4. The distance needed to stop a car varies directly as the square of its speed. It
requires 120 m to stop a car at 70 km/h. What distance is required to stop a car
at 80 km/h?

Answers

Answer 1

Answer:

156.7 m (nearest tenth)

Step-by-step explanation:

Define the variables:

Let d = distance in meters.Let v = speed in kilometers per hour.

If the distance needed to stop a car varies directly as the square of its speed:

[tex]\boxed{d \propto v^2 \implies d=kv^2}[/tex]

where k is the constant of proportionality.

Given:

d = 120 mv = 70 km/h

To find the constant of proportionality, k, substitute the given values into the equation:

[tex]\begin{aligned}\implies 120&=k(70)^2\\k&=\dfrac{120}{70^2}\\k&=\dfrac{6}{245}\end{aligned}[/tex]

Substitute the found value of k back into the formula to create an equation for the given relationship:

[tex]\implies d=\dfrac{6v^2}{245}[/tex]

To find the distance (in meters) required to stop a car at 80 km/h, substitute v = 80 into the equation:

[tex]\implies d=\dfrac{6(80)^2}{245}[/tex]

[tex]\implies d=\dfrac{6\cdot 6400}{245}[/tex]

[tex]\implies d=\dfrac{7680}{49}[/tex]

[tex]\implies d=156.73469...\; \sf m[/tex]

[tex]\implies d=156.7\; \sf m\; (nearest \;tenth)[/tex]

Therefore, the distance required to stop a car at 80 km/h is:

156.7 m (2 d.p.).

Related Questions

There are 207 public libaries in New York City. The population in New York City is 8.805 million. What was the rate of libraries per 100,000? Give your answer to the nearest hundredth.

Answers

The rate of libraries per 100000 is 88.05   .

In the question ,

it is given that ,

the number of public libraries in New York City = 207 libraries

the population of the New York City = 8.805 million

we have to find the rate of libraries per 100000  .

for this we first have to express the population in numbers .

the population 8.805 million expressed in numbers is 8805000 ,

the rate of libraries per 100000 is

= 8805000/100000

On further simplification ,

we get ,

= 88.05

Therefore , The rate of libraries per 100000 is 88.05   .

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Evaluate the exponential functions

Answers

I hope this helps. Have a great rest of your day!

write -(1/4x1/4x1/4x1/4) using exponents

Answers

The solution to the mathematical expression -(1/4x1/4x1/4x1/4) in exponent form is [tex]\mathbf{-4^{-4}}[/tex]

Writing mathematical expressions in exponents form

Number multiplication is a basic and common operation. However, the product of multiplication can be stated differently at times, whether to reduce the equation or to explain the mathematics required. Many numbers can be expressed exponentially.

The concept of exponential form is a method of expressing a number that has been multiplied by itself several times. The fundamental formula is [tex]\mathbf{y=b^x}[/tex]

Exponential expressions are simply a shorthand way of writing powers. The exponent specifies how many times the base has been utilized as a factor.

From the information given

:= -(1/4*1/4*1/4*1/4)[tex]

=-(4^{-1}\times4^{-1}\times4^{-1}\times4^{-1})[/tex][tex]=-(4^{(-1+(-1)+(-1)+(-1))})[/tex][tex]=-(4^{(-1-1-1-1)})[/tex][tex]=-(4^{(-4)})[/tex][tex]\mathbf{=-4^{-4}}[/tex]

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Which defines a circle?

two rays with a common endpoint
a piece of a line with two endpoints
a piece of a line with one endpoint
all coplanar points equidistant from a given point

Answers

The term that defines a circle is "all coplanar points equidistant from a given point". Then the correct option is D.

What is a circle?

It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.

The definition of the circle is written as "A circle is a shape comprising of all places in a plane that are at a given separation from a given point, the middle."

The circle is a two-dimensional shape.

The term that defines a circle is "all coplanar points equidistant from a given point". Then the correct option is D.

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Answer: D) all coplanar points equidistant from a given point

Step-by-step explanation:

WILL GIVE BRAINLIEST
You walk 10km North then turn and walk 5km East. What is your displacement from where you started? Show your work

Answers

Answer:

A hiker walks 10 km East, then 5 km in a direction 60 degrees North of West, then 8.7 km in a direction 30 degrees South of West. Find her resultant displacement.

Since you walk 10km North then turn and walk 5km East, your displacement from where you started is approximately 11.18 km.

How to determine the displacement

From the information given, we have that you walked 10 km north (which represents the vertical side of the triangle) and 5 km east Using the Pythagorean theorem, the displacement (d) can be determined  as;

[tex]d^2 = (10 km)^2 + (5 km)^2[/tex]

Find the square values, we get

d² = 100 km² + 25 km²

add the squares, we get

d² = 125 km²

Find the square root of both sides of the equation, we have;

d = 125km²

d =  11.18 km

Therefore, your displacement from where you started is approximately 11.18 km.

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A climbing gym charges $10 to climb each day a player of climbing shoes cost 84 it cost 169 to buy six days of climbing one pair of climbing shoes and one harness how much does a harness cost

Answers

If each day a player of climbing shoes cost 84 it cost 169 to buy six days of climbing one pair of climbing shoes and one harness. The amount that the harness cost is $25.

How to find the harness cost?

Cost of climbing = ( $10×6)

Cost of climbing = $60

Harness cost = Total cost  - (Cost of climbing  + Cost of shoes)

Harness cost =$169 - ($60 + $84)

Harness cost =$169 - $144

Harness cost =$25

Therefore $25 is the harness cost.

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Pls help me, giving brainliest 50 POINTS!

Pls show your work and not only your answers pls

Answers

Correct Answer:
9) LCM = 36; GCF = 3
10) LCM = 108; GCF = 6
11) LCM = 48; GCF = 4

Explanation:
9)
36 = 2 x 2 x 3 x 3 = 2² x 3²
3 = 3
12 = 2 x 2 x 3 = 2² x 3

LCM = 2 x 2 x 3 x 3 = 36
GCF = 3

10)
6 = 2 x 3
54 = 2 x 3 x 3 x 3 = 2 x 3³
12 = 2 x 2 x 3 = 2² x 3

LCM = 2 x 2 x 3 x 3 x 3 = 108
GCF = 2 x 3 = 6

11)
16 = 2 x 2 x 2 x 2 = 2⁴
8 = 2 x 2 x 2 = 2³
12 = 2 x 2 x 3 = 2² x 3

LCM = 2 x 2 x 2 x 2 x 3 = 48
GCF = 2 x 2 = 4

I would appreciate it if you mark my answer as brainliest.

how to find the area with a circumfernece of 18

Answers

The area of the circle with the circumference 18 units is 25.80 square units

How to calculate the area of the circle?

The given parameters are

Circumference = 18 units

As a general rule, circumference are represented by the variable C

So, we have the following representation equation

C = 18

The circumference of the circle can be calculated as

C = 2πr

Next, we substitute the value of the variable C in the above equation

i.e. C = 18

So, we have the following equation

2π * r = 18

Divide both sides by 2π

r = 9/π

The area of the circle can then be calculated using the following area formula

A = πr²

Next, we substitute the value of the variable r in the above equation

i.e. r = 9/π

A = π * (9/π)²

Evaluate the exponents

This gives

A = π * 81/π²

Evaluate the products

So, we have

A = 81/π

As a general notation, π = 3.14

So, we have the following equation

A = 81/3.14

Evaluate the quotient

A = 25.80

Hence, the area is 25.80 square units

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Which of the following choices would move this curve to the RIGHT 17 units and up 4 units: y=(x+6)^2 - 2

Answers

If we start with the parent quadratic function, then the transformation is:

g(x) =  (x - 17)^2 + 4

Which transformations move the graph in the desired way?

The definitions of translations are:

Horizontal translation:

For a general function f(x), a horizontal translation of N units is written as:

g(x) = f(x + N).

If N is positive, the shift is to the left.If N is negative, the shift is to the right.

Vertical translation:

For a general function f(x), a vertical translation of N units is written as:

g(x) = f(x) + N.

If N is positive, the shift is upwards.If N is negative, the shift is downwards.

Then if the parent function is:

f(x) = x^2

The translation of 17 units to the right and 4 units up is:

g(x) = f(x - 17) + 4 = (x - 17)^2 + 4

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A car drives 160 miles in the same amount of time that a plane flies 840 miles. The plane is going 170 mph faster than the car. How fast is the car going?

Answers

The speed of the car is 40mph

What is rate?

A rate is a ratio that compares two different quantities which have different units. For example, if we say John types 50 words in a minute, then his rate of typing is 50 words per minute. The word "per" gives a clue that we are dealing with a rate.

Distance covered by car = 160 miles

distance covered by plane = 840 miles

let the time taken to cover 160 miles by car be x

speed of car = 160/x

speed of plane which is 170mph faster than speed of car = 170 + 160/x

time taken to cover 840 miles by plane,

time = distance/speed = [tex]\frac{840}{170 + \frac{160}{x} }[/tex]

By simplifying,

time taken by plane = [tex]\frac{840x}{170x + 160}[/tex]

since it takes same time for both to get to their destination,

Then,

x =  [tex]\frac{840x}{170x + 160}[/tex]

By cross multiplying

x( 170x + 160) = 840x

divide both sides by x, it reduces to

170x + 160 = 840

170x = 840 - 160

170x = 680

x = 680/170

x = 4

Speed of car = 160/x

speed of car = 160/4

speed = 40mph

In conclusion, the care moves at the speed of 40mph

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what is the total change in the cats weight for all 3 months?

Answers

The total change in the cats weight for all 3 months is -0.5 pounds.

How to find the total change?

Since we have 3 months which is from April to June, Now let add up the change in weight in pounds so as to find the total change

Let x represent the total change

x = -0.7 + 0.5 + (- 0.3 )

x = -0.5 pounds

Therefore the -0.5 pound is the change in weight.

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7 times some number is 28. What is the number?
Equation:
Solution:

Answers

Answer:

4

Step-by-step explanation:

aint no way...this is literally 1st grade math...anyways

7(x)=28

divide both sides by 7

x=4

The vertices of &ABC are A(2. 8), B(16, 2), and C(6, 2). The perimeter of aABC is____
units, and its area is_____
square units.

Answers

For the given triangle ABC,

The perimeter of ABC is 32.443 unit
The area of ABC is 30 unit^2


What is a vertex?
A triangle is created geometrically by the intersection of three line segments. Each side of a triangle has two ends, and the three sides' endpoints may intersect at three distinct places in a plane to form the triangle. The three locations where they cross each other are referred to as a triangle's vertices.

Solution explained:

The distances are found using the distance formula:

D=[tex]\sqrt{((y2-y1)^2+(x2-x1)^2)}[/tex]

Given A(2,8),B(16,2),C(6,2)

Now, calculate the distance

AB=[tex]\sqrt{((16-2)^2+(2-8)^2)}[/tex]=[tex]\sqrt{(14^2+6^2)}[/tex]=[tex]\sqrt{232}[/tex]

BC=[tex]\sqrt{((6-16)^2+(2-2)^2)}[/tex]=[tex]\sqrt{(10^2+0)}[/tex]=10

CA=[tex]\sqrt{((2-6)^2+(8-2)^2)}[/tex]=[tex]\sqrt{(4^2+6^2)}[/tex]=[tex]\sqrt{(16+36)}[/tex]=[tex]\sqrt{52}[/tex]

Perimeter=AB+BC+CA
               =32.443 unit

For the area (we note that BC is horizontal (parallel to the x-axis)), so

Area = (1/2)base * height

        =(1/2)10*(ya-yb)

        =(1/2)10*(8-2)

        =(1/2)10*6

        =30 unit^2

Hence, the perimeter is 32.443 units and the area is 30 unit^2

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Find the coordinate of the midpoint of the segment with the given endpoints.
- 5 and 4

Answers

The midpoint of the segment with the given endpoints.-5 and 4 is -0.5.

What are coordinates?

A pair of numbers is used to express a point's position on a coordinate plane using the horizontal and vertical distinctions from the two reference axes.

What is a midpoint?

A midpoint is a point that lies on a line connecting two other locations and is in the middle of the line.

Here,

A midpoint can also be written as an average or mean of two points.

Mean of -5 and 4 = (- 5 + 4)/2 = -0.5

Hence "The midpoint of the segment with the given endpoints.-5 and 4 is -0.5".

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The tape diagram shows that Odalis is 132 cm tall, which is 150% of their sister Dalia's height.
132
Height (cm)
150%
Complete the table to show different percentages of Dalia's height.
Percentage
150% of Dalia's height
25% of Dalia's height
100% of Dalia's height

Answers

Answer:

150% = 132 cm, 25%= 22 cm, 100%= 88 cm

Given:

Height of Odalis = 132 cm

This height is 150%

Divided into 6 parts.

To find: Different percentages of Dallas's Height

Solution:

Dalia's Height = Odalis height * (100/150)

= 132 cm * (2/3)

= 88 cm.

150% of Dallas's Height is 132 cm.

25% of Dalia's Height =  1/4 * 88 = 22 cm

100% of Dalia's Height = 88 cm.

This can also be taken by parts.

6 parts =  150%

1 part =  150/6 = 25%

And 6 parts = 132 cm,

so, 1 part = 132/6 = 22cm.

so , 25% = 1 part= 22cm.

100% = 4 parts = 22*4 = 88 cm.

150% = 6 parts = 22*6 = 132 cm.

Hence, 150% = 132 cm

25%= 22 cm

100%= 88 cm

Step-by-step explanation:

Answer:The tape diagram shows that Odalis is 132 cm tall, which is 150% of their sister Dalia's height.

132

Height (cm)

150%

Complete the table to show different percentages of Dalia's height.

Percentage

150% of Dalia's height

25% of Dalia's height

100% of Dalia's height

Step-by-step explanation: Just look at the awnser

A driveway is being surfaced with concrete pavers in the shape of regular hexagons. If the driveway is 24-ft by 26-ft rectangle, and the pavers measure 6 inches across the flats, how many pavers are needed?To surface a driveway about _ pavers are needed

Answers

The number of pavers required is 961.

The area is the region defined by an object's shape. The area of a shape is the space covered by a figure or any two-dimensional geometric shape in a plane.

Given data

A driveway is being surfaced with concrete pavers in the shape of regular hexagons. If the driveway is a 24-by-26-foot rectangle with pavers 6 inches wide across the flats.

We have to determine how many pavers are needed

We know that area of a regular hexagon

A = (3√3)/2 a^2

= (3√3)/2 〖(6)〗^2

= (3 x 1.732)/2  x 36

= 93.528 sq.inches

Now area of rectangle

= l x w

= 24 x 26 x (12)2        (1feet = 12 inches)

= 89856 sq.inches

Now pavers required

= 89856/93.528

= 960.73

= 961

Therefore the number of pavers required is 961.

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Marvin is helping his teachers plan a field trip. There are 136 people going on the field trip and each school bus holds 51 people. What is the minimum number of school buses they will need to reserve for the trip?

Answers

Answer: 3 busses

Step-by-step explanation:

Please answer this as soon as possible.

Answers

The equation of the transformed graph is y = -2|x| + 2

(graph attached)

What is transformation ?

Transformation is a term used in mathematics to refer to the movements made by objects.

How to determine the coordinates of H after transformation

information from the question

equation of the preimage f(x) = |x|

A graph showing the transformed image

The image show a reflection over x axis, the transformation rule for this is

Transformation rule (x, y) → (x, -y)

applying the rule to f(x) = |x| gives -f(x) = -|x|

followed by translation 2 units up, this achieved by Transformation rule

-f(x) → -f(x) + 2

Then a vertical stretch of 2 units,  transformation rule for vertical stretch is

-2f(x) → -2|x| + 2

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I had 35 assignments for the week. The ratio for English assignments to the rest of the assignments was 2:3. How many assignments were NOT English?

Answers

Answer:

21 Assignments were NOT English.

Fill in the table using the function rule y=5x-2

Answers

The table has been shown using the function rule y = 5x - 2. (Refer to the table attached below).

What is the function rule?The relationship between the input or domain and the output or range is known as the function rule. If and only if there is a single value in the range for each domain value, a relation is a function.When the provided input values are applied, the function rule y = 2 x + 4 produces the output values displayed in the table. Now, the output numbers " are represented by and the input values are represented by. Consequently, the expression f (x) = 3 x + 1 can be used to represent the function rule y = 3 x + 1.

So, the rule is y = 5x - 2:

Now calculate values as follows:

(A) When x = 0:

y = 0 - 2y = - 2

(B) When x = 1:

y = 5 - 2y = 3

(C) When x = 2:

y = 10 - 2y = 8

(D) When x = 3:

y = 15 - 2y = 13

Therefore, the table has been shown using the function rule y = 5x - 2. (Refer to the table attached below)

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Use the Pythagorean Theorem to find the length of the hypotenuse in the triangle below.

The figure shows a right triangle with legs marked 30 and 16.

Answers

Answer:

A:

Answer:65Step-by-step explanation:C^2= A^2 + B^2C^2 = (60)^2 + (25)^2 C^2 = 4225Take the square root of CC = 65

PLEASE HELP! select all true statement on the graph

Answers

In the given graph the correct statements are:

q ⊥ n

m ║ n

p ⊥ m

What are parallel lines and perpendicular lines ?

Parallel lines are two straight lines that never intersect and are located in the same plane. They are equidistant lines that are always at the same distance from one another. Parallel lines are denoted by the apostrophe ||. AB || CD, for instance, denotes that line AB and line CD are parallel. Perpendicular lines, on the other hand, are when two lines cross at an angle of 90 degrees. The symbol stands for perpendicular lines. Line PQ is perpendicular to line RS, for instance, if PQ RS. Examine the following illustration and the characteristics of parallel and perpendicular lines to recognize and distinguish between them.

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The time difference, t, in minutes, taken for an object to travel from point A to B and the return journey is given by the equation (t+6) (t-8)=72. By solving the equation (t+6) (t-8)=72, find the time difference t in minutes.​

Answers

Answer:

t = 12

Step by step explanation:

(t + 6)(t - 8) = 72

t² - 8t + 6t - 48 = 0

t² - 2t - 120 = 0

(t + 10)(t - 12) = 0

t + 10 = 0 OR t - 12 = 0

t = -10 OR t = 12

(reject)

Annie's mother asked Annie to go buy oranges, dog food, and bug spray. Each square's side length is 1 block. How many blocks will Annie have to walk
in all if she visits the fruit stand, the pet store, and the supermarket, in that order, before returning home?
A. 14 blocks
B. 18 blocks
C. 20 blocks
D. 32 blocks

Answers

We can learn from the graph that ANNIE is required to walk 14 blocks.

What is a graph?a diagram that shows how a variable varies in relation to one or more other variables (such as a collection of points, lines, line segments, curves, or regions).: a grouping of all points whose coordinates meet a specific relation (such as a function): a group of edges and vertices connecting pairs of vertices

How to solve a graph.-

TO GRAPHICALLY SOLVE A SYSTEM OF LINEAR EQUATIONSThe first equation is graphed.Using the same rectangular coordinate system, graph the second equation.Identify whether the lines are parallel, intersect, or are one and the same line.Determine the system's remedy. Find the intersection if the lines do indeed meet.

acc to the question-

fruit vendor=(-3,7)

pet store-=(-1,6)

supermarket=(1,5)

annie's house=(1,4)

Hence,We can learn from the graph that ANNIE is required to walk 14 blocks.

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A metal strip is being installed around a rectangular workbench that is 11 feet long and 4 feet wide. If the stripping costs
$5 per foot, find the total cost of the stripping.


total cost =$?

Answers

Step-by-step explanation:

that is the same as calculating the perimeter of the rectangle (the way 1 time around the rectangle).

the perimeter of a rectangle is

2×length + 2×width

in our case that is

2×11 + 2×4 = 22 + 8 = 30 ft

the stripping costs $5 per foot, and we have 30 ft.

so, the total costs are

5 × 30 = $150

Sandy works at a clothing store. She makes $9 per hour plus earns 15% commission on her sales. She worked 76 hours over the last two weeks and had a total of $1,790 in sales before taxes.

Which of the following is closest to how much she will earn in hourly wages and commission for those two weeks?
A.
$953
B.
$371
C.
$684
D.
$269

Answers

the correct answer is A

9*76=684

1790(0.15) = 268.50

683+268.50



=952

can you graph x+y greater than or equal to 500

Answers

A graph of the given inequality (x + y ≥ 500) is shown in the image attached below.

What is a graph?

In Mathematics, a graph simply refers to a type of chart that is typically used for the graphical representation of data on both the horizontal and vertical axes of a cartesian coordinate, which are the x-coordinate and y-coordinate.

Next, we would translate the word sentence into an inequality as follows:

x + y greater than or equal to 500 ⇒ x + y ≥ 500

Subtracting x from both sides of the inequality, we have the following equation:

x + y - x ≥ 500 - x

y ≥ 500 - x

Rearranging the equation in slope-intercept form, we have:

y ≥ -x + 500

In conclusion, we can reasonably and logically deduce that both the x-intercept and y-intercept of this linear inequality (equation) is equal to 500.

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A student raises the flag up at a steady speed of 3m/s. The flag is 2kg in mass. What is the average power exerted.

Answers

The average power exerted on the flag of mass 2 kg by the student is 58.8 Watt.

What is power?

Power can defined as the rate at which work is done.

To calculate the average power exerted on the flag, we use the formula below.

Formula:

P = mgv............ Equation 1

Where:

P = Power exertedm = Mass of the flagg = Acceleration due to gravityv = Velocity at which the flag was raised

From the question,

Given:

m = 2 kgv = 3 m/sg = 9.8 m/s²

Substitute these values into equation 1

P = 2×3×9.8P = 58.8 Watt

Hence, the average power exerted is 58.8 Watt.

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Which statement is true?

Answers

Answer:

Option A

Step-by-step explanation:

The Horizontal asymptote of y = 3.10 represents that the average cost per unit will approach $3.10 as the number of units produced increases.

___________________

Hope this helps!

Have a great day!!

Katyhas$100,000inasavingsaccount.Theinterestrateis8%peryearandisnotcompounded.Howmuchwillshehaveintotalin2years? Use the formula i = prt, where i is the interest earned, p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years. $

Answers

The amount that Katy would have saved in her savings account in 2 years is $16, 000

How to find the amount saved?

Given that the interest on the savings account is not compounded, the amount that Katy would have saved in 2 years can be found by the formula:
= Principal x Interest Rate x Time

Principal = $100, 000

Interest rate = 8%

Time = 2 years

The amount that Katy would have saved is:

= Principal x Interest Rate x Time

= 100, 000 x 8% x 2

= $16, 000

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Other Questions
Put these events from the lead-up to America's entry into World War II in chronological order.The cash-and-carry policy allows the sale of arms to nations at war but only for cash.DONEThe Japanese air force attacks the US army base at Pearl Harbor.DONEThe United States declares war on Japan.DONEThe Lend-Lease Act allows Britain to buy arms from the United States on credit.DONEThe United States agrees to trade old destroyers for military bases in British territory. 10 facts of animal farm chapter 2-5 (each) given f(x) =2x^2+5, evaluate f(4) which stage of urine production involves returning water, nutrients, and electrolytes to the blood stream? A coffee company surveyed 40 potential customers to see where they wouldlike the company's new organic coffee sold. Respondents were given thefollowing four locations and asked to choose as many as they liked: grocerystores, drugstores, health food stores, and big box stores. The results aresummarized in the bar graph below, with the number of times each locationwas chosen noted above the corresponding bar. in many ethnically diverse schools, ethnic groups segregate themselves in the lunchrooms. white students often think that they would welcome black students to sit at their table but assume the black students do not like them. the black students believe the same thing about the white students. this pattern of thinking best illustrates: According to "new isu study finds eyewitness memory susceptible to misinformation after testing," eyewitness testimonies can be inaccurate due to intentioned or unintentional __________. a. repression b. pseudoforgetting c. judgment d. misinformation Hey did anyone write a oliver twist novel which you can slide to me? what's one of the main motivations for individuals in the economic system of capitalism? question 19 options: a) humanitarian concerns b) religion c) divine right d) profit There are people who believe stories should be told by a member of the group being characterized in the story. Do you think this is important? Why or why not? Provide an example of a play or a film that supports your opinion. Which of the following elements does your outline include? Check all that apply to your outline.an introduction with a clear thesis that states my claimthree clear reasons that support my claim for each of the three body paragraphsevidential support for each reason in the form of facts, statistics, and/or examplesa counterclaim, if one can be argued, that is a valid objection to my claima conclusion that reinforces my claim we learn how to treat our kin within a family. what other aspects of social life does family prepare us to navigate? Why does the graph of beta decay have horizontal change while alpha decay graphs change vertical and horizontal? for a binomial probability distribution with 8 trials and probability of success equal 0.95. what is probability of exactly six successes? (use the binomial tables) a tire manufacturer has a 60,000 mile warranty for tread life. the manufacturer considers the overall tire quality to be acceptable if less than 5% are worn out at 60,000 miles. the manufacturer tests 250 tires that have been used for 60,000 miles. they find that 3.6% of them are worn out. with this data, we test the following hypotheses.h0: the proportion of tires that are worn out after 60,000 miles is equal to 0.05.ha: the proportion of tires that are worn out after 60,000 miles is less than 0.05.in order to assess the evidence, which question best describes what we need to determine? Bret Rockford bought a home with a 11.5% adjustable rate mortgage for 20 years. He paid $10.67 monthly per thousand on his original loan. At the end of 1 year he owes the bank $70,000. Since then interest rates have increased to 13%. The bank will renew the mortgage at this rate, or Bret can pay the bank $70,000. He decides to renew and will now pay $11.72 monthly per thousand on his loan. (You can ignore the small amount of principal paid during the year.)The old monthly payment is $ .The new monthly payment is $ .The percent increase in her monthly payment (to the nearest tenth) is % how do sound waves ultimately result in the production of receptor potentials? group of answer choices the tectorial membrane squeezes the auditory nerve the basilar membrane releases neurotransmitters the eardrum has receptors that create action potentials hair cells in the cochlea vibrate, causing ion channels to open in their membrane A new hamster mutant, zip, has a daily free-running rhythm with a period of 8 hours. If you transplanted the fetal SCN from a zip animal into the brain of an adult hamster (and its own SCN lesioned), you would expect the free-running period of this adults rhythm to be Once your business is online, whatopportunities can you take advantage of?h Find the product. Simplify your answer2x (4x+2y)12xy +608x5 +4y648x5y68x5 +8xy