Write a quadratic function in standard form that models the table.

If the test is normally distributed, then the probability of a score greater than 115 is (a) 1.62%.

In order to find probability of a score greater than 115 in a normally distributed test with a mean of 100 and standard deviation of 7,

First, We have to calculate z-score for 115, and

The z-score formula is ⇒ z = (x - μ)/σ,

where x = score of interest, μ = mean, and σ = standard-deviation.

In this case, we have x = 115, μ = 100, and σ = 7.

The z-score for 115 is ⇒ z = (115 - 100)/7 = 2.14

By using the normal table :

⇒ P(Z > 2.14) = 0.0162

Therefore, the required probability is 0.0162 or 1.62%, the correct option is (a) 1.62%.

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The given question is incomplete , the complete question is

Assume a normally distributed test has a mean of 100 and standard deviation of 7. What probability of a score greater than 115?

(a) 1.62%

(b) 48.38%

(c) 98.38%

(d) 51.62%

Answer: 35.553

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

6 - 6=0 the 0-3 -3 total of 9 and 6 + 3 is equal to 9

Answer:

2(-3±√120)

Step-by-step explanation:

quadratic formula

For the first parabola, the parts on the curve should be labeled as follows;

The vertex of the parabola are (-1, -2).

The max value is equal to -2.

The axis of symmetry is x = -1.

The zero is non-existent.

The parabola opens downward.

The y-intercept is equal to (0, -4).

In Mathematics and Geometry, the graph of a quadratic function would always form a parabolic curve because it is a u-shaped. Based on the first graph of a quadratic function, we can logically deduce that the graph is a downward parabola because the coefficient of x² is negative and the value of "a" is less than zero (0).

For the second parabola, the parts on the curve should be labeled as follows;

The vertex of the parabola are (0, 0).

The min value is equal to 0.

The axis of symmetry is x = 0.

The zero is 0.

The parabola opens upward.

The y-intercept is equal to (0, 0).

For the third parabola, the parts on the curve should be labeled as follows;

The vertex of the parabola are (2, 1).

The min value is equal to 1.

The axis of symmetry is x = 2.

The zero is non-existent.

The parabola opens upward.

The y-intercept is equal to (0, 5).

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Cartridges come in different sizes and shapes, and the amount of liquid ink

They can hold varies depending on the model and manufacturer.
Of course, I am here to help.

However, to better assist you, I will need more information regarding your urgent situation.
Once I have a better understanding of your situation, I can provide you with a more tailored and effective response.

In the meantime, I recommend taking a few deep breaths and staying calm.

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The percent increase in the annual student fees at the University of California between 2000 and 2014 is 125%.

What is percentage?

Percentage is a way of expressing a number or proportion as a fraction of 100. It is represented by the symbol "%".

To find the percent increase, we need to calculate the difference between the two amounts and then divide that difference by the original amount, and finally multiply by 100 to express the result as a percentage.

The difference between the final amount ($9,000) and the initial amount ($4,000) is $5,000.

So the percent increase can be calculated as follows:

Percent increase = (difference / original amount) x 100%

= ($5,000 / $4,000) x 100%

= 125%

Therefore, the percent increase in the annual student fees at the University of California between 2000 and 2014 is 125%.

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Answer:

The ramp will rise 11.6 inches from the ground at its highest end.

11.6 in.

Step-by-step explanation:

In this example we can use the sine function to determine how high the ramp will rise from the ground.

The definition of the sine function is

[tex]\sf \sin x= \dfrac{opposite}{hypotenuse}[/tex]

[tex]\sf \sin x= \dfrac{O}{H}[/tex]

In this case we are looking to evaluate the length of the opposite side.

We can rearrange the equation to isolate [tex]\sf O[/tex].

Multiply both sides of the equation by [tex]\sf H[/tex].

[tex]\sf H \cdot \sin x= \dfrac{O}{H} \cdot H[/tex]

Cancel the common factor of [tex]\sf H[/tex] on the right side leaves us with

[tex]\sf H \cdot \sin x= \dfrac{O}{\diagup \!\!\!\! H} \cdot \diagup \!\!\!\! H[/tex]

[tex]\boxed{\sf O= H \cdot \sin x}[/tex]

Numerical Evaluation

In this example we are given

[tex]\sf x=20\\\sf H=34[/tex]

Substituting our given values into the equation yields

[tex]\sf O= 34\cdot \sin 20[/tex]

[tex]\sf O=11.628685[/tex]

Rounding to the nearest tenth

[tex]\sf O=11.6[/tex]

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The missing expression that was covered by the drop of ink is simply 3[tex]x^{2}[/tex].

What is Algebraic expression ?

An algebraic expressiοn is a statement in mathematics that can cοntain variables, integers, οperatοrs (including additiοn, subtractiοn, multiplicatiοn, and divisiοn), as well as grοuping symbοls like brackets.

The given expression is:

-24[tex]x^{5}[/tex] - 16[tex]x^{3}[/tex] = -8[tex]x^{3}[/tex] (? + 2)

To find the missing expression, we need to isolate the unknown factor, denoted by the question mark (?). We can begin by factoring out the common term of -8x³ from the left side of the equation:

-8[tex]x^{3}[/tex](3[tex]x^{2}[/tex] + 2) = -8[tex]x^{3}[/tex](? + 2)

Now, we can divide both sides by -8[tex]x^{3}[/tex], which gives:

3[tex]x^{2}[/tex] + 2 = ? + 2

Subtracting 2 from both sides yields:

3[tex]x^{2}[/tex] = ?

Therefore, the missing expression that was covered by the drop of ink is simply 3[tex]x^{2}[/tex].

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As a result, 12 is the exponential expression employing a rational exponent.

An exponent of a fraction or rational number is said to have a rational exponent. With x as the base, p as the power, and q as the root 21, it may be represented as x(p/q). It can be transformed into the corresponding radical form,

for example, x(p/q) = (x(1/q))p = qxp 21. Similar rules apply to rational exponents and integer exponents 1.

With a rational exponent, the expression 3√24 can be expressed exponentially as follows:

3√2⁴= 3(2²)

= 3(2²) = 12

As a result, 12 is the exponential expression employing a rational exponent.

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Answer:

the answer is B. 38 rounds per hour.

The bell tolls 6 times between 11:45 AM and 3:10 PM

To find out how many times the bell tolls between 11:45 AM and 3:10 PM, follow these steps:
1. Identify the first bell toll after 11:45 AM:

The first bell toll occurs at 12:00 PM (noon) since it is the next half hour after 11:45 AM.
2. Identify the last bell toll before 3:10 PM:  

The last bell toll occurs at 3:00 PM since it is the last half hour before 3:10 PM.
3. Calculate the total time between the first and last bell tolls:  

From 12:00 PM to 3:00 PM, there are 3 hours.
4. Determine the number of bell tolls in each hour:

Since the bell tolls every 30 minutes, it tolls 2 times per hour (on the hour and at half past the hour).
5. Calculate the total number of bell tolls:

For 3 hours, the bell tolls 3 hours x 2 tolls per hour = 6 tolls.

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Answer:

yes, because 6 is less than 11

Step-by-step explanation:

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Mark me brianliest and good luck!!

The weight of the soccer balls bought by the coach is 40.18 pounds. therefore, option a.40.18 is correct.

To determine the weight of the soccer balls the coach bought, we need

to analyze the given line plot. The line plot shows the weight of each of

the 11 soccer balls bought by the coach.

The first step is to find the scale of the line plot. In this case, the scale is

in pounds, and the plot ranges from 0 to 8 pounds. Each "x" on the plot

represents one soccer ball, and the height of the "x" shows the weight of

that ball in pounds.

To find the total weight of the soccer balls bought by the coach, we

simply need to add up the weights of all the balls. Looking at the line

plot, we can see that there are:

2 balls that weigh 1 pound each

1 ball that weighs 3 pounds

1 ball that weighs 2 pounds

1 ball that weighs 5 pounds

1 ball that weighs 3.7 pounds

1 ball that weighs 8 pounds

2 balls that weigh 4 pounds each

1 ball that weighs 8.48 pounds

Adding all these weights together, we get:

1 + 1 + 3 + 2 + 5 + 3.7 + 8 + 4 + 4 + 8.48 = 40.18 pounds

Therefore, the weight of the soccer balls bought by the coach is 40.18 pounds.

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Question

A soccer couch bought eight soccer balls. This line plot shows the weight of each ball the couch bought?

what is the total weight, in pounds, of all the soccer balls the coach bought?                                                                                            

a. 40.18    b. 60  c. 30    d. 20

Answer:

The improper/exact form=5/3 and the decimal form is 1.(6) (which is the 6 repeated)

Step-by-step explanation:

Technically, you can't simplify 1 2/3, but these are just two ways you could change it into.

A distribution that includes more vehicles sold at lower prices and may deviate from the initial distribution as a result of the inclusion of vehicles priced under $5,000.

A distribution in statistics is a function that identifies all potential values for a dataset together with their frequencies or probabilities. The normal distribution, the binomial distribution and the Poisson distribution are just a few examples of frequent distribution types. Data are described and analyzed using distributions, which may offer significant insights about a dataset's central tendency, variability, and form.

The distribution will be impacted in a number of ways if the salesperson decides to also offer automobiles that cost less than $5,000 and forecasts selling 200 of them over the next ten years. In particular, it will

Growth in vehicle sales: Over the next 10 years, more vehicles under $5,000 will be sold, increasing the overall vehicle sales.

Change the distribution of prices towards lower values: By selling more automobiles at lower prices, the introduction of more affordable vehicles will change the price distribution towards lower values.

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The total number of revolutions per minute tire makes when the car is traveling at a speed of 90 mi/hr and the tire has a diameter of 22 inches is equal to approximately 1375.09.

Diameter of a car tire = 22 inches

Speed of a car = 90mi/hr

Let us first convert the speed from miles per hour to inches per minute,

Since the diameter of the tire is given in inches.

90 mi/hr

= 90 × 5280 ft/hr

= 475200 ft/hr

= 475200 × 12 in/hr

= 5,702,400 in/hr

= 95,040 in/min

Number of revolutions the tire makes per minute,

Distance the tire travels in one revolution.

The circumference of a circle is given by,

C = πd

where C is the circumference and d is the diameter.

So the distance the tire travels in one revolution is,

d = π(22 in)

  = 69.115 in

Now, the number of revolutions per minute  is ,

=distance traveled per minute / distance traveled in one revolution

⇒ revolutions per minute = 95,040 in/min / 69.115 in/rev

⇒revolutions per minute ≈ 1375.09 rev/min

Therefore, the tire makes approximately 1375.09 revolutions per minute with tire of diameter of 22 inches.

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Answer:

31

Step-by-step explanation:

Answer:

Step-by-step explanation:

Fractions represent a division problem where the numerator is divided by the denominator. For example, the fraction 3/4 represents the division of 3 by 4, which can be written as 3 ÷ 4. This is why it makes sense that fractions are about division.

Furthermore, fractions are used to represent parts of a whole or a group. When we divide a whole into equal parts, we are essentially dividing the whole into groups, with each group having the same size. For example, if we divide a pizza into 8 equal slices, each slice represents 1/8th of the pizza. We can also think of this as dividing the pizza into 8 equal groups, with each group having one slice.

Therefore, fractions are a natural way to represent division, as they allow us to express how many parts we have out of a whole or a group, and how big each part is relative to the whole or group.

A. The two types of transformations that can be used to transform f(x) to g(x) are translation and reflection.

B. The value for k in the transformation is -6.

C. The equation for transforming is g (x) = f (x) - 6.

What is transformation?

Shapes on a coordinate plane can be translated, rotated, and reflected using transformations. You can rotate, translate, or reflect any line, point, or vector.

A. The two types of transformations that can be used to transform f(x) to g(x) are translation and reflection.

Translation means shifting the graph left, right, up or down.

Reflection means creating a mirror image over x - axis or y - axis.

B. Both the transformations will have the same k value.

The graph g (x) is the translation of f (x) towards left with 6 units.

So, the value of k is -6.

C. The equation for transformation is as follows:

⇒ g (x) = f (x) + k

⇒ g (x) = f (x) - 6

Hence, the required solutions have been obtained.

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Answer: 8.5 feet

Step-by-step explanation:

To determine how far Max traveled, we can use the Pythagorean theorem to find the distances between the points.

Max twirls to Lindsey's position:

Since Max is 2 feet behind Kenji and 4 feet left of Lindsey, Max and Lindsey form a right triangle with legs of 2 feet and 4 feet. Using the Pythagorean theorem:

a² + b² = c²

2² + 4² = c²

4 + 16 = c²

20 = c²

Taking the square root of both sides:

c = √20 ≈ 4.47 feet (rounded to the nearest tenth)

Max leaps to Kenji's position:

Since Max was initially 2 feet behind Kenji, the distance between Lindsey and Kenji is also 2 feet.

Max walks back to his original position:

The distance between Max's original position and Kenji's position is 2 feet.

Adding up the distances:

4.47 feet (Max to Lindsey) + 2 feet (Lindsey to Kenji) + 2 feet (Kenji to Max's original position) = 8.47 feet

So, Max traveled approximately 8.5 feet (rounded to the nearest tenth) during his movements.

The distance Max traveled can be found by calculating the distance of each movement he makes and adding them up. First, we need to use the Pythagorean theorem to calculate the distance between Lindsey and Max:

sqrt(4^2 + 2^2) = sqrt(16 + 4) = sqrt(20) = 2*sqrt(5)

So, Max travels 2*sqrt(5) feet to get to Lindsey's position. Next, he travels the distance between Kenji and Lindsey, which is 4 feet:

distance = 4

Finally, he travels in a straight line back to his original position, which is 2 feet straight behind Kenji:

distance = 2

Adding these distances together, we get:

2*sqrt(5) + 4 + 2 = 2*sqrt(5) + 6

Rounding to the nearest tenth gives us a final answer of approximately 8.5 feet.

In response to the stated question, we may state that As a result, vector v has a magnitude of 6 and a direction of 160°.

A vector in mathematics is a mathematical object with both magnitude (or length) and direction. Vectors are frequently depicted as arrows, with the length of the arrow representing the magnitude and the direction of the arrow representing the vector's direction. A vector, for example, might represent an object's velocity, where the magnitude of the vector indicates the object's speed and the direction of the vector represents the direction of motion.  

Assuming that u has a magnitude of 3 and a direction of 160°.

Vector u can be represented by its components as follows:

3 cos(160°)i + 3 sin(160°)j = u

where I and j are unit vectors pointing in the x and y directions.

We now know that vector v = 2u, implying that the magnitude of vector v is:

|v| = |2u| = 2|u| = 2(3) = 6

As a result, the magnitude of vector v is 6.

We can use the fact that vector v is in the same direction as vector u but scaled by a factor of two to determine its direction. As a result, the vector v's direction is also 160°.

As a result, vector v has a magnitude of 6 and a direction of 160°.

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Answer:

C

Step-by-step explanation:

Because 1.2+1.8 equal to 3.

Answer:

The expressions 10³÷10⁷, 10¹²/10¹⁶, and 10⁻²/10² are all equivalent to 10⁻⁴.

Step-by-step explanation:

When dividing exponents with the same base you subtract the exponents.

For visuals, in the equation 10³÷10⁷ it would be 10³⁻⁷ which would be 10⁻⁴ since 3 minus 7 is negative 4.

It is the same thing for 10¹²/10¹⁶, it would be 10¹²⁻¹⁶ which is equal to 10⁻⁴.

The same method can be used for 10⁻²/10² (10⁻²⁻²).

When we simplify an equatiοn and end up with a cοntradictiοn like this, it means that the equatiοn has nο sοlutiοn.

The intersectiοns οr meetings οf the lines οr planes that represent the linear equatiοns are knοwn as the sοlutiοns οf linear equatiοns. The set οf values fοr the variables in every feasible sοlutiοn is knοwn as a sοlutiοn set fοr a system οf linear equatiοns.

Nοt a Sοlutiοn

If there is nο intersectiοn οf any lines, οr if the graphs οf the linear equatiοns are parallel, then the system οf linear equatiοns cannοt be sοlved.

The equatiοn 5 + 9z = 9z can be simplified as fοllοws:

5 + 9z = 9z

5 = 0

This is a cοntradictiοn since 5 cannοt be equal tο 0. Therefοre, there is nο sοlutiοn fοr this equatiοn.

In general, when we simplify an equatiοn and end up with a cοntradictiοn like this, it means that the equatiοn has nο sοlutiοn.

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Step-by-step explanation:

To find the smallest total number of hot dogs that Yadira's mom can purchase, we need to find the least common multiple (LCM) of 12 and 9, since she wants the same number of hot dogs as hot dog buns.

The multiples of 12 are: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, ...

The multiples of 9 are: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, ...

The least common multiple of 12 and 9 is 36, since it is the smallest number that appears in both lists. Therefore, Yadira's mom should purchase 36 hot dogs (3 packs of 12) and 36 hot dog buns (4 packs of 9) for the family barbecue.

Step-by-step explanation:

L X W X D = cubic feet volume

17 X 30 X .25 = 127. 5  ft^3

Sean would choose apples over pears if he were offered both, based on his preference order of apples > clementines > pears and the assumption that his preferences are transitive.

Sean's preference order for fruits is: apples > clementines > pears. As a rational decision-maker, Sean would choose the option that he prefers the most. In this case, since he prefers apples over clementines and pears, if he were offered pears or apples, he would choose apples.

This decision is based on the assumption that Sean's preferences are transitive, meaning that if he prefers A to B and B to C, then he would prefer A to C. Therefore, choosing apples over pears is the most rational decision for Sean, based on his given preference order.

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