Your friend claims that the equation of a line with a slope of 7 that goes through the point (0,-4) is y = -4x + 7

What did your friend mess up?

Answer:

x = 75/4

Step-by-step explanation:

5/8 + 1 1/4 = x/10

5/8 + 5/4 = x/10

15/8 = x/10

8x = 15 × 10

8x/8 = 150/8

x = 150/8

x = 75/4

By evaluating the expression for s(tB), we can determine whether driver A crossed the finish line before or after driver B. If s(tB) is positive, it means driver A crossed the finish line before driver B. If s(tB) is negative, it means driver A crossed the finish line after driver B.

To solve the initial value problem, we start with the equation vA'(t) = -k(vA(t))^2, where vA'(t) represents the derivative of vA with respect to t.

This equation describes the deceleration of driver A, proportional to the square of his remaining speed. Rearranging and solving the differential equation, we get vA(t) = 1 / (kt + C), where C is a constant determined by the initial conditions.

To find the expression for s(t), we integrate vA(t) with respect to t: s(t) = ∫(1 / (kt + C)) dt. Integrating this expression gives us s(t) = (1/k) ln(kt + C) + D, where D is another constant determined by the initial conditions.

At t = t1 (when driver A's speed is halved, i.e., one mile after running out of gas), we have vA(t1) = vA(0) / 2. Plugging this into the expression for vA(t) from step 1, we find 1 / (k * t1 + C) = (1 / (k * 0 + C)) / 2. Simplifying, we get k = ln(2) / t1.

Using the expression for s(t) from step 2, we can find tB by settings S(tB) = 3 (since driver A was leading by 3 miles). Simplifying this equation, we find tB = (e^(3k) - C) / k. Plugging in the value of k we found in step 3, we have tB = (e^(3ln2 / t1) - C) / (ln2 / t1).

To evaluate s(tB), we substitute t = tB into the expression for s(t) from step 2, resulting in s(tB) = (1/k) ln(ktB + C) + D. Since tB depends only on vB and t1, and C and D are constants determined by the initial conditions, s(tB) depends only on vB.

If s(tB) is positive, it means driver A crossed the finish line before driver B. If s(tB) is negative, it means driver A crossed the finish line after driver B.

To learn more about expression

https://brainly.com/question/1859113

#SPJ8

From the given Venn diagram, the value of  M∩N={4,7}.

A Venn diagram is a prominent diagram type that depicts the logical relationship between sets. It was popularized in the 1880s by John Venn (1834-1923). The diagrams are used to teach elementary set theory and to show simple set relationships in probability, logic, statistics, linguistics, and computer science. To depict sets, a Venn diagram uses basic closed curves drawn on a plane. These curves are almost often circles or ellipses.

Before Venn, similar concepts had been presented. Similar ideas were proposed by Christian Weise in 1712 and Leonhard Euler (Letters to a German Princess) in 1768. Venn popularized the concept in Symbolic Logic, Chapter V "Diagrammatic Representation," 1881.

The intersection of two sets is the set of all the elements that are shared by both.

M={4,7,9,3}

N={4,7,6}

Because M and N share the numbers 4 and 7, M∩N={4,7}.

To know more about Venn diagram, visit:

https://brainly.com/question/29301560

#SPJ9

If the point A= (4,5), then the possible points on the x-axis which are 13 units from point A are (16,0) and (-8,0).

To find all possible points on the x-axis, follow these steps:

So, the possible points on the x-axis that are 13 units away from point A(4,5) are (16, 0) and (-8, 0).

Learn more about distance formula:

https://brainly.com/question/30395212

#SPJ11

The area of the rectangle is 31/3 square centimeters or 10 1/3 square centimeters as a mixed number.

To find the area of the rectangle, we need to multiply its length by its width.

First, we need to convert the mixed numbers to improper fractions:

Length = 5 1/6 cm = (6 × 5 + 1)/6 = 31/6 cm

Width = 2 2/7 cm = (7 × 2 + 2)/7 = 16/7 cm

Now, we can multiply the two fractions to get the area of the rectangle:

Area = length × width

= (31/6 cm) × (16/7 cm)

= (31 × 16) / (6 × 7) cm²

= 496/42 cm²

= 248/21 cm²

We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor (GCF), which is 8:

248/21 cm² = (8 × 31)/ (8 × 3) cm²

= 31/3 cm²

= 10 1/3 cm²

Learn more about area here

brainly.com/question/20693059

#SPJ4

the subtraction problem "-3 - 4" is equivalent to the addition problem "-3 + (-4)".

How to solve and what is subtraction?

To write the subtraction problem "-3 - 4" as an addition problem using negative numbers, we can rewrite it as follows:

-3 - 4 = -3 + (-4)

So, the subtraction problem "-3 - 4" is equivalent to the addition problem "-3 + (-4)".

Subtraction is a fundamental arithmetic operation used to find the difference between two values or quantities. It involves taking away a certain amount from a starting value, resulting in a lower value.

The starting value is called the minuend, the amount being subtracted is called the subtrahend, and the result is called the difference. Subtraction is commonly used in everyday life, such as in calculating change when making a purchase or determining how much time has elapsed between two events. It is also an important concept in more advanced mathematical topics such as algebra and calculus.

To know more about Subtraction related questions, visit:

https://brainly.com/question/2346316

#SPJ1

The expected number of tosses required to get the pattern "ht" is 2/pq +1

To find the expected number of tosses required to get the pattern "ht" with a biased coin, we can use the concept of geometric distribution. The geometric distribution models the number of independent and identically distributed (i.i.d) trials required to achieve the first success in a sequence of Bernoulli trials. In this case, we define "success" as getting the pattern "ht".

Let p be the probability of getting a "heads" on a single toss, and let q be the probability of getting a "tails" on a single toss (i.e., q=1-p).

The probability of getting "ht" on the first two tosses is simply p*q = pq. If we don't get "ht" on the first two tosses, then we have essentially reset the experiment and are back to square one. Therefore, the expected number of tosses required to get "ht" can be expressed recursively as:

E = pq(2) + (1-pq)(E+1)

The first term pq(2) represents the case where we get "ht" on the first two tosses, which takes two tosses in total. The second term (1-pq)(E+1) represents the case where we don't get "ht" on the first two tosses. In this case, we have essentially reset the experiment and are back to square one, but we have also used up two tosses, so we need to add 1 to the expected number of tosses required to get "ht".

Simplifying the above equation, we get:

E = 2pq + (1-pq)E + (1-pq)

Rearranging and solving for E, we get:

E = 2/pq + 1

Therefore, the expected number of tosses required to get the pattern "ht" is 2/pq + 1.

Learn more about pattern here:

https://brainly.com/question/14720576

#SPJ11

The six trigonometric identities are:

Trigonometry is the branch of mathematics that deals with the relationships between the angles and sides of triangles. In trigonometry, there are six basic functions, sine, cosine, tangent, cosecant, secant, and cotangent, each of which is represented by a specific letter. These functions are related to each other through a set of identities known as the trigonometric identities.

The six trigonometric identities listed above, are the most commonly used identities, and provide the relationships between the six trigonometric functions and each other. They are useful for solving trigonometric equations, simplifying trigonometric expressions, and solving problems in geometry, physics, engineering and other sciences.

The Pythagorean identity states that the sum of the squares of the sine and cosine of an angle is equal to 1, which is a fundamental relationship between the two functions. The reciprocal identities state that the reciprocal of the sine and cosine of an angle is equal to the cosecant and secant of that angle respectively.

The quotient identities state that the tangent of an angle is equal to the sine of that angle divided by the cosine of that angle, and the cotangent of an angle is equal to the cosine of that angle divided by the sine of that angle.

It's important to note that these identities are valid for all values of the angle, and are true in any angle measurement system (degrees or radians).

To know more about  trigonometric identities on the link below:

https://brainly.com/question/24377281#

#SPJ11

Answer:

Likely

Step-by-step explanation:

because 5/25 as a decimal is 0.2 so that question is likely

A function containing a variable base raised to a fixed power   is considered to be a power function.

when a function has a constant base raised to a variable power. This can be called an exponential function, not a power function A power function may be a function with a single term that is the product of a real number, a coefficient, and a variable raised to a fixed real number. It is in the form of f(x)=kx^p, where k and p are the real numbers whereas k is the coefficient.

to know more about the power function refer to the link   https://brainly.com/question/24364138?referrer=searchResults.

#SPJ4

Answer:

x=510

Step-by-step explanation:

You can first combine like terms to get x/17=30

The inverse operation of division is multiplication so you can multiply by 17 on both sides to get your final answer: x=510

Answer:

\( (\frac{2r}{3} - 7 = r + 5 \: ) \times 3 \\ 2r - 21 = 3r + 15 \\ 3r - 2r = - 21 - 15 \\ r = - 36\)

Answer: 15 mins

Step-by-step explanation:

20 ÷ 8 = 2.5 (how many Mins 1 part takes)

2.5 x 6 = 15

It will take 15 minutes does it take to make 6 parts.

The unitary method is a process by which we find the value of a single unit from the value of multiple units and the value of multiple units from the value of a single unit.

If 8 parts take 20 minutes to make then 1 part take x time which is equal to;

\(\rm x=\dfrac{20}{8}\\\\x= 2.5 \rm \ minute\)

One part takes 2.5 minutes.

The minutes does it take to make 6 parts are;

\(= 6 \times 2.5\\\\=15\)

Hence, it will take 15 minutes does it take to make 6 parts.

To know more about the unitary method click the link given below.

https://brainly.com/question/13823511

#SPJ4

Answer:

30 feet

Step-by-step explanation:

For this problem we can use ratios 6:4 and x:20. We can also write these ratios as fractions 6/4 and x/20 or 3/2 and x/20. Set the two fractions equal to each other and solve for x:

3/2 = x/20

1.5 = x/20

30 = x

Answer:

  8.5 years

Step-by-step explanation:

You want to know the number of years until 18500 depreciates to 9100 at the rate of 8% per year.

The depreciation rate given as a percentage of current value tells you the depreciation is exponential. The formula will be ...

  value = (initial value) × (1 - (depreciation rate))^t

where the rate is "per year" and t is in years.

  value = 18500·(1 -0.08)^t

  9100 = 18500·0.92^t . . . . fill in the value of interest

  9100/18500 = 0.92^t . . . . divide by 18500

  log(91/185) = t·log(0.92) . . . . take logarithms

  t = log(91/185)/log(0.92) ≈ -0.3081/-0.03621 ≈ 8.509

It will be about 8.5 years until the value is $9100.

__

Additional comment

The graph shows the solution to ...

  18500·0.92^t -9100 = 0

We find it fairly easy to locate an x-intercept, so we wrote the equation in the forms that makes the x-intercept the solution.

Answer:

The hypotenuse is opposite of the right angle.

Step-by-step explanation:

The answer is true. The curve of t-distribution has thicker tails than the curve of the standard normal distribution.

The t-distribution is also called as Student's t-distribution which is a type of probability distribution with a bell shape which is similar to  normal distribution but has thicker tails. It is used to estimate population parameters when sample sizes are small or variances are unknown. T-distributions have a higher probability of extreme values more than normal distributions which results in thicker tails.

Tail thickness is determined by a t-distribution parameter called degrees of freedom, with lower values resulting in heavier tails and higher values resulting in the t-distribution resembles standard normal distribution with a  standard deviation of 1and mean of 0.

Thus, t-distribution has thicker tails than the normal distribution.

To learn more about t-distribution refer here

https://brainly.com/question/13574945

#SPJ4

The expression to represent the number of t-shirts that Lisa can purchase is 14x + 58 = 150

From the information given, Lisa has $150 at most to spend on clothes. She wants to buy a pair of jeans for $58 and will spend the rest on t-shirts that cost $14 each.

Let the number of shirts be represented by x. The expression will be:

= (14 × x) + 58 = 150

14x + 58 = 150

Solving the expression will be:

14x + 58 = 150

14x = 150 - 58

14x = 92

x = 92/14

x = 6.5

The number of shirts that can be bought is 6.

Learn more about equations on:

brainly.com/question/2972832

#SPJ1

The values of p and q that satisfy two simultaneous equations can be determined by identifying the coordinates at which the corresponding lines intersect on a graph.

Simultaneous equations represent a system of equations that need to be solved together to find the values of the variables involved.

By graphing the equations on a coordinate plane, the points of intersection between the lines represent the values of p and q that satisfy both equations simultaneously.

These intersection points correspond to the values where the equations are true at the same time. The x-coordinate of the intersection point represents the value of p, while the y-coordinate represents the value of q.

By visually inspecting the graph, one can identify the coordinates of the intersection, which provide the solution to the simultaneous equations and represent the values of p and q that satisfy both equations.

Learn more about Equations click here :brainly.com/question/13763238

#SPJ11

Answer:

x=3

Step-by-step explanation:

f(x)=2x+6

f(x)=12

Hence:

2x+6=12

2x+6-6=12-6

2x=6

x=6/2

x=3

The Venn diagram can be used to visually represent the population and the sample, allowing for a clear identification of both entities within a given context.

A Venn diagram is a graphical representation that uses overlapping circles to illustrate the relationships between different sets. It can be helpful in identifying the population and the sample in a given context. In a Venn diagram, the population refers to the entire set or group being studied. It represents the complete collection of individuals or elements that the researcher wants to draw conclusions about. The population is typically represented by the universal set encompassing all the circles in the Venn diagram.

On the other hand, a sample is a subset or a smaller portion of the population that is selected for observation or data collection. It represents a representative portion of the population and is often used to make inferences or draw conclusions about the larger population. In the Venn diagram, the sample would be represented by the specific area or overlap between the circles that corresponds to the selected subset of the population. It is important to note that the sample is derived from the population and should ideally be representative of it to ensure the validity of any conclusions drawn.

By utilizing the Venn diagram, researchers can visually distinguish the population from the sample, aiding in understanding the relationships and subsets within the given study context.

Learn more about Venn Diagram : brainly.com/question/20795347

#SPJ11

Answer:

enlargement

Step-by-step explanation:

if scale factor > 1 then enlargement

if scale factor 0 < SF < 1 then reduction

here SF = \(\frac{6}{5}\) = 1.2 > 1 so enlargement

Answer:

Enlargement

Step-by-step explanation:

Due to the scale factor properties stating that a SF value must be more than one to become an enlargement factor, we know that 6/5 is more than one whole. Thus, the SF is enlargement.

Answer:

\(\displaystyle \large{\frac{11}{3} < \sqrt{17} < \sqrt{20}}\)

Step-by-step explanation:

( 1 ) 11/3

\(\displaystyle \large{\frac{11}{3}}\) can be converted to mixed fractions to \(\displaystyle \large{3\frac{2}{3}}\)

Therefore, 11/3 is at least around 3, almost 4. It could be more than 3.5 by approximation but not exactly 4.

( 2 ) √20

\(\displaystyle \large{\sqrt{20}=\sqrt{5\cdot 4}}\\\displaystyle \large{\sqrt{20}=\sqrt{5\cdot 2\cdot 2}}\\\displaystyle \large{\sqrt{20}=2\sqrt{5}}\)

We know that \(\displaystyle \large{\sqrt{4}=2}\) so \(\displaystyle \large{\sqrt{5} > \sqrt{4}}\) which means approximately, \(\displaystyle \large{\sqrt{20}}\) can be either at least 4.3 up to 4.4

( 3 ) √17

We know that \(\displaystyle \large{\sqrt{16} = 4}\) so \(\displaystyle \large{\sqrt{17}}\) can be at least 4.1 up to 4.2, but it’s obvious that the square root of 17 is less than square root of 20 since \(\displaystyle \large{\sqrt{a} > \sqrt{b}}\) for a > b

Hence, from least to greatest:

\(\displaystyle \large{\frac{11}{3} < \sqrt{17} < \sqrt{20}}\)

Answer:

16 ft

Step-by-step explanation:

To find the perimeter of a square you must:

1. add all of the lengths together (4+4+4+4=16)

Have a great day.

Answer:

e^5

Step-by-step explanation:

When you multiply with exponents you add ONLY the exponents and multiply the variables    

The expression when evaluated is 17

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

a = 2, b = 3, c = 4 and d = 12

Also, we have

20 - 2b/a

Substitute the known values in the above equation, so, we have the following representation

20 - 2b/a = 20 - 2 * 3/2

Evaluate

20 - 2b/a = 17

Hence, the solution is 17

Read more about expression at

https://brainly.com/question/15775046

#SPJ1

The probability of choosing a 5 and then a 6 is 1/49

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

The tiles

Where we have

Total = 7

The probability of choosing a 5 and then a 6 is

P = P(5) * P(6)

So, we have

P = 1/7 * 1/7

Evaluate

P = 1/49

Hence, the probability of choosing a 5 and then a 6 is 1/49

Read more about probability at

https://brainly.com/question/31649379

#SPJ1

Question

You randomly choose one of the tiles. Without replacing the first tile, you choose a second tile. Find the probability of the compound event. Write your answer as a fraction or percent rounded to the nearest tenth. The probability of choosing a 5 and then a 6

The number of two-points and three points shot the cruisers scored are 24 and 19 respectively.

The Cruisers scored a total of 105 points in a basketball game against the Strikers. The Cruisers had a total of 43 baskets, some of which were two-point shots and some of which were three-point shots.

Therefore, the number of two-points and three-points the cruiser scored is as follows:

let

x = number of two-points

y = number of three-points

Hence, using equation

x + y = 43

2x + 3y = 105

Multiply equation(i) by 2

2x + 2y = 86

2x + 3y = 105

subtract equation(i) from equation(ii)

y = 19

Let's find x as follows:

x = 43 - 19

x = 24

Therefore,

number of two points = 24

number of three points = 19

To learn more about equations refer :

https://brainly.com/question/18649329

#SPJ1