Given the following information, find the probability that a randomly selected student will be very short. Number of students who are very short: 45, short: 60, tall: 82, very tall: 21

Answer:

Option C (d = 14n + 50).

Step-by-step explanation:

The observations for Year 1, 2, 3, and 4 are 64, 78, 92, and 106 respectively. It can be observed that the difference between second term and the first term is 78 - 64 = 14. This is also true for the third term and the second term. In fact, the difference between the terms is fixed. This means that the sequence is an arithmetic sequence, in which the difference between the terms is fixes for all the terms. The nth term in this case is defined as:

S = a + (n-1)*d; where S is the output at a given n, a is the first term, n is the position, and d is the common difference. In this question, S = ducks (d), a = 64, and d = 14. Therefore, plugging in the values in the above formula gives:

d = 64 + (n-1)*14.

d = 64 + 14n - 14.

d = 14n + 50.

Therefore, the model which best describes the amount of ducks that will be in the pond during the nth year is d = 14n + 50, i.e. Option C!!!

Answer: Third Option

[tex]a_n =14n+50[/tex]

Step-by-step explanation:

By subtracting consecutive terms from the number of ducks each year you will get a common difference of 144.

[tex]78-64 = 14\\92-78 = 14\\106-92 = 14[/tex]

This means that the data can be modeled by the equation of an arithmetic sequence

The arithmetic sequences have the following form:

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

Where [tex]a_1[/tex] is the first term and d is the common difference between the consecutive terms.

So :

[tex]a_1 = 64[/tex]

[tex]d = 14[/tex]

Then the equation is:

[tex]a_n = 64 + 14(n-1)[/tex]

[tex]a_n = 64 + 14n-14[/tex]

[tex]a_n =14n+50[/tex]

Answer:

You might want to see if I read your ordered pairs right because it was really hard to see for me:

f(2,6)=14

f(-1,3)=5

f(6,4)=14

Step-by-step explanation:

I assume they meant to write f(x,y)=x+2y.

Doing f(2,6) now.  This means replace x with 2 and y with 6:

f(2,6)=2+2(6)=2+12=14

f(2,6)=14

Doing f(-1,3) now.  This means replace x with -1 and y with 3:

f(-1,3)=-1+2(3)=-1+6=5

f(-1,3)=5

Doing f(6,4) now. This means replace x with 6 and y with 4:

f(6,4)=6+2(4)=6+8=14

f(6,4)=14

Tha values of the function f(2, 6), f(-1, 3) and f(6, 4) are 1, 5 and 14 respectively

Give the function expressed as:

f(x, y) = x + 2y

If the coordinate point is (2, 6), then;

f(2, 6) = 2 + 2(6)

f(2, 6) = 2 + 12

f(2, 6) = 14

If  the coordinate point is (-1, 3), then;

f(-1, 3) = -1 + 2(3)

f(-1, 3) = -1 + 6

f(-1, 3) = 5

If the coordinate point is (6, 4), then;

f(6, 4) = 6 + 2(4)

f(6, 4) = 6 + 8

f(6, 4) = 14

Hence the values of the function f(2, 6), f(-1, 3) and f(6, 4) are 1, 5 and 14 respectively

Learn more on function and values here: https://brainly.com/question/4934333

Answer:

2(x-2y)/(4x-y)  =  dy/dx

Step-by-step explanation:

2x^2+y^2=8xy

Take the derivative of each term, remembering that we take the 8xy as derivative by parts)

2 * 2x dx +  *2y dy = 8 ( x dy + dx *y)

4x dx +2y dy = 8x dy + 8y dx

Subtract 2y dy from each side

4x dx +2y dy -4y dy = 8x dy - 2y dy + 8y dx

4x dx  = 8x dy - 2y dy + 8y dx

Subtract 8y dx from each side

4x dx -8y dx  = 8x dy - 2y dy + 8y dx-8y dx

4x dx -8y dx  = 8x dy - 2y dy

(4x-8y) dx = (8x-2y) dy

Factor out a 4 from the left side and a 2 from the right side

4(x-2y) dx = 2( 4x-y) dy

Cancel a 2

2(x-2y) dx = ( 4x-y) dy

Divide each side by (4x-y)

2(x-2y)/(4x-y) dx = ( 4x-y)/(4x-y) dy

2(x-2y)/(4x-y) dx =  dy

Divide by dx

2(x-2y)/(4x-y) dx/dx =  dy/dx

2(x-2y)/(4x-y)  =  dy/dx

Answer:

Part 1) [tex]c=21.9\ units[/tex]

Part 2) [tex]B=61.1\°[/tex]

Part 3) [tex]A=28.9\°[/tex]

Part 4) [tex]C=90\°[/tex]

Step-by-step explanation:

step 1

Find the length side c

Applying the Pythagoras Theorem

[tex]c^{2}=a^{2}+b^{2}[/tex]

substitute the given values

[tex]c^{2}=10.6^{2}+19.2^{2}[/tex]

[tex]c^{2}=481[/tex]

[tex]c=21.9\ units[/tex]

step 2

Fin the measure of angle B

we know that

In the right triangle

[tex]tan(B)=b/a[/tex]

substitute the given values

[tex]tan(B)=19.2/10.6[/tex]

[tex]B=arctan(19.2/10.6)=61.1\°[/tex]

step 3

Find the measure of angle A

we know that

The measure of interior angles in a triangle must be equal to 180 degrees

so

∠A+∠B+∠C=180°

Remember that in a right triangle the measure of angle C is 90 degrees

we have

[tex]B=61.1\°[/tex]

[tex]C=90\°[/tex]

substitute

[tex]A+61.1\°+90\°=180\°[/tex]

[tex]A=28.9\°[/tex]

Answer:

A = 28.9 degrees, B = 61.1 degrees, c = 21.9

Step-by-step explanation:

I got it correct on founders edtell

Answer:

q=0

r=2

s=3

t=-3

Step-by-step explanation:

q represents the value we should get from evaluating d(-8).

[tex]d(x)=-\sqrt{\frac{1}{2}x+4}[/tex]

To find d(-8) we use this function here labeled d and replace x with -8:

[tex]d(-8)=-\sqrt{\frac{1}{2}(-8)+4}[/tex]

[tex]d(-8)=-\sqrt{-4+4}[/tex]

[tex]d(-8)=-\sqrt{0}[/tex]

[tex]d(-8)=0[/tex]

So q is 0 since d(-8)=0.

r represents the value we should get from evaluating f(0).

[tex]f(x)=\sqrt{\frac{1}{2}x+4}[/tex]

To find f(0) we use this function labeled f and repalce x with 0:

[tex]f(0)=\sqrt{\frac{1}{2}(0)+4}[/tex]

[tex]f(0)=\sqrt{0+4}[/tex]

[tex]f(0)=\sqrt{4}[/tex]

[tex]f(0)=2[/tex]

So r is 2 since f(0)=2.

s represents the value we should get from evaluating f(10).

[tex]f(x)=\sqrt{\frac{1}{2}x+4}[/tex]

To find f(10) we use this function labeled f and replace x with 10:

[tex]f(10)=\sqrt{\frac{1}{2}(10)+4}[/tex]

[tex]f(10)=\sqrt{5+4}[/tex]

[tex]f(10)=\sqrt{9}[/tex]

[tex]f(10)=3[/tex]

So s is 3 since f(10)=3.

t represents the value we should get from evaluating d(10).

[tex]d(x)=-\sqrt{\frac{1}{2}x+4}[/tex]

To find d(10) we use the function labeled d and replace x with 10:

[tex]d(10)=-\sqrt{\frac{1}{2}(10)+4}[/tex]

[tex]d(10)=-\sqrt{5+4}[/tex]

[tex]d(10)=-\sqrt{9}[/tex]

[tex]d(10)=-3[/tex]

So t is -3 since d(10)=-3

q=0

r=2

s=3

t=-3

Answer:

-.1

Step-by-step explanation:

The common difference in the arithmetic sequence can be found by doing term minus a previous term.

So 0.26-0.36=-.1

or 0.16-0.26=-.1

or 0.06-0.16=-.1

or -0.04-0.06=-.1

or -0.14-(-0.04)=-.1

Answer:

$97.16 per day

Step-by-step explanation:

Total amount you have = $668.00

You have to spent $85.00  on the last day.

$668.00-85.00

=$583

It means you have $583 for the remaining 6 days in the week.

If you spend equal amount of money each day , you can calculate it by dividing remaining amount and number of days

=583/6

=$97.16

It means you can spend $97.16 per day....

Answer:

B

Step-by-step explanation:

A triangle has both x and y values making it 2D. A 1D object is a point, a 3D object is a cube or something, and a 0D object is nothing.

Hello There!

X = 6

First, we would add 5 to both sides so adding 5 to -5 is 0 and adding 5 to 7 is 12 so we would get the equation 2x = 12

Next, we would divide 2x by 2 and divide 12 by 2 and we would get a quotient of 6.

Our final answer is x = 6

Answer:

x=6

Step-by-step explanation:

2x - 5 = 7

Add 5 to each side

2x-5+5= 7+5

2x = 12

Divide by 2

2x/2 = 12/2

x = 6

Answer:

2/3

Step-by-step explanation:

To find the slope based off of two points, use the following formula:

[tex]\frac{y2-y1}{x2-x1}[/tex]

Plug in your values and simplify.

[tex]\frac{-7-1}{-3-9} \\\\\frac{-8}{-12}[/tex]

[tex]\frac{8}{12}[/tex]

[tex]\frac{2}{3}[/tex]

Answer:

2/3

Step-by-step explanation:

I like the line up and subtract strategy. At the end you just put 2nd number over 1st.

This is the slope formula; just a different way to think about the formula.

(9,1)

-(-3,-7)

=======

12, 8

So the slope is 8/12=2/3.

Answer:

(x,y)= (5,1)

Step-by-step explanation:

4x+2y=22

3x-2y=13

2y=22-4x

3x-2y=13

3x-(22-4x)=13

x=5

3·5-2y=13

y=1

(x,y)= (5,1)

Answer:

(5, 1); x = 5 and y = 1.

Step-by-step explanation:

Step 1: Add the system of equations

4x + 2y = 22

3x - 2y = 13

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

7x = 35

Step 2: Solve for x

x = 5

Step 3: Substitute the value of x in one of the original equations

4(5) + 2y = 22

Step 4: Solve for y

20 + 2y = 22

2y = 2

y = 1

Step 5: Write your answer as an ordered pair

(5, 1)

Answer:

75 dollars

Step-by-step explanation:

If an item is 50 and you want to markup 50%, you must find 50% of 50 to find how much the item will go up by from 50.

So 50% of 50 means 50% times 50.

50%=.5 or 1/2

So .5(50)=25.

The item is going up by 25 dollars.

So we started at 50 dollars.

So 50+25 is going to be the new amount.

50+25=75 is the new amount.

$75

In this question, it's asking you to find the selling price of an item after the markup.

We know that:

With the information above, we can find the answer.

A markup is pretty much an increase in a price. This means that in this context, the item's price increased by 50%

We're going to need to find how much the selling price is after the markup.

We would multiply 50 by 1.5 to find the selling price.

[tex]50*1.5=75\\\\\text{Or you can do it this way}\\\\50*0.5=25\\\\50+25=75[/tex]

With either method, you're still going to get 75.

This means that the selling price of the item after applying the markup value is $75

Answer:

Area=512 square inches

Step-by-step explanation:

According to the given data;

A side of a square = (8)³/² inches.

Area of a square = ?

To find the area of a square we use the formula:

Area = s²

Area=(8)³/²)²

Area = 8³

Area= 8*8*8

Area=512 square inches....

Answer:

62 DEGREES

Step-by-step explanation:

TWO ANGLES=2A

LARGEST ANGLE=A+3

2A+A+3=180

3A=180-3=177

A=177/3=59

LARGEST ANGLE=59+3=62

Answer:

The Largest Angle angle has a measure of 62 degrees.

Step-by-step explanation:

In triangle ABC, angle ABC equals to angle ACB.

and BAC is the largest angle.

Let angle measure of ABC and ACB angles be "x" degree.

then, measure of third angle i.e BAC will be "x + 3" degrees.

Since sum of all angles of any triangle is 180 degree.

so,  first angle + second angle + third angle = 180

       x  + x + (x + 3) = 180

        3x  = 180 - 3

         3x = 177

          x = 59 degrees

So, First angle = 59 degree

     Second angle = 59 degree

     Third Angle = 62 degree.

The Largest Angle angle has a measure of 62 degrees.

Answer:

The graph in the attached figure

Step-by-step explanation:

Let

x -----> the number of solved puzzles

y -----> the number of solved riddles

we know that

[tex]2x+y \geq 4[/tex]

The solution of the inequality is the shaded area above the solid line [tex]2x+y=4[/tex]

The slope of the solid line is negative [tex]m=-2[/tex]

The y-intercept of the solid line is the point (0,4)

The x-intercept of the solid line is the point (2,0)

therefore

The graph in the attached figure

Answer:

The graph that representss this scenario is attached.

Explanation:

You can create the graph by determining the expression that shows the relationship between the variables and then drawing the graph in a coordinate system.

1. Determine the expression that relates the variables.

a) The name of the variables is given:

x: number of solved puzzles

y: number of solved riddles

b) Point rules:

Each solved puzzle is worth two points: 2x

Each solved riddle is worth 1 point: 1y = y

Sum of points: 2x + y

The video game requires at least 4 points to advance: this means that the number of points must grater than or equal to 4 ⇒ 2x + y ≥ 4 .

In conclusion, it has been determined that the expression that rules the system of points is the inequality 2x + y ≥ 4.

2) Building the graph

Solve algebraically for y: y ≥ 4 - 2x

You want to draw the border line of the function, that is y = 4 - 2x

You have a linear function, so you need only two points to draw it. It is generally easier to work with the intercepts.

x-intercept (y = 0) ⇒ 2x + 0 = 4 ⇒ 2x = 4 ⇒ x = 2 ⇒ point (2, 0)

y-intercept (x = 0) ⇒ 2(0) + y = 4 ⇒ y = 4 ⇒ point (0, 4).

In conclusion, you can use the points (2,0) and (0,4) to draw the line that is the border of your graph.

Addtional constrains: x and y cannot be negative, so add the constrains:

       x ≥ 0 and y ≥ 0

The set of solutions of y ≥ 4 - 2x is the same line y = 4 - 2x and the region over the line, so you have to shade that portion of the graph, but only in the first quadrant (since x and are greater than or equal to zero).

plz give brainliest

Answer:

5/6

Step-by-step explanation:

There are 6 possible rolls

1 2 3 4 5 6

Only one of 6 is a five

Answer:

Step-by-step explanation:

|a| = a for a ≥ 0

|a| = -a for a < 0

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

|c² + b²|

Put b = -3 and c = -2 to the expression:

|(-2)² + (-3)²| = |4 + 9| = |13| = 13

Answer:

18+8=26

Step-by-step explanation:

Their sum would be 18 and * because they have  difference of ten. In order o get this you would have to multiply 1 X144 and so on.

Answer:

Step-by-step explanation:

Its 134 hope this helos

Answer:

43.75 liters.

Step-by-step explanation:

125% = 1.25 as a decimal fraction.

number of liters of milk = 35 * 1.25

= 43.75 liters.

Answer:

the amount of green blocks = X then you'll end up with the amount of yellow blocks

Answer:

so x can be either yellow or green

Step-by-step explanation:

Ryan has total 57 blocks (total yellow and green)

if x is either of yellow or green

then 57 -x will be either green or yellow (According to x is green or yellow)

x can be either yellow or green .

Answer:

96

Step-by-step explanation:

64 -[16 x (-3) – 2 x{17 – 25 }]​   I'm going to take a couple of steps that are very small and they can be combines along with other steps. Combine 16*-3

64 - [-48 - 2*(17 - 25)]            Combine what is inside (17 - 25)

64 - [-48 - 2*(-8)]                    Combine -2*-8

64 - [-48 + 16]                         Combine what is in the brackets.

64 - [-32]                                 Remove the brackets

64 + 32                                    Combine

96

The trick in this question is the signs.

     Measure of angle 'x' given in the picture will be 36°.

  From the picture attached,

In ΔABD,

m∠DAB = x° [Given]

AB ≅ BD [Isosceles triangle]

Therefore, opposite sides of the given triangles will measure the same.

m∠BAD = m∠BDA = x°

m∠BAD + m∠BDA + m∠ABD = 180° [By triangle sum theorem]

x° + x° + m∠ABD = 180°

m∠ABD = 180°- 2x°

m∠DBC + m∠ABD = 180° [Linear pair of angles]

m∠DBC + (180° - 2x) = 180°

m∠DBC = 2x°

In isosceles ΔBCD,

BD ≅ CD

Therefore, m∠DBC = m∠BCD = 2x°

In isosceles ΔACD,

Since, AC ≅ AD,

Therefore, m∠ACD = m∠ADC = 2x°

By applying triangle sum theorem in ΔACD,

m∠ACD + m∠DAC + m∠CDA = 180°

2x° + x° + 2x° = 180°

5x° = 180°

x = 36°

   Therefore, measure of 'x' will be 36°.

Learn more,

https://brainly.com/question/1153593

Answer:

The monthly compounded interest rate of 0.14% of Unity Bank is a better plan.

Step-by-step explanation:

Step 1 : Write the formula for calculating a monthly compound interest rate and for calculating an annually compounded interest rate.

Monthly compound interest rate = P(1+r/n)^nxt

n=12 (number of months in a year)

t=1 (number of years)

Annually compound interest rate = P(1+r/n)^nxt

n=1 (because it is for 1 year only)

t=1 (number of years=1)

Step 2 : Lets assume that P is $100 in both banks and time is 1 year.

Step 3 : Lets substitute the values to find out which one is better.

Monthly compound interest rate = P(1+r/n)^nxt

Monthly compound interest rate = 100(1+0.14/12)^12x1

Monthly compound interest rate = 114.93

114.93 - 100 = $14.93 per month

14.93 x 12 = $179.16 for 12 months or 1 year

Annually compound interest rate = P(1+r/n)^nxt

Annually compound interest rate = 100(1+1.6/1)^1x1

Annually compound interest rate = 260

260-100 = $160 for 1 year

Therefore, the monthly compounded interest rate of 0.14% of Unity Bank is a better plan.

!!

Answer:

The Unity Bank is offering a good plan.

Step-by-step explanation:

Unity Bank offers a monthly compounded interest rate of 0.14%

So, yearly rate will be = [tex]0.14\times12=1.68[/tex]% or 0.0168

Sunrise Banking offers 1.6% or 0.016 interest compounded annually.

Lets check an example with these two rates.

The compound interest formula is = [tex]A=P(1+r/n)^{nt}[/tex]

Lets take P = $1000 and t = 1 year

Case 1: when r = 1.68% and n = 12

Putting the values in formula we get

A = [tex]1000(1+0.0168/12)^{12}[/tex]

= [tex]1000(1.0014)^{12}[/tex]

A = $1016.92

Case 2: when r = 1.6% and n = 1

Putting the values in formula we get

A = [tex]1000(1+0.016/1)^{1}[/tex]

= [tex]1000(1.016)^{1}[/tex]

A = $1016.00

So, we can see that the first case gives more return than second one.

Therefore, the Unity Bank is offering a good plan.

Answer:

Your grade point average would be 2.75(B- or C+)

Step-by-step explanation:

[tex]\frac{3+4+3+1}{4} \\\frac{11}{4} \\2.75[/tex]

Final answer:

Explaining the calculation of GPA based on given grades, resulting in an approximate value rounded to the hundredths place.

Explanation:

The grade point average (GPA) for the given grades can be calculated as follows:

English: 3.0 credits, B, which is 3.0 in GPA scale

Biology: 4.0 credits, B, which is 3.0 in GPA scale

Communications: 3.0, F, which is 0.0 in GPA scale

New student seminar: 1.0, A, which is 4.0 in GPA scale

Calculating the GPA:

(3.0 + 3.0 + 0.0 + 4.0) / 11 = 10.0 / 11 = 0.91

Therefore, the grade point average would be approximately 0.91 rounded to the hundredths place.

Answer:

-1/100

Step-by-step explanation:

-(10)^-2

Exponents first

We need to make the negative in the exponent positive, which means move it to the denominator

-1

--------

10^2

-1

---------

100

Answer:

-1/100

Step-by-step explanation:

10^(-2) becomes 1/100.

-(10)^(-2) is -1/100.

Answer:

$2520

Step-by-step explanation:

Taking the dimensions of the office floor from the plan to be;

[tex]15ft*28ft[/tex]

Area of the floor to be covered will be the product of the sides dimensions

[tex]=15*28=420ft^{2}[/tex]

Cost of putting tile on the floor

1ft²=$1

420ft²=?

=[tex]\frac{420*1}{1} =420[/tex]

=$420

Cost of putting a carpet on the floor

1ft²=$5

420ft²=?

[tex]=\frac{420*5}{1} =2100[/tex]

=$2100

Estimated cost

Total estimated cost =cost for putting tiles+cost for putting carpet

=$420+$2100=$2520

To find the cost of 4 ounces of pecans, we set up a proportion comparing the cost to weight, resulting in $2.25 after rounding to the nearest cent.

To determine the cost of 4 ounces of pecans when a one-pound (16 ounces) canister costs $8.99, we set up a proportion where the cost is directly proportional to the weight.

The proportion is $8.99/16 ounces = $X/4 ounces, where X represents the cost of 4 ounces of pecans.

Multiplying both sides by 4 to solve for X gives us $X = (4 ounces × $8.99) / 16 ounces.

Simplifying this, we find that $X = $2.2475, which, when rounded to the nearest cent, gives us an answer of $2.25.

Answer:

(

x

+

4

)

(

x

+

9

)

=

0

Your answer would be x=-4 and x=-9.

Explanation::

(

x

+

4

)

(

x

+

9

)

x

times  

x

=

x

2

x

(

9

)

+

x

(

4

)

=

13

x

4

times  

9

=

36

=  

x

2

+

13

x

+

36

Answer:

So the factors of the given are:

(x-4) and (x-9).

The factored form of the given expression is (x-4)(x-9).

Step-by-step explanation:

To factore the given quadratic with leading coefficient one, you must find two numbers that add to be and multiply to be c.

a=1

b=-13

c=36

So we need two numbers that multiply to be 36 and add to be -13.

These numbers are -4 and -9 since

(-4)(-9)=36 and -4+-9=-13.

So the factors of the given are:

(x-4) and (x-9).

The factored form of the given expression is (x-4)(x-9).

Answer:  the correct option is

(B) F T → T.

Step-by-step explanation:  We are given to find the truth value of he following conditional statement :

"If the grass is red, then the snow is white."

Let us consider that

p : the grass is red. This is a false statement

and  

q : the snow is white. This is a true statement.

So, we get

p  →  q

F  → T, which is true (T).

Thus, the required answer is  F T → T

Option (B) is CORRECT.

Answer:

-9-3/1-(-7)

Step-by-step explanation:

Answer:

The slope of given line = -3/2

Step-by-step explanation:

Points to remember

slope of the line with end points (x1, y1) and (x2, y2) is given by,

Slope = (y2 - y1)/(x2 - x1)

To find the slope of the line

Here (x1, y1) = (-7, 3) and (x2, y2) = (1, -9)

Slope = (y2 - y1)/(x2 - x1)

 = (-9 - 3)/(1 - -7)

 = (-12)/8

 = -3/2

Therefore the slope of given line = -3/2