Work out the value of x.

According to the central limit theorem, the given statement is true.

In the given question we have to check the given statement is true or false.

The given statement is:

"Based on the central limit theorem, the sample mean can be used as a good estimator of the population mean, assuming that the sample size, is sufficiently large."

As we know that the average of set of data is known as a sample mean.

Regardless of the distribution of the population, the central limit theorem states that the distribution of sample means approaches a normal distribution as the sample size increases. The Central Limit Theorem is frequently thought to hold for sample sizes equal to or larger than 30.

So according to the central limit theorem, the given statement is true.

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The required distance of Cori from where he started is 35km.

Distance is a quantitative or qualitative measurement of the distance between two objects or places. Distance can refer to a physical length or an estimation based on other criteria in physics or everyday usage. Because spatial cognition is a rich source of conceptual metaphors in human thought, the term is also used metaphorically to mean a measurement of the amount of difference between two similar objects or a degree of separation. The concept of a metric space is used to codify most such conceptions of distance, both physical and metaphorical.

Given,

Cori races her friend heading south for 9 kilometers, east for 20 kilometers, then south for 6 more kilometers.

The distance of Cori from starting point=9+20+6

=15+20

=35

Hence, the required distance of Cori from where he started is 35km.

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The magnitude of 3 4j is 5. This is because the magnitude of any complex number in the form a + bi is the square root of (a² + b²). In this case, a is 3 and b is 4, and the square root of (3² + 4²) is 5.

The magnitude of a complex number is the length of a line from the origin to the point on the complex plane that represents the number. The magnitude of 3 4j can be calculated using the Pythagorean theorem.

Using the theorem, the magnitude of 3 4j is 5. This is because 3 and 4 are the lengths of the sides of a right triangle and 5 is the length of the hypotenuse. The equation to calculate the magnitude of 3 4j is the square root of 3 squared plus 4 squared. This is written as the square root of       (3² + 4²) = 5.

The magnitude of 3 4j is 5. This is because the magnitude of any complex number in the form a + bi is the square root of (a^2 + b^2). In this case, a is 3 and b is 4, and the square root of (3^2 + 4^2) is 5. This means that the magnitude of 3 4j is 5.

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The simplified form of the expression is, negative five sixths times x plus eight.

What is word problem?

A math word problem is a mathematical question that is stated as one sentence or more and asks students to use their arithmetic skills in a "real-life" situation. Therefore, in order for kids to understand the word problem, they need to be familiar with the terminology that goes along with the mathematical symbols that they are used to.

Given that:   quantity negative two thirds times x minus 6 end quantity minus quantity negative 14 plus one sixth times x end quantity

It can be write in mathematical form as,

[tex](-\frac{2}{3}x-6) - (-14+\frac{1}{6}x)[/tex]

Simplifying the parenthesis,

[tex]= -\frac{2}{3}x-6+14-\frac{1}{6}x\\ = 8 - \frac{15}{18}x\\ = 8 - \frac{5}{6}x\\= -\frac{5}{6}x+8[/tex]

Hence, the simplified form of the expression is, negative five sixths times x plus eight

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The answer for the given statement is commercialization. Bethany and Joseph are in the commercialization phase of the new-product development process, since they are preparing budgets for a new product as well as finalizing plans for the full-scale marketing and manufacturing of the new UtiliBot.

Commercialization is the process of carrying new products or services to the market. Commercialization needs a correctly-developed three-tiered product roll-out and marketing strategy, which includes the ideation phase, the business process, and the stakeholder stage. The launch or commercialization of a new product is contemplated the final stage of new product development (NPD). Commercialization consists of stages such as production, distribution, marketing, sales, and customer support.

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The triangle ABC and XZY are proved to be congruent by SAS.

Congruence of triangles: Two triangles are supposed to be harmonious assuming each of the three comparing sides are equivalent and every one of the three relating angle are equivalent in measure. These triangles can be slides, pivoted, flipped and went to be seemed to be indistinguishable.

By the rule of SAS which means, Two sides are equal thhen the angle between the two sides is also equal (SAS: side, angle, side)

BC=YZ

AC=XZ

∠ACB=∠XZY

By SAS ΔABC≅ΔXYZ

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The required point estimate of the population mean and the margin of error are 16 and 4.

The point estimate is the value of a statistic that estimate the value of the parameter.

According to given data in the question:

Given, lower point =12, upper point = 20

we know that

Population mean(x) = 12+20/2 = 16

And formula for margin o error,

x + E = upper point  , x - E = lower point

Then, 16 + E = 20

E = 4

Similarly, 16 - E = 12

E = 4

Hence, population mean and margin of error are 16 and 4 respectively.

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The insect population after five days is 1645 in population of insects increases at a rate of 290+8t+0.6t2 insects per day.

A total of 290+8t+0.6t2 insects are added to the insect population per day. If there are P insects in the population,

then dP/dt = 290 + 8 + 0.6

since there are P insects at t=0, then

[tex]\int\limits^5_0[/tex][tex]{dP = (290 + 8 + 0.6) (290+8t+0.6t2)dt}[/tex] [after 5 days]

P(5) -V(0) = 290(5)+ 4t2 + t3/5)

P= 290t + 4t2 + t3/5) (5)

Insects: 2+ (5) 3/5 - 200 (0) + 5 (0) - 2+ (0) 3/5 P(5) - 70

= 1450 + 100 + 25-0 P(5)

= 70 + 1575 P(5) = 1645.

In the same way that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations, calculus, also known as infinitesimal calculus or "the calculus of infinitesimals," is the study of continuous change in mathematics.

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The rectangle-shaped tank is 10 feet by 8 feet by 8 feet is  4800 gallons of water.

Cubic foot holds 7.5 gallons of water

We need to find the amount of gallons of water can a rectangle-shaped tank is 10 feet by 8 feet by 8 feet.

Vol = L*W*H

10 x 8 x 8

640 cubic feet

1 cubic feet hold 7.5 gallons of water

640 cubic feet hold 7.5 x 640 = 4800

Therefore, the amount of gallons of water can a rectangle-shaped tank is 10 feet by 8 feet by 8 feet is  4800 gallons of water.

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The slope of a line perpendicular to the line whose equation is 10x - 12y = -24 is 5/6

Given equation,

10x - 12y = -24

This line's parallel has the same slope as this line. Solve for y to alter the equation in order to calculate the slope.

y = mx + b

Where m is the slope and b is the y-intercept.

From the given equation,

10x - 12y = -24            

-12y = -10x - 24

y = -10x/-12 + 24/12

y = 5x/6 + 2

Therefore, m = 5/6

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The critical numbers of the function  x³ - 6x² + 15 is 0 and 4

The given function is x³ - 6x² + 15

To find the critical value first we need to find the derivative, then set the derivative f'(x) to zero

The derivative of  x³ - 6x² + 15 is

3x³⁻¹ - 2(6)x²⁻¹  = 0

3x² - 12x = 0

3x(x - 4) = 0

3x = 0

x = 0

x - 4 = 0

x = 4

so, x = 0 or 4

Therefore, the critical numbers of the function  x³ - 6x² + 15 is 0 and 4

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To reduce 1 molecule of oxygen 4 electron are required, which means  4 Nadhs are needed for the reduction of one oxygen molecule

NADH donates one electron to become NADH⁺ + e⁻

So, the number of Nadhs are needed for the reduction of one oxygen molecule is same as the number of electrons needed for the reduction of one oxygen molecule

Water has 2 hydrogen and each hydrogen needs only one electron. Hence, four electrons along with four hydrogen atoms are required to reduce one molecule of oxygen to two molecules of water.

Therefore, To reduce 1 molecule of oxygen 4 electron are required, which means  4 Nadhs are needed for the reduction of one oxygen molecule.

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The ranking is like, D (next to the end of the wrench, B=E (middle of the wrench), F next to the top of the wrench, A (top of the wrench), C (bottom of the wrench)

Given,

Forces;

D > B=E > F > A > C

We have to rank these forces (a through f) on the basis of the magnitude of the torque they apply to the wrench, measured about an axis centered on the bolt

Magnitude of torque;

The ratio of the force's and the lever arm's magnitudes yields the torque's magnitude. Force has a dimensional formula of [M1L1T2], whereas a lever arm has [L]. Consequently, [M1L2T]2 is the dimensional formula for torque.

Here,

The ranking is;

D (next to the end of the wrench, B=E (middle of the wrench), F next to the top of the wrench, A (top of the wrench), C (bottom of the wrench)

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Answer:

1640y

Step-by-step explanation:

the reason is y is known as variables constant is number 48y is a monomial that is why it is 26840y

It will take 20 minutes to dissipate the queue that resulted from blockage if

the freeway has the capacity of 4000 vph.

Mean service rate(M) = 4000vph

Mean arrival rate(λ)  = 3000vph

Block time duration of queue (r) = 5min

Time taken to dissipate the queue =  t

t = (M * r)/(M-λ)

Substitute  the given values

t  =  (4000*5)/(4000-3000)

t = 20000/1000

t = 20minutes.

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4 is the unit digit in product .

What do Units digits mean?

Unit digit in 3⁴ = 1

Unit digit in( 3⁴)¹⁶ = 1

Unit digit in 3⁶⁵ = Unit digit in( 3⁴)¹⁶ = 1 * 3 = 3

Unit digit in 6⁵⁹ = 6

Unit digit in 7⁴ = 1

Unit digit in (7⁴)¹⁷ = 1

Unit digit in 7⁷¹ =  Unit digit in (7⁴)¹⁷ * 7³  = 1 * 3 = 3

Required digit= Unit digit in ( 3 * 6 * 3 ) = 4

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The complete question is -

What is the unit digit in the product (3⁶⁵ * 6⁵⁹ * 7⁷¹ ) = ?

Solving for the unknown variable t in the natural exponent  expression 3e^9t = 100 gave

The given expression is given in natural exponent and is solved as follows

3e^9t = 100

dividing through by 3

3e^9t / 3 = 100 / 3

e^9t = 100/3

take natural logarithm of both sides

In e^9t = In (100/3)

9t = In (100/3)

divide through by 9

9t / 9 = 3.5065578 / 9

t =  0.3896175

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The correct option is B

No, it cannot be concluded that pass/fail rates are dependent on school because the p-value = 0.9373.

In statistical hypothesis testing, the alternative hypothesis is one of the suggested propositions in the hypothesis test. In general, the purpose of a hypothesis test is to demonstrate that, under the given conditions, there is sufficient evidence to support the believability of an alternate hypothesis rather than the test's exclusive statement (null hypothesis). Because it is based on a review of the literature and previous studies, it is usually congruent with the research hypothesis.

Null hypothesis : H₀ : pass/fail rates are independent on school

Alternative Hypothesis : H₁: pass/fail rates are dependent on school

Test Statistic is,

x²stat=∑(O-E)²/E

Here O is the observed frequency and E is the Expected frequency.

E=(Row total× Column total)/Grand total

O       E                  O-E        (O-E)²        (O-E)² /E

40  41.4184       -1.4184       2.-118        0.0486

33   32.6327     0.3673     0.1349       0.0041

50    48.9490    1.0510      1.1046        0.0226

59    57.5816     1.4184       2.0118        0.0349

45   45.3673      -0.3673    0.1349       0.0030

67   68.0510      -1.0510      1.1046        0.0162

                                                          Total=0.1294

Degrees of freedom=(Number of rows-1)×(Number of columns-1)

=(2-1)×(3-1)

=2

p-value=P(x²>x²stat)=P(x²>0.1294)

For 3 degrees of freedom,

P(x²>0.1294)=0.9373

Level of significance α=0.10

As p-value is 0.9373>α:0.10

Fail to reject the null hypothesis.

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The confidence interval for the mean is (10.7485, 11.6515)

Given Data:

n = 225

×= 11.2

s = 4.1

Note that, Population standard deviation([tex]\alpha[/tex]) is unknown. So we use t distribution.

Our aim is to construct a 90% confidence interval.

c = 0.90

[tex]\alpha[/tex] = 1- c = 1- 0.90 = 0.10

[tex]\alpha[/tex]/2 = 0.10/2 = 0.05

Also, d.f = n - 1 = 225 - 1 = 224

t[tex]\alpha[/tex]/2.d.f- = t[tex]\alpha[/tex]/2.n-1 = t0.05,224 = 1.652

( use t table or t calculator to find this value..)

The margin of error is given by

E = t[tex]\alpha[/tex]/2,d.f. * (s / [tex]\sqrt{n}[/tex])

= 1.652 * (4.1/ √225)

= 0.4515

Now , confidence interval for mean(\mu) is given by:

(× - E ) <  μ< x + E)

(11.2 - 0.4515) < μ < (11.2 + 0.4515)

10.7485 < μ< 11.6515

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The probability that the wheel stops on a white slice, given that the wheel stops on a number less than 9 is 1/2.

We have given that

A spinner with 8 equally size slices numbered 1 to 8 and some slices are white and other gray in colour .

Total possible outcomes = 8 = {1,2,3,4,5,6,7,8}

we have to calculate probability that the wheel stops on a white slice, given that the wheel stops on a number less than 9?

let consider two events

A : wheel stops at white

B: wheel stops on white slice and number less than 9

favourable cases for event A = 4

= { 8,4,2,1}

P( wheel stops at white colour)

= favourable cases/total possible outcomes

= 4/8 = 1/2

favourable cases for event B = 4

= {1,2,4,8}

Probability ( wheel stops white slice with numbered less than 9)= white slice with number less than 9/ total slices numbered less than 9

= 4/8 = 1/2

Hence, the required probability is 1/2.

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Complete question:

spinner has 8 equally sized slices numbered from to 1&8 Some are white and some are grey, as shown below. 1 2 3 4 5 6 7 8 . Answer the following questions Write each answer a fraction. The wheel will be spun and will stop on a slice at random (a) What Is the probabllity that the wheel stops on grey slice, glven that the (b) wheel stops on &n even-numbered slice?

Answer: The last option, [tex]8\sqrt{2}[/tex]

Step-by-step explanation:

       When looking at this triangle, there are two things we can note about it right away. First, it's a right triangle so we can use the Pythagorean theorem. Second, the two legs of the triangle are congruent (as shown by the dash lines) so both of them are equal to 8.

       Using the Pythagorean theorem we will solve.

a² + b² = c²

(8)² + (8)² = c²

64 + 64 = c²

128 = c²

c = [tex]\sqrt{128}[/tex]

c = [tex]\sqrt{64*2}[/tex]

     c = [tex]8\sqrt{2}[/tex]

The shorted life expectancy to be in top 5% is 52.225

Given that.

Mean = 44

Standard Deviation = 5

a)

Z =36 – 44/5

Z =-8/5

Z =-1.6

P(z<-1.6)=normsdist(-1.6)=0.0548

b)

P(Z > 2) = 0.05

P(Z <=) = 1 -0.05 = 0.95

z=normsinv(0.95)=1.645

shorted life expentancy to be in top 5%=

= 44+1.645*5

Shorted life expentancy to be in top 5% = 52.225

For Minitab use:

Choose Calc > Probability Distributions > Normal.

Select Inverse cumulative probability.

In Mean, enter 44.

In Standard deviation, enter 5.

In Input column, enter Probability=0.95

Hence, The shorted life expectancy to be in top 5% is 52.225.

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Answer:

loss of $825

Step-by-step explanation:

$275 x 3 =$825

Answer: 825

Step-by-step explanation:

Just times 275 by 3 and you have the answer.

The real percentage off of pant in the store was 39.99% in the store, which was less than the stated 70% off sign present on the door of store.

The percentage off will be calculated by the formula -

Percentage off = change in cost/original cost × 100

Change in cost = original cost - new cost

Change in cost = 49.99 - 30.

Performing subtraction on Right Hand Side of the equation

Change in cost = 19.99

Keep the values in formula for calculation of percentage off -

Percentage off = 19.99/49.99 × 100

Performing division on Right Hand Side of the equation

Percentage = 0.3999 × 100

Performing multiplication on Right Hand Side of the equation

Percentage = 39.99%

Thus, there was 39.99% off.

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The weight of each beef will be 6⁴

An exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.

From the information, in a butcher shop, each slab of beef weighs 6^7 pounds and there are 6^3 containers filled with beef, the weight of each beef will be:

= Total pounds / Container

= 6^7 / 6^3.

= 6^(7 - 3).

= 6^4

The weight is 6⁴.

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The number of choice out of 7 that consumer have are 42.

The term permutation alludes to a numerical computation of the quantity of ways a specific set can be sorted out. Set forth plainly, a change is a word that depicts the quantity of ways things can be requested or organized. With stages, the request for the course of action matters.

Number of choices of side dishes does a customer have,

total dishes(n)=7 , r = 2

ⁿP₂

⁷P₂

7×6 = 42

Thus required number of ways are 42.

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The constant of proportionality of the equation  y = 1 / 4 x is 1 / 4.

Proportional relationships are relationships between two variables where their ratios are equivalent.

A proportional relationship is one in which two quantities vary directly with each other. We say the variable y varies directly as x if:  

y = k x

for some constant k , called the constant of proportionality.

Therefore, let's model the equation to the y = 1 / 4 x .

Therefore, the constant of proportionality is 1 / 4.

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The evaluation of the paths of the ellipse and hyperbola are as follows;

Part A: The vertices are; (0, 36), (0, -4)

Part B: Comet H comes closest to the sun

Part C: The location of the Sun is the location of the x-coordinate of the path of both ellipse

An ellipse is the locus of a point that moves such that the sum of the distances from two points, known as the focal points, is a constant

Part A: The standard form of the equation of a hyperbola is presented as follows;

[tex]\dfrac{(x - h)^2}{a^2} -\dfrac{(y-k)^2}{b^2} =1[/tex]

Where;

(h, ,k) = The center of the ellipse

a = Vertex to center distance

c = The distance from center to foci

The equation of an ellipse is presented as follows  

[tex]\dfrac{(x - h)^2}{a^2} +\dfrac{(y-k)^2}{b^2} =1[/tex]

The vertices of the ellipse are; a + h and k + b

The specified equation is presented as follows;

Comet E = [tex]\dfrac{(y+16)^2}{400} +\dfrac{x^2}{144} =1[/tex]

The vertices for the comet E are;

(0, 20 + 16) = (0, 36) and (0, 16 - 20) = (0, -4)

Part B: Comet H = [tex]\dfrac{(y+13)^2}{144} +\dfrac{x^2}{25} =1[/tex]

The vertex of the comet H = (0, -13 + 12) = (0, -1), and (0, -13 - 12) = (0, -25)

Based on the location of the comet H close to the origin, the comet that comes closest to the Sun is comet H

Part C; The location of the Sun at the origin is the location of the x-coordinate of the center of both comets

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Answer: (-2,-1)

Step-by-step explanation: First, plot the point. Then you go to the left 4 times. Then you plot your new point. Then go down 2 times. Plot your final point.

In Mexico, 350 dollars would be equivalent to 6769.21 Mexican Pesos.

What is currency conversion?

Currency conversion is the process of exchanging one type of currency for another to facilitate transactions in which the issuer and acquirer use different currencies. Currency conversion usually incurs some additional costs for the customer.

In Mexico, 1 US dollar = 19.34 Mexican Pesos

So In Mexico, $350 = 350 * 19.34

                                 = 6769.21 Mexican Pesos.

Hence, In Mexico, 350 dollars would be equivalent to 6769.21 Mexican Pesos.

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