PLEEEEEASE HELP ME ASAP

The points (-10, 0) and (0, 5), on the path of the first boat that can be modeled by a quadratic function and the point (10, 4) on the path of the linear function modelling the second boat, indicates that besides the common starting location, the solution for the point at which the paths of the  boats cross again at (6, 3.2)

The solution to a system of equation is the value of the input variable at which the output of the equations in the system of equations are the same.

Location of the port = (-10, 0)

The vertex of the path of the first boat that can be modeled by a quadratic function = (0, 5)

Point through which the boat that follows a path that can be modeled as a linear function passes = (10, 4)

The vertex form of the equation of a parabola is; y = a·(x - h)² + k

Where;'

(h, k) = The coordinates of the vertex

(h, k) = (0, 5)

Therefore;

y = a·(x - 0)² + 5 = a·x² + 5

When x = -10, y = 0, therefore;

y = 0 = a·(-10)² + 5 = 100·a + 5

0 = 100·a + 5

a = -5/100 = -1/20

a = -0.05

The equation is therefore; y = -0.05·x² + 5

The slope of the straight line path of the other boat is; m = (4 - 0)/(10 - (-10)) = 1/5 = 0.2

The equation is therefore; y - 0 = 0.2·(x - (-10)) = 0.2·x + 2

y = 0.2·x + 2

The point where the two paths cross is therefore;

-0.05·x² + 5 = 0.2·x + 2

-0.05·x² - 0.2·x + 5 - 2

-0.05·x² - 0.2·x + 3 = 0

x = (0.2 ± √((-0.2)² - 4 × (-0.05) × 3))/(2×(-0.05))

Therefore;

x = -10 and x = 6

The x-coordinate of the point the two paths cross, besides the starting location is x = 6

Therefore;

y = 0.2 × 6 + 2 = 3.2

The point besides the common starting location, the paths of the boats cross is; (6, 3.2)

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Answer:

(–6, 3.2)

Step-by-step explanation:

The answer above is correct.

The quadratic equation 15[tex]x^{2}[/tex]-22x -7 = 0 has solution x = 1.7355 or -0.26886

In algebra, a quadratic equation (from Latin quadratus 'square') is any equation that can be rearranged in standard form as

a[tex]x^{2}[/tex] + bx + c =0

where x represents an unknown value, and a, b, and c represent known numbers. One supposes generally that a ≠ 0; those equations with a = 0 are considered degenerate because the equation then becomes linear or even simpler. The numbers a, b, and c are the coefficients of the equation and may be distinguished by calling them, respectively, the quadratic coefficient, the linear coefficient and the constant or free term.

The values of x that satisfy the equation are called solutions of the equation, and roots or zeros of the expression on its left-hand side. A quadratic equation has at most two solutions. If there is only one solution, one says that it is a double root. If all the coefficients are real numbers, there are either two real solutions, or a single real double root, or two complex solutions that are complex conjugates of each other. A quadratic equation always has two roots, if complex roots are included; and a double root is counted for two. A quadratic equation can be factored into an equivalent equation

given that

5(x-1)3x = 7(x+1)

15[tex]x^{2}[/tex]-15x = 7x +7

15[tex]x^{2}[/tex]-22x -7 = 0

x = -b ± [tex]\sqrt{b^{2}-4ac }[/tex]/2a

x = -(-22) ± [tex]\sqrt{(-22)-4(15)(-7)}[/tex] /2(15)

x = 1.7355 or -0.26886

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Answer: x = 12

Step-by-step explanation:  

Distribute the parenthesis on both sides of the equation

5x - 5 + 3x = 7x + 7

8x - 5 = 7x + 7 ( subtract 7x from both sides )

x - 5 = 7 ( add 5 to both sides )

x = 12

Therefore, your answer is: x = 12

Answer:

Step-by-step explanation:

ANSWER: 40x^2+10xy-15y^2

Lenth * Width * Height:

(4x+3y)*(2x-y)*5

Distribute 5 through the parentheses :

(20x+15y)*(2x-y)

Simplify:

40x^2-20xy+30xy-15y^2

Collect like terms:

40x^2+10xy-15y^2

As per the dimensions, the volume of rectangular-shaped glass is equal to 40x² + 10xy - 15y².

Every three-dimensional item takes up space in some way. The volume of this area is what is used to describe it. The area covered within an entity's three-dimensional bounds is referred to as its volume. The object's size is another name for it.

As per the given information in the question,

Use the formula of volume:

Length × Width × Height:

(4x+3y) × (2x-y) × 5

5 should be distributed through parenthesis:

(20x+15y) × (2x-y)

Now, simplify the above equation,

40x² - 20xy + 30xy - 15y²

Now, keep all like terms together,

40x² + 10xy - 15y²

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Answer:

Step-by-step explanation:

(attached)

Answer:

yes y/x = 5/2

Step-by-step explanation:

y/x = 5/2, 10/4=5/2, 15/6=5/2, 20/8=5/2

The type of sample that the sample taken by Marlene represents is a Convenience sample.

Researchers who use convenience sampling obtain market research data from a pool of respondents who are conveniently accessible. Because it is so rapid, easy, and economical, it is the sampling procedure that is used the most frequently. If members choose to be part of the sample, they are frequently simple to get in touch with.

Therefore, Marlene employed a convenience sampling technique by going to the park, which was close by, and taking a sample of the people present.

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Answer:

Length=18 feet

Width=7 feet

Hope this helps! :)

Step-by-step explanation:

perimeter=50

length=18

width=w

Rectangle:2l+2w=50           2(18)+2(7)=50

36+2w=50

50-36=14

14/2=7

(36+14+50)

Answer:

Segment CE is 12 units.

Step-by-step explanation:

CD and DE add together to make CE. See image.

Use this idea to write an equation. Combine like terms and solve for x. Use the x value you find to calculate the length of CE. See image.

Answer:

33.45 is the price of 11 dog food cans

The number line that represents the number 0.7 is number line (B)

From the question, we have the following parameters:

From the dots on each line, we have the following statement

At minus 0.7 on B

This statement means that

B = -0.7

Hence, the number line represented by the statement is the number line B

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The  proportion of the total variation in the sample y-values that can be explained by the estimated linear relationship between x and y is 0.48

Given:

SSR = 1.9350

SST = 4.012

we are asked to find the proportion of the total variation in the sample y-values that can be explained by the estimated linear relationship between x and y.

To find the sample proportion we need to divide.

SSR/SST

= 1.9350/4.012

= 0.48

Hence we get the required answer as 0.48

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The equation of the path to find the dimensions of the patio is x² + (x + 5)² = 841.

Here we have to find the equation of the dimensions of the patio.

Data provided:

the path = 29 meters

length of the path is 5 meters more than the width of the path.

So let us assume that the length of the path is x

with this, the width of the path is x + 5

The formula for the diagonal:

Diagonal²  = length² + width²

Putting the data we have:

29² = x² + (x +5)²

841 = x² + (x+5)²

Therefore we get the equation as x² +(x + 5)² = 841.

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Answer:

He rolled a 6, 16 times

He rolled not a 6, 4 times

Brian did not roll 6 in the dice 14 times.

Subtraction is mathematic operation. Which is used to remove terms or objects in expression.

Given, Brian is playing a game of dice. He gets 10 points for each 6 he rolls. He loses 4 points every time he does not roll a 6.

After 20 tries his score is 144 points.

If he rolled 6 each time,

his score would be 200.

Subtracting the number 144 to 200.

200 - 144

= 56

And 56/4

= 14

That means he did not roll 6, 14 times.

Therefore, 14 times he did not roll 6.

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The inequality and the maximum possible width are 12w  ≥ 132 and 11 feet respectively

An inequality is a relationship that makes a non-equal comparison between two numbers or other mathematical expressions e.g 2x > 4

If the room is 12 feet long and  Tom had enough paint to cover an area of 132 square feet. This implies Tom had paint that can cover greater or equal to 132 square feet of area. Thus:

L x w ≥ A

where l = 12 feet, A = 132 square feet

12w  ≥ 132    (This is the inequality)

To solve for width:

12w  ≥ 132

w ≥ 132 /12

w ≥ 11 feet

Therefore, the inequality is 12w  ≥ 132 and the maximum possible width is  11 feet

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Step-by-step explanation:

0.5×3×4= 6cm^2

6×8

=48cm^3

Both the given expression are equivalent expression as 5m + 4.

Given that,
to determine whether the two given expressions are equivalent ot each other,

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Given expression,
5(m + 1 ) - 1 = 2(2m + 2) + m
5m + 5 - 1 = 4m + 4 + m
5m + 4 = 5m + 4

Thus, Both the given expression are equivalent expression as 5m + 4.

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On solving the provided question, we got -  0.001 is a stronger significance level,

any of a product's characteristics taken into account in respect to a certain characteristic. especially: a term's constant component as opposed to its variable. a value that represents a quality or attribute by a number (as of a substance, device, or process)

Whenever a variable is multiplied, a coefficient is used. In this case, "z" is a variable, making 6 a coefficient. 6z stands for 6 times z. Coefficient 1 applies to variables without a value.

0.001 is a stronger significance level, It means that the probability of error for the statistic is greater than 5 in 100, therefore the researchers concluded that the research is not statistically significant.

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The greatest volume of the cone made be 4372.7 m³.

Given, a right triangle whose hypotenuse is 22 m long is revolved about one of its legs to generate a right circular cone.

Let the base of the right triangle be, b

and the height of the right triangle be, h

Using Pythagoras Theorem, we get

22² = b² + h²

484 = b² + h²

Now, the height of the cone be, h and the radius of the cone be, b

Volume of the cone =  1/3πb²h

as, b² = 484 - h²

Volume = 1/3π(484 - h²)h

Volume = 1/3π(484h - h³)

On differentiating, we get

V' = 1/3π(484 - 3h²)

h² = 484/3

h = 22/√3

h = 22√3/3

b = 22√2/√3

Volume = 1/3π(22√2/√3)(22√2/√3)(22√3/3)

Volume = 1/9√3π(22³)(2)

Volume = 4372.7 m³

Hence, the greatest volume of the cone made be 4372.7 m³.

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Answer: 144a^14 b^8

Step-by-step explanation:

(-4a^(5)b^(3))^(2)* (-3a^(2)b)^(2) = 144a^14 b^8

Answer:

60

Step-by-step explanation:

she read 60 pages in just 2 days

The probability that he hits a target at most 13 times is 0.5031 when a marksman has a 0.89 percent chance of hitting the target each time he fires.

Given that,

A marksman has a 0.89 percent chance of hitting the target each time he fires.

We have to find what is the probability that he will only hit the target 13 times out of 15 shots.

We know that,

The probability of getting exactly k successes in n trials is given by the probability mass function that is,

P(X=k)=[tex](\frac{n}{k} )p^{k}(1-p)^{n-k}[/tex]

Where [tex](\frac{n}{k})= n!/k!(n-k)![/tex]

The probability that he hits the target at most 13 times is,

1-[P(he hits 14 times)+P(he hits 15 times)]

So, calculate the probability that he hits a target 14 times as follows:

P(X=14)=[tex](\frac{15}{14} )0.89^{14}(1-0.89)^{1}[/tex]

P(X=14)=15×(0.89)¹⁴×(0.11)

P(X=14)=0.3228

And the probability that he hits a target 15 times is

P(X=15)=[tex](\frac{15}{15} )0.89^{15}(1-0.89)^{0}[/tex]

P(X=15)=1×(0.89)¹⁵×(1)

P(X=15)=0.1741

And the required probability is

=1-[P(he hits 14 times)+P(he hits 15 times)]

=1-[0.3228+0.1741]

=0.5031

Therefore, The probability that he hits a target at most 13 times is 0.5031 when a marksman has a 0.89 percent chance of hitting the target each time he fires.

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If 5 out of 200 things were flawed, the population's estimated defect percent would be 2.5%.

Percent, which is a relative figure used to denote hundredths of any amount. Since one percent (symbolized as 1%) is equal to one tenth of anything, 100 percent stands for everything, while 200 percent refers to double the amount specified. The word "percent" simply refers to "per hundred," and the sign for percentage is %. By multiplying the total or whole number by 100, one percent (or 1%) is equal to one hundredth of the whole or whole.

Here,

Total number of items=200

number of defective items=5

Percentage of defective items,

=5/200*100

=2.5%

Therefore, if 5 out of 200 things were defective, the population's estimated percentage of defective items is 2.5%.

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The least amount of extra cash Lilianna requires is $126 and the inequality is [tex]x+$68\geq 194[/tex]

What justifies an inequality?

The relationship between two values in an imbalanced algebraic statement is represented by an inequality in mathematics. One of the two variables can be larger than, more than or equal to, smaller than, or equal to another value by using a sign of inequality.

Let

The least amount of extra money is x.

The fact that

[tex]x+$68\geq 194[/tex]

The problem is represented by inequality.

Solve for x.

[tex]x+$68\geq 194\\x\geq $126[/tex]

The least amount of money Lilianna requires is $126

and inequality is [tex]x+$68\geq 194[/tex]

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The formula that represents the volume of water in the tank in terms of the number of minutes since the water began draining is v = 40 - 1.5t.

This can be seen by realizing that the volume of water in the tank decreases by 1.5 gallons per minute, so after t minutes the volume will be 40 - 1.5t. The graph of this formula is a straight line with a slope of -1.5 and an intercept of 40. This means that the graph starts at the point (0,40), which represents a tank that is full of water, and decreases linearly as the number of minutes increases.

The statement "The graph of v in terms of t represents all possible values of v and t" is true. This is because the formula v = 40 - 1.5t is defined for all possible values of t, and the graph of this formula includes all possible pairs of (v, t) values that satisfy the formula.

The statement "The point (7.5,35.75) conveys that when the tank has been draining for 7.5 minutes, it has 35.75 gallons of water remaining" is false. This is because the point (7.5,35.75) does not lie on the graph of the equation v = 40 - 1.5t. The correct point on the graph that represents the volume of water in the tank after 7.5 minutes would be (7.5,26.25), which can be found by substituting t = 7.5 into the equation v = 40 - 1.5t.

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Answer:

Step-by-step explanation:

You want to know the x- and y-intercepts of a function described by a data table.

The x-intercept is the x-value where y = 0. There is no y=0 entry in the table, and the entries there are not regular enough to support any speculation as to how the function might be extrapolated.

There is no x-intercept.

The y-intercept is shown in the table where x=0.

The y-intercept is (0, 7).

The value of z-stat is -0.6721.

What is z stat?

The relationship between a value and the mean of a group of values is quantified by a Z-stat. The Z-stat is calculated using standard deviations from the mean. When a data point's Z-stat is 0, it means that it has the same score as the mean.

One standard deviation from the mean would be indicated by a Z-stat of 1.0. Z-stats can be positive or negative; a positive value means the score is above the mean, while a negative value means it is below the mean.

Solution Explained:

We use the formula,

[tex]z = \frac{P - \pi }{\sqrt{\frac{\pi (1-\pi )}{200} }}[/tex], where P is the observed proportion, π is the hypothesized proportion

Therefore, P = 42/200 = 0.21 & π = 23/100 = 0.23

Putting the values in

[tex]z = \frac{0.21 - 0.23 }{\sqrt{\frac{0.23 (1-0.23)}{200} }}[/tex]

After calculating, z-stat is therefore equal to -0.6721

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Considering the number of trials in the data, the binomial distribution only counts the two possible states, which are typically represented as 1 (for a success) or 0 (for a failure).

The probability distribution known as the binomial distribution, which is used in statistics, quantifies the chances that a value will take one of two independent values given a particular set of conditions or hypotheses.

The fundamental presumptions of the binomial distribution are that each trial has only one possible outcome, that each trial has the same success probability, and that each trial is independent of the others or mutually exclusive.

The likelihood of success is constant from trial to trial, and subsequent trials are independent. A binomial distribution, which derives from counting successes across a series of trials, has just two possible outcomes on each trial.

Hence, Considering the number of trials in the data, the binomial distribution only counts the two possible states, which are typically represented as 1 (for a success) or 0 (for a failure).

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The probability the game lasts less than 4.5 hours is 0.2877.

μ = mean population = 5

σ = standard deviation = 0.9

The probability for the game lasts less than 4.5 hours can be calculated using z test formula.

P(x < 4.5) = P(z < [tex]\frac{x-\mu}{\sigma}[/tex] )

= P(z < [tex]\frac{4.5-5}{0.9}[/tex])

= P(z < -0.56)

Using z table for P(z < -0.56). So,

= 0.2877

Thus, the probability is 0.2877 for the game lasts less than 4.5 hours.

Your question is incomplete, but most probably your full question was

on average, an american professional football game lasts about five hours, even though the ball is actually in play only 11 minutes. assume that game times are normally distributed with a standard deviation of 0.9 hour. 1. Find the probability that a game lasts less than 4.5 hours.

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