X~N(335, 50).
Find the z-score corresponding to an observation of 284.
-1.02
6.7
1.02
-6.7

Answer:

We all must have heard the word “exponential” before. What does this word mean? Exponential means to become more and more rapid in growth. However, in mathematics, it represents a mathematical expression that has one or more exponents. Hence, we know it as an exponential form.

We can say that a thing may increase with an exponential rate when the increase becomes quicker and quicker as the thing which is talked about becomes larger.

Now let us learn more about the exponential form of numbers which is greatly used and applied in mathematics.

The 4th term of an AP is 6 if the um of the 8th and 9th term is -72, The 4th term of an AP is -18.

The sum of 8th and 9th term of an AP is given as -72.

We can use the formula for the sum of any n terms of an AP,

Sn = n/2[2a + (n-1)d]

Where,

a = first term

d = common difference

n = number of terms

Therefore,

-72 = 8/2[2a + (8-1)d]

-72 = 4[2a + 7d]

-18 = 2a + 7d

Subtracting 7d from both the sides,

-18 - 7d = 2a

Dividing both the sides by 2,

(-18 - 7d)/2 = a

a = -18/2 - (7d)/2

a = -9 - (7d)/2

For the 4th term of an AP,

a4 = a + (4-1)d

=-9 - (7d)/2 + 3d

=-9 + 6d

=-9

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P-value = 0.0384

As P-value < 0.05, reject the null hypothesis.

What is test statistic?

A statistic (a number obtained from the sample) used in statistical hypothesis testing is known as a test statistic. Usually, a hypothesis test is described in words.

A test statistic is a figure obtained from a statistical analysis. It explains how distant your observed data is from the null hypothesis, which states that there is no correlation between the variables or distinction between the sample groups.

The alternative and null hypotheses are listed below.

Lack of hypothesis H0: μ = 13

Ha: 13 Alternative Hypothesis

Statistical test, z = (xbar - mu)/(sigma/sqrt(n))

z = (11 - 13)/(8/sqrt(50))

z = -1.77

Region of Rejection

For α= 0.05, this is a left-tailed test.

Z has a critical value of -1.645.

Therefore, if z -1.645, reject H0 and accept the null hypothesis.

P-value Approach

P-value = 0.0384

As P-value < 0.05, reject the null hypothesis

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The equation with value V indicating the decrease in value of iPhone 13 with years t is V = [tex] {1000 (1 - 0.02)}^{t} [/tex].

The equation to be used for the calculation of decreased value is -

A = [tex] {P (1 - r)}^{t} [/tex]. In this formula, A is amount, P is principal, r is rate and t represents time. Based on the information in question, A will be replaced with V. So, the required formula will be -

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

Now keeping the values in formula for numerical equation -

V = [tex] {1000 (1 - 0.02)}^{t} [/tex]

Since two values are unknown here, the equation can not be solved further.

Therefore, the required equation is V = [tex] {1000 (1 - 0.02)}^{t} [/tex].

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Answer:8 cm 6 cm 8 cm 6 cm The perimeter of the shape is 8 + 6 + 8 + 6 = 28cm.

Step-by-step explanation:

Answer:

30

Step-by-step explanation:

Write the inequality as 150 + 10w > 450.

Then, solve. Draw a line on the inequality symbol, and cross out the 150. Subtract 150 from the other side. Then, divide the 10w by 10, to get w by itself. Since it's inverse operations, divide 450 by 10 as well.

You will get an answer of w > 30.

Thus, Darla needs 30 more subscribers.

Answer:

$31

Step-by-step explanation:

x=cost before tax

$32.55 = x + x * 5%  ==> solve for x

$32.55 = x + x * 5/100  

$32.55 = x + 5x/100

$32.55 = 100x/100 + 5x/100 ==> make common denominators

$32.55 = (100x+5x)/100

$32.55 = 105x/100  ==> simplify

100 * $32.55 = 100 * 105x/100  ==> multiply by 100 on both sides to remove

                                                         fractions

$3255 = 105x

x = $3255/105

x = $31

The situation for which the explicit formula of the arithmetic sequence would be used instead of the recursive formula is given as follows:

Find the 106th term when the first term is of 2 and the common difference is of 5.

An arithmetic sequence is a sequence of numbers in which the difference between two consecutive terms is always constant, called common difference d.

The recursive formula is given as follows:

f(n + 1) = f(n) + d.

The first term f(1) is given.

Hence, the recursive sequence should be used to calculate a small number of terms, such as at most 15 terms.

For a large number of terms, the explicit formula should be used, which is given as follows:

[tex]a_n = a_1 + (n - 1)d[/tex]

In which [tex]a_1[/tex] is the first term.

Hence, in this problem, the 106th term should be calculated with the explicit formula, meaning that the first option is the correct option.

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Answer: no

Step-by-step explanation:

use pythagorean theorem.

you can use a^2+b^2=c^2

the biggest value is always c(the hypotenuse) -> c=20

a and b would be 15 and 17(doesn't matter which is which)

plug it into the equation -> 15^2+17^2=20^2

225+289=400

514≠400

so no, it's not a right triangle

The iterated integral by converting to polar coordinates [tex]\int_{0}^{a}\int_{-\sqrt{a^2-y^2}}^{0}7x^2ydxdy[/tex] is 7a^4/12.

In the given question, we have to evaluate the iterated integral by converting to polar coordinates.

The given integral is

[tex]\int_{0}^{a}\int_{-\sqrt{a^2-y^2}}^{0}7x^2ydxdy[/tex]

Let polar coordinate.

x = rcosθ, y = rsinθ, x^2 + y^2 = r^2

So dxdy = rdrdθ

r from 0 to a and θ from π/2 to π

Now the integral is

[tex]\int_{0}^{a}\int_{-\sqrt{a^2-y^2}}^{0}7x^2ydxdy[/tex] = [tex]\int_{\pi/2}^{\pi}\int_{0}^{a}7(r\cos\theta)^2(r\sin\theta)drd\theta[/tex]

[tex]\int_{0}^{a}\int_{-\sqrt{a^2-y^2}}^{0}7x^2ydxdy[/tex] = [tex]\int_{\pi/2}^{\pi}\int_{0}^{a}7(r^2\cos^2\theta)(r\sin\theta)drd\theta[/tex]

[tex]\int_{0}^{a}\int_{-\sqrt{a^2-y^2}}^{0}7x^2ydxdy[/tex] = [tex]7\int_{\pi/2}^{\pi}\int_{0}^{a}r^3\cos^2\theta\sin\theta drd\theta[/tex]

Now integrating the first integral

[tex]\int_{0}^{a}\int_{-\sqrt{a^2-y^2}}^{0}7x^2ydxdy[/tex] = [tex]7\int_{\pi/2}^{\pi}\left[\frac{r^4}{4}\right]_{0}^{a}\cos^2\theta\sin\theta d\theta[/tex]

[tex]\int_{0}^{a}\int_{-\sqrt{a^2-y^2}}^{0}7x^2ydxdy[/tex] = [tex]7\int_{\pi/2}^{\pi}\left[\frac{a^4}{4}-\frac{0^4}{4}\right]\cos^2\theta\sin\theta d\theta[/tex]

[tex]\int_{0}^{a}\int_{-\sqrt{a^2-y^2}}^{0}7x^2ydxdy[/tex] = [tex]\frac{7a^4}{4}\int_{\pi/2}^{\pi}\cos^2\theta\sin\theta d\theta[/tex]

Let cosθ = t

So -sinθ = dt/dθ

So sinθdθ = -dt

[tex]\int_{0}^{a}\int_{-\sqrt{a^2-y^2}}^{0}7x^2ydxdy[/tex] = [tex]-\frac{7a^4}{4}\int_{\pi/2}^{\pi}t^2dt[/tex]

[tex]\int_{0}^{a}\int_{-\sqrt{a^2-y^2}}^{0}7x^2ydxdy[/tex] = [tex]-\frac{7a^4}{4}\left[\frac{t^3}{3}\right]_{\pi/2}^{\pi}[/tex]

[tex]\int_{0}^{a}\int_{-\sqrt{a^2-y^2}}^{0}7x^2ydxdy[/tex] = [tex]-\frac{7a^4}{4}\left[\frac{\cos^3\theta}{3}\right]_{\pi/2}^{\pi}[/tex]

[tex]\int_{0}^{a}\int_{-\sqrt{a^2-y^2}}^{0}7x^2ydxdy[/tex] = [tex]-\frac{7a^4}{12}\left[\cos^3\pi-\cos^3(\pi/2)\right][/tex]

[tex]\int_{0}^{a}\int_{-\sqrt{a^2-y^2}}^{0}7x^2ydxdy[/tex] = -7a^4/12[(-1)^3 - 0]

[tex]\int_{0}^{a}\int_{-\sqrt{a^2-y^2}}^{0}7x^2ydxdy[/tex] = 7a^4/12

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The complete question is:

Evaluate the iterated integral by converting to polar coordinates.

[tex]\int_{0}^{a}\int_{-\sqrt{a^2-y^2}}^{0}7x^2ydxdy[/tex]

The expression when expressed in its exponent is a²+c²

In mathematics, we should understand that exponent tell the power to which a number is raise.

 It shows the number of times a number multiplies itself to get the certain member.

The given expression is a*a*c*.

Using the law of multiplication that says when two or more numbers in the same base are multiplied, we add their powers.

Here a appeared twice a*a=a²

And c appeared twice that is c*c=c²

Combining the two exponents together we have that

a²+c²

In conclusion, the exponent of a*a*a*a is a²+c²

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The function that matches the graph is f(x) = (17/24)(x + 2)²(x + 6).

A graph is a diametrical representation of any function between the dependent and independent variables.

The graph is easy to understand the behavior of the graph.

As per the given graph,

The function is symmetric at x = -2 so it will be an even degree function as (x + 2)².

The function is not symmetric about x = -6 so it will have an odd degree as (x + 6)¹.

The function will be f(x) = C(x + 2)²(x + 6).

The constant will be C = 17/(2² × 6) = 17/24

Hence "The function that matches is f(x) = (17/24)(x + 2)²(x + 6)".

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Answer:

[tex]0.5\sqrt{16a^2}:\quad 2a[/tex]

Step-by-step explanation:

[tex]\sqrt{ab}=\sqrt{a}\sqrt{b},\:\quad \mathrm{\:assuming\:}a\ge 0,\:b\ge 0\\\\\sqrt{16a^2}=\sqrt{16}\sqrt{a^2}\\=0.5\sqrt{16}\sqrt{a^2}\\\\\sqrt{16}\\\mathrm{Factor\:the\:number:\:}\:16=4^2\\=\sqrt{4^2}\\\\\sqrt{4^2}=4\\=4\\=0.5\cdot \:4\sqrt{a^2}\\\sqrt{a^2}=a\\=0.5\cdot \:4a\\=2a[/tex]

Answer:

Step-by-step explanation:

105 cm

Answer: 40 tickets

Step-by-step explanation:

Divide 2,800 by 7

    40

7|  2800|

   28

   0

You get 40. The jazz band would need to sell 40 tickets to meet its goal.

(a) When he is 10 feet from the base of the light, the rate at which the length of his shadow changing is 7.5 ft/s

(b) When he is 10 feet from the base of the light, the rate at which the tip of his shadow changes is 2.5 ft/s.

We have, the height of man, CD = 6 feet

Height of light , AB = 16 feet

Rate of walk by man, dx/dt = 5 feet per second.

a) we have to calculate the rate at which the length of his shadow is moving when he is 10 feet from the base of the light.

let x feet be the distance between the light and man and y feet be the distance between the light and man's shadow(E) i.e BC = x ft. and BE = y ft.

By using ratio of similar triangles,

16/y = 6/(y - x)

On cross multiplication,

16(y - x) = 6y

16y - 15x = 6y

16y - 6y = 15x

10y = 15x

Dividing by 3 on both sides,

2y = 3x

On differentiating both sides with respect to t,

2(dy/dt) = 3(dx/dt)

dy/dt = (3/2)(dx/dt)

dy/dt = (3/2)(5)

dy/dt = 15/2

dy/dt = 7.5 ft/s

Therefore, the rate at which the length of his shadow is changing is 7.5 ft/s.

b) We have to calculate the rate at which the length of his shadow is changing when he is 10 feet from the base of the light.

Length of shadow, CE = y - x

Rate of change of shadow is calculated by differentiating length with respect to time.

d(CE)/dt = dy/dt - dx/dt

d(CE)/dt = 7.5 - 5

= 2.5 ft/s

Therefore, the rate at which the length of his shadow is changing is 2.5 ft/s.

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The solution to the maximization problem P(x, y) = 7x + 9y - 5 is 33.4

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

Objective function:  P(x, y) = 7x + 9y - 5

Subject to: x ≥ 0

y ≥ 0

2x + 3y ≤ 12

3x + 2y ≤ 12

x + y ≥ 2

Next, we plot the graph of the constraints

The vertices of the feasible region are

(0, 2), (2, 0) and (2.4, 2.4)

Substitute (0, 2), (2, 0) and (2.4, 2.4) in P(x, y) = 7x + 9y - 5

So, we have

P(0, 2) = 7(0) + 9(2) - 5 = 13

P(2, 0) = 7(2) + 9(0) - 5 = 9

P(2.4, 2.4) = 7(2.4) + 9(2.4) - 5 = 33.4

Hence, the maximum value is 33.4

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Answer: S=19cm

Step-by-step explanation:

area = s^2

s(s-5)=266

s^2-5s=266

s^2-5s-266=0

(s-19)(s+14)=0

s=19cm

19 x 19 = 266

The original dimensions of the square cardboard sheet is 19 x 19.

ax² + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable, a≠0. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated.

Given:

Let the length of each side of the original square cardboard be x cm.

After cutting off a strip of 3cm wide its dimension becomes

length = x cm and breadth= (x−5) cm

So, Area = x² - 5x

266 = x² - 5x

x² - 5x - 266= 0

x² - 19x + 14x - 266= 0

x(x - 19) + 14 (x - 19)= 0

(x- 19)( x + 14) = 0

x= 19, -14.

Hence, the original dimensions of the square cardboard sheet is 19 x 19.

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The new dilation vertices of the rectangle are J'(-15, 5), K'(-10, 10) L'(0, 0) and M'(-5, -5).

What is the Dilation of the rectangle?

Dilation occurs when a polygon grows or shrinks while maintaining its overall shape. It's similar to zooming in or out on a camera. The polygon in the figure above is a rectangle JKLM. As you move the slider on the right, the transformed rectangle J'K'L'M' grows and shrinks but retains its shape.

We have,

Rectangle JKLM with vertices:

J(-6,2), K(-4,4), L(0,0) M(-2,-2): K= 5/2

New dilation vertices of the rectangle are:

J'(-15, 5), K'(-10, 10) L'(0, 0) and M'(-5, -5)

Hence, the new dilation vertices of the rectangle are J'(-15, 5), K'(-10, 10) L'(0, 0), and M'(-5, -5).

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Answer:

(0,10)

Step-by-step explanation:

You could put any ordered pair, as long as the y value is 10.

The equation of this function is

y = 10  It is a horizontal line going through.  The y intercept is (0,10)                      

[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ D(\stackrel{x_1}{10}~,~\stackrel{y_1}{7})\qquad F(\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ x +10}{2}~~~ ,~~~ \cfrac{ y +7}{2} \right) ~~ = ~~\stackrel{\textit{\LARGE E}}{(1~~,~~-1)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ x +10}{2}=1\implies x+10=2\implies \boxed{x=-8} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{ y +7}{2}=-1\implies y+7=-2\implies \boxed{y=-9}[/tex]

The time will 90% of the population have heard the rumor are by the time of 3:48 PM.

There are commonly 3 forms of populace pyramids made out of age-intercourse distributions-- expansive, constrictive and stationary.Population is described as all nationals gift in, or briefly absent from a country, and extraterrestrial beings completely settled in a country.

This indicator indicates the variety of humans that typically stay in an area. Growth prices are the yearly adjustments in populace as a result of births, deaths and internet migration at some stage in the year.3000–240=1260

1260 folks heard in four hours=315 folks consistent with hour

90% of populace= 3000 x 0.9= 2700 folks

2700–1500=1200 folks

1200/315=3.eight hours past midday or 3.forty eight pm.

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Answer:

- When x = 0, f(x) = -5

- Each time x increases by 1, f(x) increase by 3

- f(x) = 3x - 5

Step-by-step explanation:

m = slope of the graph

m = [tex]\frac{y_{2}-y_{1}}{x_{2}-x{1}}[/tex]

m  = [tex]\frac{4- (-5)}{3-0}[/tex]

m = [tex]\frac{9}{3}[/tex]

m = 3

[tex]y - y_{1} = m ( x - x_{1})[/tex]

[tex]y - (-5) = 3 ( x - 0 )[/tex]

[tex]y = 3x - 5[/tex]

The best measure of central tendency to determine the center of the distribution of teacher salaries is the mean.

The mean is the average of all values in a set and is calculated by adding up all the values and dividing them by the number of values. This measure is particularly useful for data that follows a normal distribution, as teacher salaries are likely to do.

The mean is the most commonly used measure of central tendency and is a good indicator of the center of the data set. It is also relatively easy to calculate. So mean will be the measure of the central tendency to determine the center of the distribution of teacher salaries.

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Answer:

a=82°

b=32°

Step-by-step explanation:

x is the reflection of b

y is the reflection of a

Answer:

Step-by-step explanation:

Calculating Average Weekly Pay for Uneven Work Hours Some professions like nurses & doctors in the healthcare industry might work longer shifts where they are on for 12 hours

By using congruency, it can be calculated that

x = 6, y = 5

What are congruent triangles?

Two triangles are said to be congruent if their corrosponding sides and corrosponding angles are same. There are different axioms of congruency. They are-

AAS axiom, SAS axiom, ASA axiom, SSS axiom, RHS axiom

It is given that [tex]\Delta[/tex] ABC [tex]\cong[/tex] [tex]\Delta[/tex] BAD

So [tex]\angle[/tex]CAB = [tex]\angle[/tex]ABD [Corrosponding parts of congruent triangles are congruent]

4y = 20

y = [tex]\frac{20}{4}\\[/tex]

y = 5

Also,

AC = BD [Corrosponding parts of congruent triangles are congruent]

5x - 3 = 3x + 9

5x - 3x = 9 + 3

2x = 12

x = [tex]\frac{12}{2}[/tex]

x = 6

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The correct option is: As the sample size increases, the variability of the sampling distribution decreases. is the FALSE statement.

The probability distribution of the a statistic that is acquired by repeated sampling of a particular population is called the sampling distribution.

Thus, it is incorrect to say that as the sample size increases, the variability of the sampling distribution decreases.

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Answer: 1402

Step-by-step explanation:

Im assuming u mean [tex]6k^{4} +2k^{3} -6[/tex]

sub in the k value when k = -4

[tex]6(-4)^{4} +2(-4)^{3} -6[/tex]

1536−128−6=1402