School administrators asked a group of students and teachers which of two
school logo ideas, logo A or logo B, they prefer. This table shows the results.
Logo A
Logo B
Total
Students
67
33
100
Teachers
11
14
25
Total
78
47
125
Are being a student and preferring logo A independent events? Why or why
not?
O A. No, they are not independent, because Astudent) = 0.8 and
A student|logo A) = 0 62.
B. No, they are not independent because P(student) = 0.8 and
A student logo A) 0.86.
C. Yes, they are independent because P(student) = 0.8 and
A student logo A) 0.86
D. Yes, they are independent, because student) = 0.8 and
A student logo A) = 0.62​

Answer:

x=4

Step-by-step explanation:

We can use the leg rule

hyp          leg

------- =  -----------------

leg            part

2+6          x

------- =  -----------------

x            2

Using cross products

8*2 = x^2

16 =x^2

Take the square root of each side

4 =x

Answer:

The answer is below

Step-by-step explanation:

The possible ways of choosing r items from a total of n item is given as C(n,r) = [tex]\frac{n!}{(n-r)!r!}[/tex]

Suppose that 6 female and 6 male applicants have been successfully screened for 5 positions.

Since they are 12 finalists and only 5 positions, the total number of possible outcomes is:

[tex]Total\ number\ of \ outcome (n(s))=C(12,5)=\frac{12!}{(12-5)!5!} =792[/tex]

A)  3 females and 2​ males

The possible ways of choosing 3 females and 2​ males is given as:

[tex]n(e)=C(6,3)*C(6,2) = \frac{6!}{(6-3)!3!}* \frac{6!}{(6-2)!2!}=20*15=300[/tex]

probability of selecting 3 females and 2​ males P(E) = [tex]\frac{n(e)}{n(s)}=\frac{300}{792}=0.379[/tex]

B)  4 females and 1​ males

The possible ways of choosing 4 females and 1 males is given as:

[tex]n(e)=C(6,4)*C(6,1) = \frac{6!}{(6-4)!4!}* \frac{6!}{(6-1)!1!}=15*6=90[/tex]

probability of selecting 4 females and 1 males P(E) = [tex]\frac{n(e)}{n(s)}=\frac{90}{792}=0.1136[/tex]

C)  5 females

The possible ways of choosing 5 females  is given as:

[tex]n(f)=C(6,5) = \frac{6!}{(6-5)!5!}=6[/tex]

probability of selecting 5 females = [tex]\frac{n(f)}{n(s)}=\frac{6}{792}[/tex]

​(D) At least 4​ females

This can be done by choosing 4 females out of 6 females i.e. C(6,4) , 5 females out of 6 females i.e C(6,5) and 1 male out of six male i.e (6,1)

The possible ways of choosing atleast 4 females  is given as:

[tex]n(h)=C(6,5)*C(6,4)*C(6,1)= \frac{6!}{(6-5)!5!}* \frac{6!}{(6-4)!4!}* \frac{6!}{(6-1)!1!}=6*15*6=540[/tex]

probability of selecting atleast 4 females = [tex]\frac{n(h)}{n(s)}=\frac{540}{792}[/tex]

Answer:

D (6,1)

Step-by-step explanation:

[tex]x + 3y = 9[/tex]

[tex]y = x-5[/tex]

When [tex]y = x-5[/tex], it means we don't need to move the variables to the left side and right side. We can use [tex]y = x-5[/tex] to substitute into the first equation [tex]x + 3y = 9[/tex] directly.

[tex]x + 3y = 9[/tex]

[tex]x+3(x-5)=9[/tex]

[tex]x+3x-15=9[/tex]

[tex]4x=9+15[/tex]

[tex]4x=24[/tex]

[tex]x=6[/tex]

When x=6, we can substitute the value of x into any equation whatever you want. You can choose [tex]x + 3y = 9[/tex] or [tex]y = x-5[/tex]. I choose [tex]y = x-5[/tex] is easier to get the value of y.

When x=6, substitute into [tex]y = x-5[/tex]

[tex]y=6-5[/tex]

[tex]y=1[/tex]

Hooray, now you have the value of x and y which are x=6 and y=1.

I hope you will understand the answer.

You can ask any question here if you still cannot get the point. Don't be shy.

Answer:

d (6,1)

Step-by-step explanation:

a pex

How many magazines are there?

12 magazine.

Step by step explanation:

The ratio of stories to magazines is 4 to 3, if there are 28 stories, how many magazines are there?

Story: c

Magazine: r

C / R

C = 4K

R = 3k

4K + 3k = 28

7k = 28

K = 7/28

K = 4

Substituting:

C = 4X4 = 16

R = 3x4 = 12

Ratio of stories to magazines: 4:3

There are 28 stories, so that would mean we would have to divide 28 by 4 to get the common rate.

28/4 = 7

So, now we can substitute it to solve the amount of magazines.

4 x 7 = 28

3 x 7 = 21

Thus, there are 21 magazine and the non-simplified ration of stories to magazines is 28:21.

Answer:

1) The length of the third side is 5.607 units

2) The sum of the numbers from 1 to 100 is 5050

3) For the x-axis, foci: ((√15/28), 0) and (-(√15/28), 0)

For the y-axis, foci: (0, (√15/28)) and (0, -(√15/28))

Step-by-step explanation:

1) When two sides of the triangle are equal to 4 then the triangle is an isosceles triangle

Given that the included angle (the angle between the two sides) is 89°, we have;

The other two base angles are equal to {180 - 89)/2 = 91/2 = 45.5°

Therefore, we have from cosine rule;

a² = b² + c² - 2·b·c·cos(A)

We note that the angle opposite the third side is the included angle 89°, therefore, when we put a as the third side in the above equation, we have;

a² = 4² + 4² - 2×4×4×cos(89°)

a² = 31.44

a = 5.607

The length of the third side is 5.607 units

2) The numbers 1 to 100 form an arithmetic series with the first term, a = 1 and the common difference, d = 1 with the number of terms n = 100

The sum of an arithmetic progression, Sₙ, is given as follows;

[tex]S_n = \dfrac{n}{2}\cdot (2 \cdot a + (n - 1) d)[/tex]

Therefore, by plugging in the values, we have;

Sₙ = 100/2*(2*1 + (100 - 1)*1) = 100/2*(101) = 5050

The sum of the numbers from 1 to 100 is 5050

3) The foci of an ellipse 7·x² + 8·y² = 30 is found as follows;

Dividing both sides of the equation by 30 gives;

7/30·x² + 8/30·y² = 30/30

7/30·x² + 8/30·y² = 30/30

7/30·x² + 4/15·y² = 1

Which is of the form;

x²/a² + y²/b² = 1

For the x-axis we have

c² = a² - b²

c² = 30/7 - 15/4 = 15/28

h = 0, k = 0

Foci: ((√15/28), 0) and (-(√15/28), 0)

For the y-axis, we have;

x²/b² + y²/a² = 1

The foci are then (0, (√15/28)) and (0, -(√15/28)).

Answer:

The answer is option D.

Step-by-step explanation:

f(x) = x² + 2x

g(x) = 2x

To find (ƒ ∘ g)(2) first find (ƒ ∘ g)

To find (ƒ ∘ g) wherever you see x in f(x) replace it with g(x)

That's

(ƒ ∘ g) = (2x)² + 2(2x)

= 4x² + 4x

Substitute 2 into the expression

That's

(ƒ ∘ g)(2) = 4(2)² + 4(2)

= 4(4) + 8

= 16 + 8

= 24

Hope this helps you.

Answer:

4096

Step-by-step explanation:

used a calculator but u always do indicies first due to bidmas

Answer:

4096

Step-by-step explanation:

The little two on top of the 32 means squared or that we need to multiply 32 by itself.

So 32*32 equals 1024

Then we multiply it by 4 to give us 4096.

Answer:

a) deceleration = 0.4 m/s^2

b) distance = 320m

Step-by-step explanation:

a)

using formula a = (v-u)/t,

acceleration a = unknown (deceleration is the negative of acceleration)

final velocity v = 0 m/s (rest)

initial velocity u = 16 m/s

time t= 40s.

a = (0-16)/40

a = -0.4

Hence deceleration = 0.4 m/s^2

b)

Use formula v²-u² = 2as

distance s = unknown

0²+16² = 2(-0.4)(s)

s = 320m

Answer:

y ≤ -1/5x +1

Step-by-step explanation:

The line had an incline of -1/5 and the intersect with the y-axis is 1, so the line is given by

y = -1/5x +1

The indicated area in graph is below the line, so now you have enough to get the right inequality:

y ≤ -1/5x +1

Answer:

My answer is in the attached picture

Step-by-step explanation:

Enlarged by a scale of 2 using P as the centre of enlangment.

Answer:

Step-by-step explanation:

All you should do is to draw lines that conect each node of the triangle with the center of enlargement .

Answer:

2m/s south

Step-by-step explanation:

p = mv

Where p is the momentum, m is the mass, while v is the velocity.

Given that

m = 25kg

v = ?

p = 50kgm/s

Substituting the values into the formula.

50kgm/s = 25×v

50kgm/s = 25v

Divide both sides by 25

v = 50/25

v = 2m/s

From the option list, the answer is

2m/s south

Answer: The answer would be the second one.

Step-by-step explanation:

It is hard to explain but, I made and equation that would go with the problem which would be 2 points for every goal plus the free goals for every goal. (2g+f) and in then end it should all equal 15 so the equation so far would be 2g+f =15. This then leave you with three answers left. then I had plugged in a random number to solve it. g and f exacly should be the same number because for every goal you get a free point so if you get one goal then one extra point, if three goals then three extra points. so if you plug in 5 then 2 times 5 plus 5 is 15. The similarities between g and f is if you subtract them it is always going to be zero. Which makes the second answer correct for this problem.

Answer:

They are congruent

Step-by-step explanation:

Answer:

stratified random sampling

Step-by-step explanation:

Answer:

$147

Step-by-step explanation:

$2.00+$10.00+$30.00+$100.00+$5.00

=$147

El dinero total que tenía será de $ 147.00

Dado lo siguiente

La cantidad tenía inicialmente = $ 2.00

La cantidad dada por mamá = $ 10.00

La cantidad recibida de papá = $ 30.00

La cantidad recibida del tío y la tía = $ 100.00

Si tuviera otros $ 5,00

La cantidad total que tenía será la suma de todo el dinero que tenía y los recaudados como se muestra:

Dinero total que tenía = $ 2,00 + $ 10,00 + $ 30,00 + $ 100,00 + $ 5,00

Dinero total que tenía = $ 147.00

Por lo tanto, el dinero total que tenía será de $ 147.00.

Obtenga más información aquí: https://brainly.com/question/22309443

Answer:

c

Step-by-step explanation:

Using the sine ratio in the right triangle

sin q = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{13}{15}[/tex] , thus

∠ q = [tex]sin^{-1}[/tex] ([tex]\frac{13}{15}[/tex] ) = 60° → c

Answer:  16 one side 32 second side 48 third side

Step-by-step explanation:

16;32;48

3;4;5

Answer:

24, 32, 40

Step-by-step explanation:

We know that the ratio of the sides is 3:4:5, and that total is 96.

First I tested out some numbers by multiplying them by 3, 4, and 5

Eventually I got to 8;

8×3:8×4:8×5 --> 24:32:40 --> 3:4:5

24+32+40=96

Meaning, the sides were 24, 32, and 40

Hope this helps, and good luck!

Answer: 14

Step-by-step explanation:

P(6)- Q(2) = 4

Q(5) - R(2) = 3

R(6) - S(2) = 4

S(5) - P(2) = 3

4 + 3 + 4 + 3 = 14

Brainliest is appericiated!

Answer:

Perimeter = 14

Step-by-step explanation:

to find the perimeter first find the distance between the two points :

d=√((x2-x1)²+(y2-y1)²)

PQ:(2,2)(6,2)

d=√(6-2)^2+(2-2)^2

= √16=4

PQ=4

RS: (6,5),(2,5)

d=√(6-2)^2+(5-5)^2

d=4

RS=4

QR:(6,2),(6,5)

QR=3

SP(2,5),(2,2)

SP=3

perimeter=2length+2width

P=2l+2w

p=2(4)+2(3)

p=8+6=14

Answer:

2

Step-by-step explanation:

Lets say John had 1 apple and Sarah gave him 1 more apple. John would now have 2 apples.

Hope this helps :)

Answer:

B

Step-by-step explanation:

1=a 2=b

Answer:

No solutions.

Step-by-step explanation:

x minus 3y = 4

x - 3y = 4

2x - 6y = 8

negative 2x + 6y = 3

-2x + 6y = 3

2x - 6y = 8

-2x + 6y = 3

(2x - 2x) + (-6y + 6y) = 8 + 3

0 + 0 = 11

0 = 11

Since this statement is false, the system has no solutions.

Hope this helps!

The statement; 'x minus 3 y = 4. Negative 2 x + 6 y = 3 has no solution'

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

Given system of equation;

x minus 3y = 4 means x - 3y = 4

2x - 6y = 8

negative 2x + 6y = 3 means -2x + 6y = 3

Solving;

2x - 6y = 8

-2x + 6y = 3

(2x - 2x) + (-6y + 6y) = 8 + 3

0 + 0 = 11

0 = 11

Since this statement is false, the system has no solutions.

Learn more about equations here;

https://brainly.com/question/10413253

#SPJ2

Answer:  z = 81

Step-by-step explanation:

TW is the midsegment of ΔSUV   ⇒   UV = 2TW

Given: UV = z - 51, TW = z - 61

z - 51 = 2(z - 61)

z - 51 = 2z - 132

   -51 =  z  - 132

    81 = z

The answer is for this question is c

2(3x+2)+2(2x-1)

=10x+2

This is a polynomial

So the answer is c

Answer:

If the amount of dough for a small pizza is S, for a large pizza is L and for a medium pizza is M, we have the equations:

M = (3/2)*S

L = (5/2)*S

L = M + S

First, we can convine the second and third equation and get:

(5/2)*S = M + S

and now we can replace M by the first equation:

(5/2)S = (3/2)*S + S = 5/2 S

so we have a trivial equation, S can be any number, this means that the system of equation is not well constructed.

For example, if S = 1Kg then:

M = (3/2)kg

L = (5/2)kg = (3/2)kg + 1 kg = 5/2kg

Answer:

The equation for a small pizza is, 3/2s + s = 5/2s.

Next, to combine like terms the equation is, 5/2s = 5/2s.

After that, for opposite operations you write, 5/2s - 5/2s = 0.

When you combine the like terms for the last equation, you come up with,

0 = 0.

The small sized pizza does not have a specific size and is no longer part of the equation. Its' size can be anything, and the other sized pizzas will equal their equation towards the small pizza, still representing their same value.

Step-by-step explanation:

cheese + sauce + dough + lots of meat + fire = happiness/pizza

(HopE ThIs HeLPs) ‍

Answer:

Step-by-step explanation:

If you plot those points on a coordinate plane, you'll see that the distance from the origin up the y-axis to the point is greater than is the distance from the origin down the x-axis to the other point. That means 3 things to us: 1. the greater distance is a and the shorter is b; 2. the point (0, 11) is the vertex while the point (4, 0) is the co-vertex; and 3. this is a vertically stretched ellipse. A vertically stretched ellipse has an equation

[tex]\frac{(x-h)^2}{b^2} +\frac{(y-k)^2}{a^2} =1[/tex] where h and k are the coordinates of the center, a is the greater distance (between the center and the vertex), and b is the smaller distance (between the center and the co-vertex).  Here's what we have then thus far:

h = 0

k = 0

a = 11

b = 4

Filling in our equation then looks like this:

[tex]\frac{(x-0)^2}{4^2} +\frac{(y-0)^2}{11^2} =1[/tex] and simplifying:

[tex]\frac{x^2}{16} +\frac{y^2}{121} =1[/tex]. It appears that the last answer is the one you want, although when I teach this to my precalc students, I do not encourage them to move the x and y terms around as that answer appears to have done. But addition is also commutative so I'm sure it's acceptable (I just think it looks strange that way).

The equation of ellipse is [tex]\dfrac{y^2}{121}+\dfrac{x^2}{16}=1[/tex] option D is correct.

Important information:

The standard form of an ellipse is:

[tex]\dfrac{x^2}{b^2}+\dfrac{y^2}{a^2}=1[/tex]

Where, [tex](0,a)[/tex] is vertex and [tex](0,b)[/tex] is vertex.

Substitute [tex]a=11,b=4[/tex] in the above equation.

[tex]\dfrac{x^2}{(4)^2}+\dfrac{y^2}{(11)^2}=1[/tex]

[tex]\dfrac{x^2}{16}+\dfrac{y^2}{121}=1[/tex]

[tex]\dfrac{y^2}{121}+\dfrac{x^2}{16}=1[/tex]

Therefore, the correct option is D.

Find out more about 'Ellipse' here:

https://brainly.com/question/1548816

Answer:

Two real world situations are shown below.

Step-by-step explanation:

Initial population of a certain bacteria is 1 thousand and the population doubles in each hour. So, population of bacteria (in thousands) after x hours is

[tex]f(x)=1(2)^x[/tex]

[tex]f(x)=(2)^x[/tex]

A person invests 1 lakh rupees in shares and the amount is twice at the end of each year. So, total amount (in lakhs) after x years is

[tex]f(x)=1(2)^x[/tex]

[tex]f(x)=(2)^x[/tex]

Answer:

y = 3x/2 − 5/2

Step-by-step explanation:

Answer:  125 miles

if you do the math you will get the same answer.

Answer:

800 miles

Step-by-step explanation:

Explanation:

AC = XZ shows that the horizontal pieces are congruent. This is the "S" of "ASA" as it stands for the pair of congruent sides. We are also given angle A = angle X. This is one of the "A"s in "ASA" as it stands for pair of congruent angles.

What we're missing is the other pair of angles. We must pick C and Z because they help sandwich the two sides mentioned above. ASA has the two angles surrounding the sides; or the sides are between the angles. We can't pick B and Y, unless we were doing AAS which is a similar related idea. The order matters when it comes to ASA and AAS. However, AAS is the same as SAA.

Answer:

AC=XZ

so the correct answer is D

Answer:

a and b are examples of a vertical pair.

Step-by-step explanation:

Vertical pairs are equal to each other with the same degrees.