At what points do these graphs intersect
y=x²-x-6
y=x+2

Answer:

6

Step-by-step explanation:

Hello, please consider the following.

[tex](4+x)^2=4^2+2\cdot 4\cdot x+x^2=16+\boxed{8}x+x^2\\\\\text{ ... and not ...}\\\\16+\boxed{4}x+x^2[/tex]

So the correct equation becomes.

[tex]x^2+64=16+8x+x^2\\\\8x=64-16=48\\\\\text{ we divide by 8 both sides of the equation.}\\\\x=\dfrac{45}{8}=6[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

Error : The expression ( 4 + x )² was expanded incorrectly.

Correct Solution : x = 6

Step-by-step explanation:

The planning of the solution is correct, by Pythagorean Theorem you can say that PQ² + QO² = PO², and hence through substitution x² + 8² = ( 4 + x )². Let's look into the calculations.

PQ² + QO² = PO²,

x² + 8² = ( 4 + x )²,

x² + 8² = 16 + 8x + x²,

64 = 16 + 8x,

48 = 8x,

x = 48 / 8 = 6, x = 6

As you can see, the only error in the calculations was expanding the expression ( 4 + x )². ( 4 + x )² = 4² + 2 [tex]*[/tex] 4 [tex]*[/tex] x + x² = 4² + 8x + x² = 16 + 8x + x², not 16 + 4x + x².

Answer: 0.20

Step-by-step explanation:

The given probability distribution of number of televisions per household in a small town:

x          0       1     2      3

​P(x) ​ 0.05 0.15 0.25 0.55

To find : The probability of randomly selecting a household that has one or two televisions ( in both parts a. and b.).

The computations for this would be :

P( 1 or 2) = P(1)+P(2)

= 0.05+0.15

= 0.20

Hence, the required probability= 0.20

Answer:

Step-by-step explanation:

Answer:

18/a

Step-by-step explanation:

quotient means divide

18/a

Answer:

(A) The probability that a male spent less than $210 online before deciding to visit a store is 0.0668.

(B) The probability that a male spent between $270 and $300 online before deciding to visit a store is 0.0655.

(C) Ninety percent of the amounts spent online by a male before deciding to visit a store is less than $265.632.

Step-by-step explanation:

We are given that the reports indicate that men spend an average of $240 online before they decide to visit a store. If the spending limit is normally distributed and the standard deviation is $20.

Let X = the spending limit

The z-score probability distribution for the normal distribution is given by;

                           Z  =  [tex]\frac{X-\mu}{\sigma}[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = mean spending limit = $240

           [tex]\sigma[/tex] = standard deviation = $20

So, X ~ Normal([tex]\mu=\$240,\sigma^{2} =\$20^{2}[/tex])

(A) The probability that a male spent less than $210 online before deciding to visit a store is given by = P(X < $210)

     P(X < $210) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{\$210-\$240}{\$20}[/tex] ) = P(Z < -1.50) = 1 - P(Z [tex]\leq[/tex] 1.50)

                                                            = 1 - 0.9332 = 0.0668

The above probability is calculated by looking at the value of x = 1.50 in the z table which has an area of 0.9332.

(B) The probability that a male spent between $270 and $300 online before deciding to visit a store is given by = P($270 < X < $300)

     P($270 < X < $300) = P(X < $300) - P(X [tex]\leq[/tex] $270)

     P(X < $300) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{\$300-\$240}{\$20}[/tex] ) = P(Z < 3) = 0.9987

     P(X [tex]\leq[/tex] $270) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\leq[/tex] [tex]\frac{\$270-\$240}{\$20}[/tex] ) = P(Z [tex]\leq[/tex] 1.50) = 0.9332

The above probability is calculated by looking at the value of x = 3 and x = 1.50 in the z table which has an area of 0.9987 and 0.9332 respectively.

Therefore, P($270 < X < $300) = 0.9987 - 0.9332 = 0.0655.

(C) Now, we have to find ninety percent of the amounts spent online by a male before deciding to visit a store is less than what value, that is;

         P(X < x) = 0.90     {where x is the required value}

         P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{x-\$240}{\$20}[/tex] ) = 0.90

         P(Z < [tex]\frac{x-\$240}{\$20}[/tex] ) = 0.90

In the z table, the critical value of z that represents the bottom 90% of the area is given as 1.2816, i.e;

                     [tex]\frac{x-\$240}{\$20}=1.2816[/tex]

                     [tex]x-240=1.2816\times 20[/tex]

                     [tex]x=240 + 25.632[/tex]

                     x = 265.632

Hence, Ninety percent of the amounts spent online by a male before deciding to visit a store is less than $265.632.

Answer:

x - 3y = 12

Step-by-step explanation:

Find the point-slope form of this equation and then convert the point-slope form into standard form (ax + by = c):

y - k = m(x - h) becomes y - 2 = (1/9)(x + 6).

Multiplying all three terms by 9 removes the fraction:

3y - 6 = x + 6, or x - 3y = 12

Answer:

[tex]\huge\boxed{\sf Speed = 44.44 \ m/s}[/tex]

Step-by-step explanation:

Speed = 160 km / hr

To convert km/hr to m/s, we multiply it by [tex]\sf \frac{10}{36}[/tex]

Hence,

[tex]\displaystyle Speed = 160 \times \frac{10}{36} \ m/s\\\\Speed = \frac{1600}{36} \ m/s\\\\Speed = 44.44 \ m/s\\\\\rule[225]{225}{2}[/tex]

Hope this helped!

Answer:

distance=√[(x2-x1)²+(y2-y1)²]

√[{6-(-2)}²+ (-8-(-4))²]

√(64+16)

√[100]

10

Points given

Distance:-

[tex]\\ \sf \longmapsto \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

[tex]\\ \sf \longmapsto \sqrt{(-8+4)^2+(6+2)^2}[/tex]

[tex]\\ \sf \longmapsto \sqrt{(-4)^2+(8)^2}[/tex]

[tex]\\ \sf \longmapsto \sqrt{64+16}[/tex]

[tex]\\ \sf \longmapsto \sqrt{80}[/tex]

[tex]\\ \sf \longmapsto 8.4[/tex]

Answer:

(a) The standardized z-score for this shipment is -3.392.

(b) Yes, this an outlier.

Step-by-step explanation:

We are given that the Ball Corporation’s aluminum can manufacturing facility in Ft. Atkinson, Wisconsin, knows that the metal thickness of incoming shipments has a mean of 0.2771 mm with a standard deviation of 0.000855 mm.

Let X = the metal thickness of incoming shipments.

The z-score probability distribution for the normal distribution is given by;

                              Z  =  [tex]\frac{X-\mu}{\sigma}[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = mean thickness = 0.2771 mm

           [tex]\sigma[/tex] = standard deviation = 0.000855 mm

(a) Now, it is given that a certain shipment has a diameter of 0.2742 mm and we have to find the standardized z-score for this shipment.

So, z-score  =  [tex]\frac{X-\mu}{\sigma}[/tex]

                   =  [tex]\frac{0.2742-0.2771}{0.000855}[/tex]  = -3.392

Hence, the standardized z-score for this shipment is -3.392.

(b) Yes, we can consider this as an outlier because the standardized z-score is very large and this value is far from the population mean.

Answer:

Step-by-step explanation:

Q(x)=x² − 6x − 2

To find Q(−4) substitute the value of x which is - 4 into Q(x)

That's

Q(-4) = (-4)² - 6(-4) - 2

Q(-4) = 16 + 24 - 2

We have the final answer as

Hope this helps you

Answer:

Point O represents the center of the circle

Step-by-step explanation:

HOPE IT HELPS. PLEASE MARK IT AS BRAINLIEST

Answer:

The mean commute time in the U.S. is less than half an hour.

Step-by-step explanation:

In this case we need to test whether the mean commute time in the U.S. is less than half an hour.

The information provided is:

 [tex]n=45\\\bar x=25.5\\s=19.1\\\alpha =0.05[/tex]

(a)

The hypothesis for the test can be defined as follows:

H₀: The mean commute time in the U.S. is not less than half an hour, i.e. μ ≥ 30.

Hₐ: The mean commute time in the U.S. is less than half an hour, i.e. μ < 30.

(b)

As the population standard deviation is not known we will use a t-test for single mean.

Compute the test statistic value as follows:

 [tex]t=\frac{\bar x-\mu}{s/\sqrt{n}}=\frac{25.2-30}{19.1/\sqrt{45}}=-1.58[/tex]

Thus, the test statistic value is -1.58.

(c)

Compute the p-value of the test as follows:

[tex]p-value=P(t_{(n-1)}<-1.58)=P(t_{(45-1)}<-1.58)=0.061[/tex]  

*Use a t-table.

The p-value of the test is 0.061.

Decision rule:

If the p-value of the test is less than the significance level then the null hypothesis will be rejected and vice-versa.

p-value = 0.061> α = 0.05

The null hypothesis will not be rejected at 5% level of significance.

Thus, concluding that the mean commute time in the U.S. is less than half an hour.

Answer:

4

Step-by-step explanation:

twice her age:

10*2 = 20

24-20 = 4

Answer:

4 i believe that's the answer

Answer:

Apllying cos on the triangle

cos(angle)= Base/ Hyp

cos(34)= 29/ AB

AB= 29/0.8290

AB=34.98

Step-by-step explanation:

The length of AB is 34.98 units which the correct answer would be an option (D).

A right triangle is defined as a triangle in which one angle is a right angle or two sides are perpendicular.

Trigonometric functions are defined as the functions which show the relationship between the angle and sides of a right-angled triangle.

Given that ΔABC

∠C = 90°

Here base = BC = 29 units and hypotenuse = AB

To determine the length of AB

Apply the cosine on the given right triangle

⇒ cos(θ) = Base/hypotenuse

⇒ cos(34) = 29/ AB

∴ cos(34°) = 0.8290

⇒ 0.8290 = 29/ AB

⇒ AB= 29/0.8290

⇒ AB = 34.98 units

Hence, the length of AB is  34.98 units

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Answer:

Step-by-step explanation:

Given the system of equation;

kx - y = 2 ------------------- 1

6x - 2y = 3 -------------------- 2

Rewriting the equations in the format ax+by+c = 0

Equation 1 becomes kx - y - 2 = 0

Equation 2 becomes 6x - 2y - 3 = 0

where a₁ = k, b₁ = -1 and c₁ = -2  and a₂ = 6, b₂ = -2 and c₂ = -3

For the system of equation to have a unique solution the following must be true;

a₁/a₂ ≠ b₁/b₁

Substituting the coefficients into the condition, we will have;

k/6 ≠ -1/-2

k/6 ≠ 1/2

Cross multiplying we will have;

2k ≠ 6

k ≠ 6/2

k ≠ 3

This means that k can be any other real values except 3 for the system of equation to have a unique solution.

Answer:

17.5ml- of 10 percent solution, 17.5ml- of 20 percent solution

Step-by-step explanation:

35:100*15=5.25- ml of alkali in the base solution

Suppose we need x ml of 10 percents solution and 35-x - of 20 percents.

Then The quantity of alkali in the first one (10 percents) is x/100*10=0.1x

when in the second one we have (35-x)/100*20= 7-0.2x of alkali

0.1x+7-0.2x=5.25

7-0.1x= 5.25

0.1x=1.75

x=17.5- 0f 10 percents

35-17.5=17.5 - of 20 percents

Answer:

9

Step-by-step explanation:

13-4=9

Answer:

40.60-35=5.6

Step-by-step explanation:

Profit is cost minus the amount you sold it for

Answer:

4, 7, 10, 13

Step-by-step explanation:

Hey there!

Well in the given pattern,

-11, -8, -5, -2, 1

we can conclude that the pattern is +3 every time.

-11 + 3 = -8

-8 + 3 = -5

-5 + 3 = -2

-2 + 3 = 1

And so on

Hope this helps :)

If you know the population standard deviation (sigma), then you use the Z distribution. If sigma is not known, then you use the T distribution.

Side note: Even if sigma is not known, you could use the Z distribution if the sample size n is greater than 30. If n > 30, then the T distribution is approximately about the same as the Z distribution.

Answer:

y=2/3x - 5

Step-by-step explanation:

Since we have the slope and a point, we can make an equation in point intercept form (y=mc+b) by using the point slope form formula (y-y1)=m(x-x1), where (x1,y1) is the point you plug in.

(y-y1)=m(x-x1)

m=2/3

y1=-3

x1=3

y- -3=2/3(x-3)

y+3=2/3(x-3)

Distribute 2/3 with (x-3) by multiplying

y+3=2/3x - 2

Subtract 3 from both sides

y=2/3x - 5

Answer:

-4/5

Step-by-step explanation:

When you divide -4 from 5 you get -0.80

Answer:

the slope of the read line is also -2

Step-by-step explanation:

Answer:

B. y = -2/3x + 12

Step-by-step explanation:

Formula to find the slope when given two points on a line:

y2 - y1

x2 - x1

Substitute the two given points (6, 8) (9, 6):

6 - 8

9 - 6

Slope = -2/3x

We found the slope! And the answer choices already gave us one y-intercept, which is 12. The last thing we do is we form an equation with the information we solved and that was given to us.

y = slope (x) + y-intercept

y = -2/3x + 12

The answer choice that matches this equation is B.

In conclusion, the equation that best estimates the line of best fit shown above is answer choice B.

An equation of a line with given coordinates is y= -2/3 x+12. Therefore, option B is the correct answer.

The general equation of a straight line is y=mx+c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.

From the given graph, the coordinate points are (6, 8) and (9, 6).

We know that, the formula to find the slope of a line is slope = (y₂-y₁)/(x₂-x₁).

Here, slope = (6-8)/(9-6)

= -2/3

Substitute m=-2/3 and (x, y)=(6, 8) in y=mx+c, we get

8=-2/3 (6)+c

8=-4+c

c=12

So, equation of a line is y= -2/3 x+12

Therefore, option B is the correct answer.

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Answer:

the answer is 4

Step-by-step explanation:

so 1 rotation is like a circle 1 unit circle requires 4 quadrant to be in this is the most simplified i can get

Answer:

Solution : 4

Step-by-step explanation:

The question asks us how many polar coordinates are possible for one rotation. For one rotation there will be 4 polar coordinates, one present in each quadrant such that,

( r, theta ), ( r, theta ), ( - r, theta ), ( - r, theta )

Respectively if theta was q say,

( r, q ), ( r, - q ), ( - r, q ), ( - r, -q )

Therefore there are 4 sets of polar coordinates for one rotation, in each of the 4 quadrants.

Answer:

Step-by-step explanation:

If there are 30 students in a class with natasha in the class and natasha is to select four leaders in the class of which she is already part of the selection, this means there are 3 more leaders needed to be selected among the remaining 29 students (natasha being an exception).

Using the combination formula since we are selecting and combination has to do with selection, If r object are to selected from n pool of objects, this can be done in nCr number of ways.

nCr = n!/(n-r)!r!

Sinca natasha is to select 3 more leaders from the remaining 29students, this can be done in 29C3 number of ways.

29C3 = 29!/(29-3)!3!

29C3 = 29!/(26!)!3!

29C3 = 29*28*27*26!/26!3*2

29C3 = 29*28*27/6

29C3 = 3,654 different ways.

This means that there are 3,654 different ways to select the 4 leaders so that natasha is one of the leaders

The larger metallic object is initially at rest, so the velocity is 0 when t = 0. The speed changes after t = 3 seconds.

Answer:

It would be the last one.

Step-by-step explanation:

It says the object is initially at rest, so you look for a table with 0 m/s and you find the last table had been at rest for 0 -2  seconds. The small rocky object initially had a speed of 90 m/s and then decreased to 36 m/s as its energy transferred to the metallic object. The metallic object's speed from time 4-6s with the small rocky object equals the small rocky initial speed.

Rocky Object initial speed = 90 m/s

Rocky Object new speed = 36 m/s

Large metallic object speed after collision = 64 m/s.

64 m/s + 36 m/s = 90 m/s

Large metallic object speed after collision + Rocky Object new speed

= Rocky Object initial speed

You can also test this for kinetic energy.

Answer:

The choose C. 2

[tex]( \frac{4 ^{ \frac{5}{4} } \times 4^{ \frac{1}{4} } }{4 ^{ \frac{1}{2} } } )^{ \frac{1}{2} } = 2[/tex]

Answer:

2

Step-by-step explanation:

inside the parenthesis is equivalent to 4^(5/4 + 1/4 - 1/2) = 4¹ = 4

√4 = 2

9514 1404 393

Answer:

Step-by-step explanation:

At $12 per gigabyte, the data charge will be 12g where g is the number of gigabytes. Then the total charge is ...

  C = 12g +20

__

If C = 116, the value of g is found from ...

  116 = 12g +20

  96 = 12g . . . . . . . subtract 20

  8 = g . . . . . . . . . . divide by 12

The amount of data used is 8 gigabytes if the charge is $116.

Answer:

The square root of -16 is an imaginary number and a complex number. Sqrt(-16)=4i. We use the i to indicate that the number is imaginary since there is no number that can be multiplied by itself to get a negative number (a negative times a negative is a positive, and a positive times a positive is also a positive). So the use of i tells you immediately that it's an imaginary number. You can tell the number is complex because it has both a real and an imaginary part and could be written in the form a+bi, where a is a real number and bi is an imaginary number. In this specific case, the real part (a) is 0 and the imaginary part (bi) is 4i.

Step-by-step explanation: