A certain composite number has 4 factors and the sum of them is 96. Find the number(hint the number is divisible by 7). Just don't give me the answer by guessing. show me how you arrived at the solution elaborately i.e. show me your working in detail

Answers

Answer 1

Answer:

[tex]\huge\boxed{77}[/tex]

Step-by-step explanation:

The number can be divisible by 7.

The multiples of 7 are 7,14,21,28,35,42,49,56,63,70,77,84 and so on

Finding the factors for all of the multiples of 7:

7 => 1,7   [Not 4 factors]

14 => 1,2,7,14    [4 factors but Sum = 24]

21 => 1,3,7,21   [4 factors but Sum = 32]

28 => 1, 2, 4, 7, 14, 28    [Not 4]

35 => 1,5,7,35   [4 factors but Sum = 48]

42 => 1, 2, 3, 6, 7, 14, 21, 42     [Not 4]

49 => 1,7,49   [Not 4]

56 => 1, 2, 4, 7, 8, 14, 28, 56       [Not 4]

63 => 1, 3, 7, 9, 21, 63     [Not 4]

70 => 1, 2, 5, 7, 10, 14, 35, 70    [Not 4]

77 => 1, 7, 11, 77     [4 factors and Sum = 96]

Answer 2

Answer:

77

Step-by-step explanation:

The first factor is 1

Since it is divisible by 7, 7 will also be one of its factors.

Therefore the four factors are

1, 7, x, y

When x and y are integers

Using the following law...

The product of factors of a number in the same position (left or right) (increasing or decreasing order) is equal to the number

Counting from left

y is the first factor

x is the second factor

Counting from the right

1 is the first factor

7 is the second factor

Applying the last

y×1=x×7

y = 7x

the sum of the factors is 96

1+7+x+7x = 96

8x+8=96

8x = 88

x= 11

Hence the number is

7x = 7(11)

=77


Related Questions

If there is a positive correlation between salary and education, then based on the table shown, which of the following careers requires the most education? A graph titled Average Salaries of Various Careers, 2008 to 2009. Veterinarian, 56,000 dollars; personal trainer, 18,000 dollars; accountant, 43,000 dollars; paralegal, 34,000 dollars; architect, almost 50,000 dollars; photographer, 19,000 dollars; pharmacist, 44,000 dollars; secretary, 30,000 dollars; surveyor, 36,000 dollars; webmaster, 49,000 dollars. a. accountant b. paralegal c. photographer d. surveyor

Answers

Answer:

The correct option is;

a. Accountant

Step-by-step explanation:

The given data are;

Career,                                                                   Average Salary

Veterinarian,                                                          $56,000

Personal trainer,                                                    $18,000

Accountant,                                                           $43,000

Paralegal,                                                              $34,000

Architect,                                                               $50,000

Photographer,                                                       $19,000

Pharmacist,                                                            $44,000

Secretary,                                                              $30,000

Surveyor,                                                               $36,000

Webmaster,                                                           $49,000

Among the options given, which are, accountant (salary, $43,000), paralegal (salary, $34,000), photographer (salary, $19,000), and surveyor (salary, $36,000), the accountant, with a salary of $43,000, requires the most education.

i promise i will mark as brainiest

Answers

Your answer will be D
The answer to this question is 36.

What is the value of m in the equation 1/2m - 3/4n = 16, when n = 8?

Answers

Answer: m= 44

Step-by-step explanation:

1/2m - 3/4n = 16    when n is 8  put it into the equation and solve for m.

1/2m - 3/4(8) = 16

1/2m - 6 = 16  

          +6  +6

1/2m = 22

m = 44

Answer:

44

Step-by-step explanation:

● (1/2 )× m - (3/4) × n = 16

Replace n by 8 and the fraction by decimal numbers (1/2 = 0.4 and 3/4 =0.75)

● 0.5 × m - 0.75 × 8 = 16

● 0.5m - 6 = 16

Add 6 to both sides

● 0.5 m - 6 + 6 = 16+ 6

● 0.5 m = 22

Multiply both sides by 2

● 0.5m × 2 = 22 × 2

● m = 44

Urgent Help. The circle shown above has a radius of 5 units

Answers

Area enclosed in [tex] 2\pi[/tex] radians =$\pi r^2$

so area enclosed in $\theta$ radians=$\theta \times \frac{\pi r^2}{2\pi}= \frac{1}2\theta r^2$

does this answer your question?

Answer: 5pi

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

Explanation:

2pi radians is equal to 360 degrees.

The shaded region has a central angle 2pi/5 radians

Divide 2pi/5 over 2pi to end up with 1/5. The "2pi" terms cancel.

The shaded region is 1/5 of the full circle.

The full circle area is pi*r^2 = pi*5^2 = 25pi square units

Taking 1/5 of that leads to (1/5)*25pi = 5pi which is the area of the shaded region.

A man drove 16 mi directly east from his home, made a left turn at an intersection, and then traveled 2 mi north to his place of work. If a road was made directly from his home to his place of work, what would its distance be to the nearest tenth of a mile?

Answers

Answer:

16. 1 miles

Step-by-step explanation:

Using Pythagorean Theorem,

a^2 + b^2 = c^2

Since the road that goes from his home to work directly is c^2...

Plug in the rest of the numbers

16^2 + 2^2 = c^2

256 + 4 = c^2

260 = c^2

The reverse square of 260 is

16. 1 miles

A line is defined by the equation 2 x + y = 4. Which shows the graph of this line? On a coordinate plane, a line goes through points (negative 2, 0) and (0, 4). On a coordinate plane, a line goes through points (0, 1) and (2, 5). On a coordinate plane, a line goes through points (0, 4) and (2, 0). On a coordinate plane, a line goes through points (0, 2) and (2, 0).

Answers

Answer:

its c

Step-by-step explanation:

im pretty sure lmk if i am wrong :)

The graph of the given line  2 x + y = 4 is a straight line and the coordinates present above the line will be ( 0, 4) and ( 2, 0) hence option (C) will be correct.

What is a line?

A line section that can connect two places is referred to as a segment.

In other words, a line segment is just part of a big line that is straight and going unlimited in bdirections.

The line is here! It extends endlessly in both directions and has no beginning or conclusion.

A coordinate that is present in the line will always satisfy the equation of the line.

In the given option the coordinate  (0, 4) and (2, 0) is satisfying the given eqution by substituting the value  2 x + y = 4 hence option (C) will correct.

For more about line segment

https://brainly.com/question/25727583

#SPJ6

A 3 liter bottle of juice costs $5.70
What is the unit price for 1 liter of juice?

Answers

Answer:

$1.90

Step-by-step explanation:

Divide 5.7 by 3 to get your answer.

[tex]\frac{5.7}{3}[/tex] = 1.9

Answer:

$1.90

Step-by-step explanation:

First, write out what you know.

So, you know that you have 3 liters.

Together, they cost $5.70.

You want to know the unit price, for 1 liter.

Therefore, you would divide $5.70 by 3:

[tex]\frac{5.70}{3}=\frac{1.90}{1}=1.90[/tex]

This means that the unit price, for 1 liter of juice, would be $1.90.

Polygon ABCD is defined by the points A(-4, 2), B(-2, 4), C(1, 3), and D(2, 2). Match the coordinates of the points of the transformed polygons to their correct values. the coordinates of D′ if polygon ABCD rotates 90° counterclockwise to create A′B′C′D′ (-2, 2) the coordinates of C″ if polygon ABCD rotates 90° clockwise to create A″B″C″D″ (4, -2) the coordinates of A′′′ if polygon ABCD rotates 180° clockwise to create A′′′B′′′C′′′D′′′ (3, -1) the coordinates of B″ if polygon ABCD rotates 270° counterclockwise to create A″B″C″D″ (4, 2)

Answers

Answer:

The coordinates of D′ if polygon ABCD rotates 90° counterclockwise to create A′B′C′D′ is at (-2, 2)

The coordinates of C″ if polygon ABCD rotates 90° clockwise to create A″B″C″D″ is at (3, -1)

The coordinates of A′′′ if polygon ABCD rotates 180° clockwise to create A′′′B′′′C′′′D′′′ is at (4, -2)

The coordinates of B″ if polygon ABCD rotates 270° counterclockwise to create A″B″C″D″ is at (4, 2)

Step-by-step explanation:

A transformation is the movement of a point from its initial position to a new position. If a shape is transformed, all its points are also transformed. Types of transformation are reflection, rotation, dilation and translation.

Given Polygon ABCD is defined by the points A(-4, 2), B(-2, 4), C(1, 3), and D(2, 2).

If a point X(x, y) is rotated 90° counterclockwise, the new location X' is at (-y, x)

If a point X(x, y) is rotated 90° clockwise, the new location X' is at (y, -x)

If a point X(x, y) is rotated 180° clockwise, the new location X' is at (-x, -y)

If a point X(x, y) is rotated 270° counterclockwise, the new location X' is at (y, -x)

The coordinates of D′ if polygon ABCD rotates 90° counterclockwise to create A′B′C′D′ is at (-2, 2)

The coordinates of C″ if polygon ABCD rotates 90° clockwise to create A″B″C″D″ is at (3, -1)

The coordinates of A′′′ if polygon ABCD rotates 180° clockwise to create A′′′B′′′C′′′D′′′ is at (4, -2)

The coordinates of B″ if polygon ABCD rotates 270° counterclockwise to create A″B″C″D″ is at (4, 2)

Answer:

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.

If a point A(x, y) is rotated 90° counterclockwise, the new point is at A'(-y, x).

If a point A(x, y) is rotated 90° clockwise, the new point is at A'(y, -x). If a point A(x, y) is rotated 180° counterclockwise, the new point is at A'(-x, -y).

If a point A(x, y) is rotated 270° counterclockwise, the new point is at A'(y, -x).

Polygon ABCD is defined by the points A(-4, 2), B(-2, 4), C(1, 3), and D(2, 2).

The coordinates of D′ if polygon ABCD rotates 90° counterclockwise to create A′B′C′D′ is D'(-2, 2)

The coordinates of C″ if polygon ABCD rotates 90° clockwise to create A″B″C″D″ is C"(3, -1).

The coordinates of A′′′ if polygon ABCD rotates 180° clockwise to create A′′′B′′′C′′′D′′′ is A''"(4, -2)

The coordinates of B″ if polygon ABCD rotates 270° counterclockwise to create A″B″C″D″ is B"(4, 2)

Lenny is competing with his cousin, Jasper, in an indoor rock-climbing contest. At the start of the climb, Lenny makes his way 5 ¼ feet up the wall, while Jasper climbs 9 ¾ feet. How much farther did Jasper climb than Lenny?

Answers

Answer:

[tex]4\frac{1}{2}[/tex] feet further.

Step-by-step explanation:

Since these are mixed numbers that are both in fourths, we can easily subtract the two numbers. However, I find it easier if we first convert both mixed numbers into improper fractions.

[tex]5\frac{1}{4} = \frac{5\cdot4+1}{4} = \frac{21}{4}[/tex]

[tex]9\frac{3}{4} = \frac{9\cdot4+3}{4} = \frac{39}{4}[/tex]

Now we can subtract the numerators:

[tex]\frac{39}{4} - \frac{21}{4} = \frac{39-21}{4} = \frac{18}{4}[/tex]

[tex]\frac{18}{4}[/tex] simplifies down to [tex]\frac{9}{2}[/tex].

Converting  [tex]\frac{9}{2}[/tex] to a mixed number is easy - 2 goes into 9 4 times (8) with one remainder so:

[tex]4\frac{1}{2}[/tex] .

Hope this helped!

I dont really understand how to solve this

Answers

Answer:

2040 miles

Step-by-step explanation

Gas costs 1.35 per gallon and Jose had 81 dollars for gasoline

with this info we can find out how many gallons of gas Jose can buy.

81 divided by 1.35 is 60 gallons of gas

we also know that he can travel 34 miles for each gallon of gas

with this we can find out how far jose can travel

34 multiplied by 60 is 2040 miles

so, with $81, Jose can travel 2040 miles if gas prices are $1.35

Pauline has 35 cups of flour. She makes cakes that requires 2 1/4 cups each. How mant cakes can she bake using the 35 cups of flour?​

Answers

Answer:

15.56

Step-by-step explanation:

Total flour available=35 cups

Each cake=2 1/4 cups

Find how many cakes Pauline can bake with 35 cups of flour

Let the number of cakes she can bake with 35 cups of flour=x

x=35 cups / 2 1/4 cups

=35÷9/4

=35×4/9

=140/9

=15 5/9 cakes

=15.56 cakes approximately

How does the graph change between point A and point B?
5
4
3
B
А A
1
-2-1
6 7
8
X
-2
The graph increases
The graph decreases.
The graph remains constant.
The graph increases, then decreases.

Answers

Answer:

Step-by-step explanation:

A

Answer:

A

Step-by-step explanation:

When simplified completely, the product of a monomial and a binomial is
a trinomial.

Answers

Answer:

the answer is ; Never

Hope this answer correct :)

Answer:

the answer is never

Step-by-step explanation:

Simplify (5x3y) (2xy4)

Answers

Answer: 10x^4y^5

Step-by-step explanation:

5x^3y^1•2x^1y^4

5•2=10

x^3•x^1=x^4

y^1•y^4=y^5

10x^4y^5

I need help please i will do brainliest

Answers

On average, an okapi weighs 290 kilograms and a llama weighs 160 kilograms.

O=Okapi
L=llama

O+L=450
3L=O+190

Solving that setup equation gets us with

4L=640

Divided by 4 to get each llama weighing 160KG

160+O=450

450-160=290

Getting the okapi to weigh 290KG

Hope this helped! Have a great day!!

The residents of a city voted on whether to raise property taxes. The ratios of yes votes to no votes was 5 to 7. If there were 10,740 total votes, how many no votes were there?

Answers

Answer:

6,265 votes

Step-by-step explanation:

The residents of a city voted on whether to raise property taxes. The ratios of yes votes to no votes was 5 to 7. If there were 10,740 total votes, how many no votes were there?

Given that :

Ratio of yes votes to no votes = 5 to 7

Yes votes : no votes = 5 : 7

Total votes = 10,740

The actual number of yes votes and no votes can be obtained thus :

Sum of ratio = (5 + 7) = 12

(ratio of vote / sum of ratio) * total votes

Number of no votes :

(Ratio of no votes / total ratio) * total votes

(7 / 12) * 10,740

0.5833333 * 10,740

= 6,265 votes

Number of no votes = 6,265 votes.

1. A cone is 8cm high and has a base diameter of 12cm.its slant height is a.6cm b.8cm c.10cm d.12cm

Answers

Answer:

10

Step-by-step explanation:

it is Pythagoras theorem

6*6=36

8*8=64

64+36=100

square root of 100 is 10

Jami bought 4 cookies that cost $1.45, each. She paid with 6 one-dollar bills. how much change does Jami recive?

Answers

Answer:

$0.20

Step-by-step explanation:

4 x 1.45 = $5.80

6.00 - 5.80 = 0.20

Answer: $0.20

Step-by-step explanation:

Do 4 *$1.45 = $5.80

This is how much her total was.

She gave $6 in cash.

Subtract.

6-5.80=$.20

Evaluate the expression when a= 5 and x= -2 -a+6x Thankyou ! !

Answers

The equation would be -5+(-12), so the answer would be -17 :)

Answer:

[tex]\boxed{-17}[/tex]

Step-by-step explanation:

Hey there!

If x is -2 and a is 5 then we can plug those in,-a + 6x.

-(5) + 6(-2)

-5 + -12

= -17

Hope this helps :)

The amount of a radioactive isotope decays in half every year. The amount of the isotope can be modeled by f(x) = 346(1/2)x and f(1) = 173. What does the 1 represent?

Answers

the answer is A because it makes sense

Answer:

D

Step-by-step explanation:

i took the test and i got it right

Use the rule "subtract 6" to create a sequence of 10 numbers starting with 100. (explanation/work needed)

Answers

Answer:

100 -6 = 94

94 - 6 = 88

88 - 6 = 82

82 - 6 = 76

76 - 6 = 70      We can then show and prove 70 -> 64.

                                                                          64 -> 58

                                                                          58 -> 52

                                                                          52 -> 46

                                                                          46 -> 40

As numbers that end in 0, decrease to units that end in 4,8,2,6,and back to zero.

= all numbers that end with 0 have numbers that end in 4,8,2,6,0 when subtracting 6.

As 6 x 10 = 60 and 60 +40 = 100

We cna prove 4+8+2+6  = 20

20+20 = 40 and would continue this pattern to get to 10 we can then see the sequence of how 30/6 and proves each 5 number coordinate being 4,8,2,6,0 until we get to 10.

We then find 4,-2,-8,-14,and-20 it skips out  2 and 6 here on the neutral line but then starts and changes the sequence end numbers to -26 -32, -38,-44 and -50. This proves that-2 and -8 has significance and shows us a real sum that on negative -2 -8 = 6

The inverse of the 40 marker in the positive shows us 60

and 60 -50 = 10 being our 2nd positive closest to zero.

These were repeated twice and show 40 deducted and a further 18 as 0 counts for 2 subtractions 100-6  70-6 just like 94 +6 = 100 and like 70+6 = 76 and 40+6 = 46

3 x 6 = 18

40+ 18 = 58

100-58 = 42 and shows us a reflection again with 4 and 2

not just 4+2 = 6 it shows is 4/2 = 2  42/2 = 21 and 7 being a divider represents the first sequence group of 10 from 100 being 70 and just as significant in a decrease of 6 in relation to 100.

100-70 = 30

30-6 = 24

24 / 6 = 4

and we mark 4 as our first unit with relation to 100 and its decrease of 6 in sequence.

This may help you remember that 30 x 100 = 3000 and would be increasing by 6 x 180 times. But when we decrease from here we find 2400 a likely number as 3000-600 - 2400

This may help you remember that 400/6 = 66.6666666667 and why decrease always ends up as negative when 400 x 6 = 2400 and is a much more dividable number. and that 400 is not dividable by 6 in the first place, and may be linked to why a neutral zero number may show 4 and 10 and -2 and -8 where all these numbers divide into 400 6 just doesn't work in any even hundred number below 1200 except for 600 as we know and recall 6 divides into 30 and 18 but not into 40, just counts back to inverse 40 from 100 as its counting 2 x 30 = 60. It does divide into 2400 and that is a midway point back down to 1800 from 3000. So this may help you remember divisors of larger numbers.

What is the simplified expression for 22 • 2?
24
O 20
021
O 22
0 23

Answers

2^1 would be the answer.

2^2 x 2^3 is 32

2^4 is 16

32/16 is 2

2^1 is 2 so the answer is 2^1

Answer:

Step-by-step explanation:

When multiplying exponents of the same base, you can simply add the exponents together so 2² * 2³ = 2⁽²⁺³⁾ = 2⁵. When dividing exponents of the same base, you can simply subtract the exponents so 2⁵ / 2⁴ = 2⁽⁵⁻⁴⁾ = 2¹.

A car traveled 420 miles in 7 hours how many miles did it travel per hour?

Answers

Answer:

60 Mile per hour

Step-by-step explanation:

Hello!

To find how far something travel in a span of time we divide the distance traveled by the time it took to travel that far

420/7 = 60

The Answer is 60mph

Hope this Helps!

Answer: 60 miles per hour

Step-by-step explanation:

420 miles / 7 hours

Multiply, if possible.

Answers

Answer:

2

3

-5

0

Step-by-step explanation:

2×0+1×2=2

2×1+1×1=3

2×-3+1×1=-5

2×-2+1×4=0

Answer:

[tex]\large \boxed{\mathrm{Option \ C}}[/tex]

Step-by-step explanation:

[tex]{\mathrm{view \ attachment}}[/tex]

Lines CD and DE are tangent to circle A shown below: If Arc CE is 112°, what is the measure of ∠CDE? a 124° b 136° c 68° d 56°

Answers

Answer:

C

Step-by-step explanation:

The central angle of this is 112 degrees. That is CAE is 112 degrees. That being the case, CDE is 90 + 90 + 112  = 292 Tangents make a 90 degree angle with the center of the circle.

CDE = 360 - 292 = 68

C

The measure of ∠CDE is 68degrees

This question bothers on circle geometry;

From the diagram, we can see that ACDE will form a quadrilateral. Since the sum of angles of a quadrilateral is 360degrees, hence;

[tex]<CDE + arcCE+<C+<E=360[/tex]

From the diagram, since CD and DE are both tangential to the circle at point C and E, this shows that <E = <E = 90°

substituting the given values in the formula;

[tex]<CDE+112+90+90=360\\<CDE + 292=360\\<CDE=360-292\\<CDE =68^0[/tex]

Hence the measure of ∠CDE is 68 degrees

Learn more on circle geometry: https://brainly.com/question/24357871

PLEASE help me with this question. This is really URGENT

Answers

Answer:

c. p(10)=26,327(1+0.024)^10

Step-by-step explanation:

its just the answer

Answer:

[tex]\boxed{\sf Option \ 3}[/tex]

Step-by-step explanation:

The problem is exponential growth.

[tex]a(1+r)^t[/tex]

[tex]a = \sf initial \ amount[/tex]

[tex]r = \sf rate[/tex]

[tex]t= \sf time[/tex]

The third option is right.

[tex]P(10)=26237(1+2.4\%)^{10}[/tex]

[tex]P(10)=26237(1+0.024)^{10}[/tex]

15. Use inductive reasoning to describe the pattern. Then find the next two numbers in the pattern.
-9, -4, 1, 6, ...

Answers

Answer:

11, 16

Step-by-step explanation:

the difference between -4 and -9, 1 and -4, 6 and 1 is 5...so add 5 to 6 = 11

then 11 + 5 = 16

Answer:

11,16

Step-by-step explanation:

We are adding 5 each time

-9+5 = -4

-4+5 =1

To find the next two terms

6+5 =11

11+5 = 16

Shawn wanted to model the number 13,450 using 13,450 using base-ten blocks how many large cubes, flats, and longs does he need to model the number

Answers

Answer:

13 cubes, 4 flats, 5 longs

Step-by-step explanation:

Base-ten is basically just analyzing the place values of each number in the given value.

A cube represents 1,000, a flat represents 100, and a long represents 10.

Looking at the number 13,450, we can see that there are 13 thousands in this (13,000). This means that we will need 13 cubes.

We can also see that there are 4 hundreds in this (400), meaning we need 4 flats.

Also, there are 5 tens in this (50), so we need 5 longs.

Hope this helped!

What is the solution to the equation 1 over the square root of 8 = 4^(m + 2)? A) m = − 15 over 4 B) m = − 11 over 4 C) m = 5 over 4 D) m = 9 over 4

Answers

Answer:

B) m = -11/4

Step-by-step explanation:

What is the solution to the equation 1/sqrt(8) = 4^(m+2)

1 over the square root of 8 = 4^(m + 2)?

A) m = − 15 / 4

B) m = − 11 / 4

C) m = 5 / 4

D) m = 9 / 4

1/sqrt(8) = 4^(m+2)   apply law of exponents

1/2^(3/2) = (2^2)^(2m+4)

2^(-3/2) = (2)^(2m+4)

-3/2 = 2m+4

2m = -11/2

m = -11/4

All points of the step function f(x) are graphed
What is the domain of f(x)?
O {x4 O {x] -3 < x 54}
O {x|1 < x 54}
O {x|2

Answers

I can’t tell what those options are.

The domain is the input values of a function, therefore the x values.

In this case the interval for the domain is

-4< x <= 4
Other Questions
It is possible for two words to sound exactly the same but have different meanings and spellings. The immediate cause of war in Europe in 1914 was Group of answer choices the sinking of the British passenger liner Lusitania. a struggle between European powers for control of the international diamond trade. the German invasion of Poland. the assassination of the Archduke Franz Ferdinand. the death of Otto von Bismark in Germany. Find the distance between the points. Give an exact answer and an approximation to three decimal places.(3.1,0.3) and (2.7. - 4.9)The exact distance is(Simplify your answer. Type an exact ans The following data relate to direct materials costs for February: Materials cost per yard: standard, $1.93; actual, $2.03 Standard yards per unit: standard, 4.68 yards; actual, 4.96 yards Units of production: 9,400 Calculate the direct materials price variance. a.$4,399.20 favorable b.$940.00 unfavorable c.$4,662.40 favorable d.$4,662.40 unfavorable I will give brainliest to the right answer!! Find the vertex and the length of the latus rectum. x= 1/2 (y - 5) + 7 The twelve-year old boy has fractured his arm because of a fall from his bike. After the injury has been casted, what assessments are the least important? A man weighs 185 lb. What is his mass in grams?Please show work.Thank you Identify a feature of epic poetry in the passage Is the boxed word a SUBJECT or a VERB?Here is the information you asked for.A. SubjectB. Verb An L-R-C series circuit has L = 0.450 H,C=2.5010^5F, and resistance R. Required:a. What is the angular frequency of the circuit when R = 0? b. What value must R have to give a decrease in angular frequency of 10.0 % compared to the value calculated in Part a. A hammer is used to hit a nail into a board. Which statement is correct about the forces at play between the nail and the hammer?O The nail exerts a much smaller force on the hammer in the opposite directionO The nail exerts a much smaller force on the hammer in the same direction.The nail exerts an equal force on the hammer in the same direction.O The nail exerts an equal force on the hammer in the opposite direction. Effects of the launching of Sputnik included:________ a. protests about excessive government b. spending tax cuts that were meant to stimulate a faltering economy c. a loss of credibility for the scientists of the Soviet Union d. calls for more funding for science education in America the growth of the antiwar movement Pattern A: 0, 5, 10, 15, 20,... Pattern B: 0, 20, 40, 60, 80,... Which statement is true about the relationship between the corresponding terms of Pattern A and Pattern B? A. The terms in Pattern B is 4 times the corresponding terms in Pattern A. B. The terms in Pattern A is 1/2 times the corresponding terms in Pattern B. C. The terms in Pattern B is 20 more than the corresponding terms in Pattern A. D. The terms in Pattern A is 5 more than the corresponding terms in Pattern B. The diameter of steel rods manufactured on two different extrusion machines is being investigated. Two random samples of sizes n1"=15 and n2"=17 are selected, and the sample means and sample variances are x1 =8.73, s2=0.35, x =8.68, and s2=0.40, respectively. Assume that 1^2 = 2^2 that the data are drawn from a normal distribution.Required:a. Is there evidence to support the claim that the two machines produce rods with different mean diameters? Use alpha=0.05 in arriving at this conclusion.b. Find the P-value for thet-statistic you calculated in part (a).c. Construct a 95% confidence interval for the difference in mean rod diameter. Interpret this interval. Select three things an author may use to describe his characters.antagonistphysical featuresprotagonistconductconversation For what does reverend Paris condemn his niece Abigail A soccer ball is made of 32 pieces of leather: white hexagons and black pentagons. Each black piece borders only with white pieces, each white piece borders with three black pieces and three white pieces. How many black pieces are needed to manufacture the ball? Diagonals of a parallelogram _____ each other. Fill in the blank.The rider tugged on theof her horse to make him slow down.O reinsranesO rainsreignsNedSubmitSave and ExitMark this and tatimo How can you change a rational number to a decimal? Can you give an exsample?