29 If the zeros of a quadratic function, F, are -3 and 5, what is the equation of the axis of symmetry
of F? Justify your answer.

16,590 is the large sample needed to estimate the percentage of citizens in a certain town who favor having their water fluoridated if one wishes to be at least 99% confident that the estimate is within 1% of the true percentage.

In the given question,

At Washington University a conjecture by a faculty member in the microbiology department of dental medicine states that a couple of cups of either green or oolong tea each day will provide sufficient fluoride to protect your teeth from decay.

We have to find how large a sample is needed to estimate the percentage of citizens in a certain town who favor having their water fluoridated if one wishes to be at least 99% confident that the estimate is within 1% of the true percentage.

To find the sample size, we use the formula

n=0.25\((\frac{z_{\alpha /2}}{E})^2\)

Firstly we find the value of \(z_{\alpha /2}\)

The confidence interval is 99% or 0.99.

So \(\alpha\)=1−0.99

\(\alpha\)=0.01

So \(\alpha /2\) = 0.01/2 = 0.005

So using the standard value of z

\(z_{0.005}\) = 2.576

E = 0.01

Now putting the value

n=0.25\((\frac{{2.576}}{0.01})^2\)

n=0.25(6.636/0.0001)

n=0.25*66360

n=16,590

Hence, 16,590 is the large sample needed to estimate the percentage of citizens in a certain town who favor having their water fluoridated if one wishes to be at least 99% confident that the estimate is within 1% of the true percentage.

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Answer:

7.52 ft

Step-by-step explanation:

V = S³

425 = S³

=> S = ³√ 425

= 7.52 ft

Rounding to the nearest hundredth, the approximate length of a side of the cube is 7.37 feet.

To find the approximate length of a side of the cube, given the volume is 425 cubic feet, we can use the formula for the volume of a cube:

V = s^3

Where V is the volume and s is the length of a side.

Given V = 425 cubic feet, we need to solve for s:

425 = s^3

To find the length of a side (s), take the cube root of 425:

s ≈ ∛425 ≈ 7.368

Rounding to the nearest hundredth, the approximate length of a side of the cube is 7.37 feet.

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Answer:

i) 3

ii) 5

Step-by-step explanation:

i) -2x -5 = -11

-2x = -11 + 5

-2x = -6

x = -6 ÷ -2

= 3

ii) -2x + 6x - 8 = 12

-2x + 6x = 12 + 8

-2x + 6x = 20

(-2 + 6) x = 20

4x = 20

x = 20 ÷ 4

= 5

Answer:

Option (1)

Step-by-step explanation:

Given linear inequalities in the graph are,

\(y\geq -\frac{1}{3}x+2\)

y < 2x + 3

Here shaded area above the solid line represents the inequality,

\(y\geq -\frac{1}{3}x+2\)

And shaded area on the right side of the dotted line represents the solution set of the inequality,

y < 2x + 3

And the solution set of the system of linear inequalities will be represented by the common area of these inequalities.

Therefore, ordered pairs (2, 2), (3, 1) and (4, 2) will lie in the common shaded area.

Option (1) will be the answer.

Given expression is \((-5x + )².\)

By expanding the given expression, we have:

\((-5x + )²= (-5x + ) (-5x + )= ( )²+ 2 ( ) ( )+ ( )²\)Here, we can observe that:a = -5x

Thus, we have \(( )²+ 2 ( ) ( )+ ( )²= a²+ 2ab+ b²= (-5x)²+ 2 (-5x) ()+ ²= 25x²+ 2 (-5x) (-)= 25x²+ 10x+ ²= 5²x²+ 2×5×x+ x²= (5x + )²= kx²\), where k = 1 and p = (5x + )

Hence, the value of k and p is 1 and (5x + ) respectively. Note: In order to solve the given expression, we have to complete the square.

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The frequency of the dominant allele in the population is 0.6.

Let's begin with the fundamental Hardy-Weinberg equations.

p + q = 1 and p² + 2pq + q² = 1

whereby "q" is the recessive allele and "p" is the dominant allele.

Recessed traits are present in 16% of people, or 0.16 percent. This indicates the percentage of the population that possesses the recessive trait,

q², is 0.16.

It is possible to calculate q using the value for q². What comes next is that q = 0.4.

This information allows for the calculation of "p".

1 − q = p , which results in "p" being 0.6.

This 0.6 is the frequency at which the dominant allele is prevalent in the population.

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The complete question is:

In a population that is in Hardy-Weinberg equilibrium, 16% of the individuals show the recessive trait. What is the frequency of the dominant allele in the population?

True. In a pairwise scatter plot matrix, each scatterplot represents the relationship between two variables.

Since the scatterplot between variable X and variable Y is the same as the scatterplot between variable Y and variable X, the matrix is perfectly symmetric.

The scatterplot at the lower-left corner is indeed identical to the one at the upper-right corner. This symmetry is a result of the fact that the relationship between X and Y is the same as the relationship between Y and X.

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Answer:

\(y = 3x +1\)

Step-by-step explanation:

We can verify it by substituting the \(x\) with the numbers in the \(x\) column to get the same \(y\) in the \(y\) column.

Check:

\(y = 3(-2) +1\\y = -6 +1\\y= 5\)

It matches; therefore, the answer is \(y = 3x +1\). You can try with the other equations given and take the same steps, but it will not match.

Answer:

Step-by-step explanation:

We can split this into 20 triangles, each with an angle sum of 180 degrees.

So 180(20) = 3600 degrees.

The equation of the tangent plane to the given parametric surface at the specified point is `2x - 9y + z = -4 The equation of the tangent plane is:  18(x - 4) + 72(z - 2) = 0.

The equation of the tangent plane to the given parametric surface at the specified point is `2x - 9y + z = -4`. Explanation: Let's begin by locating the point (2, 0, 2) on the given parametric surface. r(u, v) = u^2i + 9usinvj + ucosvk So, putting u = 2, v = 0,r(2, 0) = 2^2i + 9(2sin0)j + 2cos0k= 4i + 0j + 2k = (4, 0, 2)The vector equation of the tangent plane can be defined as: (r - r0). n = 0, where n is the normal vector to the tangent plane and r0 is the point of tangency. We must first find the normal vector n at the point of tangency (2, 0, 2). n = r_u × r_vwhere r_u and r_v are partial derivatives of r with respect to u and v, respectively. r_u = 2ui + 9sinvj + cosvk; r_v = 2u cos vi - 9cos vj - usin vk Therefore, n = (2ui + 9sinvj + cosvk) x (2u cos vi - 9cos vj - usin vk)On evaluating this, we get n = - 2u i - 9 sin vj + 2 cos v k Therefore, the equation of the tangent plane is given by (r - r0).n = 0⇒ (x - 2) (-2) + (y - 0) (-9) + (z - 2) (2) = 0⇒ -2x + 4 - 9y + 2z - 4 = 0⇒ -2x - 9y + z = -4 This is the required equation of the tangent plane to the given parametric surface at the specified point.
To find the equation of the tangent plane to the given parametric surface at the specified point, we first need to find the partial derivatives with respect to u and v.

ru(u, v) = ∂r/∂u = (2u)i + (9 sin v)j + (cos v)k
rv(u, v) = ∂r/∂v = 0i + (9u cos v)j - (u sin v)k

Now, we evaluate the partial derivatives at the point (u=2, v=0):

ru(2, 0) = (4)i + (9)j + (1)k
rv(2, 0) = (0)i + (18)j - (0)k

Next, we find the cross product of ru and rv to obtain the normal vector (N) of the tangent plane:

N = ru × rv = i(9*0 - (-18)*1) - j(4*0 - 0*1) + k(4*18 - 9*0)
N = 18i + 0j + 72k

The point P on the parametric surface at (u=2, v=0) is:

P = r(2, 0) = (2^2)i + (9*2*sin(0))j + (2*cos(0))k = 4i + 0j + 2k

Finally, the equation of the tangent plane is given by:

N • (r - P) = 0

(18)(x - 4) + (0)(y - 0) + (72)(z - 2) = 0

The equation of the tangent plane is:

18(x - 4) + 72(z - 2) = 0.

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Considering that the subjects are chosen without replacement, they are not independent, and the probability cannot be found using the binomial distribution.

The binomial distribution and the hypergeometric distribution are quite similar, as:

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In quadrilateral ABCD abοve, AD || BC and CD =1/2AB. the measure οf angle is B 90°

A quadrilateral is a clοsed shape and a type οf pοlygοn that has fοur sides, fοur vertices and fοur angles. It is fοrmed by jοining fοur nοn-cοllinear pοints. The sum οf interiοr angles οf quadrilaterals is always equal tο 360 degrees.

Since AD is parallel tο BC, we have:

∠ABC + ∠BCD = 180° (interiοr angles οn the same side οf the transversal AD)We alsο knοw that CD = 1/2AB. Let's call the length οf AB "x". Then we have:

CD = 1/2AB

CD = 1/2x

Nοw, let's lοοk at triangle BCD. We knοw that the sum οf the angles in a triangle is 180°, sο we have:

∠BCD + ∠CBD + ∠BDC = 180°

We alsο knοw that ∠BCD = ∠ABC (because they are cοrrespοnding angles), sο we can substitute ∠ABC fοr ∠BCD:

∠ABC + ∠CBD + ∠BDC = 180°

Nοw, let's use the fact that CD = 1/2x tο find the length οf BD:

BD = AB - CD

BD = x - 1/2x

BD = 1/2x

Sο, BD is half the length οf AB. This means that triangle BCD is a 30-60-90 triangle, with ∠CBD = 60° and ∠BDC = 30°.

Substituting these values intο οur equatiοn abοve, we get:

∠ABC + 60° + 30° = 180°

Simplifying, we get:

∠ABC + 90° = 180°

Subtracting 90° frοm bοth sides, we get:

∠ABC = 90°

Therefοre, the measure οf angle B is 90°.

D) 90°.

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The kind of study that was conducted on the subjects who were given suplement and Placebo is termed as Experimental Study .

The active gathering of data from a primary source is observation. Observation of living things makes use of the senses. In science, observation can also entail the perception of information and the recording of that information using tools.

Because of ethical considerations or practical limitations, an observational study infers information from a sample to the population even when the researcher has no control over the independent variable.

An experiment is a technique used to confirm or deny a hypothesis, as well as assess the possibility or effectiveness of something that has never been done before. Experiments show what happens when a certain component is modified, which sheds light on cause-and-effect relationships.

The kind of study that was conducted on the subjects who were given suplement and Placebo is termed as Experimental Study .

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Answer:

Step-by-step explanation:

I don't see a graph from which to choose.  Are the brackets in "[x+1]" supposed to be parentheses, or are they absolute value signs?

The graph of functions

(F(x) = (x+1), and

(F(x) = |x+1| are both attached.

Answer:

ggddhi hhuoiss nndkdoy hsudhh jejdgbnk hehrjji

Answer:

The scale factor used is 0.4

Step-by-step explanation:

Given

\(R = (3,9)\)

\(R' = (1.2, 3.6)\)

Required

Determine the scale factor of RST

The question can be solved using scale factor formula

Scale factor is calculated as thus;

\(Scale\ Factor = \frac{New\ Length}{Old\ Length}\)

In this case; R' is the new length and R is the old length

\(Scale\ Factor = \frac{R'}{R}\)

Substitute the values of R and R'

\(Scale\ Factor = \frac{(1.2,3.6)}{(3,9)}\)

Factorize the denominator

\(Scale\ Factor = \frac{(1.2,3.6)}{2.5(1.2,3.6)}\)

\(Scale\ Factor = \frac{1}{2.5}\)

\(Scale\ Factor = 0.4\)

Hence, the scale factor used is 0.4

The Constant of proportionality represented in equation is 4.75

The Constant of Proportionality defines the value which will remain constant in the whole system of equations. In the given equation, Liv earns $9.50 for selling every two bracelets. The equation represents the sale of Liv on the basis of its price and quantity and the Total amount that she gets. The equation is represented as y = 4.75x

Here, y is the total amount she gets, x is the number of pieces that she sold, and 4.75 is the constant of proportionality. In this case, the constant can be defined as the price of one bracelet that she sells.

This constant can be derived by simply dividing the total amount by the total number of pieces that she sells. It can be represented by :

               => y/x = c , where c is the constant

               => 9.5/2 = c  => c = 4.75

Hence, the Constant of Proportionality is 4.75.

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Answer:

see below

We need to prove that KL ≅ JK .

Given :-

To prove:-

Proof:-

In ∆JKM and ∆LKM ,

Therefore by AAS congruence condition , ∆JKM ≅ ∆LKM .

Therefore,

Hence proved !

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

Explanation:

We're told that "Christopher  says that all Rational (Q) numbers are Whole (W)", which makes Christopher not correct. Some rational numbers are whole numbers. For instance, the number 7 = 7/1 is rational and it's a whole number as well.

However something like 1/2 is rational, but it's not a whole number. A whole number doesn't have any fractional or decimal part to it. It can be thought of the number of something.

Comelia is correct because all whole numbers are rational. If x is some whole number, then x = x/1 is rational as well. Replace x with any whole number you want. Her statement does not work in reverse as shown above.

When drawing a Venn diagram, the circle for "whole numbers" will be entirely inside the circle for "rational numbers", and not the other way around.

Answer:

0.94

Step-by-step explanation:

You just divide 47 by 50 and you get 0.94 bam!

This research suggests a strong correlation between the number of hours spent watching television and the level of aggression shown at school.

This correlation implies a relationship between the two variables, however, further research is needed to determine the exact cause and effect relationship between television viewing and aggression.

It can be concluded that there is a link between the number of hours spent watching television and levels of aggression exhibited in school.

However, it is impossible to determine from this correlation whether watching television directly causes increased levels of aggression in school, or if there is some other factor that is influencing both variables.

Further research is needed to determine the exact cause and effect relationship between television viewing and aggression.

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I believe the answer is 2(15t).

Answer:

15 x t hours x 2

Step-by-step explanation:

Answer:

128,340 words

Step-by-step explanation:

To create a stemplot, we first need to separate the data into "stems" and "leaves." Each stem represents the first digit(s) of each data point, while each leaf represents the last digit(s). For example, if the data point is 12.3, the stem would be 12 and the leaf would be 3.

To make a stemplot, the data should be arranged in increasing order, and then separated into stems and leaves.

However, you can use the data given and arrange it in increasing order and separate it into stems and leaves to make a stemplot. A stemplot is a good way to check if the data follow a normal distribution quite closely, the more the data is spread out and the more symmetric it is, the more likely it is to follow a normal distribution.

Also, it is important to mention that from the given data, it is not possible to conclude if the percent change in this population has standard deviation of 2.5%. This parameter can only be estimated from a sample if it follows a normal distribution which is not clear from the given data.

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Answer:

D.

Step-by-step explanation:

The best and fastest way to do this is to plug this into your calc. Once you do so, you should get 2/5 as your answer.

Answer:

Step-by-step explanation:

The quadratic equation in factored form:

We have:

Substitute them to get:

Converting this into standard form:

Answer:

\(x^{2} = 7\) and \(y^{2} = -8\)

Step-by-step explanation:

When you have a question with the midpoint (0,0), the answer for y and x will be the opposite of the endpoint numbers.

A bin size οf 40 is mοst apprοpriate fοr this set οf data: 86 94 55 67 41 59 67 74 58 49 66 68 54 20

When displaying numerical data, a histοgram divides the data intο "bins" οf identical breadth. Each categοry is represented graphically by a bar whοse height reflects the number οf data elements it cοntains. Intervals, grοups, and cοntainers are οther names fοr bins.

Given,

86 94 55 67 41 59 67 74 58 49 66 68 54 20

We arrange the data as-

20 41 49 54 55 58 59 66 67 67 68 74 86 94

Tοtal number οf data is 14.

Sο it is easy tο divide the data in 2 grοups οr bin.

Twο grοups are 20 tο 60 and 60 tο 100.

The size οf the bin is 40.

Hence the cοrrect answer is B, 40

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The probability that monofilament cables will be discovered during the next ten years and that both discoveries will occur within the next twenty years are, respectively, 0.811 and 0.833.

X = time taken to discover Negative gravity

Y = time taken to discover Monofilament Cables

X follow exponential distribution with mean = 10

Y follow exponential distribution with mean = 6

a)P(Y < y) = 1- e^(-y/mean)

 P(Y < 10)

= 1 - e^(-10/6)

= 0.8111

The probability monofilament cables will be discovered within the next 10 years is 0.8111

b)P(X <20 ,Y < 20)= P(X < 20)P(Y < 20)

= (1 - e^(-20/10)) (1 - e^(-20/6))

= 0.8338

The probability both discoveries will take place within the next 20 years

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