If Planet I is 32. 6 million miles farther from the sun than Planet​ II, then Planet III is 26. 3 million miles farther from the sun than Planet I. When the total of the distances for these three planets from the sun is 190. 5
million​ miles, how far away from the sun is Planet​ II?

The polynomial function f(x) = x³ - 5x² - 61x - 55 has the following

Real zeros: x = -5, x = -1, and x = 11.  

To find the rational zeros of a polynomial, we use the rational zeros theorem. We look at the factors of the leading coefficient and the factors of the constant coefficient.

The  states that if a polynomial function is defined as P(x) = anxn + an-1xn-1 + ... + a1x + a0 with integers, then each rational zero of the polynomial can be expressed in the form p/q where p is a factor of a0 and q is a factor of an.

For example, if P(x) = 2x³ - 5x² + 3x + 6 then p can be any factor of 6 and q can be any factor of 2.

The factors of the leading coefficient, 1, and the factors of the constant coefficient, -55, are: ±1, ±5, ±11, ±55. So the possible rational zeros are: ±1, ±5, ±11, ±55, ±1/1, ±5/1, ±11/1, ±55/1, ±1/1, ±5/1, ±11/1, ±55/1.

Simplifying the results, we have that the potential rational zeros are: ±1, ±5, ±11, ±55, ±1, ±5, ±11, and ±55.

By testing each possible rational zero, we find that x = -5, x = -1, and x = 11 are the real zeros of f(x).

Hence, using synthetic division, we get:

(x + 5)(x + 1)(x - 11) = x³ - 5x² - 61x - 55

Thus, the function can be factored over the real numbers as

f(x) = (x + 5)(x + 1)(x - 11).

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Answer:

x=130°

Step-by-step explanation:

The sum of the angel of the pentagon is equal to 540°

X+90+x+150+x=540

3x+240=540

3x=540-150

3x=390

X=130

The magnitude of the force P is 464.77 N.

STEP BY STEP EXPLANATION:

Step 1: Break down each force into components.
F = 320 N at 30°
Fx = F * cos(30°) = 320 * cos(30°) = 277.13 N (horizontal)
Fy = F * sin(30°) = 320 * sin(30°) = 160 N (vertical)

120 N is in the horizontal direction (assume positive x-direction):
Fx2 = 120 N

80 N is in the vertical direction (assume positive y-direction):
Fy2 = 80 N

Step 2: Sum up the components.
Total horizontal force (Fxtotal) = Fx + Fx2

= 277.13 + 120 = 397.13 N

Total vertical force (Fytotal) = Fy + Fy2

= 160 + 80 = 240 N

Step 3: Find the magnitude of the resultant force.
            Resultant force (R) = sqrt(Fxtotal^2 + Fytotal^2)

= sqrt(397.13^2 + 240^2) = 464.77 N

Step 4: Determine the magnitude of the force P.
Since the resultant of the four forces should act on the rim of the plate, it means that the force P should be equal in magnitude and opposite in direction to the resultant force R.

The magnitude of the force P is 464.77 N.

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There are 12 red socks and 18 black socks in a sock drawer. If you randomly choose two socks at once, the probability you get a matching pair is 50%.

The probability of getting a matching pair of socks can be calculated as follows:

First, we can calculate the total number of ways to choose 2 socks out of 30:

C(30, 2) = 30! / (2! * (30-2)!) = 435

Now, we need to calculate the number of ways to choose 2 socks such that they are both black or both red:

Number of ways to choose 2 black socks: C(18, 2) = 153

Number of ways to choose 2 red socks: C(12, 2) = 66

Therefore, the total number of ways to choose a matching pair of socks is 153 + 66 = 219.

Finally, we can calculate the probability of getting a matching pair of socks by dividing the number of ways to choose a matching pair by the total number of ways to choose 2 socks:

P(matching pair) = 219 / 435 ≈ 0.5034

Therefore, the probability of getting a matching pair of socks is approximately 0.5034 or 50.34%.

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The fence ought to be cut into 12 pieces, every one of length 28 m, to make three squares, each with a side length of 28 m. This will limit the total area encased by the fence.

To limit the total area encased by the fence, the three squares ought to have equivalent areas. Let x be the length of each side of the squares. Then the perimeter of each square is 4x, and the total length of the fence is 3(4x) = 12x. Since the total length of the fence is given to be 336 m, we have:

12x = 336

Addressing for x, we get:

x = 28

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Option A,B,C,D : Elias might have gotten the answer by calculating the percentage discounts of each item and comparing them to see which ones are the same.

To find which items have the same percent discount, we need to calculate the percent discount for each item.

For the sweater, the percent discount is (20/50) x 100% = 40%.

For the shorts, the percent discount is (12/30) x 100% = 40%.

For the shirt, the percent discount is (14/35) x 100% = 40%.

For the jeans, the percent discount is (24/60) x 100% = 40%.

Therefore, all items have the same percent discount of 40%, and option C (jeans and shirt only) is incorrect. The correct answer is A, sweater and shorts only, B, sweater, shorts, and shirt only, and D, sweater, shorts, and jeans only, have the same percent discount. Elias may have chosen C because he overlooked that the percent discount is the same for all items.

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Which items have the same percent discount?

A. sweater and shorts only

B. sweater, shorts, and shirt only

C. jeans and shirt only

D. sweater, shorts, and jeans only

Elias chose C as the correct answer. How might he have gotten that answer?

10-hole harmonicas, which can produce a wider range of notes and are more commonly used in professional music settings.

An equation is a statement that expresses the equality of two mathematical expressions using mathematical symbols such as variables, numbers, and mathematical operations. The equality is represented by an equal sign "=" between the two expressions. Equations are used to represent mathematical relationships and solve problems in various fields such as physics, chemistry, engineering, and economics.

Given by the question.

The terms "6 holes and 1/2" and "10 holes" are often used to refer to harmonicas, which are small wind instruments that produce sounds when air is blown into or drawn out of them.

The main difference between a 6-hole harmonica and a 10-hole harmonica is the number of holes on the instrument. As the name suggests, a 6-hole harmonica has 6 holes, while a 10-hole harmonica has 10 holes.

In addition to the number of holes, the two types of harmonicas may also differ in their size, range, and the specific notes that they can produce. 6-hole harmonicas are typically smaller and produce a more limited range of notes compared

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To find the probability of drawing a marble and then another marble from the bag, we need to multiply the probabilities of the individual events. This is because the two events are independent, and the outcome of the first event does not affect the outcome of the second event.

Let P(R) denote the probability of drawing a red marble, and P(B) denote the probability of drawing a blue marble. We are given that the bag contains red, blue, and green marbles, but we do not know the exact numbers of each color.

Since we replace the marble after each draw, the probability of drawing a red marble and then a blue marble can be found as:

P(RB) = P(R) x P(B)

To find P(R), we need to divide the number of red marbles in the bag by the total number of marbles. Similarly, to find P(B), we need to divide the number of blue marbles in the bag by the total number of marbles. However, since we do not know the exact numbers of each color, we cannot compute these probabilities exactly.

Therefore, we can only say that the probability of drawing a marble and then another marble is equal to the product of the probabilities of drawing each marble separately. In other words, the probability of drawing a red marble and then a blue marble is:

P(RB) = P(R) x P(B)

where P(R) and P(B) are the probabilities of drawing a red marble and a blue marble, respectively, which we cannot determine without more information about the contents of the bag.

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Answer:

Factor 64h^3+216k^9

Step-by-step explanation:

The given expression is a sum of two terms:

[64h^3+216k^9

Notice that each term has a common factor. For the first term, the greatest common factor (GCF) is 64h^3, and for the second term, the GCF is 216k^9. So we can factor out these GCFs to get:

64h^3+216k^9 = 64h^3(1 + 3k^6)

This expression cannot be factored any further, so the final answer is:

64h^3+216k^9 = 64h^3(1 + 3k^6)

If you can, give me brainliest please!

Caden's speed is 10 mph and Rahquez's speed is 16 mph faster, which is 16+6 = 32 mph

Let's use the formula: distance = rate x time

Since Caden and Rahquez are traveling towards each other, their combined distance will be 208 miles. Let's call Caden's speed "x" and Rahquez's speed "x+6", since Rahquez is traveling 6 mph faster than Caden.

Using the formula above, we can set up the equation:

208 = (x + x + 6) * 8

Simplifying, we get:

208 = (2x + 6) * 8

208 = 16x + 48

160 = 16x

x = 10

Therefore, Caden's speed is 10 mph and Rahquez's speed is 32 mph.

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The probability of getting at least one 2 given that the sum of the numbers is 7 is 2/6 or 1/3.

To find the probability that the number 2 has appeared at least once given that the sum of the numbers is 7, we need to use the concept of conditional probability.

Let's consider the possible outcomes when two dice are rolled. The total number of outcomes is 36, as each die has six possible outcomes.

Out of these 36 outcomes, there are six outcomes in which the sum of the numbers appearing on the upper faces is 7. These outcomes are (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1).

Out of these six outcomes, there are two outcomes in which the number 2 appears at least once: (1,6) and (2,5).

We can use the formula for conditional probability to verify our answer:

P(2 appears at least once | sum is 7) = P(2 appears at least once and sum is 7) / P(sum is 7)

P(2 appears at least once and sum is 7) = 2/36 = 1/18 (as there are two outcomes with a sum of 7 that have a 2 in them)

P(sum is 7) = 6/36 = 1/6

So, P(2 appears at least once | sum is 7) = (1/18) / (1/6) = 1/3, which is consistent with our previous answer.

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The ratio of SINA and COSA = 48/50 and 14/50

This is the boundary or contour length of a 2D geometric shape.

Depending on their size, multiple shapes may have the same circumference. For example, imagine a triangle made up of wires of length L.

The same wire can be used to create a square if all sides are the same length.

The length covered by the perimeter of the shape is called the perimeter. Therefore, the units of circumference are the same as the units of length.

As we can say, the surroundings are one-dimensional. As a result, you can measure in meters, kilometers, millimeters, etc.

Inches, feet, yards, and miles are other globally recognized units of circumference measurement.

According to our question,

sina = perpendicular\ hypotenuse

= 48/50

cosa= base\ perpendicular

=

14/50

Hence, The ratio of SINA and COSA = 48/50 and 14/50

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Answer:

answer is 3

Step-by-step explanation:

There is a roughly 16.85% chance that a bassist will be the first musician to register for the jazz camp.

Experimental probability is a type of probability that is based on actual observations or experiments. It is also called empirical probability

The ratio of the frequency of an occurrence to the total number of trials or observations is known as the experimental probability. In this case, the event is the first musician to sign up being a bassist.

Since there were 15 bassists out of 89 musicians who attended the camp last year, the experimental probability of the first musician to sign up being a bassist is:

Experimental probability = Number of bassists / Total number of musicians

Experimental probability = 15 / 89

Experimental probability = 0.1685 or approximately 16.85%

As a result, there is a roughly 16.85% chance that a bassist will be the first musician to register for the jazz camp.

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Answer:

2*22/7/27+1

Step-by-step explanation:

2*22/7*27+1

2*(594+1)/7

2*595/7

2*85

170 ans..

Answer:

d = 3.75

e = 8/3

Step-by-step explanation:

8/6 = 5/d = e/2

4/3 = 5/d

4d = 3 × 5

d = 3.75

4/3 = e/2

3e = 4 × 2

e = 8/3

Answer:

Step-by-step explanation:

To determine if Tammy's answer of 1 3/4 for the product of 5/7 and 1 1/4 is correct, we can perform the multiplication ourselves.

First, we need to convert 1 1/4 to an improper fraction:

1 1/4 = (4 x 1 + 1)/4 = 5/4

Then, we can multiply the fractions:

5/7 x 5/4 = 25/28

As we can see, 25/28 is not equal to 1 3/4. Therefore, Tammy's answer of 1 3/4 is incorrect. The correct answer is 25/28, which is an improper fraction. We can also express this as a mixed number: 0 25/28.

in approximately 22 years, the population would exceed the food supply, even if the country doubles its initial food supply and doubles the rate at which its food supply increases.

How to calculate the rate?

To answer these questions, we need to calculate the population and food supply at different points in time and compare them.

Let's first calculate the population after t years:

Population after t years = 2,000,000 * (1 + 4%) raise to the power t

And the food supply after t years:

Food supply after t years = 4,000,000 + 0.5 million * t

Now, let's answer the first question:

If the country doubled its initial food supply and maintained a constant rate of increase in the supply adequate for an additional 0.5 million people per year, would shortages still occur?

If the country doubles its initial food supply, the new food supply would be 8,000,000, and it would still increase at a rate of 0.5 million people per year. Let's calculate the year when the population exceeds the food supply:

Population = Food supply

2,000,000 * (1 + 4%)^t = 8,000,000 + 0.5 million * t

Solving for t, we get t ≈ 17.77 years.

So, in approximately 18 years, the population would exceed the food supply, even if the country doubles its initial food supply and maintains a constant rate of increase in the supply adequate for an additional 0.5 million people per year.

Now, let's answer the second question:

If the country doubled the rate at which its food supply increases, in addition to doubling its initial food supply, would shortages still occur?

If the country doubles the rate at which its food supply increases, the new rate would be 1 million people per year. Let's calculate the year when the population exceeds the food supply:

Population = Food supply

2,000,000 * (1 + 4%) raise to the power t  = 16,000,000 + 1 million * t

Solving for t, we get t ≈ 21.96 years.

So, in approximately 22 years, the population would exceed the food supply, even if the country doubles its initial food supply and doubles the rate at which its food supply increases.

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The theoretical probability of stopping on the color blue when spinning a spinner with the colors red, yellow, blue, and green is 25% or 1/4.

A spinner is a tool that spins around an arrow or a pointer that points towards the numbers, colors, or pictures around its edge. The probability of a certain event is the likelihood of that event occurring. In this case, we need to find the theoretical probability of stopping on the color blue.

We have four colors on the spinner, so the probability of stopping on blue can be found using the formula of theoretical probability.

The formula for theoretical probability is:

number of favorable outcomes / total number of outcomes.

Since we have four colors on the spinner, the total number of outcomes is 4. The favorable outcomes are the number of times the spinner will land on blue, which is 1.

So the probability of stopping on the color blue can be calculated as follows:

1 (favorable outcome) / 4 (total number of outcomes) = 1/4

So, the theoretical probability of stopping on the color blue is 1/4. This is because there is an equal chance of landing on any of the four colors, and since there are four colors, each has a 25% chance of being selected.

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Answer:

Step-by-step explanation:

Answer: I can’t find it please help

Step-by-step explanation:

The height of the tree is approximately 76 feet.

What is the angle of elevation?

The angle of elevation is the angle created between the line of sight and the horizontal. The angle created is an angle of elevation if the line of sight is upward from the horizontal line.

We can use tangent to set up the following two equations based on the given angles of elevation:

tan(62°) = h/x

tan(56°) = h/(x+10)

We can rearrange the first equation to solve for "h":

h = x * tan(62°)

tan(56°) = (x * tan(62°)) / (x+10)

We can solve for "x" by multiplying both sides by (x+10) and rearranging:

x = 10 * (tan(62°) - tan(56°)))

Now we can substitute this value for "x" into either of the two equations we set up earlier to find the height of the tree "h". Using the first equation, we get:

h = x * tan(62°) ≈ 76 feet

Therefore, the height of the tree is approximately 76 feet.

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Numeric (continuous) variable: the amount of zantac in milliliters that the nurse will administer.A millilitre is a unit of capacity measurement. It is one thousandth of a litre in size. In other words, a one-liter container may hold  [tex]1,000[/tex] millilitres.

A millilitre is a more manageable unit of measurement for liquid volume or capacity in the metric system. It is used to measure smaller amounts of liquid and is equal to one thousandth of a litre (1 litre = 1000 millilitres).

To calculate how many millilitres of Zantac will the nurse administer to the patient, you need to know the concentration of Zantac in the dosage form and the prescribed dose for the patient.

For example, if the patient is prescribed 150 mg of oral Zantac twice daily and has a bottle of syrup that contains 15 mg/mL of ranitidine, then the nurse will administer [tex]10 mL (150 mg / 15 mg/mL)[/tex]  of syrup per dose.

Therefore, If the patient is prescribed 50 mg of intravenous Zantac every 8 hours and has a vial of solution that contains 25 mg/mL of ranitidine, then the nurse will administer 2 mL (50 mg / 25 mg/mL) of solution per dose.

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Hence, C) The child performed every task on the list last month is the right answer.

Mathematicians utilize the unitary approach as a tool for solving proportionality-related problems. Given certain known values, it entails applying ratios and proportions to find unknown quantities. According to the unitary technique, if two quantities are connected to one another in a particular way, we can determine the value of one quantity by knowing the value of the other. This is accomplished by first determining the unit value of the given quantity, which is then multiplied or divided to yield the desired value.

given

Let's name the quantity of housework the youngster performed "x".

The total earnings can be expressed by the equation below, where the child earns an additional $12 if they finish all the chores on the chore list:

Total income = 2x plus 12

We are informed that the child accomplished all of the chores on the list for the previous month and earned $44. We may set this equal to 44 and find x by using the equation above:

2x + 12 = 44

2x = 32

x = 16

The kid finished 16 housework tasks last month.

Now that we know which of the following is true:

A) The youngster finished ten domestic duties.

This is untrue, since we determined that the child accomplished 16 domestic duties.

A) The youngster received $4 for finishing all the tasks on the list.

This is untrue because the child receives $12 for finishing the chores on the list.

B) Last month, the youngster finished all of the chores on the list.

This is accurate because we were told the child accomplished every task on the list and discovered that there were 16 in all.

Hence, C) The child performed every task on the list last month is the right answer.

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Answer: sure....... i actually understand Spanish so this is gonna be easy.

Step-by-step explanation:

Give me a few minutes to do it

Ok for startes when you find a word cross it off the word bank that is where your first mistake is......

An algebraic expression for representing the Nora's income in form of Tonya's income is given by  y = ( x / 4 ) .

Let us consider 'x' represents the Tonya's income.

And variable 'y' represents the Nora's income.

Tonya income is equal to four times of Nora's income.

This implies,

Nora's income is equal to one fourth times of Tonya's income.

⇒ y = ( x / 4 )

Rewrite an algebraic expression to represents Tonya's income in terms of Nora's income we have,

Simplify by multiplying both the sides of the algebraic expression by 4 we get,

⇒ x  = 4y

Therefore, an algebraic expression to represents the Nora's income in terms of Tonya's income is equal to y = ( x / 4 ).

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Answer:

No it can,t be in standard for

In conclusion, the relation R on the set of all integers satisfies reflexivity and symmetry but not transitivity.

To determine which properties the relation R on the set of all integers satisfy, we need to check for reflexivity, symmetry, and transitivity.

1. Reflexivity: A relation R is reflexive if for every element a in the set, (a, a) ∈ R.
In this case, we need to check if a * a ≥ 1 for all integers a.
Since any integer squared (a * a) is greater than or equal to 1, R is reflexive.

2. Symmetry: A relation R is symmetric if for every pair (a, b) ∈ R, (b, a) also ∈ R.
In this case, we need to check if a * b ≥ 1 implies b * a ≥ 1.
Since multiplication is commutative (a * b = b * a), the condition holds true, and R is symmetric.

3. Transitivity: A relation R is transitive if for every (a, b) ∈ R and (b, c) ∈ R, (a, c) also ∈ R.
In this case, we need to check if a * b ≥ 1 and b * c ≥ 1 imply a * c ≥ 1.
Let's take the counterexample: a = -1, b = 2, and c = -1. We have -1 * 2 ≥ 1 and 2 * -1 ≥ 1, but -1 * -1 ≥ 1 is false.

Therefore, R is not transitive.

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Answer:

4t - 22

Step-by-step explanation:

To find:-

Answer:-

To find out the perimeter we can simply add all the side lengths of the given figure. Since the given figure here is a rectangle, we can add up all the four sides to find the perimeter.

The four sides given to us are t-6 , t-5 , t-6 and t-5 .

Hence the perimeter of the quadrilateral would be ,

Perimeter = t-5 + t-6 + t-5 + t-6

Perimeter = 4t - 10 - 12

Perimeter = 4t - 22

Hence the perimeter of the given figure us 4t - 22.

[tex]\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(5,0){2}{\line(0,1){3}}\multiput(0,0)(0,3){2}{\line(1,0){5}}\put(0.03,0.02){\framebox(0.25,0.25)}\put(0.03,2.75){\framebox(0.25,0.25)}\put(4.74,2.75){\framebox(0.25,0.25)}\put(4.74,0.02){\framebox(0.25,0.25)}\multiput(2.1,-0.7)(0,4.2){2}{$\sf\large t-5$}\multiput(-1.4,1.4)(6.8,0){2}{$\sf\large t-6$}\put(-0.5,-0.4){\bf A}\put(-0.5,3.2){\bf D}\put(5.3,-0.4){\bf B}\put(5.3,3.2){\bf C}\end{picture} [/tex]

Answer: $ 46.50

First divided 31 by 2

Which equals...

15.50

Then add 15.50 to 31.

46.50

The answer is $46.50