Point S is between points R and T on RT. Use the information to write an equation in terms of x. Then solve the equation and find RS, ST, and RT.
RS = 2x - 8
ST = 3x - 10
RT = 17

RS =
ST=
RT=

Answer:

C. 1/8

Step-by-step explanation:

Hope this helped

Answer:

3/8 = 9/24 ; 1/3 = 8/24 ; 3/8 > 1/3

Step-by-step explanation:

You have to multiply 8 and 3 to obtein the same number as denominatoe (24).

Once you have the same number you can use < = >

For a random day with the standard deviation, the probability that there are less than 300 shoppers on a random day, is 0.00585.

Probability is a measure of the likelihood that an event will occur.

The average total number of shoppers on a grocery store in 1 day is 505; the standard deviation is 115.

Let, X be the random variable denoting the number of shoppers on a random day.

Then, X follows normal with mean 505 and standard deviation of 115.

Then, we can say that,

Z=(X-505)/115 follows standard normal with mean 0 and standard deviation of 1.

We have to find

P (250 <X< 450)

= P {(250-505)/155} < Z < {(450-505)/155}

= P (-1.64 <Z< -0.03)

Where, Z is the standard normal variate.

ρ = -1.64 <ρ< -0.03

Where, ρ is the distribution function of the standard normal variate.

From the standard normal table, this becomes

=0.00585

For a random day, the probability that there are less than 300 shoppers on a random day, is 0.00585.

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The map unit is typically a three-digit number that is used to identify a specific area on the map.

The map unit is typically a three-digit number that is used to identify a specific area on the map. .

The exact number can vary depending on the map, but it is usually located under the polygon or other shape on the map.

1. Look for the polygon or other shape on the map.

2. Look for the three-digit number located beneath the polygon or other shape.

3. This number is the map unit.

The map unit is typically a three-digit number that is used to identify a specific area on the map.

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Answer:

2/10 * 20 = 4.

hope it helps

Ellen can make a maximum of 6 batches of Cardamom cookies with her 2 fluid ounces of cardamom.

Ellen has 2 fluid ounces of cardamom in a jar. Her recipe requires 3/10 of a fluid ounce of cardamom for each batch of cardamom cookies.

We can use division to find the number of batches of cardamom cookies that Ellen can make with all of her cardamom:

2 fluid ounces ÷ (3/10 fluid ounce per batch) = (2/1) ÷ (3/10)

= (2/1) x (10/3)

= 20/3

= 6 2/3

Therefore, Ellen can make 6 batches of cardamom cookies with her 2 fluid ounces of cardamom, with 2/3 of a batch remaining.

Since she cannot make a fraction of a batch, Ellen can make a maximum of 6 batches of cardamom cookies with her 2 fluid ounces of cardamom.

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1) Gathering the data

P = 19,000

rate = 0.6% or 0.006

Period : 7 years

A =?

2) Let's plug into the formula below:

3) So the answer is:

Answer:

D

Step-by-step explanation:

it is a strange question. but I guess its meaning is to identify an expression that is structured in the same way as the generic basic expression.

3×(n + 1.8)

after doing the multiplication this gives us

3n + 3×1.8 = 3n + 5.4

so, the only answer option including 5.4 is D.

it would mean that 3n = 3.75. n = 1.25

but just to show you how strange this question is, let's have a look at the other answer options :

is 5.55 = 3n + 5.4 ?

it would mean

0.15 = 3n

n = 0.05

so, formally, this is also an expression that represents the original expression.

9.15n = 3n + 5.4

6.15n = 5.4

n = 5.4/6.15 = 0.87804878...

so, formally, this is also an expression that represents the original expression.

3.75 + 1.8 = 3n + 5.4

5.55 = 3n + 5.4

and we are back to A and therefore, formally, this is also an expression that represents the original expression.

so, many greetings from me to your teacher. he/she has to be more careful about how to phrase questions.

because here, formally, all 4 answers are theoretically correct.

The area of the new square is 128 square feet larger than the area of the original square.

When the side lengths of a square are tripled, the new square will have side lengths of 12 feet (4 feet multiplied by 3). To find the area of the original square, we use the formula A = s^2, where A is the area and s is the side length. Thus, the area of the original square is 4^2 = 16 square feet.

Similarly, the area of the new square with side lengths of 12 feet is 12^2 = 144 square feet. To determine how much larger the area of the new square is than the area of the original square, we subtract the area of the original square from the area of the new square: 144 - 16 = 128 square feet.

Therefore, the area of the new square is 128 square feet larger than the area of the original square. This means that the new square is three times nine times six times larger in terms of area compared to the original square.

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The probability of having a 5-card hand that is a flush or royal flush is 0.00196

Probability: Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty.

Flush, straight flush, and royal flush probabilities are calculated as follows: 5148/2598960≅0.00198

A flush's likelihood (while eliminating straight and royal flushes) is 5108/2598960, ≅0.00196.

Finding the fraction with the number of ways to have a flush as the numerator and the number of possible five-card hands as the denominator will allow us to determine the likelihood.

Combinations will be used to find each of these numbers (we don't care about the draw order; only about what shows up in our hand). Combinations' general formula is Cn,k=n!/(k)!(n-k)! with k=picks and n=population

Let's first determine the denominator by selecting 5 cards at random from a deck of 52 cards: C52,5=52!/(5)!(525)!

=52!/(5!)(47!)

Let's assess it!

52×51×50^10×49×48^2×47!/5×4×3×2×47!=52×51×10×49×2=2,598,960

Let's now determine the numerator.

In order to examine each hand with five cards of the same suit, we will compute all hands that feature a flush (including straight flushes, royal flushes, and flushes) (with a suit having 13 cards in total). We can say that we understand this by:

C13,5

Remember that there are 4 suites in which this might occur, but we only want 1, so multiply by C4,1. Putting it all together, we obtain:

C4,1×C13,5=4!/(1!)(4−1)!×13!/(5!)(13−5)!=4!13!/3!5!8!

Let's assess this.

4!×13×12×11×10×9^3×8!/3×2×5×4!×8!=13×12×11×3=5148

(Remember that we just calculated all hands, including straight flushes and royal flushes, that have a flush component to them!

The probability of getting a hand with a flush is:

5148/2598960≅.00198

We may exclude straight and royal flush possibilities from the 5148 flush hands by excluding those hands (which are hands with 5 consecutive value cards in the same suit, such as 3, 4, 5, 6, and 7 of hearts). Since there are four suits and 10 potential ways to get a straight (A-5, 2-6, 3-7,..., 10-A), we can subtract 4 from 5148 to get 5108 hands, which gives us the result 5108/2598960=0.00196.

The probability of having a 5-card hand that is a flush or royal flush is 0.00196

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Given:

The interior angle of a regular polygon is 132 degrees.

To find:

The given statement is possible or not.

Solution:

Let as assume the interior angle of a regular polygon with n vertices is 132 degrees.

Then, the exterior angles are

\(180^\circ-132^\circ=48^\circ\)

We have, n vertices. So, the number of exterior angles is n.

Sum of all exterior angles = 48n degrees

We know that, sum of all exterior angles of a regular polygon is always 360 degrees.

\(48n=360\)

\(n=\dfrac{360}{48}\)

\(n=7.5\)

Number of vertices is always a whole number. So, it cannot be a fraction value.

So, our assumption is wrong.

Therefore, a regular polygon cannot have an interior angle of 132 degrees.

In 2 years, Ari will need to pay off the loan.

Simple interest is the borrowing amount added only to the principal amount.

The formula to calculate the simple interest is;

                                                 S.I. = P x T x R / 100 ,

Where S.I. is simple interest , P is principal amount, T is time period and R is interest rate in a year.

Given:

Greg lends Ari $125 at an annual interest rate of 10%.

And Ari wants to pay no more than $25.00 in simple interest.

To find the time period:

Use simple interest rate formula:

A = P x R x T / 100

We have,

P = $125, R = 10, A = $25.00

Substituting all the values to the formula,

25 = 125 x 10 x T / 100

T = 25 x 100 / 1250

T = 2500 / 1250

T = 2 years.

Therefore, 2 years is the time period for the loan amount.

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Answer:

Option 1.

f(x)= 5^x

Step-by-step explanation:

1) I identified the equation as an exponential equation

2) I plugged the equations into a graphing calculator, and then did 2nd+GRAPH. The only equation with 5 in the Y column was 1.

By using implicit enumeration, the 0-1 integer programming model problem can be solved to maximize the objective function subject to the given constraints.

Implicit enumeration is a technique used to solve integer programming problems by systematically evaluating all possible combinations of decision variable values within the feasible region. In this problem, the objective is to maximize the expression 4x₁ + 5x₂ + x₃ + 3x₄ + 2x₅ + 4x₆ + 3x₇ + 2x₈ + 3x₉, where x₁, x₂, x₃, x₄, x₅, x₆, x₇, x₈, and x₉ are binary variables (0 or 1).

The problem is subject to several constraints, such as 3x₂ + x₄ + x₅ ≤ 23, x₁ + x₂ ≤ 1, x₂ + x₄ + x₅ + x₆ ≤ -1, and x₂ + 2x₃ + 3x₇ + x₈ + 2x₉ ≥ 4, among others. These constraints define the feasible region of the problem.

To solve the problem using implicit enumeration, we evaluate all possible combinations of the binary decision variables within the feasible region. We calculate the objective function value for each combination and identify the combination that maximizes the objective function.

Once we have enumerated all possible combinations, we compare the objective function values and select the combination that yields the highest value. This combination represents the optimal solution to the 0-1 integer programming problem.

By applying implicit enumeration to this problem, we can determine the values of x₁, x₂, x₃, x₄, x₅, x₆, x₇, x₈, and x₉ that maximize the objective function while satisfying the given constraints.

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Answer:

The proof of Pythagorean Theorem in mathematics is very important. In a right angle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. States that in a right triangle that, the square of a (a²) plus the square of b (b²) is equal to the square of c (c²).

Answer:

Formula 1 Racing

Step-by-step explanation:

Answer:

4.4x10⁻⁷

Step-by-step explanation:

Decimal moves 7 places to the right so the exponent if negative.

Answer:

b. 12

Step-by-step explanation:

2*2*2*2 - 8* 2 divided by 4= 12

The amount that each employee will get out of the bonus to your department will be $3,000.

What will each employee get?

You manage a staff of 9 employees in your department which means that there are 10 people in total.

The amount that each person will get from the bonus will therefore be:

= 30,000 / 10 employees

= $3,000

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The solution to log base 7 of 1 is x=0, which is the value of the power to which 7 must be raised to get the value 1.

The logarithm function is an inverse function of the exponential function, and it is defined as log_b(x) = y means b^y = x. In other words, it represents the power to which the base b must be raised to get the value x.

In this case, we are solving log_7(1), which means we are looking for the power to which 7 must be raised to get the value 1.

Since any number raised to the power of 0 is 1, we can say that 7^0 = 1, which means that log_7(1) = 0.

To solve log base 7 1, you need to find the value of x that satisfies the equation log_7(x) = 1.

Using the definition of logarithm, log_b(x) = y means b^y = x.

So to solve log7(1), we can set 1 = 7^x and get x = log7(1) = 0

So the solution to log base 7 of 1 is x=0.

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a. The probability of drawing a red ball from Box 1 is 30%.

b. If a red ball is drawn from Box 1, the probability of drawing another red ball from Box 2 on the second round is 60%.

c. If the first draw from Box 1 was black, the conditional probability of drawing a red ball from Box 3 on the second draw is 80%.

d. The probability of drawing two red balls at both draws, without any prior information, is 46%.

e. The probability of drawing a red ball at the first draw and a black ball at the second draw, without any prior information, is 21%.

a. The probability of drawing a red ball from Box 1 can be calculated by dividing the number of red balls in Box 1 by the total number of balls in Box 1. Therefore, the probability is 3/(3+7) = 3/10 = 0.3 or 30%.

b. Since a red ball was drawn from Box 1, we only consider the balls in Box 2. The probability of drawing a red ball from Box 2 is 6/(6+4) = 6/10 = 0.6 or 60%. Therefore, the probability of drawing another red ball when the first ball drawn from Box 1 is red is 60%.

c. If the first draw from Box 1 was black, we only consider the balls in Box 3. The probability of drawing a red ball from Box 3 is 8/(8+2) = 8/10 = 0.8 or 80%. Therefore, the conditional probability of drawing a red ball from Box 3 when the first ball drawn from Box 1 was black is 80%.

d. Before any draws, the probability of drawing two red balls at both draws can be calculated by multiplying the probabilities of drawing a red ball from Box 1 and a red ball from Box 2. Therefore, the probability is 0.3 * 0.6 = 0.18 or 18%. However, since there are two possible scenarios (drawing red balls from Box 1 and Box 2, or drawing red balls from Box 2 and Box 1), we double the probability to obtain 36%. Adding the individual probabilities of each scenario gives a total probability of 36% + 10% = 46%.

e. Before any draws, the probability of drawing a red ball at the first draw and a black ball at the second draw can be calculated by multiplying the probability of drawing a red ball from Box 1 and the probability of drawing a black ball from Box 2 or Box 3. The probability of drawing a red ball from Box 1 is 0.3, and the probability of drawing a black ball from Box 2 or Box 3 is (7/10) + (2/10) = 0.9. Therefore, the probability is 0.3 * 0.9 = 0.27 or 27%. However, since there are two possible scenarios (drawing a red ball from Box 1 and a black ball from Box 2 or drawing a red ball from Box 1 and a black ball from Box 3), we double the probability to obtain 54%. Adding the individual probabilities of each scenario gives a total probability of 54% + 10% = 64%.

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Answer:

B.

Step-by-step explanation:

The quickest and most fool-proof way to do this is to using a graphing calc to graph the given equations. When you do so, you should see that B is the right choice. You can also tell from the asymptotes. x cannot equal 1 or -1, so B.

Regression analysis is the process of examining the relationship between two variables. It helps to identify how one variable is affected by the other. It is used to forecast a dependent variable by making use of the relationship with the independent variable.

Regression analysis is done using various types of regressions, the most common of which is the linear regression.The formula for the straight line of a linear regression is y = mx + b. The formula tells us that the dependent variable (y) can be represented as a straight line function of the independent variable (x).

This equation is called the regression equation, and m and b are the slope and intercept of the line, respectively. The slope (m) represents the change in the dependent variable per unit change in the independent variable. The intercept (b) represents the value of the dependent variable when the independent variable is zero.

The slope and intercept are estimated by minimizing the sum of squared errors. Linear regression is one of the most widely used statistical tools because it is simple to use and provides useful insights into the relationship between two variables. Therefore, the answer is a. y = mx + b.

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Answer:

First Answer: 12.5 weeks

Third Answer: 16 minutes(I think it was a really long decimal so I rounded it up)

13.) The probability that when a tile is chosen at random it has at least 4 sides and not a hexagon = 5/18

14.) Probability that the tile is not a square and has less than 7 sides= 9/16

To calculate the probability of the given event, the formula that should be used is given as follows:

Probability = possible outcome/sample space

For 13.)

when tile has at least 4 sides;

possible outcome= 12+8 = 20

sample space = 60

p(at least 4 sides) = 20/60 = 1/3

When not a hexagon;

possible outcome = 12+15+8+6+9= 50

p(not a hexagon) = 50/60= 5/6

The probability that when a tile is chosen at random it has at least 4 sides and not a hexagon;

= 1/3×5/6

= 5/18

For 14.)

when tile is not a square;

possible outcome= 60-15= 45

p(not a square)= 45/60= 3/4

p(less than 7 sides)

possible outcome= 12+15+8+10= 45

p(less than 7 sides) = 45/60 = 3/4

Probability that the tile is not a square and has less than 7 sides= 3/4×3/4= 9/16

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The ratio of surface areas of two similar Pyramids, we need to square the ratio of their corresponding side lengths, then multiply by the ratio of their heights. The answer is D. 27:8.

The ratio of surface areas of two similar pyramids, we need to square the ratio of their corresponding side lengths, then multiply by the ratio of their heights.

Let's call the height of the larger pyramid h1 and the height of the smaller pyramid h2. We can see from the diagram that the ratio of their heights is h1/h2 = 21/14 = 3/2.

Now let's consider the ratio of their base side lengths. The larger pyramid has a base side length of 21 inches, and the smaller pyramid has a base side length of 14 inches. So the ratio of their base side lengths is 21/14 = 3/2.

Therefore, the ratio of their surface areas is:(3/2)^2 x 3/2 = 27/8

So the answer is D. 27:8.

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Answer:

25 , 1 , 34

Step-by-step explanation:

substitute x = - 12 into g(x)

g(- 12) = 1 - 2(- 12) = 1 + 24 = 25

substitute x = 0 into g(x)

g(0) = 1 - 2(0) = 1 - 0 = 1

substitute x = 4 into g(x)

- 5(1 - 2(4)) - 1 = - 5(1 - 8) - 1 = - 5(- 7) - 1 = 35 - 1 = 34

Thus, the magnitude of value of |a+b| is Sqrt (9), which simplifies to just 3.

To find the magnitude of the sum of two vectors, we need to add the two vectors together and then take the square root of the sum of their squares.

So, let's first add the two vectors together:

a+b = (3i+4j-4k) + (-2i-6j+2k)
    = i - 2j - 2k

Now, we can find the magnitude of this vector by squaring each of its components, summing them, and then taking the square root:

|a+b| = sqrt((1^2) + (-2^2) + (-2^2))
     = sqrt(1 + 4 + 4)
     = sqrt(9)
     = 3

Therefore, the value of |a+b| is Sqrt (9), which simplifies to just 3.

In summary, the magnitude of the sum of two vectors can be found by adding the vectors together, squaring each of their components, summing them, and then taking the square root.

For the given vectors a=3i+4j-4k and b=-2i-6j+2k, their sum is i - 2j - 2k, and the magnitude of this vector is 3.

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