salaries of 38 college graduates who took a statistics course in college have a mean, x, of $69,800. assuming a standard deviation, o, of $16,094, constructs a 95% confidence interval for estimating the population mean u.

Answer:

its easy

Step-by-step explanation:

Find vertex

So

The graph shifted 3 units right.

So new translation

Find y intercept

But it's at (0,1) approximately

So compression factor

Now last equation

Find value

So compression factor

So accurate equation is

Answer:

[tex]g(x)=\dfrac{2}{7}|x-3|[/tex]

Step-by-step explanation:

Translations

For [tex]a > 0[/tex]

[tex]f(x-a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]

[tex]y=a\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis by a factor of}\:a[/tex]

-----------------------------------------------------------------------------------------

Parent function:   [tex]f(x)=|x|[/tex]

The vertex of the parent function is at (0, 0) as  [tex]f(0)=|0|=0[/tex]

From inspection of the graph, the vertex of the transformed function is at (3, 0).  Therefore, there has been a translation of 3 units right:  

[tex]\implies g(x)=f(x-3)=|x-3|[/tex]

(There has not been any vertical translation since the y-value of the vertex of the parent function and the translated function is the same)

From inspection of the graph, we can see that it has been stretched parallel to the y-axis:

[tex]\implies g(x)=a\:f(x-3)=a|x-3|[/tex]

The line goes through points (10, 2) and (-4, 2).

Substituting one of these points to find a:

[tex]\implies a|10-3|=2[/tex]

[tex]\implies 7a=2[/tex]

[tex]\implies a=\dfrac{2}{7}[/tex]

Therefore,

[tex]g(x)=\dfrac{2}{7}|x-3|[/tex]

Answer:

12 red balls

4 yellow balls

2 blue balls

2 green balls

Step-by-step explanation:

set no. of yellow, blue, red and green ball as y, b, r, g respectively

y=2b

r=3y

g=b

y+b+r+g = 20 (translate all of them into b (smallest in qty)

2b + b + 3(2b) + b = 20

10b = 20

b =2

y = 4, r = 12, b =2, g =2

Answer:

141.37 ft^3

Step-by-step explanation:

No question was asked, but based off of the given information, I will assume you want to know the volume of the circular cylinder.

The volume of a circular cylinder is: v=(π)(r^2)(h)

r=3

h=5

v=(π)(3^2)(5)

v = 141.37

Answer:

32/22

Step-by-step explanation:

X+3Y= 6--------(1) ×6

6X-6Y=4--------(2)×1

6X+18Y=36---------(3)

6X-6Y= 4-----------(4)

subtracting equation(4)from (3)

22X = 32

x= 32/22

Answer: a

Step-by-step explanation:

Answer:

4 > 32

Step-by-step explanation:

The variable x represents how much each of Darren's burgers will weigh. Since he will form 4 burgers of equal weight, the expression 4x represents the total weight of the burgers.

And, since Darren will use more than 32 ounces of burger mix, 4x must be greater than 32.

This inequality shows the relationship.

4x > 32

Now, solve for x.

4x > 32

4x/4 32/4

divide 32 by 4

So the answer is x > 8

Answer:

1) 2

2) 4

3) 3

4) 1

Step-by-step explanation:

8/4 is 2

8/2 is 4

3/1 is pretty simply 3

And lastly (and kind of least)...

3/3 is 1

Hope this helped you out!

Answer:

25/33

Step-by-step explanation:

Answer:

[tex]\frac{25}{33}[/tex]

Step-by-step explanation:

we require 2 equations with the repeating digits placed after the decimal point.

let x = 0.7575..... (1) ← multiply both sides by 100

100x = 75.7575... (2)

subtract (1) from (2) thus eliminating the repeating digits

99x = 75 ( divide both sides by 99 )

x = [tex]\frac{75}{99}[/tex] = [tex]\frac{25}{33}[/tex] ← in simplest form

Using the t-distribution, it is found that the proportion in a t-distribution less than −1.4 if the samples have sizes n1=30 and n2=40 is of 0.083.

The proportion is found using a calculator, with three inputs:

In this problem, we have a left-tailed proportion, as we want the proportion that is less than a value, with test statistic t = -1.4 and 30 + 40 - 2 = 68 df, hence the proportion is of 0.083.

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Answer:

I have no idea I am so sorrt

Answer:

[tex](x-5)^2+(y-1)^2=20[/tex]

Step-by-step explanation:

Equation of a circle

[tex](x-a)^2+(y-b)^2=r^2[/tex]

(where (a, b) is the center and r is the radius)

Given:

Diameter = 2r (where r is the radius)

⇒ r = 4√5 ÷ 2 = 2√5

Substituting these values into the equation:

[tex]\implies (x-5)^2+(y-1)^2=(2\sqrt{5})^2[/tex]

[tex]\implies (x-5)^2+(y-1)^2=20[/tex]

Answer:

66.67%

If it wrong! IM SO SORRY:(

we know that

the dimensions of the first garden are------> 5 ft x 3 ft

perimeter first garden=2*[5+3]-----> 16 ft

the dimensions of the second garden are---> (5*2) ft x (3*2) ft

10 ft x 6 ft

perimeter second garden=2*[10+6]-----> 32 ft

so

The answer is

32

Answer: ac bd be 2bd

Step-by-step explanation: addion

Answer:

P(S ∪ T) = 3/4

Step-by-step explanation:

Given:

For mutually exclusive events S and T,

P(S ∪ T) = P(S) + P(T)

Therefore,

P(S ∪ T) = (5/8) + (1/8)

              = 6/8

              = 3/4

Answer:

Step-by-step explanation:

Students with 1 to 3 pairs of shoes:

Students with 13 - 15 pairs of shoes:

Solve 32 - 4:

Using the formula for calculating the area of a rhombus, the length of /AC/ is 44 units

From the question, we are to determine the length of AC

The area of a rhombus is given by

[tex]A = \frac{pq}{2}[/tex]

Where A is the area

p and q are the diagonals

Then, for the given diagram,

[tex]A = \frac{/DB/ \times /AC/}{2}[/tex]

From the given information,

A = 264 square units

/DB/ = 12 units

∴ [tex]264 = \frac{12\times /AC/}{2}[/tex]

[tex]264 = 6\times /AC/[/tex]

[tex]/AC/ = \frac{264}{6}[/tex]

/AC/ = 44 units

Hence, the length of /AC/ is 44 units

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Answer:

62.8 inches

.Step-by-step explanation:

The wire consists of 14 semicircle + 4 3/4 circles. The diameter of each circle = 8 / 4 = 2 inches.Length of a semicircle = 1/2 * pi * diameter and of a 3/4 circle it is 3/4 * pi * diameter.So the perimeter of the wire= 14 * 1/2 * 3.14 * 2 + 4 * 3/4 * 3.14 * 2= 14 * 3.14 + 4 * 3/2 * 3.14= 62.8  inches.

Answer:

62.8 inches

Step-by-step explanation:

= 14 * 1/2 * 3.14 * 2 + 4 * 3/4 * 3.14 * 2

= 14 * 3.14 + 4 * 3/2 * 3.14

= 62.8  inches.

Answer:

20

Step-by-step explanation:

28 + 8 = 36

36 - 13 = 23

23 - 3 = 20

Problem 1

a = 2500 = starting amount

b = 1 + r = 1 + 0.035 = 1.035 = growth factor

The equation is [tex]y = 2500*1.035^x[/tex] as it is in the form [tex]y = a*b^x[/tex]

Plug in y = 5000 and solve for x.

[tex]y = 2500*1.035^x\\\\5000 = 2500*1.035^x\\\\1.035^x = 5000/2500\\\\1.035^x = 2\\\\\log(1.035^x) = \log(2)\\\\x\log(1.035) = \log(2)\\\\x = \log(2)/\log(1.035)\\\\x \approx 20.148792\\\\x \approx 21\\\\[/tex]

I rounded up to get over the hurdle. This is because plugging x = 20 will lead to y being smaller than $5000, so we must use x = 21.

=========================================================

Problem 2

a = 4.22 = starting amount

b = 1 + r = 1 + 0.031 = 1.031 = growth factor

The equation goes from [tex]y = a*b^x[/tex] to [tex]y = 4.22*1.031^x[/tex]

Plug in y = 9.33 and solve for x.

[tex]y = 4.22*1.031^x\\\\9.33 = 4.22*1.031^x\\\\1.031^x = 9.33/4.22\\\\1.031^x \approx 2.21090047393365\\\\\log(1.031^x) \approx \log(2.21090047393365)\\\\x\log(1.031) \approx \log(2.21090047393365)\\\\x \approx \log(2.21090047393365)/\log(1.031)\\\\x \approx 25.9882262216245\\\\x \approx 26\\\\[/tex]

=========================================================

Problem 3

a = 400 = initial value

b = 1 + r = 1 + 0.25 = 1.25 = growth factor

The template [tex]y = a*b^x[/tex] updates to [tex]y = 400*1.25^x[/tex]

Plug in y = 3000 and isolate x.

[tex]y = 400*1.25^x\\\\3000 = 400*1.25^x\\\\1.25^x = 3000/400\\\\1.25^x = 7.5\\\\\log(1.25^x) = \log(7.5)\\\\x\log(1.25) = \log(7.5)\\\\x = \log(7.5)/\log(1.25)\\\\x \approx 9.029627\\\\x \approx 10\\\\[/tex]

Like with the first problem, I rounded up to the nearest whole number. If you tried out x = 9, then y = 2980 approximately which is short of the goal of 3000. Trying x = 10 leads to y = 3725 approximately, which is now over the goal we're after.

[tex]\\ \rm\Rrightarrow P=P_o(1+r)^t[/tex]

[tex]\\ \rm\Rrightarrow 5000=2500(1+0.035)^t[/tex]

[tex]\\ \rm\Rrightarrow 2=1.035^t[/tex]

[tex]\\ \rm\Rrightarrow log2=log1.035^t[/tex]

[tex]\\ \rm\Rrightarrow log2=tlog1.035[/tex]

[tex]\\ \rm\Rrightarrow t=\dfrac{log2}{log1.035}[/tex]

[tex]\\ \rm\Rrightarrow t=20.15[/tex]

We can't take 20 as it can cause depict in price .

#2

[tex]\\ \rm\Rrightarrow 9.33=4.22(1+0.031)^t[/tex]

[tex]\\ \rm\Rrightarrow 9.33=4.22(1.031)^t[/tex]

[tex]\\ \rm\Rrightarrow 1.031^t=2.21[/tex]

[tex]\\ \rm\Rrightarrow log1.031^t=log2.21[/tex]

[tex]\\ \rm\Rrightarrow tlog1.031=log2.21[/tex]

[tex]\\ \rm\Rrightarrow t=\dfrac{log2.21}{log1.031}[/tex]

[tex]\\ \rm\Rrightarrow t=25.97\approx 26[/tex]

#3

[tex]\\ \rm\Rrightarrow 3000=400(1+0.25)^t[/tex]

[tex]\\ \rm\Rrightarrow 30/4=1.25^t[/tex]

[tex]\\ \rm\Rrightarrow 7.5=1.25^t[/tex]

[tex]\\ \rm\Rrightarrow log7.5=log1.25^t[/tex]

[tex]\\ \rm\Rrightarrow log7.5=tlog1.25[/tex]

[tex]\\ \rm\Rrightarrow t=\dfrac{log7.5}{log1.25}[/tex]

[tex]\\ \rm\Rrightarrow t=9.03[/tex]

Same like first case

The image of the quadrilateral after the translation is added as an attachment

The given parameter represents the quadrilateral ABCD on the graph.

On this graph, we have the coordinates of ABCD to be:

A = (2, -3)

B = (-1, 3)

C = (-1, -3)

D = (-4, -4)

The translation is given as

2 units to the left and 3 units up.

Mathematically, this can be represented as

(x, y) = (x - 2, y + 3)

So, we have

A' = (0, 0)

B = (-3, 6)

C = (-3, 0)

D = (-6, -1)

Next, we plot the above coordinates on the graph (See attachment)

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Answer:

look at the photo

Step-by-step explanation:

it just is

Answer:

Step-by-step explanation:

3x^2(x +2) = 3x^3 + 6x^2 is the answer

Answer:

h ≥ 8 cm

Step-by-step explanation:

Solving :

V ≥ 32 cm³

a = 4 cm²

h ≥ 32/4

h ≥ 8 cm

Answer:

K=4

Y=16

X=4

Step-by-step explanation:

[tex]y = kx {}^{2} \\ finding \: k \: when \: y= 36 \: and \: x = 3 \\ 36 = k(3) {}^{2} \\ 36 = 9k \\ dividing \: through \: by \: 9 \\ \frac{36}{9} = \frac{9k}{9} \\ 4 = k \\ k = 4 \\ findnig \: y \: when \: x = 2 \\ y = 4(2) {}^{2} \\ y = 4 \times 4 = 16 \\ finding \: x \: when \: y = 64 \\ 64 = 4 \times x \\ 64 = 4x \\ dividing \: through \: by \: 4 \\ \frac{64}{4} = \frac{4x {}^{2} }{4} \\ 16 = x {}^{2} \\ square \: root \: bothsides \\ \sqrt{16} = x {}^{2} \\ 4 = x \\ x = 4[/tex]

Recall the double angle identity for cosine:

[tex]\cos(2x) = \cos^2(x) - \sin^2(x) = 1 - 2 \sin^2(x)[/tex]

It follows that

[tex]\sin^2(x) = \dfrac{1 - \cos(2x)}2 \implies \sin(x) = \pm \sqrt{\dfrac{1-\cos(2x)}2} \implies \csc(x) = \pm \sqrt{\dfrac2{1-\cos(2x)}}[/tex]

Since 0° < 22° < 90°, we know that sin(22°) must be positive, so csc(22°) is also positive. Let x = 22°; then the closest answer would be C,

[tex]\csc(22^\circ) = \sqrt{\dfrac2{1-\cos(44^\circ)}} = \sqrt{\dfrac2{1-\frac5{13}}} = \dfrac{\sqrt{13}}2[/tex]

but the problem is that none of these claims are true; cot(32°) ≠ 4/3, cos(44°) ≠ 5/13, and csc(22°) ≠ √13/2...

Answer:

The police caught the bank robbers(passive)

Answer:

1. it's False because the radian measure of an angle is the length..

Transcribed image text: h of the following statements as true or false. replace lace the underlined word(s) or expression to produce a true statement. The radian measure of an angle equals the length of the arc it intercepts.on the Any degree measure can be converted to radians 180 by by _. To construct the inverse of a trigonometric function, the function must be restricted to a domain on which the function is either always increasing or The length of an arc intercepted by an angle is proportional to the radius; therefore, a central angle of - in a circle with radius k will intercept an an with length kt A triangle with side lengths 7, 11.and 14 has an area of 120-21 Area : Jlo (16-706-Ingen llo

Step-by-step explanation:

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A new shape with an area of 1 square unit that is not a square can be formed by combining two small triangles

The given parameters are:

The area of each small triangle is:

Area = 0.5 square unit

Multiply both sides by 2

2 * Area of triangle = 1 square unit

Substitute Area of square = 1 square unit

2 * Area of triangle = Area of square

This means that a new shape can be formed by combining two small triangles

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