The second part of the new coaster is a parabola.

Ray needs help creating the second part of the coaster. Create a unique parabola in the pattern f(x) = (x − a)(x − b). Describe the direction of the parabola and determine the y-intercept and zeros.

Answer:

9,9,0

Step-by-step explanation:

The first two are being added, so we want them to be the highest possible, to get the highest, or greatest, number. We then are subtracting, so we want the smallest number, as we’ll get the highest if we’re taking away the least. Henceforth, we substitute a 0 in the place of the ? in 384?9. It gets us 38419, the highest number I was able to find.

Hope This Helped!

there is a function on the interval [-1,1] that does not have an absolute maximum value and an absolute minimum value is False.

By the Extreme Value Theorem, if a function f is continuous on a closed interval [a,b], then it has both an absolute maximum value and an absolute minimum value on that interval.

since the given interval [-1,1] is a closed interval and any function defined on it is continuous, it must have an absolute maximum value and an absolute minimum value.

what is function?

In mathematics, a function is a rule or a relation that maps each element from one set, called the domain, to exactly one element in another set, called the range. A function is often represented as an equation or a graph, and is commonly denoted by the symbol f(x), where x is an element of the domain and f(x) is the corresponding output or value in the range.

Functions are used to model relationships between variables, describe patterns and behaviors in various mathematical and scientific contexts, and provide a powerful tool for solving problems and making predictions. Some common types of functions include linear, quadratic, exponential, trigonometric, and logarithmic functions, each with their own unique properties and characteristics.

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Answer:

290

Step-by-step explanation:

15(12)+110

290

Answer:

170

Step-by-step explanation:

1. y=12 is given so we should put this value in the equation 5y+110

2. then the equation will be 5x12+110

3. 5x12=60

4. 60+110= 170

Answer:not a man but I think you should just relax and be yourself, high school isn’t scary at all. When you go in for orientation walk around the school and find your classes so you have a good map of where you need to go in your head already! Best of luck

Step-by-step explanation:

Answer:

c)

subtract 5 times the second equation from 2 times the first equation

Step-by-step explanation:

subtract 5 times the second equation from 2 times the first equation

This will make the coefficient of the y variable 10

for both equations

10y - 10y = 0

leaving only x

Answer:

40

Step-by-step explanation:

Therefore, the probability of getting exactly 4 calls between 8:00 AM and 9:00 AM is approximately 0.1755, rounded to four decimal places.

To calculate the probability of getting exactly 4 calls between 8:00 AM and 9:00 AM, we need to use the Poisson distribution formula. The Poisson distribution is commonly used to model the number of events occurring in a fixed interval of time or space. In this case, the mean (λ) is given as 5. The formula for the Poisson distribution is:

P(X = k) = (e*(-λ) * λ\(^k\)) / k!

Where:

P(X = k) is the probability of getting exactly k calls

e is the base of the natural logarithm (approximately 2.71828)

λ is the mean number of calls (given as 5)

k is the number of calls (in this case, 4)

k! is the factorial of k

Let's calculate the probability using the formula:

P(X = 4) = (e*(-5) * 5⁴) / 4!

P(X = 4) ≈ 0.1755

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Answer:

17

Step-by-step explanation:

Second square number is 9; 3×3

second cube number is 8; 2×2×2

9+8=17.

The equation that represents the linear function is y = 2x.

A linear equation is in the form:

y = mx + b

Where y, x are variables, m is the rate of change and b is the y intercept.

Let us assume that from the table, we get the data with points (0, 0) and (2, 4). Hence:

\(y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-0=\frac{4-0}{2-0} (x-0)\\\\y=2x\)

The equation that represents the linear function is y = 2x.

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Answer:

Step-by-step explanation:

answer is -10

Answer:

x=-9

3x+1=5x+19

    -1        -1  

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

3x=5x+18

-5x -5x

----------

-2x=18

x=-9

Answer:1250

Step-by-step explanation:

Note that the complete statement is that ΔPQR ~ Δ STR on the bases of the AAA (Angle - Angle - Angle) Similarity Theorem.

Note that the Angle-Angle-Angle (AAA) criterion for the similarity of triangles states that "If in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio (or percentage) and consequently the two triangles are similar".

In the above case, we already know that:

\(\overline{QR}\) ⊥ \(\overline{PT}\) (Given)

In relation to the above, note that if two lines join at right angles, they are perpendicular (⊥). This fact is useful since all right angles are congruent, which means that any angles created by perpendicular lines are congruent, even if formed by distinct sets of lines.

What the above means is that besides:

∠QPR ≅ ∠STR; we now know that
∠QRP ≅ ∠SRT; where both are right angles triangles.

On the basis of the sum of angles in triangles, it is correct to state that given the two statements above,

∠PQR ≅ ∠RST

Since All the corresponding triangles are similar, we can state on the bases of the AAA Similarity Theorem that:

ΔPQR ~ Δ STR

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Answer:

51.7857143% increase is the percent increase of the price of the bicycle.

Step-by-step Explanation on finding percent increase using this question:

Formula needed:

% increase = 100 x (final-initial)/ | initial |

1. % increase = 100 x (85-56)/56

2.% increase = 100 x 29/56

3. % increase = 100 x 0.517857143

4. % increase = 51.17857143 (final answer)

Round if told by directions to do so.

Answer:

Step-by-step explanation:

The implied utilization of the resources in the process can be calculated by dividing the demand rate by the total capacity of the resources. In this case, the total capacity is 1.1 + 0.93 = 2.03 clients per hour. Therefore, the implied utilization is 0.75 / 2.03 = 0.369 (or 36.9%).

The implied utilization represents the proportion of the available capacity that is being utilized to meet the demand. In this scenario, approximately 36.9% of the total capacity is being utilized to serve the clients. This indicates that there is still some unused capacity available in the process.

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Answer:

A, B, D, E

Step-by-step explanation:

Given expression:

When multiplying decimals, multiply as if there are no decimal points:

\(\implies 6 \times 154 = 924\)

Count the number of digits after the decimal in each factor:

Therefore, there is a total of 5 digits.

Put the same number of total digits after the decimal point in the product:

\(\implies (0.06) \cdot (0.154)=0.00924\)

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

Answer option A

\(\boxed{6 \cdot \dfrac{1}{100} \cdot 154 \cdot \dfrac{1}{1000}}\)

When dividing by multiples of 10 (e.g. 10, 100, 1000 etc.), move the decimal point to the left the same number of places as the number of zeros.

Therefore:

\(\implies 6 \cdot \dfrac{1}{100} \cdot 154 \cdot \dfrac{1}{1000}=(0.06) \cdot (0.154)\)

Therefore, this is a valid answer option.

Answer option B

\(\boxed{6 \cdot 154 \cdot \dfrac{1}{100000}}\)

Multiply the numbers 6 and 154:

\(\implies 6 \times 154 = 924\)

Divide by 100,000 by moving the decimal point to the left 5 places (since 100,000 has 5 zeros).

\(\implies 6 \cdot 154 \cdot \dfrac{1}{100000}=0.00924\)

Therefore, this is a valid answer option.

Answer option C

\(\boxed{6 \cdot (0.1) \cdot 154 \cdot (0.01)}\)

Again, employ the technique of multiplying decimals by first multiplying the numbers 6 and 154:

\(\implies 6 \cdot 154 = 924\)

Count the number of digits after the decimal in each factor:

Therefore, there is a total of 3 digits.

Put the same number of digits after the decimal point in the product:

\(\implies 0.924\)

Therefore, as (0.06) · (0.154) = 0.00924, this answer option does not equal the given expression.

Answer option D

\(\boxed{6 \cdot 154 \cdot (0.00001)}\)

Again, employing the technique of multiplying decimals.

As there are a total of 5 digits after the decimals:

\(\implies 6 \cdot 154 \cdot (0.00001)=0.00924\)

Therefore, this is a valid answer option.

Answer option E

\(\boxed{0.00924}\)

As we have already calculated, (0.06) · (0.154) = 0.00924.

Therefore, this is a valid answer option.

To find the displacement of the particle at time t, we need to integrate its velocity function v(t) over the interval [0, t]:

s(t) = ∫v(t) dt

s(t) = ∫(t^2 - 2t - 24) dt

s(t) = (1/3)t^3 - t^2 - 24t + C

where C is the constant of integration.

To find the value of C, we need to use the initial condition that the particle is at the position s(0) = 0. Substituting t = 0 and s(0) = 0 into the above equation, we get:

0 = 0 + 0 - 0 + C

C = 0

Therefore, the displacement of the particle at time t is given by:

s(t) = (1/3)t^3 - t^2 - 24t

To find the displacement over the entire interval [0, 6], we can substitute t = 6 into the above equation:

s(6) = (1/3)(6^3) - 6^2 - 24(6)

s(6) = 36 - 36 - 144

s(6) = -144

Therefore, the displacement of the particle over the interval [0, 6] is -144 meters.

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The coordinates of the fourth corner are (x, y) = (5, 11)

The coordinates of a square are (1,7), (5,3), and (9,7)

Let's assume the four vertices of the square be A(1,7), B(5,3), C(9,7), and D(x,y).

Now coordinates of vertices D need to be found. For that use the following property of a square:

Diagonal squares bisect each other.

Since diagonal AC and BD bisect each other at point O(p,q). Therefore O is the mid-point of both AC and BD.

midpoint=(x1+x2/2,y1+y2/2)

Now since O is the mid-point of AC. Therefore,

\(O(p,q)=(\frac{1+9}{2} ,\frac{7+7}{2} )\)

Also since O is the mid-point of BD. Therefore,

\(O(p,q)=(\frac{5+x}{2} ,\frac{3+y}{2} )\\\\= > (5,7)=(\frac{5+x}{2} ,\frac{3+y}{2} )\\\)

\(\frac{5+x}{2} =5,\frac{3+y}{2}=7\\\)

5+x=10,3+y=14

x=5,y=11

Thus coordinates of the fourth corner are (5,11)

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The fourth quadrant of the square has the following coordinates: (5,11).

The three points of a square have the following coordinates: (1, 7), (5, 3), & (9, 7).

Rectangle ABCD:

A: (1,7) (left corner)

B: (5,3) (bottom corner)

C: (9,7) (right corner)

AB is 4 up and 4 left

BC is 4 up and 4 right.

The result is that the center of the square is at a 45 ° angle (5,7).

The four locations are situated on lines that are perpendicular to the x & y axes & pass through the center, four units away (5,7).

The omitted point, shown by the letter D, is the top corner.

It will be at X = 5 since it ought to have the same X position as point B. Given that it is 4 units higher than (5,7), its y coordinate is 7 + 4 = 11.

Consequently, the omitted position is at (5,11).

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Answer:

a couple different obes

Step-by-step explanation:

there are five

Answer:

12 only.

Step-by-step explanation:

When the question is asking for f(0), it is asking for the value of y when x = 0.

We see that there is only 1 intersection at x = 0, and the y value would equal 12.

Therefore, our answer is 12 only.

Answer:

The answer is a.12 only its where the x coordinate stays 0 and the y coordinate decreases or increases

Step-by-step explanation:

Answer:

23-22i

Step-by-step explanation:

The equivalent expression of (-45 - 22i) + 2(5 - 3i)(5 + 3i) is 23 - 22i

The complex expression is given as:

(-45 - 22i) + 2(5 - 3i)(5 + 3i)

Apply the difference of two squares on the expression

(-45 - 22i) + 2(5^2 - (3i)^2)

Evaluate the squares

(-45 - 22i) + 2(25 + 9)

Expand the bracket

-45 - 22i + 68

Evaluate the like terms

23 - 22i

Hence, the equivalent expression of (-45 - 22i) + 2(5 - 3i)(5 + 3i) is 23 - 22i

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Answer:

mRT = 4√13 ≈ 14.42

mST = 10√2 ≈ 14.14

Step-by-step explanation:

Pythagorean Theorem: a² + b² = c²

Since we have right triangles, in order to find the missing side, we use Pythagorean Theorem:

mTR:

12² + 8² = c²

144 + 64 = c²

c² = 208

c = √208 = 4√13

mST:

15² = 5² + b²

225 - 25 = b²

b² = 200

b = √200 = 10√2

To get your decimals, simply evaluate the square roots:

4√13 = 14.4222

10√2 = 14.1421

Answer:

6. 56.3 degrees.

7. 70.5 degrees.

Step-by-step explanation:

6. We are given the opposite and adjacent side lengths, so we can use tangent to solve this (TOA = Tangent; Opposite over Adjacent).

tan(R) = 12 / 8

tan(R) = 3 / 2

R = cotan(3/2)

R = 56.309932474020213

So, the measure of angle R is about 56.3 degrees.

7. We are given the adjacent and the hypotenuse, so we can use cosine to solve this (CAH = Cosine; Adjacent over Hypotenuse).

cos(R) = 5 / 15

cos(R) = 1/3

R = sec(1/3)

R = 70.528779365509

So, the measure of angle R is about 70.5 degrees.

Hope this helps!

Answer: 2680

Step-by-step explanation: Find the area of one of each rectangle size and multiply by the amount the rectangle shows up

A parallelogram with equal base and height is called a rhombus. A rhombus is a parallelogram with all sides equal in length, but not necessarily at right angles. So, if a rhombus has an area greater than 64 square meters, we can find its minimum length by calculating the length of one of its sides.

A parallelogram with equal base and height is called a rhombus. A rhombus is a parallelogram with all sides equal in length, but not necessarily at right angles. So, if a rhombus has an area greater than 64 square meters, we can find its minimum length by calculating the length of one of its sides: Area = base * height > 64 square meters

Since the base and height are equal, we can write: Area = base^2 > 64 square meters

Take the square root of both sides to get the minimum length of the base: base > sqrt(64) = 8 meters

So, any rhombus with a base greater than 8 meters and height equal to its base will have an area greater than 64 square meters. The height of the rhombus will also be greater than 8 meters since it has equal sides.In conclusion, a rhombus with a base greater than 8 meters and height equal to its base will have an area greater than 64 square meters. This is because the area of a rhombus is given by the product of its base and height, and any rhombus with a base greater than 8 meters will have an area greater than 64 square meters.

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The 99% confidence interval for the true mean lifespan of the product is, [12.128, 13.872].

What is standard deviation?

The standard deviation in statistics is a measurement of how much a group of values can vary or be dispersed. A low standard deviation suggests that values are often close to the set's mean, whereas a large standard deviation suggests that values are dispersed over a wider range.

Given: A toy maker claims his best product has an average lifespan of exactly 18 years.

A skeptical product evaluator asks for evidence (data) that might be used to evaluate this claim.

The product evaluator was provided data collected from a random sample of 35 people who used the product.

Using the data, an average product lifespan of 13 years and a standard deviation of 2 years was calculated.

As sample size is large we will use z value to calculate confidence Interval 99% confidence Interval is

{x bar} Z_({1 - alpha/2}) (s/√{n})

13\ 2.576* 2/ √13

(12.128, 13.872).

Hence, the 99% confidence interval for the true mean lifespan of the product is, [12.128, 13.872].

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Answer:

Based on the graphs shown, what would you conclude about the conditions under which enzymes function in cells?

A

Enzymes are most effective at a particular pH and temperature but can function over a range of pH and temperature.

B

С

Enzymes do not have a specific pH or temperature at which they are most effective but function optimally over a range of pH and temperature.

Enzymes work equally well at the low and high ends of their temperature range but reaction rate drops quickly at the high end of their pH range

Enzymes only function at a specific pH and temperature and cannot function over a range of pH or temperature.

D

9514 1404 393

Answer:

  ≈ 17.228101 cm

Step-by-step explanation:

The area of a trapezoid is given by the formula ...

  A = (1/2)(b1 +b2)h

Filling in the given information, we have ...

  99 = (1/2)((x+4) +(x-9))(x -4) = (1/2)(2x -5)(x -4)

  198 = 2x^2 -13x +20

  2(x -3.25)^2 = 199.125

  x = 3.25 +√99.5625 ≈ 13.228101

Then the length of the larger base is ...

  x+4 = 17.228101 . . . cm

Answer:

A & B

Step-by-step explanation:

Hope this helpsss

Answer:

A and B.

Step-by-step explanation:

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