Translate the given statement into propositional logic using proposition provided :
You can see the movie only if you are over 18 years old or you have the permission of a parent. Express your answer in terms of m: “You can see the movie,” e: “You are over 18 years old,” and p: “You have the permission of a parent.”

Answer:

3.876943x10^9

7.317x10^-4

Step-by-step explanation:

3,876,943,000

Put the decimal at the end

3,876,943,000.

Move it so only 1 number is before the decimal

3.876943000

We moved it 9 places, so that is the exponent

We moved it to the left, so the exponent is positive

The three zeros at the end can be dropped because they are the last numbers to the right of the decimal

3.876943x10^9

0.0007317

Move it so only 1 number is before the decimal

00007.317

We moved it 4 places, so that is the exponent

We moved it to the right, so the exponent is negative

The four zeros at the left can be dropped because they are the last numbers to the left of the whole number

7.317x10^-4

Answer:

root 6

Step-by-step explanation:

pi*r^2 = A

6*pi*r^2 = 6A

6*r^2 = new radius squared

root 6 * r = new radius

The correct answer is option 1) The radius is multiplied by [tex]\sqrt{6}[/tex]

[tex]A = \pi r^2[/tex]
where A is the area and r is the radius.
If the area is multiplied by 6, we can represent this with the following equation:
A' = 6A
where A' is the new area and let r' be its radius.
[tex]A' = \pi (r')^2[/tex]
Substituting this into the equation for the new area gives us:
[tex]\pi (r')^2 = 6*(\pi r^2)[/tex]
To solve for r', we can divide both sides of the equation by [tex]\pi[/tex]:
[tex](r')^2 = 6r^2[/tex]
Next, take the square root of both sides to solve for r':
[tex]r' = \sqrt{6}r[/tex]
Therefore, the new radius r' is the original radius r multiplied by [tex]\sqrt{6}[/tex].

Answer: Second Option

68%

Step-by-step explanation:

First we calculate the Z-scores

We know the mean and the standard deviation.

The mean is:

[tex]\mu=27[/tex]

The standard deviation is:

[tex]\sigma=3[/tex]

The z-score formula is:

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

For x=24 the Z-score is:

[tex]Z_{24}=\frac{24-27}{3}=-1[/tex]

For x=30 the Z-score is:

[tex]Z_{30}=\frac{30-27}{3}=1[/tex]

Then we look for the percentage of the data that is between [tex]-1 <Z <1[/tex] deviations from the mean.

According to the empirical rule 68% of the data is less than 1 standard deviations of the mean.  This means that 68% of pizzas are delivered between 24 and 30 minutes

Answer:

The required standard form of  ellipse is [tex]\frac{x^2}{25}+\frac{y^2}{34}=1[/tex].

Step-by-step explanation:

The standard form of an ellipse is

[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1[/tex]

Where, (h,k) is center of the ellipse.

It is given that the center of the circle is (0,0), so the standard form of the ellipse is

[tex]\frac{x^2}{a^2}+\frac{y^2}{b^2}=1[/tex]             .... (1)

If a>b, then coordinates of vertices are (±a,0), coordinates of co-vertices are (0,±b) and focus (±c,0).

[tex]c^2=a^2-b^2[/tex]            .... (2)

If a<b, then coordinates of vertices are (0,±b), coordinates of co-vertices are (±a,0) and focus (0,±c).

[tex]c^2=b^2-a^2[/tex]            .... (3)

It is given that co-vertex of the ellipse at (5, 0); focus at (0, 3). So, a<b we get

[tex]a=5,c=3[/tex]

Substitute a=5 and c=3 these values in equation (3).

[tex]3^2=b^2-(5)^2[/tex]

[tex]9=b^2-25[/tex]

[tex]34=b^2[/tex]

[tex]\sqrt{34}=b[/tex]

Substitute a=5 and [tex]b=\sqrt{34}[/tex] in equation (1), to find the required equation.

[tex]\frac{x^2}{5^2}+\frac{y^2}{(\sqrt{34})^2}=1[/tex]

[tex]\frac{x^2}{25}+\frac{y^2}{34}=1[/tex]

Therefore the required standard form of  ellipse is [tex]\frac{x^2}{25}+\frac{y^2}{34}=1[/tex].

Answer:

Find the explicit from for the sequence [tex]t_n=t_{n-1}+4,t=6[/tex]:

[tex]a_n=4n+2[/tex]

This next question I edited a bit.  Your question just says find the four terms.  I'm assuming they meant the first four. I also changed the c to an [tex]a[/tex].

Find the first four terms of the sequence given by: [tex]a_n=n a_{n-1}-3,a_1=2[/tex]:

a) 2,1,0.-3

You might want to read that second question again because there is errors in the question or things that don't really make sense.  I made my own interpretation of the problem based on my own mathematical experience.

Step-by-step explanation:

So your first question actually says that you can find a term by taking that term's previous term and adding 4.

So more terms of the sequence starting at first term 6 is:

6,10,14,18,....

This is an arithmetic sequence.  When thinking of arithmetic sequences you should just really by thinking about equations of lines.

Let's say we have this table for (x,y):

x  |   y

----------

1      6

2    10

3     14

4     18

So we already know the slope which is the common difference of an arithmetic sequence.

We also know point slope form of a line is [tex]y-y_1=m(x-x_1)[/tex] where m is the slope and [tex](x_1,y_1)[/tex] is a point on the line.  You can use any point on the line. I'm going to use the first point (1,6) with my slope=4.

[tex]y-6=4(x-1)[/tex]

[tex]y=6+4(x-1)[/tex]    :I added 6 on both sides here.

[tex]y=6+4x-4[/tex]     :I distribute here.

[tex]y=4x+2[/tex]        :This is what I get after combining like terms.

So [tex]a_n=y[/tex] and [tex]x=n[/tex] so you have:

[tex]a_n=4n+2[/tex]

---------------------------------------------------------------------------------------

The first four terms of this sequence will be given by:

[tex]a_1,a_2,a_3,a_4[/tex]

[tex]a_1=2[/tex] so it is between choice a, c, and d.

[tex]a_n=na_{n-1}-3[/tex]

To find [tex]a_2[/tex] replace n with 2:

[tex]a_2=2a_{1}-3[/tex]

[tex]a_2=2(2)-3[/tex]

[tex]a_2=4-3[/tex]

[tex]a_2=1[/tex]

So we have to go another further the only one that has first two terms 2,1 is choice a.

Answer:

-3 is the value of k in g(x)=kf(x)

Step-by-step explanation:

Both functions cross nicely at x=-3 so I'm going to plug in -3 for x:

g(x)=kf(x)

g(-3)=kf(-3)

To solve this for k we will need to find the values for both g(-3) and f(-3).

g(-3) means we want the y that corresponds to x=-3 on the curve/line of g.

g(-3)=-3

f(-3) means we want the y that corresponds to x=-3 on the curve/line of f.

f(-3)=1

So our equation becomes:

g(-3)=kf(-3)

-3=k(1)

-3=k

So k=-3.

This is about interpretation of graphs.

Option C is correct.

We see that the best point for that is where x = -3.

we can rewrite them as;

x = -3, f(-3) = 1 and x = -3, g(-3) = -3

-3 = k(1)

Thus; k = -1/3

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[tex]|\Omega|={_{20}C_3}=\dfrac{20!}{3!17!}=\dfrac{18\cdot19\cdot20}{2\cdot3}=1140\\|A|=1\\\\P(A)=\dfrac{1}{1140}\approx0.09\%[/tex]

Answer:

0.014%

Step-by-step explanation:

To calculate the probability that she chooses that exact songs for the piano recital, you just first calculate the probability of her choosing one of them:

[tex]Probability of 1=\frac{1}{20}=.05[/tex]

This is 5%, now you multipy this with the probability of the second song after this one, since there is one less song, the total number of outcomes should be reduced to 19:

[tex]Probability of 2nd=(.05)(\frac{1}{19}[/tex]

[tex]Probability of 2nd=(0.05)(0.052}[/tex]

[tex]Probability of 2nd=0.002[/tex]

This would be .26%

To calculate the probability of the third song being chosen after the first two, we have 2 less outcomes possibles, so the total number of possibilities now is reduced to 18.

[tex]Probability of 3rd=(.0026)(\frac{1}{18}[/tex]

[tex]Probability of 3rd=(.0026)(0.055)[/tex]

[tex]Probability of 3rd=0.00014[/tex]

The probability of Noam choosing the three songs would be: 0.014%

Answer:

  loss of $12,481.38

Step-by-step explanation:

It is usually a good idea to follow directions. (See attached.)

The sum of the three profit values is -$12,481.38, indicating a loss in the 3-year period.

Answer:

[tex]x = 0 , \pi , 2\pi[/tex]

Step-by-step explanation:

The given equation is:l

[tex] \tan^{2} (x) \sec^{2} x + 2 \sec^{2} x - \tan^{2} x = 2[/tex]

Add -2 to both sides of the equation to get:

[tex] \tan^{2} (x) \sec^{2} x + 2 \sec^{2} x - \tan^{2} x - 2 = 0[/tex]

We factor the LHS by grouping.

[tex]\sec^{2} x(\tan^{2} (x) + 2 ) - 1( \tan^{2} x + 2) = 0[/tex]

[tex](\sec^{2} x - 1)(\tan^{2} (x) + 2)= 0[/tex]

We now apply the zero product property to get:

[tex](\sec^{2} x - 1) = 0 \: \: or \: \: (\tan^{2} (x) + 2)= 0[/tex]

This implies that:

[tex]\sec^{2} x = 1 \: \: or \: \: \tan^{2} (x) = - 2[/tex]

[tex] \tan^{2} (x) = - 2 \implies \tan(x) = \pm \sqrt{ - 2} [/tex]

This factor is never equal to zero and has no real solution.

[tex]\sec^{2} x = 1[/tex]

This implies that:

[tex]\sec \: x= \pm\sqrt{1} [/tex]

[tex] \sec(x) = \pm - 1[/tex]

Recall that

[tex] \frac{1}{ \sec(x) } = \cos(x) [/tex]

We reciprocate both sides to get:

[tex] \cos(x) = \pm1[/tex]

[tex]\cos x = 1 \: or \: \cos x = - 1[/tex]

[tex]\cos x = 1 \implies \: x = 0 \: or \: 2\pi[/tex]

[tex]\cos x = - 1 \implies \: x = \pi[/tex]

Therefore on the interval

[tex]0 \leqslant x \leqslant 2\pi[/tex]

[tex]x = 0 , \pi , 2\pi[/tex]

Answer:

Option A) [tex]\frac{4x+3y}{3x-4y}[/tex]

Step-by-step explanation:

The given expression is:

[tex]\frac{\frac{x}{3}+\frac{y}{4}}{\frac{x}{4}-\frac{y}{3}}[/tex]

Taking LCM in upper and lower fractions, we get:

[tex]\frac{\frac{x}{3}+\frac{y}{4}}{\frac{x}{4}-\frac{y}{3}}\\\\ =\frac{\frac{4x+3y}{12}}{\frac{3x-4y}{12}}\\\\\text{Cancelling out the common factor 12, we get:}\\\\ =\frac{4x+3y}{3x-4y}[/tex]

Therefore, the option A gives the correct answer.

Answer:

No they will not have to install a rest platform.

The ramp will be 29.88 feet long so they will not have to install a rest platform.

Step-by-step explanation:

Answer:

The correct answer is option B.  

m<3 = m<6

Step-by-step explanation:

From the figure we an see that, a and b are parallel lines and line t is the traversal on the lines.

To find the correct option

From the given figure we get

Corresponding angles are,

<1 & <5,  <2&<6, <2&<7 and <4 &<8

Alternate interior angles are,

<3 & <6  and <4 &<5

Alternate interior angles are equal.

m<3 = m<6

Therefore the correct answer is optionB

Answer:

[tex]cosZ=\frac{3}{5}[/tex]

Step-by-step explanation:

Cos of an angle by definition of its ratio is side adjacent/hypotenuse.  The side adjacent to angle Z cannot be the hypotenuse, so it has to be 6.  The hypotenuse is 10.  Therefore,

[tex]cosZ=\frac{6}{10}=\frac{3}{5}[/tex]

Answer: y = -1/4x - 4

Step-by-step explanation:

y = (-1/4)x + 2 (This is the first linear function.)

(4,3) has slope of (-1/4)x  or (1/-4)x

4(y2) - 4(y1= the new y  -1(x2) -3(x1) = new x which leads to (0,-4) so y-intercept = -4

so all in all, y = (-1/4)x -4 is the answer

Hopefully, you're able to understand this. It's difficult to explain through typed words rather than visually and through a written example.

Same y intercept as x+4y=8 through (4,3)

Y intercept is when x=0, so 4y=8, so y=2 and the y intercept is (0,2)

Answer for y intercept:  (0,2)

So we need the line through (0,2) and (4,3).  Point-point form says the line through (a,b) and (c,d) is

(c-a)(y-b) = (d-b)(x-a)

(4 - 0)(y - 2) = (3 - 2)(x - 0)

4y - 8 = x

Answer for the line:  x - 4y = -8

Check:

(0,2) is on the line: 0-4(2)  = -8 check

(4,3) is on the line 4 - 4(3) = -8 check

Answer:

y-7 = 1/2x point slope form

y = 1/2x+7  slope intercept form

Step-by-step explanation:

y=-2x+9

This equation is in the form y= mx +b so the slope is -2

We want a line perpendicular

Take the negative reciprocal

m perpendicular is - (-1/2)

m perpendicular = 1/2

We have a slope of 1/2 and a point.  We can use point slope form

y-y1 = m(x-x1)

y-7 = 1/2(x-0)  point slope form

y-7 = 1/2x

Adding 7 to each side

y-7+7 =1/2x +7

y = 1/2x+7  slope intercept form

Answer:

Δ ABC was dilated by a scale factor of 1/2, reflected across the y-axis

and moved through the translation (3 , 2)

Step-by-step explanation:

* Lets explain how to solve the problem

- The similar triangles have equal ratios between their

  corresponding side

- So lets find from the graph the corresponding sides and calculate the

  ratio, which is the scale factor of the dilation

- In Δ ABC :

∵ The length of the horizontal line is x2 - x1

- Let A is (x1 , y1) and B is (x2 , y2)

∵ A = (-4 , -2) and B = (0 , -2)

∴ AB = 0 - -4 = 4

- The corresponding side to AB is ED

∵ The length of the horizontal line is x2 - x1

- Let E is (x1 , y1) , D is (x2 , y2)

∵ E = (5 , 1) and D = (3 , 1)

∵ DE = 5 - 3 = 2

∵ Δ ABC similar to Δ EDF

∵ ED/AB = 2/4 = 1/2

∴ The scale factor of dilation is 1/2

* Δ ABC was dilated by a scale factor of 1/2

- From the graph Δ ABC in the third quadrant in which x-coordinates

 of any point are negative and Δ EDF in the first quadrant in which

 x-coordinates of any point are positive

∵ The reflection of point (x , y) across the y-axis give image (-x , y)

* Δ ABC is reflected after dilation across the y-axis

- Lets find the images of the vertices of Δ ABC after dilation and

 reflection  and compare it with the vertices of Δ EDF to find the

 translation

∵ A = (-4 , -2) , B = (0 , -2) , C (-2 , -4)

∵ Their images after dilation are A' = (-2 , -1) , B' = (0 , -1) , C' = (-1 , -2)

∴ Their image after reflection are A" = (2 , -1) , B" = (0 , -1) , C" = (1 , -2)

∵ The vertices of Δ EDF are E = (5 , 1) , D = (3 , 1) , F = (4 ,0)

- Lets find the difference between the x-coordinates and the

 y- coordinates of the corresponding vertices

∵ 5 - 2 = 3 and 1 - -1 = 1 + 1 = 2

∴ The x-coordinates add by 3 and the y-coordinates add by 2

∴ Their moved 3 units to the right and 2 units up

* The Δ ABC after dilation and reflection moved through the

  translation (3 , 2)

Answer:

The answer is

C.) BE

AD/AG=BE/BH

Answer:

Option C

Step-by-step explanation:

We have to find the value in the blank space

We are given that AC,DF and GI are parallel

We know that by middle splitting theorem

We have

[tex]\frac{JD}{AD}=\frac{JE}{BE}[/tex]

Because AC is parallel to DF and A and B are the mid points of JD and JE

[tex]\frac{JD}{GD}=\frac{JE}{EH}[/tex]

Because DF is parallel to GI

Divide  equation one by equation second then we get

[tex]\frac{GD}{AD}=\frac{EH}{BE}[/tex]

Adding one on both sides then we get

[tex]\frac{GD}{AD}+1=\frac{BE}{EH}+1[/tex]

[tex]\frac{GD+AD}{AD}=\frac{BE+EH}{BE}[/tex]

[tex]\frac{AG}{AD}=\frac{BH}{BE}[/tex]

Because BE+EH=BH and AD+GD=AG

Reciprocal on both sides then we get

[tex]\frac{AD}{AG}=\frac{BE}{BH}[/tex]

Hence, option C is true.

Answer:

4

(We didn't even need to use (9,6) )

Step-by-step explanation:

The slope-intercept form a line is y=mx+b where m is the slope and b is the y-intercept.

We are given the line we are looking for has the same y-intercept as x+2y=8.

So if we put x+2y=8 into y=mx+b form we can actually easily determine the value for b.

So we are solving x+2y=8 for y:

x+2y=8

Subtract x on both sides:

  2y=-x+8

Divide both sides by 2:

   y=(-x+8)/2

Separate the fraction:

  y=(-x/2)+(8/2)

Reduce the fractions (if there are any to reduce):

y=(-x/2)+4

Comparing this to y=mx+b we see that b is 4.

So the y-intercept is 4.

Again since we know that the line we are looking for has the same y-intercept, then the answer is 4 since the question is what is the y-intercept.

4

Answer: $80

Step-by-step explanation:

Given : Interest amount : [tex]T=\$40[/tex]

The rate of interest : [tex]r=10\%=0.1[/tex]

Time period : [tex]t=5[/tex] years

The simple interest formula is

[tex]l=prt[/tex], where l represents simple interest on an amount p for t years at a rate of r where r is expressed as a decimal.

Substitute all the values in the  formula , we get

[tex]40=p(0.1)(5)\\\\\Rightarrow\ p=\dfrac{40}{0.1\times5}=80[/tex]

Hence, the amount of money p that will generate $40 in interest at a 10% interest rate over 5 years= $80

The amount of money (p) required to generate $40 in interest at a 10% interest rate over 5 years is $80.

Given the parameters:

Simple interest l = $40

Interest rate r = 10% = 10/100 = 0.10

Time t = 5 years

To determine the amount of money (p) that will generate $40 in interest at a 10% interest rate over 5 years, we use the simple interest formula:

I = P × r × t

Solve for p:
P = I / rt

Plug in the values

P = $40 / ( 0.10 × 5 )

P = $40 / 0.5

P = $80

Therefore, the value of the principal is $80.

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Answer:

1. -10

2. [tex]x=1\pm\sqrt{2}i[/tex]

3. -1+2i

4. -3-7i

5. 13

6. rectangular coordinates are (-4.3,-2.5)

7. rectangular coordinates are (-2.5,4.3)

8. x^2 + y^2 = 8y

9. Polar coordinates of point (-3,0) are  (3,180°)

10. Polar coordinates of point (1,1) are  (√2,45°)

Step-by-step explanation:

1) Simplify (2+3i)^2 + (2-3i)^2

Using formula (a+b)^2 = a^2+2ab+b^2

=((2)^2+2(2)(3i)+(3i)^2)+((2)^2-2(2)(3i)+(3i)^2)

=(4+12i+9i^2)+(4-12i+9i^2)

We know that i^2=-1

=(4+12i+9(-1))+(4-12i+9(-1))

=(4+12i-9)+(4-12i-9)

=(-5+12i)+(-5-12i)

=5+12i-5-12i

=-10

2. Solve x^2-2x+3 = 0

Using quadratic formula to find value of x

a=1, b=-2 and c=3

[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\x=\frac{-(-2)\pm\sqrt{(-2)^2-4(1)(3)}}{2(1)}\\x=\frac{2\pm\sqrt{4-12}}{2}\\x=\frac{2\pm\sqrt{-8}}{2}\\x=\frac{2\pm2\sqrt{-2}}{2}\\x=\frac{2\pm2\sqrt{2}i}{2}\\x=2(\frac{1\pm\sqrt{2}i}{2})\\x=1\pm\sqrt{2}i[/tex]

3. If u =1+3i and v =-2-i what is u+v

u+v = (1+3i)+(-2-i)

u+v = 1+3i-2-i

u+v = 1-2+3i-i

u+v = -1+2i

4. if u = 3-4i and v = 3i+6 what is u-v

u-v = (3-4i)-(3i+6)

u-v = 3-4i-3i-6

u-v = 3-6-4i-3i

u-v = -3-7i

5. if u=(3+2i) and v=(3-2i) what is uv?

uv = (3+2i)(3-2i)

uv = 3(3-2i)+2i(3-2i)

uv = 9-6i+6i-4i^2

uv = 9-4i^2

i^2=-1

uv = 9-4(-1)

uv = 9+4

uv = 13

6. Convert (5, 7π/6)  to rectangular form

To convert polar coordinate into rectangular coordinate we use formula:

x = r cos Ф

y = r sin Ф

r = 5, Ф= 7π/6

x = r cos Ф

x = 5 cos (7π/6)

x = -4.3

y = r sin Ф

y = 5 sin (7π/6)

y = -2.5

So rectangular coordinates are (-4.3,-2.5)

7. Convert (5, 2π/3)  to rectangular form

To convert polar coordinate into rectangular coordinate we use formula:

x = r cos Ф

y = r sin Ф

r = 5, Ф= 2π/3

x = r cos Ф

x = 5 cos (2π/3)

x = -2.5

y = r sin Ф

y = 5 sin (2π/3)

y = 4.33

So rectangular coordinates are (-2.5,4.33)

8. Convert r=8cosФ to rectangular form

r.r = (8 cos Ф)r

r^2 = 8 (cosФ)(r)

Let (cosФ)(r) = y and we know that r^2 = x^2+y^2

x^2 + y^2 = 8y

9. Convert(-3,0) to polar form

We need to find (r,Ф)

r = √x^2+y^2

r = √(-3)^2+(0)^2

r =√9

r = 3

and tan Ф = y/x

tan Ф = 0/-3

tan Ф = 0

Ф = tan^-1(0)

Ф = 0°

As Coordinates are in 2nd quadrant, so add 180° in the given angle

0+180 = 180°

So,Polar coordinates of point (-3,0) are  (3,180°)

10) Convert (1,1) to polar form

We need to find (r,Ф)

r = √x^2+y^2

r = √(1)^2+(1)^2

r =√2

and tan Ф = y/x

tan Ф = 1/1

tan Ф = 1

Ф = tan^-1(1)

Ф = 45°

As Coordinates are in 1st quadrant, so Ф will be as found

So,Polar coordinates of point (1,1) are  (√2,45°)

Answer:

  D.  they are parallel​

Step-by-step explanation:

A plane can be defined by a point and a direction vector that is perpendicular to the plane. If two planes have the same direction vector (perpendicular line), then they are either the same plane or they are parallel.

If two planes are perpendicular to the same line, then they must also be parallel to each other.

If two planes are perpendicular to the same line, then they are also parallel to each other. This is because any line that intersects two parallel planes will be perpendicular to both planes.

To illustrate this, imagine two planes, A and B, that are perpendicular to the same line, L. If we draw a line, M, that intersects both planes, then M will be perpendicular to both planes A and B. This is because lines A and B are parallel to each other, and any line that intersects two parallel lines will be perpendicular to both lines.

Therefore, if two planes are perpendicular to the same line, then they must also be parallel to each other. The answer is D. they are parallel.

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Answer:

22.2 ft²

Step-by-step explanation:

The area (A) of the sector is

A = area of circle × fraction of circle

   = πr² × [tex]\frac{50}{360}[/tex]

   = π × 7.13² × [tex]\frac{5}{36}[/tex]

   = π × 50.8369 × [tex]\frac{5}{36}[/tex]

   = [tex]\frac{50.8369(5)\pi }{36}[/tex] ≈ 22.2 ft² ( nearest tenth )

Answer:

Area of smaller sector = 22.2 ft²

Step-by-step explanation:

Points to remember

Area of circle = πr²

Where 'r' is the radius of circle

To find the area of circle

Here r = 7.13 ft

Area =  πr²

 =  3.14 * 7.13²

 = 159.63 ft²

To find the area of smaller sector

Here central angle of sector is 50°

Area of sector = (50/360) * area of circle

 = (50/360) * 159.63

 = 22.17 ≈ 22.2 ft²

To find the x intercepts, we need to put the standard form equation into factored form.

Which two numbers multiply to -8 and add to -2?

[tex]-4*2=-8[/tex]

[tex]-4+2=-2[/tex]

So the factored form is

[tex](x-4)(x+2)[/tex]

That means the x intercepts are at [tex]x=4,-2[/tex]

So now we have the x intercepts.

To find the vertex, we need to convert the standard form equation into vertex form.

The formula of vertex form is [tex]y=a(x-h)^2+k[/tex]

Since the a value in the standard form equation is 1, the a value in vertex form is also one.

The h value can be found using the formula [tex]h=\frac{-b}{2a}[/tex]

Which comes out to [tex]\frac{2}{2}[/tex] or 1.

To find the k value, we can just plug in what we got for h back into the equation.

[tex](1)^2-2(1)-8=-9[/tex]

So the vertex is [tex](1,-9)[/tex].

This also means the axis of symmetry is [tex]x=-1[/tex]

Finally, to find the y intercept, we plug in 0 for x and solve.

[tex](0)^2-2(0)-8=-8[/tex]

So the y intercept is [tex](0,-8)[/tex].

Answer:

  2

Step-by-step explanation:

Only graph 2 shows a function that passes the horizontal line test. The other graphs will cross a horizontal line multiple times, meaning the function does not have an inverse.

Answer:

Step-by-step explanation:

A function is invertible if its bijective: injective and surjective at the same time. But, graphically exist the horizontal line test to know if the function is injective,  i.e., one to one: one element of the domain has a unique element in the image set.

So, in this case, the only function that can be cut once by a imaginary horizontal line is graph number 2. If we draw a horizontal line in other options, it will cut them in more than one point, meaning that they are not injective, therefore, not invertible.

Answer: 25%

Step-by-step explanation:

Given : A rectangular dartboard has an area of 648 square centimeters.

The triangular part of the dartboard has an area of 162 square centimeters.

If we assume that the dart lands in the rectangle, then the probability that it lands inside the triangle will be :-

[tex]\dfrac{\text{Area of triangular part}}{\text{Area of rectangular dart board}}\\\\=\dfrac{162}{648}=0.25[/tex]

In percent, [tex]0.25\times100=25\%[/tex]

Hence, the required probability = 25%

Answer:

  Each bouquet included 2 foil balloons and 8 latex balloons.

Step-by-step explanation:

Let f represent the number of foil balloons in each bouquet. Then 10-f is the number of latex balloons. The problem statement tells us the cost of all of the bouquets is ...

  18(1.94f +0.17(10-f)) = 94.32

We can divide by 18 to get ...

  1.94f +1.70 -0.17f = 5.24

  1.77f = 3.54 . . . . . . . . . . . . subtract 1.70

  f = 3.54/1.77 = 2 . . . . . . . . divide by the coefficient of f

The number of latex balloons is 10-2 = 8.

Each bouquet included 2 foil and 8 latex balloons.

Look at the table for the people that used Lithium.

There are 18 relapses, 6 No relapses with a total of 24 people.

The relative frequency for relapse, would be dividing the number of relapses by the total number of people.

This would be D. 18 / 24 = 75%

Final answer:

To find the probability, we use the Poisson probability formula with a mean of three. The probability of exactly four births is 0.168, the probability of at least four births is 0.361, and the probability of more than four births is 0.193.

Explanation:

To find the probability in each case, we will use the Poisson probability formula since the number of births per minute in a country follows a Poisson distribution with a mean of three.

(a) Exactly four births in a minute:

The probability of exactly four births in a minute can be calculated using the Poisson probability formula:

P(X = 4) = (e⁻³* 3⁴) / 4! = 0.168

(b) At least four births in a minute:

The probability of at least four births in a minute is the complement of the probability of having three or fewer births in a minute:

P(X ≥ 4) = 1 - P(X ≤ 3) = 1 - (P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)) = 1 - (0.049 + 0.147 + 0.221 + 0.222) = 0.361

(c) More than four births in a minute:

The probability of more than four births in a minute is the complement of the probability of having four or fewer births in a minute:

P(X > 4) = 1 - P(X ≤ 4) = 1 - (P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)) = 1 - (0.049 + 0.147 + 0.221 + 0.222 + 0.168) = 0.193

Let x = amount of 16% alloy, and y = amount of 30% alloy he should use.

Mixing the alloys will result in a compound weighing x + y = 100 grams.

For each gram of the 16% alloy used, 0.16 gram of titanium is contributed; similarly, for each gram of the 30% alloy used, there's a contribution of 0.3 gram. He wants to end up with an alloy of 23% titanium, or 23 grams (23% of 100), so that 0.16x + 0.3y = 23.

Solve the system:

[tex]x+y=100\implies y=100-x[/tex]

[tex]0.16x+0.3y=23\implies 0.16x+0.3(100-x)=23\implies7=0.14x[/tex]

[tex]\implies\boxed{x=50}\implies\boxed{y=50}[/tex]

Answer:

I think that the first one is not a rhombus but the last two are.