Two out of 15 people surveyed were left handed. Based on the data how many people would you predict to be left handed out of 405 people?
A.15
B.27
C.810
D.54

The ordered pair of the force of the parabola will be (2, -1).

It's the locus of a moving point that keeps the same distance between a stationary point and a specified line. The focus is a non-movable point, while the directrix is a non-movable line.

A parabola has a directrix of y = - 3 and a vertex at (2,1).

Since the directrix is upward, utilize the condition of a parabola that opens up or down.

(x − h)² = 4p(y − k)

The separation from the concentration to the vertex and from the vertex to the directrix is |p|. Deduct the worth of the directrix from the y direction of the vertex to track down p.

p = − 1 + 1 / 2

p = − 1/2

Then the equation is given as,

(x − 2)² = 4(1/2)(y + 1)

(x − 2)² = 2(y + 1)

The ordered pair of the force of the parabola will be (2, -1).

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Answer:

n = 10

Step-by-step explanation:

1n + 1 = 11

Subtract 1 from both sides of the equation:

1n + 1 - 1 = 11 - 1

1n + 0 = 10

n = 10

We need to find the inequality that represents how the $55 I have can be spent in the fair.

The required inequality is \(12+1.75x\leq55\), and the possible number of rides is \(24\).

Admission cost = $12

Cost of each ride = $1.75

Let \(x\) be the number of rides taken.

Total cash = $55

So, the inequality will be \(12+1.75x\leq55\)

Solving the inequality

\(1.75x\leq55-12\\\Rightarrow x\leq\dfrac{55-12}{1.75}\\\Rightarrow x\leq 24.57\)

So, the maximum number of rides taken can be \(24\).

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When changing the sign of the constant a from positive to negative, the domain remains the same. But the range changes.

A function's range is the set of all values it can accept, whereas its domain is the set of all values for which it is defined.

Consider the given function f(x)=a|x|. Let us consider "a" takes positive values that is \(a\geq0\). Then, the given function is defined as follows,

\(f(x)=\begin{cases}a(x)=ax}\; &x\geq0\\{a(-x)=-ax\;&x < 0\end{cases}\)

Then, the domain will be \(\text{domain}=\mathbb{R}\{(-\infty, \infty)\) and the range will be given as \(\text{Range} = \text{only non-negative real numbers} = \mathbb{R}^++\{0\}\).

Now let us consider "a" takes negative values that is a<0. Then, the given function is defined the same and the domain will remain the same. But the range will be given as \(\text{Range} = \text{only negative real numbers} = \mathbb{R}^-+\{0\}\).

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Answers:

(a)  9 cm

(b)  2 cm

======================================

Work shown for part (a)

A = s^2

s = sqrt(A)

s = sqrt(81)

s = 9

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

Work shown for part (b)

P = 4s

s = P/4

s = 8/4

s = 2

The side length of the square with area of 81 cm² is :

The side of the square with the perimeter of 8 m is :

Solution:

We're given the area of a square : 81 cm².

To find one of its sides, we need to take the square root of that.

So we have:

\(\sf{Side\:length{\square}=\sqrt{81}} \\ \\ \sf{Side\:length\square=9}\)

We know that if we take the square root of 81, we will get two solutions: 9 and -9; however we cannot use -9, because having a negative side length is impossible.

__________________________

To find the side length when given the perimeter, we divide it by 4, because the formula for a square's perimeter is P = 4a.

So if we rearrange that for a, we will get : a = P/4.

where a = side length

Solving,

The steps for using a compass and straightedge to construct a square is:

Given:

Let AB the length of one side given.

Steps:

a. Using your straightedge, draw a reference line, if one is not provided.

b. Copy the side of the square onto the reference line, starting at a point labeled A'.

c. Construct a perpendicular at point B' to the line through \(AB\).

d. Place your compass point at B', and copy the side of the square onto the perpendicular B'G. Label the end of the segment copy as point C.

e. With your compass still set at a span representing AB, place the compass point at C and swing an arc to the left.

f. Holding this same span, place the compass point at A' and swing an arc intersecting with the previous arc. Label the point of intersection as D.

g. Connect points A' to D, D to C, and C to B' to form a square.

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Answer: 14, and 9 i think

Answer:

8π/3 or 8.37 or rounded up 8.4

Check the picture below.

\(tan(\theta )=\cfrac{\stackrel{opposite}{282}}{\underset{adjacent}{137}}\implies \theta =tan^{-1}\left( \cfrac{282}{137} \right)\implies \theta \approx 64^o\)

Make sure your calculator is in Degree mode.

We need to find the slope and y-intercept using the table values:

To find the slope take two points and use the slope formula:

P2 (1, 0.75) andP2 (0,0)

So, our slope is 4/3

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

Now, look at the table when x values 0.

The Point (0,0) is the y-intercept because is when x=0.

a) The probability that an individual distance is greater than 210.90 cm is of: 0.047 = 4.7%.

b) The probability that the mean for 20 randomly selected distances is greater than 196.20 cm is of: 0.7673 = 76.73%.

c) The normal distribution can be used as the underlying distribution is normal.

The z-score of a measure X of a variable that has mean symbolized by \(\mu\) and standard deviation symbolized by \(\sigma\) is obtained by the rule presented as follows:

\(Z = \frac{X - \mu}{\sigma}\)

By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

The Central Limit Theorem can be applied when at least one of these conditions is true:

The mean and the standard deviation for this problem are given as follows:

\(\mu = 197.5, \sigma = 8\)

The probability that an individual distance is greater than 210.90 cm is one subtracted by the p-value of Z when X = 210.90, hence:

Z = (210.9 - 197.5)/8

Z = 1.675

Z = 1.675 has a p-value of 0.9530.

1 - 0.9530 = 0.047 = 4.7%.

For 20 distances, the standard error is of:

\(s = \frac{8}{\sqrt{20}} = 1.79\)

Hence the probability that the mean for 20 randomly selected distances is greater than 196.20 cm is one subtracted by the p-value of Z when X = 196.2, considering the standard error calculated as follows:

Z = (196.2 - 197.5)/1.79

Z = -0.73

Z = -0.73 has a p-value of 0.2327.

1 - 0.2327 = 0.7673 = 76.73%.

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The slope of the line passing through the points (3, 4) and (5, 8) is 2.

We have,

To find the slope of a line passing through two points (x₁, y₁) and (x₂, y₂), you can use the formula:

slope = (y₂ - y₁) / (x₂ - x₁)

In this case,

The points are (3, 4) and (5, 8).

Let's substitute these values into the formula:

slope = (8 - 4) / (5 - 3)

= 4 / 2

= 2

Therefore,

The slope of the line passing through the points (3, 4) and (5, 8) is 2.

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Yes, Dr. Lawrence is collecting a representative sample.

The term representative sample is a term that is used to describe a group of individuals who are selected from a population and that are meant to represent the population as a whole. The sample that Dr. Lawrence is collecting is representative because she is selecting 55 women and 45 men from the university. This means that the sample is reflective of the proportion of men and women in the university as a whole.

Dr. Lawrence is the director of counseling services at her university. She is planning to conduct a survey of 100 students at the university to see how aware they are of the counseling services that are offered at the university. She wants the proportion of men and women in her sample to reflect the proportion in the university as a whole (55% women and 45% men).

To increase the probability of a representative sample, Dr. Lawrence could use a different sampling method, such as random sampling or stratified sampling, that ensures that all members of the population have an equal chance of being selected for the sample.

Dr. Lawrence plans to stand in the student union and ask people to participate until she has given the survey to 55 women and 45 men. Thus, Dr. Lawrence is collecting a representative sample.

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Answer:

The answer is 13.57m^2

Step-by-step explanation:

On Edmentum I got it right.

Answer:

Step-by-step explanation:

It is a parrallelogram, the two lines are Parallel to each other meaning they will never cross each other

The given xy- plane is a parallelogram.

A plane figure is called a parallelogram when it have four sides, in which opposite sides are parallel to each other and each side is equal in length to its opposite side.

If \((x_{1},y_{1} })\) and \((x_{2},y_{2})\) are the two points then the distance between these points is given by

\(d=\sqrt{(x_{2}-x_{1}) ^{2} +(y_{2}-y_{1} ) ^{2} }\)

Where, d is the distance between two points.

According to the given question

We have a plane figure PSTO

And the coordinates of points P, S, T, and O are (a, b), (a + c, b), (c, 0) and (0,0) respectively.

Now, the length of the sides by distance formula

PS = \(\sqrt{(a-a-c)^{2}+(b-b)^{2} }\)

PS = \(\sqrt{c^{2}+0 }\)

PS = c

Similarly,

ST =\(\sqrt{(a+c-c)^{2}+(b-0)^{2} }\)

ST = \(\sqrt{a^{2} +b^{2} }\)

TO = \(\sqrt{(c-0)^{2}+(0-0)^{2} }\)

TO = \(\sqrt{c^{2} }\)

TO = c

And, PO = \(\sqrt{(a-0)^{2}+(b-0)^{2} }\)

PO = \(\sqrt{a^{2} +b^{2} }\)

From the above calculation we found that

PS = TO

PO = ST

⇒ Length of the  opposite sides of the plane figure are equals.

And from the given figure we can see that the opposite sides are also parallel to each other.

Therefore, the given xy- plane is a parallelogram.

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Answer:

See below

Step-by-step explanation:

Best way to do this is to convert the equation to vertex form and that will tell you several points you can graph:

\(y=x^2-4x-1\\y+5=x^2-4x-1+5\\y+5=x^2-4x+4\\y+5=(x-2)^2\\y=(x-2)^2-5\)

Here, we can see that the vertex of the parabola is (2,-5) and that the axis of symmetry is x=2. You can also quickly get the y-intercept since plugging in x=0 gets you (0,-1). Finding a few more points should be pretty simple from here on out since your equation is more condensed.

Find the area of the room by multiplying the length by the width:

Area of room = 20 x 12 = 240 square feet.

Find the area of the tile: 2x 2 = 4 square feet.

To find the number of tiles divide the area of the room by the area of a tile:

240/4 = 60

They will need 60 tiles.

Answer:

120

Step-by-step explanation:

20*12=240

240/2=120

Answer:

its B :)

Step-by-step explanation:

trust me bb

Absolute represented by |x| where x is a number means making the numer positive irrespective of its formal state

1) |-2|<|1|

2< 1

The above statement is false

2) |1|<|0|

1<0

The above statement is also false

3) |-1|<|-2|

1<2

The above statement is true

4) |1| > |-2|

1 > 2

The above statement is false too

Answer:

45 miles in 3 days

Step-by-step explanation:

if she drives 3 miles an hour for 5 hours a day that would be 3x5=15

15x3 days=45 miles in 3 days

Answer:

a)

Step-by-step explanation:

Y=k/x........(1)

Put y and x in (1) to get:

3=k/5

K=15

Now put k=15 in (1):

Y=15/x

b)

Y=k/x as x=45

Y=15/45

Y=1/3

Answer:

? = 50°

Step-by-step explanation:

? = 180° - 130° = 50°

Answer:

x = 4

Step-by-step explanation:

Given the equation:

\(\displaystyle{4^x - 4^0 - 255=0}\)

We know that \(\displaystyle{a^0 = 1}\) where a ≠ 0. Therefore,

\(\displaystyle{4^x - 1 - 255=0}\\\\\displaystyle{4^x - 256=0}\)

Add both sides by 256, so we have:

\(\displaystyle{4^x=256}\)

Factor 256 out:

256 = 2 x 128 = 2 x 2 x 2⁶ = 2⁸

Therefore, 256 = 2⁸.

\(\displaystyle{4^x=2^8}\)

Convert to the same base:

\(\displaystyle{\left(2^2\right)^x=2^8}\\\\\displaystyle{2^{2x} = 2^8}\)

When two sides have same base, solve the equation through exponents:

\(\displaystyle{2x=8}\)

Divide both sides by 2, so we have:

\(\displaystyle{x=4}\)

t is the parameter, n is the unit normal vector, and κ is the curvature of the space curve.

To find t, n, and κ for the space curve r(t)=-ti-(a cos h (t/a))j, first calculate the position vector r, which is r(t)=-ti-(a cos h (t/a))j. Then, calculate the derivative of the position vector to find the tangent vector t, which is t=i+(t/a)sin h(t/a)j. Next, calculate the second derivative of the position vector to find the normal vector n, which is n=(-(1/a) sin h(t/a))i+(1/a2)(cos h(t/a))j. Lastly, calculate the curvature κ by dividing the magnitude of the second derivative of the position vector by the square of the magnitude of the first derivative, which is κ=(1/a2)(cos h(t/a))/(1+(t/a) sin h(t/a))2.

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Answer:

7.50

Step-by-step explanation

Multiply 1.50 by 5 and you get 7.50.

Answer: a. 3+13n

b. About 3 newspapers

Step-by-step explanation:

a. T=total thickness of newspapers on a skid in inches

T=3+13n

b. 3'=3 ft

1 ft=12 inches

3 ft=3*12 inches

3 ft=36 inches

36=3+13n

13n=33

n=2.54 ==> About 3 newspapers

Answer:

Actual distance is 4500 cm (45 m).

Step-by-step explanation:

A scale is a representative fraction that can be used to either increase or decrease proportionally the dimension of a given object.

scale = \(\frac{distance on map}{actual distance}\)

It is in the form of a ratio.

From the question, Distance on map = 4.5 cm,

scale = 1 : 1000

        = \(\frac{1}{1000}\)

scale = \(\frac{distance on map}{actual distance}\)

Let the actual distance be represented by d.

So that,

\(\frac{1}{1000}\) = \(\frac{4.5}{d}\)

⇒  d = 4.5 x 1000

       = 4500

    d = 4500

The actual distance is 4500 cm (45 m).