Joseph drives 125 miles in 2 1/2 hour. At the same rate, how far will he be able to travel in 6 3/4 hours?

Answer:

b. 41.43gallons

Step-by-step explanation:

no of gallon = distance/rate(fuel economy)

=1243/30

=41.4333333333gallons

Answer:

5 meters

Step-by-step explanation:

Answer:

5 meters

Step-by-step explanation:

;)

Part (a)

x = number of adults

y = number of students

5x = amount all of the adults paid ($5 each)

2y = amount the students paid ($2 each)

5x+2y = total amount of money for adults and students combined

The total amount (5x+2y) must be more than $150

So we end up with 5x+2y > 150 as the inequality.

This inequality involves the boundary line 5x+2y = 150 which goes through the y and x intercepts of (0,75) and (30,0) respectively. We use a dashed line for the boundary to mean that points on the boundary are not included as solution points.

We shade above the dashed boundary line to finish off the graph.

Refer to figure (a) shown below.

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

Part (b)

x = number of adults

y = number of students

x+y = total number of people

120 seats is the max capacity so x+y cannot exceed this value.

x+y = 120 or x+y < 120

Or in short x+y ≤ 120 is the inequality

This involves the boundary line x+y = 120 which goes through the y and x intercepts of (0,120) and (120,0). We shade below the solid boundary line.

Refer to figure (b) shown below.

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

Part (c)

Now imagine we overlapped the blue region from part (a) and the red region from part (b)

We'll get the purple region shown in figure (c). At this point, I'm only considering cases when x ≥ 0 and when y ≥ 0. It's not possible to have a negative number of people, so that's why we focus on the upper right quadrant of the xy grid.

This purple region consists of all (x,y) points that make ALL of the inequalities to be true. Exclude any points on the dashed boundary.

For example, if we picked the point (x,y) = (50,40) then this point is in the purple region. We can confirm its a solution by checking each inequality.

5x+2y > 150

5*50+2*40 > 150

250+80 > 150

330 > 150  .... which is true

and,

x+y ≤ 120

50+40 ≤ 120

90 ≤ 120 ... which is also true

Furthermore, both x and y are nonnegative making x ≥ 0 and y ≥ 0 to be true as well. Every inequality mentioned is true for (x,y) = (50,40) to fully confirm the solution point. There are other possible solutions such as (40,60) and (80,20) which I'll let you verify.

If we stick to the (50,40) from earlier, then this means 50 adults and 40 students went to the concert.

Other answers are possible

1 1/4

4 fits into five once, leaving 1/4 left making it a mixed number.

The final result of the integral is:

∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,

where Li(x) is the logarithmic integral function and C is the constant of integration.

We have,

To solve the integral ∫ (log(1 + x²) / (x + 1)²) dx, we can use the method of substitution.

Let's substitute u = x + 1, which implies du = dx. Making this substitution, the integral becomes:

∫ (log(1 + (u-1)²) / u²) du.

Expanding the numerator, we have:

∫ (log(1 + u² - 2u + 1) / u²) du

= ∫ (log(u² - 2u + 2) / u²) du.

Now, let's split the logarithm using the properties of logarithms:

∫ (log(u² - 2u + 2) - log(u²)) / u² du

= ∫ (log(u² - 2u + 2) / u²) du - ∫ (log(u²) / u²) du.

We can simplify the second integral:

∫ (log(u²) / u²) du = ∫ (2 log(u) / u²) du.

Using the power rule for integration, we can integrate both terms:

∫ (log(u² - 2u + 2) / u²) du = log(u² - 2u + 2) / u - 2 ∫ (log(u) / u³) du.

Now, let's focus on the second integral:

∫ (log(u) / u³) du.

This integral does not have a simple closed-form solution in terms of elementary functions.

It can be expressed in terms of a special function called the logarithmic integral, denoted as Li(x).

Therefore,

The final result of the integral is:

∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,

where Li(x) is the logarithmic integral function and C is the constant of integration.

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Answer:

zeroay horizontal stretch vertical shrink

Step-by-step explanation:

1+1=2

To sketch the graph of the function y = 4(4)^x, we can start by plotting a few points to get an idea of the shape of the graph.

Let's choose some x-values and calculate the corresponding y-values:

For x = -2, y = 4(4)^(-2) = 4(1/16) = 1/4

For x = -1, y = 4(4)^(-1) = 4(1/4) = 1

For x = 0, y = 4(4)^0 = 4(1) = 4

For x = 1, y = 4(4)^1 = 4(4) = 16

For x = 2, y = 4(4)^2 = 4(16) = 64

Now we can plot these points on a coordinate plane and connect them to form the graph of the function.

The graph of y = 4(4)^x will start at the point (0, 4) and increase rapidly as x increases. It is an exponential growth function where the base is 4.

The domain of the function is all real numbers since there are no restrictions on the values of x.

The range of the function is the set of positive real numbers greater than zero. As x increases, y grows without bound, approaching positive infinity but never reaching zero or becoming negative.

The mechanical advantage of the given machine is 40, Velocity ratio is 80 and efficiency is 0.5.

The given question is concerned with finding the mechanical advantage, velocity ratio and efficiency of a weight lifting machine.

The problem has provided the following information:

Weight of the object, W = 1 kN = 1000 NEffort applied, E = 25 NHeight through which the object is lifted, h = 100 mm = 0.1 m Distance through which the effort is applied, d = 8 m

We know that, mechanical advantage = load/effort = W/E and velocity ratio = distance moved by effort/distance moved by the load.Mechanical advantage

The mechanical advantage of the given machine is given by; Mechanical advantage = load/effort = W/E= 1000/25= 40Velocity ratioThe velocity ratio of the given machine is given by;

Velocity ratio = distance moved by effort/distance moved by the load.= d/h = 8/0.1= 80EfficiencyThe efficiency of the given machine is given by;

Efficiency = (load × distance moved by load) / (effort × distance moved by effort)Efficiency = (W × h) / (E × d)= (1000 × 0.1) / (25 × 8)= 0.5

Therefore, the mechanical advantage of the given machine is 40, velocity ratio is 80 and efficiency is 0.5.

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Answer:

all

Step-by-step explanation:

Answer: 48 more monthly payments

Step-by-step explanation:

Answer:

((1+2)x3) + (4x5) = 29

Step-by-step explanation:

Since 4x5 = 20 and 3x3 = 9, and 9 + 20 = 29, we put parenthesis around 1+2,

we get,

((1+2)x3) + (4x5) = 29

This is true because,

(3x3) + (4x5) = 29

(9) + (20) = 29

29 = 29

Answer:

3x-4y-9

Step-by-step explanation:

Combine like terms

Check the picture below.

\((5x)+(5x)+(4x+3)(4x+3)=132\implies 18x+6=132\implies 18x=126 \\\\\\ x=\cfrac{126}{18}\implies x=7\hspace{9em}\underset{RS }{\stackrel{ 5(7) }{\text{\LARGE 35}}}\)

Answer:

39

Step-by-step explanation:

12+2×12+3

12+24+3

36+3

39

PEMDAS

Answer: D

Step-by-step explanation: You're Welcome

*Answer*

15:47

Step-by-step explanation:

He left; 15:03

Walk for; 12mins

Spends extra;4min

So by my side,

I'll sum up those values we're having to find the total time that was spent

12+4= 16mins

So, at that time when he reached at the station it was 15:19 when we add those extra mins

And so I think it'll 15:47

My thought told me so though

Answer:

The answer is 375

Step-by-step explanation:

You divide 500 by four and then you get 125. And then after you want to multiply 125 by 3 the numerator and then you get 375. And the way you get four in the equation is when you divide the number by the denominator.

Answer:

375.)

Step-by-step explanation:

First, let's write the problem:

500/1 × 3/4

Now in these types of problems, you can simplify by using a trick.

Do you see how 500 and 4 are across each other? Since 500 is divisible by 4:

500 ÷ 4 = 125.

So now we have 125/1 × 3/1 which is a lot easier to work with.

125 × 3 = 375

1 × 1 = 1

375/1 or 375

Therefore, 375 seats are filled.

x = 301/56

Algebra is the branch of mathematics that deals with numbers and values which are represented with letters and symbols.

Sometimes, we do not want to mention a particular number, we can represent the number by a letter or a suitable symbol. This approach is algebraic.

For example, d + d = 2d

This is an example of an algebraic expression

Given the algebraic expression,

\(3\frac{1}{8} \div (x - 4 \frac{7}{28} ) = \frac{17}{18} + 1 \frac{5}{6} \)

Step 1:

Simplify the expression by converting the mixed numbers into improper fractions:

25/8 ÷ ( x - 119/28) = 17/18 + 11/6

Step 2: Simplify the right side of the equation

25/8 ÷( x - 119/28) = 17/18 + 33/18

25/8 ÷( x - 119/28) = 50/18

Step 3: Multiply both sides of the equation by (x - 119/28)

25/8 = 50/18 × (x - 119/28)

Step 4: Multiply both sides of the equation by (18/50)

25/8 × (18/50) = (x - 119/28)

Step 5: Simplify the left side of the equation

9/8 = (x - 119/28)

Step 6: Add 119/28 to both sides of the equation

9/8 + 119/28 = x

Step 7: Calculate the value of x:

x = 9/8 + 119/28

= 63/56 + 238/56

= 301/56

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This kind of statistical study is called a meta analysis.

The aim of a scientific study is often to establish cause and effect relationships. The studies examine the effect of one variable on another in order to identify patterns.

A study based on many previous studies is called meta analysis. This kind of study examines data obtained from several independent studies on a particular subject and tries to arrive at meaningful conclusions.

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Answer:

3 Stamps left

Step-by-step explanation:

275/8=34.375

34*8=272

275-272=3

Answer: 3

The solution to the linear system is c = -6 and d = 3.

To solve the linear system using the elimination strategy, we can eliminate one variable by adding or subtracting the equations. Let's solve the first linear system:

(1) 12c + 28d = 12

(2) -20c + 16d = 168

To eliminate one variable, we can multiply equation (1) by 5 and equation (2) by 3, which will result in opposite coefficients for 'c'. This will allow us to eliminate 'c' when adding the equations together:

(1) 60c + 140d = 60

(2) -60c + 48d = 504

Now, we can add the equations:

(60c + 140d) + (-60c + 48d) = 60 + 504

188d = 564

d = 564/188

d = 3

Substituting the value of 'd' back into equation (1):

12c + 28(3) = 12

12c + 84 = 12

12c = 12 - 84

12c = -72

c = -72/12

c = -6

The solution to the linear system is c = -6 and d = 3.

Now let's analyze the second linear system:

(1) 7x - 3y = 43

(2) 7x - 3y = 13

By comparing the two equations, we can see that they have the same coefficients for both 'x' and 'y', and the constant terms on the right side are different. This means the lines represented by the equations are parallel and will never intersect.

The linear system has no solution.

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Answer: Consider me the brainiest. The answer is... Decimal form =4.083

Exact form= 49/12

The mixed number form=4 1/12

How do we solve fractions step by step?

Conversion a mixed number 2  1/3 to a improper fraction: 2 1/3 = 2  1/3 = 2 3 + 1/3 = 6 + 1/3 = 7/3

To find a new numerator

A;   Multiply the whole number 2 by the denominator 3. Whole number 2 equally 2 * 3/3 = 6/3

b) Add the answer from the previous step 6 to the numerator 1. The new numerator is 6 + 1 = 7

c) Write a previous answer (new numerator 7) over the denominator 3.

Two and one-third are seven-thirds.

Conversion a mixed number 1  3/4 to a improper fraction: 1 3/4 = 1  3/4 = 1 · 4 + 3/4 = 4 + 3/4 = 7/4

To find a new numerator:

a) Multiply the whole number 1 by the denominator 4. Whole number 1 equally 1 * 4/4 = 4/4

b) Add the answer from the previous step 4 to the numerator 3. The new numerator is 4 + 3 = 7

c) Write a previous answer (new numerator 7) over the denominator 4. One and three quarters are seven quarters.

Add: 7/3 + 7/4 = 7 · 4/3 · 4 + 7 · 3/4 · 3 = 28/12 + 21/12 = 28 + 21/12 = 49/12 It

is suitable to adjust both fractions to a common (equal, identical) denominator for adding, subtracting, and comparing fractions.  The common denominator you can calculate as the least common multiple of both denominators - LCM(3, 4) = 12.  It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 3 × 4 = 12. In the following intermediate step, it cannot further simplify the fraction result by cancelling.  In other words - seven thirds plus seven quarters is forty-nine twelfths.

Answer: A (4)

Step-by-step explanation: -5 (-2) - 6 = 4

Answer:

x=3 y=1 i it's the answer❤

The monthly cell phone bill when shared data equals zero is given as follows:

$26.

The slope-intercept representation of a linear function is given by the equation presented as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

The intercept of the line in this problem is given as follows:

b = 26.

Hence $26 is the monthly cell phone bill when shared data equals zero.

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Answer:

The selling price of the diamond necklace at Shamin Jewelers after 10% discount is:

$442 * 0.9 = $397.80

The selling price of the same necklace at the competitor's store after 34% and 14% discount is:

$527 * 0.66 * 0.86 = $247.08

So, Shamin Jewelers needs to offer an additional discount to meet the competitor's price:

$397.80 - $247.08 = $150.72

To calculate the additional rate of discount, we divide the difference by the original selling price at Shamin Jewelers and multiply by 100:

($150.72 / $442) * 100 = 34.11%

Therefore, Shamin Jewelers must offer an additional 34.11% discount to meet the competitor's price.

Step-by-step explanation:

Answer:

\(\huge\boxed{\sf 38}\)

Step-by-step explanation:

= a³ + b (6 + c)

Put a = 2, b = 3 and c = 4

= (2)³ + 3 (6 + 4)

= 8 + 3(10)

= 8 + 30

\(\rule[225]{225}{2}\)

Answer:

Step-by-step explanation:

the requied answer is 38.

according to the question the value of a=2,b=3,c=4.

here,

to find the value of   a³ + b (6 + c)we have to do it in steps:

step 1: solve the bracket (6+4) =10.

step 2:  solve the value of a³ =8.

now put these values ,

=8+3(10)

=38.

The limit lim(x approaches 0) (cosec(2x) - x*cosec³(x)) is undefined.

We have,

To evaluate the limit of the expression as x approaches 0, we can simplify the expression first.

The expression is given as lim(x approaches 0) (cosec(2x) - x cosec³(x)).

Using trigonometric identities, we can rewrite cosec(2x) as 1/sin(2x) and cosec³(x) as 1/(sin(x))³.

Substituting these into the expression,

We get lim(x approaches 0) (1/sin(2x) - x (1/(sin(x))³)).

Now, let's evaluate the limit term by term:

lim(x approaches 0) (1/sin(2x)) = 1/sin(0) = 1/0 (which is undefined).

lim(x approaches 0) (x (1/(sin(x))³))

= 0 (1/(sin(0))³)

= 0 x 1/0 (which is also undefined).

Since both terms of the expression are undefined as x approaches 0, we cannot determine the limit of the expression.

Therefore,

The limit lim(x approaches 0) (cosec(2x) - x*cosec³(x)) is undefined.

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