Which one of the following examples represent a repeating decimal?

The common difference of the sequence is -1/2

From the question, we have the following parameters that can be used in our computation:

3/8, -1/8, -5/8, -9/8

The common difference is the difference between successive terms

So, we have

Difference = -1/8 - 3/8

Evaluate the difference

Difference = -1/2

Hence, the common difference is -1/2

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Answer:

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The pedestal is the combination of two rectangular prisms.

One of them has dimensions:

Its volume is:

The other one has dimensions:

Its volume is:

Total volume is:

Answer:

112 in³

Step-by-step explanation:

The pedestal is made up of two rectangular prisms.

[tex]\boxed{\begin{minipage}{5.8 cm}\underline{Volume of a rectangular prism}\\\\$V=w\cdot l\cdot h$\\\\where:\\ \phantom{ww}$\bullet$ $w$ is the width of the base. \\ \phantom{ww}$\bullet$ $l$ is the length of the base.\\\phantom{ww}$\bullet$ $h$ is the height of the prism.\\\end{minipage}}[/tex]

The dimensions of the largest rectangular prism are:

Therefore, the volume of the largest rectangular prism is:

[tex]\begin{aligned}\implies V&=2 \cdot 9 \cdot 4\\&=18 \cdot 4\\&=72\;\rm in^3\end{aligned}[/tex]

The dimensions of the smaller rectangular prism are:

Therefore, the volume of the smaller rectangular prism is:

[tex]\begin{aligned}\implies V&=2 \cdot 5 \cdot 4\\&=10\cdot 4\\&=40\;\rm in^3\end{aligned}[/tex]

The volume of the pedestal is the sum of the volumes of the largest and smaller rectangular prisms:

[tex]\implies V=72+40=112\; \rm in^3[/tex]

Therefore, the volume of the pedestal is 112 in³.

Answer: 48.6 minutes

Step-by-step explanation:

First find the total square feet:

9 x 9 = 81

Next, divide this by the increments give:

81 / 75 = 1.08

Now, the increments were each 45 minutes, so multiply this by the product:

45 x 1.08 = 48.6

Answer and explanation: The equation for the slope-intercept form is y=mx+b. M represents the slope and b is y-intercept/when x= 0.

We have to arrange the given equation into the form y=mx+b.

3x+2y=-14, We want to somehow isolate y.

2y=-14-3x, We can move all the terms that don't have y to the right

y=(-14-3x)/2, We can get rid of the 2 by dividing by 2 on both sides

y=-7-(3/2)x, We can distribute the division by 2 to both terms on the right

y=-(3/2)x-7, We can now just rearrange the terms

The equation is now in the form y=mx+b as -3/2 is m and -7 is b. Your answer to the first question is A.

For part B, we can use the equation for part A. We know m or the slope is -3/2 so our answer is also A.

Answer:

5 km / 15 km/h = 0.3333 hours

Step-by-step explanation:

This is calculated by dividing the distance he has to travel (5 km) by his average speed (15 km/h) and then converting the result to minutes.

0.3333 hours x 60 minutes/hour = 20 minutes

The likelihood that the basketball player will convert at least six of his or her eight free throw tries is 0.32.

The simple definition of probability is the likelihood that something will occur. We can discuss the probabilities of different outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics refers to the study of events subject to probability.

The ratio of all potential cases to the number of cases that are favorable to an event determines its likelihood when there is no reason for us to believe that any one of these circumstances will happen more frequently than any other, making them all equally likely.

The likelihood that an event will occur is quantified by probability. The probability of an event is the relative frequency throughout time of that event. Probabilities are all numbers between 0 and 1, inclusive—that is, any numbers between 0 and 1.

Therefore, the correct answer is option d) 0.32.

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Any triangle's three interior angles add up to 180 degrees, according to the Triangle Sum Theorem.

Any triangle's three interior angles add up to 180 degrees, according to the Triangle Sum Theorem. m∠1+m∠2+m∠3=180∘.

Here,

According to the triangle sum theorem, a triangle's total angles equal 180°. Therefore, using the Substitution property

=> (3x)° + 90° + (x+10)° = 180°,

=>  m(A,B,C) = 180.

To find x, combine similar terms to get

=> 4x + 100 = 180. Then, using the subtraction condition of equality, convert => 13 1/2 to 80.

=> Finally, divide 80 by  5 ( 13 1/2) to find x.

The substitution property may be used to get the measure of the angle A, yielding mA = 5 ( 13 1/2) °.

When the expression is finally simplified, m < A = 66 2/3.

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Answer:

m=5000 members

Step-by-step explanation:

15000-2500=12500

12500/25=500

The company Sea Esta can elect a president, vice-president, secretary and treasurer in 495 different ways.

What is Combination in Mathematics?

In mathematics, a combination is a way of selecting a certain number of items from a larger set of items, without regard to the order in which the items are selected. It is a way to count the number of distinct subsets of a given size from a larger set.

The formula for combination is:

(n!) / (r! * (n-r)!)

The company Sea Esta has 12 members on its board of directors, and they need to elect a president, vice-president, secretary, and treasurer. The number of ways to elect these four positions is determined by using the formula of combination, which is:

Where n is the total number of options (in this case, the number of board members) and r is the number of positions to be filled (in this case, 4).

So, the number of ways to elect a president, vice-president, secretary, and treasurer is:

(12!) / (4! * (12-4)!) = (1211109) / (4321) = 495

Therefore, the company Sea Esta can elect a president, vice-president, secretary and treasurer in 495 different ways.

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His altitude at the halfway point is -50 feet

Step-by-step explanation:

At the start of his hike, his altitude is -120 feet.

His altitude had dropped 70 feet.

His altitude at the halfway point of his hike is

= -120 + 70 = -50

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We decide on 320 as the best-predicted value. EV(node 4) = 320. The answer is option (a).

What is Probability?

Simply put, the probability is the likelihood that something will occur. When we don't know how an event will turn out, we might discuss the likelihood or likelihood of several outcomes. Statistics is the study of occurrences that follow a probability distribution.

Probability of S1 = 0.6

Probability of F = 0.40

Value of node y =?

As per the given value if probability of S1 = 0.6

Then the probability of S2 = 0.4

Using payoff values in table equation from except value.

[tex]EV(d_{i})=[/tex] ∑ [tex]V_{ij} S_{J}[/tex]

where [tex]V_{ij}[/tex] = value of payoff

We compute the expected value for each of decisions

EV(Node 8) = 0.6*100+0.4*300

                  = 180

EV(Node 9) = 0.6*400+0.4*200

             = 320

For Node 4, We select the best value from node 8 and node9

The best decision attractive is the line complex branch that  EV(node 8) = 180, For node 9,

Therefore, We select the best-predicted value i.e 320.

EV(node 4) = 320

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The answer is pint of milk

A mixture refers to the mix that is derived as a result of mixing two or more items or substances in a certain ratio or proportion.

Given here: 1 tablespoon of grape juice is mixed into the milk and 1 tablespoon of this mixture is mixed with grape juice.

Thus the milk is more contaminated as the latter mixture contains some amount of grape juice and as a result the grape juice mixture is not contaminated to the extent of the pint of milk.

Hence, The answer is pint of milk

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Part (a)

[tex]\lim_{h \to 0} \frac{(h-1)^5+1}{h} \\ \\ =\lim_{h \to 0} \frac{5(h-1)^4}{1} \\ \\ =\boxed{5}[/tex]

Part (b)

[tex]y+1=5(x+1) \\ \\ y+1=5x+5 \\ \\ \boxed{y=5x+4}[/tex]

Answer:

a) The total cost of purchasing the car that is worth $32,000 with the harmonized sales tax (HST) of 13% is $36,160.

b) By leasing the car instead of purchasing it outright, the customer will save $14,760.

c) The lease options for the lessee after returning the car include:

A lease is a financing option for the use of capital assets.

With a lease, the lessee uses the asset for a specific period and the lessor receives periodic payments.

There are operating and finance (capital) leases.  Though, under new accounting standards, all leases are to be classified as finance leases.

Value of the car = $32,000

Harmonized Sales Tax (HST) = 13%

Cost of the car with HST = $36,160 ($32,000 x 1.13)

Down payment = $1,000

Financing part = $35,160 ($36,160 - $1,000)

Installment payments = 48

Periodic payments = $425

Total lease cost = $21,400 ($1,000 + 48 x $425)

Savings (advantages) from leasing = $14,760 ($36,160 - $21,400)

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Step-by-step explanation:

a. 21/100

b.31/100

c. 4/25

d. 3/25

You need to know the direction of the line and at least one point on it in order to parametrize a line. x is  5 + 4.0t ,y is  0 + 4.0t

x = 5 + 4.0t

y = 0 + 4.0t

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On solving the provided question we can say that the Measure of complementary angles   ∠ZY is 40 degrees.

When the sum of the measurements of two angles is 90 degrees, they are said to be complimentary.For instance, the angles of 30 and 60 degrees are supplementary. A supplementary angle is two angles combined to make a 180 degree angle, while a supplemental angle is two angles combined to make a 90 degree angle. Two angles are referred to as complimentary if their total is 90 degrees. Alternatively said, a right angle is created by the complementary angles (90 degrees).

Since ∠ZS and ∠ZY are complementary,

∠ZY+∠ZS=45                                                                                       We also have another relation which says

∠ZS=2∠ZY -30

Substituting 2. in 1. gives

∠ZY+2∠ZY -30=90

3∠ZY=120

∠ZY=40

Hence the measure of angle is 40 degrees.

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Answer:

D

Step-by-step explanation:

26+169=0

The value of x and y in right angle triangle is  16√2 and 16

What is a Right Angle Triangle ?

A right triangle is a triangle having one right angle or two perpendicular sides. It is also referred to as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or previously rectangled triangle. The relationship between the sides and various angles of the right triangle serves as the basis for trigonometry.

The Pythagorean theorem, often known as Pythagoras' theorem, in Euclidean geometry relates the three sides of a right triangle. This statement states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides.

In the triangle 2 angles are 90° and 45° respectively.

The third angle is  = 180°+90°-45°=45°

The triangle is issosceles triangle

So the side which is not x is 16.

Now by using Pythagoras Theorem

x = √16^2+16^2 = 16√2

The value of x is 16√2

The value of y is y^2 + 16^2 = 16√2^2

y^2 = 512 - 256

y^2 = 256

y = 16

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Answer:

15/487 or 0.0308008= 0.03

Step-by-step explanation:

You must solve to isolate the x variable.

This is false, hence, the portion of the graph which does not contain (0, 0) is shaded.

Given the inequalities :

y ≥ 2x + 1

y ≤ 2x - 2

From y ≥ 2x + 1 ;

Since the inequality sign is ≥, a solid line is used to draw the straight line graph of  y ≥ 2x + 1

From :

y = mx + c

Where, m = slope ; c = intercept

Hence, a straight line graph with ;

Intercept, c = 1 (where the line crosses the y-intercept)

Slope, m = 2

Consider a point, which isn't on the line ;

Take point (0,0) and use it to test the inequality :

0 ≥ 2(0) + 1

0 ≥ 0 + 1

0 ≥ 1

Since this is untrue, the area of the graph that does not contain (0, 0) is shaded.

From : y ≤ 2x - 2

Since the inequality sign is ≤, a solid line is used to draw the straight line graph of  y ≤ 2x - 2

Graph the line y ≤ 2x - 2, with ;

Intercept, c = - 2

Slope = 2

Consider a point, which isn't on the line ;

Take point (0,0) and use it to test the inequality y ≤ 2x - 2:

0 ≤ 2(0) - 2

0 ≤ 0 - 2

0 ≤ - 2

This is untrue, hence the area of the graph that doesn't include (0, 0) is shaded.

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Answer:

Expressions B and C

Step-by-step explanation:

A: 20^2 - 18^2 = 400 - 324 = 76 (not A)

B: 8(4^2) + 2^4 = 128 + 16 = 144 (which is equivalent to 12^2)

C: 15^2 - 3^4 = 225 - 81 = 144 (which is equivalent to 12^2)

Hope this helps!

Answer:

18

Step-by-step explanation:

One trip around the gym would be 138 ft.

If we cut the diagonal, we use the Pythagorean theorem to find the distance of the hypotenuse, which is 51 ft.

One trip with the shortcut is 119 ft. (24 + 45 + 51 = 119).

Subtract 119 ft. from 138 feet and you have 18 ft. shorter route than walking the entire perimeter.

For you to make 5 pecan pies, it would be necessary to buy 1.9 pounds of pecans.

Based on the information displayed on the label 1 cup of pecans is equal to 99 grams.

We know 1 pecan pie requires  1 3/4 cups or 1.75 cups (3/4 = 0.75)

1.75 x 5 = 8.75 cups in total

Now, let's calculate this in grams:

8.75 x 99 = 866.22 grams

Finally, let's calculate the pounds

1 pound = 453

 x           = 866.22

x = 866.22 / 453 = 1.9

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Answer:

4 * 24 - 9 = 87 cookies left.

Step-by-step explanation:

Answer:

[tex]k = 2[/tex]

Step-by-step explanation:

[tex]\textrm{P(blue \;bead)} = \dfrac{\textrm{Number of blue beads}}{\textrm{Total number of beads}}\\\\\textrm {Number of blue beads } = k\\\\\textrm{Total number of beads } = k + 4\\\\[/tex]

[tex]\textrm{P(blue \;bead)} = \dfrac{k}{k+4}\\\\[/tex]

[tex]\textrm{We are given this probability as } \dfrac{1}{3}\\\\\textrm{So,}\\\\\dfrac{k}{k+4} = \dfrac{1}{3}\\\\[/tex]

Cross-Multiplying this equation we get
[tex]k\cdot 3 = 1 \cdot (k + 4)\\\\\longrightarrow 3k = k + 4\\\\3k - k = 4\\\\2k = 4\\\\k = 2\\\\[/tex]

Let f be a function defined on all of that satisfies the additive condition is,

f(x) = [tex]kx[/tex] for every x∈ R.

It is given that:

f: R → R is a continuous function such that:

[tex]f(x+y)[/tex] = [tex]f(x) + f(y)[/tex]    ∀  x , y ∈ R  (Equation-1)

Now, let us assume f(1)=k

Also,

f(0) = 0( Since, f(0)=f(0+0)

That is,

f(0)=f(0)+f(0)

By using property (1)

Also,

f(0)=2f(0)

That is,

2f(0)-f(0)=0

That is,

f(0)=0  )

Also,

f(2)=f(1+1)

That is,

f(2)=f(1)+f(1)         ( By using property (1) )

i.e.

f(2)=2f(1)

That is,

f(2)=2k

Similarly for any m ∈ N

f(m)=f(1+1+1+...+1)

That is,

f(m)=f(1)+f(1)+f(1)+ ....... +f(1) (m times)

That is,

f(m)=mf(1)

That is,

f(m) = [tex]mk[/tex]

Now,

f(1) = [tex]f(\frac{1}{n} +\frac{1}{n} +......\frac{1}{n} )[/tex]

f(1) = [tex]f(\frac{1}{n} )+f(\frac{1}{n} )+......f(\frac{1}{n} )[/tex]

f(1) = n [tex]f(\frac{1}{n} )[/tex]

f(1) = k

[tex]f(\frac{1}{n} )[/tex] = k * [tex]\frac{1}{n}[/tex]

Also,

when x∈ Q

[tex]x = \frac{p}{q}[/tex]

Then,

[tex]f(\frac{p}{q})[/tex] = [tex]f(\frac{1}{q} )+ f(\frac{1}{q} )+ .....f(\frac{1}{q} )[/tex]

[tex]f(\frac{p}{q})[/tex] = p * [tex]f(\frac{1}{q} )[/tex]

[tex]f(\frac{p}{q})[/tex] = [tex]p\frac{k}{q}[/tex]

[tex]f(\frac{p}{q})[/tex] = [tex]k\frac{p}{q}[/tex]

So,

[tex]f(x) = kx[/tex] for all x belongs to Q

Now, as we know that:

Q is dense in R.

So Э x∈ Q' such that Э a seq < [tex]x_{n}[/tex] >  belonging to Q such that:

< [tex]x_{n}[/tex] > ⇒[tex]x[/tex]

Now, we know that: Q'=R

This means that:

Э α ∈ R

such that Э sequence [tex]a_{n}[/tex] such that:

[tex]a_{n}[/tex] belongs to Q,

[tex]a_{n}[/tex] ⇒ [tex]\alpha[/tex]

[tex]f(a_{n} )= ka_{n}[/tex]

( since [tex]a_{n}[/tex] belongs to Q )

Let f is continuous at x=α

This means that:

[tex]f(a_{n} )[/tex] ⇒ [tex]f(\alpha )[/tex]

k [tex]a_{n}[/tex] ⇒ [tex]f(\alpha )[/tex]

k [tex]a_{n}[/tex] ⇒ k [tex]\alpha[/tex]

This means that:

[tex]f(\alpha )[/tex] = k [tex]\alpha[/tex]

This means that:

f(x) = [tex]kx[/tex] for every x∈ R

Therefore,

Let f be a function defined on all of that satisfies the additive condition is,  f(x) = [tex]kx[/tex] for every x∈ R.

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The percentage of  concentration of sugar in water will be 166.67%.

Concentration is the ability to focus on a single task or activity for an extended period of time. It requires both mental and physical effort, and involves staying attentive and motivated. Concentration helps us achieve our desired outcomes and complete tasks more efficiently. It also improves our ability to retain information, allowing us to better understand and remember what we have learned. Practicing concentration can lead to improved mental health, increased productivity, and better problem solving skills.

50/30 = x/100

30x = 100 × 50

30x = 5000

x = 166.67 %

Thus, The percentage of  concentration of sugar in water will be 166.67%.

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