if the midpoint between (3, 4) and (5, y) is (4, -2), what is the value of y?​

To solve this problem, we need to find the lengths of the two pieces when the wire is cut into two parts. Let's denote the length of each leg of the triangle as\(\(x\).\)

The perimeter of the triangle is the sum of the lengths of its three sides. Since the two legs are equal in length, the perimeter can be expressed as \(\(2x + x = 3x\).\)

The length of the wire is given as 71 cm, so we have the equation \(\(3x = 71\).\)

Solving for\(\(x\),\) we divide both sides of the equation by 3:

\(\(x = \frac{71}{3}\).\)

Now that we know the length of each leg of the triangle, we can proceed to the next part of the problem.

The circumference of a circle is given by the formula \(\(C = 2\pi r\)\), where\(\(C\)\)is the circumference and r is the radius. In this case, the wire of length xis bent into the shape of a circle, so we can set the circumference equal to x and solve for the radius r:

\(\(x = 2\pi r\).\)

Substituting the value of x we found earlier, we have:

\(\(\frac{71}{3} = 2\pi r\).\)

Solving for r, we divide both sides of the equation by \(\(2\pi\):\)

\(\(r = \frac{71}{6\pi}\).\)

Therefore, the two pieces of wire will have lengths\(\(\frac{71}{3}\)\)cm and the radius of the circle will be\(\(\frac{71}{6\pi}\)\) cm.

In summary, when the 71 cm wire is cut into two pieces, one piece will have a length o\(\(\frac{71}{3}\)\)cm, which can be bent into the shape of an equilateral triangle with legs of equal length, and the other piece can be bent into the shape of a circle with a radius of \(\(\frac{71}{6\pi}\)\) cm.

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The travelled distance of the traveller is equal to 195 kilometers.

According to the statement of the problem, a traveller already walked a third part of his trail and if he travels the half of his trail, then the half of his trail shall be covered. Mathematically, the travelled distance shall be described by following expression:

x = d / 3

x + 65 = d / 2

Where:

Now we proceed to determine the travelled distance:

d / 3 + 65 = d / 2

d / 2 - d / 3 = 65

3 · d - d = 390

2 · d = 390

d = 195

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Answer: C.

33,374 = 4,450 + 1,033t

Step-by-step explanation:

33,374 is the height to be achieved

4,450 is the starting elevation

1,033 feet/min is the rate of climb.

33,374 - 4,450 = 28924 ft is the elevation to be gained  

We want to know how many minutes it will take to add 28924 ft to the elevarion.  We can find that by setting 28924 ft = (1,033 ft/min)*t, where t is in minutes.

So the equation 33,374 = 4,450 + 1,033t summarizes these steps in one equation:

(33,374 - 4,450) = elevation needed

(1,033 ft/min)*t = elevation delivered as a function of time, t

Set them equal to each other:

(33,374 - 4,450) = (1,033 ft/min)*t

Rearrange:

33,374 = 4,450 + 1,033t     Answer C.

Answer:

0 liters

Step-by-step explanation:

The first step in solving this problem is to find the volume of water that was originally in the tank when it was filled up to of its height. Since the tank is rectangular, we can use the formula for the volume of a rectangular prism:

Volume of tank = length x width x height = 100 cm x 80 cm x 30 cm = 240,000 cm³

Since the tank was filled up to of its height, the volume of water in the tank at this point is:

Volume of water in tank = 100 cm x 80 cm x 30 cm x 0.5 = 1,200,000 cm³

To find the amount of water that was poured into the tank to fill it up to 3 of its height, we need to subtract the volume of water that was originally in the tank from the total volume of water when it is 3 filled, which is 384 liters or 384,000 cm³ (since 1 liter = 1000 cm³):

Volume of water poured into tank = Volume of water when 3 filled - Volume of water in tank at of its height

= 384,000 cm³ - 1,200,000 cm³

= -816,000 cm³

Wait a minute, this result is negative, which means there was no water poured into the tank to reach the 3 filled level. In fact, it suggests that there was an excess of water that had to be removed from the tank to reach the desired level. This could be because the dimensions of the tank were not exact or because the tank was not level when filled to the first level.

Therefore, the answer to the problem is 0 liters or 0 cm³.

Note: It is important to always check the result of a calculation to ensure it makes sense in the context of the problem. In this case, the negative volume of water poured into the tank indicates that there may be an error in the problem statement or in the measurements provided.

Answer:

The numbers are 65, 67, and 69

Step-by-step explanation:

Hi there!

We need to find 3 consecutive odd integers.

Consecutive numbers are numbers that follow each other (ex. 1, 2, 3, 4)

We're given that 5 times the first number + 4 times the second + 3 times the third = 800

Let's make the first number x

Since the second number is consecutive to the first and odd, it will be x+2 (Why? Well, let's say x is 5. In that case, x+1=6, which is even. However, x+2=7)

Therefore, the third number is x+4 (once again, if x is 5, x+3=8, but x+4=9)

5 times the first number is 5x

4 times the second is 4(x+2)

3 times the third is 3(x+4)

And of course, that equals 800

As an equation, it'll be:

5x+4(x+2)+3(x+4)=800

open the parenthesis

5x+4x+8+3x+12=800

combine like terms

12x+20=800

Subtract 20 from both sides

12x=780

Divide by 12 on both sides

x=65

The first number is x, so the first number is 65

The second number is x+2, or 65+2=67

The third number is x+4, or 65+4=69

Hope this helps!

We have the following:

These two angles are congruent, therefore they are equal, we can do the following equality:

Therefore the value of x is equal to 16

we have

a0=0

a(i+1)=2ai+1

Verify

For i=0

a(0+1)=2(0)+1

a(1)=1

For i=1

a(1+1)=2(1)+1

a(2)=3

For i=2

a(2+1)=2(3)+1

a(3)=7

therefore

Answer:

Day 5 ................

Answer:

0.857

Step-by-step explanation:

                   ----------------

               7  |   6

7 goes 0 times into 6, so we write a 0.

                       0.

                   ----------------

               7  |   6.0

Add .0 to 6 to get 6.0

7 goes 8 times into 60.

8 × 7 = 56

                       0.8

                   ----------------

               7  |   6.0

                  -    5.6

                ------------

60 - 56 = 4

Write another 0, 6.00, and bring down a zero.

                       0.8

                   ----------------

               7  |   6.00

                  -    5.6

                ------------

                           40

7 goes 5 times into 40.

                      0.85

                   ----------------

               7  |   6.00

                  -    5.6

                ------------

                           40

                      -    35

                      ---------

40 - 35 = 5

Add another 0 to 6.00 to get 6.000; bring down that zero.

Now you have 50.

                      0.857

                   ----------------

               7  |   6.000

                  -    5.6

                ------------

                           40

                      -    35

                      ---------

                              50

7 goes 7 times into 50.

7 × 7 = 49

Add a zero, bring down a zero,

                      0.857

                   ----------------

               7  |   6.0000

                  -    5.6

                ------------

                           40

                      -    35

                      ---------

                              50

                          -   49

                         -----------

                                  10

7 goes 1 time into 10.

You end up with 0.8571

                     0.8571

                   ----------------

               7  |   6.0000

                  -    5.6

                ------------

                           40

                      -    35

                      ---------

                              50

                          -   49

                         -----------

                                  10

                              -     7

                          -----------

                                    3

0.8571 rounds to 0.857

Answer:

MODE IS WHEN A NUMBER APPEARS MORE OFTEN IN A SET OF NUMBERS

Step-by-step explanation:

Example 2,3,8,6,5,3,4 , the mode is 3 because it appears more often

Have a great day

Answer:

\(\displaystyle \int {4x^6 - 2x^3 + 7x - 4} \, dx = \boxed{ \frac{4x^7}{7} - \frac{x^4}{2} + \frac{7x^2}{2} - 4x + C }\)

General Formulas and Concepts:
Calculus

Integration

Integration Rule [Reverse Power Rule]:
\(\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C\)

Integration Property [Multiplied Constant]:
\(\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx\)

Integration Property [Addition/Subtraction]:
\(\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx\)

Step-by-step explanation:

Step 1: Define

Identify given.

\(\displaystyle \int {4x^6 - 2x^3 + 7x - 4} \, dx\)

Step 2: Integrate

∴ we have found the given integral.

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Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

Answer:

3,628,800 (aka "10!")

Step-by-step explanation:

The first letter in the code can be 10 possible letters.

Since every letter can only be used once, the second letter can only be 9 possible letters.

E.G.: If the first letter is A, the second letter is B-J.

The third letter would be 8 possible letters, than the fourth would be 7, etc.

In math form, figuring out the possible combinations would be written out as so:

10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1

An easier way to write this out would be using "10!", which stands for "10 Factorial"

The result of the above equals 3,628,800.

Answer:

1. cups of coffee sold

2.Y = 605.7 - 5.943x

3. -0.952

4. 70.84

Step-by-step explanation:

1. the dependent variable in this question is the cups of coffee sold

2. least square estimation line

Y = a+bx

we have y as the cups of coffee sold

x as temperature.

first we will have to solve for a and then b

∑X = 450

∑Y = 960

∑XY = 61600

∑X² = 35500

∑Y² = 221800

a = ∑y∑x²-∑x∑xy/n∑x²-(∑x)²

a = 960 * 35500-450*61600/6*35500-450²

a = 6360000/10500

= 605.7

b = n∑xy - ∑x∑y/n∑x²-(∑x)²

= 6*61600 - 450*960/6*35500 - 450²

= -5.943

the regression line

Y = a + bx

Y = 605.7 - 5.943x

3. we are to find correlation coefficient

r = n∑xy - ∑x∑y multiplied by√(n∑x²-(∑x)² * (n∑y² - (∑y)²)

= 6*61600 -960*450/√(6*35500 - 450²)*(6*221800 - 960²)

=-62400/√4296600000

= -62400/65548.5

= -0.952

4. we have to predict sales of a 90 degree day fro the regression line

Y = 605.7 - 5.943x

y = 605.7 - 5.943(90)

y = 605.7 - 534.87

= 70.84

The mass of solid sodium acetate required to mix with 50.0 mL of 0.1 M acetic acid to prepare a pH 4 buffer is 20.1 g

To prepare a pH 4 buffer, we need to use the Henderson-Hasselbalch equation

pH = pKa + log([A-]/[HA])

where pH is the desired pH, pKa is the dissociation constant of acetic acid (1.76), [A-] is the concentration of the acetate ion, and [HA] is the concentration of acetic acid

We can rearrange the Henderson-Hasselbalch equation to solve for the ratio of [A-]/[HA]

[A-]/[HA] = 10^(pH - pKa)

Substituting the given values, we have

[A-]/[HA] = 10^(4 - 1.76) = 48.937

We want to make a buffer by mixing solid sodium acetate with 50.0 mL of 0.1 M acetic acid. Let's assume that all of the acetic acid is converted to acetate ion and that the volume of the solution remains constant.

The number of moles of acetic acid in 50.0 mL of 0.1 M solution is

moles of acetic acid = 0.1 mol/L x 0.050 L = 0.005 mol

Since [A-]/[HA] = 48.937, the number of moles of acetate ion required to make the buffer is

moles of acetate ion = 48.937 x 0.005 mol = 0.245 mol

The molar mass of sodium acetate is 82.03 g/mol. To calculate the mass of solid sodium acetate required, we can use the following equation

mass of sodium acetate = moles of acetate ion x molar mass of sodium acetate

mass of sodium acetate = 0.245 mol x 82.03 g/mol = 20.1 g

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The value of x for the intersecting chords is derived to be 14 which makes option C correct.

The property of intersecting chords states that in a circle, if two chords intersect, the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord.

x × 32 = 16 × 28

32x = 448

32x/32 = 144/32 {divide through by 32}

x = 14

Therefore, the value of x for the intersecting chords is derived to be 14

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Answer:

1/15

Step-by-step explanation:

2/3*5/5 - 3/5*3/3( we are multiplying and dividing by the same number in order to get the same denominator. as 5/5 = 1 and 3/3= 1)

2/3*5/5 - 3/5*3/3

= 10/15-9/15

= 1/15

Answer: 6 thousandths but if you’re talking about the second six then it would be 6 ten thousandths

Step-by-step explanation:

Answer:

if you mean the place value of the last 6 it would be 6 thousandths if you mean the 2nd to last  it would be 6 hundredths.

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

slope = (y₂ - y₁) / (x₂ - x₁)

         = (7 - 2) / (4 - 3)

         = 5 / 1

         = 5

The slope of the line passing through the points (3 2) and (4 7) is 5

The formula for calculating the slope of a line passing through the point (3 2) and (4 7) is expressed as:

\(m=\frac{y_2-y_1}{x_2-x_1} \\m=\frac{7-2}{4-3}\\m=\frac{5}{1} \\m=5\)

Hence the slope of the line passing through the points (3 2) and (4 7) is 5

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Answer:   -2

:)

Step-by-step explanation:

The probability of the Doubles" means both dice show the same number is 36.

When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.

The probabilities of these two outcomes must be added in order to get the likelihood of rolling an even number or doubles, but since we have already tallied those outcomes twice, the probability of rolling both doubles and an even number must be subtracted. The probability of rolling doubles and an even number is 1/36 since rolling two sixes is the only method to get a double and an even number.

The likelihood of rolling an even number or doubles is thus:

The formula for P(even number or doubles) is P(even number) = P(even number) + P(doubles) - P(even number and doubles) = 1/2 + 1/6 - 1/36 = 19/36.

The odds of rolling an even number or two doubles are 19/36.

Therefore, the probability of the Doubles" means both dice show the same number is 36.

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The sets U and A are U = {0, 1, 2, 3.....,9} and A = {2, 4, 6, 8}

The sets are given as:

U = The set of one-digit numbers

A = {x: x is an even natural number less than or equal to 9}

One-digit numbers are numbers 0 - 9.

So, we have

U = {0, 1, 2, 3.....,9}

Natural numbers are numbers from 1.

Even natural numbers can be divided by 2 without remainder'

So, we have

A = {2, 4, 6, 8}

Hence, the sets U and A are U = {0, 1, 2, 3.....,9} and A = {2, 4, 6, 8}

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Answer:

Step-by-step explanation:

The equation connecting z and p is:

z = x + (1/p)

To find z when p = 6, we can use the values of x and y when p = 2 and p = 4 to calculate the corresponding value of z when p = 6.

When p = 2, x = 4 and y = 1, so z = 5

When p = 4, x = 16 and y = 0.25, so z = 16.25

Therefore, when p = 6, x = 36 and y = 0.167, so z = 36.167

The probability of Miguel selecting a tile number less than 3 from each bag -1 is 1/5 and bag-2 is 2/5.

The given tiles in bag-1 = {2, 4, 5, 8, 9}

Total number of tiles in bag-1 = 5

The number of tiles less than number 3 in the bag - 1 = 1

The probability of Miguel selecting a tile number less than 3 =

number of tiles less than 3 / total number of tiles = 1/3

The given tiles in bag-2 = {0, 1, 3, 6, 7}

Total number of tiles in bag-2 = 5

The number of tiles less than number 3 in the bag-2 = 2

The probability of Miguel selecting a tile number less than 3 =

number of tiles less than 3 / total number of tiles = 2/3

From the above analysis, we solved the problem.

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Answer:

i say the answer is either 1/2 because true or false or 5/10 because you have a 50/50 chance but im more on the 1/2

Step-by-step explanation:

mark  brainlest please

Answer:

(d) -12

Step-by-step explanation:

3a = _____

a = -4

3(-4) = ___

3(-4) = -12

The answer is (d) -12

Answer: x = 138

Step-by-step explanation:

\(108+117+x=3 * 121\\3 * 121 = 363\\Rearrange unknown terms to the left side of the equation\\x=(363-108)-117\\\\255-117=138\\x=138\)

The number of people were 200 in the theater when it was full.

What is a theater?

In architecture, a theatre, usually spelled theatre, is a structure or area where a play can be conducted in front of spectators. The term comes from the Greek theatron, which means "a place of seeing." The actual performance usually takes place on a stage in a theatre.

Given that, the theater was full when the movie began.

76 people leave the theater before end the movie. At the end of the movie, there is 124 people left.

Apply algebraical operation that is addition to find the required answer.

Therefore, the number of people that was present at the beginning of the movie is (76 + 124) = 200.

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Answer:

$755.83

Step-by-step explanation:

689.98x109.5%=755.5281

Round to hundreth= 755.53