What is the approximate positive value of the x-coordinate of the point of intersection of p(x)=5x^2-3 and q(x)=2x+1

Answer:

A.

Step-by-step explanation:

Since you are trying to find x, you have to divide both sides by 4 to isolate x and get your answer.

Answer:

Step-by-step explanation:

y = -3x - 2

5x + 2y = 15

5x + 2(-3x -2) = 15

5x -6x - 4 = 15

-x - 4 = 15

-x = 19

x = -19

y = -3(-19) - 2

y = 57 - 2

y = 55

(-19, 55)

solution is b

Answer:

the correct answer is a reflection over the y axis

Step-by-step explanation:

The best description of the transformation shown will be;

''Reflection over the y - axis.''

What is Translation?

A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.

Given that;

The transformation is shown in figure.

Now,

Clearly, A'B'C'D' is the mirror image of the ABCD across the y - axis.

So, The best description of the transformation shown will be;

''Reflection over the y - axis.''

Thus, The best description of the transformation shown will be;

''Reflection over the y - axis.''

Learn more about the translation visit:

https://brainly.com/question/1046778

#SPJ6

Answer:

B

Step-by-step explanation:

The range is all values of y. Y goes from -1 to 1. Please mark brainliest.

Answer:

see below

Step-by-step explanation:

The domain of the function is the possible x values

The domain is all real values since x can be any number

The range of the function is the possible y value

The values of y go from -1 to 1 so

-1 ≤y≤1

Complete Question

Suppose the weight of Chipotle burritos follows a normal distribution with mean of 450 grams, and variance of 100 grams2 . Define a random variable to be the weight of a randomly chosen burrito.

(a) What is the probability that a Chipotle burrito weighs less than 445 grams? (3 points)

(b) 20% of Chipotle burritos weigh more than what weight

Answer:

a

   [tex]P(X < 445 )= 0.3085[/tex]

b

  [tex]k = 458.42[/tex]

Step-by-step explanation:

From question we are told that

     The population mean is [tex]\mu = 450 \ g[/tex]

      The variance is [tex]var = 100 \ g^2[/tex]

      The  consider weight is  [tex]x = 445 \ g[/tex]

The  standard deviation is mathematically represented as

     [tex]\sigma = \sqrt{var}[/tex]

substituting values

     [tex]\sigma = \sqrt{ 100}[/tex]

     [tex]\sigma = 10[/tex]

Given that weight of Chipotle burritos follows a normal distribution the  the probability that a Chipotle burrito weighs less than x grams is mathematically represented as

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

Where  [tex]\frac{X - \mu }{\sigma }[/tex] is  equal to z (the standardized values of the random number X )

So

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

substituting values

     [tex]P(X < 445 ) = P (Z < \frac{445 - 450 }{10} )[/tex]

      [tex]P(X < 445 ) = P (Z <-0.5 )[/tex]

Now from the normal distribution table  the value for [tex]P (Z <-0.5 )[/tex]  is  

      [tex]P(X < 445 ) = P (Z <-0.5 ) = 0.3085[/tex]

=>   [tex]P(X < 445 )= 0.3085[/tex]

Let the  probability  of the Chipotle burritos weighting more that k be 20% so  

       [tex]P(X > k ) = P ( \frac{X - \mu }{\sigma } > \frac{k - \mu }{\sigma } ) = 0.2[/tex]

=>    [tex]P (Z> \frac{k - \mu }{\sigma } ) = 0.2[/tex]

=>    [tex]P (Z> \frac{k - 450}{10 } ) = 0.2[/tex]

From the normal distribution table the value of z  for  [tex]P (Z> \frac{k - \mu }{\sigma } ) = 0.2[/tex] is  

    [tex]z = 0.8416[/tex]

=>   [tex]\frac{k - 450}{10 } = 0.8416[/tex]

=>   [tex]k = 458.42[/tex]

Answer:

900.

Step-by-step explanation:

66 tens are 660.

and 24 tens are 240.

so, It is 900!

I suppose the curve is [tex]r(\theta)=e^\theta[/tex].

Tangent lines to the curve have slope [tex]\frac{dy}{dx}[/tex]; use the chain rule to get this in polar coordinates.

[tex]\dfrac{dy}{dx}=\dfrac{dy}{d\theta}\dfrac{d\theta}{dx}=\dfrac{\frac{dy}{d\theta}}{\frac{dx}{d\theta}}[/tex]

We have

[tex]y(\theta)=r(\theta)\sin\theta\implies\dfrac{dy}{d\theta}=\dfrac{dr}{d\theta}\sin\theta+r(\theta)\cos\theta[/tex]

[tex]x(\theta)=r(\theta)\cos\theta\implies\dfrac{dx}{d\theta}=\dfrac{dr}{d\theta}\cos\theta-r(\theta)\sin\theta[/tex]

[tex]r(\theta)=e^\theta\implies\dfrac{dr}{d\theta}=e^\theta[/tex]

[tex]\implies\dfrac{dy}{dx}=\dfrac{e^\theta\sin\theta+e^\theta\cos\theta}{e^\theta\cos\theta-e^\theta\sin\theta}=\dfrac{\sin\theta+\cos\theta}{\cos\theta-\sin\theta}[/tex]

The tangent line is horizontal when the slope is 0, which happens wherever the numerator vanishes:

[tex]\sin\theta+\cos\theta=0\implies\sin\theta=-\cos\theta\implies\tan\theta=-1[/tex]

[tex]\implies\theta=\boxed{-\dfrac\pi4+n\pi}[/tex]

(where [tex]n[/tex] is any integer)

The tangent line is vertical when the slope is infinite or undefined, which happens when the denominator is 0:

[tex]\cos\theta-\sin\theta=0\implies\sin\theta=\cos\theta\implies\tan\theta=1[/tex]

[tex]\implies\theta=\boxed{\dfrac\pi4+n\pi}[/tex]

Answer:

D. 0.002

Step-by-step explanation:

Given;

total number of sample, N = 500 elements

50 elements are to be drawn from this sample.

The probability of the first selection, out of the 50 elements to be drawn will be = 1 / total number of sample

The probability of the first selection = 1 / 500

The probability of the first selection = 0.002

Therefore, on the first selection, the probability of an element being selected is 0.002

The correct option is "D. 0.002"

On the first selection, the probability of an element being selected is 0.002. Option D is correct.

Given information:

A population consists of 500 elements. so, the total number of samples will be [tex]N = 500[/tex] .

We want to draw a simple random sample of 50 elements.

The probability is defined as the preferred outcomes divided by the total number of samples.

So, the probability of first selection will be calculated as,

[tex]P=\dfrac{1}{500}\\P=0.002[/tex]

Therefore, on the first selection, the probability of an element being selected is 0.002.

For more details, refer to the link:

https://brainly.com/question/18722707

Answer:

The probability is 40%

Step-by-step explanation:

a) There are ten pieces of paper with ten numbers

Probability of selecting four pieces of paper = 4/10 or 40%

Probability that the four numbers selected will have a sum greater than 82 = 82/205 = 40%

Therefore, the probability of selecting four numbers that have a sum greater than 82 out of ten numbers totalling 205 is 40%.

b) Probability is the ratio of the number of outcomes favourable for the event to the total number of possible outcomes.   In other words, it is a measure of the likelihood of an event (or measure of chance).

Answer:

Piecewise function;

y = 2x - 2 where x < 2

       4 where 2 ≤ x ≤ 5  

       y = x + 1 where x > 5

Step-by-step explanation:

Function graphed represents the piecewise function.

1). Equation of the line with y-intercept (-2) and slope 'm'.

 Since, slope of the line = [tex]\frac{\text{Rise}}{\text{Run}}[/tex]

                                        = [tex]\frac{2}{1}[/tex]

                                        = 2

 Therefore, equation of this segment will be in the form of y = mx + b,

 ⇒ y = 2x - 2 where x < 2

2). Equation of a horizontal line,

 y = 4  where 2 ≤ x ≤ 5

3). Equation of the third line in the interval x > 5

 Let the equation of the line is,

 y = mx + b

 Where m = slope of the line

 b = y-intercept

 Here, slope 'm' = [tex]\frac{\text{Rise}}{\text{Run}}[/tex]

                           = [tex]\frac{2}{2}[/tex]

                           = 1

 Equation of this line will be,

 y = 1(x) + b

 y = x + b

 Since, this line passes through (5, 6),

 6 = 5 + b

 b = 6 - 5 = 1

 Therefore, equation of this line will be,

 y = x + 1 where x > 5

 Graphed piecewise function is,

 y = 2x - 2 where x < 2

       4 where 2 ≤ x ≤ 5  

       y = x + 1 where x > 5

Answer:

Pencil = $0.25

Marker = $1.00

Eraser = $1.75

Step-by-step explanation:

Let P denote pencils, M denote markers and E denote erasers. The quantities of each item and total amounts spent by each person can be modeled into the following linear system:

[tex]7P+8M+7E=22\\4P+8M+6E=19.5\\6P+4M+7E=17.75[/tex]

Solving the linear system:

[tex]7P-4P+8M-8M+7E-6E=22-19.5\\3P+E=2.5\\E=2.5-3P \\\\7P+8M+7E-2*(6P+4M+7E)=22-2*17.75\\-5P-7E=-13.5\\-5P*-7*(2.5-3P)=-13.5\\16P=-13.5+17.5\\P=0.25\\E=2.5-0.25*3\\E=1.75\\7P+8M+7E =22\\7*0.25+8M+7*1.75 =22\\8M=8\\M=1[/tex]

The price of each item is:

Pencil = $0.25

Marker = $1.00

Eraser = $1.75

Answer:

2m-9

Step-by-step explanation:

m-4+m-5

=m+m-4-5

=2m-9

Answer:

2m-9

Step-by-step explanation:

m-4+m-5

take the like terms

= 2m-4-5

= 2m-9

Sorry if that didn't help

Answer:

12.5%

Step-by-step explanation:

There is only one number 5 from a total of 8 parts.

1 out of 8.

1/8 = 0.125

P(5) = 12.5%

Answer:

12.5%

Step-by-step explanation:

Spinner divided in parts = 8

Number 5 = 1

P(5) = 12.5%

Answer: -32

Step-by-step explanation:

I'm just going to plug in and break down the equation to make it more understandable and easier to comprehend

-(3^2) - (4*3) -11

-(9)- (12) -11

-9 - 12 - 11

-21 -11

-32

Answer:

a) 0.65 mpg

b) Between 24.99 mpg and 28.01 mpg.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation, which is also called standard error, [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question, we have that:

[tex]\mu = 26.50, \sigma = 3.25, n = 25, s = \frac{3.25}{\sqrt{25}} = 0.65[/tex]

a. What is the standard error of X and the mean from a random sample of 25 fill-ups by one driver?

s = 0.65 mpg

b. Within what interval would you expect the sample mean to fall, with 98 percent probability?

From the: 50 - (98/2) = 1st percentile

To the: 50 + (98/2) = 99th percentile

1st percentile:

X when Z has a pvalue of 0.01. So X when Z = -2.327.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]-2.327 = \frac{X - 26.50}{0.65}[/tex]

[tex]X - 26.50 = -2.327*0.65[/tex]

[tex]X = 24.99[/tex]

99th percentile:

X when Z has a pvalue of 0.99. So X when Z = 2.327.

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]2.327 = \frac{X - 26.50}{0.65}[/tex]

[tex]X - 26.50 = 2.327*0.65[/tex]

[tex]X = 28.01[/tex]

Between 24.99 mpg and 28.01 mpg.

Answer:

Graphed below.

Step-by-step explanation:

The slope of the line is -1/3.

The y-intercept is at (0, 2).

The x-intercept is at (6, 0).

Answer:

B. 533in²

Step-by-step explanation:

Step 1: Find the area of the rectangle

A = lw

A = (29)13

A = 377

Step 2: Find the leg of the triangle

13 + 11 = 24

Step 3: Find the area of the triangle

A = 1/2bh

A = 1/2(24)(13)

A = 12(13)

A = 156

Step 3: Add the areas of the 2 figures together

377 + 156 = 533

Answer:

x = 1, x = .333

Step-by-step explanation:

Answer:

x = 1 and x = 1/3

Step-by-step explanation:

Here the coefficients of this quadratic are a = 3, b = -4 and c = 1.

The discriminant is b^2 - 4ac, or (-4)^2 - 4(3)(1) = 16 - 12 = 4.

Thus, the roots are:

      -(-4) ± √4        4 ± 2

x = ---------------- = -------------   =>  x = 1 and x = 1/3

          2(3)                  6

Answer:

w = 15

Step-by-step explanation:

-9(w + 585) = -360w

-9w -5265 = -360w

351w = 5265

w=15

Answer:

There are 172 butterflies  in the conservatory.

Step-by-step explanation:

Given

ratio of butterflies to total number of flying insects is 36 to 100

total number of butterflies / total number of flying insects = 36 / 100 = 9/25

Create a table for how many butterflies there are for 1, 50, and 100 flying insects.

Let the number of butter flies be x

when total no. of insects = 1

total number of butterflies / total number of flying insects  =9/25=x/1

=> 9/25= x/1

=> x = 9/25

____________________________________

when total no. of insects = 50

total number of butterflies / total number of flying insects  =9/25=x/50

=> 9/25= x/50

=> x = 9/25 * 50 = 18

_______________________________________

when total no. of insects = 100

total number of butterflies / total number of flying insects  =9/25=x/100

=> 9/25= x/100

=> x = 9/25 * 100= 36

Thus, table is

butterfly    total no of insects

   9/25            1

     50             18

     100            36

______________________________________________

Given there There are 450 total flying insects in the conservatory

again using the same ratio and taking no. of butterflies as x

total number of butterflies / total number of flying insects  =9/25=x/450

9/25=x/450

=>x = 9/25 * 450 = 9*18 = 172

Thus, there are 172 butterflies  in the conservatory.

Answer:

There are 162 butterflies  in the conservatory.

Step-by-step explanation:

Given

ratio of butterflies to total number of flying insects is 36 to 100

total number of butterflies / total number of flying insects = 36 / 100 = 9/25

Create a table for how many butterflies there are for 1, 50, and 100 flying insects.

Let the number of butter flies be x

when total no. of insects = 1

total number of butterflies / total number of flying insects  =9/25=x/1

=> 9/25= x/1

=> x = 9/25

____________________________________

when total no. of insects = 50

total number of butterflies / total number of flying insects  =9/25=x/50

=> 9/25= x/50

=> x = 9/25 * 50 = 18

_______________________________________

when total no. of insects = 100

total number of butterflies / total number of flying insects  =9/25=x/100

=> 9/25= x/100

=> x = 9/25 * 100= 36

Thus, table is

butterfly    total no of insects

  9/25            1

    50             18

    100            36

______________________________________________

Given there There are 450 total flying insects in the conservatory

again using the same ratio and taking no. of butterflies as x

total number of butterflies / total number of flying insects  =9/25=x/450

9/25=x/450

=>x = 9/25 * 450 = 9*18 = 162

Thus, there are 162 butterflies  in the conservatory.

Answer:

42°

Step-by-step explanation:

This is right triangle and sum of 2 angles is 90°:

y+48°=90°

so y= 90°- 48°= 42°

Answer:

120 inches cubed

Step-by-step explanation:

The formula for finding the volume of a rectangular prism is length * width * height.

In this case, 8 inches long is the length, 5 inches is the width, and 3 inches is the height.

So multiplying all of those together gets you 120 inches cubed.

Answer:

100,000 meters

Step-by-step explanation:

There are 1000 meters in a kilometer so there are 100,000 meters in 100 kilometers.

Answer:

it is 100000 kilometers

Step-by-step explanation:

use the metric system and you get 10000 kilometers.

Answer:

182.8125

Step-by-step explanation:

Given:

y = x^3

from [2,5] using 6 subdivisions

deltax = (5 - 2)/6 = 3/6 = 0.5

hence the subdivisions are:

[2, 2.5]; [2.5, 3]; [3, 3.5]; [3.5, 4]; [4, 3.5]; [4.5, 5]

hence the right endpoints are:

x1 = 2.5; x2 = 3; x3 = 3.5; x4 =4; x5 = 4.5; x6 = 5

now the area is given by:

A = deltax*[2.5^3 + 3^3 + 3.5^3 + 4^3+ 4.5^3 + 5^3]

A = 0.5*365.625

A = 182.8125

Area using Right Endpoint approximation is 182.8125

The area of the region is an illustration of definite integrals.

The approximation of the area of the region R is 182.8125

The given parameters are:

[tex]\mathbf{f(x) = x^3}[/tex]

[tex]\mathbf{Interval = [2,5]}[/tex]

[tex]\mathbf{n = 6}[/tex] ------ sub intervals

Using 6 sub intervals, we have the partitions to be:

[tex]\mathbf{Partitions = [2,2.5]\ u\ [2.5, 3]\ u\ [3,3.5]\ u\ [3.5,4]\ u\ [4,4.5]\ u\ [4.5,5]}[/tex]

List out the right endpoints

[tex]\mathbf{x= 2.5,\ 3,\ 3.5,\ 4,\ 4.5,\ 5}[/tex]

Calculate f(x) at these partitions

[tex]\mathbf{f(2.5) = 2.5^3 = 15.625}[/tex]

[tex]\mathbf{f(3) = 3^3 = 27}[/tex]

[tex]\mathbf{f(3.5) = 3.5^3 = 42.875}[/tex]

[tex]\mathbf{f(4) = 4^3 = 64}[/tex]

[tex]\mathbf{f(4.5) = 4.5^3 = 91.125}[/tex]

[tex]\mathbf{f(5) = 5^3 = 125}[/tex]

So, the approximated value of the definite integral is:

[tex]\mathbf{\int\limits^5_2 {f(x)} \, dx \approx \frac{1}{2}(\sum f(x))}[/tex]

This becomes

[tex]\mathbf{\int\limits^5_2 {f(x)} \, dx \approx \frac{1}{2}(15.625 + 27 + 42.875 + 64+91.125 + 125)}[/tex]

[tex]\mathbf{\int\limits^5_2 {f(x)} \, dx \approx \frac{1}{2} \times 365.625}[/tex]

[tex]\mathbf{\int\limits^5_2 {f(x)} \, dx \approx 182.8125}[/tex]

Hence, the approximation of the area of the region R is 182.8125

Read more about definite integrals at:

https://brainly.com/question/9897385

Answer:

A

90 degrees

anticlockwise.

Step-by-step explanation:

It looks much more complicated than it really is. I don't know how to explain this in any other form but to give the answers.

1 A

The center of rotation is where the 90 degree angle has its vertex. So that would be A.

1 B

Follow x. It rotates 90 degrees. So every point must rotate 90 degrees.

1 C

The direction is against the way the clock tells time, so the direction of rotation is anticlockwise.

Answer:

0.13

Step-by-step explanation:

First let's find the probability of finding the first species or the second species:

P(A or B) = P(A) + P(B) - P(A and B)

P(A or B) = 0.61 + 0.08 - 0.28

P(A or B) = 0.41

Then, to find the probability of finding one or another but not both, we just need the symmetric difference of the events, that is: P(A or B) - P(A and B):

P(A or B) - P(A and B) = 0.41 - 0.28 = 0.13

Answer:

(- 5, - 7 )

Step-by-step explanation:

Equate f(x) and g(x), that is

2x + 3 = - 4x - 27 ( add 4x to both sides )

6x + 3 = - 27 ( subtract 3 from both sides )

6x = - 30 ( divide both sides by 6 )

x = - 5

Substitute x = - 5 into either of the 2 functions for y- coordinate

Substituting into f(x)

f(- 5) = 2(- 5) + 3 = - 10 + 3 = - 7

Thus point of intersection = (- 5, - 7 )

Answer:

Step-by-step explanation:

t=V100-50/4

t=V50/4=1.76≈1.8 s

when h=0

t=V100/4=10/4=2.5 s

Answer:  a) (5√2)/4 ≈ 1.77 seconds

               b) 5/2 = 2.5 seconds

Step-by-step explanation:

[tex]t=\dfrac{\sqrt{100-h}}{4}\\\\\\h=50\rightarrow t=\dfrac{\sqrt{100-50}}{4}\\\\\\.\qquad \qquad =\dfrac{\sqrt{50}}{4}\\\\\\.\qquad \qquad =\large\boxed{\dfrac{5\sqrt2}{4}}\\\\\\\\h=0\rightarrow t=\dfrac{\sqrt{100-0}}{4}\\\\\\.\qquad \qquad =\dfrac{\sqrt{100}}{4}\\\\\\.\qquad \qquad =\dfrac{{10}}{4}\\\\\\.\qquad \qquad =\large\boxed{\dfrac{5}{2}}[/tex]

Answer:

x=35

Step-by-step explanation:

Answer:

30, 150, 120, and 60 degrees

Step-by-step explanation:

Since the sum of the interior angles in a quadrilateral is 360 degrees:

y+5y+4y+2y=360

12y=360

y=30

2y=60, 4y=120, 5y=150

Hope this helps!

Step-by-step explanation:

y+5y+ 4y + 2y=360°(sum of a Quadrilateral)

12y=360°

divide both sides by 12

y=30°

5y=(5×30)=150°

4y=(4×30)=120°

2y=(2×30)=60°