Quadrilateral BCDE is a kite. What is BF?
B
20
С
12
E
F
D

Answer:

  4

Step-by-step explanation:

Let's try this a different way than perhaps the usual way. Let r represent the reciprocal of the number.

  r(1/r -1) -1/2r = 5/8

  1 -r -1/2r = 5/8 . . . . . . eliminate parentheses

  -3/2r = -3/8 . . . . . . . . collect terms, subtract 1

  (-3/2)/(-3/8) = 1/r = 4 . . . . . divide by (-3/8)r because we actually want 1/r

The number is 4.

_____

Check

The reciprocal of the number is 1/4.

1 less than the original number is 4 -1 = 3. The product of these is 3/4.

__

Half the reciprocal of the original number is (1/2)(1/4) = 1/8.

Then the difference between these is ...

  3/4 -1/8 = (6 -1)/8 = 5/8 . . . . as required.

Answer:

a) The 95% confidence interval for the mean amount of time Americans age 15 or older spend eating and drinking each day is (1.49, 1.57).

d) The nutritionist is 95% confident that the mean amount of time spent eating or drinking per day for any individual is between 1.49 and 1.57 hours.

(c and b can not be concluded from the confidence interval)

Step-by-step explanation:

We have to calculate a 95% confidence interval for the mean.

The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.

The sample mean is M=1.53.

The sample size is N=1082.

When σ is not known, s divided by the square root of N is used as an estimate of σM:

[tex]s_M=\dfrac{s}{\sqrt{N}}=\dfrac{0.71}{\sqrt{1082}}=\dfrac{0.71}{32.89}=0.022[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=1082-1=1081[/tex]

The t-value for a 95% confidence interval and 1081 degrees of freedom is t=1.962.

The margin of error (MOE) can be calculated as:

[tex]MOE=t\cdot s_M=1.962 \cdot 0.022=0.042[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=M-t \cdot s_M = 1.53-0.042=1.49\\\\UL=M+t \cdot s_M = 1.53+0.042=1.57[/tex][tex]LL=M-t \cdot s_M = 1.53-0.042=1.49\\\\UL=M+t \cdot s_M = 1.53+0.042=1.57[/tex]

The 95% confidence interval for the mean is (1.49, 1.57).

Answer:

x: -5,  -3,   0,  1,  4

y:-23, -15, -3, 1, 13        for the function.

x:-23, -15, -3, 1, 13

y: -5,   -3,  0,  1,  4         for the inverse.

Step-by-step explanation:

we know that if we have the function f(x) = y, then the inverse of f(x) (let's call it g(x)) is such that:

g(y) = x.

now we have

y=4x-3

y=(1/4)x+3/4

The only table that works for our first function is:

x: -5,  -3,   0,  1,  4

y:-23, -15, -3, 1, 13

You can see this by replacing the values of x and see if the value of y also coincides.

Then, using the fact that the other table must be for the inverse, we should se a table with the same values, but where the values of x and y are interchanged.

The second table is that one:

x:-23, -15, -3, 1, 13

y: -5,   -3,  0,  1,  4

Answer: B and D

x:-23, -15, -3, 1, 13

y:-5, -3, 0, 1, 4

x:-5, -3, 0, 1, 4

y:-23, -15, -3, 1, 13

Step-by-step explanation:

Answer:

51.56% probability that the mean weight of the sample of cows would differ from the population mean by greater than 11lbs if 49 cows are sampled at random from the herd

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question, we have that:

[tex]\mu = 3181, \sigma = 119, n = 49, s = \frac{119}{\sqrt{49}} = 17[/tex]

What is the probability that the mean weight of the sample of cows would differ from the population mean by greater than 11lbs if 49 cows are sampled at random from the herd

Lower than 3181 - 11 = 3170 lbs or greater than 3181 + 11 = 3192 lbs. Since the normal distribution is symmetric, these probabilities are equal. So i will find one of them, and multiply by 2.

Probability of mean weight lower than 3170 lbs:

This is 1 subtracted by the pvalue of Z when X = 3170. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{3170 - 3181}{17}[/tex]

[tex]Z = -0.65[/tex]

[tex]Z = -0.65[/tex] has a pvalue of 0.2578

2*0.2578 = 0.5156

51.56% probability that the mean weight of the sample of cows would differ from the population mean by greater than 11lbs if 49 cows are sampled at random from the herd

Answer:

The mean of depth is 12.75cm.

The variance of depth is of 13.02 cm².

Step-by-step explanation:

An uniform probability is a case of probability in which each outcome is equally as likely.

For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.

The mean of the uniform distribution is:

[tex]M = \frac{a+b}{2}[/tex]

The variance of the uniform distribution is given by:

[tex]V = \frac{(b-a)^{2}}{12}[/tex]

Uniform distribution on the interval (6.5, 19)

This means that: [tex]a = 6.5, b = 19[/tex]

So

Mean:

[tex]M = \frac{6.5+19}{2} = 12.75[/tex]

The mean of depth is 12.75cm.

Variance:

[tex]V = \frac{(19 - 6.5)^{2}}{12} = 13.02[/tex]

The variance of depth is of 13.02 cm².

Answer:

[tex]\fbox{\begin{minipage}{5em}A = 18.3\end{minipage}}[/tex]

Step-by-step explanation:

Given:

Dan was thinking of a number.

Dan adds 10 to it, then doubles it and gets an answer of 56.6.

Solve for:

Dan's original number

Step 1: Clarify the problem:

Denote Dan's original number as A

Dan adds 10 to A => 10 + A, then

Dan doubles this sum => 2 x (10 + A), then

Dan gets an answer of 56.6 => 2 x (10 + A) = 56.6

Step 2: Solve for the defined equation:

2 x (10 + A) = 56.6

Let's divide both sides of equation by 2:

2 x (10 + A)/2 = 56.6/2

We simplify both sides after division:

10 + A = 28.3

Let's transfer all numbers to the right side, except A (the sign of 10 is changed from + to -)

A = 28.3 - 10

Let's perform the subtraction to get A:

A = 18.3

Hope this helps!

:)

Answer:

2/7

Step-by-step explanation:

Since Rebecca is garunteed to pick a poodle, there are 7 puppies left. There are 2 retrievers so the probability is 2/7

Answer:2/7

Step-by-step explanation:

Answer:

2160ft³

Step-by-step explanation:

V=whl=10·18·12=2160ft³

Answer:

( 5 ^ -2)^4

= 5 ^ -8

= 1 /5^8

= 1 / 390,625

Answer:Please include images of the graphs!

Step-by-step explanation:

Look at each graph given. Ensure that there is a line, and that you can locate two points on the line given.

Use the following equation to get the slope:

m (slope) = (y₂ - y₁)/(x₂ - x₁)

Note that you can obtain the numbers for the equation by getting two points on the number line. Plug in the numbers by variables:

(x₁ , y₁) & (x₂ , y₂)

In this equation, make sure that the slope (m) will equal 1/4 (given).

The full equation that you will use is:

1/4 =  (y₂ - y₁)/(x₂ - x₁)

Find the graph that will satisfy this equation.

Answer:

D.

Step-by-step explanation:

It's a right triangle so

[tex]x^2=40^2+9^2[/tex]

x = 41

Due to the symmetry of the paraboloid about the z-axis, you can treat this is a surface of revolution. Consider the curve [tex]y=x^2[/tex], with [tex]1\le x\le2[/tex], and revolve it about the y-axis. The area of the resulting surface is then

[tex]\displaystyle2\pi\int_1^2x\sqrt{1+(y')^2}\,\mathrm dx=2\pi\int_1^2x\sqrt{1+4x^2}\,\mathrm dx=\frac{(17^{3/2}-5^{3/2})\pi}6[/tex]

But perhaps you'd like the surface integral treatment. Parameterize the surface by

[tex]\vec s(u,v)=u\cos v\,\vec\imath+u\sin v\,\vec\jmath+u^2\,\vec k[/tex]

with [tex]1\le u\le2[/tex] and [tex]0\le v\le2\pi[/tex], where the third component follows from

[tex]z=x^2+y^2=(u\cos v)^2+(u\sin v)^2=u^2[/tex]

Take the normal vector to the surface to be

[tex]\dfrac{\partial\vec s}{\partial u}\times\dfrac{\partial\vec s}{\partial u}=-2u^2\cos v\,\vec\imath-2u^2\sin v\,\vec\jmath+u\,\vec k[/tex]

The precise order of the partial derivatives doesn't matter, because we're ultimately interested in the magnitude of the cross product:

[tex]\left\|\dfrac{\partial\vec s}{\partial u}\times\dfrac{\partial\vec s}{\partial v}\right\|=u\sqrt{1+4u^2}[/tex]

Then the area of the surface is

[tex]\displaystyle\int_0^{2\pi}\int_1^2\left\|\dfrac{\partial\vec s}{\partial u}\times\dfrac{\partial\vec s}{\partial v}\right\|\,\mathrm du\,\mathrm dv=\int_0^{2\pi}\int_1^2u\sqrt{1+4u^2}\,\mathrm du\,\mathrm dv[/tex]

which reduces to the integral used in the surface-of-revolution setup.

Answer:

[tex]-5x^{4} -20x^{3} -5x-20[/tex]

Step-by-step explanation:

[tex]-5[(x^{3} +1)(x+4)][/tex]

Use the FOIL method for the last two groups.

[tex]-5(x^{4} +4x^{3} +x+4)[/tex]

Now, distribute the -5 into each term.

[tex]-5x^{4} -20x^{3} -5x-20[/tex]

Step-by-step explanation:

You can take the inverse of a function by replacing all x-values in the equation with y-values and vice versa and subsequently solving for y:

Equation given:

[tex]f(x) = \frac{-x}{x+2}[/tex]

Replace all x-values with y and all y-values with x:

[tex]x = \frac{-y}{y+2}[/tex]

Solve for y:

[tex]x(y+2) = -y\\\\xy + 2x = -y\\\\2x = -y - xy\\\\2x = y(-1+-x)\\\\-\frac{2x}{x+1} =y[/tex]

This is the inverse of f(x), where x ≠ 2..

Answer:

22%

Step-by-step explanation:

Car's price is reduced by 8% or 0.92 times a year

after 3 years it will make:

or

Answer:

Hello!

Here is your answer:

22%

I hope I was able to help you.  If not, please let me know!

Step-by-step explanation:

Answer:

For this problem we can use the following proportional rule:

[tex] \frac{73 mi}{25 gal}= \frac{x}{75 gal}[/tex]

Where x represent the number of miles that we can travel with 75 gallons. For this case we can use this proportional rule since by definition [tex] D=vt[/tex]. If we solve for x we got:

[tex] x =75 gal (\frac{73 mi}{25 gal}) =219mi[/tex]

And the best answer would be:

219 mi

Step-by-step explanation:

For this problem we can use the following proportional rule:

[tex] \frac{73 mi}{25 gal}= \frac{x}{75 gal}[/tex]

Where x represent the number of miles that we can travel with 75 gallons. For this case we can use this proportional rule since by definition [tex] D=vt[/tex]. If we solve for x we got:

[tex] x =75 gal (\frac{73 mi}{25 gal}) =219mi[/tex]

And the best answer would be:

219 mi

Answer:

[tex] P(X\leq x) =\frac{x-a}{b-a}, a \leq x \leq b[/tex]

And using this formula we have this:

[tex] P(X<11) = \frac{11-0}{12-0}= 0.917[/tex]

Then we can conclude that the probability that that a person waits fewer than 11 minutes is approximately 0.917

Step-by-step explanation:

Let X the random variable of interest that a woman must wait for a cab"the amount of time in minutes " and we know that the distribution for this random variable is given by:

[tex] X \sim Unif (a=0, b =12)[/tex]

And we want to find the following probability:

[tex] P(X<11)[/tex]

And for this case we can use the cumulative distribution function given by:

[tex] P(X\leq x) =\frac{x-a}{b-a}, a \leq x \leq b[/tex]

And using this formula we have this:

[tex] P(X<11) = \frac{11-0}{12-0}= 0.917[/tex]

Then we can conclude that the probability that that a person waits fewer than 11 minutes is approximately 0.917

Answer:

dose in MCG = 10.2 mcg

Total volume to be sent home = 1.836 ml (1836μl)

Step-by-step explanation:

weight of patient = 680g

dosage in mcg of medication = 15mcg/kg

This means that

for every 1kg weight, 15mcg is given,

since 1kg = 1000g, we can also say that for every 1000g weigh, 15mcg is given.

1000g = 15mcg

1g = 15/1000 mcg = 0.015 mcg

∴ 680g = 0.015 × 680 = 10.2 mcg

Dosage in MCG = 10.2 mcg

Next, we are also told ever ml volume of the drug contains 50 mcg weight of the drug (50mcg/ml). This can also be written as:

50mcg = 1 ml

1 mcg = 1/50 ml = 0.02 ml

∴ 10.2 mcg = 10.2 × 0.02 = 0.204 ml

since the medication is to be taken TID (three times daily) for 3 days, the total number of times the drug is to be taken = 9 times.

therefore, the total volume required = 0.204 × 9 = 1.836 ml (1836 μl)

Answer: False

Step-by-step explanation:

We can write tan(x) = sin(x)/cos(x)

if cos(x) tends to 1, and sin (x) tends to 0 (this happens aronund the point x = 0)

then we have:

Tan(x) = 0/1 = 0

Then the statement is false, as cos(x) approaches 1 and sin(x) approaches 0, tan(x) also approaches 0.

Answer:

A . 0.85 + (0.15 +(-3)) = -2

B . [(-3)+(-3)]+(-3) = - 9

Step-by-step explanation:

Explanation:-

Associative  property with addition

(a+(b+c)) = (a+b) + c

A)

Given 0.85 + (0.15 +(-3)) = (0.85 +0.15)+(-3)

                                       = 1 - 3

                                       = -2

B)  Given [(-3)+(-3)]+(-3) = ( (-3)+[( -3)+(-3))]

                                     = ( -3 +[-3-3]

                                    =  -3 -6

                                    = -9

Final answer:-

A . 0.85 + (0.15 +(-3)) = -2

B . [(-3)+(-3)]+(-3) = - 9

The probability that it also rained that day would be 0.30

Answer:

Step-by-step explanation:

1) d

2) c

1) 3 hearts, 7 other shapes that isn't hearts

2) 2 triangs, 5 circles

Answer:

1) d

2) c

Step-by-step explanation:

looks like i was wrong last time lol, this is right for sure tho, i see what i did wrong, sorry

Answer:

(a) -2,0 and 2,5 and (b) 2,-1 and 10,9

Question:

The question is incomplete without the answer choice. Let's consider the following:

A line has a slope of -4/5. Which ordered pairs could be points on a line that is perpendicular to this line? select two options

a) -2,0 and 2,5

b) -4,5 and 4,-5

c) -3,4 and 2,0

d) 1,-1 and 6,-5

e) 2,-1 and 10,9

Step-by-step explanation:

The ordered pairs that could be points on a line that is perpendicular to this line would have same slope as that of the line.

Let's check out the slope of the options.

The line has slope = -4/5

Slope = m = (y subscript 2 -y subscript 1)/(x subscript 2 - x subscript 1)

The coordinates is in the form of (x,y)

Find attached the workings.

a) -2,0 and 2,5

m = 5/4

b) -4,5 and 4,-5

m = -5/4

c) -3,4 and 2,0

m = -4/5

d) 1,-1 and 6,-5

m = -4/5

e) 2,-1 and 10,9

m = 5/4

Two lines are perpendicular if (m subscript 1) × (m subscript 2) = -1

In other words, the slopes

of the two lines must be negative reciprocals of each other.

If 1st slope = -4/5

For the lines to be perpendicular, the slope of every other line = 5/4

2nd slope = 5/4

The ordered pairs that are points on the line perpendicular to the line:

(a) -2,0 and 2,5 and (b) 2,-1 and 10,9

Answer:AandE

Step-by-step explanation:

Answer:

[tex]=3\frac{5}{6}[/tex]

Step-by-step explanation:

[tex]2\frac{1}{2}+1\frac{1}{3}\\\mathrm{Add\:whole\:numbers}\:2+1:\quad 3\\\mathrm{Combine\:fractions}\:\frac{1}{2}+\frac{1}{3}:\quad \frac{5}{6}\\=3\frac{5}{6}[/tex]

Answer:

The 99% confidence interval for the percentage of Phoenix residents who support mandatory sick leave for food handlers is between 85.40% and 92.60%.

Step-by-step explanation:

Confidence interval for the proportion:

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 zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

For this problem, we have that:

[tex]n = 500, \pi = \frac{445}{500} = 0.89[/tex]

99% confidence level

So [tex]\alpha = 0.01[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.89 - 2.575\sqrt{\frac{0.89*0.11}{500}} = 0.8540[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.89  + 2.575\sqrt{\frac{0.89*0.11}{500}} = 0.9260[/tex]

For the percentage:

Multiply the proportion by 100.

0.8540*100 = 85.40%

0.9260*100 = 92.60%

The 99% confidence interval for the percentage of Phoenix residents who support mandatory sick leave for food handlers is between 85.40% and 92.60%.

Answer:

1/5

Step-by-step explanation:

switch sides, delete both common factors and your stuck with 5k=1. then you put both in a fraction and it gets you 1/5

Answer:

Step-by-step explanation:

No Solutions

There will be no solutions when the left side is inconsistent with the right side:

  2x +5 +2x +3x = 7x +1

  7x +5 = 7x +1 . . . . . . no value of x will make this true

__

One Solution

There will be one solution when the left side and right side are not inconsistent and not the same.

  2x +5 +2x +3x = 6x +1

  7x +5 = 6x +1

  x = -4 . . . . . . . . add -6x-5 to both sides

__

Infinitely Many Solutions

There will be an infinite number of solutions when the equation is true for any value of x. This will be the case when the left side and right side are identical.

  2x +5 +2x +3x = 7x +5

  7x +5 = 7x +5 . . . . . true for all values of x

_____

Comment on these solutions

You have not provided the contents of any of the drop-down menus, so we cannot say for certain what the answers should be--except in the case of "infinitely many solutions." For "no solutions", the coefficient of x must be 7 and the constant must not be 5. For "one solution" the coefficient of x cannot be 7, and the constant can be anything.

Answer:

No Solutions: 7x+1

One Solution: 6x+1

Infinitely Many Solutions: 7x+5

Answer:

"According to the 68-95-99.7 rule, we expect 95% [95.45%] of head breadths to be" between 4.1 inches and 8.9 inches.

Step-by-step explanation:

According to the 68-95-99.7 rule, approximately:

Then, if we have--from the question--that:

We have to remember that two parameters characterize a normal distribution: the population's mean and the population's standard deviation. So, mathematically, the distribution we have from question is [tex] \\ N(6.5, 1.2)[/tex].

For 95% (95.45%) of the head breadths, we expect that they are two standard deviations below and above the population's mean.

For solving this, we need to use the cumulative standard normal distribution (in case we need to find probabilities) and also use standardized values or z-scores:

[tex] \\ z = \frac{x - \mu}{\sigma}[/tex] [1]

A z-score "tells us" the distance from the mean in standard deviations units. If the z-score is positive, it is above the mean. If it is negative, it is below the mean.

Since 95% (95.45%) of the head breadths are two standard deviations (above and below the mean), we have (using [1]):

[tex] \\ \pm2 = \frac{x - \mu}{\sigma}[/tex]

But we already know that [tex] \\ \mu=6.5[/tex] inches and [tex] \\ \sigma=1.2[/tex] inches.

Thus (without using units) for values above the population's mean:

[tex] \\ 2 = \frac{x - 6.5}{1.2}[/tex]

Solving the equation for x, we multiply by 1.2 at each side of [1] :

[tex] \\ 2 * 1.2 = \frac{x - 6.5}{1.2} * 1.2[/tex]

[tex] \\ 2 * 1.2 = (x - 6.5)\frac{1.2}{1.2}[/tex]

[tex] \\ 2 * 1.2 = (x - 6.5)\frac{1.2}{1.2}[/tex]

[tex] \\ 2 * 1.2 = (x - 6.5)*1[/tex]

[tex] \\ 2 * 1.2 = x - 6.5[/tex]

Adding 6.5 at each side of the previous equation:

[tex] \\ (2 * 1.2) + 6.5 = x - 6.5 + 6.5[/tex]

[tex] \\ (2 * 1.2) + 6.5 = x + 0[/tex]

[tex] \\ (2 * 1.2) + 6.5 = x[/tex]

Therefore, the raw value, x, in the distribution that is two standard deviations above the population's mean is:

[tex] \\ x = (2 * 1.2) + 6.5[/tex]

[tex] \\ x = 2.4 + 6.5[/tex]

[tex] \\ x = 8.9[/tex] inches.

For two standard deviations below the mean, we proceed in the same way:

[tex] \\ -2 = \frac{x - 6.5}{1.2}[/tex]

[tex] \\ -2*1.2 = x - 6.5[/tex]

[tex] \\ (-2*1.2) + 6.5 = x[/tex]

[tex] \\ x = (-2*1.2) + 6.5[/tex]

[tex] \\ x = -2.4 + 6.5[/tex]

[tex] \\ x = 4.1[/tex] inches

Therefore, "according to the 68-95-99.7 rule, we expect 95% [95.45%] of head breadths to be" between 4.1 inches and 8.9 inches.

The graph below shows these values, and the shaded area represents 95% of the data, or, to be more precise, 95.45% (0.954499).  

Answer:

C

Step-by-step explanation:

A cylinder is formed when rotating the 3-D figure around y-axis

answer: D) 439.85

Step-by-step explanation:

we are given the price of the bike which is $413.

we are also given the sales tax which is 6.5%.

sales tax is added to the original price to give us our total. so in order to find the total cost we need to find what the 6.5% sales tax is and add it to our original price. to find the sales tax number in dollars we need to set up our formula. The easiest formula is to use a proportion. X is out of 413 = 6.5% is out of 100%. X/413=6.5/100. We can then cross multiply then divide. 6.5 times 413=2,684.5. then divide 2684.5÷100= 26.845.

we need to round up to the nearest cent since we are working with dollars and cents 26.85. 26.85 is 6.5% of the price of the bike which is 413. Now we just simply add the tax to the original price and we get the cost. 413+26.85=439.85

Answer:    The answer is D) 439.85

Step-by-step explanation: