The graph of f(t) = 4.2 shows the value of a rare coin in year t. What is the
meaning of the y-intercept?

A. When it was purchased (year 0), the coin was worth $2.

B. When it was purchased (year 0), the coin was worth $4.

C. In year 1, the coin was worth $8.

D. Every year the coin is worth 4 more dollars.

Answer:

[tex]\bar X =\frac{2.3+3.1+2.8+1.7+0.9+4+2.1+1.2+3.6+0.2+2.4+3.2}{12}=2.29[/tex]

[tex] s=1.09[/tex]

Step-by-step explanation:

For this case we have the following data given:

2.3 3.1 2.8

1.7 0.9 4.0

2.1 1.2 3.6

0.2 2.4 3.2

Since the data are assumedn normally distributed we can find the standard deviation with the following formula:

[tex]\sigma =\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n}}[/tex]

And we need to find the mean first with the following formula:

[tex]\bar X = \frac{\sum_{i=1}^n X_i}{n}[/tex]

And replacing we got:

[tex]\bar X =\frac{2.3+3.1+2.8+1.7+0.9+4+2.1+1.2+3.6+0.2+2.4+3.2}{12}=2.29[/tex]

And then we can calculate the deviation and we got:

[tex] s=1.09[/tex]

Answer:

X ~ Norm ( 2.29167 , 1.09045^2 )

Step-by-step explanation:

Solution:-

- The (GPA) for 12 randomly selected college students are given as follows:

            2.3 , 3.1 , 2.8 , 1.7 , 0.9 , 4.0 , 2.1 , 1.2 , 3.6 , 0.2 , 2.4 , 3.2

- We are to assume the ( GPA ) for the college students are normally distributed.

- Denote a random variable X: The GPA secured by the college student.

- The normal distribution is categorized by two parameters:

- The mean ( u ) - the average GPA of the sample of n = 12. Also called the central tendency:

                        [tex]Mean ( u ) = \frac{\sum _{i=1}^{\ 12 }\: Xi }{n}[/tex]

Where,

           Xi : The GPA of the ith student from the sample

           n: The sample size = 12

          [tex]Mean ( u ) = \frac{2.3 + 3.1 + 2.8 + 1.7 + 0.9 + 4.0 + 2.1 + 1.2 + 3.6 + 0.2 + 2.4 + 3.2}{12} \\\\Mean ( u ) = \frac{27.5}{12} \\\\Mean ( u ) = 2.29167[/tex]

- The other parameter denotes the variability of GPA secured by the students about the mean value ( u ) - called standard deviation ( s ):

          [tex]s = \sqrt{\frac{\sum _{i=1}^{\ 12 }\: [ Xi - u]^2}{n} } \\\\\\\sum _{i=1}^{\ 12 }\: [ Xi - u]^2 = ( 2.3 - 2.29167)^2 + ( 3.1 - 2.29167)^2 + ( 2.8 - 2.29167)^2 + ( 1.7\\\\ - 2.29167)^2+ ( 0.9 - 2.29167)^2 + ( 4 - 2.29167)^2 + ( 2.1 - 2.29167)^2 + ( 1.2 - 2.29167)^2 +\\\\ ( 3.6 - 2.29167)^2 + ( 0.2 - 2.29167)^2 + ( 2.4 - 2.29167)^2 + ( 3.2 - 2.29167)^2 \\\\\\\sum _{i=1}^{\ 12 }\: [ Xi - u]^2 = 14.26916 \\\\\\s = \sqrt{\frac{ 14.26916 }{12} } \\\\s = \sqrt{1.18909 } \\\\s = 1.09045[/tex]

- The normal distribution for random variable X can be written as:

                 X ~ Norm ( 2.29167 , 1.09045^2 )

Answer:95 degrees

Step-by-step explanation: That’s what it is closest to

Answer:

The answer is [tex]\pi(\pi-6)[/tex]

Step-by-step explanation:

Recall that green theorem is as follows: Given a field F(x,y) = (P(x,y),Q(x,y)) and a closed curve C that is counterclockwise oriented. If P and Q are continuosly differentiable, then

[tex]\oint_C F\cdot dr = \int_{R} \frac{\partial P }{\partial y}-\frac{\partial P }{\partial x} dA[/tex]

where R is the region enclosed by the curve C.

In this particular case, we have the following field [tex]F(x,y) = (4xy^2,2x^3+y)[/tex]. We are given the description of the region R as [tex]0\leq y \leq \sin(x), 0\leq x \leq \pi[/tex]. So, in this case (calculations are omitted)

[tex]\frac{\partial P}{\partial y} = 8xy, \frac{\partial Q}{\partial x} = 6x[/tex]

Thus,

[tex]\oint_C F\cdot dr =\int_{0}^{\pi}\int_{0}^{\sin(x)}(8xy-6x)dydx[/tex]

So,

[tex] \int_{0}^{\pi}\int_{0}^{\sin(x)}(8xy-6x)dydx=\int_{0}^{\pi}4x\left.y^2\right|_{0}^{\sin(x)}-6x\left.y\right|_{0}^{\sin(x)} = \int_{0}^{\pi} 4x\sin^2(x)-6x\sin(x)dx[/tex]

Since [tex]\sin^2(x) = \frac{1-\cos(2x)}{2}[/tex], then

[tex] \int_{0}^{\pi} 4x\sin^2(x)-6x\sin(x)dx = \int_{0}^{\pi} 2x(1-\cos(2x))-6x\sin(x)dx[/tex]

Consider the integrals

[tex] I_1 = \int_{0}^{\pi} x\cos(2x)dx, I_2 = \int_{0}^{\pi}x\sin(x)dx[/tex]

Then, by using integration by parts (whose calculations are omitted) we get

[tex]\int_{0}^{\pi} x\cos(2x) = \left.\frac{x\sin(2x)}{2}+\frac{\cos(2x)}{4}\right|_{0}^{\pi} = \frac{\pi\sin(2\pi)}{2}+\frac{\cos(2\pi)}{4}- \frac{0\sin(2\cdot 0)}{2}+\frac{\cos(2\cdot 0)}{4}=0[/tex]

[tex] \int_{0}^{\pi}x\sin(x) = \left.-x\cos(x)+\sen(x)\right |_{0}^{\pi} = -\pi\cos(\pi)+\sen(\pi)- (-0\cdot \cos(\pi)+\sin(0)) = \pi[/tex]

Then, we have that

[tex]\int_{0}^{\pi} 2x(1-\cos(2x))-6x\sin(x)dx = \left.x^2\right|_{0}^{\pi} -2I_1-6I_2 = \pi^2-2\cdot 0 -6\pi = \pi(\pi-6)[/tex]

Answer:

0.95

Step-by-step explanation:

Let's convert this into a fraction that has a denominator of 100. In order to do so, we need to multiply the numerator and denominator both by 5 (because 20 * 5 = 100):

[tex]\frac{19}{20}* \frac{5}{5} =\frac{95}{100}[/tex]

So, we have 95/100, which is technically 95 divided by 100. Whenever we divide something by a power of 10, like [tex]10^n[/tex], where n is any integer, we move the decimal point of the dividend n places to the left.

Here, we have 100, which is [tex]10^2[/tex], so we want to move the decimal point of 95 (which equals 95.0) 2 places to the left:

0.95

Hope this helps!

Answer:

   £1800

Step-by-step explanation:

The lower price is 80% of the original, so the original price is ...

   £1440 = 0.80×original

   £1440/0.80 = original =  £1800

The price before the decrease was  £1800.

Answer:

The lateral surface area of cube = 4

Step-by-step explanation:

Explanation:-

Given perimeter of the cube is 12

let 'a' be the base of cube

we know that the perimeter of cube formula = 12 a

        12 a= 12

           a = 1

The side of cube = 1cm

The lateral surface area of cube = 4 × a²

                                                      = 4 X (1)²

                                                      = 4

Final answer:-

The lateral surface area of cube = 4

Answer:

Check the explanation

Step-by-step explanation:

Scatter plot

x---square feet

y---rent

SolutionA:

Kindly check the attached image below:

THERE EXISTS A WEAK POSITIVE RELATIONSHIP BETWEEN SQUARE FEET AND RENT .

AS SQUARE FEET INCREASES RENT INCREASES

SolutionB:

Rent=0.4932(squarefeet)+992.99

slope=m=0.4932

Y intercept=992.99

SolutionC:

Interpretation of slope:

slope =m=change in rent/change in square foot

For a unit increase in square feet rent increases by 0.4932

Interpretation of y intercept:

when square feet=0 rent is 992.99

Solutiond:

when squarefeet=800

Rent=0.4932(squarefeet)+992.99

=Rent=0.4932(800)+992.99

=1387.55

Answer:

Check the explanation

Step-by-step explanation:

The fundamentals

A continuous random variable can take infinite values in the range associated function of that variable. Consider [tex]f\left( x \right)f(x)[/tex] is a function of a continuous random variable within the range [tex]\left[ {a,b} \right][a,b][/tex] , then the total probability in the range of the function is defined as:

[tex]\int\limits_a^b {f\left( x \right)dx} = 1 a∫b​ f(x)dx=1[/tex]

The probability of the function [tex]f\left( x \right)f(x)[/tex] is always greater than 0. The cumulative distribution function is defined as:

[tex]F\left( x \right) = P\left( {X \le x} \right)F(x)=P(X≤x)[/tex]

The cumulative distribution function for the random variable X has the property,

[tex]0 \le F\left( x \right) \le 10≤F(x)≤1[/tex]

The probability density function for the random variable X has the properties,

[tex]\\\begin{array}{c}\\{\rm{ }}f\left( x \right) \ge 0\\\\\int\limits_{ - \infty }^\infty {f\left( x \right)dx} = 1\\\\P\left( E \right) = \int\limits_E {f\left( x \right)dx} \\\end{array} f(x)≥0[/tex]

Kindly check the attached image below to see the full explanation to the question above.

Answer:

they can get at most 6 drinks

Step-by-step explanation:

5 (17.5) + 2x ≤100

87.5 + 2x≤100

2x≤ 12.5

x≤6.25

Answer:

0 to 6 drinks, but no more.

Step-by-step explanation:

Answer:

82%

Step-by-step explanation:

Final answer:

The probability that Sophia was assigned Golem given that her software crashed is approximately 82%, calculated using Bayes' Theorem.

Explanation:

When software crashes and we want to know the likelihood Sophia was using Golem, we need to consider both the probability of being assigned Golem and the probability of that software crashing. This is known as the application of Bayes' Theorem, which is a way to find conditional probabilities. In this case, we calculate as follows:

We want to find the probability that Sophia was assigned Golem given that her software crashed (P(G|C)). We use the formula:

P(G|C) = (P(C|G) * P(G)) / (P(C|G) * P(G) + P(C|F) * P(F))

Inserting the above probabilities yields:

P(G|C) = (0.10 * 7/10) / ((0.10 * 7/10) + (0.05 * 3/10))

P(G|C) = 0.07 / (0.07 + 0.015)

P(G|C) = 0.07 / 0.085

P(G|C) = 0.8235 or approximately 82%

Expressed as a whole-number percentage, the probability that Sophia was using Golem is 82%.

Answer:

in fraction form: -1/36, 1/216, -1/1296

in decimal form: -.03, .005, -.0008

Step-by-step explanation:

Each term is the previous term divided by -6:

-36 ÷ -6= 6

6 ÷ -6= -1

and so on...

-1/36

The numbers divide by -6 each time

The requried, water depth is less than the minimum required depth of 4 inches, and the water is not deep enough for the flowers.

To determine if the water depth in the spherical vase is sufficient for the flowers, we need to compare the height of the water to the minimum required depth of 4 inches.

Given that the surface of the water forms a circle with a diameter of 5 inches, we can calculate the radius of this circle by dividing the diameter by 2.

Radius = Diameter / 2

Radius = 5 inches / 2

Radius = 2.5 inches

Since the shape of the vase is spherical, the water depth will be equal to the radius.

Therefore, the water depth in the spherical vase is 2.5 inches.

Since the water depth is less than the minimum required depth of 4 inches, the water is not deep enough for the flowers.

Learn more about circle here:
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Final answer:

Given that the spherical vase’s surface water diameter is 5 inches, translating to a radius of 2.5 inches at the water's surface level, the maximum depth at the center might be close to 2.5 inches, falling short of the 4 inches required for fresh cut flowers. Therefore, the water is not deep enough for the flowers.

Explanation:

The question asks if the water in a spherical vase, with a surface diameter of 5 inches, is adequate (at least 4 inches deep) for fresh cut flowers. To determine this, we need to consider the properties of a sphere and how the depth of water relates to its diameter.

Since the diameter of the water's surface is given as 5 inches, the radius of the spherical vase (at the water's surface level) is 2.5 inches. The depth of the water in a spherical vase does not evenly translate to its diameter because the shape curves upwards from every point on its surface. However, considering that the vase is filled to a level where the diameter is 5 inches, we must acknowledge that the depth in the very center might be more but decreases as we move towards the edge of the water's surface.

Given the spherical shape, the maximum depth of the water could be close to the radius of 2.5 inches in the center, assuming the vase is filled to exactly half its height. This depth is less than the required 4 inches for fresh cut flowers. Therefore, without a specific height indication of the water level relative to the vase's total height, and based on the central depth potentially being 2.5 inches at most, it is unlikely the flowers would have the required 4 inches of water depth across the entirety of the vase's base.

Answer:

a) "This is an upper-tail test because the company wants to show the stands will hold 525 pounds (or more) easily."

b) "They will decide the stands are safe when they're not."

c) "They will decide the stands are unsafe when they are in fact safe."

Step-by-step explanation:

a) As the alternative hypothesis Ha is μ>575, the rejection region lays in the upper tail. Then, it is an upper-tail test.

They are testing the claim that the stand supports an average of 575 pounds or more, and are looking for statistical evidence for that claim.

"This is an upper-tail test because the company wants to show the stands will hold 525 pounds (or more) easily."

b)  A Type I error happens when a true null hypothesis is rejected.

This would mean that a stands that doesn't really hold 575 pounds or more has passed the test. The stand would appear more safe than it is.

"They will decide the stands are safe when they're not."

c) A Type II error happens when a false null hypothesis failed to be rejected. In this case, a safe stand, that suports 575 pounds or more, does not pass the test.

"They will decide the stands are unsafe when they are in fact safe."

Final answer:

The hypothesis test in question is an upper-tail test aiming to prove that the stands can support more than 575 pounds. A Type I error would misclassify safe stands as unsafe, while a Type II error would incorrectly certify unsafe stands as safe.

Explanation:

a) This is an upper-tail test because the goal is to show that the metal stand can support more than the standard set weight (>575 pounds). This is vital to ensure that the product holds significantly more weight than the heaviest TVs, thereby providing a safety margin.

b) A Type I error occurs if the inspectors reject the null hypothesis when it is actually true. In this context, it means they will incorrectly deem the stands to be unsafe when they are actually safe.

c) A Type II error occurs if the inspectors fail to reject the null hypothesis when it is false. In this scenario, it means that the inspectors will wrongfully certify the stands as safe when they are, in fact, not capable of holding the standard weight.

Answer:

QS + QR > RS

QR + RS > QS

RS + QS > QR    

Step-by-step explanation:

    ∧ ∧

( Ф∨Ф)

Answer:

hm here <3

Step-by-step explanation:

1 RS

2 QS

3 QR

<3

Answer:

x = 2.298

Step-by-step explanation:

we have to use the sin formula which is sin = opp / hyp

sin 50 = x / 3

x = 3 sin 50

x = 2.298

Complete question:

CHECK ATTACHMENT FOR THE DIAGRAM.

Answer:

Angle 7 is 76°

Step-by-step explanation:

From the diagram, notice that angle 4 = angle 5

That is,

Δ4 = Δ2

Because vertically opposite angles are equal.

Δ4 = 7x

Δ2 = 126

So

126 = 7x

Divide both sides by 7

x = 126/7 = 18

Again, angle 5 = angle 7

Δ5 = Δ7

Because vertically opposite angles are equal.

Since Δ5 = (4x + 4)°

And x = 18

Then

Δ7 = 4(18) + 4 = 72 + 4 = 76°

Answer:

£155

Step-by-step explanation:

look at the formula

first solve 12 minutes per light switches

12*10(lightswitches)= 120 minutes

we know that 120 minutes = 2 hours

the task says that she charges £30 per hour

so, 2 hours+ 2 hours= 4 hours

now do

4*30= £120

120+35(call-out fee)= £155

I really hope this helped.

Answer:

36 degrees.

Step-by-step explanation:

Total Sum of the Exterior Angle of a Regular Polygon[tex]=360^0[/tex]

One Exterior Angle of a n-sided regular polygon[tex]=\dfrac{360^0}{n}[/tex]

A decagon has 10 sides.

One Exterior Angle of a decagon[tex]=\dfrac{360^0}{10}=36^0[/tex]

Therefore, the measure x of the angle between the house and the pool is 36 degrees.

Final answer:

To find the measure x of the angle between the house and a pool shaped as a regular decagon, calculate the exterior angle of the decagon, which is 36 degrees. This is the angle measure sought in the question.

Explanation:

The question involves finding the measure x of the angle between the house and the pool, where the pool is in the shape of a regular decagon.

First, let's recall that a regular decagon is a ten-sided polygon with all sides and angles equal. The sum of the interior angles of any polygon can be calculated using the formula (n-2) × 180, where n is the number of sides. For a decagon, n = 10, so the sum of the interior angles is (10-2) × 180 = 1440 degrees. Since all angles in a regular decagon are equal, each interior angle measures 1440 ° / 10 = 144 °.

Now, to find the measure x of the angle between the house and the pool, we need to understand that the exterior angle of the decagon will be involved, as this is the angle made between one side of the decagon (lying against the house) and an extension of an adjacent side. The measure of an exterior angle of a regular polygon is 360 ° / n. For our decagon, this is 360 ° / 10 = 36 °.

Therefore, the measure x of the angle between the house and the pool is 36 °, which is the measure of the exterior angle of the regular decagon.

Answer:

We accept H₀  the weaning weights of cows at this ranch is 610 lbs

Step-by-step explanation:

We assume normal distribution

Population mean      μ₀  = 610  lbs

Population standard deviation     unknown

sample size  n = 41

degree of fredom    df = n - 1    df  =  41 - 1   df = 40

Sample mean    X = 578  lbs

Sample standard deviation   s  =  87

As we don´t know standard deviation of the population we will use t- student test, furthemore, as  we are looking for any difference upper and lower we are in presence of a two tails test

Test Hypothesis    Null  hypothesis    H₀                X  =  μ₀

Alternative hypothesis                         Hₐ                X  ≠  μ₀

Now at α  = 0,01 ,   df  = 40   and two tail test we find   t = 2,4347

We have in t table

30 df           t  =  2,457        for       α  = 0,01

60 df           t  = 2,390         for      α   = 0,01

Δ = 30               0,067

     10                    x  ??       x = 0,022

then  2,457  -  0,022  =  2,4347

t = 2,4347

Now we compute the interval:

X ±  t * ( s/√n)    ⇒   578  ±  2,4347 * ( 87/√41)

578  ±  2,4347 * 13,59

578  ±  33,09

P [ 578 + 33,09  ;  578 - 33,09 ]

P ( 611,09 ; 544,91]

We can see that vale 610 = μ₀   is inside the iinterval , so we accept H₀ the weaning weight of cows in the ranch is 610 lbs

Answer:i think is [tex]30r2[/tex]

Step-by-step explanation:

Answer:

30r^3

Step-by-step explanation:

The answer is 30r^3 because first you multiply 5r and 6r and then you add the exponents of them together.

5r * 6r=30r

the exponent of 5r is two and the exponent of 6r is one so you add those together.

hope this helped

Answer:

The distribution of sample proportion Americans who can order a meal in a foreign language is,

[tex]\hat p\sim N(p,\ \sqrt{\frac{p(1-p)}{n}})[/tex]

Step-by-step explanation:

According to the Central limit theorem, if from an unknown population large samples of sizes n > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.

The mean of this sampling distribution of sample proportion is:

 [tex]\mu_{\hat p}=p[/tex]

The standard deviation of this sampling distribution of sample proportion is:

[tex]\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}[/tex]

The sample size of Americans selected to disclose whether they can order a meal in a foreign language is, n = 200.

The sample selected is quite large.

The Central limit theorem can be applied to approximate the distribution of sample proportion.

The distribution of sample proportion is,

[tex]\hat p\sim N(p,\ \sqrt{\frac{p(1-p)}{n}})[/tex]

It's a goofy question.  These sides satisfy the triangle inequality, 7 < 4+5, so we can draw as many triangles as we care to with those sides.

The more interesting question is how many non-congruent triangles can we draw with those sides?   The answer is only 1, because by SSS all triangles with those sides will be congruent.

If we're asking about how many triangles with these sides cannot be mapped to each other through translation and rotation, the answer is two, basically a pair of reflected copies.

So much for deconstructing this lousy question.  Let's go with

Answer: 1

When two triangles are congruent, corresponding sides and angle both are equal.

Only one triangle can be drawn that fit the given description.

it is given that, A triangle has sides of length 7 cm, 4 cm, and 5 cm.

Two triangles that have corresponding congruent sides are congruent (SSS).

If triangle ABC has the sides AB=7 cm, AC=4 cm, BC=5 cm  and the triangle MNP has MN=7 cm, MP=4 cm, and PN=5 cm then

                    [tex]AB=MN=7 cm\\\\AC=MP=4 cm\\\\BC=PN=5cm[/tex]

Hence,  based on the axiom of congruent triangles side–side–side (SSS) triangle ABC is congruent with triangle MNP.

Learn more about the triangles here:

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