which expotential function has a y-intercept of (0, -4)?



HELP WILL MARK BRAINLIEST

In mathematics, Stirling's approximation (or Stirling's formula) is a factorial approximation. A good approximation that gives accurate results even for small values ​​of n. It is named after James Stirling and was first given by Abraham de Moivre, although relevant but less accurate.

Factorial is one of thein mathematics. It is also an important mathematical concept ubiquitous concepts used in data science. Factors are used to model probability distributions in Poisson processes. The probability mass function of the Poisson distribution has a factorial formula in the denominator. You can't find the probability of a Poisson random variable without a way to compute the factorial.

Factorials are also related to combinatorics. For example, hmm! is the number of permutations of n unique objects. From the point of view of statistical mechanics, entropy is defined as a combinatorial problem. Entropy also has its own definition in information theory. Comparing the two alternative definitions, they are identical.

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Answer:

2

Step-by-step explanation:

The value of the standard deviation does not change and remains the same.

Given, a retired statistic professor has recorded final exam results for decades. the mean final exam score for the population of a student is 82.4 with a standard deviation of 6.5.

The mean μ = 82.4

The standard deviation σ = √[ ((x - μ)2 + (y - μ)2 + (z - μ)2)/3 ]

we have to find the variance,

We now add a constant k to each data value and calculate the new mean μ'.

μ' = ((x + k) + (y + k) + (z + k)) / 3 = (x + y + z) / 3 + 3k/3 = μ + k

We now calculate the new mean standard deviation σ'.

σ' = √[ ((x + k - μ')2 +(y + k - μ')2+(z + k - μ')2)/3 ]

Note that x + k - μ' = x + k - μ - k = x - μ

also y + k - μ' = y + k - μ - k = y - μ and z + k - μ' = z + k - μ - k = z - μ

Therefore σ' = √[ ((x - μ)2 +(y - μ)2+(z - μ)2)/3 ] = σ

If we add the same constant k to all data values included in a data set, we obtain a new data set whose mean is the mean of the original data set PLUS k. The standard deviation does not change.

Hence, the standard deviation does not change.

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The area of the triangle is 48 square units.

To calculate the length of each side of the triangle ACB, the radii of the circles should be added respectively.

Length of side BC = 9+3 = 12 units

Length of side CA = 3+5 = 8 units

Length of side BA = 9+5 = 14 units

Area of triangle = (1/2 × Base × Height) square units

Area of triangle ACB = 1/2 × CA× BC sq units

                          Area = 1/2 × 8 × 12 = 48 sq units

Hence, the area of triangle ACB is 48 square units.

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Answer:

47.91 units²

Step-by-step explanation:

The radius of each circle is:

Therefore, the side lengths of the triangle are:

Heron's Formula allows us to find the area of a triangle in terms of its side lengths.

[tex]\boxed{\begin{minipage}{8 cm}\underline{Heron's Formula}\\\\$A=\sqrt{s(s-a)(s-b)(s-c)}$\\\\where:\\ \phantom{ww}$\bullet$ $A$ is the area of the triangle. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the side lengths of the triangle. \\ \phantom{ww}$\bullet$ $s$ is half the perimeter.\\\end{minipage}}[/tex]

The perimeter of a two-dimensional shape is the distance all the way around the outside. Therefore, half the perimeter of the triangle is:

[tex]\implies s=\dfrac{14+12+8}{2}=17[/tex]

To calculate the area of the triangle, substitute the sides lengths and the value of s into Heron's formula and solve for A:

[tex]\implies A=\sqrt{17(17-14)(17-12)(17-8)}[/tex]

[tex]\implies A=\sqrt{17(3)(5)(9)}[/tex]

[tex]\implies A=\sqrt{2295}[/tex]

[tex]\implies A=47.906158268...[/tex]

[tex]\implies A=47.91\; \sf units^2\;\;(nearest\;hundredth)[/tex]

The transfer function for the given integrator circuit in terms of frequency,f and imaginary unit,j is expressed as [tex]T(f)=-j0.00628f[/tex]

The figure of the integrator is shown at bottom of the answer.

The transfer function of an integrator can be expressed in form of impedances of the circuit elements connected to the op-amp.

Assume the impedance at the input side be [tex]Z_1[/tex] and impedance of the feedback be [tex]Z_2[/tex]

We can observe that at input, in consists of capacitor with capacitance,C [tex]= 0.1\mu F=10^{-7}F[/tex]

and at the feedback loop, the circuit element is a resistor with resistance,R [tex]= 10k\Omega = 10^4 \Omega[/tex]

Now,

the transfer function for an integrator can be written as ,

[tex]T(f) = -\frac{Z_2}{Z_1}[/tex]

We know that,

impedance of capacitor is [tex]Z_1=\frac{1}{j\omega C}=\frac{1}{j2\pi f C}[/tex]

impedance of resistor is [tex]Z_2=R[/tex]

Now,

[tex]T(f)=-\frac{R}{\frac{1}{j2\pi fC}}\\\\T(f)=-R*j2\pi f C\\\\T(f)=-j10^4*2\pi f 10^{-7}\\\\T(f)=-j0.00628f[/tex]

Hence, the transfer function is [tex]T(f)=-j0.00628f[/tex]

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The radius of the sphere with the given point and the center is √238.

Here we have to find the radius of the sphere.

Given data:

The point on the surface of a sphere is (-4, -6, 10) and the point on the center is (2, 3, -1).

The formula for the radius:

r² = (x2 - x1)² + (y2 - y1)² + (z2 - z1)²

where (x1, y1, z1) = point on the center

(x2, y2, z2) = point on the sphere

Now putting the values we have

r² = (-4-2)² + ( -6-3)² + ( 10 +1)²

  =( -6)² +(- 9)²  + (11)²

  = 36 + 81 + 121

  = 238

r = √238.

Therefore the radius is √ 238.

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(a) Class interval of a given data is 36.

(b) Frequency distribution is 44.

We have given that,

total frequency = 44

lower limit = $70

number of class = 5

(a) we have to find class interval,

Class interval =  [tex]\frac{Max. number - min. number}{no. of classes}[/tex]

here maximum number is 264 and minimum number is 84

Class interval = [tex]\frac{264 - 84}{5}[/tex]

                      = [tex]\frac{180}{5}[/tex]

Class interval = 36

we have to round our value to the next multiple of 5

so the class interval will be 40.

(b) A frequency distribution is the pattern of frequencies of a variable. It is the number of times each possible value of a variable occurs in a dataset. There are three types of frequency distribution such as Cumulative frequency distribution, Relative frequency distribution, Relative cumulative frequency distribution.  

The frequency distribution is as follows:

Class interval           Frequency

 70 - 110                         6

 111 - 151                          5

152 - 192                       10

193 - 233                       14

234 -  274                       9

Total                              44

This is the organize data into a frequency distribution.

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Howard Steele needs to invest  $117,817.77 today so that he may withdraw $12,000 each year for the next 20 years

Simple interest is often a predetermined percentage of the principal amount borrowed or lent paid or received over a specific time period.

Borrowers are required to pay interest on interest in addition to principal since compound interest accrues and is added to the accrued interest from prior periods.

We know the equation, [tex]P = \frac{A\times(1-(1+r)^{-n}}{r}[/tex] the annuity, and the present value of money, P, can be connected.

P = 12000, r = 0.08 and n = 20.

∴ [tex]12000 = \frac{A\times(1-(1.08)^{-20}}{0.08}[/tex].

A = $117,817.77.

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Answer: True.

Because the trapezoid is isosceles, the base angles are congruent by default.

Given isosceles trapezoid ABCD

Sides AB and DC are congruent

By the SAS postulate, triangles ABC and DCB are congruent

Therefore, segment AC is congruent to segment DB

The equation of the line parallel to y = 6 and passing through (-1, 8) is y = 8.

The slope or gradient of a line is a number that describes both the direction and the steepness of the line.

Given that, an equation of the line that passes through (-1, 8) and is parallel to the line y = 6.

Slope of the parallel lines are equal to each other, therefore, solving for c,

8 = -1x0 + c

c = 8

Hence, The equation of the line parallel to y = 6 and passing through (-1, 8) is y = 8.

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Answer:

[tex]f(x)=x^2(x-a)^2(x-b)^4(x-c)[/tex]

Step-by-step explanation:

There is a double root at [tex]x=0[/tex], which corresponds to [tex]x[/tex] raised to an even power.

There are also 2 more double roots and one more single root. This corresponds to two factors raised to an even power and one factoe raised to an odd power.

The only option that satisfies this is Option 1.

The graphical representation of the polynomial function is given by the relation f ( x ) = x² ( x - a )²( x - b )⁴ ( x - c )

Graphs behave differently at various x-intercepts. Sometimes the graph will cross over the x-axis at an intercept. Other times the graph will touch the x-axis and bounce off.

Identify the even and odd multiplicities of the polynomial functions' zeros.

Using end behavior, turning points, intercepts, and the Intermediate Value Theorem, plot the graph of a polynomial function.

The graphs cross or are tangent to the x-axis at these x-values for zeros with even multiplicities. The graphs cross or intersect the x-axis at these x-values for zeros with odd multiplicities

Given data ,

Let the polynomial equation be represented as f ( x )

Now , the value of f ( x ) is

f ( x ) = x² ( x - a )²( x - b )⁴ ( x - c )

The factors (x - a), (x - b), and (x - c) indicate that the function has roots at x = a, x = b, and x = c. These roots are of multiplicity 2, 4, and 1 respectively, which means that they are repeated in the factors (x - a)², (x - b)⁴, and (x - c), respectively.

The factor x² indicates that the graph of the function opens upward, since the leading coefficient is positive.

Overall, the graph of this function will have eight "humps" or "bumps" corresponding to its eight roots, and the heights and shapes of these bumps will depend on the values of a, b, and c.

Hence , the graph of the function is plotted

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The classification of the triangle according to its side lengths and vertices would be scalene triangle.

To classify the triangle, you first need to find the lengths of the sides of the triangle. You can do this by finding the distance between the vertices given.

To find the vertices, the formula is:

= √ ( ( x₂ - x₁ ) ² + ( y ₂ - y ₁) ² )

The length of AB is therefore 3.61 units

The length of BC is 8.54 units

The length of AC is 10 units.

None of the side lengths of this triangle are the same so it is a scalene triangle.

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a. When vector is added to vector , the resultant is vector such that its magnitude and direction is proportional to the resultant magnitude and direction of the component vectors.

b. ∅ = (Rx/Ry)

Vectors are used to represent physical quantities in terms of magnitude and direction. Vectors can be added using the parallelogram method or the triangle addition method. The magnitude and direction of the resulting vector are generally proportional to the magnitude and direction of the component vectors.

I have every vector in 2D that has both vertical and horizontal components.

There are vectors say:  A = xi + yj

                              and, B =zi + wj

For example, adding two vectors gives the result

R = (x +z)i + (y + w) j.

The - component has y +w as z and the y component as w. The sum has the horizontal component as x + z and the vertical component as y + w. So we get the y component of the resulting vector R = A+ y component of B

The direction of the angle is found as

tan∅ = Rx/Ry

     ∅ = (Rx/Ry)

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a) The length of segment A'B' is given as follows: 4 units.

b) The length of segment B'B is given as follows: 4 units.

The two similar triangles in this problem are given as follows:

ABC and A'B'C'.

Then side lengths of ABC are given as follows:

12, 9 and 2 + x.

The equivalent side lengths on triangle A'B'C' are given as follows:

y, 3 and 2.

When the triangles are similar, the side lengths are proportional, hence the following equation is built:

12/y = 9/3 = 2+x/2.

Then the length of segment A'B' is obtained as follows:

12/y = 9/3

12/y = 3

3y = 12

y = 12/3

y = 4.

The length of segment B'B is x, hence it is obtained as follows:

9/3 = 2+x/2.

2 + x = 6

x = 4 units.

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Answer:

there was 30 people at her birthday party

Triangle ABC and triangle XYZ are congruent thus ∆ABC and XYZ are similar

Similar triangles are triangles that have the same shape, but their sizes may vary. All equilateral triangles, squares of any side lengths are examples of similar objects.

if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.

line DY bisects AC and line ZE bisects line AB.

Therefore line AD is congruent to line AE and line CD is congruent to line EB.

therefore AB = CD and similar XY = YZ

therefore ∆ABC and ∆XYZ are similar

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Answer:

34

× 12

---------

8

60

40

+ 300

----------

= 408

From given data we can conclude that there is no influence of age on how many hours a person spends doing/reading/answering emails in a week.

In this question, the given data has 2 categories of age and the number of hours per week someone spends on email.

Let H0(null hypothesis): age has any influence on how many hours a person spends doing/reading/answering emails in a week.

Ha = age has no influence on how many hours a person spends doing/reading/answering emails in a week.

36 and under   over 36       x - y          (x - y)²

      28                  0              28             784

       4                   2               2                 4

       2                   0               2                 4

      25                  1              24               576

      15                  5              10               200

       3                   2                1                  1

      15                  4               11               121

      20                  8               12               144

      10                  5                5                  25

       1                  10               -9                 81

                            Total :        86             1940

Using the formula for t-score:

t = (∑D / N)/[√(∑D² - (∑D)²/N)/(N-1)N]

where

∑D = sum of differences

∑D² = sum of squared differences

(∑D)² = square of sum of differences

t = (86 / 10)/[√(1940 - 7396/10)/(10-1)10]

t = 8.6/√((1940 - 739.6)/90)

t = 8.6 /√(1200.4/90)

t = 8.6 /√13.34

t = 2.35

The p-value with degree of freedom = 9 and alpha-level = 0.05 is 0.021653

Since calculated value is greater than the p-value, we reject the null hypothesis.

Therefore, age has no influence on how many hours a person spends doing/reading/answering emails in a week.

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The number of bags of grass seed that Amanda should use to spread her yard is 16.65 bags, meaning she needs to buy not more than 17 bags, using mathematical operations.

The basic mathematical operations we use are subtraction, addition, division, and multiplication.

In this situation, we use the division operation.

The division operation involves four parts:

The area of the yard = 4,995 ft²

1 yard = 3 feet

Area of the yard = 1,665 square yards(4,995/3)

The number of bags per 100 square yards = 1 bag

For 1,665 square, the number of bags = 16.65 bags (1,665 ÷ 100)

Thus, Amanda requires 16.65 bags of the grass seed for her yard.

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The relationship between x and y is and the constant of variation is 24.

What is inversely proportional?

One kind of proportionality relationship is inverse proportion. If two quantities are inversely related, one will increase while the other will decrease. Building a wall would be an example of an inverse proportion in action.

Given that x and y are inversely proportion.

Assume that the relationship between x and y is

y = k/x where k is constant of variation.

Putting x = 3 and y = 8 in y = k/x :

8 = k/3

Multiply both sides by 3:

k = 8 × 3

k = 24

Putting x = 4 and y = 6 in y = k/x :

6 = k/4

Multiply both sides by 4:

k = 6 × 4

k = 24

The relationship is y = 24/x and the constant of variation is 24.

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Answer:

x and y are not inversely proportional.

Image:

Answer:

30/4+5•3-9

= 7.5+15-9

= 22.5-9

= 13.5

Step-by-step explanation:

After analyzing the given data we will get to know that all the options mentioned above are true.

A = BUC, B is a singleton set, and A = CU2 if A is the set of all prime numbers, B is the set of all even prime numbers, and C is the set of all odd prime numbers. Therefore, option D - All of the specified - is the answer to this question.

We've got

The entire set of prime numbers is A.

A = {2, 3, 5, 7, 11, 13}

B is a collection of even prime numbers.

B = {2}

C is a collection of all odd prime numbers.

C = {3, 5, 7, 11, 13,}

We are aware that the only even prime number is two. As a result, Set B is a singleton set because it only has one element.

Additionally, if we combine sets B and C, we will obtain set A, which contains all prime numbers.

Thus, we obtain A = B U C.

Since B = 2 is a singleton set, if we have A = B U C, we can also say A = C U 2.

Therefore, each of the aforementioned choices is appropriate.

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Answer: they didnt distribute the 7 to the 4.5

Step-by-step explanation:

when distributing something outside of a parenthesis, you have to distribute it to all terms within the parenthesis, not just the variable

Answer:

I don't know the answer of this questions

The number of capybaras that you will get after 14 days is given as follows:

3 capybaras.

Initially, the number of capybaras that you have is given as follows:

2 capybaras.

The pattern is then given as follows:

The time composed by 14 days is of 2 weeks, then the procedure will finish on the Monday 2 weeks from now.

The number of capybaras in that Monday than can be calculated step by step as follows:

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We have evidence that this is not a symmetrical die the standardized residuals is 9.5699.

Given that,

The following frequencies are found for the number of pips up when the die comes to rest, assuming a die is tossed 1000 times. Find out if there is proof that this die is not symmetrical using the chi-squared goodness of fit test. The standardized residuals should be noted.

x₁           x₂           x₃           x₄         x₅           x₆

163        178        142        150       183        184

We know that,

          observed       expected         Op-Ep         (Op-Ep)²/Ep

x₁          163                 166.7                -3.7               0.082

x₂          178                 166.7                 11.3              0.7659

x₃          142                 166.7                -24.7            3.6598

x₄          150                 166.7                -16.7             1.673

x₅          183                 166.7                16.3               1.5938

x₆           184                 166.7               17.3               1.7954

                                                                                 -----------

                                                                                 9.5699

Expected = 1/nΣXa=1/6(1000)=166.7

Therefore, We have evidence that this is not a symmetrical die the standardized residuals is 9.5699.

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The equivalent measure of the angle when converted from radians to degrees is 128.57 degrees

From the question, we have the following parameters that can be used in our computation:

Angle = \large \frac{5\pi}{7}radians to degrees.

This angle can be properly expressed

So, we have the following representation

Angle = 5π/7 radians

Also, the angle can be further expressed

So, we have the following representation

Angle = 5/7 π radians

As a general rule of angle conversion, we have

π radians = 180 degrees

Substitute the known values in the above equation, so, we have the following representation

Angle = 5/7 * 180 degrees

Evaluate the products

Angle = 128.57 degrees

Hence, the measure of the angle in degrees is 128.57 degrees

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Answer the angle when converted from radians to degrees is 128.57 degrees

Angle = 5π/7 radians

Angle = 5/7 π radians

π radians = 180 degrees

Angle = 5/7 * 180 degrees

Evaluate the products

Angle = 128.57 degrees

The factors of the polynomial x³+3x²-x-3 are (x+1)(x-1)(x+3).

A factor is a number that divides another number, leaving no remainder.

Given is a polynomial, x³+3x²-x-3

x = -1 is the root of the polynomial, which it will completely divide the polynomial x³+3x²-x-3,

On dividing, we get,

(x³+3x²-x-3)÷(x+1) = (x²+2x-3)

Factorizing, (x²+2x-3), we get,

(x-1)(x+3)

Hence, The factors of the polynomial x³+3x²-x-3 are (x+1)(x-1)(x+3).

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