Five lemonades and two cookles cost $1.50. Two lemonades and five cookles cost $2.70. How much does one cookle and one lemonade cost?

Step-by-step explanation:

To calculate the amount of money in the account at the end of 4 years, we can use the formula for simple interest:

I = P * r * t

Where:

I = Interest earned

P = Principal amount (initial deposit)

r = Annual interest rate (as a decimal)

t = Time period (in years)

Plugging in the given values, we get:

I = $50,000 * 0.025 * 4

I = $5,000

This means that over the course of 4 years, the account will earn $5,000 in interest.

To find the total amount in the account at the end of 4 years, we simply add the interest earned to the initial deposit:

Total amount = $50,000 + $5,000

Total amount = $55,000

Therefore, at the end of 4 years, there will be $55,000 in the account if you deposit $50,000 into a bank account that earns 2.5% simple interest annually.

Answer:

Step-by-step explanation:

[tex]\tt y=x+2\\3x+3y=6[/tex]

Substitute y= y=x+2 into 3x+3y=6

Solve for x :-

Cancel 6 from both sides:-

Divide both sides by 6:-

Now, Let's solve for y:-

Substitute x = 0 into y=x+2

Therefore, x = 0 and y = 2.

_________________

Check:-

To check a system of equations by substitution, we plug the values for x and y into the equations, If both simplified are true then your answer is correct.

Equation 1 :-

y = x + 2

Equation 2 :-

3x+3y=6

__________________________

Hope this helps!

The 9th term of the sequence is approximately 30.234.

In mathematics, a sequence is an ordered list of numbers or other mathematical objects, such as functions, matrices, or vectors. Each member of the sequence is called a term, and the position of each term in the sequence is identified by its index or subscript.

Looking at the given terms, we can observe that each term is less than the previous term and the difference between consecutive terms is decreasing. Therefore, the sequence is decreasing and the difference between consecutive terms is decreasing by a factor of 2 each time.

Using this pattern, we can find the common difference between consecutive terms as follows:

60 - 80 = -20

45 - 60 = -15

We see that the difference between consecutive terms decreases by a factor of 2 each time. Therefore, the next difference would be:

-15 / 2 = -7.5

So, the next term would be:

45 - 7.5 = 37.5

We can continue this pattern to find the 9th term as follows:

Term 1: 80

Term 2: 60

Term 3: 45

Term 4: 37.5

Term 5: 33.75

Term 6: 31.875

Term 7: 30.9375

Term 8: 30.46875

Term 9: 30.234375

Therefore, the 9th term of the sequence is approximately 30.234.

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The linear equation that passes through (-9, -9) and has the slope m = 0 is:

y = -9

A general linear equation can be written in slope-intercept form as.

y = m*x + b

Where m is the slope and b is the y-intercept.

Here we want to find the equation of a line that passes through (-9, -9) and that has the slope m = 0.

Repplacing the slope we will get:

y = 0*x + b

And no we want it to pass throug (-9, -9), replacing these values we will get:

-9 = 0*-9 + b

-9 = b

Then the linear equation is:

y = -9

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Answer:

I hope that this answers your question!

Answer:

Step-by-step explanation:

To find the critical points of the function f(x,y), we need to find all points where both partial derivatives ∂f/∂x and ∂f/∂y are equal to zero.

We first find ∂f/∂x by differentiating f(x,y) with respect to x and treating y as a constant:

∂f/∂x = 4x + 2y + 2

We then find ∂f/∂y by differentiating f(x,y) with respect to y and treating x as a constant:

∂f/∂y = 2x + 2y

To find the critical points, we need to solve the following system of equations simultaneously:

4x + 2y + 2 = 0

2x + 2y = 0

We can solve the second equation for y:

2y = -2x

y = -x

Substituting this into the first equation, we get:

4x + 2(-x) + 2 = 0

2x + 2 = 0

2x = -2

x = -1

Substituting x = -1 into y = -x, we get:

y = -(-1) = 1

Therefore, the critical point is (-1,1).

To verify that this point is a minimum, we can use the second partial derivative test. We first find the second partial derivatives:

∂²f/∂x² = 4

∂²f/∂y² = 2

∂²f/∂x∂y = 2

The discriminant of the Hessian matrix is:

∂²f/∂x² * ∂²f/∂y² - (∂²f/∂x∂y)² = (42) - (22) = 4

Since the discriminant is positive and the second partial derivative with respect to x is positive, the critical point (-1,1) is a local minimum.

Therefore, the point (-1,1) is the only critical point of the function f(x,y), and it is a local minimum.

Answer:

Step-by-step explanation:

To calculate the volume of sand needed to fill the long jump pit to a depth of 0.07 meters, we need to know the length and width of the pit.

Assuming that the long jump pit is a rectangular prism, we can use the formula:

Volume = length x width x depth

Let's say the length of the pit is 8 meters and the width is 3 meters. Then the volume of sand needed to fill the pit to a depth of 0.07 meters would be:

Volume = 8m x 3m x 0.07m

Volume = 1.68 cubic meters

Therefore, we would need 1.68 cubic meters of sand to fill the long jump pit to a depth of 0.07 meters.

The equation of the line in slope-intercept form is: y = -25x + 100. A negative slope indicates that the battery percentage is decreasing over time.

Part A:

To write the equation of a line in slope-intercept form, we need to know the slope (m) and y-intercept (b) of the line.

From the given information, we know that the y-intercept is 100 and the x-intercept is 4. This means that after 4 hours, the battery percentage is 0%.

To find the slope, we can use the slope formula:

m = (y2 - y1)/(x2 - x1)

Choosing two points on the line, one being the y-intercept (0,100) and the other being the x-intercept (4,0), we can plug in the values:

m = (0 - 100)/(4 - 0) = -25

Therefore, the equation of the line in slope-intercept form is:

y = mx + b

y = -25x + 100

Part B:

To determine the equation, we used the fact that the y-intercept was 100 and the x-intercept was 4. We then found the slope of the line using the slope formula with two points on the line. Plugging the slope and y-intercept into the slope-intercept form equation y = mx + b gives us the final equation.

Part C:

The slope of the line is -25, which means that for every hour that passes, the battery percentage decreases by 25%. Therefore, the slope represents the rate of change of the battery percentage with respect to time. A negative slope indicates that the battery percentage is decreasing over time.

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Using the compound interest formula, it is obtained that it would take approximately 9.9 years for the account balance to reach $20,000.

What is Compound Interest?

The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest. Compound interest is commonly abbreviated C.I. in mathematics.

We can use the formula for compound interest to solve this problem -

[tex]A = P(1 + \frac{r}{n})^{(nt)}[/tex]

where A is the account balance, P is the principal (the initial investment), r is the annual interest rate (as a decimal), n is the number of times per year the interest is compounded, and t is the time (in years).

In this case, we have P = 5000, r = 0.09 (9% annual interest), n = 4 (compounded quarterly), and A = 20000. We want to find t.

Substituting these values into the equation, we get -

[tex]20000 = 5000 \big(1 + \frac{0.09}{4} \big)^{(4t)}[/tex]

Dividing both sides by 5000, we get -

[tex]4 = \big(1 + \frac{0.09}{4} \big)^{(4t)}[/tex]

Taking the natural logarithm of both sides, we get -

ln(4) = 4t ln(1 + 0.09/4)

Solving for t, we get -

t = ln(4) / (4 ln(1 + 0.09/4))

Simplifying the equation, we get -

t ≈ 9.9

Therefore, the time value is obtained as 9.9 years.

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Answer:

x = 2 or x = 4

Step-by-step explanation:

The equation:

Has two solutions:

The values of x can be found by graphing the two functions ([tex]y = 2^{x}[/tex] and [tex]y = x^{2}[/tex]) and finding their points of intersection, or you can use numerical methods to solve the equation.

To check our work, we can simply insert 2 and 4 in as y.

For 2:

You can see that it is the same.

For 4:

They are also the same.

Therefore, x can equal either 2 or 4.

The equation that is used to determine the number of cords in a pile of wood h ft tallis is the number of cords = 280×h×128.

What is an equation?

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical declaration that illustrates the equality of two mathematical expressions.

Given that

The number of cords in a pile l ft long, w ft wide, and h ft tall can be estimated using the equation number of cords=lwh128.

The length of the wood pile is 14 ft and the wide is 20 ft.

The product of length and width is lw = 14×20 = 280 ft².

Putting lw= 280 in the equation number of cords=lwh128:

number of cords = 280×h×128

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0.08 rounded for the nearest hundredth

Answer:

B. 120o

Step-by-step explanation:

A parallelogram is a flat 2d shape which has four angles. The opposite interior angles are equal. The angles on the same side of the transversal are supplementary, that means they add up to 180 degrees. Hence, the sum of the interior angles of a parallelogram is 360 degrees.

t + 2t = 180

3t = 180

t = 180/3 = 60

m∠Z  = 2t = 2(60) = 120

Answer:

Calculate the arc length according to the formula above: L = r * θ = 15 * π/4 = 11.78 cm. Calculate the area of a sector: A = r² * θ / 2 = 15² * π/4 / 2 = 88.36 cm².

Step-by-step explanation:

The answer to this question is 0.6826, or 68.26%. To calculate this probability, we need to use the z-score formula.

The z-score formula is a statistical measurement that is used to identify how far a raw score is from the mean score of a population. It is calculated by subtracting the population mean from an individual raw score and then dividing the difference by the population standard deviation.

This formula allows us to convert a given value into a standardized score relative to the mean and standard deviation of the normal distribution. In this case, the z-score for 27.42 is -1 and the z-score for 34.08 is 1.

We can then use the cumulative normal distribution function to calculate the probability of x being between 27.42 and 34.08. This function allows us to calculate the area under the normal distribution curve between two given points. Since the normal distribution is symmetrical, the area under the curve between -1 and 1 is 0.6826 or 68.26%. This is the probability of x being between 27.42 and 34.08.

To summarize, in order to calculate the probability of x being between 27.42 and 34.08, we need to calculate the z-scores of these two values and then use the cumulative normal distribution function to calculate the area under the curve between the two z-scores. The area under the curve between -1 and 1 is 0.6826 or 68.26%, which is the probability of x being between 27.42 and 34.08.

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If the rope is to be doubled or tripled up around the perimeter of each site, the actual amount of rope needed will be greater than 315 meters.

Amount is a term used to describe the total of something. It can refer to a quantity of money, a number of items, or a measure of any other type of resource. Amounts are typically expressed as a numerical value, and they can be represented in different units depending on the type of resource. For example, an amount of money could be expressed in dollars, whereas an amount of time could be expressed in hours.

To calculate the amount of rope needed for both sites, we will first need to calculate the perimeter of each site. The perimeter of Site A is 180 meters (60 + 40 + 40 + 40) and the perimeter of Site B is 135 meters (45 + 45 + 45).

To calculate the total amount of rope needed for both sites, we will need to add the two perimeters together. The total amount of rope needed for both sites is 315 meters (180 + 135).

It is important to note that 315 meters of rope is the minimum needed to rope off both sites. Depending on the desired spacing between the rope and the sites, the actual amount of rope needed may be greater than 315 meters.  Additionally, if the rope is to be doubled or tripled up around the perimeter of each site, the actual amount of rope needed will be greater than 315 meters.

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If the rope is to be doubled or tripled up around the perimeter of each site, the actual amount of rope needed will be greater than 315 meters.

Amount is a term used to describe the total of something. It can refer to a quantity of money, a number of items, or a measure of any other type of resource. Amounts are typically expressed as a numerical value, and they can be represented in different units depending on the type of resource. For example, an amount of money could be expressed in dollars, whereas an amount of time could be expressed in hours.

To calculate the amount of rope needed for both sites, we will first need to calculate the perimeter of each site. The perimeter of Site A is 180 meters (60 + 40 + 40 + 40) and the perimeter of Site B is 135 meters (45 + 45 + 45).

To calculate the total amount of rope needed for both sites, we will need to add the two perimeters together. The total amount of rope needed for both sites is 315 meters (180 + 135).

It is important to note that 315 meters of rope is the minimum needed to rope off both sites. Depending on the desired spacing between the rope and the sites, the actual amount of rope needed may be greater than 315 meters.  Additionally, if the rope is to be doubled or tripled up around the perimeter of each site, the actual amount of rope needed will be greater than 315 meters.

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Answer:

Let the total number of cows in the herd be represented by "x". Then, according to the problem:

The first son received half the herd, or (1/2)x cows.

The second son received one fourth of the herd, or (1/4)x cows.

The third son received one fifth of the herd, or (1/5)x cows.

The fourth son received 48 cows.

We can write an equation to represent the total number of cows in the herd:

(1/2)x + (1/4)x + (1/5)x + 48 = x

To solve for "x", we can start by simplifying the fractions:

5/10x + 2/10x + 2/10x + 48 = x

Combining like terms, we get:

9/10x + 48 = x

Subtracting 9/10x from both sides, we get:

48 = 1/10x

Multiplying both sides by 10, we get:

x = 480

Therefore, the original herd had 480 cows.

Answer:

B. linear

Step-by-step explanation:

x     y

0     9

1      9 + 8

2      9 + 2(8)

3      9 + 3(8)

4      9 + 4(8)

=> linear function

Answer:

The probability that exactly 20 out of 25 adult smartphone users use their smartphones in meetings or classes is approximately 0.002.

The possible values of ∠L are 118.9 degrees (rounded to 10th of a degree).

A polygon with three sides and three angles is a triangle. It is one of the simplest geometric shapes.

To find the measure of angle L in ΔLMN, we can use the fact that the sum of the angles in a triangle is 180 degrees:

∠L + ∠M + ∠N = 180

We know that ∠N = 61 degrees, so we can substitute that value in and simplify:

∠L + ∠M + 61 = 180

∠L + ∠M = 119

We also know that the length of LM is 150 inches and the length of LN is 890 inches. We can use the Law of Cosines to find the measure of angle M:

cos M = (150² + 890² - LM²) / (2 × 150 × 890)

cos M = 0.999989 (rounded to 6 decimal places)

M = cos⁻¹(0.999989)

M ≈ 0.00114 radians

M ≈ 0.0655 degrees (rounded to 10th of a degree)

Now we can substitute the value of M into the equation we derived earlier and solve for angle L:

∠L + 0.0655 + 61 = 180

∠L = 118.9345

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Answer:2 4/9

Step-by-step explanation:

Answer:

To use the distributive property to solve 99 x 3, we can write it as:

99 x 3 = (90 + 9) x 3 (decomposing 99 as 90 + 9)

= 90 x 3 + 9 x 3 (using distributive property)

= 270 + 27

= 297

Therefore, 99 times 3 using the distributive property equals 297.

Step-by-step explanation:

To find out how long it will take for the arrow to hit the enemy on the bridge, we need to find the time when the height of the arrow is 45 feet (the height of the enemy's head above the ground).

So, we can set h(t) equal to 45 and solve for t:

h(t) = − 16t²+60t + 9.5

45 = −16t² + 60t + 9.5

Rearranging the equation, we get:

16t² - 60t - 35.5 = 0

To solve for t, we can use the quadratic formula:

t = (-b ± sqrt(b² - 4ac)) / 2a

where a = 16, b = -60, and c = -35.5

Plugging in the values, we get:

t = (-(-60) ± sqrt((-60)² - 4(16)(-35.5))) / 2(16)

Simplifying the expression inside the square root, we get:

t = (60 ± sqrt(3600 + 2272)) / 32

t = (60 ± sqrt(5872)) / 32

t ≈ 0.81 or t ≈ 3.69

Since we're looking for the time when the arrow hits the enemy, we need to choose the positive solution: t ≈ 3.69 seconds.

Therefore, it will take approximately 3.69 seconds for the arrow to hit the enemy on the bridge with a perfect headshot.

Correct option is B, modification that can be made to this loan to make it a viable option, given Giselle's situation Change the interest to 5.5%.

Giselle may either lower the interest rate to 5.5% or increase the down payment to 18% down in order to make the 20% down, 30-year fixed loan option financially feasible. Giselle's maximum monthly payment of $746.50 is exceeded by the monthly payment for the current loan option. The monthly payment would rise if the loan was shortened to 15 years, rendering it unprofitable. As a result, Giselle should choose a mortgage with a lower interest rate or put more money down in order to bring the monthly payment within her means.

Given Giselle's circumstances, the modification that may be made to this loan to make it an attractive alternative is to raise the interest rate to 5.5%.

Changes to the loan that will be made:

Price of acquisition: $163,000

Monthly income equals $2,986

25% of people are unwilling to spend money.

$33,000 is the down payment.

20% decline rate

Analysis

163,000 less $33,000 is the balance of the loan.

Amount remaining on loan is $130,000.

Condo loan balance = $163,000.20

Condo loan balance = $32,600

Down rate increase equals $163,000 x 20.25%

A higher down payment equals $33,007.50

The optimal solution, based on the research above, is to change the interest rate to 5.5% because it will result in a lower overall payment cost and make the loan amount a viable option.

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In summary, a change in a value in a data set can have varying impacts on the measures of central tendency and dispersion, depending on the value that was changed and its relationship to the other values in the data set.

Why it is?

The measures of central tendency, such as mean, median, and mode, and the measure of dispersion, range, can be impacted by a change in a value in a data set.

Mean: The mean is calculated by adding all the values in a data set and then dividing by the total number of values. If a value in the data set changes, the sum of the values will change, and thus the mean will also change. The impact of the change on the mean will depend on the value that was changed and how much it differs from the other values in the data set.

Median: The median is the middle value in a data set, when the values are arranged in order. If a value in the data set changes, the position of the median may change, depending on where the new value falls in the order of the values.

Mode: The mode is the value that appears most frequently in a data set. If a value in the data set changes, the mode may change, depending on whether the new value becomes the most frequent value or not.

Range: The range is the difference between the highest and lowest values in a data set. If a value in the data set changes, the range may change, depending on how much the new value differs from the highest or lowest value in the data set.

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The probability that the number of games you win is (a) exactly five, (b) more than six, and (c) less than three will be 0.196, 0.0082 and 0.056 respectively.

How are probabilities defined?

A probability is indeed a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages spanning form 0% to 100% can be used to describe probabilities.

1/3 of players will succeed in a game of rock-paper-scissors. Choose nine games of rock-paper-scissors, and let X represent the number of victories. With n=9 and p=1/3, X has a random variable.

(a) The likelihood of winning all five games in a row is:

P(X=5) = (9 choose 5)(1/3)⁵(2/3)⁴ = 0.196

Depending on the situation, this likelihood might or might not be seen as uncommon because it is neither extremely high nor extremely low.

(b) The probability of winning more than six games is:

P(X > 6) = P(X = 7) + P(X = 8) + P(X = 9)

= [(9 choose 7)(1/3)⁷(2/3)²] + [(9 choose 8)(1/3)⁸(2/3)¹] + [(9 choose 9)(1/3)⁹(2/3)⁰]

= 0.0082

The fact that this likelihood is so low suggests that winning and over six games is exceptional.

(c) The likelihood of winning two or fewer games is:

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

= [(9 choose 0)(1/3)⁰(2/3)⁹] + [(9 choose 1)(1/3)¹(2/3)⁸] + [(9 choose 2)(1/3)²(2/3)⁷]

= 0.056

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Answer: 15.54 degrees.

Step-by-step explanation:

To find the average temperature, we need to add up all the temperatures and then divide by the number of days:

Average temperature = (14.6 + 15.2 + 15.8 + 16.1) / 5

= 77.7 / 5

= 15.54

Therefore, the average temperature over the 5 consecutive days in October is approximately 15.54 degrees.

1- 58000

2- 232000

3- 1245.43

4- 506354.8

The given polynomial written in standard form is: 3z⁴ + 2z³ + 5z

Degree: 4

Leading Coefficient: 3

Classification: Trinomial

Writing a polynomial in standard form simply means that we put the term with the highest exponent in it first and then the one with the second highest exponents second, and so on.

The polynomial we are given is:  5z + 2z³ + 3z4

Writing it in standard form gives us:

3z⁴ + 2z³ + 5z

The degree of the polynomial is defined as the value of the exponent in the leading term (if we are assuming a single variable). Thus, this given polynomial is of degree 4.

The leading coefficient is the number that the first term is multiplied by and in this problem that would be 3.

There are three terms in the given polynomial (the first term is 3z⁴, the second term is 2z³, and the 3rd term is 5z). Thus, it is a trinomial.

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