The volume of a cylinder is 770cm³. It has a height of 5cm. Find its radius.

Here the conjecture we can made is :

The sum of interior angles i.e. ∠A and ∠B is equal to the exterior angle at C.

The exterior angle of any triangle is defined as the angle which is at the outside boundaries of that triangle. whereas, the interior angle is defined as the angle which is inside the triangle. In the other words if the triangle has the point within the angle it is in the interior of the angle , but if the point is outside then is it said to be in the exterior of the angle for that triangle.

In mathematics, the two angles are called as adjacent angles if they have a common vertex or we can say they are angle of a common vertex in the triangle.

we can define the adjacent angle as the angles which have common side and common vertex and they don't overlap.

According to the exterior angle property, if a side of a triangle is made, then the exterior angle formed is always equals to the sum of  two interior angles opposite to each other in the triangle.

Thus on the basis of exterior angle property we can make the conjecture that, "the measure of an exterior angle is equal to the sum of measures of its nonadjacent interior angles".

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Answer:

There is 2121.80 in the account after 2 years.

Step-by-step explanation:

Use the formula A = P(1 + r)^t  where P = initial amount, A = amount after t years and r = the rate (as a decimal).

So, for this problem:

Amount after 2 years = 2000(1 + 0.03)^2

= £2121.80

Answer:

120

Step-by-step explanation:

We start with the equation:

[tex]\frac{1}{3}x-\frac{3}{8}x -\frac{7}{24}x =-40[/tex]

We need to set the fractions into equal denominations so we can sum them all together:

[tex]\frac{8}{24}x-\frac{9}{24}x -\frac{7}{24}x =-40\\[/tex]

Now sum the fractions:

[tex]\frac{8-9-7}{24}x=-40\\\\ \frac{-8}{24}x=-40[/tex]

Multiple both sides by 24 to eliminate denominator on left side of equation:

[tex]-8x=-960[/tex]

Divide both sides by -8 to get the value of x:

[tex]x=120[/tex]

The sum of the given finite series is 25

The summation notation means that we have to add the terms of the given series with n moves from the lower limit to the upper limit.

The given series is:

      [tex]\sum\limits^5_{n=1} {(2n-1)}[/tex]

In this series, the lower limit is n = 1 while the upper limit is n=5.

n = 1  ⇒ 2n - 1 =  2(1) -1 = 1

n = 2  ⇒ 2n - 1 = 2(2) -1 = 3

n = 3  ⇒ 2n - 1 = 2(3) -1 = 5

n = 4  ⇒ 2n - 1 = 2(4) -1 = 7

n = 5  ⇒ 2n - 1 = 2(5) -1 = 9

Hence,

[tex]\sum\limits^5_{n=1} {(2n-1)}=1+3+5+7+9[/tex]

We can evaluate the sum of the series directly, or by using the sum formula as follow:

S(n) = n/2 [a(1) + a(n)]

Substitute n = 5, a(1) =1, and a(n) = 9:

S(5) = 5/2 (1 + 9) = 25

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The total number of band members and dancers in the halftime show in all rows were 276.

A row is an arrangement of things in a straight line next to each other.

if there are n rows and each row has m members then total number of members = m* n

Given that marching band was in 3 sections and each section has 8 rows of  8 players , then players in each section of marching band  = 8 *8 = 64

As, there are 3 such sections then total number of marching band players =3*(players in each section) = 3* 64 = 192

Given that there are 2 sections of dancers and each section has 6 rows of 7 dancers.

Then, dancers in each section of  dancers = 6*7 =42

As there are two such sections, then the total dancers = 2* 42 = 84

total no of band members and dancers = 192+84 = 276

Therefore, The total number of band members and dancers in the halftime show were 276.

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Answer:

see explanation

Step-by-step explanation:

1

(5p² - 3) + (2p² - 3p³) ← remove parenthesis

= 5p² - 3 + 2p² - 3p³ ( collect like terms , largest exponent first )

= - 3p³ + 7p² - 3

2

(a³ - 2a²) - ( 3a² - 4a³) ← distribute second parenthesis by - 1

= a³ - 2a² - 3a² + 4a³ ( collect like terms, largest exponent first )

= 5a³ - 5a²

3

(- 4[tex]k^{4}[/tex] + 14 + 3k²) + (- 3[tex]k^{4}[/tex] - 14k² - 8) ← remove parenthesis

= - 4[tex]k^{4}[/tex] + 14 + 3k² - 3[tex]k^{4}[/tex] - 14k² - 8 ← collect like terms, largest exponent first

= - 7[tex]k^{4}[/tex] - 11k² + 6

4

(3 - 6[tex]n^{5}[/tex] - 8[tex]n^{4}[/tex]) - (- 6[tex]n^{4}[/tex] - 3n - 8[tex]n^{5}[/tex]) ← distribute second parenthesis by - 1

= 3 - 6[tex]n^{5}[/tex] - 8[tex]n^{4}[/tex] + 6[tex]n^{4}[/tex] + 3n + 8[tex]n^{5}[/tex] ( collect like terms, largest exponent first )

= 2[tex]n^{5}[/tex] - 2[tex]n^{4}[/tex] + 3n + 3

5

(y³ - 7[tex]x^{4}[/tex][tex]y^{4}[/tex]) + (- 10[tex]x^{4}[/tex]y³ + 6y³ + 4[tex]x^{4}[/tex][tex]y^{4}[/tex] ) - (  [tex]x^{4}[/tex]y³ + 6[tex]x^{4}[/tex][tex]y^{4}[/tex])

remove parenthesis from first 2 and distribute third by - 1

= y³ - 7[tex]x^{4}[/tex][tex]y^{4}[/tex] - 10[tex]x^{4}[/tex]y³ + 6y³ + 4[tex]x^{4}[/tex][tex]y^{4}[/tex] - [tex]x^{4}[/tex]y³ - 6[tex]x^{4}[/tex][tex]y^{4}[/tex]

collect like terms

note the term with the largest exponent is [tex]x^{4}[/tex][tex]y^{4}[/tex]

= (- 7[tex]x^{4}[/tex][tex]y^{4}[/tex] - 6[tex]x^{4}[/tex][tex]y^{4}[/tex] ) + (- 10[tex]x^{4}[/tex]y³ - [tex]x^{4}[/tex]y³) + (y³ + 6y³)

= - 13[tex]x^{4}[/tex][tex]y^{4}[/tex] - 11[tex]x^{4}[/tex]y³ + 7y³

Answer:

k = 1

This is because when g(x) = 8, f(x) = 8

and when g(x) = 2, f(x) = 2

and this continues throughout the graph

Answer: d=90 degrees

e=69 degrees

f=111 degrees

Step-by-step explanation:

69+f=180 ==> a straight line is 180 degrees and is called a straight angle. The angles that make up the straight line add up to 180 degrees.

69-69+f=180-69

f=180-69

f=111 degrees

e+f=180 ==> a straight line is 180 degrees and is called a straight angle. The angles that make up the straight line add up to 180 degrees.

e+111=180

e+111-111=180-111

e=180-111

e=69 degrees

d+90=180 ==> if there is a tiny box between an angle, that means that the angle is a right angle which measures 90 degrees.

d-90+90=180-90

d=180-90

d=90 degrees

Answer: D

Step-by-step explanation:

The weight of the baby increased by a 20%

We know that the initial weight of the baby is 20 pounds, so that will be our 100%, and we can write:

20lb = 100%

Then the weight is 24 lb, so that will represent another percentage X, we can write:

24lb = X

We can solve this for X, taking the quotient between the relations:

(24lb/20lb)  = X/100%

(24lb/20lb)*100% = X = 120%

So we can see that the weight of the baby increased by a 20%

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Pizza costing $24 is being delivered to Brian's home. The change $7.72 he get if he uses two $20 bills as payment.

Given that,

Pizza costing $24 is being delivered to Brian's home.

He pays the amount in addition to the 7% sales tax and 15% tip.

In addition, he pays the delivery price of $3, which is added on after tax and tip.

We have to find how much change does he get if he uses two $20 bills as payment.

To figure out the sales tax

$24×0.07=$1.68

To figure out the tip

$24×0.15=$3.6

The Total cost=$24+$1.68+$3.6+$3=$32.28

Now, To find change we have to add the Total cost and the bill

Change=2($20)-$32.28

Change=40-32.28

Change=$7.72

Therefore, The change $7.72 he get if he uses two $20 bills as payment.

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The transformation of the given function g(x) = ¹/₂|x + 4| - 3 using the format h(x) = a|bx + c| + d, gives;

a = ¹/₂

b = -1

c = 6

d = 3

We are given the function;

g(x) = ¹/₂|x + 4| - 3

Now, we are told that the function is first translated by 6 units upwards, and so this means a transformation of;

g(x) + 6 = ¹/₂|x + 4| - 3 + 6

g'(x) = ¹/₂|x + 4| + 3

Now, we are told that it now undergoes a transformation of 2 units to the right, this gives;

g"(x) =  ¹/₂|x + 4 + 2| + 3

g"(x) = ¹/₂|x + 6| + 3

Finally, after undergoing a transformation of reflection in the y-axis, we have; h(x) = ¹/₂|-x + 6| + 3

For the format of;

h(x) = a|bx + c| + d, it means that we have;

a = ¹/₂

b = -1

c = 6

d = 3

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ΔJKL has 53.28 units of side length.

So,

The formula for the perimeter of the side of a triangle: √(x₂−x₁)²+(y₂−y₁)²

Filling the values in the formula, we obtain:

Then, each side of the triangle will be: 53.28 units

Therefore, ΔJKL has 53.28 units of side length.

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There is not enough evidence

An indicator of how much a group of numbers vary or are dispersed is the standard deviation. [1] When the standard deviation is low, the values are more likely to fall within a narrow range, also known as the expected value, whereas when the standard deviation is high, the values tend to be closer to the mean.

For  1.5 moles substrate concentration per liter

Reaction ( n2 ) = 15 runs

average velocity ( x2 ) = 7.5 micromoles per 30 minutes

standard deviation ( s2 ) = 1.5

For 2.0 moles substrate concentration per liter

Reaction( n1 ) = 12 runs

(x1) = 8.8 micromoles on average per 30 minutes

standard deviation ( s1 )  = 1.2

Show Reason to believe that this increase in substrate conc causes an increase in mean velocity

Hypothesis test

H0 : μ1 - μ2 = 0.5

H1 : μ1 - μ2  > 0.5

significance level ( ∝) = 0.01

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Answer: BC=17

Step-by-step explanation:

AC=AB+BC

27=10+BC

27-10=10-10+BC

BC=27-10

BC=17

If B is the midpoint of AC and C is the midpoint of BD, then AB=CD.

Given that B is midpoint of AC and C is the midpoint of BD.

We are required to prove that AB is equal to CD.

Midpoint is the point which divides the line segment into two equal parts.

If B is midpoint of AC then,

2AB=AC-----1

2BC=AC-----2

If C is midpoint of BD then,

2BC=BD-----3

2CD=BD-----4

From 1 & 2

2AB=2BC

AB=BC

Put the value of BC from 3.

AB=BD/2

Now put the value of BD from 4.

AB=2CD/2

AB=CD

Hence proved

Hence if B is the midpoint of AC and C is the midpoint of BD, then AB=CD.

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Answer:

50 ohms.

Step-by-step explanation:

Volts = current * resistance

110 = 2.2 * r

R = 110 / 2.2

  = 50 ohms.

Answer:

1) y=5/4

2) y=−6

Step-by-step explanation:

Let's solve the equation step by step.

1) 2xy - x = 3

(2)(2)y - 2 = 3

4y - 2 = 3

4y−2=3

Step 1: Add 2 to both sides.

4y−2+2=3+2

4y=5

Step 2: Divide both sides by 4.

4y/4 = 5/4

y=5/4

2) 2y + xy = 6

2y−3y=6

Step 1: Simplify both sides of the equation.

2y−3y=6

2y+−3y=6

(2y+−3y)=6(Combine Like Terms)

−y=6

−y=6

Step 2: Divide both sides by -1.

−y/−1 = 6/−1

y=−6

The solution of t in 100 t=70 /240 is t= 7/2400

The equation is given as

100 t=70 /240

Divide both sides of the equation by 100

So, we have

t=70 /240 * 1/100

Evaluate

t= 7/2400

Hence, the solution of t in 100 t=70 /240 is t= 7/2400

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Answer:

25 + 5x = 30 + 2x

At 5/3s of an hour is when the cost of both tubing companies are the same.

This is when the price of both companies both hit $33.33

Step-by-step explanation:

25 + 5x = 30 + 2x

move variables by subtracting

25 + 3x = 30

move constants by subtracting  

30 - 25 = 5

5 = 3x

x = 5/3

Answer:

-10

Step-by-step explanation:

Convert to improper fractions and do the math

-8/3 - 22/3  

-30/3

-10

[tex]Answer:\ a_n=34-8n[/tex]

Step-by-step explanation:

26, 18, 10, 2

18-26=-8

10-18=-8

2-10=-8

This is an arithmetic progression:

[tex]a_n=a_1+(n-1)d,\\a_1=26\ \ \ \ \ d=-8\ \ \ \ n=1,\ 2,\ 3,\ 4\\a_n=26+(n-1)(-8)\\a_n=26+(n)(-8)+(-1)(-8)\\a_n=26-8n+8\\a_n=34-8n[/tex]

The expression that relates the measure of <1 and arcs QP and arcSP is expressed as m<1 = 1/2(arcQR+arcSP)

When two chords intersect inside a circle, the angle formed is half of the sum of the subtended arcs.

From the given diagram, the intercepted arcs are arcQR and arcSP and the measure of the interior angle is <1.

Using the theorem above, the expression that relates the measure of <1 and arcs QP and arcSP is expressed as:

m<1 = 1/2(arcQR+arcSP)

The measure of the angle <1 is equivalent to half the sum of arcQR and arcSP.

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The rental company to hat Oscar should use is the second company because it's cheaper.

The total amount charged for the first boat will be:

= 100 + 35h

where h = number of hours

= 100 + 35(8)

= 100 + 260

= $360

The amount charged for the second company will be:

= 50 × 8

= 400

Therefore, the rental company to hat Oscar should use is the second company because it's cheaper.

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It would take the test administrator 48 seconds to allow for the performance of the task

So, if we want 97.5 percent, we must look it up in our z table. So I need to find the z score that is closest to.975, which is 1.96.

The 97.5th percentile point of the standard normal distribution is a quantity often used in probability and statistics for statistical computations. This figure is around 1.96, which means that 95% of the area under a normal curve is within 1.96 standard deviations of the mean.

As a result, the z score for the 97.5th percentile would be multiplied by the class standard deviation. As a result, we obtain;

1.96*6 = 11.76

Then, this new time gotten would be added to the first mean of the class,

As a result, we have 36+11.76 = 47.76 which is approximately 48

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Answer:

n=21

Step-by-step explanation:

3n-21=2n

subtract 3n from each side

-21=-1n

two negatives become a positive

Missing term i.e., the second term of the sequence is 5.

As the series is in an arithmetic sequence, so we have an equation

[tex]a_{n}[/tex] = a +(n-1)d

Where a = first number of the series

           n = number of term

           d= common difference

As we know the 3rd term of the sequence, so by this we can find the common difference.

So we have,

9 = 1 +(3-1)d

8=2d

d=4

common difference = 4

Now we have to find the 2nd term or the missing term of the sequence, so we have

[tex]a_{2}[/tex] = 1 +(2-1)4

   = 1+ 1×4

   = 1+4

   = 5

Therefore the 2nd term is 5.

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The time exactly halfway between 42.60 seconds and 49.24 seconds is 45.92 seconds.

Halfway simply means the midpoint between two values. It is the distance between two values divided by two. It can also mean the average of the two values.

If the women's 400m world record is 42.60 seconds and the 16th fastest women's 400m runner ran it in 49.24 seconds, to find the exact halfway of these two records means to find the average of these two records of time. Add the two records of time and divide by two.

n = (42.60 + 49.24)/2

n = 91.84/2

n = 45.92 seconds

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Answer:

42

Step-by-step explanation:

= 10+8^3/16

= 10+512/16

= 10+32

= 42