A researcher looked at characteristics of elementary school students and,
in particular, observed whether students satisfied any of the following
criteria:
A = The student lived with at least one of their biological parents
B = The student lived with at least one grandparent
C = The student lived with two parents who were legally married
D = The student lived with only one parent
Which of the events above are mutually exclusive? Select all that apply.
1.) A,C
2.) A,D
3.) C,D
4.) B,C

(Side note: I put down options 3&4 but got it wrong, not sure what I’m missing?)

Answer:

1. [tex]Area=16\,\pi=50.265[/tex]

2.- [tex]\frac{b}{a} =-8[/tex]

3.  [tex]y=\frac{1}{2} x^2+3x+\frac{5}{2}[/tex]

4.  [tex]a+b+c=\frac{17}{4}[/tex]

5.   the vertex is located at: (3, 10)

Step-by-step explanation:

1. If we rewrite the formula of the conic given by completing squares, we can find what conic we are dealing with:

[tex](x^2-2x)+(y^2+6y)=6\\\,\,\,\,\,\,+1\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,+9\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,+10\\(x-1)^2+(y+3)^2=16\\(x-1)^2+(y+3)^2=4^2[/tex]

which corresponds to a circle of radius 4, and we know what the formula is for a circle of radius R, then:

[tex]Area=\pi\,R^2=\pi\,4^2=16\,\pi=50.265[/tex]

2.

If x=4 is the axis of symmetry of the parabola

[tex]y=ax^2+bx+c[/tex]

then recall the formula to obtain the position of the x-value of the vertex:

[tex]x_{vertex}=-\frac{b}{2a} \\4=-\frac{b}{2a}\\4\,(-2)=\frac{b}{a} \\\frac{b}{a} =-8[/tex]

3.  

From the graph attached, we see that the vertex of the parabola is at the point: (-3, -2) on the plane, so we can write the general formula for a parabola in vertex form:

[tex]y-y_{vertex}=a\,(x-x_{vertex})^2\\y-(-2)=a\,(x-(-3))^2\\y+2=a(x+3)^2[/tex]

and now find the value of the parameter "a" by requesting the parabola to go through another obvious point, let's say the zero given by (-1, 0) at the crossing of the x-axis:

[tex]y+2=a\,(x+3)^2\\0+2=a(-1+3)^2\\2=a\,2^2\\a=\frac{1}{2}[/tex]

So the equation of the parabola becomes:

[tex]y+2=\frac{1}{2} (x+3)^2\\y+2=\frac{1}{2} (x^2+6x+9)\\y+2=\frac{1}{2} x^2+3x+\frac{9}{2} \\y=\frac{1}{2} x^2+3x+\frac{9}{2} -2\\y=\frac{1}{2} x^2+3x+\frac{5}{2}[/tex]

4.

From the location of the focus of the parabola as (4, 3) and the directrix as y=1,  we conclude that we have a parabola with dominant vertical axis of symmetry, displaced from the origin of coordinates, and responding to the following type of formula:

[tex](x-h)^2=4\,p\,(y-k)[/tex]

with focus at: [tex](h,k+p)[/tex]

directrix given by the horizontal line [tex]y=k-p[/tex]

and symmetry axis given by the vertical line [tex]x=h[/tex]

Since we are given that the focus is at (4, 3), we know that [tex]h=4[/tex], and that [tex]k+p=3[/tex]

Now given that the directrix is: y = 1, then:

[tex]y=k-p\\1=k-p[/tex]

Now combining both equations with these unknowns:

[tex]k+p=3\\k=3-p[/tex]

[tex]1=k-p\\k=1+p[/tex]

then :

[tex]1+p=3-p\\2p=3-1\\2p=2\\p=1[/tex]

and we now can solve for k:

[tex]k=1+p=1+1=2[/tex]

Then we have the three parameters needed to write the equation for this parabola:

[tex](x-h)^2=4\,p\,(y-k)\\(x-4)^2=4\,(1)\,(y-2)\\x^2-8x+16=4y-8\\4y=x^2-8x+16+8\\4y=x^2-8x+24\\y=\frac{1}{4} x^2-2x+6[/tex]

therefore: [tex]a=\frac{1}{4} , \,\,\,b=-2,\,\,and\,\,\,c=6[/tex]

Then [tex]a+b+c=\frac{17}{4}[/tex]

5.

The vertex of a parabola can easily found because they give you the roots of the quadratic function, which are located equidistant from the symmetry axis. So we know that is one root is at [tex]x=3+\sqrt{5}[/tex]and the other root is at [tex]x=3-\sqrt{5}[/tex]

then the x position of the vertex must be located at x = 3 (equidistant from and in the middle of both solutions. Then we can use the formula for the x of the vertex to find b:

[tex]x_{vertex}=-\frac{b}{2a}\\3=-\frac{b}{2\,(-2)}\\ b=12[/tex]

Now, all we need is to find c, which we can do by using the rest of the quadratic formula for the solutions [tex]x=3+\sqrt{5}[/tex]  and [tex]x=3-\sqrt{5}[/tex] :

[tex]x=-\frac{b}{2a} +/-\frac{\sqrt{b^2-4\,a\,c} }{2\,a}[/tex]

Therefore the amount [tex]\frac{\sqrt{b^2-4\,a\,c} }{2\,a}[/tex],  should give us [tex]\sqrt{5}[/tex]

which means that:

[tex]\sqrt{5}=\frac{\sqrt{b^2-4\,a\,c} }{2\,a} \\5=\frac{b^2-4ac}{4 a^2} \\5\,(4\,(-2)^2)=(12)^2-4\,(-2)\,c\\80=144+8\,c\\8\,c=80-144\\8\,c=-64\\c=-8[/tex]

Ten the quadratic expression is:

[tex]y=-2x^2+12\,x-8[/tex]

and the y value for the vertex is:

[tex]y=-2(3)^2+12\,(3)-8=-18+36-8=10[/tex]

so the vertex is located at: (3, 10)

Answer:

(f * g)(x) has a final product of 16x² + 8x.

Step-by-step explanation:

When you see (f * g)(x), this means that we are going to be multiply f(x) and g(x) together.

f(x)=8x

g(x)=2x+1

Now, we multiply these terms together.

(8x)(2x + 1)

Use the foil method to multiply.

16x² + 8x

So, the product of these terms is 16x² + 8x.

Answer:

SOLUTION SET={x<-3/2   or   x≥48/5} option A

Step-by-step explanation:

12x+7<-11                           and            5x-8≥40

solving the both inequalities

12x+7-7<-11-7                     and             5x-8+8≥40+8

12x<-18                              and              5x≥48

12x/12<-18/12                     and               5x/5≥48/5

x<-3/2                                and               x≥48/5

SOLUTION SET={x<-3/2   or   x≥48/5}

i hope this will help you :)

"can't exceed 975" means this is the largest value possible for C. So we could have C = 975 or smaller. We write this as [tex]C \le 975[/tex] which is read as "C is less than or equal to 975".

Answer:

5

Step-by-step explanation:

Answer:

The correct answer option is: No solutions exist because the situation describes two lines that have the same slope and different y-intercepts.

Answer: D, 28 bottles.

Step-by-step explanation:

This can be translated to:

26.5 liters of water and 8.25 liters of orange juice are mixed together. All that mixture  is bottled in bottles of  1.25 liters. How many bottles are needed  to fill all the orange juice mixture?

the total mass of mixture that we have is:

26.5 L + 8.25 L = 34.75 L.

if we want to divide it into groups of 1.25 L, we have:

N = 34.75/1.25 = 27.8

So we have 27.8 groups of 1.25L this means that we need 27.8 bottles.

But we can not have a 0.8 of a bottle, so we must round it up to 28 bottles.

Then the correct option is D:

Answer:

1/2

Step-by-step explanation:

The numbers that are 6 or even on the cards are 2, 4, and 6.

3 cards out of a total of 6 cards.

3/6 = 1/2

Answer:

1/2 chance

Step-by-step explanation:

There are 3 numbers that fit the rule, 2, 4, and 6. 3/6 chance of picking one or 1/2, simplified.

Answer: y=x+1

Step-by-step explanation:

y+1=1(x+2)

y+1=x+2

y=x+1

Hope this helps:)

Answer:

The answer is:

A. It is in the quadrants I and III.

Step-by-step explanation:

I am not sure if this is correct, but I tried my best :)

I hope this helped~

Answer:

y-int = C/B

Step-by-step explanation:

Ax + By = C

y-int = C/B

Answer:

I hope this helps.

Step-by-step explanation:

Answer:

  the height of the cylinder is 7 units greater than the radius

Step-by-step explanation:

When you match the forms of the equations ...

  [tex]V=\pi r^2(r+7)\\V=\pi r^2h[/tex]

you see that the factor (r+7) corresponds to the height (h) of the cylinder. That is ...

  the height of the cylinder is 7 units greater than the radius.

Answer:

Step-by-step explanation:

Hello, this is a geometric sequence so we are looking for a multiplicative factor.

[tex]a_0=600\\\\a_1=a_0 \cdot \boxed{\dfrac{1}{2}} = 300 = 600 \cdot \boxed{\dfrac{1}{2}}\\\\a_2=a_1 \cdot \boxed{\dfrac{1}{2}} = 150= 300 \cdot \boxed{\dfrac{1}{2}}\\\\a_3=a_2 \cdot \boxed{\dfrac{1}{2}} = 75 = 150 \cdot \boxed{\dfrac{1}{2}}[/tex]

So, the explicit formula is for n

[tex]\boxed{a_n=a_0\cdot \left(\dfrac{1}{2}\right)^n=600\cdot \left(\dfrac{1}{2}\right)^n}}[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

The explicit rule is aₙ = a₀(1/2)ⁿ = 600(1/2)ⁿ for the given geometric sequence.

The geometric series defined as a series represents the sum of the terms in a finite or infinite geometric sequence. The successive terms in this series share a common ratio.

The nth term of a geometric progression is expressed as

Tₙ = arⁿ⁻¹

Where a is the first term, r is the common ratio.

We have been given that geometric sequence as:

600, 300, 150, 75, ...

To determine the explicit rule for the geometric sequence, we have to find the common ratio.

Here the first term (a₀) is 600

So the common ratio = 300/600 = 150/300 = 75/150 = 1/2

Thus, the explicit formula for n would be:

aₙ = a(1/2)ⁿ = 600(1/2)ⁿ

Therefore, the explicit rule is aₙ = a(1/2)ⁿ = 600(1/2)ⁿ for the given geometric sequence.

Learn more about the geometric series here:

brainly.com/question/21087466

#SPJ2

Answer:

x = 16

Step-by-step explanation:

(whole secant) x (external part) = (tangent)^2

(x+2) * 2 = 6^2

2(x+2) = 36

Divide each side by 2

x+2 = 18

Subtract 2

x+2-2 = 18-2

x = 16

Answer:

x = 16

Step-by-step explanation:

According to tangent-secant Theorem:

(Tangent)² = (External Part of the secant)(Whole Secant)

(6)² = (2)(2+x)

36 = 4+2x

Subtracting 4 from both sides

36-4 = 2x

=> 2x = 32

Dividing both sides by 2

Answer:

The difference of the functions is (f-g)(x) = 3x - 3

Step-by-step explanation:

In the problem, we are asked to find the difference of the two functions, f(x) and g(x). When we see (f-g)(x), this means that we are going to subtract g(x) from f(x).

f(x) = 5x - 2

g(x) = 2x + 1

(f-g)(x) = (5x - 2) - (2x + 1)

Distribute the negative to (2x + 1)

(f-g)(x) = 5x - 2 - 2x - 1

Combine like terms. Make sure your answer is in standard form.

(f-g)(x) = 3x - 3

So, the answer to the equation is (f-g)(x) = 3x - 3

Answer:

A. f(1)=9, f(n+1)=f(n)-4 for n> or equal to 1

Step-by-step explanation:

Given the sequence:

We can easily calculate the difference of terms:

As the difference of terms is same and equal to -4, it is the AP (arithmetic progression)

This sequence can be defined In the form of function as:

All the above matches the first answer choice:

Answer:show the table so I can help

Step-by-step explanation:

Answer:

  (3.6, 0), (0, -2)

Step-by-step explanation:

To find the y-intercept, set x=0:

  -5·0 +9y = -18

  y = -18/9 = -2

To find the x-intercept, set y=0:

  -5x +9·0 = -18

  x = -18/-5 = 3.6

The intercepts are ...

  x-intercept: 3.6

  y-intercept: -2

Answer:

$1.08

Step-by-step explanation:

30 days × (2 hrs/day) × (150 W) × (1 kW / 1000 W) × (0.12 $/kWh) = $1.08

please see the attached picture for full solution..

Hope it helps..

Good luck on your assignment...

Answer:

Se pagará $7200.

Step-by-step explanation:

La ecuación del costo puede descomponerse en dos factores que luego se multiplican:

1) Siendo A el area del del muro, la parte del costo que depende del área se calcula como un tercio (1/3) del doble (2) del área A. Este factor se puede escribir como:

[tex]C_1=(1/3)\cdot 2 \cdot A=(2/3)\cdot A[/tex]

2) Siendo T el número de trabajadores, el siguiente factor es el triple del numero de trabajadores T. Esto es:

[tex]C_2=3T[/tex]

Multiplicando ambos factores, tenemos la ecuacion del costo en función de A y T:

[tex]C=C_1\cdot C_2=(2/3)A\cdot 3T=2 AT[/tex]

Si se planea pintar un muro de 1200m² y se contrataran a 3 trabajadores, el costo será:

[tex]C=2AT=2(1200)(3)=7200[/tex]

Answer:

50 deg

Step-by-step explanation:

In an right triangle, the acute angles are complementary. That means their measures have a sum of 90 deg.

m<C + m<B = 90

7x - 20 + 4x = 90

11x = 110

x = 10

m<ACB= 7x - 20

m<ACB = 7(10) - 20

m<ACB = 70 - 20

m<ACB = 50

Answer: m<ACB = 50 deg

Answer:

Step-by-step explanation:

1l ........8.5 miles

x l .......6 miles

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

x=6*1/8.5

x=0.70 l

2*0.7=1.4 l petrol/day ( to work and come back home)

5*1.4=7 l/week ( 5 days works in a week)

7*1.26=8.82 L /week

8.82>8.5

The petrol costs more

So the answer is NO

Answer:

(Option A) . No, because the histogram of the data is not bell shaped, there is more than one outlier, and line points in the normal quantile plot do not lie reasonably close to a straight line.

Step-by-step explanation:

After plotting the histogram, you will see that the data does not represent the normal distribution because the histogram is not bell shaped and there are two outliers.

Answer:

the last one is correct

Step-by-step explanation:

hello,

-4(-11+4n)-3(-2n+9) = 44 - 16n + 6n - 27 = -10n + 17

hope this helps

Answer:

56%

Step-by-step explanation:

We have a grid with 10 columns and 10 rows making 100 equal sized squares, they tell us that 5 rows are unshaded. Therefore half is unshaded, like so:

5 rows = 50 squares

They also tell us that the sixth row has 6 squares unshaded, which means that in total they would be:

 50 + 6 = 56 squares

Knowing that the total is 100, the percentage would be:

56/100 = 0.56, that is, 56% are unshaded

Answer:

Perimeter is when you add up all of the sides, and the area is when you multiply length times width.

Answer:

18107.32

Step-by-step explanation:

Set up the exponential function in the form:

       [tex]P = P_0(R)^t[/tex]

so P is the new population, [tex]P_0[/tex] is the original population, R is the rate of increase in population, and t is the time in years.

You have to use the information given to find the rate that the population is increasing and then use that rate to find the new population after more time passes.

[tex]13000 = 6000(R)^7\\\\\\frac{13000}{6000} = R^7\\\\\sqrt[7]{\frac{13000}{6000} } = R\\\\\\ R = 1.116786872[/tex]

Now that you found the rate, you can use the function to find the population after another 3 years.

[tex]P = 13000(1.116786872)^3\\P = 18107.32317\\[/tex]

So the population is 18107, rounded to the nearest whole number.

Answer:

data bar

Step-by-step explanation:

Answer:

chart

Step-by-step explanation:

Answer:

a) [g ° h](x)  = 3x² +6

b) [h ° g](x) =3 x²+36x+108

Step-by-step explanation:

Explanation:-

a)

Given g(x) = x+6 and h(x) = 3x²

Given [g ° h](x) = g(h(x))

                          = g(3x²)       (∵ h(x) =3x²)

                         = (3x²)+6      (∵ g(x) =x+6)

∴ [g ° h](x)  = 3x² +6

b)

Given [h ° g](x) = h (g(x))

                          = h(x+6)     (∵ g(x) =x+6)

                         = 3 (x+6)²    (∵ h(x) =3x²)

                         = 3 (x²+2(6)x+36)    (∵ (a + b)² = a²+2ab+b²)

                         = 3 (x²+12x+36)

                        = 3 x²+36x+108)

     ∴ [h ° g](x) =3 x²+36x+108

Answer:

Step-by-step explanation:

hello,

I assume that you mean

[tex]h(x)=\dfrac{12}{x-1}[/tex]

so first of all let's take x real different from 1 , as this is not allowed to divide by 0

[tex](hoh^{-1})(x)=x=h(h^{-1}(x))=\dfrac{12}{h^{-1}(x)-1} \ \ \ so\\h^{-1}(x)-1=\dfrac{12}{x} \\\\h^{-1}(x)=1+\dfrac{12}{x}[/tex]

and this is defined for x real different from 0

hope this helps