Jules is participating in the first round of a math competition. She competes in one contest a month in each of the first ten months of the school year. She can earn up to 100 points on each contest. On each of the first five contests she averaged 68 points. On the next three contests she averaged 80 points. In order to advance to the next round of the competition, she must obtain a minimum total of 750 points on the ten contests. What is the minimum average Jules requires on the final two contests in order to able to advance to the next round of the competition?

The total number of tasks Terrence completed. By substituting the value of 'x' with the number of tasks Terrence completed

The factor 'x' in the expression '90x - 20' represents the total number of tasks that Terrence completed in the game.

To understand why, let's break down the given information. It states that Shelly and Terrence completed a different number of tasks. Shelly earned 90 points on each task, so the total number of tasks she completed is not represented by 'x'.

On the other hand, Terrence's total points were 20 less than Shelly's total. This means that Terrence's total points can be calculated by subtracting 20 from Shelly's total points. Since Shelly earned 90 points on each task, her total points would be 90 multiplied by the number of tasks she completed.

So, the expression '90x - 20' represents Terrence's total points in the game, where 'x' represents the total number of tasks that Terrence completed. By substituting the value of 'x' with the number of tasks Terrence completed, we can calculate his total points.

Therefore, the correct answer is: The total number of tasks Terrence completed.

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Answer:

22 (4th option)

Step-by-step explanation:

The side lengths are useless.

Pay attention to the angles.

<QRP=68 degrees.

Vertical angles make it so <SRT=68

180-90(right angle)-68=22 degrees

The given sequence does not have a common difference (d) as it is a geometric sequence. The recurrence relation is aₙ = aₙ₋₁ * 2, and the closed-form solution is aₙ = 3 * 2^(n-1). This solution is proven using induction.

To find the common difference (d) in the given sequence, we need to observe the pattern between consecutive terms.

The given sequence is: 3, 6, 12, 24, 48

To go from one term to the next, we can see that each term is obtained by multiplying the previous term by 2. This suggests that the sequence is a geometric sequence with a common ratio of 2.

Let's calculate the common difference (d) using the formula for the common ratio in a geometric sequence:

Common Ratio (r) = (second term) / (first term)

r = 6 / 3 = 2

Since the common difference (d) is the difference between consecutive terms in an arithmetic sequence, and we have identified the given sequence as a geometric sequence, we can conclude that there is no common difference (d) in this sequence. Instead, we have a common ratio (r) of 2.

To write the recurrence relation for this sequence, we can use the formula:

aₙ = aₙ₋₁ * r

where aₙ represents the nth term of the sequence and r is the common ratio.

In this case, the first term (a₁) is 3 and the common ratio (r) is 2. Therefore, the recurrence relation is:

aₙ = aₙ₋₁ * 2

To find the closed-form solution for this geometric sequence, we can use the formula:

aₙ = a₁ * r^(n-1)

where aₙ represents the nth term, a₁ is the first term, r is the common ratio, and n is the position of the term.

In this case, the first term (a₁) is 3, the common ratio (r) is 2, and n represents the position of the term.

The closed-form solution for this geometric sequence is:

aₙ = 3 * 2^(n-1)

To prove this closed-form solution using induction, we need to show that it holds true for the base case (n = 1) and then demonstrate that if it holds true for any arbitrary term, it also holds true for the next term.

Base case (n = 1):

Using the closed-form solution, when n = 1, we have:

a₁ = 3 * 2^(1-1) = 3 * 2^0 = 3 * 1 = 3

This matches the first term of the given sequence, which is 3. Therefore, the closed-form solution holds true for the base case.

Inductive step:

Assume that the closed-form solution holds true for an arbitrary term, let's say, aₖ, where k ≥ 1. In other words, assume that:

aₖ = 3 * 2^(k-1)

Now, let's consider the next term, aₖ₊₁. Using the recurrence relation, we have:

aₖ₊₁ = aₖ * 2

aₖ₊₁ = (3 * 2^(k-1)) * 2

aₖ₊₁ = 3 * 2^k

This matches the closed-form solution when n = k + 1. Therefore, if the closed-form solution holds true for aₖ, it also holds true for aₖ₊₁.

We can conclude that the closed-form solution, a = 3 * 2(n-1), is proven by induction for the given geometric sequence since the base case holds true and the inductive step has been shown.

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The length of the model car based on the information is 0.8 feet.

It should be noted that scale simply shows the relationship between a measurement on a model as well as the corresponding measurement on the actual object.

From the information, the model car is constructed with a scale of 1:15.

When the actual car is 12 feet long, the length of the model will be illustrated as x. This will be:

= 1/15 = x / 12

Cross multiply

15x = 1 × 12

15x = 12

Divide

x = 12 / 15

x = 0.8

The length is 0.8 feet.

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Answer:

385 Miles

Step-by-step explanation:

Find the Unit Value

105:3 = 35:1

Multiply

35 x 11 = 385

Answer:

6(base) x 3.5(Height) = 21, 21 divided by 2 (x 1/2) = 10.5

10.5(area of triangle) x 7.75(width) = 81.375

Formula of an area of a triangle:

BH x 1/2

Base x Height x 1/2(basically just dividing by 2)

Now the base:

1.5 x 7.75 x 6 = 69.75

Now let's add the two given volumes:

81.375+ 69.75 = 151.125 ft^3 is your answer.

the total distance traveled by the particle over the time period is 14/3 meters.

To find the displacement of the particle over the time period, we need to integrate the velocity function v(t) over the given interval.

A) Displacement:

The displacement is given by the definite integral of the velocity function v(t) over the interval [1, 6]:

Displacement = ∫[1, 6] (t^2 - 2t - 8) dt

To evaluate this integral, we can use the power rule of integration:

Displacement = [(1/3) * t^3 - t^2 - 8t] evaluated from 1 to 6

= [(1/3) * (6^3) - 6^2 - 8 * 6] - [(1/3) * (1^3) - 1^2 - 8 * 1]

= [72 - 36 - 48] - [1/3 - 1 - 8]

= -12 - (-22/3)

= -12 + 22/3

= (-36 + 22)/3

= -14/3

Therefore, the displacement of the particle over the time period is -14/3 meters.

B) Total Distance:

To find the total distance traveled by the particle over the time period, we need to consider the absolute value of the velocity function and integrate it over the interval [1, 6]:

Total Distance = ∫[1, 6] |t^2 - 2t - 8| dt

Since the velocity function is already non-negative for the given interval, we can calculate the total distance by evaluating the integral of v(t) directly:

Total Distance = ∫[1, 6] (t^2 - 2t - 8) dt

Using the same integral from part A, we can evaluate it as:

Total Distance = (-14/3) meters

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The number of waffles can be made from 15 eggs are, 20 waffles.

the waffles can be calculates as follows

4 cups of fluor + 6 eggs +2 tbsp oil = 8 waffles

we need 6 eggs to make 8 waffles

So, the waffles can we make from 15 eggs = \(\frac{8}{6} X 15 = 20\) waffles

Hence, the number of waffles can be made from 15 eggs are 20 waffles.

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Answer: no sorry it looks fine to me

The overall heat transfer coefficient (U) represents the combined effect of the individual resistances to heat transfer and depends on the design and operating conditions of the heat exchanger.

The concentric tube heat exchanger with a hot stream having a specific heat capacity of cH = 2.5 kJ/kg.K.

A concentric tube heat exchanger, hot and cold fluids flow in separate tubes, with heat transfer occurring through the tube walls. The parallel flow mode means that the hot and cold fluids flow in the same direction.

To analyze the heat exchange in the heat exchanger, we need additional information such as the mass flow rates, inlet temperatures, outlet temperatures, and the overall heat transfer coefficient (U) of the heat exchanger.

With these parameters, the heat transfer rate using the formula:

Q = mH × cH × (TH-in - TH-out) = mC × cC × (TC-out - TC-in)

where:

Q is the heat transfer rate.

mH and mC are the mass flow rates of the hot and cold fluids, respectively.

cH and cC are the specific heat capacities of the hot and cold fluids, respectively.

TH-in and TH-out are the inlet and outlet temperatures of the hot fluid, respectively.

TC-in and TC-out are the inlet and outlet temperatures of the cold fluid, respectively.

Complete answer:

A concentric tube heat exchanger is built and operated as shown in Figure 1. The hot stream is a heat transfer fluid with specific heat capacity cH= 2.5 kJ/kg.K ...

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Answer:

8th floor

Step-by-step explanation:

Because he went up twice

Answer:

(25 ÷ 5 ) ÷ 4

Step-by-step explanation:

solve the equation for the variable. Then plug that variable value into the expression and simplify to get the answer.

Answer:

C

Step-by-step explanation:

the quotient of 25 and 5 is 25 ÷ 4 , then multiply this by 4 , so

4 × (25 ÷ 5 ) → C

Answer:

$216/4=$54

Step-by-step explanation:

You would have to divide to find the quotient because you have to find the cost of one sweater, and the question gave the total price, when you divide the total, in this case is $216 by the 4 sweaters you should get $54 for one! To check you can do 54x4 and you will get $216!

The m values that allow the quadratic equation \(x^2 + mx + 4\) to have two independent real roots are m in the open range (-∞ , -4) (4 , ∞). This may be expressed in interval notation as:

m ∈ (-∞, -4) ∪ (4, ∞).

The quadratic formula tells us that the quadratic equation's roots

\(x^2 + mx + 4 = 0\)

are provided by:

\(x = (-m\) ± \(sqrt(m^2 - 16))/2\)

The discriminant \((m^2- 16)\)must be positive, i.e., \(m^2\) > 16, for the quadratic to have two separate real roots. As a result, we have two instances to consider:

Case 1: m > 4. Because \((-m + sqrt(m^2 - 16)/2\)and\((-m - sqrt(m^2 - 16)/2\)are both real and unique in this case, the quadratic has two separate real roots.

Case 2: m < -4. In this situation, \((-m + sqrt(m^2 - 16)/2\) is negative, whereas\((-m - sqrt(m^2 - 16)/2\) is positive, indicating that the quadratic has two separate real roots.

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Comparing the means of the two samples, we find that the difference between the means is significant. Therefore, we can reject the claim and conclude that male and female high school students have different exam scores.

To perform the two-sample t-test, we first calculate the standard error of the difference between the means using the formula:

SE = sqrt((s1^2 / n1) + (s2^2 / n2))

Where s1 and s2 are the population standard deviations of the male and female students respectively, and n1 and n2 are the sample sizes. Plugging in the values, we have:

SE = sqrt((47^2 / 49) + (4.3^2 / 53))

Next, we calculate the t-statistic using the formula:

t = (x1 - x2) / SE

Where x1 and x2 are the sample means. Plugging in the values, we have:

t = (239 - 21.1) / SE

We can then compare the t-value to the critical t-value at α = 0.01 with degrees of freedom equal to the sum of the sample sizes minus 2. If the t-value exceeds the critical t-value, we reject the null hypothesis.

In this case, the t-value is calculated and compared to the critical t-value using the provided standard normal distribution table. Since the t-value exceeds the critical t-value, we can reject the claim that male and female high school students have equal exam scores.

Therefore, the correct answer is:

B. Male and female high school students have different exam scores.

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Answer:

5.63

Step-by-step explanation:

The value of x in the given triangle is 5.62 cm.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

The given triangle is a right angle triangle

We have to find the value of x

We know that by cosine function is a ratio of adjacent side and hypotenuse

cos 62 = x/ 12

0.469 = x/12

Apply cross multiplication

x=12×0.469

x=5.63

Hence, the value of x in the given triangle is 5.62 cm.

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a) If you draw one card at random, the probability it is a two or a four is 4/52 or 1/13.

b) If you draw one card at random, the probability it is a spade or a King is 16/52 or 4/13.

c) If you draw two cards at random, the probability of drawing two hearts, with replacement is

(13/52) × (13/52) = 169/2704 or 1/16.

d) If you draw two cards at random, the probability of drawing two Aces, without replacement is (4/52) × (3/51) = 12/2652 or 1/221.

Solution details:

a) If you draw one card at random, the probability it is a two or a four is 4/52 or 1/13.

There are four 2s and four 4s in the deck.

Therefore, the probability of drawing one of these cards is 4/52.

Simplifying it, 1/13.

b) If you draw one card at random, the probability it is a spade or a King is 16/52 or 4/13.

There are four Kings in the deck, and there are 13 spades in the deck, including the King of spades.

There are four Kings, including the King of spades.

Four plus 13 equals 16 total cards.

The probability of drawing one of these cards is 16/52.

Simplifying it, 4/13.

c) If you draw two cards at random, the probability of drawing two hearts, with replacement is

(13/52) × (13/52) = 169/2704 or 1/16.

There are 13 hearts in the deck, and we’re assuming that you’re drawing with replacement.

As a result, the probability of drawing two hearts is (13/52) × (13/52).

Simplifying it, 169/2704.  

d) If you draw two cards at random, the probability of drawing two Aces, without replacement is (4/52) × (3/51) = 12/2652 or 1/221.

Since the first ace has a probability of 4/52, or 1/13, the probability of the second ace is 3/51.

This is since one card has been removed from the deck, making it 51 instead of 52.

Multiplying the two probabilities gives us (4/52) × (3/51) or 12/2652. Simplifying it, 1/221.

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When you do not recognize a power of 4 which it equals 128 then the proper technique to solve this equation 4x=128 is; Find intersections on the graph of y = 4ˣ and y = 128.

Consider the given equations;

y = 4ˣ and y = 128

Since, the power of 4 equals 128 is unknown.

Thus, draw the graph of equation  y = 128. and y = 4ˣ .

Consider the intersected point from the graph.

Thus, when you do not recognize a power of 4 which it equals 128 then the proper technique to solve this equation 4x=128 is;

Find intersections on the graph of y = 4ˣ and y = 128.

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The lengths of the legs are 5 and 12.

Let ' a ' represent the length of the right triangle's shorter leg.

Other leg length equals a + 7

The hypotenuse must be at least 13 cm long.

a² + (a + 7)² = 132

a² + a² + 49 + 14a = 132

a² + 7a − 60 = 0

The equation's roots are a=5 and a=12.

Given that length is positive, a=5 is a valid root.

Thus, the two legs of the supplied right triangle are 5 and 12.

⇒ 5² + 12²

  = 25 + 144 = 169 which equals 13²

Therefore, the lengths of the legs are 5 and 12.

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Answer:

The length of legs are 12 and 5 .

Given that,

In a right angled triangle,

Hypotenuse= 13cm

One leg of a right triangle is 7 cm less than the length of the other leg.

Let,

One side of the triangle is x.

And the other side of the triangle is x-7.

As we know,

A/q pythagoras theorem, the square of the hypotenuse is equal to the other sides of the right angled triangle.

h²= p² + b²

So,

(x)² + (x-7)² = 13² (Pythagoras theorem)

x² + x² - 14x + 49 = 169 {(a-b)² expansion}

2x² - 14x + 49 = 169

2x² - 14x = 169 - 49

2x² - 14x = 120

2(x² - 7x) = 120

x² - 7x = 120/2

x² - 7x - 60= 0

x² + 5x - 12x - 60 = 0

x(x+5) - 12(x+5)= 0

(x+5) (x-12)= 0

Now,

x+5 = 0

x = -5 ( not considered because value is negative)

And,

x- 12 = 0

x= 12

If x is equal to 12, then x-7 equals to

12-7 = 5

Both sides are 12 and 5.

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The total number of cookies baked during the week if a bakery baked 1,244 trays of 26 chocolate chip cookies and also 694 trays of 19 sugar cookies are 336530.

To calculate the total number of cookies we have to find the number of chocolate chip and sugar cookies.

The total number of chocolate cookies is given by the product of the number of cookies in a tray and the number of trays.

Trays of chocolate chip cookies = 1244

Number of chocolate chip cookies per tray = 26

Total number of chocolate chip cookies = 1244 * 26

= 32344

Similarly, the total number of sugar cookies is given by the product of the number of cookies in a tray and the number of trays.

Trays of sugar cookies = 694

Number of sugar cookies per tray = 19

Total number of chocolate chip cookies = 694 * 19

= 13186

Total number of cookies = total number of chocolate chip cookies + sugar cookies

= 32344 + 13186

=336530

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P(Y = an odd integer) = p / (1 - q²), where Y follows a geometric distribution with success probability p and q = 1 - p.

To find the probability of Y being an odd integer, we must sum the probabilities of all odd outcomes. In a geometric distribution, the probability of the k-th success is given by P(Y = k) = q^(k-1)p, where k is the number of trials. For odd integers, we have k = 2n - 1, where n is a positive integer. Therefore, the probability of Y being an odd integer is:

P(Y = an odd integer) = Σ [q^(2n-2)p], summed over all positive integers n.

We can factor out p, which gives:

P(Y = an odd integer) = pΣ [q^(2n-2)], summed over all positive integers n.

This is a geometric series with common ratio q². The sum of an infinite geometric series is given by:

Sum = a / (1 - r), where a is the first term and r is the common ratio.

Here, a = 1 (the first term when n=1) and r = q². Therefore,

P(Y = an odd integer) = p / (1 - q²), as required.

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The Hardy-Weinberg equation is a mathematical formula used to calculate the frequency of alleles (alternative forms of genes) in a population.

It states that the frequency of alleles and genotypes in a population will remain constant from generation to generation in the absence of other evolutionary influences.

The equation is expressed as: p² + 2pq + q² = 1

In this equation, p represents the frequency of the dominant allele in the population, and q represents the frequency of the recessive allele.

The superscripts 2 represent the proportion of individuals in the population that are homozygous for that allele (meaning they have two copies of the same allele), while the 2pq term represents the proportion of individuals that are heterozygous (meaning they have one copy of each allele).

The sum of these terms is always equal to 1, as it represents the entire population.

This equation assumes several conditions: that the population is large, randomly mating, with no mutations, migration, natural selection, or genetic drift.

In reality, these conditions are rarely met, and the Hardy-Weinberg equation serves as a useful model for understanding how allele frequencies can change over time due to various evolutionary influences.

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Answer:

x = -19; y = 25/3

Step-by-step explanation:

Step 1: solve the equation with only one variable

Isolate the variable (x)

x + 10 = -9

x = -9 - 10

x = -19

Step 2: input new information into the other equation

If x = -19, then:

2(-19) - 6y = 12

Isolate the variable (y)

-38 - 6y = 12

-6y = 12 + 38

-6y = 50

y = 50 ÷ 6

y = 50/6

Simplify

y = 25/3

Step-by-step explanation:

There are 4 parks, each with 25 hectares

since this is area it needs to be calculated in m^2

25×10,000= 250,000

each park has 25 hectares, which is 250,000m^2 ×4=1,000,000

there are 6 trees planted for every 400m^2

1,000,000/ 400= 2,500

2,500×6 is 15,000

15,000 trees are planted

\(\\ \sf\longmapsto 2^3+6^5\)

\(\\ \sf\longmapsto 2^3+(2\times 3)^5\)

\(\\ \sf\longmapsto 8+2^5\times 3^5\)

\(\\ \sf\longmapsto 8+32\times 243\)

\(\\ \sf\longmapsto 40+7776\)

\(\\ \sf\longmapsto 7784\)

Answer:

2*2*2= 8

6*6*6*6*6= 7,776

7,776+8=

7,784

Answer:

23

Step-by-step explanation:

you just add 6 to every one

The relationship between operating cost per hour and the number of passenger seats is shown by the equation of the least squares regression line, where y=1136+14.673x is the expected operating cost per hour and x is the number of passenger seats.

a plane figure in geometry with four equal sides and four right angles of 90 degrees. A square is both an equilateral rectangle and a special kind of parallelogram (an equilateral and equiangular one).

In Euclidean geometry, a parallelogram is a simple quadrilateral having two sets of parallel sides. The confronting or opposed sides and the opposing angles of a parallelogram are of equal length.

based on the available facts;

y=1136+14.673x

where

x= number of passenger seat

y=predicted operating cost per hour.

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