Janet and Patrick surveyed a total of 219 people. Out of the 137 girls who were surveyed, 28 said summer was their favorite season and 12 said that winter was their favorite.

The results showed 22 boys said that spring was their favorite season and 8 boys said winter was their favorite.

A total of 45 people said that summer was their favorite season and a total of 74 people said that fall was their favorite season.

In this activity, you will construct two-way frequency tables to help Janet and Patrick analyze the data they gathered from their survey.

Part A
Create a two-way frequency table to represent the results of the survey by entering the appropriate data in each box.

Answer and Step-by-step explanation:

The equation should look like this:

-9(x - 86) = x - 48

Distribute the -9.

-9x + 774 = x - 48

Add 48 and 9x to both sides of the equation.

822 = 10x

Divide both sides of the equation by 8.

82.2 = x

[tex]\frac{411}{5}[/tex] = x  -- Fraction Form

#teamtrees #PAW (Plant And Water)

9514 1404 393

Answer:

  x = 10·cos(θ) -4·cot(θ)

Step-by-step explanation:

Apparently, we are to assume that the horizontal lines are parallel to each other.

The relevant trig relations are ...

  Sin = Opposite/Hypotenuse

  Cos = Adjacent/Hypotenuse

If the junction point in the middle of AB is labeled X, then we have ...

  sin(θ) = 4/BX   ⇒   BX = 4/sin(θ)

  cos(θ) = x/XA   ⇒   XA = x/cos(θ)

Then ...

  BX +XA = AB = 10

Substituting for BX and XA using the above relations, we get

  4/sin(θ) +x/cos(θ) = 10

Solving for x gives ...

  x = (10 -4/sin(θ))·cos(θ)

  x = 10·cos(θ) -4·cot(θ) . . . . . simplify

_____

We used the identity ...

   cot(θ) = cos(θ)/sin(θ)

Answer:

Her grant in four years time will be of $13108.

Step-by-step explanation:

Exponential equation:

An exponential equation has the following format:

[tex]A(t) = A(0)(1+r)^t[/tex]

In which A(0) is the initial value and r is the growth rate, as a decimal.

A student get a grant of $10000 a year assuming her grant is increased by 7% each year

This means that [tex]A(0) = 10000, r = 0.07[/tex]

So

[tex]A(t) = A(0)(1+r)^t[/tex]

[tex]A(t) = 10000(1+0.07)^t[/tex]

[tex]A(t) = 10000(1.07)^t[/tex]

What will her grant be in four years time?

This is A(4). So

[tex]A(t) = 10000(1.07)^t[/tex]

[tex]A(4) = 10000(1.07)^4 = 13108[/tex]

Her grant in four years time will be of $13108.

Answer:

n = 106

Step-by-step explanation:

Given  

p = 0.5 and 1-p = q = 0.5

Margin of error = 0.08  

Confidence level = 90%  

Z score for 90% confidence level =     1.65

As we know -  

Margin of error = z * Sqrt (pq/n)

Substituting the given value, we get –  

0.08 = 1.65 * Sqrt (0.5*0.5/n)

Squaring both the sides and solving, we get  

n = 1.65^2*0.5^2/0.08^2

n = 106.34 = 106

Step-by-step explanation:

2x - 10y > -20

=> x - 5y > -10

or x - 5y +10 > 0

Answer:

20

Step-by-step explanation:

mean is average

add all numbers get 160

divide by number of numbers (8) and get 20

Answer:

when you find the mean of a data set, you add all the numbers up then you divide the sum by the numbers in total. the sum is 160, you then divide by total of number which is 8 . your answer is 20. not sure if that made sense lol

Answer:

Kindly check explanation

Step-by-step explanation:

Given the formula :

Pn = 25.8(1.0219)^h to predict the population of Ghana ;

The equation given is in the form of an exponential function:

The general form of an exponential distribution :

y = ab^x

a = Initial value ; b = constant multiplier or growth or Decay factor

Comparing :

The number in parenthesis = 1.0219 = b

b = Decay or growth factor :

Since b > 1 ; then We have a growth factor;

b = 1 + rate

1.0219 = 1 + rate

Rate = 1.0219 - 1

Rate = 0.0219

Hence, the population is growing at a rate of about (0.0219)*100% = 2.19%

Answer:

20

Step-by-step explanation:

100/5=20

Answer:

the answer would be B: 2.125lb.

Answer: B; 2.125lb

Step-by-step explanation: 34 ounces to pounds is 2.13lb (rounded, the exact number is 2.125lb

Answer:

62 miles per hour

Step-by-step explanation:

620mile/10hrs

62miles/hr

62 miles per hour

Answer:

angle B=74°

Step-by-step explanation:

the shapes are similar

Answer:

One equation can be y = 3/4X +2

Step-by-step explanation:

Any equation that has a slope of 3/4 will be parallel to the line 4Y = 3X + 5 because the slope is the same. This can also be shown visually using any graphing calculator.

There is a formula for the total interior angles of a polygon:

180(sides−2)=total interior angles

One of the angles is 100 and all the others are 110.

We can rewrite the equation.

Assume there is x number of sides.

There are x−1 number of angles, 110 degrees

180(x−2)=100+110(x−1)

180x−360=100+110x−110

70x−360=100−110

70x−360=−10

70x=3507x=35

x=5

There are 5 sides to the polygon.

We can check our answer:

180(sides−2)=total interior angles

Therefore it is true:

The polygon has 5 sides

I HOPE IT HELPS

HAVE A GREAT DAY

#Liliflim

Answer:

4! = 24

Step-by-step explanation:

4! = 4 * 3 * 2 * 1

4! = 24

Answer:

Hobbies give teenagers a chance to meet new people, discover new passions, develop skills outside of school, and do something all kids (yes, teens are part kid) should do: have fun. ... That's where hobbies come in. Hobbies are a great way for teens to form an identity outside their family.

Step-by-step explanation:

Answer:

ok ok ok ok ok ok ok ok

Step-by-step explanation:

i don't know

Answer:

a) 12989 Ib

b) 2756.3 Ib

Step-by-step explanation:

Density of milk = 64.6 Ib/ft^3

Diameter of tank = 8 ft

radius = 4 ft

a) Calculate force exerted by milk on one end of tank when Tank is full

pressure on strip ≈ 64.6 ( 4 - yi ) i.e. surface of milk = 4

Total force = 129.2 *  [tex]\int\limits^4_4 {4-y} \sqrt{16-y^2} \, dx[/tex]

∴Force exerted  = 129.2 * Area of semicircle( radius =4 ) * radius

                        = 129.2* 8π * 4 ≈  12989 Ib

b) Force exerted when Tank is half full

pressure on strip ≈ 64.6 ( 0 - yi )  i.e. surface of milk = 0

Total force = 129.2 * [tex]\int\limits^0_4 {0-y} \sqrt{16-y^2} \, dx[/tex]

∴ Force exerted ≈ 2756.3 Ib

Let's solve the equation:

9x + 27 =  9 ( x + 2 ) + 9 ← Distribute 9 to the x and 2

9x + 27 = 9x + 18 + 9 ← Combine like terms

9x + 27 = 9x + 27 ← Subtract 27 from both sides

9x = 9x

0 = 0  

{Infinitely many solutions would be correct because no matter what x is, it will always equal each other the both sides of the equation because it is 9 times x on both sides.}

hope this helps..........

Answer:

x=1

Step-by-step explanation:

9x+27=9(x+2)+9

9x+27=9x+18+9

9x+27=9x+27

9x=9x

x=1

9514 1404 393

Answer:

Step-by-step explanation:

A Hamiltonian circuit visits each node once and returns to its start. There is no simple way to determine if such a circuit exists.

__

For graph 2, if there were a circuit, paths ACB, ADB, and AEB would all have to be on it. Inclusion of all of those requires visiting nodes A and B more than once, so the circuit cannot exist.

__

For graph 3, the circuit must include paths BAD and DFE. That only leaves node C, which can be reached from both nodes B and E, so path ECB completes the circuit.

Answer:

final answer:

y-1= 3x_6

To solve our given problem, we must find the equation of the tangent line of the function f(x)=(x−1)3, at x=2.

.

.

Answer:

$460

Step-by-step explanation:

Thus, a product that normally costs $400 with a 15 percent discount will cost you $340.00, and you saved $60.00. You can also calculate how much you save by simply moving the period in 15.00 percent two spaces to the left, and then multiply the result by $400 as follows: $400 x .15 = $60.00 savings.

Answer:

Tn = -13n +37

ordered list is 24, 11 , -2 , -15, -28 ,-41

Answer:

(-2) is the index of y make value 1/y².

Step-by-step explanation:

We need to find what index of y makes value 1/y².

Here, the numerator is 1 and the denominator is y².

We know that,

[tex]\dfrac{1}{a^x}=a^{-x}[/tex]

So, the given expression is :

[tex]\dfrac{1}{y^2}=y^{-2}[/tex]

Hence, (-2) is the index of y make value 1/y².

Answer:

A

Step-by-step explanation:

slant height of the exagon = side/2 * √3 = 2.5√3 cm

area of the hexagon = (side * slant height)/2 * 6 = (5 * 2.5√3)/2 * 6 = 64,951905 cm^2

Volume of the prism = area of the hexagon * height = 974,278579 cm^3

Volume of the cylinder = radius^2 *  pi * height = 36 * pi * 15 = 1.696,460033 cm^3

volume of the kaleidoscope = 722,181454 cm^3

Answer:

C.   G(x) = (x+3)^3

Step-by-step explanation:

Inside the parenthesis, adding or subtracting numbers moves the shape along the x-axis. BUT signs have opposite effects. Adding a number moves the shape towards the negative side. Subtracting a number moves it to the positive side.

Answer:

x = 10

Step-by-step explanation:

m∠KNL = 90

10x - 10 = 90

10x = 100

x = 10

Answer:

a) Brain sweep out 4 radians

b) Brian is -0.3922 km to the right of the center of the ski trail

c) Brian is -0.4541 km above of the center of the ski trail

Step-by-step explanation:

Given the data in the question;

circular ski trail radius = 0.6 km

Derek starts at the 3-o'clock position and travels 2.4 km in the counter-clockwise direction.

a) How many radians does Brian sweep out?

arc length = 2.4 km

from the diagram;

arc length = rθ

θ = arc length / r

θ = 2.4 / 0.6

θ = 4 radians

Therefore, Brain sweep out 4 radians

b) When Brian stops skiing, how many km is Brian to the right of the center of the ski trail?

from the diagram;

x = rcosθ

we substitute

x = 0.6 × cos(4)

x = 0.6 × -0.65364

x = -0.3922 km

Therefore Brian is -0.3922 km to the right of the center of the ski trail

c) When Brian stops skiing, how many km is Brian above of the center of the ski trail?

from the diagram;

m = rsinθ

m = 0.6 × -0.7568

m = -0.4541 km

Therefore, Brian is -0.4541 km above of the center of the ski trail

Step-by-step explanation:

Hey there!

According to the question;

Side (a) = 4cm

To find : area

Now;

[tex]area = \frac{ \sqrt{3} }{4} {(a)}^{2} [/tex]

[tex]or \: area = \frac{ \sqrt{3} }{4} ( {4)}^{2} [/tex]

[tex]area \: = 4 \sqrt{3} [/tex]

Therefore, area of triangle is 6.92 cm² or 4√(3) cm².

Hope it helps!