In our decimal​ system, we distinguish odd and even numbers by looking at their ones​ (or units) digits. If the ones digit is even​ (0, 2,​ 4, 6,​ 8), the number is even. If the ones digit is odd​ (1, 3,​ 5, 7,​ 9), the number is odd. Determine whether this same criterion works for numbers expressed in base four

Answer:

21

Step-by-step explanation:

so this is the way i learned it

compare side to side so CA is 12 and LM is 9 so its 4/3

CB is 8 LN is 6 so its 4/3

so AB is 8 so MN would have to be 4/3 which would made MN 6 so MNL would be 21

Answer:

21

Step-by-step explanation:

ΔLMN ≅ ΔABC with a scale factor of 0.75

If Line AB is similar to Line MN, then Line MN is 6.

Perimeter of ΔLMN

9+6+6=

15+6=

21

Answer:

  12√2 feet ≈ 16.97 feet

Step-by-step explanation:

For the dimensions shown in the attached diagram, the distance "a" along the ladder from the ground to the fence is ...

  a = (6 ft)/sin(x) = (6 ft)/sin(0.82) ≈ 8.206 ft

The distance along the ladder from the top of the fence to the wall is ...

  b = (6 ft)/cos(x) = (6 ft)/cos(0.82) ≈ 8.795 ft

__

In general, the distance along the ladder from the ground to the wall is ...

  L(x) = a +b

  L(x) = 6/sin(x) +6/cos(x)

This distance will be shortest for the case where the derivative with respect to x is zero.

  L'(x) = 6(-cos(x)/sin(x)² +sin(x)/cos(x)²) = 6(sin(x)³ -cos(x)³)/(sin(x)²cos(x²))

This will be zero when the numerator is zero:

  0 = 6(sin(x) -cos(x))(1 -sin(x)cos(x))

The last factor is always positive, so the solution here is ...

  sin(x) = cos(x)   ⇒   x = π/4

And the length of the shortest ladder is ...

  L(π/4) = 6√2 + 6√2

  L(π/4) = 12√2 . . . . feet

_____

The ladder length for the "trial" angle of 0.82 radians was ...

  8.206 +8.795 = 17.001 . . . ft

The actual shortest ladder is ...

  12√2 = 16.971 . . . feet

Answer:

Let's solve your equation step-by-step.

[tex]x^7+64x^4=0[/tex]

Step 1: Factor left side of equation.

[tex]x^4(x+4)(x^2-4x+16)=0[/tex]

Step 2: Set factors equal to 0.

[tex]x^4=0[/tex]  or  [tex]x+4=0[/tex]  or  [tex]x^2-4x+16=0[/tex] 

[tex]x^4=0[/tex]  or  [tex]x=0[/tex]  

Answer:

I hope this help you :)

Answer:

A warranty of 6.185 years should be provided.

Step-by-step explanation:

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.

In this question, we have that:

[tex]\mu = 8.2, \sigma = 1.3[/tex]

What warranty should be provided so that the company is replacing at most 6% of their blenders sold?

The warranty should be the 6th percentile, which is X when Z has a pvalue of 0.06. So X when Z = -1.55.

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

[tex]-1.55 = \frac{X - 8.2}{1.3}[/tex]

[tex]X - 8.2 = -1.55*1.3[/tex]

[tex]X = 6.185[/tex]

A warranty of 6.185 years should be provided.

Answer:

x=1

Step-by-step explanation:

sqrt(x+3) = sqrt(5x-1)

Square each side

x+3 = 5x-1

Subtract x from each side

3 = 4x-1

Add 1 to each side

4 =4x

Divide by 4

x=1

Answer:

x= 1

Step-by-step explanation:

[tex]\sqrt{x+3}=\sqrt{5x-1}[/tex]

Square both sides.

x + 3 = 5x - 1

Subtract 3 and 5x on both sides.

x - 5x = -1 - 3

-4x = -4

Divide -4 into both sides.

-4x/-4 = -4/-4

x = 1

Answer:

2x - y - 3 = 0

Step-by-step explanation:

Find slope-intercept form first: y = mx + b

Step 1: Pick out 2 points

In this case, I picked out (2, 1) and (0, -3) from the graph

Step 2: Using slope formula y2 - y1/x2 - x1 to find slope

-3 - 1/0 - 2

m = 2

Step 3: Place slope formula results into point-slope form

y = 2x + b

Step 4: Plug in a point to find b

-3 = 2(0) + b

b = -3

Step 5: Write slope-intercept form

y = 2x - 3

Step 6: Move all variables and constants to one side

0 = 2x - 3 - y

Step 7: Rearrange

2x - y - 3 = 0 is your answer

Answer:

- The center line is at 16.5 ounces.

- The standard deviation of the sample mean = 0.112 ounce.

- The UCL = 16.836 ounces.

- The LCL = 16.154 ounces.

Step-by-step explanation:

The Central limit theorem allows us to write for a random sample extracted from a normal population distribution with each variable independent of one another that

Mean of sampling distribution (μₓ) is approximately equal to the population mean (μ).

μₓ = μ = 16.5 ounces

And the standard deviation of the sampling distribution is given as

σₓ = (σ/√N)

where σ = population standard deviation = 0.25 ounce

N = Sample size = 5

σₓ = (0.25/√5) = 0.1118033989 = 0.112 ounce

Now using the 3 sigma limit rule that 99.5% of the distribution lies within 3 standard deviations of the mean, the entire distribution lies within

(μₓ ± 3σₓ)

= 16.5 ± (3×0.112)

= 16.5 ± (0.336)

= (16.154, 16.836)

Hope this Helps!!!

Answer:

24

Step-by-step explanation:

Since you are given almost everything, you just simply divide by 5=>

120/5 = 24

Hope this helps

Answer:

5/3 is an improper fraction because 5 is higher then 3. So the correct way of writing it would be 1 2/3.

Step-by-step explanation:

Answer:

x = 2

Step-by-step explanation:

the equation of the line can be found using the slope intercept form

y = mx +b

y= -3/2 x + 3

x intercept is found by setting y=0 bc that will give you the x-value at which the line crosses the x -axis so

0 = -3/2x+3 (subtract the 3 on both sides) would cancel out the + 3 and would

-3 = -3/2 x  (divide by -3/2 on both sides to cancel out the -3/2)  

x = 2

Answer:

A

Step-by-step explanation:

The area of a kite is half of the product of the length of the diagonals, or in this case 16*12/2=96 square feet. Hope this helps!

Answer:

a. 96 ft^2

Step-by-step explanation:

You can cut the kite into 2 equal triangle halves vertically.

Then you can use the triangle area formula and multiply it by 2 since there are 2 triangles.

[tex]\frac{1}{2} *12*8*2=\\6*8*2=\\48*2=\\96ft^2[/tex]

The kite's area is a. 96 ft^2.

Answer:

[tex]1/\sqrt{2}[/tex]

Answer:

B

Step-by-step explanation:

Answer:

a) 0.6426 = 64.26% probability that the sample mean will be within +/- 5 of the population mean.

b) 0.9544 = 95.44% probability that the sample mean will be within +/- 10 of the population mean.

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 = 200, \sigma = 50, n = 100, s = \frac{50}{\sqrt{100}} = 5[/tex]

a. What is the probability that the sample mean will be within +/- 5 of the population mean (to 4 decimals)?

This is the pvalue of Z when X = 200 + 5 = 205 subtracted by the pvalue of Z when X = 200 - 5 = 195.

Due to the Central Limit Theorem, Z is:

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

X = 205

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

[tex]Z = \frac{205 - 200}{5}[/tex]

[tex]Z = 1[/tex]

[tex]Z = 1[/tex] has a pvalue of 0.8413.

X = 195

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

[tex]Z = \frac{195 - 200}{5}[/tex]

[tex]Z = -1[/tex]

[tex]Z = -1[/tex] has a pvalue of 0.1587.

0.8413 - 0.1587 = 0.6426

0.6426 = 64.26% probability that the sample mean will be within +/- 5 of the population mean.

b. What is the probability that the sample mean will be within +/- 10 of the population mean (to 4 decimals)?

This is the pvalue of Z when X = 210 subtracted by the pvalue of Z when X = 190.

X = 210

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

[tex]Z = \frac{210 - 200}{5}[/tex]

[tex]Z = 2[/tex]

[tex]Z = 2[/tex] has a pvalue of 0.9772.

X = 195

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

[tex]Z = \frac{190 - 200}{5}[/tex]

[tex]Z = -2[/tex]

[tex]Z = -2[/tex] has a pvalue of 0.0228.

0.9772 - 0.0228 = 0.9544

0.9544 = 95.44% probability that the sample mean will be within +/- 10 of the population mean.

(a): The required probability is [tex]P(195 < \bar{x} < 205)=0.6826[/tex]

(b): The required probability is [tex]P(190 < \bar{x} < 200)=0.9544[/tex]

A numerical measurement that describes a value's relationship to the mean of a group of values.

Given that,

mean=200

Standard deviation=50

[tex]n=100[/tex]

[tex]\mu_{\bar{x}}=200[/tex]

[tex]\sigma{\bar{x}} =\frac{\sigma}{\sqrt{n} } \\=\frac{50}{\sqrt{100} }\\ =5[/tex]

Part(a):

within [tex]5=200\pm 5=195,205[/tex]

[tex]P(195 < \bar{x} < 205)=P(-1 < z < 1)\\=P(z < 1)-P(z < -1)\\=0.8413-0.1587\\=0.6826[/tex]

Part(b):

within [tex]10=200\pm 10=190,200[/tex]

[tex]P(190 < \bar{x} < 200)=P(-1 .98 < z < 1.98)\\=P(z < 2)-P(z < -2)\\=0.9772-0.0228\\=0.9544[/tex]

Learn more about the topic Z-score:

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Answer: x = -5

Step-by-step explanation:

If you factor each denominator, you can find the LCM.

[tex]\dfrac{2}{x^2-x-12}=\dfrac{1}{x^2-16}\\\\\\\dfrac{2}{(x-4)(x+3)}=\dfrac{1}{(x-4)(x+4)}\\\\\\\text{The LCM is (x-4)(x+4)(x+3)}\\\\\\\dfrac{2}{(x-4)(x+3)}\bigg(\dfrac{x+4}{x+4}\bigg)=\dfrac{1}{(x-4)(x+4)}\bigg(\dfrac{x+3}{x+3}\bigg)\\\\\\\dfrac{2(x+4)}{(x-4)(x+4)(x+3)}=\dfrac{1(x+3)}{(x-4)(x+4)(x+3)}\\[/tex]

Now that the denominators are equal, we can clear the denominator and set the numerators equal to each other.

2(x + 4) = 1(x + 3)

2x + 8 = x + 3

x  + 8 =       3

x        =      -5

Answer:

[tex]x = 1-10t\\y = -6+16t\\z = 7-12t[/tex]

Step-by-step explanation:

We are given the coordinates of points P(1,-6,7) and Q(-9,10,-5).

The values in the form of ([tex]x,y,z[/tex]) are:

[tex]x_1=1\\x_2=-9\\y_1=-6\\,y_2=10\\z_1=7\\z_2=-5[/tex]

[tex]$\vec{PQ}$[/tex] can be written as the difference of values of x, y and z axis of the two points i.e. change in axis.

[tex]\vec{PQ}=<x_2-x_1,y_2-y_1,z_2-z_1>[/tex]

[tex]\vec{PQ} = <(-9-1), 10-(-6),(-5-7)>\\\Rightarrow \vec{PQ} = <-10, 16,-12>[/tex]

The equation of line in vector form can be written as:

[tex]\vec{r} (t) = <1,-6,7> + t<-10,16,-12>[/tex]

The standard parametric equation can be written as:

[tex]x = 1-10t\\y = -6+16t\\z = 7-12t[/tex]

Answer:

Volume of a cone = 1/3πr²h

h = height

r = radius

r = 3cm h = 4cm

Volume = 1/3π(3)²(4)

= 36 × 1/3π

= 12π

= 36.69cm³

= 37cm³ to the nearest tenth

Hope this helps

Answer:

37.7

_______

NOT 37

Step-by-step explanation:

v = [tex]\frac{1}{3}[/tex] · [tex]\pi[/tex] · [tex]r^{2}[/tex] · [tex]h[/tex]

v = [tex]\frac{1}{3}[/tex] · [tex]\pi[/tex] · [tex]3^{2}[/tex] · [tex]4 = 12\pi = 37.69911 =[/tex] 37.7

Answer:

We need a sample of at least 1937.

Step-by-step explanation:

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].

The margin of error is:

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

For this problem, we have that:

[tex]\pi = 0.72[/tex]

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

How large a sample should be if you want your estimate to be within 0.02 with 95% confidence.

We need a sample of at least n.

n is found when M = 0.02. So

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

[tex]0.02 = 1.96\sqrt{\frac{0.72*0.28}{n}}[/tex]

[tex]0.02\sqrt{n} = 1.96\sqrt{0.72*0.28}[/tex]

[tex]\sqrt{n} = \frac{1.96\sqrt{0.72*0.28}}{0.02}[/tex]

[tex](\sqrt{n})^{2} = (\frac{1.96\sqrt{0.72*0.28}}{0.02})^{2}[/tex]

[tex]n = 1936.16[/tex]

Rounding up to the nearest number.

We need a sample of at least 1937.

Answer:

a.1.90 years

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1-0.99}{2} = 0.005[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].

So it is z with a pvalue of [tex]1-0.005 = 0.995[/tex], so [tex]z = 2.575[/tex]

Now, find the margin of error M as such

[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

In this question:

[tex]n = 25, \sigma = 3.8[/tex]

So

[tex]M = 2.575*\frac{3.8}{\sqrt{25}} = 1.90[/tex]

So the correct answer is:

a.1.90 years

Answer:

En álgebra, el teorema del factor es un teorema que vincula factores y ceros de un polinomio. Es un caso especial del teorema del resto polinómico.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Ray

Answer:

ray

Step-by-step explanation:

ray is a part of a line that has an endpoint in one side and extends indefinitely on the opposite side. hence, the answer is ray

hope this helps

Complete question is;

In a certain community, 8% of all people above 50 years of age have diabetes. A health service in this community correctly diagnoses 95% of all person with diabetes as having the disease, and incorrectly diagnoses 10% of all person without diabetes as having the disease. Find the probability that a person randomly selected from among all people of age above 50 and diagnosed by the health service as having diabetes actually has the disease.

Answer:

P(has diabetes | positive) = 0.442

Step-by-step explanation:

Probability of having diabetes and being positive is;

P(positive & has diabetes) = P(has diabetes) × P(positive | has diabetes)

We are told 8% or 0.08 have diabetes and there's a correct diagnosis of 95% of all the persons with diabetes having the disease.

Thus;

P(positive & has diabetes) = 0.08 × 0.95 = 0.076

P(negative & has diabetes) = P(has diabetes) × (1 –P(positive | has diabetes)) = 0.08 × (1 - 0.95)

P(negative & has diabetes) = 0.004

P(positive & no diabetes) = P(no diabetes) × P(positive | no diabetes)

We are told that there is an incorrect diagnoses of 10% of all persons without diabetes as having the disease

Thus;

P(positive & no diabetes) = 0.92 × 0.1 = 0.092

P(negative &no diabetes) =P(no diabetes) × (1 –P(positive | no diabetes)) = 0.92 × (1 - 0.1)

P(negative &no diabetes) = 0.828

Probability that a person selected having diabetes actually has the disease is;

P(has diabetes | positive) =P(positive & has diabetes) / P(positive)

P(positive) = 0.08 + P(positive & no diabetes)

P(positive) = 0.08 + 0.092 = 0.172

P(has diabetes | positive) = 0.076/0.172 = 0.442

Using formula:

[tex]P(\text{diabetes diagnosis})\\[/tex]:

[tex]=\text{P(having diabetes and have been diagnosed with it)}\\ + \text{P(not have diabetes and yet be diagnosed with diabetes)}[/tex]

[tex]=0.08 \times 0.95+(1-0.08) \times 0.10 \\\\=0.08 \times 0.95+0.92 \times 0.10 \\\\=0.076+0.092\\\\=0.168[/tex]

[tex]\text{P(have been diagnosed with diabetes)}[/tex]:

[tex]=\frac{\text{P(have diabetic and been diagnosed as having insulin)}}{\text{P(diabetes diagnosis)}}[/tex]

[tex]=\frac{0.08\times 0.95}{0.168} \\\\=\frac{0.076}{0.168} \\\\=0.452\\[/tex]

Learn more about the probability:

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Answer:

The second graph.

Step-by-step explanation:

0-9: 6 numbers

10-19: 2 numbers

20-29: 1 number

30-39: 3 numbers

40-49: 1 number

50-59: 2 numbers

60-69: 0 numbers

70-79: 5 numbers

80-89: 3 numbers

90-99: 1 number

Answer: height = 13.24 m

Step-by-step explanation:

Draw a picture (see image below), then set up the proportions to find the length of QB.  Then input QB into either of the equations to find h.

Given: PQ = 10

          ∠TPB = 23°

          ∠TQB = 32°

[tex]\tan P=\dfrac{opposite}{adjacent}\qquad \qquad \tan Q=\dfrac{opposite}{adjacent}\\\\\\\tan 23^o=\dfrac{h}{10+x}\qquad \qquad \tan 32^o=\dfrac{h}{x}\\\\\\\underline{\text{Solve each equation for h:}}\\\tan 23^o(10+x)=h\qquad \qquad \tan 32^o(x)=h\\\\\\\underline{\text{Set the equations equal to each other and solve for x:}}\\\tan23^o(10+x)=\tan32^o(x)\\0.4245(10+x)=0.6249x\\4.245+0.4245x=0.6249x\\4.245=0.2004x\\21.18=x[/tex]

[tex]\underline{\text{In put x = 21.18 into either equation and solve for h:}}\\h=\tan 32^o(x)\\h=0.6249(2.118)\\\large\boxed{h=13.24}[/tex]

Answer:

A) 0.028

Step-by-step explanation:

Given:

Sample size, n = 115

Population parameter, p = 0.1

The X-Bin(n=155, p=0.1)

Required:

Find the standard deviation of the normal curve that can be used to approximate the binomial probability histogram.

To find the standard deviation, use the formula below:

[tex]\sigma = \sqrt{\frac{p(1-p)}{n}}[/tex]

Substitute figures in the equation:

[tex]\sigma = \sqrt{\frac{0.1(1 - 0.1)}{115}}[/tex]

[tex]\sigma = \sqrt{\frac{0.1 * 0.9}{115}}[/tex]

[tex]\sigma = \sqrt{\frac{0.09}{115}}[/tex]

[tex] \sigma = \sqrt{7.826*10^-^4}[/tex]

[tex] \sigma = 0.028 [/tex]

The Standard deviation of the normal curve that can be used to approximate the binomial probability histogram is 0.028

Answer: x=45°

Step-by-step explanation:

Angles opposite from each other are equal. The angle 160 degrees in red on the bottom encompasses two angles: BEG and CEG. Angle BEG is on the opposite side as FEA which means it is equal to x.

Since angle FED on the other side is 115, you subtract 115 from 160 to get 45 degrees.

Answer: x=45°

The angle BEG, which is opposite to the angle FEA, is determined to be 45 degrees.

According to the information provided, in a figure with an angle of 160 degrees (red angle on the bottom), there are two angles labeled as BEG and CEG. It is stated that the angle BEG is opposite to the angle FEA, making them equal, so we can represent this angle as x.

Additionally, it is mentioned that the angle FED on the other side measures 115 degrees.

To find the value of x, we subtract 115 degrees from the angle of 160 degrees.
=160-115
= 45

Thus, the solution is x = 45°.

For more details about the angle visit the link below: https://brainly.com/question/16959514

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The radioactive compound has a half-life of around 3.09 hours.

The period of time needed for a radioactive substance's initial quantity to decay by half is known as its half-life. The half-life of a drug may be calculated as follows if the rate of decay is proportionate to the amount of the substance existing at time t:

Let t be the half-life of the substance, then after t hours, the amount of the substance present will be,

100 mg × [tex]\dfrac{1}{2}[/tex] = 50 mg.

At time 6 hours, the amount of the substance present is,

100 mg × (1 - 3%) = 97 mg.

Given that the amount of material available determines how quickly something degrades,

The half-life can be calculated as follows:

[tex]t = 6 \times \dfrac{50}{ 97} = 3.09 \ hours[/tex]

Therefore, the half-life of the radioactive substance is approximately 3.09 hours.

Learn more about half-life:

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Answer:

Hiking: 28%

Canoeing: 16%

Swimming: 24%

Fishing: 32%

Step-by-step explanation:

21 + 12 + 18 + 24 = 75 (there are 75 campers)

21 out of 75 = 28%

12 out of 75 = 16%

18 out of 75 = 24%

24 out of 75 = 32%

Hope this helps!

Please mark Brainliest if correct

Answer:

a prism is a three dimensional shape with the same width all the way through.

Step-by-step explanation:

Step-by-step explanation:

i think this will help.