Adam has $15$ of a certain type of rare coin and is interested in knowing how much this collection is worth. He discovers that $5$ of these coins are worth $12$ dollars in total. Assuming that the value of each coin is the same, how many dollars is his entire collection worth?

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

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:

Inequality Form:

x≥130

Step-by-step explanation:

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

Answer:

y = 1 and x = 1

Step-by-step explanation:

We are given the equation  y=−5x+6    and    y=3x-2

because both of these equations have y on one side we can substitute the equation as

-5x+6 = 3x-2

(subtract 3x)

-8x+6 = -2

(subtract 6)

-8x = -8

(divide by -8)

x=1

Then all we need to do is put x into the equation

y=-5(1) +6

y = -5+6

y = 1

Answer:

-11

Step-by-step explanation:

Our function is 2x-13x+5

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:

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:

x > 9

Step-by-step explanation:

Simply divide both sides by 4:

4x/4 > 36/4

x > 36/4

x > 9

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▹ Answer

x > 9

▹ Step-by-Step Explanation

4x > 36

---     --- → x > 9

4       4

Hope this helps!

- CloutAnswers ❁

Brainliest is greatly appreciated!

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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.

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:

Third graph from the top

Step-by-step explanation:

A proportional relationship is a straight line that goes through the point (0,0)

Answer:

Step-by-step explanation:

The third straight graph, since a proportion is a relationship in which a second variable is changed by a same value all the time (linear).

Hope this helps, if not, tell me and I shall try again

Answer:

94 cm

Step-by-step explanation:

The formula for finding the circumference of a circle is;

Circumference = 2πr

where π = [tex]\frac{22}{7}[/tex] or 3.14 and

r = radius

Here radius is 15 cm so;

Circumference = [tex]2 * \frac{22}{7} * 15[/tex]

                         = [tex]\frac{660}{7}[/tex]cm

                         = 94.28cm

                         = 94 cm (  rounded to the nearest centimetre )

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:

undefined

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:

0.5kg

2kg

0.7kg

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Answer:<5 and <4 are exterior angles

Step-by-step explanation:

Because they are the only ones outside it they are the only ones that are exterior angles!

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Answer:

for AL Its 3 and 4

Answer:

The margin of error of this confidence interval is MOE=0.085.

Step-by-step explanation:

The confidence interval bounds are usually calculated from a sample statistic substracting (for the lower bound) or adding (for the upper bound) the margin of error. This margin of error depends on the confidence level, the standard deviation and the sample size.

Then, if the lower and upper bound are calculated this way, we can calculate the margin of error as:

[tex]LB=p-MOE\\\\UB=p+MOE\\\\UB-LB=(p+MOE)-(p-MOE)=2\cdot MOE\\\\\\MOE=\dfrac{UB-LB}{2}=\dfrac{0.26-0.09}{2}=\dfrac{0.17}{2}=0.085[/tex]

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:

1/6

1/14

5/64

3/8

Step-by-step explanation:

Easiest and fastest way to evaluate these is to plug it into a calc.

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

Answer:

The answer is explained below

Step-by-step explanation:

The steps to prioritize the mission with a scoring version are as follows:

Collection: This step consists of collecting and collecting all of the details associated with the mission.

Classification: This step consists of prioritization of the challenge based on a category method.

Verification: This step includes approval and verification of all classified projects.

They are then carried out in this order because these steps make certain safety, connectivity, integrity, cost-effectiveness, and right challenge implementation. Each step depends on the previous step. They are connected to every other; therefore, they are carried out in a particular sequence.

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:

the first one

Step-by-step explanation:

i assume they want to know how many cookies are in each box so you take the total number of cookies and divide by the number of boxes which is four so t/4 = b since they don't give you an amount of cookies

Answer:

t/4 = b aka the first one

Step-by-step explanation:

t/4 is the same as b

Answer:12.4

Step-by-step explanation:

hyp=16,opp=x

sin 51°=[tex]\frac{x}{16}[/tex]

cross multipy

sin 51° x 16 = x

x=0.7771 x 16

x≅12.4

12 teachers...

Hope this helps.....

The time it takes them to make 1300 soccer kicks together is 51 minutes

Writing this as a coordinate (x, y). If Kendra can make 120 soccer kicks in 3 minutes and Jovani can make 100 soccer kicks in 4 minutes, this can be written in a coordinate form as (3, 120) and (4, 100)

The standard linear equation is given as y = mx + b

Get the slope:

m = 100-120/4-3

m = -20/1

m = -20

Get the y-intercept:

Recall that y = mx + b

120 = -20(3) + b

120 = -60 + b

b = 180

The required equation is g(x) = -20x + 180

To determine the time it will take them to make 1300 soccer kicks together, substitute g(x) = 1300 and find "x"

1300 = -20x + 180

20x = 1200 - 180

20x = 1020

x = 51 minutes

Hence the time it takes them to make 1300 soccer kicks together is 51 minutes

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Answer:

Shifting/Translating the function

Step-by-step explanation:

Answer:

Step-by-step explanation:

nice

Answer:

C ( 11 , -11 )

Step-by-step explanation:

Solution:-

We are given two points in the cartesian coordinate system as:

                   A ( 3 , -5 )              B ( 13 , -15 )

The point C lies on the line segment from A to B. The ratio of segment given is:

                              AC / AB = 4 / 5

To solve such type of problems. We will use vector equation of line AC.

To form a vector equation of line representing AB. We will first determine the direction vector ( d ) that is parallel to the line AB as follows:

                 d = OB - OA

                 d = < 13 , -15 > - < 3 , -5 >  

                 d = < 10 , -10 >

The fixed point on the line is taken. We will take point A. The vector equation of line from point A to point B is expressed as:

                < x , y > = OA + s*d

                < x , y > = < 3, -5 > + s* < 10 , -10 >  

The above equation satisfies all the points that lies on the line AB. To determine the coordinates of ( C ). We will plug in the appropriate value of parameter ( s ) and evaluate.

So point C is 4/5 th the magnitude of the distance AB from A. Hence, s = 4/5 as follows:

               < x , y > = < 3 , -5 > + ( 4/5 ) * < 10 , -10 >  

               < x , y > = < 3 , -5 > + < 8 , -8 >  

              < x , y > = < 11 , -11 >   ... Answer

Answer:

w=7

Step-by-step explanation:

1. -8+5w=27

2. add 8 to both sides: 8+-8+5w=27+8

3. Simplify: 5w=35

4. Divide both sides by 5: 5w/5=35/5

5. w=7

Hope This Helps :)

Answer:

w = 7

Step-by-step explanation:

-8 + 5w = 27

Add 8 on both sides.

-8 + 5w + 8 = 27 + 8

5w = 35

Divide both sides by 5.

5w/5 = 35/5

w = 7