Noah travels 135 mph by train, while Eric travels 60 mph by car. Eric takes two hours longer. Create a second equation that shows how long it would take Eric.

The exponential equation of log(x+4) (x²+3x-7) =3 is x²+3x-7 = (x+4)³

Exponential equations are equations in which variables occur as exponents. For example, exponential equations are in the form a^x=b^y.

To solve exponential equations with same base, use the property of equality of exponential functions .

The law of logarithm states;

If loga b = x

b = a^x

Using the rule;

log(x+4) (x²+3x-7) = 3

x²+3x-7 = (x+4)³

therefore the exponential equation of log(x+4) (x²+3x-7) = 3 is x²+3x-7 = (x+4)³

learn more about exponential equation from

https://brainly.com/question/2456547

#SPJ1

The correct statement regarding the proportional relationships is given as follows:

D. The first bucket will be completely filled 11 minutes before the second bucket.

A proportional relationship is a type of relationship between two quantities in which they maintain a constant ratio to each other.

The equation that defines the proportional relationship is given as follows:

y = kx.

In which k is the constant of proportionality, representing the increase in the output variable y when the constant variable x is increased by one.

For the first bucket, the equation is given as follows:

y = 0.4x.

Meaning that 0.4 gallons are inserted each minute, hence the time to insert 2 gallons is given as follows:

2/0.4 = 5 minutes.

For the second bucket, the constant is taken from the graph as follows:

k = 0.5/4

k = 0.125.

Hence the time is given as follows:

2/0.125 = 16 minutes.

Hence the difference is of:

16 - 5 = 11 minutes.

More can be learned about proportional relationships at https://brainly.com/question/7723640

#SPJ1

The requried domain and range of the given graph are a set of all real values i.e. (-∞, ∞).

Consider the given figure,
The domain is said to be the values of the set of dependent variables, in the given case the value on the x-axis, represents the domain.
The domain is given as all real value i.e. (-∞, ∞)

Similarly, the range is represented by the y-axis and given as (-∞, ∞).

Learn more about the domain and range here:

https://brainly.com/question/29452843

#SPJ1

The value of the expression "A- 2--0.5x47" is 25.5.

Using the order of operations (PEMDAS) we first simplify the multiplication before subtracting from 2:

2 - (-0.5 x 47)

= 2 - (-23.5)

When subtracting a negative number, we can think of it as adding the positive value. Therefore, we can rewrite the expression as:

2 + 23.5

= 25.5

Therefore, the value of the expression "A- 2--0.5x47" is 25.5.

In conclusion, to determine whether a given value is a solution to an equation, we need to know what the equation is. However, given an expression, we can simplify it and then substitute a value for the variable to determine whether it is a solution.

for such more question on  expression

https://brainly.com/question/16763767

#SPJ11

Question

which value is a solution  A- 2-( -0.5x47)

The other solution to the equation x³ + 3x² - x = |x-1| is approximately x~ = -2.6.

1. Start by plotting the graphs of both sides of the equation on a graphing calculator.

2. The left side of the equation, x³ + 3x² - x, can be plotted as a curve.

3. The right side of the equation, |x-1|, can be plotted as a V-shaped graph with the vertex at (1, 0).

4. Find the intersection points of the two graphs.

5. By observing the graph, it can be seen that the two given solutions, a~ = -0.7 and b~ = 0.5, are present.

6. Identify the other solution, which is the third intersection point.

7. Determine the approximate x-coordinate of the third intersection point by reading the value from the graph.

8. Round the obtained x-coordinate to the nearest tenth.

9. The other solution is approximately x~ = -2.6.

For more such questions on equation, click on:

https://brainly.com/question/17145398

#SPJ11

The absolute increase from the younger group to the older group is 59.9% - 14.3% = 45.6%. Rounding to the nearest point, the answer is 46 points.

The absolute increase is the difference between two values, regardless of the direction of change. In this case, we want to find the absolute increase in the percentage of people who vote from the younger group (20-25 years old) to the older group (60-65 years old).

To find the absolute increase, we subtract the percentage of people who vote in the younger group from the percentage of people who vote in the older group, taking the absolute value of the result.

So, the absolute increase in the percentage of people who vote from the younger group to the older group is:

|59.9% - 14.3%| = 45.6%

This means that the percentage of people who vote in the older group is 46 percentage points higher than the percentage of people who vote in the younger group.

Learn more about the average rate of change here:

https://brainly.com/question/28744270

#SPJ1

The coefficient of a²b² in the expansion of (2a - b)⁴ is 24

From the question, we have the following parameters that can be used in our computation:

(2a - b)⁴

When the expression is expanded, we have

(2a-b)⁴ = (2a-b)(2a-b)(2a-b)(2a-b)

So, we have

(2a-b)⁴ = 16a⁴ - 32a³b + 24a²b² - 8ab³ +b⁴

Consider an expression ax where the variable is x

The coefficient of the variable in the expression is a

Using the above as a guide, we have the following:

The coefficient of a²b² in the expansion is 24

Read more about expression at

https://brainly.com/question/15775046

#SPJ1

The requried, 20 youths use both iPhone and Samsung, and 200 youths use neither iPhone nor Samsung.

Let A be the set of youths using only iPhones, B be the set of youths using only Samsung, and C be the set of youths using both. Then, we have:

|A| = 150

|B| = 770

|A ∪ B| = 900

We want to find |C| and |A ∩ B| (which is the number of youths using both).

Using the inclusion-exclusion principle, we have:

|A ∪ B| = |A| + |B| - |A ∩ B|

900 = 150 + 770 - |A ∩ B|

|A ∩ B| = 20

So, 20 youths use both iPhone and Samsung.

To find the number of youths who use neither, we can use the fact that:

|A ∪ B ∪ C| = 1100

|A ∪ B ∪ C| = |A| + |B| + |C| - |A ∩ B| - |A ∩ C| - |B ∩ C| + |A ∩ B ∩ C|

Plugging in the values we know, we get:

1100 = 150 + 770 + |C| - 20 - |A ∩ C| - |B ∩ C| + |A ∩ B ∩ C|

|C| - |A ∩ C| - |B ∩ C| + |A ∩ B ∩ C| = 200

Since the number of youths using both is 20, we have:

|A ∩ C| = |B ∩ C| = |A ∩ B ∩ C| = 0

So, we can simplify the equation to:

|C| = 200

Therefore, 200 youths use neither iPhone nor Samsung.

Learn more about probability here:

https://brainly.com/question/30034780

#SPJ1

Answer: Trust me I don't know either

Step-by-step explanation:

For asking questions about whatever in life I guess

Answer:

Step-by-step explanation:

No

for it to be a right angle triangle the longest side would have to be the square root of 8 squared plus 11 squared which is 13.6

answer

no Pythagorean theorem doesnt work

steps

8²+11² should equal 17²

BUT

121+64=185

17²=289

Answer:

BC is 32 cm

Step-by-step explanation:

Answer:

Corresponding angles is the answer to your question

Amount of ice cream can the cone hold is, 9.8 inches³

We have to given that;

An ice cream cone has a height of 6 inches and a diameter of 2.5 inches.

Hence, We get;

Radius of cone = 2.5 / 2 = 1.25 inches

Since, We know that;

Volume of cone is,

V = πr²h/3

v = 3.14 × 1.25² × 6 / 3

V = 9.8 inches³

Hence, Amount of ice cream can the cone hold is, 9.8 inches³

To learn more about the volume visit:

brainly.com/question/24372707

#SPJ1

Answer:

[tex]\\[/tex]

Step-by-step explanation:

In the first year, the trainers will be worth 80% of their original value, which is:

[tex]\rm\implies{£100 \times 0.8 = £80}[/tex]

[tex]\\[/tex]

In the second year, they will be worth 80% of their value after the first year:

[tex]\rm\implies{£80 \times 0.8 = \boxed{\boxed{\sf{\:\:\:\green{£64}\:\:\:}}}}[/tex]

[tex]\\[/tex]

[tex]\\[/tex]

[tex]\therefore[/tex] The trainers will be worth £64 in 2 years' time.

The probability of drawing an orange marble and a blue marble without replacement is:P(Orange and Blue without replacement) = (3/10) * ((N - 4) / (N - 1))

The probability of drawing an orange marble and a blue marble without replacement, we need to consider the total number of marbles and the number of desired outcomes.

Let's assume we have a bag of marbles containing both orange and blue marbles. The total number of marbles in the bag is not given, so we'll consider it as an unknown value, denoted as N.

First, we need to calculate the probability of drawing an orange marble on the first draw. Since there is no replacement, the probability of drawing an orange marble on the first draw is given by the ratio of the number of orange marbles to the total number of marbles:

P(Orange on first draw) = Number of orange marbles / Total number of marbles

Next, after the first marble is drawn, the bag will contain one less marble, and the number of orange marbles and blue marbles will change accordingly. Assuming we drew an orange marble on the first draw, the number of orange marbles will decrease by 1, and the total number of marbles will decrease by 1.

Now, we need to calculate the probability of drawing a blue marble on the second draw, given that an orange marble was drawn on the first draw. The probability is calculated as:

P(Blue on second draw | Orange on first draw) = Number of blue marbles / Total number of marbles after the first draw

Since there is no replacement, the total number of marbles after the first draw is N - 1.

Finally, to find the probability of drawing an orange marble and a blue marble without replacement, we multiply the probabilities of the two events:

P(Orange and Blue without replacement) = P(Orange on first draw) * P(Blue on second draw | Orange on first draw)

To simplify the calculation, we can substitute the given values:

P(Orange on first draw) = 3/10 (assuming there are 3 orange marbles out of 10 marbles in total)

P(Blue on second draw | Orange on first draw) = (N - 4) / (N - 1) (assuming there are N - 4 blue marbles left in the bag after drawing an orange marble)

Therefore, the probability of drawing an orange marble and a blue marble without replacement is:

P(Orange and Blue without replacement) = (3/10) * ((N - 4) / (N - 1))

For more questions on probability.

https://brainly.com/question/30390037

#SPJ8

Answer:

The North American Free Trade Agreement (NAFTA) among the United States, Canada and Mexico went into effect on January 1, 1994. It is the first trade agreement the United States has entered into with a geographically-close developing country and has raised concerns about its economic effect, particularly on U.S. communities and workers. Since the mid-1980s, when Mexico began reducing trade restrictions, the U.S. and Mexican economies have become more highly integrated. This is evidenced by the rapid growth in U.S. merchandise trade with Mexico, which is now 12% of all U.S. trade

Step-by-step explanation:

The additional reason will be JK/PQ = KL/QR.

Option C is correct.

Given that are two triangles, ΔJKL and ΔPQR, where ∠K ≅ ∠Q, we need to determine a reason to show ΔJKL and ΔPQR are similar,

So, we know that the similar triangles have congruent corresponding angles and corresponding sides are in equal ratio,

So, from the options if we take JK/PQ = KL/QR we can prove that the triangles are similar by SAS rule.

Hence the option C is correct.

Learn more about similarity click;

https://brainly.com/question/26451866

#SPJ1

The height of the triangle must increase by 4.29 feet so that the area would increase by 1.2 square feet.

To calculate the area of a triangle, you can use the formula presented as follows:

[tex]\sf Area = \huge \text(\dfrac{1}{2}\huge \text) \times base \times height[/tex]

In which the parameters are given as follows:

Considering the triangle that has a base of 14 feet and a height of 6 feet, the area of the triangle is given as follows:

[tex]\sf A = 0.5 \times 14 \times 6[/tex]

[tex]\sf A = 42 \ square \ feet.[/tex]

An increase of 1.2 square feet would lead to an area of 43.2 square feet, hence the height would be of:

[tex]\sf 4.2h = 43.2[/tex]

[tex]\sf h = \dfrac{43.2}{4.2}[/tex]

[tex]\sf h = 10.29 \ feet[/tex].

Then the increase in the height would be of:

[tex]\sf 10.29 - 6 = 4.29 \ feet[/tex].

More can be learned about the area of a triangle at brainly.com/question/21735282

The required expression is 10000x[tex](1.1)^{t}[/tex]/(45 + 4t).

The expression representing the number of students serviced by the school system in the town of Emor, t years from 2000 is:

s(t) = 10000x[tex](1.1)^{t}[/tex]

And the expression representing the number of classrooms in the town of Emor, t years from 2000 is:

C(t) = 450 + 4t

The expression D (t) represents the average number of students per classroom in Emor's school system t years from 2000.

Then the average number of students per classroom can be computed by:

Average number of students/classroom = Number of students/Number of classrooms

D(t) = s(t)/c(t)

      = 10000x[tex](1.1)^{t}[/tex]/(45 + 4t)

Thus,

The formula = 10000x[tex](1.1)^{t}[/tex]/(45 + 4t).

To learn more about exponential function visit:

https://brainly.com/question/14355665

#SPJ1

Answer:

Step-by-step explanation:

1. The figure  is a rectangular prism.

Formula: V = lwh

Given: 13 ft x 7ft x 9 ft

Substitute the values to the formula and solve.

V = lwh

V = 13ft(7ft)(9ft)

V = 819 ft³

2. The given figure is a triangular prism. Notice that the base forms a right triangle.

Formula: V = 1/2bhl

Given:

b = 9m

h = 12m

l = 16 m

Substitute the given values to the formula and solve.

V = 1/2(9m)(12m)(16m)

V = 864 m³

3. This is a cylinder

Formula: V = πr²h

Given:

r = 11 yd

h = 26 yd

Solve:

V = π (11yd)²(26yd)

V = 9883.45 yd³

4. The figure is a rectangular prism.

Formula: V = lwh

Given dimensions: 9m x 9m x 13.5m

Solve:

V = 9m(9m)(13.5m)

V = 1093.5 m³

5. The figure is a triangular prism

Formula: V = 1/2bhl

Given:

b = 15yd

h = 13 yd

l = 24 yd

Solve:

V = 1/2 (15yd)(13yd)(24yd)

V = 2340 yd³

The expressions that are equivalent to the one below  is [tex]2 ^{(5+x) }[/tex], option C.

Based on the definition of power multiplication properties, The Product of Powers Property serves as one that stressed that in a cae wehereby we are multiplying two exponents with the same base, then the exponents  can be multiplied and keep the base.

It shoud be noted that when  want to simplify the expressions [tex]2x^4[/tex]by [tex]6x2[/tex] , the base wil will be kept whereby  we add the exponent.

The given expression is [tex]2^5.2^x[/tex], which can be simplified as;

= [tex]2^5.2^x[/tex]

=[tex]2 ^{(5+x) }[/tex]

Learn more about expressions at:

https://brainly.com/question/14202616

#SPJ1

1. The best equation for circle A is (x + 4)² + (y + 2)² = 9. Option D

2. The equation of the circle with coordinates (1, 1) (1, 11) is (x - 1)² + (y - 6)² = 25. Option A

1. For the equation of circle A, we can pick out the coordinates we see.

Circle A has its midpoint at (-4, -2) and its edges at (-4, 1) and (-4, -5).

The equation of a circle in a plane is (x - h)² + (y - k)² = r²

the circle has a radius of 3 units (from -2 to 1 or from -2 to -5)

(x - (-4))² + (y - (-2))² = 3²

when we simplify, it becomes (x + 4)² + (y + 2)² = 9

2. The equation of a circle with diameter AB. A (1, 1), B(1, 11) is

h = (x₁ + x₂)/2 ⇒(1 + 1)/2 = 1

k = (y₁ + y₂)/2⇒ (1 + 11)/2 = 6

the center of the circle is at (1, 6).

A and B which are (1, 1) and (1, 11), it's clear that the diameter is 10 units (11 - 1). Thus, the radius is 5 units.

(x - h)² + (y - k)² = r²

Substituting the obtained values we get

(x - 1)² + (y - 6)² = 5²

which becomes

(x - 1)² + (y - 6)² = 25

Find more exercises on  equation of circle;

https://brainly.com/question/23799314

#SPJ1

The linear regression equation that best fits the data is y = 3.04x + 5.8.

Using a graphing calculator, we can plot the data points and find the linear regression model that best fits the data.

The linear regression equation that best fits the data is

y = 3.04x + 5.8.

Therefore, the answer is: y=3.04x+5.8.

Learn more about Regression Model here:

https://brainly.com/question/14983410

#SPJ1

The limit as n approaches infinity of ((n+1)⁶-(n-1)⁶)/((n+1)⁵+(n-1)⁵) is 6.

To evaluate the limit as n approaches infinity of the expression ((n+1)⁶-(n-1)⁶)/((n+1)⁵+(n-1)⁵), we can simplify it using algebraic manipulations.

Let's expand the numerator and denominator using the binomial:

Numerator:

((n+1)⁶-(n-1)⁶) = [n⁶ + 6n⁵ + 15n⁴ + 20n³ + 15n² + 6n + 1] - [n⁶ - 6n⁵ + 15n⁴ - 20n³ + 15n² - 6n + 1]

= 12n⁵ + 40n³ + 12n

Denominator:

((n+1)⁵+(n-1)⁵) = [n⁵ + 5n⁴ + 10n³ + 10n² + 5n + 1] + [n⁵ - 5n⁴ + 10n³ - 10n² + 5n - 1]

= 2n⁵ + 20n³ + 2n

Now, let's simplify the expression by canceling out common terms:

((n+1)⁶-(n-1)⁶)/((n+1)⁵+(n-1)⁵) = (12n⁵ + 40n³ + 12n) / (2n⁵ + 20n³ + 2n)

As n approaches infinity, we can see that the highest power of n in the numerator and denominator is n⁵.

We can divide all terms by n⁵ to determine the limit:

lim(n→∞) [(12n⁵ + 40n³ + 12n) / (2n⁵ + 20n³ + 2n)]

= lim(n→∞) [(12 + 40/n² + 12/n⁴) / (2 + 20/n² + 2/n⁴)]

= 12/2

= 6

For similar questions on limit

https://brainly.com/question/30679261

#SPJ11

If you have a system of two equations with two unknowns, and the graphs of the two equations do not intersect, the system must have no solution.

option C.

When we have a system of two linear equations in two variables, it can be represented graphically as two lines in a plane. The solution to the system corresponds to the point of intersection of these lines.

If the two lines do not intersect, then they are parallel. In this case, there is no point that satisfies both equations, which means that there is no solution to the system of equations.

In other words, if the two graphs do not intersect, it means that there are no values of the two unknowns that can simultaneously satisfy both equations.

Learn more about no solution here: https://brainly.com/question/27247133

#SPJ1

Answer: 9" x 10" x 11" = 990 cubic inches.

990 cubic inches / 5 minutes = 198 cubic inches per minute

22" x 23" x 33" = 16698 cubic inches

16698/198 = 84 and 1/3 minutes

1 hour 24 minutes and 20 seconds

Answer:

I would go with 900 but I’m not for sure

Step-by-step explanation:

Answer:

  C.  18/48 and 21/56

Step-by-step explanation:

You want to identify pairs of ratios that are proportional.

Ratios are proportional when they have the same value. We can check whether the values are the same by reducing each ratio to lowest terms.

The attached calculator display shows the proportional ratios are ...

  18/48 and 21/56 . . . . choice C

__

Additional comment

Both of these reduce to 3/8. You can remove a factor of 6 from the numbers of the first ratio, and a factor of 7 from the numbers of the second ratio to reduce both of them to 3/8.

<95141404393>

Answer: C.  18/48 and 21/56

Step-by-step explanation:  Hope it helps

The probability that at least six hamburgers are contaminated in a random sample of 10 hamburgers is approximately 0.2 or 20%

We can approach this problem using the binomial distribution, where:

n = 10 (the sample size)

p = 0.25 (the probability of a hamburger being contaminated)

q = 1 - p = 0.75 (the probability of a hamburger not being contaminated)

We want to find the probability that at least six hamburgers are contaminated, which can be expressed as:

P(X ≥ 6) = P(X = 6) + P(X = 7) + ... + P(X = 10)

where X is the number of contaminated hamburgers in the sample.

Using the binomial probability formula, we can calculate each individual probability:

P(X = b) = (n choose b) x pᵇ x q⁽ⁿ⁻ᵇ⁾

where (n choose k) represents the number of ways to choose k items from a set of n items, and is calculated as:

(n choose k) = n! / (k! x (n-k)!)

Using a calculator or software, we can find each individual probability and sum them up to get the total probability:

P(X ≥ 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)

= (10 choose 6) x 0.25⁶ x 0.75⁴ + (10 choose 7) x 0.25⁷ x 0.75³ + (10 choose 8) x 0.25⁸ x 0.75² + (10 choose 9) x 0.25⁹ x 0.75¹ + (10 choose 10) x 0.25¹⁰ x 0.75⁰

= 0.0197

= 0.02

To learn more about the probability;

brainly.com/question/11234923

#SPJ1

Step-by-step explanation:

One complete revolution is one circumference

circumference of a circle is found using the formula  circumf = pi * d

so    308 m = pi * d   or

                  308 m / pi = diameter = 98 m   (a VERY large bicycle wheel!)