What is the value of x in the equation (StartFraction one-half EndFractionx + 12) = StartFraction one-half EndFraction(StartFraction 2 Over 3 EndFraction left-parenthesis StartFraction one-half EndFraction. x plus 12 right-parenthesis equals left-parenthesis StartFraction one-half EndFraction left-parenthesis StartFraction one-third EndFraction x plus 14 right-parenthesis minus 3.x + 14) – 3?

Answer:

Answer: (0.4356,0.4844)

Step-by-step explanation:

Use Ti 84

use function "1-PropZInt".

Enter x = 736

         n = 1600

         c= 0.95

Answer: (0.4356,0.4844)

Answer:

  2.908 s

Step-by-step explanation:

The "work" is most easily done by a graphing calculator. We only need to tell it the equation of motion.

For speeds in feet per second, the appropriate equation for vertical ballistic motion is ...

  h(t) = -16t² +v₀t +s₀

where v₀ is the initial vertical velocity in ft/s and s₀ is the initial height in feet. The vertical velocity is the vertical component of the initial velocity vector, so is (65 ft/s)(sin(44°)). We want to find t for h=0.

  0 = -16t² +65sin(44°) +4

Dividing by -16 gives ...

  0 = t^2 -2.82205t -0.2500

Using the quadratic formula, we find ...

  t ≈ (2.82205 ±√(2.82205² -4(1)(-0.25))/2 ≈ 1.41103 +√2.24099

  t ≈ 2.90802

It will take about 2.908 seconds for the discus to reach the ground.

_____

Comment on the question

You're apparently supposed to use the equation for ballistic motion even though we know a discus has a shape that allows it to "fly". It doesn't drop like a rock would.

Answer:

Step-by-step explanation

p - the price of pizza

c- the price of a bottle of coke

p = c+3.2

3p + c=19.4

3* (c+3.2)+c=19.4

3*c+3*3.2+c=19.4

3c+c+9.6=19.4

4c+9.6=19.4

-9.6 -9.6

4c=9.8

:4. :4

c=2.45

p=2.45+3.2=5.65

verify : 3*5.65+2.45=16.95+2.45=19.40

Answer:

total surface area = 672 cm^2

Step-by-step explanation:

radius of hemisphere, r = 7 cm

radius of base of cone, r = 7 cm

height of cone, h = 22-7 = 15 cm

slant length of cone, L = sqrt(7^2+15^2) = sqrt(274)

Area of the cone

= pi r L

= pi * 7 * sqrt(274)

= 115.87 pi

= 364.02 cm^2

Area of hemisphere

= 2 pi r^2

= 2 pi * 7^2

= 307.88 cm^2

Total surface area = 364.02 + 307.88 = 671.89 cm^2

Answer:

z = 85°

Step-by-step explanation:

By inscribed angle theorem:

The measure of inscribed angle is half the measure of the arc intercepted by it.

[tex]\therefore z = \frac{1}{2} \times 170 \degree \\ \\ \huge \orange {\boxed {\therefore z = 85 \degree}} [/tex]

The answer is Ferris wheel, since it is a circular object and will display symmetry even when rotated.

Answer:

Minimum: $25,200

Maximum: $44,800

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:

[tex]\mu = 35000, \sigma = 5000[/tex]

What are the minimum and the maximum starting salaries of the middle 95% of the graduates

Minimum: 50 - (95/2) = 2.5th percentile.

Maximum: 50 + (95/2) = 97.5th percentile

2.5th percentile:

X when Z has a pvalue of 0.025. So X when Z = -1.96.

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

[tex]-1.96 = \frac{X - 35000}{5000}[/tex]

[tex]X - 35000 = -1.96*5000[/tex]

[tex]X = 25200[/tex]

The minimum is $25,200

97.5th percentile:

X when Z has a pvalue of 0.975. So X when Z = 1.96.

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

[tex]1.96 = \frac{X - 35000}{5000}[/tex]

[tex]X - 35000 = 1.96*5000[/tex]

[tex]X = 44800[/tex]

The maximum is $44,800

Answer:

Step-by-step explanation:

Given the number of liver transplants performed in a particular country in year x approximated by f (x) = -239.7+ 2390lnx where x≥5. If x = 5 corresponds to year 1995. x will be equivalent to 23 in the year 2013.

a) Number of transplant in 2013 can be gotten by substituting x = 18 into the equation above.

f (x) = -239.7+ 2390lnx

f (23) = -239.7+ 2390ln 23

f (23) = -239.7+ 2390(3.14)

f(23) = 7264.9

The number of liver transplant in 2013 is approximately 7265

b) If f (x) = -239.7+ 2390lnx

f'(x) = 2390 * 1/x

f'(23) = 2390/23

f'(23) = 103.913

Answer:

  C.)  f(x) = 3.56(2.04^x)

Step-by-step explanation:

The ratios of adjacent table values is about 2, so that is the approximate base of the exponential factor.

A graphing calculator figures the best fit is ...

  f(x) = 3.66(2.02^x) . . . . closest to choice C

__

Choices A and D are logarithmic functions, not exponential functions. Choice B has too large a base.

Answer:

f(x) = 3.56(2.04)^x

Step-by-step explanation:

I took the test

The table of the probability is missing, so i have attached it.

Answer:

μ = 0.919

The interpretation of this is that;on the average, an individual aged 15 years or older has been involved in 0.919 marriages.

Step-by-step explanation:

The expected value which is also called mean value is denoted by the symbol μ. It is defined as the sum of the product of each possibility x with it's probability P(x) as the formula;

μ = Σx.P(x) = (0 × 0.272) + (1 × 0.575) + (2 × 0.121) + (3 × 0.027) + (4 × 0.004) + (5 × 0.001)

μ = 0.919

Thus, the interpretation of this is that;on the average, an individual aged 15 years or older has been involved in 0.919 marriages.

The interpretation of the mean of the random variable X is 0.919.

Here the interpretation should represent the average and it should be individual aged 15 years or more so it should be involved in 0.919 marriage.

Now the mean is

μ = Σx.P(x) = (0 × 0.272) + (1 × 0.575) + (2 × 0.121) + (3 × 0.027) + (4 × 0.004) + (5 × 0.001)

μ = 0.919

Hence, The interpretation of the mean of the random variable X is 0.919.

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Answer:

The order in which you solve the operations will provide different results and to be able to get the right answer you have to be familiar with the order of operations to know the appropiate steps to solve an operation. According to the order of operations in mathematics, exponents are given precedence over addition and multiplication. Because of that, the exponent is the first you have to solve.

3 + 2 * 3^2

3+2*9

Then, mutiplication is given precedence over addition:

3+18

Now, you can solve the addition and the result is: 21

Because of this, the answer is:

• 3 +( 2 * (3^2)) = 21

Answer:

Mean increase or decrease (same quantity) according to the quantity of the increment or reduction

As all elements were equally affected the standard deviation will remain the same

Step-by-step explanation:

For the original set of salaries: ( In thousands of $ )

51, 53, 48, 62, 34, 34, 51, 53, 48, 30, 62, 51, 46

Mean = μ₀ = 47,92

Standard deviation  =  σ = 9,56

If we raise all salaries in the same amount  ( 5 000 $ ), the nw set becomes

56,58,53,67,39,39,56,58,53,35,67,56,51

Mean   =  μ₀´  = 52,92

Standard deviation  =  σ´ = 9,56

And if we reduce salaries in the same quantity ( 2000 $ ) the set is

49,51,46,60,32,32,49,51,46,28,60,49,44

Mean μ₀´´ = 45,92

Standard deviation  σ´´ = 9,56

What we observe

1.-The uniform increase of salaries, increase the mean in the same amount

2.-The uniform reduction of salaries, reduce the mean in the same quantity

3.-The standard deviation in all the sets remains the same.

We can describe the situation as a translation of the set along x-axis (salaries). If we normalized the three curves we will get a taller curve (in the first case) and a smaller one in the second, but the  data spread around the mean will be the same

Any uniform change in the data will directly affect the mean value

Uniform changes in values in data set will keep standard deviation constant

Answer:

1.875

Step-by-step explanation:

To find the expected winnings, we need to find the probability of all cases possible, multiply each case by the value of the case, and sum all these products.

In the die, we have 6 possible values, each one with a probability of 1/6, and the value of each output is half the value in the die, so we have:

[tex]E_1 = \frac{1}{6}\frac{1}{2} + \frac{1}{6}\frac{2}{2} +\frac{1}{6}\frac{3}{2} +\frac{1}{6}\frac{4}{2} +\frac{1}{6}\frac{5}{2} +\frac{1}{6}\frac{6}{2}[/tex]

[tex]E_1 = \frac{1}{12}(1+2+3+4+5+6)[/tex]

[tex]E_1 = \frac{21}{12} = \frac{7}{4}[/tex]

Now, analyzing the coin, we have heads or tails, each one with 1/2 probability. The value of the heads is 2 wins, and the value of the tails is the expected value of the die we calculated above, so we have:

[tex]E_2 = \frac{1}{2}2 + \frac{1}{2}E_1[/tex]

[tex]E_2 = 1 + \frac{1}{2}\frac{7}{4}[/tex]

[tex]E_2 = 1 + \frac{7}{8}[/tex]

[tex]E_2 = \frac{15}{8} = 1.875[/tex]

Answer:

2/11

Step-by-step explanation:

9 out of 11 are pirates

11-9 =2

2 are not pirates

2 out of 11 are not pirates

2/11

Answer:

all real numbers greater than or equal to zero

Step-by-step explanation:

The domain of the real function f(x) = sqrt(x) is

all real numbers greater than or equal to zero

because when x < 0, then f(x) will become complex, which does not belong to a real function.

Answer:

[tex]\boxed{\sf \ \ \text{Jori is 42} \ \ }[/tex]

Step-by-step explanation:

Hello,

Let's not J Jori's age

Pamela is 7 years older than Jori so here age is J + 7

The sum of their age is 91 so

J + ( J + 7 ) = 91

<=>

2J + 7 = 91  subtract 7

2J = 91 - 7 = 84  divide by 2

J = 84/2 = 42

So Jori is 42 and Pamela is 49

hope this helps

Answer:

line passes through the vertex

Step-by-step explanation:

f(x)=-3(x+2)^2+4

x=-2 it is the x of the vertex

Answer: Albert is wrong

Step-by-step explanation:

You first have to subtract Plant B's measurement from Plant A's measurement.

3 7/8-2 1/4 => 3 7/8-2 2/8

If you solve it you get 1 5/8. Since it cannot be reduced this is the final answer.

Answer:

[tex] P(X=8)[/tex]

And using the probability mass function we got:

[tex]P(X=8)=(20C8)(0.58)^8 (1-0.58)^{20-8}=0.0486[/tex]

Step-by-step explanation:

Let X the random variable of interest, on this case we now that:

[tex]X \sim Binom(n=20, p=1-0.42=0.58)[/tex]

The probability mass function for the Binomial distribution is given as:

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

Where (nCx) means combinatory and it's given by this formula:

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

And we want to find this probability:

[tex] P(X=8)[/tex]

And using the probability mass function we got:

[tex]P(X=8)=(20C8)(0.58)^8 (1-0.58)^{20-8}=0.0486[/tex]

The probability of exactly eight successful trials is 0.0486 and this can be determined by using the formula of the probability mass function.

Given :

According to the binomial distribution, the probability mass function is given by:

[tex]\rm P(X) = \; (^nC_x )(p^x)(1-p)^{n-x}[/tex]

where the value of n is 20 and the value of (p = 1 - 0.42 = 0.58).

Now, substitute the values of known terms in the above expression of probability mass function.

[tex]\rm P(X=8) = \; (^{20}C_8 )((0.58)^8)(1-0.58)^{20-8}[/tex]

Simplify the above expression in order to determine the probability of exactly eight successful trials.

P(X = 8) = 0.0486

For more information, refer to the link given below:

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Answer:

Imani traveled faster because her distance surpassed Linda's distance after the fourth hour.

Step-by-step explanation:

1. Understand the slope:

      Ok, so the slope basically tells us how fast Imani and Linda traveled, so if we solve for the slope we know how fast Imani and Linda traveled.

2. Find Linda's slope:

      - Take any two points: (0,10) and (1, 65).

      Slope = (y1 - y2)/(x1 - x2)

                = (65-10)/(1-0)

                   = 55

    Since the slope is 55, we know her speed is 55 miles per hour.

2. Find Imani's slope:

      - Take any two points: (0,0) and (1, 60).

      Slope = (y1 - y2)/(x1 - x2)

                = (60-0)/(1-0)

                   = 60

    Since the slope is 60, we know her speed is 60 miles per hour.  

3. Compare: Since 60>55, we know Imani traveled faster. If we look at options, we can see there's only one answer which shows that Imani traveled faster, so that must be the answer.

Linda travelled faster than Imani. Therefore, option A and B are correct options.

The coordinates from the given graph are (2, 120) and (4, 240).

Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them. The length of the lines and position of the points do not matter.

Slope with (2, 120) and (4, 240) is

Slope (y2-y1)/(x2-x1)

= (240-120)/(4-2)

= 120/2

= 60

Put m=60 and (x, y)=(2, 120) in y=mx+c, we get

120=60(2)+c

c=0

So, equation is y=60x

Put x=0, 1, 2, 3 and 4, we get

y= 0, 60, 120, 180, 240

(0, 0), (1, 60), (2, 120), (3, 180) and (4, 240)

Linda travelled faster than Imani. Therefore, option A and B are correct options.

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Answer:

33% probability that he or she has a basic model

Step-by-step explanation:

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Has an extended warranty

Event B: Basic model

Probability of an extended warranty:

48% of 33%(basic model)

48% of 100 - 33 = 67%(deluxe model).

So

[tex]P(A) = 0.48*0.33 + 0.48*0.67 = 0.48[/tex]

Intersection:

48% of 33%(basic model with extended warranty).

So

[tex]P(A \cap B) = 0.48*0.33 = 0.1584[/tex]

How likely is it that he or she has a basic model

[tex]P(B|A) = \frac{0.1584}{0.48} = 0.33[/tex]

33% probability that he or she has a basic model

Answer:

  (x, y, z) = (45°, 57°, 78°)

Step-by-step explanation:

The problem statement tells you ...

  x + y + z = 180

  -3x +y +z = 0

  0x -y +z = 21

__

Subtracting the second equation from the first gives ...

  4x = 180

  x = 45 . . . . . . divide by 4

Substituting this into the first equation and adding the third equation gives ...

  (45 +y +z) +(-y +z) = (180) +(21)

  2z = 156 . . . . simplify, subtract 45

  z = 78 . . . . . . divide by 2

  y = z -21 = 57

The angle measures are ...

  (x, y, z) = (45°, 57°, 78°)

Answer:  18 in²

Step-by-step explanation:

S(fig1)=32 in² . We know that the figures are similar and  the correspondonding sides are a1=12  and a2=9

So the coefficient of similarity is k=9/12=3/4

S(fig2)=S(fig1)*k²

S(fig2)=32*(3/4)²=32*9/16=18 in²

The solution is A = 18 inches²

The proportion relation is given by k = 3/4 and the value of A = 18 inches²

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

The proportional equation is given as y ∝ x

And , y = kx where k is the proportionality constant

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Given data ,

Let the proportion equation be represented as A

Now , the constant of proportionality be k

From the figures , the two figures are similar

Constant of proportionality k = ( side of first figure / side of second figure)

k = 9/12

k = 3/4

Now , the area of the first figure A = 32 ( k )²

On simplifying the equation , we get

A = 32 ( 3/4 )²

A = ( 32 x 9 ) / 16

A = 2 x 9

A = 18 inches²

Therefore , the value of A is 18 inches²

Hence , the proportion is A = 18

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Answer:

z-test.

Step-by-step explanation:

We want to perform an hypothesis test for a population mean.

In the case that the standard deviation of the population is known and the population distribution is normal, even if the sample is small, we will use a z-test.

The usual case is to not know the standard deviation of the population, in which case a t-test is adequate instead of a z-test, taking into account the degrees of freedom of the sample.

Answer:

-The independent variable is whether the motivational signs were posted, and the dependent variable is the amount of use of the stairs.

-Nominal scale.

Step-by-step explanation:

Independent variable: In research methods, the term "independent variable" is described as the variable that is being altered, manipulated, or changed by an investigator to see its effects on the dependent variable in specific research or experiment.

Dependent variable: In research methods, the term "dependent variable" is described as the variable that is being measured, analysed, or tested in an experiment by the experimenter or researcher. The dependent variable is being directly affected by the independent variable.

Nominal scale: In research methods, the term "nominal scale" is determined as one the different measurement scales in which a specific number is being served as labels or tags only and to classify and identify an object.

Answer:

9 - 4 1/2 = 4 1/2.

To calculate this you can do (9 - 4 - 1) + (1 - 1/2).

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▹ Answer

4 1/2 or 4.5

▹ Step-by-Step Explanation

[tex]9 - 4\frac{1}{2} \\= 9 - \frac{9}{2} \\Common denominator = 2\\\\\frac{18}{2} - \frac{9}{2} \\= \frac{9}{2} \\\\= 4 \frac{1}{2} or 4.5[/tex]

Hope this helps!

CloutAnswers ❁

Brainliest is greatly appreciated!

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Answer:

A. y=-2x-4

Step-by-step explanation:

The slope is negative when the line is going down from up.

Options B and D are wrong.

The y-intercept is (0, -4) as shown in the graph.

Option C is wrong.

y = mx + b

y = -2x - 4

Answer:

t = 5.6 day

t =5 days 14 hours 24 minutes

Step-by-step explanation:

Half life is the time it will take for the original value or quantity I'd a particular substance to decrease by half of it's original self.

N = N•e(-kt)

N• = 25

K = 0.1229

Then

N = 25/2 = 12.5

The reason because at the half life , it's original value will decrease to half.

Let's solve for the half life t

N = N•e(-kt)

12.5 = 25e(-0.1229t)

12.5/25 = e(-0.1229t)

0.5 = e(-0.1229t)

In 0.5 =-0.1229t

-0.69314 = -0.1229t

-0.69314/-0.1229 = t

5.6399 = t

To the nearest tenth

5.6 days = t