Change Y - 4X = 0 to the slope-intercept form of the equation of a line.

Answer:

D. 4 real roots and 0 complex roots

Step-by-step explanation:

If I assume that the function you are saying is

[tex]F(x)=x^4+x^3-5x^2+x-6[/tex]

There should be up to "4 roots," there can't be more or less than 4 total solutions. First, we need to check how many sign changes are there in this function. There are 3 positive real roots. Now lets check for negative roots.

[tex]F(-x)=x^4-x^3-5x^2-x-6[/tex]

There are is only 1 negative real root. Since we basically have 4 real roots, and the max is 4. There should be 4 real roots and 0 complex roots.

Answer:

Step-by-step explanation:

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have

[tex](-3;\ -8)\to x_1=-3;\ y_1=-8\\(4;\ 6)\to x_2=4;\ y_2=6[/tex]

Substitute:

[tex]m=\dfrac{6-(-8)}{4-(-3)}=\dfrac{6+8}{4+3}=\dfrac{14}{7}=2[/tex]

The formula for the slope m of the line that passes through two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is the following:

[tex]m=\dfrac{y_1-y_2}{x_1-x_2}[/tex]

We have points (4,6) and (-3,-8). Let's plug these values into the formula for slope:

[tex]m=\dfrac{6-(-8)}{4-(-3)}[/tex]

[tex]=\dfrac{14}{7}=2[/tex]

The slope of the line passing through the two points is 2. Let me know if you need any clarifications, thanks!

Answer:

[tex]\Large \boxed{-\dfrac{5}{4}(x+3)(x+1)(x-2)}[/tex]

Step-by-step explanation:

Hello,

Based on the indication, we can write this polynomial as below, k being a real number that we will have to identify (degree = 3 and we have three zeroes -3, -1, and 2).

   [tex]\Large \boxed{k(x+3)(x+1)(x-2)}[/tex]

We know that the point (1,10) is on the graph of this function, so we can say.

[tex]k(1+3)(1+1)(1-2)=10}\\\\4*2*(-1)*k=10\\\\-8k=10\\\\k=\dfrac{10}{-8}=-\dfrac{5}{4}[/tex]

Then the solution is:

[tex]\large \boxed{-\dfrac{5}{4}(x+3)(x+1)(x-2)}[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

Yes.

Step-by-step explanation:

1+1=2

3+5=8

7+1=8

9+23=32

5+13=18

An odd number is an even number plus 1, and 1 plus 1 is an even number. even numbers added together are also always even numbers, so two even numbers (in the second example it'd be 2+1 & 4+1, so 2 and 4) plus an even number(1+1=2) must be an even number.

Answer:

cars are dum

Step-by-step explanation:

Answer:

work is shown and pictured

Answer:

The answer is 15.6/31 or 1/2

Step-by-step explanation:

The data in the question is sufficient to find an answer for it.

1. I look at the temperature and rainfall chart for Brighton, United Kingdom.

2. Check for rainy season and dry season.

3. The rainy season lasts approximately 5 months while the dry season (which still has some rainfall) lasts approximately 7 months. All together, 12 months of the calendar year.

4. July happens to fall within the dry season. The temperature and rainfall statistics are observed.

The number of rainfall days is 15.6 and we know there are 31 days in July.

If the approximate number of days it rains in Brighton, in July, is 15.6 then the probability of rainfall in the month is 15.6/31 which is = 0.503 or 0.5

Therefore, there's a 50% chance of having rainfall in Brighton, on any day in the month of July.

In fraction, 0.5 = 1/2

Answer: [tex]\dfrac{1}{12}[/tex]

Step-by-step explanation:

Given: Emily has a box with 4 different colored tiles: one red, one green, one blue and one yellow.

We assume that repetition is not allowed

Total number of ways to draw two tiles = [tex]^4P_2=\dfrac{4!}{(4-2)!}[/tex]  [By permuattaions]

[tex]=\dfrac{4\times3\times2}{2}=12[/tex]

Favourable outcome = First green then red  (only one way)

So, the probability of drawing the green before the red [tex]=\dfrac{\text{favorable outcomes}}{\text{Total outcomes}}[/tex]

[tex]=\dfrac{1}{12}[/tex]

hence, the required probability =[tex]\dfrac{1}{12}[/tex]

Answer:

woman is 37, girl is 7

Step-by-step explanation:

7(x-2) = y-2

4(x+3) = y+3

7x - 14 = y - 2

7x - 12 = y

4x + 9 = y

3x - 21 = 0

x = 7

y = 37

Answer:

A. (1, -2)

Step-by-step explanation:

We can substitute the variables of x and y into the inequality of [tex]y < -|x|[/tex].

Let's start with A, -2 being y and 1 being x.

[tex]-2 < - |1|[/tex]

The absolute value of 1 is 1, and negating that gets us -1.

[tex]-2 < -1[/tex]

Indeed, -2 is less than -1! So A is a solution to the inequality.

Let's test the rest of them, just in case.

For B:

[tex]-1 < -|1|[/tex]

Absolute value of 1 is 1, negating it is -1.

[tex]-1<-1[/tex]

-1 is EQUAL to -1, not less than it, so is not a solution to the inequality.

Let's try C.

[tex]0 < -|1|[/tex]

Absolute value of 1 is 1, negating it is -1.

[tex]0 < -1[/tex]

0 is GREATER than -1, so that is not a solution to the inequality.

Hope this helped!

Answer:

The probability is  [tex]P(X \ge 20 ) = 0.3707[/tex]

Step-by-step explanation:

From the the question we are told that

    The population proportion is  p =  0.60

    The sample size is  n  =  31

The  mean is evaluated as

       [tex]\mu = n * p[/tex]

substituting values  

       [tex]\mu = 31 *0.60[/tex]

       [tex]\mu = 18.6[/tex]

The standard deviation is evaluated as

    [tex]\sigma = \sqrt{n * p * (1- p )}[/tex]

substituting values  

    [tex]\sigma = \sqrt{31 * 0.6 * (1- 0.6 )}[/tex]

    [tex]\sigma = 2.73[/tex]

The  the probability that at least 20 of them have looked at their score in the past six months is mathematically represented as

     [tex]P(X \ge 20) = 1- P(X < 20)[/tex]

 applying normal approximation we have that

     [tex]P(X \ge 20) = 1- P(X < (20-0.5))[/tex]

   Standardizing

         [tex]1 - P(X < 20) = 1 - P(\frac{X - \mu }{\sigma} < \frac{19.5 - \mu }{\sigma } )[/tex]

         [tex]1 - P(X < 20) = 1 - P(Z < \frac{19.5 - 18.6 }{2.73 } )[/tex]

         [tex]1 - P(X < 20) = 1 - P(Z < 0.33)[/tex]

Form the standardized normal distribution table we have that

      [tex]P(Z < 0.0512)[/tex] = 0.6293

=>   [tex]P(X \ge 20 ) = 1- 0.6293[/tex]

=>   [tex]P(X \ge 20 ) = 0.3707[/tex]

Answer:

outside the circle i think

Step-by-step explanation:

Answer:

inside the circle

Step-by-step explanation:

Answer:

lmkjhvjgcfnhjkhbmgnc gfghh

Step-by-step explanation:

Answer:

Barts total cost is (c)213.36

Step-by-step explanation:

First, you subtract 6% from $219

=204.92

add shipping,

+7.50

=213.36

Hope this helps <3

Answer:

C. $213.36

Step-by-step explanation:

The original price is $219 and the discount is 6% which is equal to $13.14

$219 - $13.14 + $7.50 (shipping cost) = $213.36

Circumference of the cylinder :

C = 2 x pi x r

C = 2 x 3.14 x 25 = 157 cm

Multiply the circumference by number of wraps:

157 x 50 = 7,850 cm long ( 78.5 meters)

Answer:

a)the proportion of student is 0.1082

b)

H1: p = .08

H2: p not equal to 0.08

H1: p =0 .08

H2: p < .08

H1: p =0 .08

H2: p >0 .08

c)z=1.45

d) the p value is 0.1470

e)null hypothesis cannot be accepted,There is no enough evidence to reject the  null hypothesis.

Step-by-step explanation:

CHECK THE ATTACHMENT FOR DETAILED EXPLANATION

Answer:

1.7

Step-by-step explanation:

1. Find the volume of Glass 2 (volume of a cone = 1/3πr² ·h)

1/3 · 3.14 · 2.5² · 6 = 39.25 cm³

2. Subtract the volume of Glass 2 from the amount of water poured

60 - 39.25 = 20.75 cm³

3. Set up the equation for Glass A using x for the height being solved for (volume of a cylinder = πr² · h)

3.14 · 2² · x = 20.75

12.56x = 20.75

4. Solve for x by dividing both sides by 12.56 (round to the nearest tenth)

x = 1.7

The answer should be 1.7

Explanation:

For any quadrilateral that is inscribed in a circle, ie has all four points on the circle like this, the opposite angles are always supplementary. They add to 180 degrees.

x+125 = 180

x+125-125 = 180-125 ... subtract 125 from both sides

x = 55

Answer:

x= -5, -1

Step-by-step explanation:

To find the zeroes of a function,

First expand the terms to get the form  [tex]ax^{2} + bx +c[/tex] where 'a, b, and c' are constants

     [tex]f(x)= (x+3)^{2} -4[/tex]

    [tex]f(x)= x^{2}+6x+9-4[/tex]

    [tex]f(x)= x^{2} +6x +5[/tex]

Now, factor the equation

This can be done using the quadratic formula or other methods

  One simple method is to find the two values that would get:

A good way to verify is to expand the terms and make sure the function looks the same

In this case, the equation can broken into

    f(x)= (x+1)*(x+5)

Now, look at each term individually and set each of them to equal 0

   x+1 =0

   x+5=0

Solve for x in each case

  x= -1

  x= -5

Now, ordering them from least to greatest would be: x= -5, -1

Answer:

Option A - There is sufficient evidence to conclude that the proportion of people wearing seat belts is less than 65%

Step-by-step explanation:

The police officers claim is that the proportion of people wearing seat belts is less than 65%.

Now, we are told that the p - value is 0.277.

In hypothesis, for a significance value of 0.05, if the P value is less than 0.05, we reject the null hypothesis and if P value is greater than or equal to 0.05, we fail to reject the null hypothesis.

Now, since the significance level is 5% = 0.05,we can see that the P-value is greater than the significance value of 0.05. Thus, we fail to reject the police claim that the proportion of people wearing seat belts is less than 65%.

So the correct option is A.

Answer:

Probability of obtaining no more than two defective tubes = 0.816

Step-by-step explanation:

The Probability of obtaining no more than two defective tubes in a randomly selected sample of 15 tubes is obtained using the binomial distribution formula: nCr × p^r × q^(n -r).

Where n is number of samples;

r is maximum number of defective tubes, r ≤ 2;

p is probability of defective tubes = 10% or 0.1

q is probability of non-defective tubes, q = 1 - p

Further explanations and calculations are given in the attachment below:

Answer:

The dentist should fail to reject the Null hypothesis

Step-by-step explanation:

From the question we are told that

       The sample size is  n =  400

       The  sample  mean is  [tex]\= x = 149[/tex]

       The  level of significance is  5%  = 0.05  

       The  Null hypothesis is  [tex]H_o : p = 0.40[/tex]

        The Alternative  hypothesis is  [tex]H_a : p < 0.40[/tex]

         The  p-value is  [tex]p-value = 0.131[/tex]

Looking at the given data we can see that the p-value is greater than the level of significance hence the dentist should fail to reject the Null hypothesis  

Answer:

The correct option is (D).

Step-by-step explanation:

In this case, we need to test whether the  mean pulse rate (in beats per minute) of students in a large math class is greater than 71.

The hypothesis can be defined as follows:

H₀: The mean pulse rate of students in a large math class is not greater than 71, i.e. μ ≤ 71.

Hₐ: The mean pulse rate of students in a large math class is greater than 71, i.e. μ > 71.

It is provided that the sample mean pulse rate, of a simple random sample of the students is 71.7.

The sample mean is not very different from the population mean.

So, it cannot be said in confidence that the sample is unusual.

Thus, the correct option is (D).

"The sample is not unusual if the claim is true. The sample is not unusual if the claim is false. Therefore, there is not sufficient evidence to support the claim."

Answer:

Step-by-step explanation:

Hello!

Miguel has four chips, two have the number "1", one has the number "3" and the other has the number "5"

If the experiment is "choosing two chips and looking at their numbers" there are the following possible outcomes:

S= {(1,1)(1,3)(1,5)(3,1)(5,1)(3,5)(5,3)}

The sample space for the experiment has 7 possible combinations.

a)

Be X: the amount of money Miguel will receive or owe.

If two chips with the same number are chosen he will receive $2

If the chips have different number he will owe $1

Looking at the possible outcomes listed above, out of the 7, in only one he will select the same number (1,1)

So the probability of him receiving $2 will be 1/7

Now out of the 7 possible outcomes, 6 will make Miguel owe $1, so you can calculate its probability as: 6/7

  xi  | $2 | -$1

P(xi) | 1/7 | 6/7

b)

To calculate the expected value or mean you have to use the following formula:

[tex]\frac{}{X}[/tex]= ∑[xi*P(xi)]= (2*1/7)(-1*6/7)= -4/7= $-0.57

c)

The expected value is $-0.57, meaning that Miguel can expect to owe $0.57 at the end of the game.

d)

To make the game fair you have to increase the probability of obtaining two chips with the same number. Any probability close to 50% will make the game easier. For example if you change the experiment so that for earning $2 the probability is 4/7 and for owing $1 the probability is 3/7, the expected earnings will be:

(2*4/7)+(-1*3/7)= $0.71

I hope this helps!

Answer:

Below

Step-by-step explanation:

The length of this triangle is 3x+1 and the width is x.

The perimeter P is:

P= 2(3x+1)+2*x

P= 6x+2+2x

P= 8x+2

Let's evaluate it when x=1/2

●1/2 =0.5

P= 8*0.5+2 =4+2= 6 ft

●●●●●●●●●●●●●●●●●●●●●●●●

The area A is:

A = (3x+1)*x

A= 3x^2 +x

Let's evaluate it when x=0.5 feet

A= 3*0.5^2 +0.5

A= 3*0.25+0.5

A= 0.75 +0.5

A= 1.25 ft^2

Answer:C

Step-by-step explanation:

Pemdas

3+5(10)

5*10=50

3+50=53

Answer:16.1%

Step-by-step explanation:

Answer:

The investment needs the rate of growth to be approximately 16.1%.

Step-by-step explanation:

Answer:

Option b.

Step-by-step explanation:

Note: The given expression is not in correct form. Consider the given expression is [tex]i^0\times i^1\times i^2\times i^3\times i^4[/tex].

Let as consider the given expression is  

[tex]i^0\times i^1\times i^2\times i^3\times i^4[/tex]

We know that,

[tex]i^0=1,i^2=-1,i^3=-i,i^4=1[/tex]

Using these values, we get

[tex]i^0\times i^1\times i^2\times i^3\times i^4=1\times i\times (-1)\times (-i)\times 1[/tex]

[tex]=i^2[/tex]

[tex]=-1[/tex]

The value of given expression is -1.

Therefore, the correct option is b.

Answer:

I think that is the C

Step-by-step explanation:

Answer:

Option B is the correct answer.

Step-by-step explanation:

here, arc RT =162°

as in question given that the value of arc RT is 162° the value of angle RST is 1/2 of 162°.

so, its value must be 81°only.

hope it helps..

Answer:

b

Step-by-step explanation: