Is (1,2), (2,3) (3,4), (4,5) a function?

Answer:

3056.6 cm^2

Step-by-step explanation:

A = (pi)r^2 = 3.14 * 31.2 cm * 31.2 cm = 3056.6 cm^2

Answer: 3056.60 sq. cm.

Step-by-step explanation:

Area of a circle = π x r^2

= 3.14 x 31.2^2

= 3056.60

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:

  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:

It’s 0.12

Step-by-step explanation:

Took test

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:

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

Answer:

B

Step-by-step explanation:

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:

The 95% confidence interval for the population proportion of tenth graders reading at or below the eighth grade level is (0.2087, 0.2507).

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].

For this problem, we have that:

Suppose a sample of 1537 tenth graders is drawn. Of the students sampled, 1184 read above the eighth grade level. So 1537 - 1184 = 353 read at or below this level. Then

[tex]n = 1537, \pi = \frac{353}{1537} = 0.2297[/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].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2297 - 1.96\sqrt{\frac{0.2297*0.7703}{1537}} = 0.2087[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2297 + 1.96\sqrt{\frac{0.2297*0.7703}{1537}} = 0.2507[/tex]

The 95% confidence interval for the population proportion of tenth graders reading at or below the eighth grade level is (0.2087, 0.2507).

Answer:

Second option is the correct choice.

Step-by-step explanation:

"The discriminant is −4, so the equation has no real solutions."

[tex]x^2-4x+5=0\\\\a=1,\:b=-4,\:c=5:\\\\b^2-4ac=\left(-4\right)^2-4\cdot \:1\cdot \:5=-4[/tex]

Best Regards!

Answer: B

The discriminant is −4, so the equation has no real solutions.

Step-by-step explanation:

Just took quiz EDG2021

Mark Brainliest

Answer:

0.75 ML of insulin contains 75 units of insulin

Step-by-step explanation:

U - 100 insulin hold 100 units of insulin per ml

This means that:

1 ML = 100 units

∴ 0.75 ML = 100 × 0.75 = 75  units

Therefore 0.75 ML of insulin contains 75 units of insulin

Step-by-step explanation:

Concepto    20 pies, 20´ × 8´ × 8´6" 40 pies High Cube, 40´ × 8´ × 9´ 6"

Ancho  2352 mm / 7´9" 2352 mm / 7´9"

Altura 2393 mm / 7´10" 2698 mm / 8´10"

Capacidad 33,2 m³ / 1172 ft³ 76, m³ / 2700 ft³

ESPERO QUE TE AYUDE :D

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:

https://brainly.com/question/5512053

Answer:

0.7396 = 73.96% probability that the subsystem operates longer than 1000 hours.

Step-by-step explanation:

For each component, there are only two possible outcomes. Either they fail in less than 1000 hours, or they do not. The components operate independently. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

Eight components:

This means that [tex]n = 8[/tex]

Probability of 0.45 of failing in less than 1,000 hours.

So 1 - 0.45 = 0.55 probability of working for longer than 1000 hours, which means that [tex]p = 0.55[/tex]

Find the probability that the subsystem operates longer than 1000 hours.

We need at least four of the components operating. So

[tex]P(X \geq 4) = P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 4) = C_{8,4}.(0.55)^{4}.(0.45)^{4} = 0.2627[/tex]

[tex]P(X = 5) = C_{8,5}.(0.55)^{5}.(0.45)^{3} = 0.2568[/tex]

[tex]P(X = 6) = C_{8,6}.(0.55)^{6}.(0.45)^{2} = 0.1569[/tex]

[tex]P(X = 7) = C_{8,7}.(0.55)^{7}.(0.45)^{1} = 0.0548[/tex]

[tex]P(X = 8) = C_{8,8}.(0.55)^{8}.(0.45)^{0} = 0.0084[/tex]

[tex]P(X \geq 4) = P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) = 0.2627 + 0.2568 + 0.1569 + 0.0548 + 0.0084 = 0.7396[/tex]

0.7396 = 73.96% probability that the subsystem operates longer than 1000 hours.

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:

AB = 37 units.

Step-by-step explanation:

Solve for AB using the Pythagorean theorem:

c² = a² + b² (c being AB in this instance)

Plug in the values of the legs of the triangle:

c² = 12² + 35²

c² = 144 + 1225

c² = 1369

c = √1369

c = 37

Therefore, AB = 37.

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:

$2.70+/-$0.33

= ( $2.37, $3.03)

Therefore, the 90% confidence interval (a,b) = ( $2.37, $3.03)

Step-by-step explanation:

Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

The confidence interval of a statistical data can be written as.

x+/-zr/√n

Given that;

Mean x = $2.70

Standard deviation r = $0.93

Number of samples n = 22

Confidence interval = 90%

z(at 90% confidence) = 1.645

Substituting the values we have;

$2.70+/-1.645($0.93/√22)

$2.70+/-1.645($0.198276666210)

$2.70+/-$0.326165115916

$2.70+/-$0.33

= ( $2.37, $3.03)

Therefore, the 90% confidence interval (a,b) = ( $2.37, $3.03)

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:

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:

So in this problem, we're told that a polynomial is fact herbal and it's not a perfect square. Try no meal or a difference of two squares. Can you factor the pie? Nomi bite or polynomial without finding the G C F. So no Jacey after is allowed. So if it's not a perfect squared, try no meal. So not a perfect square. We know it's not this, and we also know it's not a difference of two squirt if it's not any of these or if it's not either of these, but we can't find the G. C F. There are three different ways we could find the factored form. You could do it by grouping where you separating the polynomial into two parts and factor them individually before combining. You could also use the sum or a difference of cubes. This is for a cubic or a um, polynomial of third degree, and you could also use fractional or negative exponents. So even if you can't find the G c f or use these methods, there are still three ways you can factor the

Step-by-step explanation:

Glad i could help!

Answer:

The relative change from 6546 and 4392 is 49.04

Step-by-step explanation:

Answer:

(1) a. 0.0009

(2) d. 0.640

(3)

(4)Not disjoint

(5) a. nearly 0.

(6)b. 0.919

Step-by-Step Explanation:

(1)Probability of a baby being born with a birth defect =3%=0.03

The probability that both babies have birth defects=0.03 X 0.03= 0.0009.

(2)The probability of contracting the influenza virus each year = 20%=0.2

Therefore, the probability of not contracting the influenza virus =1-0.2=0.8

The probability that neither baby catches the flu in a given year:

=0.8 X  0.8

=0.64

(3)

P(A)=0.1

P(B)=0.6

P(A or B)=P(A)+P(B)=0.1 + 0.6 =0.7

P(A and B)=P(A)XP(B)=0.1 X 0.6 =0.06

(4)

P(A)=0.2

P(B)=0.9

Event A and B cannot be disjoint.

(5)

The probability of an American woman aged 20 to 24 having Chlamydia infection  [tex]=\dfrac{2791.5}{100000}[/tex]

The probability that three randomly selected women in this age group have the infection

[tex]=\dfrac{2791.5}{100000} \times \dfrac{2791.5}{100000} \times \dfrac{2791.5}{100000} \\\\=0.00002175\\\approx 0[/tex]

(6)The probability of an American woman aged 20 to 24 not having Chlamydia infection  [tex]=1-\dfrac{2791.5}{100000}[/tex]

The probability that three randomly selected women in this age group do not have the infection

[tex]=\left(1-\dfrac{2791.5}{100000}\right)^3\\\\=0.9186\\\approx 0.919[/tex]

Answer:

3x+7

Step-by-step explanation:

Three times a number, let x be the number and 7 so plus 7

The algebraic expression for the given phrase is 3x+7. Therefore, the correct answer is option A.

The given phrase is "the sum of three times a number and seven".

Variables and constants are combined to generate algebraic expressions using a variety of techniques. Terms comprise expressions. A term is the sum of several elements. Both numerical and algebraic (literal) factors are acceptable.

Let the unknown number be x.

Three times of a number = 3x

The number 7 is added to the  obtained sum.

That is, 3x+7

So, the expression is 3x+7

The algebraic expression for the given phrase is 3x+7. Therefore, the correct answer is option A.

To learn more about an expression visit:

https://brainly.com/question/28170201.

#SPJ4

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:

24

Step-by-step explanation:

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

120/5 = 24

Hope this helps

Answer:

C (the third graph)

Step-by-step explanation:

This graph's function has a domain and range that both exclude one value, which is 0. The x and y values are never 0 in the function, as it approaches 0 but never meets it.

Answer:

see below

Step-by-step explanation:

This graph has an asymptote at y = 0 and x=0

This excludes these values

The domain excludes x =0

The range excludes y=0

Answer:

Solution,

a. Given,

X=4

y=3

Now,

[tex]2x + y \\ = 2 \times 4 + 3 \\ = 8 + 3 \\ = 11[/tex]

b. Given,

a=-2

b=5

Now,

[tex] {a}^{2} + b \\ = {( - 2)}^{2} + 5 \\ = 4 + 5 \\ = 9[/tex]

hope this helps...

Good luck on your assignment..

Answer:

Brianliest!

Step-by-step explanation:

4

1 in 500

500 x 4 = 2000

4 in 2000