A Lunar Rover carrying an astronaut wearing a space suit and backpack weighs 880 pounds 13 ounces. The astronaut wearing a space suit and backpack weighs 379 pounds 5 ounces. What is the weight of the Lunar Rover? lbs. oz.

Answer:

The answer is 3

Step-by-step explanation:

x×108=y

x×2²×3³=y

3×108=324

The sales tax rate is 6%

If the sales-tax rate is 6%, the tax paid on an $8.50 purchase would be:

Tax = 0.06 x $8.50

Tax = $0.51

Therefore, the total cost of the purchase including sales tax would be:

Total cost = $8.50 + $0.51

Total cost = $9.01

The sales tax rate is 6%.

to know more about sales tax

brainly.com/question/29442509

#SPJ1

The distribution over the random variable X, representing the number of kids between Izzy and Lizzy in line, is given by P(X=x) = 1/2, 1/4, 1/6, and 1/12 for x=1, 2, 3, and 4, respectively.

Let us assume that the other two kids are named A and B. We can represent the order of the four kids as a string of letters: ALIB or ALBI or ABLI or ABIL or AIBL or AILB. There are 4! = 24 possible ways to order the four kids, and in half of them, Izzy comes before Lizzy, and in half of them, Lizzy comes before Izzy. So there are 12 possible orders in which Izzy comes before Lizzy.

In 6 of these orders, there is one kid between Izzy and Lizzy (e.g., AILB). In 3 of these orders, there are two kids between Izzy and Lizzy (e.g., ABLI). In 2 of these orders, there are three kids between Izzy and Lizzy (e.g., ALBI). And in 1 of these orders, there are four kids between Izzy and Lizzy (e.g., ABIL).

Therefore, the distribution over x is

P(X=1) = 6/12 = 1/2

P(X=2) = 3/12 = 1/4

P(X=3) = 2/12 = 1/6

P(X=4) = 1/12

So the probability mass function of X is

P(X=x) =

1/2 if x=1

1/4 if x=2

1/6 if x=3

1/12 if x=4

Learn more about probability mass function here

brainly.com/question/30765833

#SPJ4

The simplified expression is 4(x - 3y).

logarithm, the exponent or power to which a base must be raised to yield a given number. Expressed mathematically, x is the logarithm of n to the base b if bx = n, in which case one writes x = logb n. For example, 23 = 8; therefore, 3 is the logarithm of 8 to base 2, or 3 = log2 8.

Using the following logarithmic identities:

log a (bc) = log a (b) + log a (c)

log a (b/c) = log a (b) - log a (c)

We can simplify the expression as follows:

2㏒4 x - 6 log4 y = 2(㏒4) x - 6(㏒4) y

= 2(㏒4) x - 2(㏒4)3 y

= 2(㏒4)(x - 3y)

Now, we can simplify further by using the fact that ㏒4 = 2:

2(㏒4)(x - 3y) = 2(2)(x - 3y) = 4(x - 3y)

Therefore, the simplified expression is 4(x - 3y).

Learn more about exponent or power here

https://brainly.com/question/15722035

#SPJ1

To find the inverse of a function, we need to swap the positions of x and y and then solve for y. In other words, we replace f(x) with y and then solve for x.

x = 5y - 6

Next, we'll solve this equation for y:

x + 6 = 5y

y = (x + 6)/5

According to the information, he test statistic for this sample is 5.

To calculate the test statistic for the Wilcoxon signed-rank test, we need to calculate the differences between the "before" and "after" engagement ratings and rank them in order of their absolute values.

Student Before After Difference Absolute Difference Rank

1 30 40 10 10 1

2 20 40 20 20 2

3 32 37 5 5 3

4 43 46 3 3 4

5 48 44 -4 4 5

The sum of the ranks for the positive differences is 1 + 2 + 3 + 4 = 10, and the sum of the ranks for the negative differences is 5.

The smaller of the two sums (in this case, the sum of the ranks for the negative differences) is the test statistic for the Wilcoxon signed-rank test.

Therefore, the test statistic for this sample is 5.

Learn more about statistic in: https://brainly.com/question/29093686

#SPJ1

Saanvi paid £5329.39 for the boat 13 years ago. This is based on the assumption that the boat depreciated at a constant rate of 2.5% per year. It is important to note that there could be other factors that affect the value of the boat, such as maintenance, repairs, and upgrades, which are not accounted for in this calculation.

How to solve the question?

To find out how much Saanvi paid for the boat, we can use the concept of depreciation. Depreciation is the reduction in value of an asset over time. In this case, the boat has depreciated at a rate of 2.5% per year.

Let the initial value of the boat be 'P'. After one year, the value of the boat would be 97.5% of P. After two years, it would be 95% of P, and so on. We can write this mathematically as:

Value of the boat after n years = P x (0.975)^n

We are given that the value of the boat after 13 years is £3115. Therefore, we can write:

3115 = P x (0.975)^13

Solving this equation for P, we get:

P = 3115 / (0.975)^13

P = 5329.39

Therefore, Saanvi paid £5329.39 for the boat.

In conclusion, Saanvi paid £5329.39 for the boat 13 years ago. This is based on the assumption that the boat depreciated at a constant rate of 2.5% per year. It is important to note that there could be other factors that affect the value of the boat, such as maintenance, repairs, and upgrades, which are not accounted for in this calculation.  

To know more about deprecition visit:-

https://brainly.com/question/27971176

#SPJ1

The decimal that represents the fraction of the $30.00 Maggie spent is 0.6.

Now, let's talk about decimals. Decimals are a way of expressing parts of a whole number in a fraction of 10. For example, 0.5 is the same as 1/2. In your situation, Maggie spent $18.00 out of $30.00. To figure out what decimal represents the fraction of the $30.00 Maggie spent, we need to divide the amount she spent by the total amount she had.

So, we can write this as a fraction:

$18.00 / $30.00

To turn this fraction into a decimal, we divide the numerator (top number) by the denominator (bottom number) using long division or a calculator.

$18.00 / $30.00 = 0.6

Another way to say this is that Maggie spent 60% of the money she had in her wallet.

To know more about decimal here

https://brainly.com/question/9543292

#SPJ4

a) The probability that the third hole drilled is the first to yield a productive well is given by the following sequence of events: the first two holes must be unproductive, followed by a productive third hole. The probability of each of these events happening is:

- Probability of an unproductive hole: 0.8

- Probability of two unproductive holes in a row: 0.8

The corrected statement should look like this:
```java
int[] hours = {8, 12, 16};
```

It looks like you are trying to create an integer array in Java called "hours" and initialize it with the values 8, 12, and 16. The given statement has incorrect syntax.
Declare the integer array using "int[]" followed by the variable name "hours".

This tells the Java compiler that you want to create an array of integers called "hours".
Use the assignment operator "=" to assign values to the array.
Enclose the values you want to assign to the array within curly braces "{" and "}" and separate each value with a comma.
The corrected statement should look like this:
```java
int[] hours = {8, 12, 16};
```
Now, the "hours" integer array is initialized correctly with the given values.

The syntax for declaring and initializing an integer array in Java is:

```java
data Type[] array

Name = {value1, value2, value3, ...};
```
In this case, "data Type" is "int", "array

Name" is "hours", and the values are 8, 12, and 16.
Remember to keep your code clean and concise to avoid syntax errors and make it easier for others to understand.

For similar question on statement.

https://brainly.com/question/26134656

#SPJ11

By using Pythagorean theorem, we find that the shortest distance from Krista's home to her work is approximately 1.19 miles.

To find the shortest distance from Krista's home to her work, we can use the Pythagorean theorem. Let's convert the distances to a common unit, such as miles

Distance from grocery store to work = 500 m = 0.31 miles (since 1 mile = 1609.34 meters)

Total distance from home to work = 2 km = 1.24 miles (since 1 mile = 1.609 km)

Let's call the distance from Krista's home to the grocery store "x". Then, we can set up the following equation

x^2 + 0.31^2 = 1.24^2

Simplifying and solving for x, we get

x^2 = 1.24^2 - 0.31^2 = 1.4223

x = √1.4223 ≈ 1.19 miles

Therefore, the shortest distance is approximately 1.19 miles.

To know more about Pythagorean theorem:

https://brainly.com/question/14930619

#SPJ4

--The given question is incomplete, the complete question is given

" Krista needs to stop at the grocery store on the way home from her work. What is the shortest distance, in miles, from Krista's home to her work? the distance from grocery store to work is 500m, and the total distance from home to work is 2km"--

The value of the line integral ∫_C F.dr for the given circle C and vector field F is -2πr

To evaluate the line integral ∫_C F.dr, we first need to parameterize the circle C. We can do this by letting x = r cos(t) + 1, y = r sin(t) + 1, and z = 3 - x - y = 1 - r cos(t) - r sin(t), where 0 ≤ t ≤ 2π and r is the radius of the circle.

We can then compute the differential of r with respect to t

dr/dt = (-r sin(t))i + (r cos(t))j - r(sin(t) + cos(t))k

Next, we can evaluate F at the point (x,y,z) on C:

F = (z - y)i + (x - 2)j + (y - x)k

= (1 - r cos(t) - r sin(t) - (r sin(t) + 1))i + (r cos(t) - 1)j + ((r sin(t) + 1) - r cos(t))k

= (-r cos(t) - r sin(t) - 2)i + (r cos(t) - 1)j + (r sin(t) - r cos(t) + 1)k

We can then compute the dot product of F with dr/dt:

F · dr/dt = (-r cos(t) - r sin(t) - 2)(-r sin(t)) + (r cos(t) - 1)(r cos(t)) + (r sin(t) - r cos(t) + 1)(-r(sin(t) + cos(t)))

= r^2(sin(t) + cos(t)) - 2r(cos(t) + sin(t)) - r^2(sin(t) + cos(t)) + r(sin(t) + cos(t)) - r(sin(t) + cos(t))

= -r(cos(t) + sin(t))

Finally, we can evaluate the line integral

∫_C F.dr = [tex]\int\limits^{2\pi }_0[/tex] F · dr/dt dt

=  [tex]\int\limits^{2\pi }_0[/tex]  [-r(cos(t) + sin(t))] dt

= -2πr

Learn more about line integral here

brainly.com/question/28081626

#SPJ4

The given question is incomplete, the complete question is:

Find ∫_C F.dr where C is circle of radius in the plane x +Y +2 = 3, centered at (1, 1, 1) and oriented clockwise when viewed from the origin_ F= (z - y)i + (x - 2)j + (y - x)k

answer below

Step-by-step explanation:

4 is the answer

just sub in 2 for x

To reduce the width of a confidence interval, you can use a smaller sample size and decrease the level of confidence, or use a larger sample size and decrease the level of confidence.

What are the factors?

what are factorsIn mathematics, a factor is a number that divides another number without leaving a remainder.

The combination of factors that would definitely cause the confidence interval to become wider is to use a larger sample and increase the level of confidence or to use a smaller sample and increase the level of confidence.

When using a larger sample size, the standard error of the mean decreases, and the interval will become narrower. Conversely, when using a smaller sample size, the standard error of the mean increases, and the interval will become wider. However, increasing the level of confidence will also increase the width of the interval as a wider interval is required to capture the true population parameter with a higher level of confidence.

Therefore, to reduce the width of a confidence interval, you can use a smaller sample size and decrease the level of confidence, or use a larger sample size and decrease the level of confidence.

To learn more about factors from the given link:

brainly.com/question/14209188

#SPJ1

The analysis of the bank statement thus, given below. Since the result is negative, this means that Andre would still have a negative balance after depositing $100, and therefore would still be in debt.

1. If we put withdrawals and deposits in the same column, they can be represented as positive and negative values in a single column. Deposits would be represented with positive values, and withdrawals would be represented with negative values.

2. Andre's new balance would be $16.37. We can calculate this by subtracting $40 (the withdrawal) from his previous balance of $56.37:

$56.37 - $40 = $16.37

3. If Andre deposits $100 in this account, he will no longer be in debt. We can calculate his new balance by adding his previous balance and the deposit, and then subtracting any withdrawals:

$56.37 + $100 = $156.37 (balance after the deposit)

$156.37 - $28.50 - $37.91 - $16.43 - $42.00 - $72.50 - $45.00 - $50.00 - $10.03 - $62.47 = -$49.47

Since the result is negative, this means that Andre would still have a negative balance after depositing $100, and therefore would still be in debt.

Learn more about bank statement at:

https://brainly.com/question/22786262

#SPJ1

The painting will be worth approximately $11,592.74 in 5 years when it increases at a rate of 3%

A quantity increases at a steady pace proportionate to its present value in an exponential growth pattern. In other words, a quantity expands more quickly the larger it is. Y = ab raise to x, where an is the starting value, b is the growth factor (i.e., the amount by which the quantity increases each time period), and x is the number of time periods, is frequently used to represent exponential growth.

The value of the painting after 5 years can be calculated using the exponential growth formula:

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

Substituting the values  P = $10,000, r = 0.03, n = 1, and t = 5 we have:

A = 10000(1 + 0.03/1)^(1*5)

A = $11,592.74

Hence, the painting will be worth approximately $11,592.74 in 5 years.

Learn more about exponential growth here:

https://brainly.com/question/12490064

#SPJ1

Answer:

Vertex = (-3, -4)

Step-by-step explanation:

The given graph is a parabola that opens upwards.

The vertex of a parabola that opens upwards is its lowest point (minimum value).

From inspection of the given graph, the lowest point is (-3, -4).

Therefore, the vertex of the parabola is (-3, -4).

There are 73,701 different 6-card hands (from a standard deck) with at least 3 kings.

To calculate the number of 6-card hands with at least 3 K's, the problem can be divided into:

Case 1:

Exactly 3 Kings

There are 4 ways to choose 3 kings to put in the hand, then there are 48 cards left to choose the remaining 3 cards (because we used 3 cards in a 52-card deck). Therefore, the number of 6-card hands with exactly 3 kings is:

4 * (48 choose 3) = 4 * 17,296 = 69,184

Case 2:

Exactly 4 Kings

There are 4 ways to choose 4 kings to put in the hand, then there are 48 cards left to choose the remaining 2 cards. Therefore, the number of 6-card hands with exactly 4 kings is:

4 * (48 choose 2) = 4 * 1.128 = 4.512

Case 3:

Exactly 5 kings

There are 4 ways to choose the 5 kings in the hand, then there is only one card left to choose from (because we used 5 of the 52 cards in the deck of cards). Therefore, the number of 6-card hands with exactly 5 kings is:

4*1=4

Case 4:

6 cards are king

There is only one way to choose all 6 cards as king.

Therefore, the total number of 6-card hands with at least 3 kings is:

69,184 + 4,512 + 4 + 1 = 73.701

So there are 73,701 different 6-card hands with at least 3 kings.  

learn more about the deck of cards

brainly.com/question/30519560

#SPJ4

The probability of someone randomly selecting a computer that does not have a virus is 0.8.

Total number of computers = 20

Virus affected = 4

Perfect computers = 20 - 4 = 16

The probability of choosing a computer that does not have a virus is equivalent to the number of computers without a virus and divided by the total number of computers in the lab.

The probability of selecting a computer without a virus is:

P(C) = 16/20

Simplifying this fraction, we get:

P(20 - 4 = 16) = 4/5

P(20 - 4 = 16) = 0.8

Therefore we can conclude that the probability of someone randomly selecting a computer that does not have a virus is 0.8.

To learn more about Probability,

https://brainly.com/question/30034780

#SPJ4

Answer:

[tex]a_{n}[/tex] = - 5n - 2

Step-by-step explanation:

there is a common difference between consecutive terms , that is

a₂ - a₁ = - 12 - (- 7) = - 12 + 7 = - 5

a₃ - a₂ = - 17 - (- 12) = - 17 + 12 = - 5

a₄ - a₃ = - 22 - (- 17) = - 22 + 17 = - 5

a₅ - a₄ = - 27 - (- 22) = - 27 + 22 = - 5

this indicates the sequence is arithmetic with nth term

[tex]a_{n}[/tex] = a₁ + d(n - 1)

a₁ is the first term and d the common difference

here a₁ = - 7 and d = - 5 , then

[tex]a_{n}[/tex] = - 7 - 5(n - 1) = - 7 - 5n + 5 = - 5n - 2

The value of m∠1 in the given diagram is 113 (last option)

From the diagram given above, we obtained the following data:

Considering the above, we can easily obtain the value of m∠1 as follow:

m∠1 + 67 = 180 (angle on a straight line)

Collect like terms

m∠1 = 180 - 67

m∠1 = 113

Thus, we can conclude from the above calculation that the value of m∠1 is 113 (last option)

Learn more about vertically opposite angle:

https://brainly.com/question/29747440

#SPJ1

Answer:

x = 4√5 ≈ 8.94 (2 d.p.)

y = 8√5 ≈ 17.89 (2 d.p.)

Step-by-step explanation:

To find the values of x and y, use the Geometric Mean Theorem (Leg Rule).

The altitude drawn from the vertex of the right angle perpendicular to the hypotenuse separates the hypotenuse into two segments. The ratio of the hypotenuse to one leg is equal to the ratio of the same leg and the segment directly opposite the leg.

[tex]\boxed{\sf \dfrac{Hypotenuse}{Leg\:1}=\dfrac{Leg\:1}{Segment\;1}}\quad \sf and \quad \boxed{\sf \dfrac{Hypotenuse}{Leg\:2}=\dfrac{Leg\:2}{Segment\;2}}[/tex]

From inspection of the given right triangle RST:

Substitute the values into the formulas:

[tex]\boxed{\dfrac{20}{y}=\dfrac{y}{16}}\quad \sf and \quad \boxed{\dfrac{20}{x}=\dfrac{x}{4}}[/tex]

Solve the equation for x:

[tex]\implies \dfrac{20}{x}=\dfrac{x}{4}[/tex]

[tex]\implies 4x \cdot \dfrac{20}{x}=4x \cdot \dfrac{x}{4}[/tex]

[tex]\implies 80=x^2[/tex]

[tex]\implies \sqrt{x^2}=\sqrt{80}[/tex]

[tex]\implies x=\sqrt{80}[/tex]

[tex]\implies x=\sqrt{4^2\cdot 5}[/tex]

[tex]\implies x=\sqrt{4^2}\sqrt{5}[/tex]

[tex]\implies x=4\sqrt{5}[/tex]

Solve the equation for y:

[tex]\implies \dfrac{20}{y}=\dfrac{y}{16}[/tex]

[tex]\implies 16y \cdot \dfrac{20}{y}=16y \cdot \dfrac{y}{16}[/tex]

[tex]\implies 320=y^2[/tex]

[tex]\implies \sqrt{y^2}=\sqrt{320}[/tex]

[tex]\implies y=\sqrt{320}[/tex]

[tex]\implies y=\sqrt{8^2\cdot 5}[/tex]

[tex]\implies y=\sqrt{8^2}\sqrt{5}[/tex]

[tex]\implies y=8\sqrt{5}[/tex]

The correct option - D. 25sin²(15%) is the value of the [5sin(15%)]² found using concept of squaring.

When a number is multiplied by itself, the result is a square number. As an illustration, 25 is a square number since it is composed of 5 groups of 5, or 5 x 5. This is also known as "five squared,".

Given that-

= [5sin(15%)]²

Using the property of indices that:

(ab)² = a².b²

= (5)²sin(15%)²

On simplification:

= 25 sin(15%)²

This can be written as -

= 25 sin²(15%)

Thus, the value of [5sin(15%)]² is found as - 25 sin²(15%).

know more about the squaring:

https://brainly.com/question/27307830

#SPJ1

Always check the quantity in each package to determine the appropriate number of hotdog bun packages needed for the given number of hotdog packages.
The dependent variable in this situation is the number of packages of hotdog buns needed, as it relies on the number of packages of hotdogs (the independent variable).

We want to know the dependent variable when considering the number of packages of hotdog buns needed for a certain number of packages of hotdogs.

Let me explain this relationship:
First, let's define the terms involved.

The dependent variable is the variable that depends on another variable (called the independent variable).

In this case, we are examining the relationship between the number of packages of hotdogs and the number of packages of hotdog buns needed.
The independent variable is the number of packages of hotdogs.

This is because the number of hotdog buns needed depends on the number of hotdogs you have.
The dependent variable, in this case, is the number of packages of hotdog buns needed.

This variable depends on the number of packages of hotdogs, as you need a certain amount of buns to accommodate the hotdogs.

To determine the relationship between these two variables, we would likely use a proportion or a ratio.

For example, if one package of hotdogs contains 10 hotdogs and one package of hotdog buns contains 10 buns, then the ratio is 1:1, meaning you need one package of hotdog buns for every package of hotdogs.
This relationship may vary depending on the number of hotdogs and buns in each package.

Remember to examine the proportion between the two variables to ensure you have the correct amount of buns for the hotdogs.

For similar question on proportion.

https://brainly.com/question/14869217

#SPJ11

(13) Angle A, angle B and angle C are collinear and are proved.

(14) Based on corresponding angles theorem, X is bisector of angle A.

The sum of the measures of collinear angles is always 180 degrees, as they together form a straight angle.

If we consider triangle PCQ;

Since line CP = line CQ; then angle P = angle Q = x

m∠PCQ = 180 - 2x

If we consider triangle PBQ;

Since line PB = line BQ; then angle P = angle Q = x

m∠PBQ = 180 - 2x

If we consider triangle PAQ;

Since line AP = line AQ; then angle P = angle Q = x

m∠PAQ = 180 - 2x

Thus, angle A, angle B and angle C are collinear.

14. To prove that X is a bisector A;

Draw a line parallel to AN from point B to opposite side, call this point Y

Angle formed from line M to line BY, is a corresponding angle to angle formed from line M to line AN.

If X is the bisector of angle B, then it is also a bisector angle A since both angles are equal.

Learn more about collinear angles here: brainly.com/question/30367908

#SPJ1

They simply measured their urinary sodium and potassium levels and followed them for cardiovascular events. Therefore, this is an observational study.

This study is an observational study. The reason for this classification is that the researchers did not manipulate the variables (urinary sodium and potassium excretion) and instead collected data on the participants' natural behaviours and outcomes (risk of clinical cardiovascular disease) over time. In experimental and quasi-experimental studies, researchers actively manipulate variables to assess the cause-and-effect relationships between them, which is not the case in this study.

Therefore, They simply measured their urinary sodium and potassium levels and followed them for cardiovascular events. Therefore, this is an observational study.

Learn more about Observational Study here: brainly.com/question/28191144

#SPJ11

This is an observational study that aims to determine the relationship between urinary sodium (and potassium) excretion and the risk of clinical cardiovascular disease among patients with chronic kidney disease.

This is an observational study aimed at investigating the relationship between urinary sodium (and potassium) excretion and the risk of clinical cardiovascular disease (CVD) among patients with chronic kidney disease (CKD).

The study included 3,939 racially and ethnically diverse participants, approximately half of whom had diabetes, recruited from 7 clinical centers in the United States between 2003 and 2008. Eligible participants had age-specific estimated glomerular filtration rate (eGFR) criteria of 20 to 70 ml/min/1.73 m2 and did not have a history of kidney transplant, dialysis for at least 1 month, glomerulonephritis requiring immunosuppression, advanced heart failure, cirrhosis, or polycystic kidney disease.

The study used a prospective design, where data were collected over a period of time, to estimate the mean of three 24-hour urine samples from each participant.

Urinary sodium and potassium levels were measured using flame emission spectrophotometry, and cardiovascular clinical outcomes were assessed using a standard medical event questionnaire at all follow-up contacts.

Medical records were requested for event verification, and two physicians adjudicated each cardiovascular event and classified them as either probable or definite.

Since the researchers did not intervene or manipulate any variables, this study is an observational study.

The researchers observed and measured the relationship between urinary sodium (and potassium) excretion and the risk of CVD among participants with CKD over a period of time.

The study's findings may provide valuable insights into the relationship between urinary sodium and potassium excretion and CVD risk among CKD patients, which could inform future interventions to reduce CVD risk in this population.

For similar question on observational study.

https://brainly.com/question/25257437

#SPJ11

The actual distance between the two towns is 337.5 miles.

What is distance?

Distance is the measure of how far apart two objects or locations are from each other. It is usually measured in units such as meters, kilometers, miles, or feet. Distance is a scalar quantity, meaning it has only magnitude and no direction.

If 1/2 inch on the map represents 75 miles in reality, then 1 inch on the map would represent 150 miles (twice the distance of 1/2 inch).

So, to find the actual distance between the two towns, we need to multiply the distance on the map (2 1/4 inches) by the conversion factor (150 miles per inch):

2 1/4 inches * 150 miles per inch = (9/4) inches * 150 miles per inch

Simplifying:

(9/4) inches * 150 miles per inch = 337.5 miles

Therefore, the actual distance between the two towns is 337.5 miles.

To learn more about distance from the given link:

https://brainly.com/question/30923151

#SPJ1

The next time the walking and bus tours will start at the same time is 11:45 a.m.

What is the lcm?

The LCM is multiple which is useful if fractions need to be expressed in the same name, when the other number is multiple, LCM will have the larger number:

To find out when the walking and bus tours will start at the same time, we need to find the least common multiple (LCM) of 25 and 45, which is the smallest time interval that is a multiple of both 25 minutes and 45 minutes.

The prime factorization of 25 is 5 * 5, and the prime factorization of 45 is 3 * 3 * 5. To find the LCM, we take the highest power of each prime factor that appears in either factorization, so:

LCM = 3 * 3 * 5 * 5 = 225

Therefore, the walking and bus tours will start at the same time every 225 minutes, or 3 hours and 45 minutes. To find the next time they will start at the same time, we need to add 225 minutes to the starting time of 8:00 a.m.

8:00 a.m. + 3 hours and 45 minutes = 11:45 a.m.

Hence, the next time the walking and bus tours will start at the same time is 11:45 a.m.

To learn more about the LCM visit:
https://brainly.com/question/233244

#SPJ1

Answer: -12d+(4/(4d+7))

Step-by-step explanation:

To simplify the expression –48d^2 – 132d – 80 ÷ (4d + 7), we can use long division:

           -12d

      ____________

   4d + 7 | -48d^2 - 132d - 80

            48d^2 + 84d

            ___________

                       - 48d - 80

                       + 48d + 84

                       ___________

                                4

Therefore, the simplified expression is -12d + (4/(4d + 7))

The equivalent ratio of dollars to pizza for 4 pizzas is 12 : 1.

A ratio is a comparison of two or more quantities that are related to each other in some way. It is expressed as a fraction or using the "colon" notation.

If Mike pays 12 dollars for one pizza, the ratio of dollars to pizza is:

12 : 1

To find the equivalent ratio for 4 pizzas, we need to keep the ratio of dollars to pizza constant. We can do this by multiplying both the numerator and denominator of the ratio by 4, since we are now dealing with 4 pizzas instead of 1. This gives us:

12 x 4 : 1 x 4

Simplifying this ratio gives us:

48 : 4

We can further simplify this ratio by dividing both the numerator and denominator by 4, which gives us:

12 : 1

Therefore, the equivalent ratio of dollars to pizza for 4 pizzas is 12 : 1.

To know more about ratio visit:

https://brainly.com/question/12024093

#SPJ1