Leo’s family needs to cross a bridge. Because it is night, they must have a flashlight to cross. Dad takes one minute, mother three minutes, Leo six minutes, brother eight minutes, grandpa 12 minutes, and a maximum of two people can cross the bridge at a time, there is only one flashlight, and the power can only support 30 minutes. The bridge crossing time is calculated according to the slow person. How can Leo’s family cross the bridge before the flashlight runs out?



PLEASE FAST IM RUNNING OUT OF TIME ILL GIVE BRAINLIEST

The remote interior angles of ∠1 are ∠2 and ∠6.

Corresponding angles in a triangle are those angles which are contained by a congruent pair of sides of two similar (or congruent) triangles.

The remote interior angles of ∠1 is determined by applying the principle of corresponding angles as shown below;

∠1 = ∠2 ( vertical opposite angles are equal )

∠1 = 180 - ∠5 ( corresponding angles  are equal )

180 - ∠5  = ∠ 6 ( vertical opposite angles are equal )

So we can conclude that, ∠1 = ∠6.

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Answer:

x = \(\frac{t(a+p)}{4}\)

Step-by-step explanation:

Given

a = \(\frac{4x}{t}\) - p ( isolate term in x by adding p to both sides )

a + p = \(\frac{4x}{t}\) ( multiply both sides by t )

t(a + p) = 4x ( divide both sides by 4 )

\(\frac{t(a+p)}{4}\) = x

Answer      18cm by-step explanation: 3 plus 15 is 18

Answer:

a= 126 degrees

b= 54 degrees

r= 54 degrees

s= 126 degrees

Step-by-step explanation:

Answer:

D. 15 is correct.

I did the quiz.

Answer:

The answer is B the only answer that I believe is correct

Step-by-step explanation:

a) To determine the better value for money between a 250g tin of coffee for R29.49 and a 750g tin of coffee for R69.99, we need to calculate the price per gram for each tin.

b) To calculate the price per gram, we divide the total price by the weight in grams. For the 250g tin of coffee, the price per gram is R29.49/250g = R0.11796 per gram. For the 750g tin of coffee, the price per gram is R69.99/750g = R0.09332 per gram.

a) To compare the value for money, we need to calculate the price per gram for each tin of coffee.

b) For the 250g tin of coffee, we divide the price of R29.49 by the weight of 250g to find the price per gram, which is approximately R0.11796 per gram.

Similarly, for the 750g tin of coffee, we divide the price of R69.99 by the weight of 750g to find the price per gram, which is approximately R0.09332 per gram.

Comparing the price per gram, we can see that the 750g tin offers a lower price per gram compared to the 250g tin. Therefore, in terms of value for money, the 750g tin is a better option.

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Answer:

c -2

x=0

y=3x-2

=3×0-2

=0-2

=-2

The width of the deck is 1 foot.

Let's assume that the width of the deck is x feet. Then the dimensions of the entire pool and deck will be (12+2x) by (20+2x) feet.

The area of the entire pool and deck will be the area of the pool plus the area of the deck:

(12+2x)(20+2x) = area of pool + area of deck

We know the area of the pool is 12 x 20 = 240 square feet, and we are given that the total area of the deck is 68 square feet. So we can write:

(12+2x)(20+2x) = 240 + 68

Expanding the left-hand side:

\(240 + 24x + 40x + 4x^2 = 308\)

Rearranging and simplifying:

\(4x^2 + 64x - 68 = 0\)

Dividing both sides by 4:

\(x^2 + 16x - 17 = 0\)

We can solve for x using the quadratic formula:

\(x = (-b \pm \sqrt{(b^2 - 4ac)}) / 2a\)

where a = 1, b = 16, and c = -17. Plugging in the values, we get:

\(x = (-16 \pm \sqrt({16^2 - 4(1)(-17))}) / 2(1)\\x = (-16 \pm \sqrt{(400)}) / 2\\x = (-16 \pm 20) / 2\)

Therefore, the possible values for x are -18/2 = -9 and 2/2 = 1. However, since the width of the deck cannot be negative, the only valid solution is x = 1.

Therefore, the width of the deck is 1 foot.

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Step-by-step explanation:

435.5 X 5 = 2177.5 g are in the bag

Answer:

w<4

Step-by-step explanation:

i used distributive property then combined like terms to get to -2w-4<-12 and added 4 to both sides to get -2w<-8 then i divided -2 from both sides to get w<4

Answer:

x ≥ −42

Step-by-step explanation:

Let's solve your inequality step-by-step.

x/7≥−6

Step 1: Simplify both sides of the inequality.

\(\frac{1}{7}x\geq -6\)

Step 2: Multiply both sides by 7.

\(7*(\frac{1}{7}x)\geq (7)*(-6)\)

x ≥ −42

Answer:

3h−3k

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let the horizontal distance is x

Use tangent to solve this:

Answer:

x = 5

Step-by-step explanation:

-3 * (x-3) = -6

3x+9 = -6 (divide by 3)

-x + 3 = -2 (minus 3)

-x = -5 (multiply by -1)

x = 5

Answer & Step-by-step explanation:

Answer:

He worked 30 hours at a lower paying job.

Step-by-step explanation:

First do 2 + 3 + 2 + 3 + 2 + 3 + 2 + 3 + 2 + 3 + 2 + 3 + 2 + 3 + 2 + 3 + 2 + 3 + 2 + 3 ( 20 + 30) to get 50

now remove all 2's to get 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 (thats 30)

An there you go!

The asymptotic notation relationship between the functions \(f(n) = n^3 (8 + 2 cos 2n)\) and \(g(n) = n^2 + 2n^3 + 3n\) is f(n) ∈ Θ(g(n)). Therefore, the growth rates of f(n) and g(n) are primarily determined by the cubic terms, and they grow at the same rate within a constant factor.

To determine the asymptotic notation relationship between the functions \(f(n) = n^3 (8 + 2 cos 2n)\) and \(g(n) = n^2 + 2n^3 + 3n\), we need to compare their growth rates as n approaches infinity.

Θ (Theta) Notation: f(n) ∈ Θ(g(n)) means that f(n) grows at the same rate as g(n) within a constant factor. In other words, there exists positive constants c1 and c2 such that c1 * g(n) ≤ f(n) ≤ c2 * g(n) for sufficiently large n.

o (Little-o) Notation: f(n) ∈ o(g(n)) means that f(n) grows strictly slower than g(n). In other words, for any positive constant c, there exists a positive constant n0 such that f(n) < c * g(n) for all n > n0.

ω (Omega) Notation: f(n) ∈ ω(g(n)) means that f(n) grows strictly faster than g(n). In other words, for any positive constant c, there exists a positive constant n0 such that f(n) > c * g(n) for all n > n0.

Now let's analyze the given functions:

\(f(n) = n^3 (8 + 2 cos 2n)\\g(n) = n^2 + 2n^3 + 3n\)

Since both functions have the same dominant term, we can say that f(n) ∈ Θ(g(n)) because they grow at the same rate within a constant factor. The other notations, o and ω, are not applicable here because neither function grows strictly faster nor slower than the other.

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The estimated cost of the new 3000-ft2 heat exchange system for the plant retrofit can be calculated using the power-sizing exponent and the price index. Based on the given information, the rough estimate for the cost of the new heat exchanger system is approximately $108,984.

To estimate the cost of the new heat exchange system, we need to consider the price index and the power-sizing exponent. The price index provides a measure of the change in prices over time. In this case, the price index 7 years ago was 1360, and the current price index is 1478.

To calculate the cost estimate, we can use the following formula:

Cost estimate = (Cost of previous heat exchanger) × (Current price index / Previous price index) × (New size / Previous size) ^ power-sizing exponent

Using the given information, the cost of the previous heat exchanger was $75,000, the previous size was 1200 ft2, and the new size is 3000 ft2.

Plugging in these values into the formula, we get:

Cost estimate = ($75,000) × (1478 / 1360) × (3000 / 1200) ^ 0.55

Simplifying the calculation, we find:

Cost estimate ≈ $108,984

Therefore, a rough estimate for the cost of the new 3000-ft2 heat exchanger system for the plant retrofit is approximately $108,984. It's important to note that this is just an estimate and the actual cost may vary based on specific factors and market conditions.

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Answer: 8

Step-by-step explanation:

Let the number be represented by x.

Two less than three times a number is the same as six more than twice the number. This will be:

(3 × x) - 2 = (2 × x) + 6

3x - 2 = 2x + 6

Collect like terms.

3x - 2x = 6 + 2

x = 8.

The number is 8

Using monthly payment formula, the Smith Family's total monthly payment is approximately $2,360.99.

To calculate the total monthly payment for the Smith Family, we need to consider the mortgage payment, insurance, property tax, and HOA fees.

1. Mortgage Payment:

The loan amount is the house price minus the down payment:

$350,000 - $70,000 = $280,000.

To calculate the monthly mortgage payment, we need to determine the interest rate and loan term. Since you mentioned it's a 15-year loan, we'll assume an interest rate of 4% (which can vary depending on market conditions and the borrower's credit).

We can use a mortgage calculator formula to calculate the monthly payment:

M = P [i(1 + i)ⁿ] / [(1 + i)ⁿ⁻¹]

Where:

M = Monthly mortgage payment

P = Loan amount

i = Monthly interest rate

n = Number of months

The monthly interest rate is the annual interest rate divided by 12, and the loan term is 15 years, which is 180 months.

i = 4% / 12 = 0.00333 (monthly interest rate)

n = 180 (loan term in months)

Plugging in the values into the formula:

M = $280,000 [0.00333(1 + 0.00333)¹⁸⁰] / [(1 + 0.00333)¹⁸⁰⁻¹]

Using a calculator, the monthly mortgage payment comes out to be approximately $2,014.99.

2. Insurance:

The monthly insurance payment is given as $66.

3. Property Tax:

The monthly property tax payment is given as $230.

4. HOA Fees:

The HOA fees are stated as $600 per year. To convert this to a monthly payment, we divide by 12 (months in a year): $600 / 12 = $50 per month.

Now, let's add up all these expenses:

Mortgage payment: $2,014.99

Insurance: $66

Property tax: $230

HOA fees: $50

Total monthly payment = Mortgage payment + Insurance + Property tax + HOA fees

Total monthly payment = $2,014.99 + $66 + $230 + $50

Total monthly payment = $2,360.99

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The function f(x)=x²+5x+6 at the values of the independent variable :

a) f(2)=20. b) f(x+1)=x²+7x+12. c) f(−x)=x²−5x+6.

Here, we have,

the given function is: f(x)=x²+5x+6

now, we have to evaluate for the given values.

a) a. To evaluate f(x)=x²+5x+6 at x=2, we substitute x=2 into the function:

f(2) = 2²+5*2+6

     =4+10+6

     =20

Therefore, f(2)=20.

b. To evaluate f(x+1), we substitute x+1 into the function:

f(x+1)=(x+1)² +5(x+1)+6

      =x²+2x+1+5x+5+6

      =x²+7x+12

Therefore, f(x+1)=x²+7x+12.

c. To evaluate f(−x), we substitute −x into the function:

f(−x)=(−x)²+5(−x)+6

     =x²−5x+6

Therefore, f(−x)=x²−5x+6.

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Answer: It's A

Step-by-step explanation:

i just had that question i got it right

The original number in the word problem is 77.

Let's call the original two-digit number "x".

Information from the problem

the sum of the digits in x is 14.

So, we can write the number as x = 10a + b,

where a and b are the tens and ones digit, respectively, and a + b = 14.

Reversing and doubling the original number gives us 2(10b + a)

= 20b + 2a.

Adding the original number, x, and the doubled, reversed number, 2(10b + a),

we have 3x = 222.

Substituting x = 10a + b

3(10a + b) = 222

30a + 3b = 222

30a = 222 - 3b

Since the sum of the digits is 14, a + b = 14, so we can substitute for a in the equation:

30(14 - b) = 222 - 3b

420 - 30b = 222 - 3b

198 = 27b

Dividing both sides by 27, we find:

b = 7

So, the original number is x = 10a + b = 10(14 - 7) + 7 = 77.

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Answer:

keep going you got it

Step-by-step explanation:

Answer:

178

Step-by-step explanation:

A=2(wl+hl+hw)=

2·(4·11+3·11+3·4)=178

Since 400 is less than 424.9, we can conclude that Marcia does have enough paint to cover the top surface of the frame, given the area of 400 square inches.

To determine if Marcia has enough paint to cover the top surface of the frame, we need to calculate the area of the top surface of the frame.

The radius of the mirror alone is 21 inches, and the radius of the mirror and frame combined is 24 inches. Therefore, the width of the frame can be calculated by subtracting the mirror's radius from the radius of the combined mirror and frame.

Width of the frame = (Radius of the mirror and frame) - (Radius of the mirror)

Width of the frame = 24 inches - 21 inches

Width of the frame = 3 inches

The top surface of the frame can be considered as a circular band with an outer radius of 24 inches and an inner radius of 21 inches. To find the area of the top surface, we need to calculate the difference between the areas of the outer circle and the inner circle.

Area of the outer circle = π * (Radius of the mirror and frame)^2

Area of the outer circle = π * (24 inches)^2

Area of the inner circle = π * (Radius of the mirror)^2

Area of the inner circle = π * (21 inches)^2

Area of the top surface of the frame = Area of the outer circle - Area of the inner circle

Area of the top surface of the frame = (π * (24 inches)^2) - (π * (21 inches)^2)

Area of the top surface of the frame = (π * 576 square inches) - (π * 441 square inches)

Area of the top surface of the frame = 135π square inches

Now, we know that Marcia has enough paint to cover 400 square inches of the frame. We can compare this value to the area of the top surface of the frame (135π square inches) to determine if she has enough paint.

400 square inches < 135π square inches

To find the approximate value of π, we can use 3.14 as a reasonable estimate. Let's substitute it into the inequality:

400 < 135 * 3.14

400 < 424.9

Since 400 is less than 424.9, we can conclude that Marcia does have enough paint to cover the top surface of the frame, given the area of 400 square inches.

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The correct values for a, b, c, d, and e are a = 16, b = 29, c = 24, d = 22, and e = 30 for group of 75 students on asking whether they like Algebra or Geometry.

For the values of a, b, c, d, and e, we can use the information provided in the table. Let's break it down step-by-step:

We are given that a total of 75 math students were surveyed. Therefore, the total number of students should be equal to the sum of the students who like algebra, the students who like geometry, and the students who do not like either subject.

75 = 45 (Likes Algebra) + 53 (Likes Geometry) + 6 (Does Not Like Either)

Simplifying this equation, we have:

75 = 98 + 6

75 = 104

This equation is incorrect, so we can eliminate options c and d.

Now, let's look at the information given for the students who do not like geometry. We know that a + b = 6, where a represents the number of students who like algebra and do not like geometry, and b represents the number of students who do not like algebra and do not like geometry.

Using the correct values for a and b, we have:

16 + b = 6

b = 6 - 16

b = -10

Since we can't have a negative value for the number of students, option a is also incorrect.

The remaining option is option e, where a = 29, b = 16, c = 24, d = 22, and e = 30. Let's verify if these values satisfy all the given conditions.

Likes Algebra: a + c = 29 + 24 = 53 (Matches the given value)

Does Not Like Algebra: b + d = 16 + 22 = 38 (Matches the given value)

Likes Geometry: c + d = 24 + 22 = 46 (Matches the given value)

Does Not Like Geometry: b + e = 16 + 30 = 46 (Matches the given value)

All the values satisfy the given conditions, confirming that option e (a = 29, b = 16, c = 24, d = 22, and e = 30) is the correct answer.

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R = C (S/P)^k where C = ±C' is a constant of integration. This is the general solution to the differential equation.

To solve the differential equation dR/R = k S/P, we can separate the variables and integrate both sides with respect to their respective variables:

dR/R = k S/P

ln|R| = k ln|S/P| + C

where C is an arbitrary constant of integration. Exponentiating both sides, we get:

|R| = e^(k ln|S/P| + C)

|R| = e^(ln|S/P|^k) e^C

|R| = C' (S/P)^k

where C' = e^C is another arbitrary constant of integration. Since the absolute value of R is always positive, we can drop the absolute value signs and write:

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Answer:

well if she was paid equally each hour it would've been $13.50, so I'd pick C since its closest