1. If f(x) = x + 3 and g(x) = x² + 2x - 3, find [gxf](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 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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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 ) = ?

Answer:

The equality sign should be present in the null hypothesis during hypothesis testing. In a two-tailed hypothesis test, the rejection region's area in each tail is equal to [tex]\alpha[/tex]. If you choose an alpha of 0.01 then beta will equal 0.99

The transformations is rotate 180° and translate down.

Transformations:

Transformations can be non-rigid (when the preimage's size or shape is unaltered) or stiff (where the size is changed but the shape remains the same). These are the fundamental guidelines that this concept abides by. It is a straightforward approach to alter 2D forms. Planar transformations and spaces can be distinguished from one another using the dimensions of the operand sets. Their characteristics can also be used to classify them.The image of a shape will resemble the pre-image when its size is increased or decreased. The dimensions of the comparable figures are proportionately equal.

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Answer:

45

Step-by-step explanation:

Based on the given conditions, formulate: [tex]5.5\div\text{tan}7^o[/tex]

Calculate the approximate value: [tex]\frac{5.5}{0.122785}[/tex]

Calculate: [tex]44.793745[/tex]

Find the closest integer: 45

Answer: 45

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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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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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.

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

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 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 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 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 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: 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 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 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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Two shapes of the same size and shape are congruent. There are five conditions or rules for two triangles to be congruent. They are SSS, SAS, ASA, AAS, and RHS joint properties.

Triangle Congruence:

The congruence of two or more triangles depends on the measurements of their sides and angles. The three sides of a triangle determine its size, and its three angles determine its shape.

Two triangles are considered congruent if their pairs of corresponding sides and corresponding angles are equal.

SSS (side-side-side) :

According to this criterion, two triangles are congruent if his three sides of one triangle are equal to the corresponding sides of the other triangle.

ASA ( Angle-Side-Angle ) :

According to the ASA criterion, two triangles are congruent if any two angles and the inner side of one triangle between them are equal to the corresponding angles and inner sides of the other triangle.

SAS (Side Angle Side)

According to this criterion, two triangles are congruent if two sides and included angles of one triangle are equal to the corresponding sides and included angles of the other corresponding triangle.

AAS ( Angle - Angle Side) :

According to the AAS standard, two triangles are congruent if any two angles and the excluded side of one triangle are equal to the corresponding angles and the excluded side of the other triangle

RHS (Right Angle Two-sided)

According to this criterion, two triangles are congruent if the hypotenuse and side of one right triangle are equal to the hypotenuse and corresponding side of another right triangle.

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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 creation of anxiety to decrease maladaptive behavior occurs in  Aversion therapy; the induction of relaxation to increase an adaptive behavior occurs in Systematic desensitization.

Given,

In the question:

The question is based on fill in the blanks:

The creation of anxiety to decrease maladaptive behavior occurs in _____ therapy; the induction of relaxation to increase an adaptive behavior occurs in _____.

Let's Know:

Maladaptive Behaviour:

Maladaptive behaviors are things that you do that may shield you from changing in accordance with circumstances. Frequently found in those with social nervousness issue (SAD), maladaptive behaviors are utilized to attempt and lessen tension and dread at the time. You may accidentally build up these propensities to adapt in social and execution circumstances since it feels like they are helping you deal with your anxiety.  

Now, According to the question:

The creation of anxiety to decrease maladaptive behavior occurs in _____ therapy; the induction of relaxation to increase an adaptive behavior occurs in _____.

Hence, In the first fill up :

The answer is Aversion.

In the second fill up:

The answer is Systematic desensitization.

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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 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 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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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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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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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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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 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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