Florencia cannot spend more than $60 on clothes. She wants to buy jeans for $22 and spend the rest on shirts. Each shirt costs $8. Write and inequality to describe this situation.

Answer:

\(\Huge \boxed{\boxed{\texttt{\bf{\$2346.09} } } }\)

Step-by-step explanation:

We can use the compound interest formula to get the final value of a $2000 investment at an interest rate of 2% compounded quarterly for 8 years, using:

\(\LARGE \boxed{\tt{A = P(1 + \frac{r}{n})^{nt}}}\)

Substituting the values:

So, the final value of the investment after 8 years would be approximately $2346.09.

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In the given IS-LM model, the equilibrium real output, Y, and the equilibrium value of consumption, C, can be determined using the IS and LM equations. The IS equation relates output to the interest rate, while the LM equation represents the equilibrium condition in the money market. By substituting the given values into the equations, we can find the equilibrium values.

The IS equation is given by: Y = 1,586.27 - 3,145.45i.

The LM equation is given as: i = 0.04.

To find the equilibrium real output, we substitute the value of i from the LM equation into the IS equation:

Y = 1,586.27 - 3,145.45 * 0.04.

Calculating the right side of the equation, we have:

Y = 1,586.27 - 125.82,

Y ≈ 1,460.

Therefore, the equilibrium real output, Y, is approximately 1,460.

To find the equilibrium value of consumption, we substitute the equilibrium real output, Y, into the consumption function:

C = 217 + 0.51Y.

Substituting Y = 1,460, we have:

C = 217 + 0.51 * 1,460.

Calculating the right side of the equation, we find:

C ≈ 984.

Therefore, the equilibrium value of consumption, C, is approximately 984.

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All the possible composite numbers which is a whole number value for n between 20 and 80 are 49 and 77.

Method 1:

n is a composite number, that is, the product of two or more (not necessarily different) primes. Prime factors are never 2, 3, or 5. This is because at least one of the specified fractions is not included in the lowest term. The possible prime factors of n are 7, 11, 13, 17, and so on. Composites using these factors are 7 × 7, 7 × 11, 7 × 13, 11 × 11, and so on. Because only the first two composites are between 20 and 80, the only possible values ​​for n are 49 and 77.

Method 2:

Identify the integers between 20 and 80 that do not apply.

Start with the numbers 21, 22, 23. . ., 79. Since 2/n, 3/n, and 5/n are the lowest terms, we drop the multiples of 2, 3, and 5. This leaves 23, 29, 31, 37, 41, 43, 47, 49, 53, 59, 61, 67, 71, 73, 77, and 79. The possible values ​​of n are 49 and 77.

49 and 77 are possible composite whole number values for n between 20 and 80.

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Answer:

10

Step-by-step explanation:

8 + 2 = 10

Part A

Let's say we measure a board length and we measure 18.639 cm. Now let's say we round to the nearest tenth. That would lead to 18.6 cm. The question is "What is the largest value we can measure such that we round to the nearest tenth to get 18.7 cm?"

Well we could measure 18.7 cm exactly, but there are values we could measure that are larger to round to that value. We could measure 18.71 or 18.72, etc etc all the way up to 18.74; once we get to 18.75, it will round to 18.8

So this means that the largest we can measure is 18.74 and it is the upper bound we're after.

=========================================================

Part B

We use the same idea as part A, but now we're extending out one more decimal place.

We could measure 58.37 cm exactly or we could measure 58.371 or we could do 58.372, etc until we arrive at 58.374

By the time we get to 58.375, it will round to 58.38 and that's not what we're after. So the highest we can go is 58.374 cm

Answer:

P(A) = 4/7.

Step-by-step explanation:

Probability it does not occur = 3/7 so probability it does is 1 - 3/7.

P(A) = 1 - 3/7 = 4/7.

The exponential model that calculates the concentration of bacteria after x weeks can be represented by the equation B(x) = 2.1 million * (3^x), the concentration after 1.6 weeks would be approximately 14.87 million bacteria per milliliter.

This equation assumes that the concentration triples each week, starting from the initial concentration of 2.1 million bacteria per milliliter.

To estimate the concentration after 1.6 weeks, we can substitute x = 1.6 into the exponential model. B(1.6) = 2.1 million * (3^1.6) ≈ 14.87 million bacteria per milliliter. Therefore, after 1.6 weeks, the estimated concentration of bacteria in the river would be approximately 14.87 million bacteria per milliliter.

The exponential model B(x) = 2.1 million * (3^x) represents the concentration of bacteria after x weeks, where the concentration triples each week. By substituting x = 1.6 into the equation, we estimate that the concentration after 1.6 weeks would be approximately 14.87 million bacteria per milliliter.

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The largest area that can be enclosed if 88 feet of fencing material is available is 484 feet².

Given, a barn has a perimeter of 88 feet.

Now, the perimeter of the rectangle i.e. Barn is 88 feet.

Perimeter = 2(l + b)

88 = 2(l + b)

l + b = 44

b = 44 - l

Now, area = l × b

Area = l × (44 - l)

Area = 44l - l²

On differentiating both the sides, we get

A' = 44 - 2l

On putting A' = 0

44 - 2l = 0

l = 22

Now, for l = 22 the area will be the largest.

if l = 22

then, 22 + b = 44

b = 22

So, the largest area will be 22×22 = 484

Hence, the largest area that can be enclosed if 88 feet of fencing material is available is 484 feet².

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Step-by-step explanation:

a)

with step 1 to 3 we see that the numbers of squares serving the length of the sidelines is following the step number 1:1.

so, step 1 has a side length of 1 square.

step 2 has a side length of 2 squares.

step 3 has a side length of 3 squares.

so, we expect step 4 to have a side length of 4 squares.

but the first statement says "5-by-5", so, the side length is 5.

therefore, this statement is false.

and yes, we expect step 15 to have a side length of 15.

and the shift of the single square from the bottom left to the top right is also correct.

therefore, the statement is true.

b)

step 4 = 4×4 = 16 squares

step 15 = 15×15 = 225 squares

c)

no.

just look at step 1.

y = 1² - 1 = 1 - 1 = 0.

but I can clearly see that there is 1 square.

d)

it makes an n×n array. which is the same as n².

The possible dimensions (length and width) of the field are:(10 m × 13 m) or (13 m × 10 m) and (11 m × 12 m) or (12 m × 11 m).

Given that Aaron has 47m of fencing to build a three-sided fence around a rectangular plot of land that sits on a riverbank. The fourth side of the enclosure would be the river.

The area of the land is 266 square meters.To find the possible dimensions (length and width) of the field, we can use the given information.The length of fencing required = 47 m.

Since the fence needs to be built on three sides of the rectangular plot, the total length of the sides would be 2l + w = 47.1. When l = 10 and w = 13, we have:

Length of the field, l = 10 m Width of the field, w = 13 mArea of the field = l × w = 10 × 13 = 130 sq. m2. When l = 11 and w = 12,

we have:Length of the field, l = 11 m

Width of the field, w = 12 m

Area of the field = l × w = 11 × 12 = 132 sq. m

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The probability of both rice and carrots being served with dinner is 23.4%.

The probability of Alvin's mother serving rice with dinner can be expressed using the formula P(Rice) = 0.78. This means that the probability of Alvin's mother serving rice with dinner is 78%. The probability of Alvin's mother serving carrots with dinner can be expressed using the formula P(Carrots) = 0.30. This means that the probability of Alvin's mother serving carrots with dinner is 30%. To calculate the combined probability of both rice and carrots being served with dinner, we can use the formula P(Rice and Carrots) = P(Rice) * P(Carrots) = 0.78 * 0.30 = 0.2340. This means that the probability of both rice and carrots being served with dinner is 23.4%.

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Answer:

10

Step-by-step explanation:

10 goes into 30, 70, and 20.

To find the area inside the larger loop and outside the smaller loop of the limaçon r = 1 2 + cos(θ), we need to first plot the curve on a polar graph.

From the graph, we can see that the curve has two loops - one larger loop and one smaller loop. The larger loop encloses the smaller loop.

To find the area inside the larger loop and outside the smaller loop, we can use the formula:

Area = 1/2 ∫[a,b] (r2 - r1)2 dθ

where r2 is the equation of the outer curve (larger loop) and r1 is the equation of the inner curve (smaller loop).

The limits of integration a and b can be found by setting the angle θ such that the curve intersects itself at the x-axis. From the graph, we can see that this occurs at θ = π/2 and θ = 3π/2.

Plugging in the equations for r1 and r2, we get:

r1 = 1/2 + cos(θ)
r2 = 1/2 - cos(θ)

So the area inside the larger loop and outside the smaller loop is:

Area = 1/2 ∫[π/2, 3π/2] ((1/2 - cos(θ))2 - (1/2 + cos(θ))2) dθ

Simplifying and evaluating the integral, we get:

Area = 3π/2 - 3/2 ≈ 1.07

Therefore, the area inside the larger loop and outside the smaller loop of the limaçon r = 1 2 + cos(θ) is approximately 1.07. Note that this area is smaller than the total area enclosed by the curve, since it excludes the area inside the smaller loop.
To find the area inside the larger loop and outside the smaller loop of the limaçon given by the polar equation r = 1 + 2cos(θ), follow these steps:

1. Find the points where the loops intersect by setting r = 0:
1 + 2cos(θ) = 0
2cos(θ) = -1
cos(θ) = -1/2
θ = 2π/3, 4π/3

2. Integrate the area inside the larger loop:
Larger loop area = 1/2 * ∫[r^2 dθ] from 0 to 2π
Larger loop area = 1/2 * ∫[(1 + 2cos(θ))^2 dθ] from 0 to 2π

3. Integrate the area inside the smaller loop:
Smaller loop area = 1/2 * ∫[r^2 dθ] from 2π/3 to 4π/3
Smaller loop area = 1/2 * ∫[(1 + 2cos(θ))^2 dθ] from 2π/3 to 4π/3

4. Subtract the smaller loop area from the larger loop area:
Desired area = Larger loop area - Smaller loop area

After evaluating the integrals and performing the subtraction, you will find the area inside the larger loop and outside the smaller loop of the given limaçon.

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it is 1 1/2

the answer is 1 1/2

Answer:( D ) 1 1/2

Step-by-step explanation:

Answer:

let one number be x and the other be x + 12

sum = 48

x + x + 12 = 48

2x + 12 = 48

2x = 48 - 12

2x = 36

x = 36 by 2

x = 18

therefore x = 18 and x+12= 18+12=30

so the answer is 18 and 30

Have a good day! ^^

Step-by-step explanation:

The probability that the sample mean would be greater than 148.6 millimeters is 0.017

The spread of all the data points in a data collection is taken into account by the variance, which is a measure of dispersion.

Given  Population mean μ= 147

Population Variance σ^2 = 25

So, population SD = 5

Size of sample = n = 44 Sample mean = x

To find P( y > 148.6) :

SE =σ/√n =

5/√44= 0.7538

Transforming to Standard Normal Variate:

Z = (x - μ )/SE    

= (148.6 - 147)/0.7538    

= 2.1226

From Table of Area Under Standard Normal Curve, corresponding to Z = 2.1226, area = 0.4830.

So, required probability = 0.5 - 0.4830 = 0.017

The probability that sample mean would be greater than 148.6 millimeters is 0.017

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Step-by-step explanation:

8 volume

Answer:

10.41

Step-by-step explanation:

hehe

Answer:

11

Step-by-step explanation:

Total number of pencils needed = 125 × 2 = 250

Total number of boxes = \(\frac{250}{24}\) = 10.416

the teacher need to buy 11 boxes

a) The probability that the bank is empty is approximately 0.0026.

b) the average time the customer spends waiting to be called is approximately -0.25 c) hours the average number of customers in the bank is -1.5 d) the average number of customers waiting to be served is approximately 9.

To answer these questions, we can use the M/M/4 queuing model, where the arrival rate follows a Poisson distribution and the service time follows an exponential distribution. In this case, we have four bank tellers, so the system is an M/M/4 queuing model.

Given information:

Arrival rate (λ) = 12 customers per hour

Service rate (μ) = 1 customer every 15 minutes (or 4 customers per hour)

(a) To calculate the probability that the bank is empty, we need to find the probability of having zero customers in the system. In an M/M/4 queuing model, the probability of having zero customers is given by:

P = (1 - ρ) / (1 + 4ρ + 10ρ² + 20ρ³)

where ρ is the traffic intensity, calculated as ρ = λ / (4 * μ).

ρ = (12 customers/hour) / (4 customers/hour/teller) = 3

Substituting ρ = 3 into the formula, we have:

P = (1 - 3) / (1 + 4 * 3 + 10 * 3² + 20 * 3³) ≈ 0.0026

Therefore, the probability that the bank is empty is approximately 0.0026.

(b) The average time the customer spends waiting to be called is given by Little's Law, which states that the average number of customers in the system (L) is equal to the arrival rate (λ) multiplied by the average time a customer spends in the system (W). In this case, we want to find W.

L = λ * W

W = L / λ

Since the average number of customers in the system (L) is given by L = ρ / (1 - ρ), we can substitute this into the equation to find W:

W = L / λ = (ρ / (1 - ρ)) / λ

W = (3 / (1 - 3)) / 12 ≈ -0.25

Therefore, the average time the customer spends waiting to be called is approximately -0.25 hours, which is not a meaningful result. It seems there might be an error in the given data.

(c) The average number of customers in the bank (L) can be calculated as:

L = ρ / (1 - ρ) = 3 / (1 - 3) = -1.5

Therefore, the average number of customers in the bank is -1.5, which is not a meaningful result. It further suggests an error in the given data.

(d) The average number of customers waiting to be served can be calculated as:

\(L_q\) = (ρ² / (1 - ρ)) * (4 - ρ)

Substituting ρ = 3, we have:

\(L_q\\\) = (3² / (1 - 3)) * (4 - 3) ≈ 9

Therefore, the average number of customers waiting to be served is approximately 9.

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Answer:

89

Step-by-step explanation:

Given that Wendy took 2 tests and scored, 77 and 80 respectively, let x represent the grade of Wendy's third test.

To get an average grade of 82, let's generate an equation to find x (Wendy's grade on her third test).

Average grade = sum of all 3 grades all over 3

\( 82 = \frac{77 + 80 + x}{3} \)

\( 82 = \frac{157 + x}{3} \)

Multiply 3 by both sides

\( 82*3 = \frac{157 + x}{3}*3 \)

\( 246 = 157 + x \)

Subtract 157 from each side of the equation

\( 246 - 157 = 157 + x - 157 \)

\( 89 = x \)

Wendy must score 89 on her third test to have an average of 82.

Answer:

19.7 miles

Step-by-step explanation:

29-9.3=19.7

Answer:15/3

Step-by-step explanation:

1. subtract 20-5

2. subtract -3-(-6)

1. The word that describes a pattern in nature that is also exhibited in the external appearances of animals is "symmetry."

Symmetry refers to the balanced arrangement of parts or elements. In nature, many animals display symmetry in their body structure, such as butterflies with their symmetrical wings.

2. The word that describes a pattern exhibited by objects when their similar parts are regularly arranged around a central axis and the pattern looks the same after a certain amount of rotation is "rotational symmetry."

Rotational symmetry occurs when an object can be rotated and still maintain its original appearance. For example, a circle has rotational symmetry because it looks the same after any amount of rotation.

3. The word that describes curved patterns made by a series of circular shapes revolving around a central point is "spiral."

Spirals can be seen in various aspects of nature, like the arrangement of petals in a sunflower or the shape of a seashell.

4. The word that describes a pattern exhibited by objects that do not change their size and shape even if they are moved to another location is "translation symmetry."

Translation symmetry means that an object can be moved without altering its characteristics. For instance, a rectangle has translation symmetry because it remains the same even if it is shifted horizontally or vertically.

5. The word that describes an exact correspondence of form and constituent configuration on opposite sides of a dividing line or plane or about a contour or an axis is "reflection symmetry" or "mirror symmetry."

Reflection symmetry means that an object can be divided into two equal halves, and each half is a mirror image of the other. For example, the letter "A" exhibits reflection symmetry when it is divided vertically down the middle.

Now, moving on to the second part of the question, which involves finding values in the Fibonacci sequence:

1. Fib(8) = 13
2. Fib(19) = 4181
3. Fib(23) = 28,657

1. To find Fib(8), we can use the Fibonacci sequence. Fib(1) = 1, Fib(2) = 1, and each subsequent term is the sum of the previous two terms. So, Fib(3) = Fib(1) + Fib(2) = 1 + 1 = 2.

Similarly, Fib(4) = 2 + 1 = 3, Fib(5) = 3 + 2 = 5, Fib(6) = 5 + 3 = 8, and Fib(7) = 8 + 5 = 13. Therefore, Fib(8) is 13.

2. To find Fib(19), we can continue using the Fibonacci sequence. By applying the same pattern of adding the previous two terms, we find that Fib(19) is 4181.

3. Given that Fib(22) = 17,711 and Fib(24) = 46,368, we can determine Fib(23) by subtracting the known terms

. Since Fib(23) = Fib(24) - Fib(22),

we have Fib(23) = 46,368 - 17,711 = 28,657.

In summary:
1. Fib(8) = 13
2. Fib(19) = 4181
3. Fib(23) = 28,657

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the values of x and y that make the points (1,2,3), (5,7,1), and (x,y,2) collinear are x = 2 and y = 4.

Let's consider the direction ratios of the given points:

Point 1: (1, 2, 3)

Direction ratios: (1-0, 2-0, 3-0) = (1, 2, 3)

Point 2: (5, 7, 1)

Direction ratios: (5-1, 7-2, 1-3) = (4, 5, -2)

Point 3: (x, y, 2)

Direction ratios: (x-1, y-2, 2-1) = (x-1, y-2, 1)

Since the direction ratios should be proportional, we can set up the following proportion:

(1, 2, 3) / (4, 5, -2) = (x-1, y-2, 1) / (4, 5, -2)

This gives us the following ratios:

1/4 = (x-1)/4

2/5 = (y-2)/5

3/-2 = 1/-2

Simplifying these ratios, we get:

1 = x - 1

2 = y - 2

3 = 1

Solving these equations, we find:

x - 1 = 1

x = 2

y - 2 = 2

y = 4

Therefore, the values of x and y that make the points (1,2,3), (5,7,1), and (x,y,2) collinear are x = 2 and y = 4.

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The 90% confidence interval for μ is (9.70, 9.90) (rounded to two decimal places).

To construct a confidence interval for the population mean μ, we can use the formula:

Confidence Interval = \(\bar x\) ± z * (σ / √n)

Given that c = 0.90, we want to construct a 90% confidence interval. This means that the confidence level (1 - α) is 0.90, and α is 0.10. Since it is a two-tailed test, we divide α by 2, resulting in α/2 = 0.05.

To find the z-value corresponding to a 0.05 significance level, we can look up the value in the standard normal distribution table or use a calculator. The z-value for a 0.05 significance level is approximately 1.645.

Now, let's substitute the given values into the confidence interval formula:

Confidence Interval = 9.8 ± 1.645 * (0.8 / √49)

Simplifying further:

Confidence Interval = 9.8 ± 1.645 * (0.8 / 7)

Confidence Interval = 9.8 ± 0.094

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Answer:

im believing 57

Step-by-step explanation:

please mark this answer as brainliest

Answer:

1/2

Step-by-step explanation:

Answer:

130

Step-by-step explanation:

Form a simple equation:

x/100 = 1.3

x= 1.3 * 100

x = 130

GIVE BRAINLIEST PLEASE ITS MY BIRTHDAY

Answer:

130

Step-by-step explanation:

Just like before, do the opposite and multiple by 100

1.3 * 100 = 130

May I please have a Brainliest? I put a lot of thought and effort into my answers, so I would really appreciate it!

Answer:

no 8x is the no a questions

Answer:

x3 − 2x + x3  ⇒ cubic

4x2 − 6x − 8x2  ⇒ quadratic

6x − 6 + 6x  ⇒ linear

5 + 4x2 − 4x2 + 5  ⇒ constant

Step-by-step explanation:

For the other question its

Classify each polynomial as a monomial, binomial, or trinomial. Combine like terms first.

x3 + 3x3 + 2x  ⇒ binomial

2x3 + 5x + 3x4 − x  ⇒ trinomial

4x − 5x + x − 2  ⇒ monomial

6x2 + 5 − 2x2 − 9  ⇒ binomial

The study conducted by the Gallup News Service, asking 1,004 adults about their level of concern regarding global warming, is a cross-sectional study.

The study conducted by the Gallup News Service, where 1,004 adults were surveyed and asked about their level of concern regarding global warming, can be categorized as a cross-sectional study. In a cross-sectional study, data is collected at a specific point in time from a sample of individuals or units from a population. In this case, the survey gathered information from a group of adults at a particular time to understand their level of concern regarding global warming.

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Answer:

its 9

Step-by-step explanatioso yeah

The nth term of the sequence is given by n² + a and the sum of first 4 term is S₄ = 2

An arithmetic progression is a sequence of numbers in which each term is derived from the preceding term by adding or subtracting a fixed number called the common difference "d"

The general form of an Arithmetic Progression is a, a + d, a + 2d, a + 3d and so on. Thus nth term of an AP series is Tn = a + (n - 1) d, where Tₙ = nth term and a = first term. Here d = common difference = Tₙ - Tₙ₋₁

Sum of first n terms of an AP: Sₙ = ( n/2 ) [ 2a + ( n- 1 ) d ]

Given data ,

Given that the nth term of the sequence is n² + a

Let's use this formula to find the value of the sixth term:

6th term = 6^2 + a = 36 + a = 29

Subtracting 36 from both sides, we get:

a = 29 - 36 = -7

So the formula for the nth term of the sequence becomes n^2 - 7.

Now, to find the sum of the first four terms of the sequence, we can simply substitute n = 1, 2, 3, and 4 in the formula and add them up:

S₄ = 1² - 7 + 2² - 7 + 3² - 7 + 4² - 7

S₄ = (-6) + (-3) + 2 + 9

S₄ = 2

Hence , the sum of the first four terms of the sequence is 2.

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