If we express $2x^2 + 6x + 11$ in the form $a(x - h)^2 + k$, then what is $h$? (ignore the $)

Let's think about this. MQ is given to be a length of 24 units, PR a length of 10 whilst we must determine what length PM must be in order to satisfy the criteria of parallelogram MPQR to be a rhombus.

Assume this figure is a rhombus, rhombus MPQR. If that is so, all sides must be congruent, and the diagonals must be perpendicular ( ⊥ ) by " Properties of a Rhombus. " That would make triangle( s ) MRQ and say RMP isosceles, and by the Coincidence Theorem, MS ≅ QS, and RS ≅ PS. Therefore -

[tex]MS = 1 / 2( 24 ) = 12 = QS,\\RS = 1 / 2( 10 ) = 5 = PS[/tex]

PS and MS are legs of a right triangle, so by Pythagorean Theorem we can determine the hypotenuse, or in other words the length of PM. This length would make parallelogram MPQR a rhombus,

[tex]( PM )^2 = ( MS )^2 + ( PS )^2,\\PM^2 = ( 12 )^2 + ( 5 )^2,\\PM^2 = 144 + 25 = 169\\-----\\PM = 13[/tex]

And thus, PM should be 13 in length to make parallelogram MPQR a rhombus.

Answer:

Step-by-step explanation:

(a) The linear approximation of g(x) at x=b will be ...

  g(x) ≈ g'(b)(x -b) +g(b)

Using the given relations, this is ...

  g'(3) = 3² +7 = 16

  g(x) ≈ 16(x -3) -1

Then the points of interest are ...

  g(2.95) ≈ 16(2.95 -3) -1 = -1.8

  g(3.05) ≈ 16(3.05 -3) -1 = -0.2

__

(b) At x=3, the slope of the curve is increasing, so the tangent lies below the curve. The estimates are too small. (Matches description A.)

Answer:

Yes. There is enough evidence to support the claim that the proportion of Americans feel the United States could develop a way to protect itself from atomic bombs in 1945 is significantly greater than 0.5.

Step-by-step explanation:

The question is incomplete:

In October 1945, the Gallup organization asked 1487 randomly sampled Americans, "Do you think we can develop a way to protect ourselves from atomic bombs in case other countries tried to use them against us?" with 788 responding yes. Did a majority of Americans feel the United States could develop a way to protect itself from atomic bombs in 1945? Use the α=0.05 level of significance.

This is a hypothesis test for a proportion.

The claim is that the proportion of Americans feel the United States could develop a way to protect itself from atomic bombs in 1945 is significantly greater than 0.5.

Then, the null and alternative hypothesis are:

H_0: \pi=0.5\\\\H_a:\pi>0.5

The significance level is 0.05.

The sample has a size n=1487.

The sample proportion is p=0.53.

[tex]p=X/n=788/1487=0.53[/tex]

The standard error of the proportion is:

[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.5*0.5}{1487}}\\\\\\ \sigma_p=\sqrt{0.000168}=0.013[/tex]

Then, we can calculate the z-statistic as:

[tex]z=\dfrac{p-\pi-0.5/n}{\sigma_p}=\dfrac{0.53-0.5-0.5/1487}{0.013}=\dfrac{0.03}{0.013}=2.288[/tex]

This test is a right-tailed test, so the P-value for this test is calculated as:

[tex]\text{P-value}=P(z>2.288)=0.011[/tex]

As the P-value (0.011) is smaller than the significance level (0.05), the effect is  significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the proportion of Americans feel the United States could develop a way to protect itself from atomic bombs in 1945 is significantly greater than 0.5.

Answer: C. A function only

Step-by-step explanation:

There is not relation to the dots on the graph.

The graph represents a relation only.

Hence option D is correct.

Since we know that

A function is a mathematical concept that describes a relationship between two sets, where each element in the first set (the domain) corresponds to exactly one element in the second set (the range). In simpler terms, a function is a rule that assigns each input value a unique output value.

In contrast, a relation is a general concept that describes any set of objects that have some kind of relationship to each other. In mathematics, a relation is often represented as a set of ordered pairs and can be visualized as a graph. For example, a relation could be a set of all points on a circle, represented as an ordered pair of x and y coordinates.

As we can see in the graph

There is more than one value for the number represented on the X-axis

We can see that at a particular age, there is more than one gray hairs worker.

Hence the graph represents a relation only.

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Answer:

D. [tex]tan(30^\circ+45^\circ)[/tex] is the correct answer.

Step-by-step explanation:

The given situation can be represented as a figure attached in answer area.

B is the base of tree.

C is the base of wires.

A and D are the end of 2 wires supporting the tree.

[tex]\angle DCB =45^\circ\\\angle ACB =75^\circ\\[/tex]

Here, we need to find the Height of the tree which is represented the by side AB.

and we are given that bases of wires and tree base are at a distance 4 ft.

i.e. side BC = 4 ft

If we look at the [tex]\triangle ABC[/tex], we are given the base BC and the [tex]\angle ACB[/tex], and the perpendicular is to be find out.

We can use trigonometric identity:

[tex]tan\theta =\dfrac{Perpendicular}{Base}[/tex]

[tex]tan 75^\circ = \dfrac{AB}{BC}\\\bold {tan (45+30)^\circ }= \dfrac{AB}{4}\\\Rightarrow AB = \bold {tan (45+30)^\circ } \times 4 = 14.93\ ft[/tex]

Hence, D. [tex]tan(30^\circ+45^\circ)[/tex] is the correct answer.

Answer:

D

Step-by-step explanation:

Answer:

Assuming a Poisson distribution for the weekly sales, the probability that the store will sell exactly seven card tables in a given week is 0.060

Step-by-step explanation:

In order to calculate the probability that the store will sell exactly seven card tables in a given week we would have to calculate the following formula:

probability that the store will sell exactly seven card tables in a given week= e∧-λ*λ∧x/x!

According to the given data furniture store sells four card tables in a week, hence λ=4

Therefore, probability that the store will sell exactly seven card tables in a given week=e∧-4*4∧7/7!

probability that the store will sell exactly seven card tables in a given week=0.060

Assuming a Poisson distribution for the weekly sales, the probability that the store will sell exactly seven card tables in a given week is 0.060

Answer:

Its 69.1 cm

Step-by-step explanation:

To find circumstance of any circle main formula is 2*pie*r .

Here pie is equal to 3.14 approx and r =11 cm

so

2*3.14*11 = 69.08 cm

This little difference is just because of pie's approximately value used

Answer:

The population of four years ago was 100,783 inhabitants

Step-by-step explanation:

The population of the city after t years is given by the following equation:

[tex]P(t) = P(0)(1-r)^{t}[/tex]

In which P(0) is the initial population and r is the decrease rate, as a decimal.

2 years later, that is to say two years ago, the population of this same city was 81,000 inhabitants and today it is 65,610.

This means that:

[tex]P(2) = 81000, P(4) = 65610[/tex]

We are going to use this to build a system, and find P(0), which is the initial population(four years ago).

P(2) = 81000

[tex]P(t) = P(0)(1-r)^{t}[/tex]

[tex]81000 = P(0)(1-r)^{2}[/tex]

[tex](1-r)^{2} = \frac{81000}{P(0)}[/tex]

P(4) = 65610

[tex]P(t) = P(0)(1-r)^{t}[/tex]

[tex]65100 = P(0)(1-r)^{4}[/tex]

[tex]65100 = P(0)((1-r)^{2})^{2}[/tex]

Since [tex](1-r)^{2} = \frac{81000}{P(0)}[/tex]

[tex]65100 = P(0)(\frac{81000}{P(0)})^{2}[/tex]

Using P(0) = x

[tex]65100 = x(\frac{81000}{x})^{2}[/tex]

[tex]65100 = \frac{6561000000x}{x^{2}}[/tex]

[tex]65100x^{2} = 6561000000x[/tex]

[tex]65100x^{2} - 6561000000x[/tex]

[tex]x(65100x - 6561000000) = 0[/tex]

x = 0, which does not interest us, or:

[tex]65100x - 6561000000 = 0[/tex]

[tex]65100x = 6561000000[/tex]

[tex]x = \frac{6561000000}{65100}[/tex]

[tex]x = 100,783[/tex]

The population of four years ago was 100,783 inhabitants

Answer:

Inequality Form:

x≥130

Step-by-step explanation:

isolate the variable by dividing each side by factors that don’t contain the variable.

Answer:

1,474,951.

Step-by-step explanation:

Given a population that increases by a constant percentage, we can model the population's growth using the exponential model.

[tex]P(t)=P_o(1+r)^t,$ where \left\{\begin{array}{lll}P_o=$Initial Population\\r$=Growth rate\\$t=time (in years)\end{array}\right\\P_o=919,716\\r=3.7\%=0.037\\$t=13 years[/tex]

Therefore, the population of the city in 13 years time will be:

[tex]P(t)=919,716(1+0.037)^{13}\\\\=919,716(1.037)^{13}\\\\=1,474,950.9\\\\\approx 1,474,951[/tex]

The population be at that time will be approximately 1,474,951.

Answer:

a. 0.5413

b. 20

c. 0.3724

d. 4.4721

Step-by-step explanation:

Solution:-

- We will start by defining a random variable X.

                     X : The number of support requests arrived

- The event defined by the random variable ( X ) is assumed to follow Poisson distribution. This means the number of request in two distinct time intervals are independent from one another. Also the probability of success is linear within a time interval.

- The time interval is basically the time required for a poisson event to occur. Consequently, each distributions is defined by its parameter(s).

- Poisson distribution is defined by " Rate at which the event occurs " - ( λ ). So in our case the rate at which a support request arrives in a defined time interval. We define our distributions as follows:

                                   X ~ Po ( λ )

Where,                        λ = 1 / 30 mins

Hence,

                                   X ~ Po ( 1/30 )

a)

- We see that the time interval for events has been expanded from 30 minutes to 1 hour. However, the rate ( λ ) is given per 30 mins. In such cases we utilize the second property of Poisson distribution i.e the probability of occurrence is proportional within a time interval. Then we scale the given rate to a larger time interval as follows:

                                   λ* =  [tex]\frac{1}{\frac{1}{2} hr} = \frac{2}{1hr}[/tex]

- We redefine our distribution as follows:

                                   X ~ Po ( 2/1 hr )

- Next we utilize the probability density function for poisson process and accumulate the probability for 2 to 4 request in an hour.

                           [tex]P ( X = x ) = \frac{e^-^l^a^m^b^d^a . lambda^x}{x!}[/tex]

- The required probability is:

                   [tex]P ( 2 \leq X \leq 4 ) = P ( X = 2 ) + P ( X = 3 ) + P ( X = 4 )\\\\P ( 2 \leq X \leq 4 ) = \frac{e^-^2 . 2^2}{2!} + \frac{e^-^2 . 2^3}{3!} + \frac{e^-^2 . 2^4}{4!}\\\\P ( 2 \leq X \leq 4 ) = 0.27067 + 0.18044 + 0.09022\\\\P ( 2 \leq X \leq 4 ) = 0.5413[/tex]            Answer    

b)

We will repeat the process we did in the previous part and scale the poisson parameter ( λ ) to a 10 hour work interval as follows:

                               λ* = [tex]\frac{2}{1 hr} * \frac{10}{10} = \frac{20}{10 hr}[/tex]

- The expected value of the poisson distribution is given as:

                             E ( X ) = λ

Hence,

                            E ( X ) = 20  (10 hour work day)    .... Answer

c)

- We redefine our distribution as follows:

                                   X ~ Po ( 20/10 hr )

- Next we utilize the probability density function for poisson process and accumulate the probability for 20 to 24 request in an 10 hour work day.

                           [tex]P ( X = x ) = \frac{e^-^l^a^m^b^d^a . lambda^x}{x!}[/tex]

- The required probability is:

                   [tex]P ( 20 \leq X \leq 24 ) = P ( X = 20 ) + P ( X = 21 ) + P ( X = 22 )+P ( X = 23 ) + P ( X = 24 )\\\\P ( 20 \leq X \leq 24 ) = \frac{e^-^2^0 . 20^2^0}{20!} + \frac{e^-^2^0 . 20^2^1}{21!} + \frac{e^-^2^0 . 20^2^2}{22!} + \frac{e^-^2^0 . 20^2^3}{23!} + \frac{e^-^2^0 . 20^2^4}{24!} \\\\P ( 20 \leq X \leq 24 ) = 0.0883 +0.08460 +0.07691 +0.06688+0.05573\\\\P ( 20 \leq X \leq 24 ) = 0.3724[/tex]            Answer  

c)

The standard deviation of the poisson process is determined from the application of Poisson Limit theorem. I.e Normal approximation of Poisson distribution. The results are:

                                σ = √λ

                                σ = √20

                                σ = 4.4721 ... Answer

E(m) = 2000 + 0.15( m - 20000) is the function calculates his monthly earnings.

The composition of a function is an operation in which two functions say f and g generate a new function say h in the sort of manner that h(x) = g(f(x)). It method right here characteristic g is carried out to the characteristic of x. So, basically, a feature is implemented to the end result of another feature.

In systems engineering, software engineering, and pc science, a function version or practical model is an established illustration of the capabilities (activities, movements, procedures, operations) inside the modeled system or situation vicinity.

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Answer:

8.) $7325.98

9.) $8218.10

Step-by-step explanation:

Compounded Interest Rate Formula: A = P(1 + r/n)^nt

Simply plug in our known variables into the formula:

A = 6000(1 + 0.04/12)^60 = 7325.98

A = 5000(1 + 0.05/4)^40 = 8218.10

Answer:

  y = -1000x +11000

Step-by-step explanation:

Given:

  (x, y) = (sales price, number sold) = (3, 8000), (6, 5000)

Find:

  slope-intercept equation for a line through these points

Solution:

When given two points, it often works well to start with the 2-point form of the equation for a line.

  y = (y2 -y1)/(x2 -x1)(x -x1) +y1

Filling in the given points, you have ...

  y = (5000 -8000)/(6 -3)/(x -3) +8000

  y = (-3000/3)(x -3) +8000

  y = -1000x +3000 +8000 . . . . eliminate parentheses

  y = -1000x +11000 . . . . the desired equation

Answer:

A) According to the regression equation, regardless of whether or not smoking is allowed in bars, the number of cigarette packs sold per 1000 people decreases by approximately 1424 for each additional dollar of cigarette tax.

Step-by-step explanation:

Given the regression equation:

PACKS i= 57221.431732 − 1423.696906TAXi + 155.441784BARSi + eᵢ.

BARS i= 1 if city i allows smoking in bars

BARSi = 0 if city i does not allow smoking in bars

R2 = 0.351292

P-value = 0.086529

Conlusion:

Simnce p value, 0.0865 is greater than level of significance, 0.05, BARS is not significant. Thus, allowing smoking in bars increase cigarette sales, since the coefficient of BARS is positive.

Correct answer is option A.

According to the regression equation, regardless of whether or not smoking is allowed in bars, the number of cigarette packs sold per 1000 people decreases by approximately 1424 for each additional dollar of cigarette tax.

Answer:

Shifting/Translating the function

Step-by-step explanation:

Answer:

Step-by-step explanation:

nice

Answer:

3/13

Step-by-step explanation:

There are a total of 13 fish (6+ 7 = 13). There are 3 small, red fish. (1/2 · 6 = 3). Put the number of small, red fish over the total number of fish because the small, red fish is being selected from the entire tank of fish. 3/13 cannot be simplified any further.

Answer:

[tex]a_n = 10-3(n - 1)[/tex]

10 + 7 + 4 + 1 + -2 + -5

Step-by-step explanation:

Explicit Arithmetic Formula: [tex]a_n = a_1 + d(n-1)[/tex]

To find d, take the common difference between 2 numbers.

To find the other terms of the sequence, plug them into the explicit formula or subtract 3 from the given numbers.

Answer:

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Step-by-step explanation:

Using the slope formula

m = (y2-y1)/ (x2-x1)

and the given points

m = ( 8 - -1)/( 2-2)

    = (8+1) / 0

We cannot divide by 0 so the slope is undefined

Answer:

  $450,000

Step-by-step explanation:

  chad = (1/3)profit

  3×chad = profit = 3×$150,000 . . . . multiply the equation by 3; fill given value

  profit = $450,000

The company's overall profits were $450,000.

Answer:

x = - [tex]\frac{5}{3}[/tex] , x = 1

Step-by-step explanation:

Given

2x - 5 = - 3x² ( add 3x² to both sides )

3x² + 2x - 5 = 0 ← in standard form

Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 3 × - 5 = - 15 and sum = + 2

The factors are - 3 and + 5

Use these factors to split the x- term

3x² - 3x + 5x - 5 = 0 ( factor the first/second and third/fourth terms )

3x(x - 1) + 5(x - 1) = 0 ← factor out (x - 1) from each term

(x - 1)(3x + 5) = 0 ← in factored form

Equate each factor to zero and solve for x

3x + 5 = 0 ⇒ 3x = - 5 ⇒ x = - [tex]\frac{5}{3}[/tex]

x - 1 = 0 ⇒ x = 1

12 teachers...

Hope this helps.....

Answer: D, 6

Step-by-step explanation:

Match each side from XYZ to ABC (you are trying to find the scale factor of triangle 1 to triangle 2)  into a fraction then simplify

Ex 30/5= 6 or  24/6= 6 or 18/3

Answer:

0.5kg

2kg

0.7kg

b668_*;

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gcjoxfj

vxfhb

Answer:

Height of the building is 40 feet

Step-by-step explanation:

From the figure attached,

Height of the person DE = 5 feet

Let height of the building BC = h feet

Since, ΔABC ~ ΔADE,

Their corresponding sides will be proportional,

[tex]\frac{DE}{BC}=\frac{AD}{AB}[/tex]

[tex]\frac{5}{h}=\frac{13}{104}[/tex]

h = [tex]\frac{104\times 5}{13}[/tex]

h = 40 feet

Therefore, height of the building is 40 feet.

Answer:

190 cans

Step-by-step explanation:

Total cans collected by Jacob and Dustin for the school can job = 245

Amount of cans they both gave to Dustin's little sister = 55

Now because they gave out cast out of the total they initially had, there would be a deduction in the amount both boys would now have.

To determine the amount the boys are left with, we would deduct 55 casts from the amount they had which 245.

Amount of cans left = 245-55 = 190

Amount of cans left for the boys class = 190 cans

Answer:

F(4)=1/3*4^4

F(4)=256/3

Step-by-step explanation:

4^4=256

(1/3)*(256)=

256/3

Simply replace X with 4

Answer:

F(4)=1/3*4^4

F(4)=256/3

Step-by-step explanation:

4^4=256

(1/3)*(256)=

256/3

Step-by-step explanation:

2 is the answer because:

72/2=36

108/2=54

Answer:

2

Step-by-step explanation:

Well divisible means the lowest numbers it can be divided by.

So we can make a chart.

72 -  1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

108 - 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108

So besides 1, 2 is the lowest divisible number between 108 and 72.