Use the graph of ƒ to find ƒ(2).
0.5
–8
–0.5
Does not exist

Answer:

a) The 90% confidence interval for the proportion of teenagers who have 5 or more servings of soft drinks a week is (0.2982, 0.481).

b) 30% = 0.3 is part of the confidence interval, which means that there is no evidence that a higher proportion of teenagers have 5 or more servings of soft drinks a week than the general population.

Step-by-step explanation:

Question a:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

A survey of 77 teenagers finds that 30 have 5 or more servings of soft drinks a week.

This means that [tex]n = 77, \pi = \frac{30}{77} = 0.3896[/tex]

90% confidence level

So [tex]\alpha = 0.1[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].  

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3896 - 1.645\sqrt{\frac{0.3896*0.6104}{77}} = 0.2982[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3896 + 1.645\sqrt{\frac{0.3896*0.6104}{77}} = 0.481[/tex]

The 90% confidence interval for the proportion of teenagers who have 5 or more servings of soft drinks a week is (0.2982, 0.481).

Question b:

30% = 0.3 is part of the confidence interval, which means that there is no evidence that a higher proportion of teenagers have 5 or more servings of soft drinks a week than the general population.

Answer: [tex]Rs.3,69,000[/tex]

Step-by-step explanation:

Given

average monthly salary of a worker is [tex]Rs.8200[/tex]

If there are 45 workers in a factory

Total expenditure is calculated by taking the product of Average monthly salary and no of workers in the factory

[tex]\Rightarrow 8200\times 45\\\Rightarrow Rs.3,69,000[/tex]

Answer:

8 x 9

Have a nice day!

Answer:

It cannot be 0

Step-by-step explanation:

it can also be positive number :2/4

it can be odd number too:3/9

it is bigger than numerator bcoz we have to divide it for numerator

So, 0 number cannot be put as denominator in fraction is true statement

Answer:

I'm sorry but I don't know this one

Answer:

217 is the perfect swuare i think

Answer:

D

Step-by-step explanation:

The coordinate of the new rectangle after the reflection across will be Q'(-3, -2), R'(-1, -4), S'(2, -1), and T'(0, 1). Then the correct option is D.

A spatial transformation is each mapping of feature space to itself and it maintains some spatial correlation between figures.

The reflection does not change the shape and size of the geometry. But flipped the image.

Rectangle QRST with vertices Q(-3, 2), R(-1, 4), S(2, 1), and T(0, -1).

The coordinate of the new rectangle after the reflection across is given as,

Q' = (-3, -2)

R' = (-1, -4)

S' = (2, -1)

T' = (0, 1)

The coordinate of the new rectangle after the reflection across will be Q'(-3, -2), R'(-1, -4), S'(2, -1), and T'(0, 1). Then the correct option is D.

More about the transformation of a point link is given below.

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Answer:

  (b)  x = -2

Step-by-step explanation:

The graph shows the lines intersect at (x, y) = (-2, 3).

The x-coordinate of the solution is x = -2.

Answer:

21

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan theta = opp/ adj

tan 60 = x / 7 sqrt(3)

7 sqrt(3)  tan 60 = x

7 sqrt(3) sqrt(3) = x

7*3 = x

21 = x

Answer:

The slope is undefined.

Step-by-step explanation:

The line must pass through the points (10,-3) and (10,-8), meaning that it must be vertical. The slope of a line is undefined if the line is vertical.

15,068 mi/hr

Step-by-step explanation:

[tex]22100\:\frac{\text{ft}}{\text{s}}×\frac{1\:\text{mi}}{5280\:\text{ft}}×\frac{60\:\text{s}}{1\:\text{min}}×\frac{60\:\text{min}}{1\:\text{hr}}[/tex]

[tex]=15,068\:\text{mi/hr}[/tex]

The speed of 22100 feet per second will be 15068.18 miles per hour.

Multiplication or division by a numerical factor, selection of the correct number of significant figures, and unit conversion are all steps in a multi-step procedure.

Unit conversion is the expression of the same property in a different unit of measurement. Time, for example, can be expressed in minutes rather than hours, and distance can be converted from miles to kilometres, feet, or any other length measurement.

Given that the speed of the satellite is 22100 feet per second. The speed in miles per hour will be calculated as,

22100 ft /s = ( 22100 x 3600 ) / 5280

22100 ft/s = 79560000 / 5280

22100 ft/s = 15068.18 miles per hour

To know more about unit conversion follow

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Explanation:

Focus entirely on the triangle on the right side. The other parts of the drawing are not necessary. In my opinion, they are distracting filler.

Refer to the diagram below.

We have an unknown adjacent side, let's call it x, that's along the horizontal part of the triangle.

The hypotenuse however is known and it is 19 ft

We use the cosine ratio to tie the two sides together

cos(angle) = adjacent/hypotenuse

cos(75) = x/19

19*cos(75) = x

x = 19*cos(75)

x = 4.9175618569479 which is approximate

x = 4.9

The base of the ladder is roughly 4.9 feet away from the base of the house.

Side note: make sure your calculator is in degree mode.

Answer:

E

Step-by-step explanation:

Since all the numbers are hundredths decimals, let multiply by the power of 2 of the base 10. So let multiply the equation by

[tex]10 {}^{2} [/tex]

So our new equation is

[tex]3 3{x}^{2} + 71x - 14 = 0[/tex]

Solve by AC method

[tex]ac = - 462[/tex]

[tex]b = 71[/tex]

We must think of two numbers that

Multiply to -462 and Add to 71. Set up equation

The numbers are 77 and -6.

So our new equation is

[tex] {33x}^{2} + 77x - 6x - 14 = 0[/tex]

Solve by factoring by grouping

[tex](33 {x}^{2} + 77x) - (6x - 14)[/tex]

Factor out 11 for the first equation

[tex]11x(3x + 7) - 2(3x + 7)[/tex]

So our factors are

[tex](11x - 2)(3x + 7)[/tex]

Set each equal to zero

[tex]11x - 2 = 0[/tex]

[tex]11x = 2[/tex]

[tex]x = \frac{2}{11} [/tex]

[tex]3x + 7 = [/tex]

[tex]3x = - 7[/tex]

[tex]x = \frac{ - 7}{3} [/tex]

By taking the addition of the values in the table and overestimating a little bit, the correct option is B: $60.00

Here we have the following table of average costs:

Assuming you eat these 3 per day, the total cost in food per day is the sum of all the values in the table.

It gives:

Total cost: $12.98 + $18.95 + $26.58 = $48.51

Notice that these are average costs, so you should budget a little bit over that just in case, then the correct option is $60, which is the first option over the average total cost.

Learn more about additions:

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Answer:

45

Step-by-step explanation:

Answer:

what are the answers

Step-by-step explanation:

9514 1404 393

Answer:

Step-by-step explanation:

A suitable statistics calculator can tell you the coefficients of the linear regression equation. In the attached, we put the given x- and y-values into a table and asked for the best fit equation. Rounded to tenths, the equation is ...

  y = 32.1x +779.9

The year 2010 is 12 years after 1998, so we can find the desired projection using x=12.

  y = 32.1×12 +779.9 = 385.2 +779.9 = 1165.1

The number of cases is projected to be 1165 in 2010.

_____

We wonder if using the button "Open Statistics Calculator" will let you solve this question yourself.

Answer:

Step-by-step explanation:

cotθ = cosθ/sinθ = 2/3

sinθ = 3/√(2²+3²) = 3/√13

cscθ = 1/sinθ = √13/3

Answer:

Step-by-step explanation:

Use the change-of-base rule.

Answer:

(y, -x)

Step-by-step explanation:

Rotation of 90°

(Clockwise)

(x, y)  ---> (y, -x)

Rotation of 90°

(CounterClockwise)

(x, y) --> (-y, x)

Rotation of 180°

(Both Clockwise and Counterclockwise)

(x, y) ---> (-x, -y)

Rotation of 270°

(Clockwise)

(x, y) ---> (-y, x)

Rotation of 270°

(CounterClockwise)

(x, y) ---> (y, -x)

Answer:

{(121, 63), (180, 71), (140, 67), (108, 65), (165, 72)}

Step-by-step explanation:

We have:

Weight as a function of height.

Give the points for these students that represent height as a function of weight:

Inverse of the input, that is, in the (x,y) format, (x,y) -> (y,x), the coordinates are exchanged, and thus, the correct option is:

{(121, 63), (180, 71), (140, 67), (108, 65), (165, 72)}

Answer:

[tex]3 \sqrt{2} [/tex]

Step-by-step explanation:

[tex] \sqrt{(9 \times 2)} [/tex]

Take the square root of 9 out of the square root and leave the 2 in.

Answer:

3[tex]\sqrt{2}[/tex]

Step-by-step explanation:

Using the rules of radicals

[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex] , then

[tex]\sqrt{3}[/tex] × [tex]\sqrt{6}[/tex]

= [tex]\sqrt{3(6)}[/tex]

= [tex]\sqrt{18}[/tex]

= [tex]\sqrt{9(2)}[/tex]

= [tex]\sqrt{9}[/tex] × [tex]\sqrt{2}[/tex]

= 3[tex]\sqrt{2}[/tex]

If y (0) = -1/3, then

-1/3 = 1 / (1 + C e ⁻⁰)

Solve for C :

-1/3 = 1 / (1 + C )

-3 = 1 + C

C = -4

So the particular solution to the DE that satisfies the given initial condition is

[tex]\boxed{y=\dfrac1{1-4e^{-x}}}[/tex]

Answer:

The point is a solution

Step-by-step explanation:

y = x^2

Substitute the point into the equation and see if it is true

0 = 0^2

0=0

True

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Answer:

  382 cm²

Step-by-step explanation:

The side facing is a trapezoid with bases 8 and 14 cm, and height 7 cm. Its area is ...

  A = 1/2(b1 +b2)h

  A = (1/2)(8 +14)(7) = 77 . . . . cm²

The perimeter of the face is ...

  7 cm + 8 cm + 9 cm + 14 cm = 38 cm

The total surface area is the sum of the lateral area and the base area.

  SA = LA + BA

  SA = (38 cm)(6 cm) + 2×(77 cm²) = 228 cm² + 154 cm²

  SA = 382 cm²

The surface area of the composite figure is 382 square centimeters.

_____

Additional comment

The lateral area is the width of a rectangular face (6 cm) times the total of all of the lengths of those faces. That total is the perimeter of the trapezoidal base (38 cm).

There are two trapezoidal bases that contribute area. The first calculation figured the area of one of them.

Answer:

180000 people

1 : 2

$40

80 stores

Step-by-step explanation:

1.)

Population in 2020 are equal : Let population =

City A increased by 20% From 120,000 in 2015

(1 + 0.2) * 120,000 = (1.2 * 120,000) = 144,000

Hence, city A = 144,000.

Since, city A and B have equal population ; city B also has a population of 144000 in 2020.

Let population in 2015 = x

(1 - 0.2) * x = 144000

0.8x = 144000

x = 144000/0.8

x = 180,000

2.)

Let proportion of 20% butter = x and proportion of 50% butter = 1 - x

0.2x + 0.5(1 - x) = 0.4

0.2x + 0.5 - 0.5x = 0.4

-0.3x + 0.5 = 0.4

-0.3x = 0.4 - 0.5

-0.3x = - 0.1

x = 0.1/0.3

x = 0.3333

(1-x) = 1 - 0.33333 = 0.6666%

0.3333% of 20% butter

0.6666% of 50% butter

Hence ;

0.3333 : 0.6666

1 : 2

3.)

Let original price of book = x

Discount on sale = 30%

Sale price = $28

Sale price = original price * (1 - discount)

$28 = (1 - 0.3) * x

$28 = 0.7x

x = $28/0.7

x = $40

4.)

Let total number of stores = x

Store surveys needed = 32

40% of total stores = 32 stores

0.4x = 32

x = 32 / 0.4

x = 80

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Answer:

  (b)  0 = -78

Step-by-step explanation:

Subtracting 6 times the first equation from the second will give ...

  (4x +15y) -6(2/3x +5/2y) = (12) -6(15)

  0 = -78

Answer:

the answer is b

Step-by-step explanation:

The exact amount of oil that leaks out for 0 ≤ t ≤ 10 is given by the integral,

[tex]\displaystyle\int_0^{10}r(t)\,\mathrm dt[/tex]

Then the upper and lower estimates of this integral correspond to the upper and lower Riemann/Darboux sums. Since r(t) is said to be decreasing, this means that the upper estimate corresponds to the left-endpoint Riemann sum, while the lower estimate would correspond to the right-endpoint sum.

So you have

• upper estimate:

(8.8 L/h) (2 h - 0 h) + (7.6 L/h) (4 h - 2h) + (6.8 L/h) (6 h - 4h) + (6.2 L/h) (8 h - 6h) + (5.7 L/h) (10 h - 8 h)

= (2 h) (8.8 + 7.6 + 6.8 + 6.2 + 5.7) L/h)

= 70.2 L

• lower estimate:

(7.6 L/h) (2 h - 0 h) + (6.8 L/h) (4 h - 2h) + (6.2 L/h) (6 h - 4h) + (5.7 L/h) (8 h - 6h) + (5.3 L/h) (10 h - 8 h)

= (2 h) (7.6 + 6.8 + 6.2 + 5.7 + 5.3) L/h)

= 63.2 L

Answer:

[tex](12\frac{1}{3} *2)+(10\frac{3}{4} *2)\\\\=(\frac{12(3)+1}{3} *2)+(\frac{10(4)+3}{4} *2)\\\\=\frac{37*2}{3} +\frac{43*2}{4} \\\\=\frac{74}{3} +\frac{86}{4} \\\\=\frac{74(4)+86(3)}{3*4} \\\\=\frac{296+258}{12} \\\\=\frac{554}{12}[/tex]