A study was conducted on students from a particular high school over the last 8 years. The following information was found regarding standardized tests used for college admittance. Scores on the SAT test are normally distributed with a mean of 1029 and a standard deviation of 205. Scores on the ACT test are normally distributed with a mean of 22.7 and a standard deviation of 5. It is assumed that the two tests measure the same aptitude, but use different scales.

If a student gets an SAT score that is the 50-percentile, find the actual SAT score.
SAT score =
Round answer to a whole number.

What would be the equivalent ACT score for this student?
ACT score =
Round answer to a whole number.

If a student gets an SAT score of 1501, find the equivalent ACT score.
ACT score =
Round answer to a whole number.

Answer:

41)  Yes, the relation is a function.

42)  The domain of the function is [-2, 4].

43)  The range of the function is [-1, 3].

Step-by-step explanation:

A relation is a set of ordered pairs where each input (x-value) is associated with one or more outputs (y-values).

A function is a special type of relation where each input (x-value) is associated with exactly one output (y-value).

We can determine if a graphed relation is a function by applying the Vertical Line Test. It states that if a vertical line intersects the graph at more than one point, then the relation does not pass the test and is not a valid function.

As the given graph passes the Vertical Line Test, the relation is a function.

[tex]\hrulefill[/tex]

The domain of a function is the set of all possible input values (x-values).

The range of a function is the set of all possible output values (y-values).

From inspection of the given graph, the continuous curve begins in quadrant II at point (-2, 1) and ends in quadrant IV at point (4, -1).

The endpoints of the graph are represented by closed circles, which means that the corresponding x and y values are included in the domain and range.

Therefore, the domain of the function is the x-values of the endpoints: [-2, 4].

The minimum point of the curve is endpoint (4, -1) and the maximum point is (0, 3). Therefore, the range of the function is the y-values of the minimum and maximum points: [-1, 3].

The Intel pays $7,760 to Bally Manufacturing on August 14.

The first step in calculating what Intel Corporation pays Bally on August 14 is to determine the net price of the machinery after the trade discount and the return of $100 due to defects.

The trade discount of 40% is calculated as follows:

Discount = List price × Discount rate

Discount = $13,100 × 0.40 = $5,240

So the net price of the machinery after the trade discount is:

Net price = List price - Discount

Net price = $13,100 - $5,240 = $7,860

After Intel returns $100 of machinery, the cost of the machinery is further reduced to:

Net price after return = Net price - Return

Net price after return = $7,860 - $100 = $7,760

Since the payment terms are 3/10 EOM (end of month), Intel receives a discount of 3% if payment is made within 10 days. The 10-day period begins on August 1 and ends on August 10 (the payment due date). Since Intel pays the bill on August 14, payment is late and the 3% discount does not apply.

For such more questions on pays

https://brainly.com/question/25793394

#SPJ8

The y-intercept of the line of best fit can be interpreted as the predicted test grade when no time is spent on homework, which in this case is approximately 72. However, it is important to consider the limitations and potential sources of error in any statistical analysis.

In statistics, linear regression is a commonly used statistical method for analyzing the relationship between two variables, such as time spent on homework and test grades. A line of best fit, also known as a regression line, is a line that summarizes the linear relationship between the variables. In this case, the line of best fit has an equation of y = 7.9 x + 72.
The y-intercept of the line is the point where the line intersects with the y-axis. It represents the value of y when x is equal to zero. In other words, it is the predicted test grade when no time is spent on homework. According to the given equation, the y-intercept is 72. This means that if a student spends no time on homework, they can still expect to receive a test grade of 72.
However, it is important to note that this interpretation assumes that the line of best fit is an accurate representation of the relationship between time spent on homework and test grades. Additionally, there may be other variables that influence test grades, such as innate ability, test-taking skills, or external factors like test anxiety or distractions during the exam.
for such more questions on time

https://brainly.com/question/26862717

#SPJ8

The simplified expression is [tex]-4x^2 + 3x + 1[/tex], which is a quadratic polynomial. Option D.

To simplify the expression [tex](8x^2 + 3x) - (12x^2 - 1)[/tex], we can distribute the negative sign to each term within the parentheses:

[tex]8x^2 + 3x - 12x^2 + 1[/tex]

Next, we can combine like terms by adding or subtracting coefficients of similar powers of x:

[tex](8x^2 - 12x^2) + 3x + 1[/tex]

Simplifying further, we have:

[tex]-4x^2 + 3x + 1[/tex]

The resulting polynomial [tex]-4x^2 + 3x + 1[/tex] is a quadratic polynomial since it has a highest power of x^2 (the exponent of x is 2), which is[tex]-4x^2.[/tex]Quadratic polynomials are polynomials of degree 2 and can be represented by a parabola when graphed.

In summary, the simplified expression [tex](8x^2 + 3x) - (12x^2 - 1)[/tex] simplifies to [tex]-4x^2 + 3x + 1[/tex] , which is a quadratic polynomial. So Option D is correct

For more question on quadratic visit:

https://brainly.com/question/1214333

#SPJ8

Note the complete question is

Answer:

7

Step-by-step explanation:

The line represented by the equation y = 7 is a horizontal line that passes through the y-axis at 7, so the y intercept of this line is 7

To sketch the graph of the function y = 4(4)^x, we can start by plotting a few points to get an idea of the shape of the graph.

Let's choose some x-values and calculate the corresponding y-values:

For x = -2, y = 4(4)^(-2) = 4(1/16) = 1/4

For x = -1, y = 4(4)^(-1) = 4(1/4) = 1

For x = 0, y = 4(4)^0 = 4(1) = 4

For x = 1, y = 4(4)^1 = 4(4) = 16

For x = 2, y = 4(4)^2 = 4(16) = 64

Now we can plot these points on a coordinate plane and connect them to form the graph of the function.

The graph of y = 4(4)^x will start at the point (0, 4) and increase rapidly as x increases. It is an exponential growth function where the base is 4.

The domain of the function is all real numbers since there are no restrictions on the values of x.

The range of the function is the set of positive real numbers greater than zero. As x increases, y grows without bound, approaching positive infinity but never reaching zero or becoming negative.

Let's analyze Jenny's bowling expenses, considering the cost of renting bowling shoes and the price per game. By determining the total amount she paid and using the given information, we can calculate the number of games Jenny bowled.

Step-by-step explanation:

Let's set the number of games Jenny bowled as 'x'.

Jenny paid $2.75 for renting the bowling shoes and $4.25 for each game. The total amount she paid is $24.

The total amount Jenny paid for the games can be represented as: $4.25 * x.

So, the equation can be set up as:

$2.75 + $4.25 * x = $24.

To find the value of 'x', we need to solve the equation.

Subtracting $2.75 from both sides:

$4.25 * x = $24 - $2.75.

$4.25 * x = $21.25.

Dividing both sides by $4.25:

x = $21.25 / $4.25.

x = 5.

Answer: Therefore, Jenny bowled a total of 5 games.

Answer:

Quadratic equation. Linear would be a straight line and exponential would continue to grow; only quadratic equations are shaped like parabolas.

linear

if you add 2 cats to a tree and took one down you would have 0 in the tree so if you add 2+2=4 you can find every answer in the book.

your wellcomed

Answer:

only god knows

Step-by-step explanation:

because they didn't give us an answer on how many text messages anyone sent

Work Shown:

21/35 = (7*3)/(7*5) = 3/5

The length of the other diagonal is 11.25 cm.

Area is the measure of a region's size on a surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object.

In this question, we are given the following:

The area of a kite is 180. One of the diagonals is 16.

What is the length of the other diagonal?

The details of the solution are as follows:

We know that,

The area of a kite is the product of the diagonals divided by 2:

[tex]\text{A} = \dfrac{(\text{d}^1 \times \text{d}^2)}{2}[/tex]

You can substitute what we have:

[tex]180= \dfrac{(16 \times \text{d}^2)}{2}[/tex]

And solve.

[tex]180 = 16 \times \text{d}^2[/tex]

[tex]\text{d}^2=\dfrac{180}{16}[/tex]

[tex]\text{d}^2=\bold{11.25 \ cm}[/tex]

Therefore, the length of the other diagonal = 11.25 cm.

To know more on Area, visit:

https://brainly.com/question/27701864

At a temperature of 20°C, the mouse would burn approximately 1,567.44 calories each day.

According to the given model C = 0.37219T + 1,560, where C represents the number of calories an idle mouse burns each day and T represents the temperature of its environment in °C.

To find the most comfortable temperature for an idle mouse, we need to determine the temperature at which the mouse burns the least amount of calories per day.

To find this temperature, we can minimize the equation C = 0.37219T + 1,560. To do so, we take the derivative of C with respect to T and set it equal to zero:

dC/dT = 0.37219 = 0

Solving this equation, we find that the derivative is a constant value, indicating that the function C = 0.37219T + 1,560 is a linear equation with a slope of 0.37219. This means that the mouse burns the least calories at any temperature, as the slope is positive.

Therefore, there is no specific "most comfortable" temperature for an idle mouse in terms of minimizing calorie burn. However, if we consider the range of temperatures mice typically encounter, we can find a temperature where the calorie burn is relatively low.

For example, if we take a temperature of 20°C, we can calculate the calorie burn:

C = 0.37219 * 20 + 1,560

C = 7.4438 + 1,560

C ≈ 1,567.4438 calories per day

Therefore, at a temperature of 20°C, the mouse would burn approximately 1,567.44 calories each day.

For more such questions temperature,click on

https://brainly.com/question/25677592

#SPJ8

answer: 13/2 or 6 1/2

step-by-step explanation:

hihi so basically your problem is making a solvable equation so w variables and stuff

heres my explanation !

the difference of a number and 2 is b-2

twice the difference of a number and 2 would be 2(b-2)

number 9 = 9 (duh lol)
so

2(b-2) = 9

2b - 4 = 9

2b = 13

improper: b = 13/2
mixed: b = 6 1/2

Given that the side of a square field is 52 m so, the area of the square field is 2704 m².

The side of a square field is given as 52 m.

Now, Let’s find the area of the square field using the given information.

As we know, area of a square can be calculated by using the formula:

A = a², where ‘a’ is the side of the square.

Now, by substituting the given value of ‘a’ in the given formula above we will get the area of the square field as,

A = (52)²

A = 2704 m²

Therefore, the area of the square field of given side i.e. 52m is 2704 m².

For more such questions on area visit:

https://brainly.com/question/25292087

#SPJ8

Terri have to react 1.42 seconds before the volleyball hits the ground.

Quadratics can be defined as a polynomial equation of a second degree, which implies that it comprises a minimum of one term that is squared. It is also called quadratic equations. The general form of the quadratic equation is:

[tex]\text{ax}^2 + \text{bx} + \text{c} = 0[/tex]

Given data:

The height can be modeled by a quadratic equation.

[tex]h(t)=-16t^2+v_0t+h_0[/tex]

Where h is the height and t is the time.

[tex]h(t)=-16t^2+19.5t+4.5[/tex]

[tex]-16t^2+19.5t+4.5=0[/tex]

[tex]a = -16, b = 19.5, c = 4.5[/tex]

It looks like a quadratic equation. we can solve it by quadratic formula.

[tex]\dfrac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]

[tex]\rightarrow t=\dfrac{-19.5\pm\sqrt{(-19.5)^2-4\times(-16)(4.5)} }{2(-16)}[/tex]

[tex]\rightarrow t=\dfrac{-19.5\pm\sqrt{380.25+288} }{-32}[/tex]

[tex]\rightarrow t=\dfrac{-19.5\pm25.851 }{-32}[/tex]

[tex]\rightarrow t=\dfrac{-19.5-25.851 }{-32}, \ t=\dfrac{-19.5+25.851 }{-32}[/tex]

[tex]\rightarrow t=1.42, \ t=-0.20[/tex]

Time cannot be in negative. So neglect t = –0.235.

Hence, Terri have to react 1.42 seconds before the volleyball hits the ground.

To know more about quadratic equations, visit:

https://brainly.com/question/30098550

Using the physics concept of projectile motion and inputting the given values into the appropriate equation, we can determine the time it takes for the volleyball to hit the ground after being served

This question is a classic use of physics, more specifically, the concept of projectile motion. Here, the volleyball can be conceived as a projectile. When Patricia serves the ball upward, the ball will first ascend and then descend due to gravity.

Let's use the following equation which is a version of kinematic equations to solve this problem, adjusting for the fact that we're dealing with an initial height of 4.5 ft and an ending height of 0 ft (when the ball hits the ground). The equation y = yo + vot - 0.5gt² , where:

Setting y=0, yo=4.5 feet, vo=19.5 feet/second, and g=32.2 feet/second², and plug these values into the equation, we'll get a quadratic equation in the form of 0 = 4.5 + 19.5t - 16.1t². Solve that equation for t to find the time it takes for the ball to hit the ground.

https://brainly.com/question/29545516

#SPJ2

Out of the four children attending the party, with only two spots left, there are six different ways to select two children to fill those spots.

If there are four children and only two spots left at the party, we need to determine the number of combinations possible for selecting two children out of the four. To calculate this, we can use the concept of combinations from combinatorics.

Combinations refer to the selection of items from a larger set without considering the order. In this case, the order in which the children are selected does not matter; we only need to know which two children are chosen. The formula for combinations is given by:

C(n, r) = n! / (r! * (n - r)!)

where n is the total number of items (in this case, children) and r is the number of items we want to select (in this case, the two available spots at the party).

Using the formula, we can substitute n = 4 and r = 2:

C(4, 2) = 4! / (2! * (4 - 2)!)

Simplifying further:C(4, 2) = 4! / (2! * 2!)

Now, let's calculate the factorial terms:

4! = 4 * 3 * 2 * 1 = 24

2! = 2 * 1 = 2

Substituting the factorial terms:

C(4, 2) = 24 / (2 * 2)

Simplifying the denominator:

C(4, 2) = 24 / 4 = 6

Therefore, there are 6 different combinations possible for selecting two children out of the four to fill the two available spots at the party.

For more question on children visit:

https://brainly.com/question/26423521

#SPJ8

Note the correct question is

4 childen go to a party but there is only 2 spots left. How many combinations  are there?

To find the center and radius of the circle represented by the inequality [tex]\displaystyle \sf x^{2} +y^{2} -12y-12\leq 0[/tex], we can complete the square for the y terms.

The inequality can be rewritten as:

[tex]\displaystyle \sf x^{2} +( y^{2} -12y) -12\leq 0[/tex]

To complete the square for the y terms, we need to add and subtract [tex]\displaystyle \sf ( 12/2) ^{2} =36[/tex] inside the parentheses:

[tex]\displaystyle \sf x^{2} +( y^{2} -12y+36) -36-12\leq 0[/tex]

Simplifying, we have:

[tex]\displaystyle \sf x^{2} +( y-6)^{2} -48\leq 0[/tex]

Now we can rewrite the inequality in the standard form of a circle equation:

[tex]\displaystyle \sf ( x-h)^{2} +( y-k)^{2} \leq r^{2}[/tex]

Comparing this with the obtained equation, we can identify the center and radius of the circle:

Center: [tex]\displaystyle \sf ( h,k)=( 0,6)[/tex]

Radius: [tex]\displaystyle \sf r=\sqrt{48}[/tex]

Therefore, the center of the circle is at [tex]\displaystyle \sf ( 0,6)[/tex], and its radius is [tex]\displaystyle \sf \sqrt{48}[/tex].

[tex]\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}[/tex]

♥️ [tex]\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}[/tex]

The graph of the function f(x)=√(x + 1) is in the first option

A radical graph, also known as a square root graph, represents the graph of a square root function. A square root function is a mathematical function that takes the square root of the input variable.

The general form of a square root function is f(x) = √(ax + b) + c,

where a, b, and c are constants that determine the characteristics of the graph.

In the given function:

a = 1

b = 1

c = 0

The graph is plotted and attached

Learn more about square root graph at

https://brainly.com/question/1777875

#SPJ1

The required probability is 3 √7 / 32.

Given, a square with sides of length 4 units and a red-shaded triangle with sides 3 units, 3 units and 4 units. We need to find the probability that a randomly selected point within the square falls in the red-shaded triangle.To find the probability, we need to divide the area of the red-shaded triangle by the area of the square. So, Area of square = 4 × 4 = 16 square units. Area of triangle = 1/2 × base × height.

Using Pythagorean theorem, the height of the triangle is found as: h = √(4² − 3²) = √7

The area of the triangle is: A = 1/2 × base × height= 1/2 × 3 × √7= 3/2 √7 square units. So, the probability that a randomly selected point within the square falls in the red-shaded triangle is:  P = Area of triangle/Area of square= (3/2 √7) / 16= 3 √7 / 32.

for such more questions on  probability

https://brainly.com/question/29070527

#SPJ8

The missing values in the quantitative reasoning given are : -2, 13 and 9

Given the rule :

We can deduce that :

For the left circle :

circle = -6 - (-4) = -6 + 4 = -2

For the right circle :

circle = 11 - (-2) = 11 + 2 = 13

For the left square :

square = 13 + (-4)

square = 13 -4 = 9

Therefore, the missing values are : -2, 13 and 9

Learn more on puzzle: https://brainly.com/question/27645967

#SPJ1

In the given question, it is stated that a premium candy manufacturer makes chocolate candies that, when finished, vary in color. The hue value of a randomly selected candy follows an approximately normal distribution with mean 30 and a standard deviation of 5. A quality inspector discards 12% of the candies due to unacceptable hues (which are equally likely to be too small or too large). So, the largest hue value that the inspector would find acceptable is 36.85

We are required to find out the largest hue value that the inspector would find acceptable. We are given that the mean value is 30, standard deviation is 5, and 12% of candies are discarded due to unacceptable hues. Now, we need to find out the largest hue value that the inspector would find acceptable.

To find the largest acceptable hue value we can use the Z score formula. Z = (X - μ) / σ

Now, substituting the values in the formula we have: Z = (X - 30) / 5

This value corresponds to the percentile of the distribution. We are required to find the largest hue value that the inspector would find acceptable and given that 12% of the candies are discarded due to unacceptable hues. So, the acceptable percentile would be 100% - 12% = 88% or 0.88

Now, using the z-score table or calculator, we can find the Z value corresponding to the 88th percentile. Z = 1.17

Now, we can use this Z score value to find the corresponding X value by using the Z-score formula and solving for X.1.17 = (X - 30) / 5

Solving for X,X = 30 + 5(1.17)X = 36.85. Therefore, the largest hue value that the inspector would find acceptable is 36.85 (rounded to two decimal places).

For more questions on: standard deviation

https://brainly.com/question/475676

#SPJ8  

Answer:

1/2 of an hour ( I think )

Step-by-step explanation:

The second longest time that was recorded was 2/3/4 (whole/numerator/denominator) of a hour while the second shortest time was 2/1/4 of a hour. When you subtract 2/1/4 from 2/3/4 you end up with 2/4. Since 2/4 can be simplified to 1/2 you would say there is a 1/2 hour different between the second longest and second shortest time spent reading.

The rocket is at a height of 1876.1 meters after 9 seconds,the velocity of the rocket after 9 seconds is 143.8 m/s and  the acceleration of the rocket after 9 seconds is -9.8 m/s².

To find the height of the rocket when it was initially launched, we can plug in t = 0 into the equation h(t) = -4.9t² + 232t + 185.

h(0) = -4.9(0)² + 232(0) + 185

     = 0 + 0 + 185

     = 185

Therefore, the rocket was initially launched at a height of 185 meters.

To find the height of the rocket after 9 seconds, we can plug in t = 9 into the equation h(t) = -4.9t² + 232t + 185.

h(9) = -4.9(9)² + 232(9) + 185

     = -4.9(81) + 2088 + 185

     = -396.9 + 2088 + 185

     = 1876.1

Therefore, the rocket is at a height of 1876.1 meters after 9 seconds.

To find the velocity of the rocket after 9 seconds, we can take the derivative of the height function h(t) with respect to time (t) and evaluate it at t = 9.

The velocity function v(t) is the derivative of h(t) with respect to t:

v(t) = dh/dt = d/dt(-4.9t² + 232t + 185)

       = -9.8t + 232

v(9) = -9.8(9) + 232

       = -88.2 + 232

       = 143.8

Therefore, the velocity of the rocket after 9 seconds is 143.8 m/s.

To find the acceleration of the rocket after 9 seconds, we can take the derivative of the velocity function v(t) with respect to time (t) and evaluate it at t = 9.

The acceleration function a(t) is the derivative of v(t) with respect to t:

a(t) = dv/dt = d/dt(-9.8t + 232)

       = -9.8

a(9) = -9.8

Therefore, the acceleration of the rocket after 9 seconds is -9.8 m/s².

For more such questions on acceleration,click on

https://brainly.com/question/26246639

#SPJ8

Answer:

The values of b that satisfy the equation are:

b = (2√3 - 3) / 2

b = (-2√3 - 3) / 2

In other words, b can take the values (2√3 - 3) / 2 or (-2√3 - 3) / 2.

Step-by-step explanation:

To find the values of b that satisfy the equation 3(2b + 3)² = 36, we can solve for b by following these steps:

1. Divide both sides of the equation by 3:

  (2b + 3)² = 12

2. Take the square root of both sides:

  √[(2b + 3)²] = √12

  Simplifying further:

  2b + 3 = ±√12

3. Subtract 3 from both sides:

  2b = ±√12 - 3

4. Divide both sides by 2:

  b = (±√12 - 3) / 2

  Simplifying further:

  b = (±√4 * √3 - 3) / 2

  b = (±2√3 - 3) / 2

Therefore, the values of b that satisfy the equation are:

b = (2√3 - 3) / 2

b = (-2√3 - 3) / 2

In other words, b can take the values (2√3 - 3) / 2 or (-2√3 - 3) / 2.

[tex]\sqrt{200y^2} ~~ \begin{cases} 200=&2\cdot 10\cdot 10\\ & 2\cdot 10^2 \end{cases}\implies \sqrt{2\cdot 10^2 y ^2}\implies 10y\sqrt{2}[/tex]

The inequality tha calculates the possible values of x is x < 2

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

The figure

Where, we have

3x + 2 < 10

And, we have

2x + 6 < 10

Evaluate the expressions

So, we have

3x < 8 and 2x < 4

Evaluate

x < 8/3 and x < 2

Hence, the inequality tha calculates x is x < 2

Read more about inequality at

https://brainly.com/question/32124899

#SPJ1

Answer:

Ryan had a head start of 10 meters

Step-by-step explanation: