Determine (Freshman) Small Cafeteria). Interpret this answer in the context of the situation.

SOLUTION

At the same time t,

Train 1 would have covered a distance of 80t, since distance = average speed x time.

Train 2 would have covered a distance of 70t.

Now both added should give 210 miles

That is 80t + 70t = 210

150t = 210

t = 210/150

t = 1.4 hours

We have that

So the answer is the first one.

In this case, we'll have to carry out several steps to find the solution.

Step 01:

data:

score:

mean = 76

standard deviation = 12

Step 02:

probability:

normal distribution:

normal distribution diagram:

mean + 1 standard deviation = 76 + 12 = 88

probability (class average score is above 80):

p (score > 80) = 34% + 13.5% + 2.4% + 0.1% = 50% = 0.5

The answer is:

p (score > 80) = 50% = 0.5

according to the graph, inequality is:

Answer:

-2

Explanation:

By properties of logarithms, the logarithm of a fraction is equal to the difference of logarithms, so

Now, log₆(1) = 0 and log₆36 = 2, so

Therefore, the answer is -2

The required exponential function f(x) = (4)(2)ˣ which is passes through the two points (-1,2) and (3,32).

An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.

It is a relation of the form y = aˣ  in mathematics, where x is the independent variable

Let the formula for an exponential function would be as

⇒ f(x) = abˣ  

The exponential function passes through the two points (-1,2) and (3,32).

f(-1) = 2

f(3) = 32

2 = ab⁻¹

2b = a

32 = ab³

Substitute the value of a = 2b in the above equation,

32 = 2b×b³

32 = 2b⁴

b⁴ = 16

b⁴ = 2⁴

b = 2

Substitute the value of b = 2 in the equation a = 2b,

So a = 2×2 = 4

⇒ f(x) = (4)(2)ˣ  

Therefore, the required exponential function f(x) = (4)(2)ˣ  

Learn more about exponential function here:

brainly.com/question/11487261

#SPJ1

To find the area using four rectangles, we will use the following equation:

We have the inequality:

Let's find out 3 solutions, as follows:

3x - 4 > 5

Adding 4 at both sides of the inequality:

3x - 4 + 4 > 5 + 4

3x > 9

Dividing by 3 at both sides, we have:

3x/3 > 9/3

x > 3

Now, we can find 3 solutions that fulfill the condition of the inequality:

x = 4, x = 5, x = 6

These three solutions are > 3

Answer:

C 40

Step-by-step explanation:

794 is about 800

18 is about 20

800/20=40

Remember that

The difference of squares is of the form

In this problem we have

so

a=3x

b=4y^2

therefore

Apply the difference of squares

Answer

252 ft²

Step-by-step explanation

1 yard is equivalent to 3 feet. Using this conversion factor, the equivalence of 7 yd is:

Similarly, the equivalence of 4 yards is:

Therefore, the length of the bed is 21 ft and the width is 12 ft.

Finally, the area of the bed (a rectangle) is calculated as follows:

Answer:

Explanation:

To get the plot of h(x), we just plot the given values of y at the given values of x.

For example, we are told that between x = -3.5 and -2.5, h(x) = -3. Therefore, the plot gives

The hollow circle tells us that the value x = -3.5 itself is not included. The solid circle tells us that x = -.2.5 is included. All this comes from the fact that the interval given is -3.5 < x ≤ -2.5.

Using the same method for other entries on the graph, we get our desired plot.

When you multiply two numbers, one of them greater than 0 and the other one lower than 1. The result is a number that is lower than the first one, that is, a number lower than the number greate than 0.

ANSWER:

6150 meters

STEP-BY-STEP EXPLANATION:

To calculate the difference between the two days we must calculate the subtraction of the values corresponding to the days Wednesday and Thursday.

Now, we convert this value in kilometers to meters, knowing that 1 kilometer is equal to 1000 meters:

Answer:

Explanation:

Let the side opposite the river = x

Let the adjacent side to the river = y

a) Since the cost of a bag of popcorn is $6 and the cost of a drink is $4,

Therefore, the answer to the first question is $58.

b) Substitute 5 for p and 7 for d in the expression above; therefore,

The total cost is given by the equation T=6p+4d, where T is in dollars, p is the number of bags of popcorn and d is the number of drinks.

Therefore, the scalar multiplication of vector -7/4 w is given by

Hence, the linear combination is 7/8 i + 21/8 j

From the information given, the slope (m) of the equation is -1.5. This means that there is an inverse relationship between the Lenght of the Candle and the number of hours. Where, the longer the number of hours, the smaller the length of the candle. See further explanation below.

The slope of a line is its steepness as it goes from LEFT to RIGHT. The slope is the proportion of a line's rise, or vertical change, to its run, or horizontal change. The slope of a line is always fixed (it never changes) regardless of whatever two locations on the line are chosen.

When dealing with a linear relationship, the question is usually represented in this format:

y = mx + b; where
m = slope and

b= y-intercept (or constant)

From the case above, the equation shows the relationship between time   (t) the candle spends burning and the length of the candle (l).

Logically, we can infer that there will be a negative relationship between the two but first lets us determine the slope.

Restating the equation in intercept format, we have:

L = 15 - 1.5t................................1; in intercept format the slope we have

L = -1.5t + 15   ...........................2.

Where L [tex]\sim[/tex] y; m [tex]\sim[/tex] -1.5 and t [tex]\sim[/tex] x; and b [tex]\sim[/tex] 15

Hence we can state that the m (slope) = -1.5 and that if plotted on a graph, the line crosses the y-axis at y = 15 where x = 0.

Also, if L (that is y) is set to zero, then the total time taken for ALL the candles to burn is 10 hours.

See attached graph as proof.

The logical interpretation above is hence confirmed that there is an inverse relationship between x and y. This means that the longer the time, the shorter the length of the candle.

This also means that the length of the candle cannot be or is not longer than 15.

Learn more about slopes:

https://brainly.com/question/3493733

#SPJ1

The slope of the equation is -3/2 describing the rate at which the length of the candle is decreasing.

We know lines have various types of equations, the general type is

Ax + By + c = 0.

We know slope is the rate of change of the y-axis with respect to the x-axis

also, rise over run which is (y₂ - y₁)/(x₂ - x₁).

The burning equation of the candle is represented by  L = 15 - 1.5t.

Where L = length of the candle and any point of time and t = time in hours.

Now, we'll need two points from this equation to obtain the slope.

At, t = 2, L = 12. and at t = 4, L = 9.

So, the two points are (2, 12) and (4, 9).

∴ Slope(m) = (9 - 12)/(4 - 2).

Slope(m) = -3/2.

The slope of this equation describes the rate at which the height of the candle is changing.

learn more about slopes here :

https://brainly.com/question/16941905

#SPJ1

Given:

There are given that the expression:

Explanation:

Multiply -9b into the value of bracket.

So,

Final answer:

Hence, the equation is shown below:

Angle shown x is corresponding angle to 110 degree angle shown (from property of transversal cutting a pair of parallel lines).

hence

x = 110

Based on the number of bags of flour that were taken by the trucks and the number that were in the warehouse, the amount of kilograms left in the warehouse is 1,860 kg

First, find the number of bags that were taken by the trucks by the formula:

= Number of trucks x Number of bags per truck

= 8 x 12

= 96 bags

This means that the number of bags left are:

= 127 bags - 96 bags taken

= 31 bags left

The number of kilograms of flour left is:

= Number of bags left x Number of kilograms per bag

= 31 x 60

= 1,860 kg

Find out more on kilograms at https://brainly.com/question/11083065

#SPJ1

The subtraction of the mixed fractions and presenting the result in simplest form gives;

[tex] \displaystyle{9 \frac{2}{5} - 4 \frac{4}{5} = 14 \frac{1}{5}} [/tex]

A mixed fraction is one that has both a quotient part as a whole number, the remainder, as the numerator of the fraction part, and the divisor as the denominator of the fraction part.

The equation involves the subtraction of mixed fractions, which are expressed as follows;

[tex] \displaystyle{9 \frac{2}{5} - 4 \frac{4}{5} } = [/tex]

To subtract the mixed fractions, the mixed fraction can first be rearranged into improper fractions as follows;

[tex] \displaystyle{ \frac{5 \times 9 + 2}{5} - \frac{5 \times 4 + 4}{5} = \frac{47}{5} + \frac{24}{5} }[/tex]

[tex] \displaystyle{ \frac{47}{5} + \frac{24}{5} = \frac{71}{5} }[/tex]

The result of the addition of the improper fraction which is also an improper fraction can be rearranged into partial fractions again as follows;

71 = 5 × 14 + 1

Which gives;

[tex] \displaystyle{ \frac{71}{5} = 14 \frac{1}{5} }[/tex]

Therefore;

[tex] \displaystyle{9 \frac{2}{5} - 4 \frac{4}{5} = 14 \frac{1}{5}} [/tex]

Learn more about mixed and improper fractions here:

https://brainly.com/question/1055953

#SPJ1

We need to find the multiples of 4 using the next given set:

The multiples of 4 are given by

4*1 =4

4*2 = 8

4*3= 12

4*4=16

4 *5 =20

Then:

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20​.

Answer:

the length of the diagonal AC is;

Explanation:

Given the parallelogram ABCD, diagonals AC and BD intersect at point E.

Recall that the diagonals of a parallelogram bisect each other;

So;

substituting AE and CE;

To calculate the length of AC;

Therefore, the length of the diagonal AC is;

Let's begin by listing out the given information:

18 students passed

Total students = 25

Number of people who did not pass = 25 - 18 = 7

7 out of 25 students did not pass. This has its percentage as:

Therefore, 28% of the students did not pass

The mean and the median for each data-set are given as follows:

5-th grade students:

7-th grade students:

A dot plot shows the number of times that each observation appears on a data-set.

Hence the hours of the 5th-graders are as follows:

1, 1, 2, 2, 2, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 8, 8

The mean is the sum of all the numbers of hours divided by the number of students,  hence:

Mean = (2 x 1 + 3 x 2 + 1 x 3 + 4 x 4 + 5 x 5 + 5 x 6 + 2 x 7 + 2 x 8)/(2 + 3 + 1 + 4 + 5 + 5 + 2 + 2) = 4.67.

There are 24 elements in the data-set, hence the median is the mean of the 12th and the 13th element, as follows:

Median = (5 + 5)/2 = 5.

Hence the hours of the 7th-graders are as follows:

0,0, 1, 1, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7.

Hence the mean is:

Mean = (2 x 0 + 2 x 1 + 3 x 2 + 5 x 3 + 5 x 4 + 3 x 5 + 3 x 6 + 1 x 7)/24 = 3.46.

The 12th element is of 3, the 13th of 5, hence the median is:

Median = (3 + 5)/2 = 4.

More can be learned about dot plots at https://brainly.com/question/24309209

#SPJ1

We can consider

x = length of the painting

20 ft wall long

we want at least 3 ft per side so the total available length is 20-6= 14

x must be shorter than 14

inequality

x< 20-2(3)

x<14

We solve as follows:

-12x - 2y = 30

2(-4x + y = -5)

---------------------

-12x -2y = 30

-8x + 2y = -10

--------------------

-20x = 20 => x = -1

Now we replace the value of x in one of the original equations to solve for y, that is:

-4(-1) + y = -5 => 4 + y = -5 => y = -9

So, the solution is the point (-1, -9).

∠1 is 31.5°

∠2 is 148.5°.

Given:

∠1 = x

∠2 = 5x-9

The measure of ∠1 and ∠2 are supplementary angles.

First, the value of x can be calculated as,

Substitute the value of x in ∠2.

Hence, the measure of ∠1 is 31.5° and the measure of ∠2 is 148.5°.