A university wants to determine the average salary of its graduating computer science majors. the university asks the graduating classes of 50 students to share their starting salaries when hired. the 50 students had an average salary of $100,000 with a standard deviation of $2,000. find a 95% confidence interval for the average starting salary of computer science majors from the university.

Answer:

288 cm³

Step-by-step explanation:

cuboid formular: lengtg×width×height

Answer:

V = 288 cm³

Step-by-step explanation:

the volume (V) of a cuboid is calculated as

V = length × width × height

  = 8 × 9 × 4

  = 72 × 4

  = 288 cm³

Answer:

One side is 40 cm and the adjacent side is 50 cm

Step-by-step explanation:

We can use a rectangle because a rectangle is a parallelogram.  Draw a rectangle.  Write the width as x and the length as x + 10.  We find the perimeter by adding all 4 side lengths.

Two side lengths are x and two side lengths are x + 10.  If we add all of this together we get 180

x +x +x+10+x+10 = 180

4x + 20 = 180  Combine the like terms.  There are 4 x's and 10+10 is 20

4x = 160  Subtract 20 from both sides

x  = 40  Divide both sides by 4

So, two sides are 40 and two sides are 50, this will add up to 180

Answer:

40 cm & 50 cm

Step-by-step explanation:

one side = X cm (??)

the other side =X+10 cm

Solve

2(x+x+10)=180

x+x+10=90

2x=80

x = 80/2

x=40

therefore

x+10=50cm

Hello,

y = ax + b where a is the slope ! so here the slope is 6

Answer:

x = 8

Step-by-step explanation:

[tex]\frac{9x}{4y}=1[/tex]

[tex]\frac{9x}{4*18} =1[/tex]

9x = 72

x = 8

Substitute -6 in a and -5 in b

5(-6) + 5(-5)

-30+(-25)

=-55

Hope it helps!

Answer:

-55

5x-6 = -30

5 x -5 = -25

-25 + -30 = -55

Step-by-step explanation:

hope this helps

The equation in which b varies directly as the square root of c is b = 50 · √c. (Correct choice: B)

In this problem we have a case of direct variation between two variables, which is mathematically described by a direct proportionality model, whose form and characteristics are shown below:

b ∝ √c

b = k · √c      (1)

Where k is the proportionality constant.

First, we determine the value of the constant of proportionality by substituting on b and c and clearing the variable: (b = 100, c = 4)

k = b / √c

k = 100 / √4

k = 100 / 2

k = 50

Then, the equation in which b varies directly as the square root of c is b = 50 · √c. (Correct choice: B)

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In the case above, the correct vectors are:

The solution for the Ship's vector are:

Note that the Horizontal aspect = 30 cos 30  

                                                   = 25.98.

For the  Vertical aspect = 30 sin(-30)

                                        = -15.

Hence it will be  <25.98, -15>.

In regards to the current's vector:

The Horizontal aspect=  5 sin 20

                                       = 1.71.

The Vertical aspect = 5 cos 20

                                     = 4.7.

Hence it will be <1.71, 4.7>.

Therefore, In the case above, the correct vectors are:

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The equation of the parallel line is  2y-x=-7

A parallel line will have the same slope, but different intercept. Let's assume C in the intercept of this parallel line. Therefore, equation of the parallel would be,

2y-x=C, coefficients of x and y remain the same, since parallel lines.

This line passes through (3, -2). Therefore, substituting those values, we will get value of C.

2.(-2) -3=C

C=(-7)

The equation of the parallel line is therefore 2y-x=-7

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Answer:

See below

Step-by-step explanation:

I am not sure about number 22.  I think that they are asking you to apply the same rules to the point (4, -7), if that is what they mean, the answer is (8,10)

Answer:

y = x + 2

Step-by-step explanation:

You can find the slant asymptote using polynomial long division because the numerator is one degree higher than the denominator.

(x^2+x+4)/(x-1)

I'm not sure how to show long division but you should get:

x+2 with remainder 6

Then your slant asymptote is y = x + 2

You can graph it on Desmos to verify

The probability would be 3/125 in the given conditions.

As there are 105 items, of which 30 are bats. The probability for that draw is 30/105.

There are now 104 items remaining, of which 15 are gloves. The probability of getting a glove now is 15/104.

There are now 103 items remaining, of which 60 are balls. The probability of getting a ball now is 60/103.

The probability of all three occurring = product of three

15/104* 30/105* 60/103

= 3/125

Hence the probability is 3/125.

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The value of sin(∝) is -√56/15

The given parameter is:

cos(∝) = -13/15

To determine the sine, we use the following identity

sin^2(∝) = 1 - cos^2(∝)

So, we have:

sin^2(∝) = 1 - (-13/15)^2

This gives

sin^2(∝) = 1 - 169/225

Evaluate the difference

sin^2(∝) = 56/225

Take the square root of both sides

sin(∝) = ±√56/15

sin(∝) is negative in quadrant III.

So, we have:

sin(∝) = -√56/15

Hence, the value of sin(∝) is -√56/15

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Answer:

using pythagoras theorem

Answer:

Step-by-step explanation:

for the first one, it is x=2

for the second one, it is x=9

The surface area of the composite figure is 444m².

Given a composite figure which is shown in the question.

The  area of ​​a shape (in square units) is the number of unit squares required to cover the entire area without gaps or overlaps. If a hologram has planes, those faces are called faces.

Firstly, we will find the area of front and end triangles by using the formula

Area=(1/2)×b×h and we will multiply this area by 2 because we are finding the area of two same triangles.

Here, h=6 and b=16 and substitute these values in the formula, we get

A₁=2×(1/2)×16×6

A₁=2×8×6

A₁=96m²

Now, we will find the area of the left and right side rectangles which joined both the triangles.

We will find the area by using the formula Area=l×b and we will multiply this area by 2 because we are finding the area of two same rectangles.

here, l=10 and b=5 and substitute these values in the formula, we get

A₂=2×10×5

A₂=100m²

Further, we will find the area of the front and end side rectangles that joined both by the base of the triangles.

We will find the area by using the formula Area=l×b and we will multiply this area by 2 because we are finding the area of two same rectangles.

here, l=16 and b=4 and substitute these values in the formula, we get

A₃=2×16×4

A₃=128m²

Furthermore,  we will find the area of the left and right side rectangles which joined by the front and end rectangles.

We will find the area by using the formula Area=l×b and we will multiply this area by 2 because we are finding the area of two same rectangles.

here, l=4 and b=5 and substitute these values in the formula, we get

A₄=2×4×5

A₄=40m²

Now, we will find the area of the base of the composite figure which is rectangle.

We will find the area by using the formula Area=l×b.

here, l=16 and b=5 and substitute these values in the formula, we get

A₅=16×5

A₅=80m²

So, the surface area of the given composite figure will be

Surface area=A₁+A₂+A₃+A₄+A₅

Surface area=96m²+100m²+128m²+40m²+80m²

Surface area=444m²

Hence, the surface area of the given composite figure is 444m².

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Answer:

f(1) = 81

Step-by-step explanation:

f(n + 1) = 1/3 f(n)

⇔ f(n) = 3 × f(n + 1)

……………………………

if f(3) = 9  ⇒  f(2) = 3 × f(3) = 3 × 9 = 27

Then

f(1) = 3 × f(2) = 3 × 27 = 81

Answer:

10%.

Step-by-step explanation:

There are a total of 40 numbers.

Number of permutations of 3 numbers from 40

= 40 P 3

= 40! / (40-3)!

= 59,280.

The total of even numbers is (38 - 2) / 2 + 1 = 19.

Number of permutations of 3

=  19P 3

=  5814

So Prob(all even) = 5814/59280

= 0.098077

= 9.8%

= 10% to nearest whole number.

1) [tex]\overline{JK} \perp \overline{MN}[/tex]

2) [tex]\angle JKM[/tex] is a right angle (perpendicular lines form right angles)

3) [tex]\triangle JKM[/tex] is a right triangle (definition of a right triangle)

4) [tex]\angle 1[/tex] and [tex]\angle 2[/tex] are complementary (the acute angles of a right triangle are complementary)

The center of the circle = (8, -4)

The radius of the circle =  [tex]\sqrt{76}[/tex]

The given equation of the circle is:

[tex]x^2+y^2-16x+8y+4=0[/tex]

The equation can be expressed and simplified as:

[tex]x^2-16x+y^2+8y=-4\\\\x^2-16y+8^2+y^2+8y+4^2=-4+8^2+4^2\\\\(x-8)^2+(y+4)^2=-4+64+16\\\\(x-8)^2+(y+4)^2=76[/tex]

The general equation of a circle is:

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

Comparing the two equations:

The center, (a, b) = (8, -4)

The radius, r = [tex]\sqrt{76}[/tex]

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The windows width in the drawing according to the task content is; 9.6inches.

According to the task content, the window's actual width on the house is given as; 48 inches.

Hence, since, the window's width on the drawing is 20% of the actual width, it follows that;

Windows drawing width = 20% × 48 = 9.6 inches.

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The function that has a domain of all real numbers is:

A. [tex]y = 2x^{\frac{1}{3}} - 7[/tex].

The domain of a function is the set that contains all possible input values for the function.

If a function has an even root, equivalent to an exponent of [tex]\frac{1}{n}[/tex] with n even, the domain is only positive values, while if the exponent is odd, the domain is all real values.

Researching the problem on the internet, the function with odd exponent is:

A. [tex]y = 2x^{\frac{1}{3}} - 7[/tex].

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Each one of the smaller angles  x = 120 degrees and the larger angle = 2x = 2 × 120 = 240 degrees

The angle of an octagon can be found as follows;

An octagon is a polygon that has 8 sides.

The sum of angles in an octagon is 1080 degrees.

Therefore,

x + x + x + x + x + x + x + 2x = 1080

Hence,

9x = 1080

divide both sides by 9

x = 1080 / 9

x = 120

Therefore, each one of the smaller angles  x = 120 degrees and the larger angle = 2x = 2 × 120 = 240 degrees

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Answer:

(x + 3)^2 + (y - 2)^2 = 25 .

Step-by-step explanation:

The center is at (-3, 2) and the radius is 5.

General form is

(x - h)^2 + (y - k)^2 = r^2

So here we have:

(x  - (-3)^2 + (y - 2)^2 = 5^2

(x + 3)^2 + (y - 2)^2 = 25

Step-by-step explanation:

volume = length • width • height

by making width subject

V=LWH

W=V/LH

W= 54/8×3

W=54/24

W=9/4

W=2.25

Answer:

10 just find the difference between the two

Step-by-step explanation:

16-6=10

Wangmo have 6 years of teaching experience.

Two algebraic expressions having same value and symbol '=' in between are called as an equation.

Let Wangmo has x years of experience.

Jigsel has 6 more years of teaching experience than Wangmo.

So, Jigsel has x + 6 years of experience.

According to the question,

the two of them have 16 years of teaching experience altogether.

That means,

we have the equation,

(x+6) + x = 16

2x = 16 -6

2x = 10

x = 10/2

x = 5

Therefore, Wangmo has 6 years of experience.

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The measure for the unknown angle is 65 degrees.

The two perpendicular lines form a right angle. A right angle would always have a value of 90 degrees.

In order to determine the unknown angle, subtract 25 degrees from 90 degrees.

90 - 25 = 65 degrees

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Using volume of ball bearings, a manufacturer makes 10 ball bearings from 5.2 cm³ of molten steel to make ball bearings that each have a diameter of 1 centimeter.

According to the question,

It takes 5.24 cubic centimeters of molten steel to make ball bearings that each have a diameter of 1 centimeter.

Radius = 1/2 = 0.5 cm

volume V of one ball bearing is: V=(4/3)*π*r³

= 4/3 * π * (0.5)³

=0.524 cm³

In order to find number of ball bearings out of molten steel only if we divide the volume of steel by the volume of the ball bearing

5.24/0.524=10.

Hence, using volume of ball bearings, a manufacturer makes 10 ball bearings from 5.2 cm³ of molten steel to make ball bearings that each have a diameter of 1 centimeter.

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Answer: 4/7

Step-by-step explanation:

You pick one black sock, meaning there are 14 socks remaining in the drawer, 8 of which are black. Thus, the probability is 8/14, which simplifies to 4/7.

A cone is a 3-dimensional shape that consists of a circular or flat surface and a curved side. Thus the volume of the given cone is 4.1 [tex]mi.^{3}[/tex]

A cone is a 3-dimensional shape that consists of a circular or flat surface and curved side. Its volume can be determined by;

The volume of a cone = [tex]\frac{1}{3}[/tex] [tex]\pi[/tex][tex]r^{2}[/tex]h

where r is the radius of its flat surface, and h is its height.

From the given question, we have to determine the value of h using the Pythagoras theorem.

Such that;

[tex]/Hyp/^{2}[/tex] = [tex]/Adj 1/^{2}[/tex] + [tex]/Adj 2/^{2}[/tex]

[tex]4^{2}[/tex] = [tex]h^{2}[/tex] + [tex]1^{2}[/tex]

16 = [tex]h^{2}[/tex] + 1

[tex]h^{2}[/tex] = 15

h = [tex]\sqrt{15}[/tex]

Thus the volume of the cone = [tex]\frac{1}{3}[/tex] [tex]\pi[/tex][tex]r^{2}[/tex]h

                             =  [tex]\frac{1}{3}[/tex]x [tex]\frac{22}{7}[/tex] x [tex]1^{2}[/tex]x    [tex]\sqrt{15}[/tex]

                             = 4.0574

Therefore the volume of the given cone is 4.1 [tex]mi.^{3}[/tex]

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Answer:

8.048 liters

Step-by-step explanation:

Convert 8542 ml to liters:  (8542 ml)(1 liter/1000 ml) = 8.542 liters

Now subtract 0.458 liters to find the amount that a fish tank can hold:

 8.542 liters

-0.458  liters

8.048 liters is the fish tank capacity