) + 1 y = 1, to determine the line's y-intercept.

Take note that the line's graph's y-intercept is also 1.

The line's graph includes points (2,4).

Put the coordinates of the location into the above equation to see if it matches the coordinates of (2,4) or not:

4 = (3/2)(2) + 1

4 =4

The equation is accurate.

Consequently, it can be claimed that the following equation reflects the graph.

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Answer:

f(-1) = -3

Step-by-step explanation:

f(x) =-2x-5

f(-1) = -2(-1)-5  ==> plug in -1 for x

f(-1) = 2-5

f(-1) = -3

The y-intercept is the point the graph intersects the y-axis. It is represented by the constant c in the equation of a straight line graph, y = m·x + c

6. The y-intercept is 7

8. The y-intercept is 0

12 a. The error is taking the x-intercept as the y-intercept

b. Please find attached the graph of line with a y-intercept of 3 drawn with MS Excel

A straight line graph is the graph of a linear equation.

The slope-intercept form of the equation of a straight line graph is y = m·x + c, where;

m = The slope of the graph

c = The y-intercept

6 The y-intercept is the point the graph crosses the y-axis.

The line crosses the y-axis at the point (0, 7)

8. The point at which the graph crosses the y-axis is (0, 0)

12. The graph in the question is a straight line graph that passes through the points (3, 0), and (0, -4)

The x-intercept of the graph is 3

The y-intercept of the graph is -4

a. The possible error of the graph that is an example of a line with a y-intercept of 3 is therefore, mistaking the y-intercept for the x-intercept

b. Please find attached the graph of the line y = x + 3 that has a y-intercept of 3 drawn with MS Excel on the graph of the question with equation y = (4/3)·x - 4

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The answer is in simplest form is 672.

The simplest form is the  smallest possible equivalent of the fraction of the number. Steps for finding to  the simplest form: Search  for the common factors in to the numerator and the denominator. Check whether one of the numbers  in the fraction is a prime for  number.

As per the given question the number are

910

238

We have to find 910-238

So,

910-238

We have to calculate sum or difference

And we got 672.

Thus, the answer is 672 or 6.72×10^2 ( in alternate form).

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[tex]a=\sqrt{5^2-4^2}=3 \\ \\ b=\sqrt{5^2-4^2}=3 \\ \\ \therefore x=3+3=\boxed{6}[/tex]

Answer:

Given g(x)=4x+6

f(x)=12x+8

f(g(x))=f(4x+6)

=12(4x+6)+8 (substitute g(x) in f(x) )

=48x+72+8

= 48x+80

The equation of Total Charges will be $1.95 + ($2.7 * x)

What is Linear Equation in One Variable?

A linear equation is a one-variable equation of a straight line. The variable's only power is 1. Linear equations in one variable have the form ax + b = 0 and are solved using simple algebraic techniques.

Solution:

The equation of Total Charges will be

Let, the total distance in miles be x

Then,

Total Charges = $1.95 + ($2.7 * x)

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Answer:

a b c or d?

Step-by-step explanation:

Answer: If a superball is dropped from a height of h feet and left to bounce forever, the total time needed for all this bouncing to take place can be represented by the formula:

t = h / (r - 1)

where t is the total time, h is the height from which the ball is dropped, and r is the rebound ratio of the ball.

The rebound ratio of the ball is the fraction of the ball's initial height that it bounces back up after each bounce. For example, if a ball has a rebound ratio of 0.5, it will bounce back up to half its initial height after each bounce.

The total time needed for the ball to bounce forever is equal to the height from which the ball is dropped divided by the difference between the rebound ratio and 1. This is because the ball will bounce back up a fraction of its initial height after each bounce, and the total time needed for all the bounces to take place is determined by the difference between the height of the ball and the fraction of the height that it bounces back up.

Given that P(E)= 0.30 and P(F)= 0.47, the probability of P(E or F) if E and F are mutually exclusive will be 0.77.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement 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. A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

Here,

P(E)=0.30

P(F)=0.47

P(E∩F)=0 as they are mutually exclusive

P(E∪F)=P(E)+P(F)-P(E∩F)

=0.30+0.47

P(E∪F)=0.77

The probability of P(E or F) if E and F are mutually exclusive will be 0.77 given that P(E)= 0.30, and P(F) = 0.47.

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Answer:

25.

Step-by-step explanation:

1. if according to the condition 'm∠2 is three times m∠1', then it is possible to write: 3m∠1=m∠2, then

2. if according  to  the condition m∠WXZ=m∠1+m∠2, then it is possible to write it as:

m∠WXZ=m∠1+3m∠1; ⇔m∠WXZ=4*m∠1;

3. if according to the condition m∠WXZ=100, then

100°=4*m∠1, then

m∠1=100°:4=25°.