Write a linear function with the values f(0) = - 5 and f(3) = 4

Answer:(4,-25)

Step-by-step explanation:

To find the number of licorice ropes r that came in the bag, the equation would be r = 27.

A system of equations is two or more equations that can be solved to get a unique solution.

Each student gets 3 licorice ropes to decorate the roof of his or her gingerbread house.

Let the number of licorice ropes that came in the bag be r.

The equation formed:

Therefore, to find the number of licorice ropes r that came in the bag, the equation would be r = 27.

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Each transformation affects the shape and position of the graph. It is important to carefully consider the order of the transformations and their impact on the equation.

1. Horizontal Shift (c):
If there is a horizontal shift, the equation becomes y = (x - c)^3.
For example, if there is a shift of 2 units to the right, the equation would be y = (x - 2)^3.

2. Vertical Shift (d):
If there is a vertical shift, the equation becomes y = x^3 + d.
For example, if there is a shift of 3 units upwards, the equation would be y = x^3 + 3.

3. Vertical Stretch (a):
If there is a vertical stretch or compression, the equation becomes y = a * x^3.
For example, if there is a vertical stretch by a factor of 2, the equation would be y = 2 * x^3.

4. Reflection (along the x-axis):
If there is a reflection along the x-axis, the equation becomes y = -x^3.
This flips the graph of the original function upside down.

5. Reflection (along the y-axis):
If there is a reflection along the y-axis, the equation becomes y = (-x)^3.
This mirrors the graph of the original function.

6. Combined Transformations:
If there are multiple transformations, we can apply them in the order they are given. For example, if there is a vertical stretch by a factor of 2 and a horizontal shift of 3 units to the right, the equation would be y = 2 * (x - 3)^3.

Remember, each transformation affects the shape and position of the graph. It is important to carefully consider the order of the transformations and their impact on the equation.

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Answer:

Games to make? or play? If play then I suggest age of empires 2 DE, the games insane

Step-by-step explanation:

Steps to calculate the area are shown below and the figure is attached below.

The steps of calculating the area of the given figure are,

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Answer:

They travel 5/18 in one hour

Step-by-step explanation:

Answer:

In an hour the car can cover 5/18 of the distance

Answer:

C. Q1 = 99; Q2 = 106.5; Q3 = 109

Step-by-step explanation:

73, 98, 99, 99, 105, 108, 109, 109, 110, 110

✔️The median = Q2

The median = (105+108)/2 = 106.5

✔️Q2 is the middle part of the lower set of data to your left below the median.

73, 98, [99,] 99, 105, 108, 109, 109, 110, 110

Thus, Q2 = 99

✔️Q3 is the middle part of the upper set of data to your right above the median.

73, 98, 99, 99, 105, 108, 109, [109,] 110, 110

Thus, Q3 = 109

The upper specification limit is 2.520 mm, and the lower specification limit is 2.480 mm.  The process is not capable according to the purchaser's requirement of a capability index of 1.50.

(a) The upper specification limit (USL) is calculated by adding the process mean (2.500 mm) to the upper tolerance (0.020 mm), resulting in 2.520 mm. The lower specification limit (LSL) is calculated by subtracting the lower tolerance (0.020 mm) from the process mean, resulting in 2.480 mm.

(b) The process capability index (Cp) is calculated by dividing the tolerance width (USL - LSL) by six times the standard deviation. In this case, the tolerance width is 0.040 mm (2.520 mm - 2.480 mm) and the standard deviation is 0.004 mm. Therefore, Cp = 0.040 mm / (6 * 0.004 mm) = 1.25.

(c) The purchaser requires a capability index (Cpk) of 1.50, which measures how well the process meets the specification limits. Since Cp (1.25) is less than the desired Cpk (1.50), the process is not capable according to the purchaser's requirement. It is not good enough for the supplier either, as the Cp is less than the desired level.

(d) If the process mean were to drift to 2.497 mm, the Cp value would remain the same at 1.25. Since the Cp value is still less than the desired Cpk of 1.50, the process would still not be good enough for the supplier's needs, even with the changed process mean.

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The amount of wrapping paper that is required is; c. 202 sq. in.

The formula for the surface area of a rectangular cuboid is given as:

SA = 2(lw + lh + hw)

where;

l = length

h = height

w = width

We are given;

Length; l = 3 in.

Width; w = 7 in.

Height; h = 8 in.

Thus, surface area is;

SA = 2((3*7) + (3*8) + (8*7))

SA = 2(21 + 24 + 56)

SA = 2(101)

SA = 202 sq. in

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Answer:

18 miles

Step-by-step explanation:

the ratio is miles/minute

10/50=0.2

so no just multiply the amount of minute you want 0.2*90= 18 miles

Answer and Step-by-step explanation:

In an hour and a half, Dana would go 18 miles since she's going a mile at regular intervals, so if she's trekking for an additional forty minutes, she will bicycle 8 miles. This implies that you'd increase five minutes by 8 miles (recall it's a mile for every 5 minutes) and that would give you forty. At that point simply add that to the 50 minutes she's been cycling as of now.

The minimum number of students that must be in the professor's class in order to guarantee that at least 2 answer sheets are identical is 1025.

In order to answer this question, we need to use the Pigeonhole Principle, which states that if there are n pigeonholes and more than n objects, then at least one pigeonhole must contain more than one object.
In this case, the "pigeonholes" are the different possible combinations of answers for the 5 questions, and the "objects" are the students in the class.

Since there are 4 possible responses for each question, there are 4^5 = 1024 possible combinations of answers.
Now, suppose there are only 1023 students in the class.

Each student can choose one of the 1024 possible combinations of answers, and since there are more students than combinations, at least one combination must be chosen by two or more students.

Here are 5 questions, the total number of different answer sheets is 4^5 = 1024.

This represents the "pigeonholes." 3.

To guarantee that at least two answer sheets are identical, we need 1024 + 1 = 1025 students. This represents the "pigeons.

" According to the Pigeonhole Principle, if there are n pigeonholes and n+1 pigeons, at least one pigeonhole must contain at least two pigeons.

In this case, having 1025 students (pigeons) ensures that at least two students have identical answer sheets (pigeonholes).
But we want to guarantee that at least 2 answer sheets are identical.

This means we need to have one more student than the number of possible combinations, so that there is no way for each combination to be chosen by a different student.

Therefore, the minimum number of students required in the professor's class is 1024 + 1 = 1025.
So if there are 1025 or more students in the class, we can be sure that at least two answer sheets must be identical.

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15% of the time, the probability that student who chose to walk has been late.

From the stated data-

37.5% of the 40% of students who walk to school have been late.

Thus,  37.5% of 40%

= 0.375 x 0.40

= 0.1500

= 15%

Thus, 15% of the time, the student who chose to walk has been late atleast once .

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The complete question is-

At a large high school 40 percent of the students walk to school, 32 percent of the students have been late to school at least once, and 37.5 percent of the students who walk to school have been late to school at least once. One student from the school will be selected at random. What is the probability that the student selected will be one who both walks to school and has been late to school at least once?

1. Three examples of situations where consistency is important:

Healthcare: when treating patients, healthcare providers must follow consistent procedures and protocols to ensure that every patient receives the same level of care.

Financial transaction: when making financial transactions, it is important to follow regular security rules to prevent fraud.

Support rules: Adherence to consistent rules and regulations in sports is essential to ensure fair play and the safety of all participants.

2. The number 0 is important in mathematical systems because it represents the absence of a number and serves as a placeholder. Without zero, our mathematical system would be affected in many ways. For example, writing the number 100 would be difficult without the zero. Without the invention of zero, progress in mathematics would have been delayed.

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Recall Euler's theorem: if \(\gcd(a,n) = 1\), then

\(a^{\phi(n)} \equiv 1 \pmod n\)

where \(\phi\) is Euler's totient function.

We have \(\gcd(9,32) = 1\) - in fact, \(\gcd(9,32^k)=1\) for any \(k\in\Bbb N\) since \(9=3^2\) and \(32=2^5\) share no common divisors - as well as \(\phi(9) = 6\).

Now,

\(37^{32} = (1 + 36)^{32} \\\\ ~~~~~~~~ = 1 + 36c_1 + 36^2c_2 + 36^3c_3+\cdots+36^{32}c_{32} \\\\ ~~~~~~~~ = 1 + 6 \left(6c_1 + 6^3c_2 + 6^5c_3 + \cdots + 6^{63}c_{32}\right) \\\\ \implies 32^{37^{32}} = 32^{1 + 6(\cdots)} = 32\cdot\left(32^{(\cdots)}\right)^6\)

where the \(c_i\) are positive integer coefficients from the binomial expansion. By Euler's theorem,

\(\left(32^{(\cdots)\right)^6 \equiv 1 \pmod9\)

so that

\(32^{37^{32}} \equiv 32\cdot1 \equiv \boxed{5} \pmod9\)

Answer: 1/2

Explanation: There are 5 vowels and 5 consonants in the word believable. So to find the consonant, you have to do a fraction with consonant as numerator and the total number of letters as the denominator. Since there are 5 consonants and 10 letters in total, the simplest form will be 1/2.

Answer:

The sine of cx in the triangle is the opposite side/the hypotenuse

sin(cx) = 7/25

sin(cx) = 0.28

cx = sin^-1 (0.28)

cx = 16.26 degrees

The vertex and range are (-2, -3) and y >= -3 respectively

The equation is given as:

y = |x +2| - 3

The above equation is an absolute value equation

An absolute value equation is represented as:

y = a|x - h| + k

Where

Vertex = (h, k)

So, we have

Vertex = (-2, -3)

Also, we have

a = 1

Since a is positive, then the vertex is a minimum

Hence, the vertex and range are (-2, -3) and y >= -3 respectively

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Considering the extremas, the graph D represents the situation in this problem.

For this problem, we have that 33 days is the period between the relative maximums of the function, hence graph D represents the situation in this problem.

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The fishing company caught approximately nearest to the whole number is 1,390,332 fish over the first 14 years, with a 3% decrease in the number of fish caught each year.

How many fish has a fishing company caught in total?

To calculate the total number of fish caught over 14 years, we need to calculate the number of fish caught each year and add them together.

We know that in the first year, the company caught 130,000 fish. In the second year, the company caught 3% less than in the first year, which is:

130,000 - (3/100) * 130,000 = 126,100 fish

In the third year, the company caught 3% less than in the second year, which is:

126,100 - (3/100) * 126,100 = 122,237 fish

We can continue this pattern for the next 11 years to find the number of fish caught in each year, or we can use a formula to calculate it. The nth term of a geometric series has the following formula:

\(a \times r^{n-1}\)

Where a represents the first term, r represents the common ratio, and n represents the term number. In this case, the first term is 130,000 and the common ratio is 0.97 (since the number of fish caught decreases by 3% each year). So the formula for the number of fish caught in the nth year is:

\(130{,}000 \times 0.97^{n-1}\)

We can use this formula to calculate the number of fish caught in each year from year 2 to year 14, and then add them all together to find the total:

130,000 + 126,100 + 122,237 + ... + 65,489

Using a calculator, we can find that the sum is approximately 1,390,332 fish. Rounded to the nearest whole number, the company caught a total of 1,390,332 fish over the first 14 years.

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As similarity theorem, the value of x that will make the triangles similar by SSS similarity theorem is 77.

Similarity theorem:

In math, similarity theorem refers the line segment splits two sides of a triangle into proportional segments if and only if the segment is parallel to the triangle's third side.

Given,

Here we need to find the t value of will make the triangles similar by the similarity theorem.

For example, we are told that the 2 triangles are similar by SSS theorem.

Here we know that, SSS means Side - Side -Side and it is a congruence theorem which states that the 3 corresponding sides of two triangles have same ratio, then we can say that the two triangles are congruent by SSS theorem

Therefore, in the triangles ,applying the SSS postulate gives;

=> x/35 = 44/20

Then by applying the multiplication property of equality, let us multiply both sides by 35 to get;

=> x = (44 * 35)/20

When we simplify this one then we get,

=> x = 77

Therefore, the value of x is 77.

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Answer:

\(5m+8=16\)

Step-by-step explanation:

\(5m+8=16 \\ \\ 5m=8 \\ \\ m=1.6 \neq 2\)

Answer:

9*9=81 so 9 times...

Answer: 669.4$ you do 670-60% or -0.60

Answer:

The answer is 268 dollars. Look below for more information.

Step-by-step explanation:

If Luna's original price is 670 dollars and the new price is 60 off, then we need to figure out 60 percent of 670 which is 402. Then we subtract 402 from 670 getting 268. That is how we can figure out how to find prices with a sale.

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Answer:B.Sample space

Step-by-step explanation:

Evaluating the integral using power rule and substitution gives:

\((121 + z^{2}) ^{\frac{1}{2} } + C\)

We want to evaluate the integral given as:

\(\int\limits {\frac{z}{\sqrt{121 + z^{2} } } } \, dz\)

We can use a substitution.

Let's set u = 121 + z²

Thus:

du = 2z dz

Thus:

z*dz = ¹/₂du

Now, let's substitute these expressions into the integral:

\(\int\limits {\frac{z}{\sqrt{121 + z^{2} } } } \, dz = \int\limits {\frac{1}{2} } \, \frac{du}{\sqrt{u} }\)

To simplify the expression further, we can rewrite as:

\(\int\limits {\frac{1}{2} } \, u^{-\frac{1}{2}} {du}\)

Using the power rule for integration, we finally have:

\(u^{\frac{1}{2}} + C\)

Plugging in 121 + z² for u gives:

\((121 + z^{2}) ^{\frac{1}{2} } + C\)

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The probability that at least 2 of the dinners selected are pasta dinners is approximately 0.7456.

The probability of selecting at least 2 pasta dinners can be found by calculating the probability of selecting exactly 2, 3, 4, or 5 pasta dinners and adding those probabilities together. To do this, we'll use the formula:

P(at least 2 pasta dinners) = P(2 pasta dinners) + P(3 pasta dinners) + P(4 pasta dinners) + P(5 pasta dinners)

To calculate each of these probabilities, we'll use the formula:

P(k pasta dinners) = (C(k, 10) * C(5-k, 8)) / C(5, 18)

where C(n, r) is the number of ways to choose r items from a set of n items (the combination formula).

Using this formula, we get:

P(2 pasta dinners) ≈ 0.4545

P(3 pasta dinners) ≈ 0.2469

P(4 pasta dinners) ≈ 0.0420

P(5 pasta dinners) ≈ 0.0022

Therefore:

P(at least 2 pasta dinners) ≈ 0.4545 + 0.2469 + 0.0420 + 0.0022 ≈ 0.7456

So, the probability that at least 2 of the dinners selected are pasta dinners is approximately 0.7456.

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