Gus has a lunch food budget of $190 per month. He spends an average of $5 per day on lunch. Which of the following equations represents how much money is left in his lunch budget after x days of buying lunch?
A.
y = 5x - 190
B.
y = 190 - 5x
C.
y = 190x - 5
D.
y = 190 + 5x

the interval over which the graph of f(x) = -(x + 3) - 1 is decreasing is (-∞, +∞).

What is a function?

A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.

The given function is:

f(x) = -(x + 3) - 1

To find the interval over which the function is decreasing, we need to find the values of x where the function's derivative is negative.

The derivative of the function is:

f'(x) = -1

The derivative is a constant, which means the function has a constant slope of -1. Since the slope is negative, the function is decreasing over its entire domain.

Therefore, the interval over which the graph of f(x) = -(x + 3) - 1 is decreasing is (-∞, +∞).

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Answer:

1/4

Step-by-step explanation:

Answer:

0.25

Step-by-step explanation:

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6 tables are required. Each prime number attender should serve 3 customers each.

The prime numbers between 1 and 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

All the numbers other than prime numbers are composite numbers.

The composite numbers from 1 to 100 are: 1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100.

Now, as there are 25 primes and 75 composites in the group that visited the restaurant, we can calculate the number of tables required by dividing the number of people by the seating capacity of each table.

Each table has a seating capacity of 15, so the number of tables required will be: Number of tables = (Number of customers)/(Seating capacity of each table)Number of customers = 25 (the number of primes) + 75 (the number of composites) = 100Number of tables = 100/15 = 6 tables

Therefore, 6 tables are required.

Now, as each prime number attender has to serve an equal number of customers, we need to calculate how many customers each one should serve.

Each prime attender has to serve 75/25 = 3 customers each, as there are 75 composites and 25 primes.

Thus, each prime number attender should serve 3 customers each.

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Answer:

Step-by-step explanation:

The magnitude of an earthquake is a measure of the amount of energy released during the earthquake. A stronger magnitude generally means a more powerful earthquake.

It is 1.39 standard devaitions away from the mean.

Since the mean x = 51.84 inches and the standard deviation, σ = 8.05 inches.

The amount of rainfall last year was X = 63 inches.

The difference between X and the mean x is d = X - x

= 63 - 51.84 in

= 11.16 in

To find the number of standard devaitions X is from the mean, n, we divide d by the standard deviation,σ.

So, n = d/σ

= 11.16 in/8.05 in

= 1.39

So, it is 1.39 standard devaitions away from the mean.

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its expanded form is 400+80+5

Answer:Step 2: Divide both sides by 5.

Step-by-step explanation:

Answer:

Step-by-step explanation:

add -61 on both sides:

5x - 61 + 61 = 20 + 61

simplify

5x = 81

divide 5 on both sides:

5x = 81

5      5

x = 81

      5

Answer:

y = 3. last option is correct answer for 2nd question.

Step-by-step explanation:

f(x) just means y.

horizontal asymptote is y = 'something.'

the graph crosses y = 4, so y = 4 cannot be asymptote.

y = 3 is since the graph never quite touches it.

as for ∞, we see that as x approaches -∞, y almost reaches 3. but not quite. also, as x approaches +∞, y approaches +∞.

so the last option is the correct answer.

By estimation, 3.9 turns into 4 and 5.3 turns into 5. The answer after estimation is 20 while the real answer is 20.67. Well u see by estimation we get an answer of two places right. So, real answer should also have two places.Place the decimal point after it.y43

Step-by-step explanation: i dont know if I'm right or not

we round down the second decimal place to get: 690.31

Rounding off is a mathematical process used to approximate a number to a specified degree of accuracy or precision. This is typically done to simplify calculations, improve readability, or make the number easier to work with.

When rounding off a number, you typically look at the digit in the place that you are rounding to, as well as the digit immediately to its right. Depending on the value of that right digit, you either round up or down. If the right digit is 5 or greater, you round up, and if it is less than 5, you round down.

Rounding off is the process of approximating a number to a specified degree of accuracy or precision.

To round off 690.3146 to the nearest hundredth, we need to look at the digit in the third decimal place, which is 4. Since 4 is less than 5, we round down the second decimal place to get: 690.31

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To be 95% confident that the estimate of the Percentage of computers with a new operating system is in error by no more than 4 percentage points, the programmer needs to survey at least 601 computers.

The sample size (n) needed to estimate the percentage of computers using a new operating system with a 95% confidence level and an error margin of no more than 4 percentage points, we need to use the formula for sample size estimation for proportions.

The formula is:

n = (Z^2 * p * (1-p)) / E^2

Where:

- n is the sample size

- Z is the z-score corresponding to the desired confidence level (for 95% confidence level, the z-score is approximately 1.96)

- p is the estimated proportion (since nothing is known about the percentage of computers with the new operating system, we assume p = 0.5 for maximum variability)

- E is the desired margin of error (in this case, 4 percentage points, which is 0.04 in decimal form)

Now, let's substitute the values into the formula and calculate the sample size (n)

n = (1.96^2 * 0.5 * (1-0.5)) / 0.04^2

n = (3.8416 * 0.25) / 0.0016

n = 0.9604 / 0.0016

n ≈ 600.25

Since the sample size must be a whole number, we round up to the nearest integer.

n = 601

Therefore, to be 95% confident that the estimate of the percentage of computers with a new operating system is in error by no more than 4 percentage points, the programmer needs to survey at least 601 computers.

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The solutions to the system of equations are (x₁, y₁) = (9 / 2, 11) and (x₂, y₂) = (- 1, 0).

Herein we find a system formed by one linear equation and one nonlinear equation (quadratic equation). First, we equalize the two equations to eliminate the variable y:

2 · x² - 5 · x - 7 = 2 · x + 2

2 · x² - 7 · x - 9 = 0

2 · [x² - (7 / 2) · x - 9 / 2] = 0

2 · (x - 9 / 2) · (x + 1)

There are two solutions to x: x₁ = 9 / 2, x₂ = - 1. And the solutions for y are:

y₁ = 2 · (9 / 2) + 2

y₁ = 11

y₂ = 2 · (- 1) + 2

y₂ = 0

Then, the solutions to the system of equations are (x₁, y₁) = (9 / 2, 11) and (x₂, y₂) = (- 1, 0).

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Answer:

it will take them 1.71 hours to finish cutting the lawn if they work together.

Step-by-step explanation:

If Marsha cuts the lawn by herself it will take her 3 hours, this mean that in one hour she cuts 1/3 of the lawn.

On the other hand Bob needs one more hour to finish the lawn, this means it takes him 4 hours to cut it and therefore he cuts 1/4 of the lawn per hour.

Now, to know how much they cut by working together we need to sum up the amount of lawn they cut per hour:

Working together in one hour: Marsha's one hour + Bob's one hour

Working together in one hour: \(\frac{1}{3}+ \frac{1}{4}=\frac{4+3}{12}=\frac{7}{12}\)

Therefore, working together they will cut 7/12 in one hour.

Now, to know how long will it take it to cut the entire lawn (which is equivalent to 12/12), we can write this in terms of proportions

Time        Total amount of lawn

1 hour               7/12

x hours             12/12

Solving for x (to know the amount of hours it will take them) we have:

\(x=\frac{12}{12}\)÷\(\frac{7}{12}\)=\(1\)×\(\frac{12}{7}=\frac{12}{7}=1.714\)

Rounded to the nearest hundredth, we have that working together it will take them 1.71 hours to finish cutting the lawn.

Answer:

1. Janell runs 3.8 times the number of miles that Jean runs.

3.5 x 3.8 = 13.3

2. Cora should save $625 per month to meet her goal of $7,485.00.

1 year = 12 months

625 x 12 = 7,500.00

The Pythagoras theorem states that in a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides.

From the given Pythagoras theorem above, the mathematical representation of the theorem would be written below as follows;

C² = a²+b²

Where:

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Answer:

4

Step-by-step explanation:

4 is the coefficient because its infront of the variable

Answer:

Sydney is 92

Step-by-step explanation:

99-7= 92

Answer:The reciprocal of 2/3 is 3/2. The product of 2/3 and its reciprocal 3/2 is 1.

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Because To get a single x you would have to divide 5x by 5. Whatever you do to one side you have to do to the other so you would do 5 x/5 and get 10/5 and then x=10/5 and 10/5 equals 2 so...x=2 , Hope this helped!

Cliff pays a total interest of approximately $679.90 on his $5,000 loan.

To calculate the total interest paid on the loan, we need to use the formula for compound interest:

\(A = P(1 + r/n)^{(nt)}\)

Where:

A is the final amount (loan amount + interest)

P is the principal (loan amount)

r is the annual interest rate (in decimal form)

n is the number of times interest is compounded per year

t is the number of years

Given that Cliff takes out a $5,000 loan with a fixed annual interest rate of 7% compounded monthly, we can substitute the values into the formula:

P = $5,000

r = 7% = 0.07

n = 12 (monthly compounding)

t = 2 years

\(A = 5000(1 + 0.07/12)^{(12 \times 2)\)

Calculating this expression:

A ≈ 5000\((1.00583)^{(24)\)

A ≈ 5000(1.13598)

A ≈ 5679.90

The final amount (A) is the loan amount plus the total interest paid. Therefore, to find the total interest paid, we subtract the principal (P) from the final amount (A):

Total Interest = A - P

Total Interest = 5679.90 - 5000

Total Interest ≈ $679.90

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9

Step-by-step explanation:

PEMDAS

inside parentheses we have 3*2 = 6

9-6 =3

3^2 = 9

Step-by-step explanation:

the center of the circle is the midpoint of the diameter.

and the radius is the distance of the midpoint to either endpoint (or simply half of the distance between the diameter endpoints).

the midpoint between points A and B

(xm, ym) = ((xa + xb)/2, (ya + yb)/2)

in our case the midpoint (center of the circle) is

((-6 + 2)/2, (10 + 3)/2) = (-4/2, 13/2) = (-2, 6.5)

about the radius

diameter² = (-6 - 2)² + (10 - 3)² = (-8)² + 7² = 64 + 49 =

= 113

diameter = sqrt(113) = 10.63014581...

radius = diameter / 2 = 5.315072906... ≈ 5.315

Answer: A rotation followed by a reflection. The two figures are congruent because (I'm not sure about this one because I don't know the options that the drop-down menu provides.)

Answer: slope equals 2/3

Step-by-step explanation:

Reccesive disorders are more  common because they are not easily eliminated by natural selection.

The autosomal dominant disorders refers to those disorders that have no gender preference and have possible male to male transmission.

The  autosomal dominant disorders are much more rare than the recessive disorders because they do not occur on a s-ex-linked chromosome. Note also that it is more common to have dominant mutations eleiminated by the process of natural selection.

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Answer:

0.1875

Step-by-step explanation:

Let A be the event that  class two has been chosen . So the probability of A would be P (A) = 1/2= 0.5

Now class two has 9 girls out of total 24 students . So the probability of chosing the girl would be= P (B=) 9/24= 0.375

So the probability that Classroom #2 was chosen at random, given that a girl was chosen is given by = P(A) . P(B)= 0.5 * 0.375= 0.1875

Another way of finding the probability that Classroom #2 was chosen at random, given that a girl was chosen is by drawing a tree diagram.

P (1/2) Class 1 ------------------------5 boys

                      -------------------------11 girls  (11/16)

P (1/2)  Class 2 -------------------------15 boys

                     -----------------------9 girls  P (9/24)   Class 2 was chosen (0.5) *9/24

The confidence interval is 0.559 < p < 0.641 and expected value is 0.600

To construct a confidence interval for the true population proportion, we can use the formula:

p ± Z * √((p × (1 - p)) / n)

Where:

p = sample proportion (336/560)

Z = critical value for the desired confidence level

95% confidence = Z-value of approximately 1.96

n = 560

Let's calculate the confidence interval:

p = 336/560 ≈ 0.600

Z ≈ 1.96 (for a 95% confidence level)

n = 560

Plugging these values into the formula:

p ± Z × √((p × (1 - p)) / n)

0.600 ± 1.96 × √((0.600 × (1 - 0.600)) / 560)

0.600 ± 1.96 × √((0.240) / 560)

0.600 ± 1.96 × √(0.0004285714)

0.600 ± 1.96 × 0.020709611

0.600 ± 0.040564459

The confidence interval is:

0.559 < p < 0.641

Therefore, the 95% confidence interval for the true population proportion of adults with children is 0.559 < p < 0.641.

For proportions, the expected value is simply the sample proportion, which is approximately 0.600.

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