Homer is 30 feet below sea level and Marge is 45 feet above sea level. Bart’s elevation is at the exact midpoint of those two values. What is the expression that model this problem, and which is Bart’s elevation?

Answer:

constant of proportionality, k is 3

Step-by-step explanation:

constant, k= y/x

k=9/3

 = 3

Answer:

  x = 10

Step-by-step explanation:

You want the value of x in triangle RST with angle bisector UT dividing RS into parts RU=3x and US=x+2, while RT=40 and ST=16.

The angle bisector divides the sides of the triangle proportionally;

  3x/40 = (x +2)/16

  6x = 5x +10 . . . . . . . multiply by 80

  x = 10 . . . . . . . . . subtract 5x

The value of x is 10.

<95141404393>

Turn me into a superhero

The difference in volume between the two compartments is given as follows:

346.4 cm³.

The volume of a prism is obtained as the multiplication of the area of the base of the prism by the height of the prism, as follows:

The height of the base of the prism in this problem is given as follows:

h² + 5² = 10²

\(h = \sqrt{10^2 - 5^2}\)

h = 8.66.

Hence the base is composed as follows:

Hence the base area is given as follows:

Ab = 5 x 8.66 + 2 x 1/2 x 5 x 8.66

Ab = 86.6 cm².

The height is given as follows:

7 cm.

Hence the volume is:

7 x 86.6 = 606.2 cm³.

The height of the taller prism is given as follows:

11 cm.

Hence the volume is:

11 x 86.6 = 952.6 cm³.

Hence the difference of volumes is of:

952.6 - 606.2 = 346.4 cm³.

More can be learned about the volume of a prism at https://brainly.com/question/23766958

#SPJ1

Answer:

The following data relates the time a student spends on an online test with the final score: (8 points, 20 minutes), (22 points, 40 minutes), (33 points, 58 minutes), (38 points, 120 minutes). Use your TI83 to determine the linear regression equation, and choose the best response below a. Points = -9.3(minutes) +0.26

Step-by-step explanation:

That's literally it hehe

Answer:

D. a = 60 and b = 58.8

Step-by-step explanation:

Z-score:

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Z-score for data point a is 0.

This means that a is the mean, that is, a = 60.

The z-score for data point b is -0.4.

This means that b must be a value below the mean, that is, a value below 60.

The option that satisfies a = 60 and b < 60 is option D, which is the answer.

The solutions of the quadratic equation:

9x² -12x - 4 = 0

are x  = 12.944 and x  = -0.278

Here we want to solve the quadratic equation:

9x² -12x - 4 = 0

To solve it we can use the quadratic formula, we will get:

\(x = \frac{12 \pm \sqrt{(-12)^2 - 4*9*(-4)} }{2*9} \\\\x = \frac{12 \pm 17}{18}\)

Then the two solutions are:

x = (12 + 17)/18 = 12.944

x = (12- 17)/18 = -0.278

Learn more about quadratic equations:

https://brainly.com/question/1214333

#SPJ1

Answer:

Area of big rectangle - area of mini rectangle

56in2 - 3in2

B. 53 in2

Step-by-step explanation:

Separate the two rectangleulsr shapes. 3x6 which equals 18.

8-3=5

5×7= 35

35+18= 53

B. 53 in sq

Answer:

x=45

Step-by-step explanation:

i hope its right good luck :)

i think im wrong

Answer: 11.11%

17:153*100 =

(17*100):153 =

1700:153 = 11.11

Answer:

the surface area of the rectangular prism is 572cm².

Step-by-step explanation:

The surface area of a rectangular prism can be calculated using the formula 2lw + 2lh + 2wh, where l is the length, w is the width, and h is the height. Plugging in the values you provided, we get:

2 * 4cm * 15cm + 2 * 4cm * 14cm + 2 * 15cm * 14cm = 572 cm²

So the surface area of the rectangular prism is 572 square centimeters.

Answer:

25 less than 19

Step-by-step explanation:

Required

Determine the odd one among the list of options

Start by taking the options one after the other;

1. 19 less than 25:

This implies 25 - 19

2. 25 less than 19

This implies 19 - 25

3. 19 subtracted from 25

This implies 25 - 19

4. 25 minus 19

This implies 25 - 19

From the above analysis, the off option is option (2);

Answer:

25 less than 19

Step-by-step explanation:

Required

Determine the odd one among the list of options

Start by taking the options one after the other;

1. 19 less than 25:

This implies 25 - 19

2. 25 less than 19

This implies 19 - 25

3. 19 subtracted from 25

This implies 25 - 19

4. 25 minus 19

This implies 25 - 19

From the above analysis, the off option is option (2);

Answer:

87,010 cents is the SP.

Step-by-step explanation:

MP = $1400

VAT = 13%

Discount = 45%

so,

discount amount = 45% of MP

= 45% of $1400

= 45/100 * $1400

= 9/20 * $1400

= 9* $70

= $630

so,

MP - discount amount

= $1400 - $630

= $770(SP)

so,

VAT amount = 13% of SP

= 13% of $770

= 13/100 * $770

= $100.1

so,

SP + VAT

= $770 + $100.1

= $870.1

so,

$1 = 100 cents

$870.1 = 100*870.1

= 87,010 cents

The lateral and the total surface area of the rectangular pyramid are 182 square cm and  278 square cm

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

Length = 6 cm

Width = 8 cm

Height = 6.5 cm

The lateral surface area of the rectangular pyramid is calculated as

LA = 2 *(L + W)H

So, we have

LA = 2 *(6 + 8) * 6.5

Evaluate

LA = 182

The total surface area of the rectangular pyramid is calculated as

TA = 2 * (LW + LH + HW)

So, we have

TA = 2 * (8 * 6 + 8 * 6.5 + 6.5 * 6)

Evalaute

TA = 278

Hence, total surface area of the rectangular pyramid is 278 square cm

Read more about surface area at

https://brainly.com/question/26403859

#SPJ1

Answer:

a=3; (3,5) and (4,0) for the graph  

Step-by-step explanation:

ax-y=4

x=3, y=5 so...

a(3)-5=4

3a-5=4

+5 +5

3a=9

/3 .  /3

a=3

For the graph, use (3,5) and substitute x and y for anything:

ax-y=4

if x=0...

a(0)-y=4

-y=4

y=4

a=3; (3,5) and (4,0) for the graph!

The set (A U B) n (A U C) is {2, 5, 7, 10}. A.

To find the set (A U B) n (A U C), we first need to calculate the union of sets A and B, and then calculate the union of that result with set C. Finally, we find the intersection of these two sets.

Set A U B:

The union of sets A and B, denoted as A U B, is the combination of all elements from both sets without any repetitions.

A contains the elements 2, 5, 7, and 10, while B contains the elements 1, 2, and 3.

A U B consists of the elements {1, 2, 3, 5, 7, 10}.

Set (A U B) U C:

Next, we calculate the union of the set (A U B) with set C, denoted as (A U B) U C. A U B contains the elements {1, 2, 3, 5, 7, 10} and C contains the elements {1, 2, 3, 4, 5}.

Taking the union of these two sets results in {1, 2, 3, 4, 5, 7, 10}.

Finding the intersection:

Finally, we find the intersection of (A U B) U C with A U C. A U C consists of the elements {2, 5, 7, 10}.

The intersection of these two sets is the combination of common elements.

The common elements are {2, 5, 7, 10}.

For similar questions on set

https://brainly.com/question/13458417

#SPJ8

Sarah's fuel efficiency is approximately 32.91 miles per gallon.

From the question, we are to calculate Sarah's fuel efficiency.

To find Sarah's fuel efficiency in miles per gallon, we need to convert the distance she drove to miles and the amount of gasoline she used to gallons.

From the given information,

1 km = 0.6214 mi

1 gal = 3.8 L

First, let's convert the distance from kilometers to miles:

691.4 km × 0.6214 mi/km = 430.10196 mi

So, Sarah drove a distance of 430.1 miles.

Also,

Convert the amount of gasoline from liters to gallons:

49.7 L ÷ 3.8 L/gal = 13.0789 gal

So, Sarah used 13.0789 gallons of gasoline.

Calculate her fuel efficiency in miles per gallon:

Fuel efficiency = distance ÷ gasoline used

Fuel efficiency = 430.1 mi ÷ 13.0789 gal

Fuel efficiency = 32.9065 mi/gal

Hence, Sarah's fuel efficiency is 32.91 mi/gal

Learn more on Calculating fuel efficiency here: https://brainly.com/question/27021605

#SPJ1

Answer:

Step-by-step explanation: you sjxhbtdtbd

Answer:

\(x=-\frac{4}{5}\)

Step-by-step explanation:

\(6=\frac{3}{4}(10x+16)\\\mathrm{or,\ }6\times 4=3(10x+16)\\\\\mathrm{or,\ }24=30x+48\\\\\mathrm{or,\ }-24=30x\\\\\mathrm{\therefore}\ x=-\frac{4}{5}\)

Answer:

If x is replaced with -x the graph will stay the same because the absolute value makes 2 values so a negative number and a positive one.

Step-by-step explanation:

Go search it up on desmos.

Answer:

True

Step-by-step explanation:

I remembered learning this definition for a matrix:

A Matrix is an arrangement of numbers into rows and columns

so yes matrices consist of rows and columns

a) The dot product of v and -v is -1.

b) The dot product of v + w and v – w is 2v.w

c) The dot product of v – 2w and v + 2w is 4||w||^2 - 4v.w

(a) For any unit vector v, the dot product of v and -v can be found as follows:

v · -v = ||v||||-v||cos(θ) = ||v||||v||cos(180°) = -||v||^2 = -1, where ||v|| represents the magnitude of the vector v and θ is the angle between the vectors.

Since v and -v are unit vectors, their magnitudes are equal to 1, so ||v||^2 = 1. Thus, the dot product of v and -v is -1.

(b) For any unit vectors v and w, the dot product of v + w and v – w can be found as follows:

(v + w) · (v – w) = ||v + w||||v – w||cos(θ) = (||v||||v|| + 2v · w + ||w||||w||)cos(θ) = 2v · w

where θ is the angle between the vectors v + w and v – w, and v · w is the dot product of v and w.

(c) For any unit vectors v and w, the dot product of v – 2w and v + 2w can be found as follows:

(v – 2w) · (v + 2w) = ||v – 2w||||v + 2w||cos(θ) = (||v||||v|| + 4||w||||w|| - 4v · w)cos(θ) = 4||w||^2 - 4v · w

where θ is the angle between the vectors v – 2w and v + 2w, and v · w is the dot product of v and w.

To learn more about vectors click on,

https://brainly.com/question/14376687

#SPJ4

Evaluating [log2(3)].[log3(4)].[log4(5)]...[log63(64)] is 6

We can use the property that [log_a(b)]=[log_c(b)/log_c(a)] to simplify the expression. Applying this property repeatedly, we get:

[log2(3)].[log3(4)].[log4(5)]...[log63(64)]

= [log2(3)/log2(2)].[log3(4)/log3(3)].[log4(5)/log4(4)]...[log63(64)/log63(62)]

= [log2(3)/1].[log3(4)/1].[log4(5)/1]...[log63(64)/1]

= log2(3) log3(4) log4(5) ... log63(64)

Now, we can use the identity [log_a(b)log_b(c)log_c(d)...log_y(z)] = log_a(z) to combine the logarithms into a single logarithm with a base of 2:

log2(3) log3(4) log4(5) ... log63(64) = log2(64)

Since 2^6 = 64, we have:

log2(64) = 6

Therefore,  [log2(3)].[log3(4)].[log4(5)]...[log63(64)] evaluates to 6.

learn more about logarithmic terms at:https://brainly.com/question/25710806

#SPJ1

Answer:

$ 140,104.96  

Step-by-step explanation:

The amount the bank will the individual is the present value of the total mortgage payment.

monthly mortgage payment=28%*$36,000/12=$840

the payment is meant for 30 years but 360 months i.e 12*30

the amount of loan is the present value of $840 monthly for 360 months with 0.5% interest rate per month

=pv(rate,nper,-pmt,fv)

rate is 0.5%

nper is 360 months

pmt is $840 per month

fv is the total payments which is unknown

=pv(0.5%,360,-840,0)=$140,104.96  

The loan amount is closest to $ 140,104.96  

Given

The floor plan of a house is,

After installing new hardwood flooring , you also need to install base board around the bottom of the walls.

To find: How many feet of base board will you need to buy?

Explanation:

It is given that,

The floor plan of a house is,

After installing new hardwood flooring , you also need to install base board around the bottom of the walls.

That implies,

The perimetr of the base board is,

Hence, we need to buy 108ft of base board.

9514 1404 393

Answer:

Step-by-step explanation:

The latus rectum is the horizontal chord through the focus. It intersects the parabola at a point that is equidistant from the focus and the directrix (as all points on the parabola are). The vertex is half the distance from the focus to the directrix, so the points of intersection are twice as far horizontally from the focus as they are vertically from the vertex.

The short of it is this: draw a line with slope 1/2 through the vertex. Where it intersects the parabola is one end of the latus rectum. The y-coordinate of the point will be the y-coordinate of the focus.

Here, the vertex is (-1, 4). A line of slope 1/2 through that point will intersect the parabola at (-3, 3). This means the focus is (-1, 3), one unit below the vertex. That -1 unit is the value of p. The location of the directrix is that 1 unit in the opposite direction from the vertex, at y = 5.

Answer:

c.

Step-by-step explanation:

as this can take on any value (with as many digits after the decimal point as necessary) between certain interval limits.

all the others are usually either pure integers (and every real number in between them is not valid) or at most have finite fractions (like 1/2 or 1/4 points for scores, and between these no value is valid).

The distance from the north most ship to the observation is 2.9 miles and the distance from the south most ship to the observation is 9.9 miles.

The bearing is defined as the angle measured clockwise from the north direction. A ship is anchored off a long straight shoreline that runs north and south.

From two observation points miles apart on shore, the bearings of the ship are 52 degrees and 134 degrees respectively. To find the distance from the ship to each of the observation points, we can use trigonometry.

Let's call the distance from the north observation point to the ship x, and the distance from the south observation point to the ship y. The bearings from the north and south observation points can be drawn as follows:

[asy]

unitsize(1cm);

pair O = (0,0), N = (-2,0), S = (2,0), A = (-2,1), B = (2,-1);

draw(O--N--A,Arrow);

draw(O--S--B,Arrow);

\(label("$52^\circ$", N + 0.3*dir(52), NE);\)

\(label("$134^\circ$", S + 0.3*dir(134), SE);\)

draw(O--A--B--cycle,dashed);

\(label("$x$", (N+A)/2, W);\)

\(label("$y$", (S+B)/2, E);\)

[/asy]

We can use the tangent function to find x and y, since we have the angle and opposite side.

From the north observation point, we have:

\($$\tan(52^\circ) = \frac{x}{2}$$$$x = 2\tan(52^\circ) \approx 2.95$$\)

From the south observation point, we have:

\($$\tan(134^\circ) = \frac{y}{2}$$$$y = 2\tan(134^\circ) \approx 9.88$$\)

Therefore, the distance from the north most ship to the observation is 2.9 miles and the distance from the south most ship to the observation is 9.9 miles.

Know more about  trigonometry   here:

https://brainly.com/question/13729598

#SPJ8

Let x be the number of 5 point questions and y be the number of 15 point questions.

So we have,

5x+15y = 350 ....... (1)

Also, x + y = 40

So,

Substituting the value of x in first equation,

Therefore,

Thus, there are 25 questions of 5 points and 15 questions of 15 points.