"A firefighter stood on the middle rung of a ladder. When the smoke became less thick, the firefighter moved up 4 rungs. Then it got too hot, and the firefighter moved down 6 rungs. Later, the firefighter went up 7 rungs and stayed there till the fire was out. After the fire was out, the firefighter climbed the remaining 4 rungs and entered the building. How many rungs does the ladder have?"

The cost for making the sign is $812.38

Step-by-step explanation:

Radius = 28 cm

Cost of aluminum per square cm = $0.33

Area of the sign = π(r x r)

= (3.14) (28 x 28)

= (3.14) (784)

= 2461.76 square cm

Total cost to make the sign = 2461.76 x 0.33

= 812.38

The cost for making the sign is $812.38

To find the cost of making the circular aluminum sign, first calculate the area of the circle, then multiply the area by the cost per square centimeter. The total cost is $812.65.

To determine the cost to make a circular aluminum sign with a radius of 28 centimeters, we first need to find the area of the circle. The formula for the area of a circle is:

→ A = πr²

Given:

→ Radius, r = 28 cm

→ π ≈ 3.14

We can now calculate the area:

→ A = 3.14 × (28 cm)²

→ A = 3.14 × 784 cm²

→ A = 2,462.56 cm²

Next, we calculate the cost of the aluminum sheet:

→ Cost = Area × Price per cm²

→ Cost = 2,462.56 cm² × $0.33/cm²

→ Cost = $812.65

Therefore, it will cost $812.65 to make the circular aluminum sign.

Answer:

9

Step-by-step explanation:

Consecutive means in a row

x = 1st number

x+1 = 2nd number

x+x+1 = 17

Combine like terms

2x+1 = 17

Subtract 1 from each side

2x+1-1=17-1

2x = 16

Divide each side by 2

2x/2 =16/2

x=8

x+1 = 9

The larger number is 9

Final answer:

To find the number of different ways Jacob can arrange 3 books on a single bookshelf out of 12 books, we use the concept of permutations. The number of arrangements is 1320.

Explanation:

To find the number of different ways Jacob can arrange 3 books on a single bookshelf out of 12 books, we use the concept of permutations. Permutations calculate the number of ways to arrange objects in a specific order. In this case, we need to find the number of permutations of 3 books out of 12, which can be calculated using the formula:

P(n, r) = n! / (n - r)!

Where n is the total number of books (12) and r is the number of books to be arranged (3).

Substituting the values into the formula, we get:

P(12, 3) = 12! / (12 - 3)! = 12! / 9!

Calculating the factorial, we have:

12! = 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 479,001,600

9! = 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 362,880

Now, dividing the factorial values, we can calculate the number of arrangements:

P(12, 3) = 479,001,600 / 362,880 = 1320

Therefore, Jacob can arrange 3 books on a single bookshelf in 1320 different ways.

Answer: the first one

Step-by-step explanation:

Answer:

A or the first one on the left

Answer:

The answer for this question is 4.

Step-by-step explanation:

2+2=4

Answer:

B

Step-by-step explanation:

Answer: B

Step-by-step explanation:

If you have a negative exponent its like you divide it

10^-2 = 0.01 then multiply it by 5 = 0.01 x 5 = 0.05

Answer:

The option which is an exception is;

c) The sample sizes are large

Step-by-step explanation:

Here the requirement to perform a two sample t procedure are as follows;

1. The two samples have equal variance, hence the variance should be known

2. The samples for which the two sample t procedure is performed must be independent

3. The data are in alignment with the normal distribution probability

4. The samples are random samples taken from the different respective population

Since the sample size is known, we do not assume that the sample size are large.

Therefore options a), b) and d) are all correct except option c).

Answer:

As the size of a school building increases, the number of student musicians increases because the scatterplot has a cluster that increases from left to right.

Step-by-step explanation:

Answer:

a is the answer

Step-by-step explanation:

Answer:

Mass is a measure of the amount of matter in an object. Mass is usually measured in grams (g) or kilograms (kg). ... An object's mass is constant in all circumstances; contrast this with its weight, a force that depends on gravity. Your mass on the earth and the moon are identical.

Answer:

Step-by-step explanation:

The ratio of 6

11

compares money spent on eggs to money spent on cereal. This is a part-to-part comparison, not a part-to-whole comparison.

Answer:

-47b + 19

Step-by-step explanation:

Answer:

74°

Step-by-step explanation:

All interior angles of a triangle add up to 180°, so to find the measure of the third angle here, we can use this:

180 - (90+16)

180 - 106

= 74°

Hope this helps!

Answer:

The probability that none will have high blood pressure is 0.0281

Step-by-step explanation:

The correct question is as follows;

Twenty percent of Americans ages 25 to 74 have high blood pressure. If 16 randomly selected Americans ages 25 to 74 are selected, find each probablility. a. None will have high blood pressure

This is a binomial problem. We shall solve in that line

The probability of success is 20% or 0.2 [(Americans ages 25 to 74 have high blood pressure)] p = 0.2

The probability of failure q is thus 1-p = 1-0.2 = 0.8

The probability of none is thus;

P(X= 0) = 16C0 p^0 q^16

= 16C0 * 0.2^0 * 0.8^16 = 0.0281

A. 2C(s) + 2H₂(g) + 52.5 kJ → C₂H₄ shows that the enthalpy of formation of C₂H₄ is 52.5 kJ/mol.

Step-by-step explanation:

Enthalpy of formation of C₂H₄ is given as 52.5 kJ/mol.

There are 4 options given and they are:

A. 2C(s) + 2H₂(g) + 52.5 kJ → C₂H₄

B. 2C(s) + 4H(g) + 52.5 kJ → C₂H₄

C. 2C(s) + 2H₂(g) → C₂H₄ + 52.5 kJ

D. 2C(s) + 4H(g) → C₂H₄ + 52.5 kJ

Here the reactants absorb some energy from the surroundings and gives the product and it is an endothermic reaction.

So A and B is taken into account, but in B there are 4 H atoms involved in the reaction. So in the reaction A hydrogen molecules are involved and also energy is absorbed by the reactants.

So option A is the answer.

Answer: 2C(s) + 2H₂(g) + 52.5 kJ → C₂H₄

Answer:

y = 6+3x

Step-by-step explanation:

If y = f(x), it means y is depending on x. This shows that y is the independent variable and x is the dependent variable.

y variable will be the output depending on the input variable x.

According to the function rule, “The output is 6 greater than three times the input." This can be expressed mathematically as 3x+6 (x being the input)

Three times the input = 3x

6 greater than three times the input = 6+3x

Since y is output then;

y = 6+3x

The function rule is [tex]\boldsymbol{y=6+3x}[/tex].

A function rule is an equation that represents the relationship of the dependent and independent variables.

[tex]\boldsymbol{x}[/tex] is the independent variable.

[tex]\boldsymbol{y}[/tex] is the dependent variable.

The output is [tex]6[/tex] greater than three times the input.

[tex]y=6+3x[/tex].

So, the function rule is [tex]\boldsymbol{y=6+3x}[/tex].

Find out more information about function here:

https://brainly.com/question/14674614?referrer=searchResults

Answer:

C(t)=30+3.5t

Step-by-step explanation:

Yeah this is the answer

Answer:

C(t)=30+3.5t

Step-by-step explanation:

Time increases by 2, the average difference in the cost is approximately 7.

So if d is the common difference of the function modeling this relationship, then  2d≈72.

Therefore,  d≈ 7/2 = 3.5

Since the initial cost of the land is 30 thousand dollars, the function that best models its cost t years since 1990 is C(t)=30+3.5t

Answer:

x=-80

Step-by-step explanation:

Answer:

[tex]x=-80[/tex]

Step-by-step explanation:

[tex]a) (-4)x=320\\\\x=\frac{320}{-4} \\\\x=-80[/tex]

Step-by-step explanation:

Speakers =£ 31.5

Headphones =£ 4.8

Book =£ 3.85

Mobile phone =£ 36

mouse = £12.75

DVD =£ 10.2

Hope it will help you :)

Answer:

Therefore the rate change of distance between the car and the person at the instant, the car is 24 m from the intersection is 12 m/s.

Step-by-step explanation:

Given that,

A person stand 10 meters east of an intersection and watches a car driving towards the intersection from the north at 13 m/s.

From Pythagorean Theorem,

(The distance between car and person)²= (The distance of the car from intersection)²+ (The distance of the person from intersection)²+

Assume that the distance of the car from the intersection and from the person be x and y at any time t respectively.

∴y²= x²+10²

[tex]\Rightarrow y=\sqrt{x^2+100}[/tex]

Differentiating with respect to t

[tex]\frac{dy}{dt}=\frac{1}{2\sqrt{x^2+100}}. 2x\frac{dx}{dt}[/tex]

[tex]\Rightarrow \frac{dy}{dt}=\frac{x}{\sqrt{x^2+100}}. \frac{dx}{dt}[/tex]

Since the car driving towards the intersection at 13 m/s.

so,[tex]\frac{dx}{dt}=-13[/tex]

[tex]\therefore \frac{dy}{dt}=\frac{x}{\sqrt{x^2+100}}.(-13)[/tex]

Now

[tex]\therefore \frac{dy}{dt}|_{x=24}=\frac{24}{\sqrt{24^2+100}}.(-13)[/tex]

               [tex]=\frac{24\times (-13)}{\sqrt{676}}[/tex]

               [tex]=\frac{24\times (-13)}{26}[/tex]

               = -12 m/s

Negative sign denotes the distance between the car and the person decrease.

Therefore the rate change of distance between the car and the person at the instant, the car is 24 m from the intersection is 12 m/s.

The rate of change of the distance between the car and the person is [tex]\(-\frac{65}{12}\)[/tex] meters per second, indicating decreasing distance.

To find the rate of change of the distance between the car and the person at the given instant, we can use the concept of related rates. We'll use the Pythagorean theorem to relate the distances involved.

Step 1:

Establish variables.

Let (x) represent the distance the car has traveled north from the intersection, and let (y) represent the distance between the car and the person.

Step 2:

Formulate the equation using the Pythagorean theorem.

[tex]\[x^2 + y^2 = 24^2\][/tex]

Step 3:

Differentiate both sides of the equation with respect to time.

[tex]\[2x\frac{dx}{dt} + 2y\frac{dy}{dt} = 0\][/tex]

Step 4:

Plug in the given values and solve for [tex]\(\frac{dy}{dt}\)[/tex].

Given that the car is traveling north, [tex]\(\frac{dx}{dt} = 13\)[/tex]m/s.

When the car is 10 meters east, [tex]\(x = 10\).[/tex]

At that instant, when the car is 24 meters from the intersection, [tex]\(y = 24\).[/tex]

[tex]\[2(10)(13) + 2(24)\frac{dy}{dt} = 0\]\[260 + 48\frac{dy}{dt} = 0\]\[\frac{dy}{dt} = -\frac{260}{48} = -\frac{65}{12}\][/tex]

The rate of change of the distance between the car and the person at that instant is [tex]\(\boxed{-\frac{65}{12}}\)[/tex] meters per second. The negative sign indicates that the distance is decreasing.

Answer:

The mean, μ is 2.5063 and

The standard deviation, σ = 2.0499 × 10⁻²

Step-by-step explanation:

Here we have

[tex]z = \frac{x- \mu}{\sigma}[/tex]

[tex]z \sigma ={x- \mu}{}[/tex] and

10% have length < 2.48 in while

5% have length > 2.54 in

and

From the z score table

Critical z at 10% to the left = -1.282

Critical z at 5% to the right = 1.645

Therefore, the equations become

-1.282σ = 2.48 - μ → μ -1.282σ = 2.48

1.645σ = 2.54 - μ → μ + 1.645σ = 2.54

Solving the above equations gives

The mean, μ = 2.5063 and

The standard deviation, σ = 2.0499 × 10⁻².

Final answer:

Using the Z-score method and the percentages provided, two equations are set up and solved simultaneously to determine the mean and standard deviation of the lengths of the nails.

Explanation:

Given the information that 10% of the nails produced are shorter than 2.48 inches and that 5% are longer than 2.54 inches, and assuming the lengths are normally distributed, we can determine the mean (μ) and standard deviation (σ) of the lengths of the nails. We can use the Z-score formula which is (X - μ) / σ, where X is the value of the length, μ is the mean, and σ is the standard deviation.

Here, we have two Z-scores corresponding to the given percentages. For 10%, the Z-score is approximately -1.28, and for 5%, the Z-score is approximately 1.645. Now, setting up two equations,

(2.48 - μ) / σ = -1.28

(2.54 - μ) / σ = 1.645
we have a system of equations with two unknowns. Solving these equations simultaneously gives us the values for the mean and standard deviation of nail lengths.

To solve the system, multiply the first equation by σ to get μ = σ * -1.28 + 2.48 and the second equation by σ to get μ = σ * 1.645 + 2.54. By setting these two equations for μ equal to each other, you can solve for σ and afterwards find μ.

To solve the given system of equations:

1. (2.48 - μ) / σ = -1.28

2. (2.54 - μ) / σ = 1.645

We can use the method of substitution or elimination. Let's use the substitution method.

From equation 1, we can isolate  μ :

(2.48 - μ) / σ = -1.28

2.48 - μ = -1.28σ

μ = 2.48 + 1.28σ

Now, we substitute this expression for μ into equation 2:

(2.54 - (2.48 + 1.28σ)) / σ = 1.645

(2.54 - 2.48 - 1.28σ) / σ = 1.645

(0.06 - 1.28σ) / σ = 1.645

0.06 - 1.28σ = 1.645σ

0.06 = 1.645σ + 1.28σ

0.06 = 2.925σ

Now, we solve for  σ :

σ = [tex]\frac{0.06}{2.925}[/tex]

σ ≈ 0.0205

Now that we have found the value of \( σ \), we can substitute it back into the expression we found for \( μ \) to find its value:

μ = 2.48 + 1.28σ

μ = 2.48 + 1.28(0.0205)

μ ≈ 2.48 + 0.02628

μ ≈ 2.50628

So, the solution is approximately  μ ≈ 2.50628  and  σ ≈ 0.0205 .

Answer:

A=153.938 or 154

Step-by-step explanation:

A= pi r^2

A=pi(7)^2

A=pi(49)

A=153.938 or 154

Answer:

49π or 153.86

Step-by-step explanation:

Hi there,

The formula for area of a cirlcle is A = [tex]\pi[/tex][tex]r^{2}[/tex]

So, to find the area, simply plug in the radius into the equation.

A = π * [tex]7^{2}[/tex]

A = 49π

The area is either 49π or if you use 3.14 for pi, it's 153.86.

Hope this helps!

- Emily

Answer:

maybe 15 students or 63 students and if not I am sorry of that's wrong

Answer:

1; after 2 months

2; $130

Step-by-step explanation:

In this question, we are trying to compare the fees to be paid in two different gyms, to determine when the amount paid would be equal and also what this amount would be.

Now since we do not know the exact number of months, we can represent this unknown by x

so mathematically, at the end of m months, at the first gym , Casey would have paid a total of 50 + 40m

For the second gym, at the end of the second month, casey would have paid a total of 65m only

now we need to know when these fees would be the same. we simply equate what we have on both ends

mathematically, that is 50 + 40m = 65m

65m-40m = 50

25m = 50

m = 50/25

m = 2 months

The fees to be paid is

50 + 40(2) = 65(2) = $130

Answer:

3 people

Step-by-step explanation:

$51/$17 = 3 people

- We know to start with $51 dollars because that is the total price of the meal.

- We also know each meal costs $17.

- Next, ask youself what we are trying to find? We are trying to find how many people are eating.

- Therefore to find that we need to take our starting amount $51 divided by $17 because that is the cost of 1 meal.

- $51/$17 = 3 people (whole cost/individual cost = # of people)

- To check this take 3 x 17 = 51 (Now we know it is correct)

- If you would like a further explanation please let me know.

The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

Lydia is at a coffee shop and knows  she can spend no more than $65

before tax. She sees this price list in  the coffee shop.

Dark Roast Coffee    $7.50

Pumpkin Spice Coffee   $10.50

Breakfast Tea   $23.50

if Lydia buys 1/2 pound of the Breakfast Tea and 2 pounds of the Dark Roast coffee, how many 1- pound bags of Pumpkin Spice coffee can she buy?

Given Information:

Shopping Budge = $65

Price of   Dark Roast Coffee = $7.50

Price of Pumpkin Spice Coffee  = $10.50

Price of  Breakfast Tea  = $23.50

Amount of Breakfast Tea required = 1/2 pound

Amount of Dark Roast coffee required = 2 pounds

Required Information:

How many 1-pound  Pumpkin Spice Coffee can she buy = ?

Answer:

n = 3 bags of 1-pound Pumpkin Spice Coffee

Step-by-step explanation:

We are given that the amount of Breakfast Tea required is 1/2 pound so the cost of Breakfast Tea is

Cost of Breakfast Tea = 1/2*23.50 = $11.75

We are also given that the amount of Dark Roast coffee required is 2 pounds so the cost of Dark Roast coffee is

Cost of Dark Roast coffee = 2*7.50

Cost of Dark Roast coffee = $15

We know that total Lydia's total budget is $65

11.75 + 15 + 10.50x = 65

Where x represents the amount of Pumpkin Spice coffee required

10.50x = 65 - 11.75 - 15

10.50x = 38.75

x = 3.64 pounds

That means Lydia can buy 3.64 pounds of Pumpkin Spice coffee.

Now assuming that the Pumpkin Spice coffee is sold only in 1-pound bags then the required number of bags that Lydia can buy is

n = 3.64 pound/1-pound

n = 3.64

Since bags cannot be in fraction so

n = 3 bags

Note: we can not round off to 4 bags since that would surpass the given budged.

Answer:  

Last one: 5x - 3√y + 1

Step-by-step explanation:

8x + √1 - √9y - √9x^2

8x + 1 - 3√y - 3x

5x + 1 - 3√y

5x - 3√y + 1

CAN YOU PLEASE MARK MY ANSWER BRANLIEST

Which equation represents a proportional relationship?

C. y=1/2x+3

The question is not very clear, since the most logical thing is to think that the fraction is with respect to the number of baby teeth, if so:

6/20 and 3/10, these would be the two fractions.

But the literal question is to express the number 6, as a fraction.

We can do it by multiplying and dividing by the same number, for example:

6 * 2/2 = 12/2

6 * 10/10 = 60/10

This would be the two fractions.

The probability of choosing a sandwich at random with turkey and Swiss on wheat bread is calculated by multiplying the independent probabilities of selecting each component. With 2 bread choices, 3 meat choices, and 2 cheese choices, the calculated probability is 1/12.

To find the probability of choosing a sandwich at random with turkey and Swiss on wheat bread, we consider the possible options for each category that can be selected independently. We have 2 bread options (white or wheat), 3 meat options (ham, turkey, or chicken), and 2 cheese options (cheddar or Swiss). To find the probability of one specific combination, we multiply the probabilities of each choice.

The probability of selecting wheat bread is 1/2 because there are 2 options for bread. The probability of selecting turkey as the meat is 1/3 since there are 3 meat options. Finally, the probability of selecting Swiss cheese is 1/2, as there are 2 cheese options.

The combined probability is the product of these probabilities:

(1/2) * (1/3) * (1/2) = 1/12

So, the probability of randomly choosing a sandwich with turkey and Swiss on wheat bread is 1/12.

The probability of randomly selecting a sandwich with turkey and Swiss on wheat bread is 1 out of 12 possible combinations.

To find the probability of choosing a sandwich at random that is turkey and Swiss on wheat, we need to calculate the total number of possible different sandwich combinations and then find the probability of the one specific combination. There are 2 types of bread (white, wheat), 3 types of meat (ham, turkey, chicken), and 2 types of cheese (cheddar, Swiss). The total number of sandwich combinations is the product of the number of choices for each component: 2 * 3 * 2 = 12.

Only one of these combinations is turkey and Swiss on wheat. Therefore, the probability of randomly selecting a turkey and Swiss on wheat sandwich is 1 out of the total number of combinations. Mathematically speaking, the probability (P) is P =  1/12.

The deli sandwich scenario is related to a fundamental concept in statistics and probability, where you assess the outcomes of a certain event given a set of choices.

Answer:

Combine like terms is the first step.

Step-by-step explanation:

Subtract '122-7' on both sides and that gives you [tex]2x^2=-115[/tex]