Prove for
mathematical
induction is the statement
is true
3+7+11+... (4n-1) = n(2n+1)

Answer:

9 x =108

Step-by-step explanation:

Let the number of candies be x.

According to the question,

x=108/9

We can also write it as,

9 x=108

By the way ,each child will get 12 candies.

Thank you!

Answer:

$336

Step-by-step explanation:

$14.75(8) + $14.75(2)(4) - (8 hours of normal shift) + (double pay rate)(for 4 hours)

= $118 + $118 - Add

= $336

Answer:

Ok so to help you out, first, off you need to be sure that the sets domain and range use the proper variable. After that, you are going to want to just plug it into the equation. I am going to link a screenshot to the correct answer if you are still have trouble finding it.

Anyways hoped this helped and I got to this question in time c:

Answer:

A. has a constant proportion of 1/4.

Answer:

or,x2-x=6

or,x2-x-6=0

or,x2-3x+2x-6=0

or,x(x-3)+2(x-3)=0

or,(x-3)(x+2)=0

so either x=3

or x=-2

Answer:

The answer is 90+0+0.1+0.02+0.005.

Step-by-step explanation:

The reason for my answer is because 90 is in the tens place. 90+0 is equal to 90 so that's why it is a +0 after the 90. Now, we have a decimal. After the decimal, we have 125. It is +0.1 because the 1 in 90.125 is in the tenths place. Next, it is +0.02 because the 2 in 90.125 is in the hundredths place. Last but not least, it is +0.005 because the 5 in 90.125 is in the thousandths place.

Answer:

42 inches

Step-by-step explanation:

1 ft = 12 inch

Answer:

42 inches.

Step-by-step explanation:

Unit of measurement:

1 foot = 12 inches.

3 ft x 12 inches = 36 inches.

1/2 foot x 12 inches = 12/2 = 6 inches.

36 inches + 6 inches = 42 inches

42 inches is your answer.

~

Answer: The new slope is -(2/3)

Step-by-step explanation:

Ok, we know that our line can be written as:

y = (2/3)*x + b

where b is the y-intercept, and here does not really matter.

Ok, remember that if we have a point (x, y) and we reflect it over the x-axis, the new point will be (x, -y).

For our linear equation, the point (x, y) can be written as:

(x, y = (2/3)*x + b) = (x,  (2/3)*x + b)

Now, after the reflection, our point is:

(x, - ( (2/3)*x + b)) = (x, -(2/3)*x - b)

Then our new line is y = -(2/3)*x - b

The new slope is -(2/3)

Answer:

step 2

Step-by-step explanation:

9 = -3(e - 2)

9 = -3e + 6

9-6 = -3e

3 = -3e

divide both sides by -3

-1 = e

Answer:

The two missing sides are : 79.54m and 58.62m

Step-by-step explanation:

first we look for the missing angle in the triangle

so now we use sine rules:

Let us make:

so :

so the side facing 35° = 79.54m

To find the area of this triangle

Answer:

b

Step-by-step explanation:

Answer:

It is, indeed, a reduction. But, the scale factor of the dilation should be a fraction instead of a whole number, since the shape has shrunk.

Instead of [tex]\frac{KN}{K'N'}[/tex], it should be [tex]\frac{K'N'}{KN}[/tex]. That would make it (4 - 2) / (8 - 4) = 2 / 4 = 1/2.

Hope this helps!

Answer:

[tex]t = 1.45[/tex] or [tex]t = 0.86[/tex]

Step-by-step explanation:

Given

[tex]h=3+37t-16t^2[/tex]

Required

Find all values of t when height is 23 feet

To solve this, we simply substitute 23 for h

[tex]23=3+37t-16t^2[/tex]

Collect  like terms

[tex]16t^2 - 37t - 3 + 23=0[/tex]

[tex]16t^2 - 37t +20=0[/tex]

Solve t using quadratic formula;

[tex]t = \frac{-b\±\sqrt{b^2 - 4ac}}{2a}[/tex]

Where a = 16, b =-37 and c = 20

[tex]t = \frac{-(-37)\±\sqrt{(-37)^2 - 4*16*20}}{2*16}[/tex]

[tex]t = \frac{37\±\sqrt{(-37)^2 - 4*16*20}}{2*16}[/tex]

[tex]t = \frac{37\±\sqrt{1369 - 1280}}{32}[/tex]

[tex]t = \frac{37\±\sqrt{89}}{32}[/tex]

[tex]t = \frac{37\±9.43}{32}[/tex]

[tex]t = \frac{37+9.43}{32}[/tex] or [tex]t = \frac{37-9.43}{32}[/tex]

[tex]t = \frac{46.43}{32}[/tex] or [tex]t = \frac{27.57}{32}[/tex]

[tex]t = \frac{46.43}{32}[/tex] or [tex]t = \frac{27.57}{32}[/tex]

[tex]t = 1.45[/tex] or [tex]t = 0.86[/tex]

Answer:

False.

Step-by-step explanation:

In a data where two variables are observed simultaneously, such data is termed to be Bivariate Data. When this data are represented graphically, such a diagrammatic representation is called scatter diagram. In a scatter diagram, all the points lie on or near one particular line. This line is called the regression line.

Recall that the equation for a straight line in the gradient intercept form is y = ax+b .

As an approximation , one can fit the regression line by first computing x and y. The regression line should pass through (x,y) in such a way that the remaining scatter points are evenly distributed on both sides of the line. Therefore, Simple linear regression methods can be used for studying relationship among maximum five variables is a false statement.

Answer: 0.98

Step-by-step explanation:

given data:

probability they won a game = 58% = 0.58

since outcome of games are independent, and percentage would remain same as 2014.

probablility that Dodgers wins atleast 1 of their next 7 games

= 1 - p

= 1 - ( 0.58 )^ 7

= 1 - 0.02208

= 0.98

probabikotun that Dodgers would win one of their next seven games is 0.98

Answer:

24

Step-by-step explanation:

For ABCD the three longest are:

60,40,30

60 to 40 is 20

40 to 30 is 10

so each time it's decreasing by 1/2

For EFGH the two shortest are:

6 and 12

12 to 6 is 1/2

Assuming there is a pattern

it logically would be 24

as 12(2)=24

Answer:

y=2(x-1)+5

Step-by-step explanation:

We know that it is 5 dollars for the first minute so we know the equation will start off with +5.

Than for the rest of the minutes, we have to make sure to subtract one from them, because the first number is worth 3 dollars more. Which is why it is x-1.

Then we multiply the new value times 2, because each additional minute is 2 dollars more.

Answer:

0.0016

Step-by-step explanation:

Batting average, p = 0.26

n = 7

x = 6

With p = 0.26 as success rate

1-p is equal to failure rate which is = 0.74

We have to solve this by using the binomial distribution formula.

P(X= x)

= nCx * p^x * (1-p)^(n-x)

P(X = 6)

=7C6 × 0.26^6 ×(1-0.26)^(7-6)

= 7 × 0.0003089 × 0..74¹

= 0.0016

So probability that he has exactly 6 hits in his next 7 bats is equal to 0.0016.

Answer:

A. 5x + 6x = 70 degrees

Step-by-step explanation:

5x + 6x = 110 degrees because the sum of two interior angles in a triangle is equal to an exterior angle.

Answer:

The first option is not the same point in polar coordinates as (-3, 1.236). This proves that inverting the signs of r and θ does not generally give the same point in polar coordinates.

Step-by-step explanation:

Let's think about the position of this point. As you can tell it lies in the 4th quadrant, on the 3rd circle of this polar graph.

Remember that polar coordinates is expressed as (r,θ) where r = distance from the positive x - axis, and theta = angle from the terminal side of the positive x - axis. Now there are two cases you can consider here when r > 0.

Given : (- 3, 1.236), (3,5.047), (3, - 7.518), (- 3, 1.906)

We know that :

7.518 - 1.236 = 6.282 = ( About ) 2π

5.047 + 1.236 = 6.283 = ( About ) 2π

1.236 + 1.906 = 3.142 = ( About ) 2π

Remember that sin and cos have a uniform period of 2π. All of the points are equivalent but the first option, as all of them ( but the first ) differ by 2π compared to the given point (3, - 1.236).

Answer:

B

Step-by-step explanation:

P(AUB)=P(A)+P(B)-P(A∩B)

191/400=7/20+P(B)-49/400

P(B)=191/400+49/400-7/20=240/400-7/20=12/20-7/20=5/20=1/4

The value of P(B) is 1/4.

The probability is defined as the possibility of an event is equal to the ratio of the number of favorable outcomes and the total number of outcomes.

For an experiment having q number of outcomes, the number of favorable outcomes can be denoted by p. The formula to calculate the probability of an event is as follows:

Probability(Event) = Favorable Outcomes/Total Outcomes = p/q

Given data as :

P(A) = 7/20,

P(A∪B) = 191/400,

P(A∩B) = 49/400 ,

P(AUB) = P(A) + P(B) - P(A∩B)

Substitute the values of P(A), P(A∪B) and P(A∩B) in formula,

191/400 = 7/20 + P(B) - 49/400

Rearrange the terms in the equation,

P(B) = 191/400 + 49/400 - 7/20

P(B) = 240/400 - 7/20

P(B) = 12/20 - 7/20

P(B) = 5/20

P(B) = 1/4

Hence, the value of P(B) is 1/4.

Learn more about probability here :

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Answer:

2.5$ per pound

Step-by-step explanation:

The cost of 4 pounds of cherries cost 10$

So to khow the price of 1 pound we must divide 10 by 4.

● 10/4 = 2.5

So 1 pound costs 2.5$

[tex]\bold{\text{Answer:}\quad R(t)=-0.96\sin\bigg(\dfrac{\pi}{182.5}t}\bigg)+2.3}[/tex]

Step-by-step explanation:

The equation of a sin function is: y = A sin (Bx - C) + D     where

D = 2.3

It is given that t = 0 is located at 2.30.  The sin graph usually starts at 0 so the graph has shifted up 2.3 units.  --> D = 2.3

A = -0.96

The amplitude is the difference between the maximum (or minimum) and the centerline.  A = 2.30 - 1.44 = 0.96

The minimum is given as the next point. Since the graph usually has the next point as its maximum, this is a reflection so the equation will start with a negative. A = -0.96

B = π/182.5

It is given that [tex]\frac{1}{4}[/tex] Period = 91.25  --> P = 365

B = 2π/P

  = 2π/365

  = π/182.5

C = 0

No phase shift is given so C = 0

Input A, B, C, & D into the equation of a sin function:

[tex]R(t)=-0.96\sin\bigg(\dfrac{\pi}{182.5}t-0}\bigg)+2.3[/tex]

Answer:

Area = 18 square units

Step-by-step explanation:

To find the area of the triangle, let's go through the following steps:

(i) Let the vertices be;

A = (7, -3)

B = (4, -3)

C = (4, 9)

(ii) The sides of the triangle are therefore,

AB, BC and CA

(iii) Using the distance formula, calculate the lengths of AB, BC and CA

[tex]AB = \sqrt{(7-4)^2 + ( -3 - (-3))^2}[/tex]

[tex]AB = \sqrt{3^2 + (0)^2}\\[/tex]

[tex]AB = \sqrt{9}[/tex]

[tex]AB = 3[/tex]

[tex]BC = \sqrt{(4-4)^2 + ( -3 - 9)^2}[/tex]

[tex]BC = \sqrt{0^2 + (-12)^2}[/tex]

[tex]BC = \sqrt{144}[/tex]

[tex]BC = 12[/tex]

[tex]CA = \sqrt{(4-7)^2 + ( 9 - (-3))^2}[/tex]

[tex]CA = \sqrt{(-3)^2 + (12)^2}[/tex]

[tex]CA = \sqrt{9 + 144}[/tex]

[tex]CA = \sqrt{153}[/tex]

[tex]CA = 12.4[/tex]

(iv) Now that we have all the sides, let's calculate the area of the triangle using the Heron's formula.

Area = [tex]\sqrt{p(p-a)(p-b)(p-c)}[/tex]

Where;

p = [tex]\frac{a + b + c}{2}[/tex]

a, b and c are the sides of the triangle.

In our case,

let

a = AB = 3

b = BC = 12

c = CA = 12.4

∴ p = [tex]\frac{3 + 12 + 12.4}{2}[/tex]

p = 13.7

Area = [tex]\sqrt{p(p-a)(p-b)(p-c)}[/tex]

Area = [tex]\sqrt{13.7(13.7-3)(13.7-12)(13.7-12.4)}[/tex]

Area =  [tex]\sqrt{13.7(10.7)(1.7)(1.3)}[/tex]

Area =  [tex]\sqrt{323.9639}[/tex]

Area  = 17.999

Area = 18 square units

OR

To get the area of the triangle, we can use a much simpler approach.

Since the triangle is a right triangle,

(i) the hypotenuse, which is the longest side is CA = 12.4

(ii) the other two sides are AB and BC. These two sides will form the right angle.

Therefore, we can use the relation:

Area = [tex]\frac{1}{2}[/tex] x base x height

Where;

the base or height can either be AB or BC

Area = [tex]\frac{1}{2}[/tex] x 3 x 12

Area = 18 square units

PS: In a right triangle, the other two sides apart from the hypotenuse form the right angle.

Answer:

Mean= $21.5067

Median = $15.8

Standard deviation= $19.02

Coefficient of skewness= $0.8991

Step-by-step explanation:

Mean =( $4.0 +$6.0 +$7.4+ $10.6 +$12.5+ $13.6+ $15.4+ $15.8 +$16.8

+$17.4+ $19.1 +$22.3+ $37.1 +$43.2 +$81.4)/15

Mean =$ 322.6/15

Mean= $21.5067

Median= middle number

Median = $15.8

Variance=( ($4.0-.$21.5)²+( $6.0. -.$21.5)²+( $7.4 -.$21.5)²+( $10.6 -.$21.5)²+( $12.5 -.$21.5)²+( $13.6. -.$21.5)²+ ($15.4 -.$21.5)²+( $15.8 -.$21.5)²+ ( $16.8 -.$21.5)²+ ($17.4-.$21.5)² +($19.1 -.$21.5)²+ ($22.3 -.$21.5)²+ ($37.1 -.$21.5)²+ ($43.2-.$21.5)²+( $81.4-.$21.5)²)/15

Variance=$ 5424.79/15

Variance=$ 361.65

Standard deviation= √ variance

Standard deviation= √361.65

Standard deviation= $19.02

Coefficient of skewness

=3( mean-median)/standard deviation

= 3(21.5-15.8)/19.02

= 3(5.7)/19.02

= 17.1/19.02

Coefficient of skewness= 0.8991

Answer:

160 miles

Step-by-step explanation:

We can use a ratio to solve

220 miles         x miles

--------------- = ----------------------

5.5 hours          4 hours

Using cross products

220 *4 = 5.5x

880 = 5.5x

Divide each side by 5.5

880/5.5 = x

160 miles

Answer:

[tex]\large \boxed{\mathrm{C. \ 160 \ miles}}[/tex]

Step-by-step explanation:

We can solve this problem by ratios.

Let x be the missing value.

[tex]\displaystyle \frac{220}{5.5} =\frac{x}{4}[/tex]

Cross multiply.

[tex]5.5 \times x = 220 \times 4[/tex]

[tex]5.5x=880[/tex]

Divide both sides by 5.5.

[tex]\displaystyle \frac{5.5x}{5.5} =\frac{880}{5.5}[/tex]

[tex]x=160[/tex]

Answer:

1260

Step-by-step explanation:

(7!)/ (2!times 2!)

7 factorial divided by 2factorial times 2 facotiral

The number of distinguishable ways the letters of the following word can be arranged 'MILLION' is 1260.

The different arrangements which can be made out of a given number of objects by taking out some or all at a time are called permutations.

The number of different permutations of n objects with m₁ repeated items, m₂ repeated items,...,mₙ repeated items can be calculated as;

m!/(m₁!)(m₂!)...(mₙ!)

Here, the letter of the word 'MILLION' is a total of 7 letters.

So, the number of possible arrangements will be

(7!)/ (2!times 2!)

= 1260

Therefore the number of distinguishable ways the letters of the following word can be arranged 'MILLION' is 1260.

Learn more about permutations here -

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[tex]\dfrac{x}{5}=-2\\\\x=-10[/tex]

Answer:

[tex]\huge \boxed{{x=-10}}[/tex]

Step-by-step explanation:

[tex]\displaystyle \frac{x}{5} =-2[/tex]

We need the x variable to be isolated on one side of the equation, so we can find the value of x.

Multiply both sides of the equation by 5.

[tex]\displaystyle \frac{x}{5}(5) =-2(5)[/tex]

Simplify the equation.

[tex]x=-10[/tex]

The value of x that makes the equation true is -10.

Answer:

When a shape is congruent they are equal in shape, size, and measure. Although if a shape is similar they will be the same shape, but not the same size, instead they will be proportionate.

Step-by-step explanation:

Answer:

CongruentCongruent figures are identical in size, shape and measure. SimilarTwo figures are similar if they have the same shape, but not necessarily the same size.

Step-by-step explanation:

Answer:

Step-by-step explanation:

We could start by listing multiples of 4 and looking for patterns. Do  

you know what a multiple of a number is?  It's that number multiplied  

by another number. So the first multiple of 4 is 4x1, the second  

multiple of 4 is 4x2=8, the third multiple of 4 is 4x3=12, etc.  

Let's make a table of multiples of 4 from 1 to 100, with columns A-E  

across the top and rows 1-5 down the left-hand side:

    A      B      C      D      E

1    4      8     12     16     20

2   24     28     32     36     40

3   44     48     52     56     60

4   64     68     72     76     80

5   84     88     92     96    100

Now let's look at these multiples, remembering that there will be nine  

more tables like this one from 101-1000.

Let's look for 6,7,8,9, and 0 in the columns first. Aha! We can erase  

all of columns B, D, and E because there's a 6 or an 8 or a 0 in each  

number in those columns.  Now we're left with just:

    A      C  

1    4     12  

2   24     32  

3   44     52  

4   64     72  

5   84     92  

Now let's look at the rows. Wow! We can eliminate rows 4 and 5 because  

they have 6, 7, 8, or 9, leaving:

    A      C  

1    4     12  

2   24     32  

3   44     52  

Just 6 numbers left!

So if from 1-100 there are 6 multiples of four that do not contain any  

of the digits 6, 7, 8, 9, or 0, how many multiples of four like this  

are there from 1-1000?