A standardized​ exam's scores are normally distributed. In a recent​ year, the mean test score was 1491 and the standard deviation was 312. The test scores of four students selected at random are 1910​, 1230​, 2190​, and 1380. Find the​ z-scores that correspond to each value and determine whether any of the values are unusual.

9514 1404 393

Answer:

  Sally's work: StartFraction b Over 12 EndFraction = 16. B = 192

Step-by-step explanation:

Of the offered choices, the only one that is solved correctly is Sally's work.

Here are the solutions for the equations the students wrote:

  [tex]\dfrac{12}{b}=16\ \rightarrow\ 12=16b\ \rightarrow\ \dfrac{12}{16}=b=0.75\\\\\dfrac{b}{12}=16\ \rightarrow\ b=12\cdot16=192[/tex]

_____

Comment on the wrong answers

The "solution" value of 1.3 appears to be a rounded version of 16/12, a value that will not show up as a solution to any of the equations written.

Comment on dimensional analysis

The dimensions of "16" are "cases." The dimensions of "12" are "bottles per case", or bottles/case. Multiplying this by the number of cases, gives the number of bottles. This is where I'd start:

  (bottles/case)×(cases) = bottles    ⇒    12×16 = b

The ratios the students wrote had units of ...

  b/12 = (bottles)/(bottles/case) = cases = 16

and (incorrectly) ...

  12/b = (bottles/case)/(bottles) = 1/cases = 16 . . . . wrong

It can be useful to consider what the numbers represent. That can help avoid math mistakes.

a bought 16 cases of water bottles. There were 12 water bottles in each case. Four students wrote and solved equations to find b, the number of bottles that Clara bought. Which student wrote and solved the equation correctly?

Maya’s work:

StartFraction b Over 12 EndFraction = 16. b = 1.3

Larissa’s work:

12 b = 16. b = 1.3

Sally’s work:

StartFraction b Over 12 EndFraction = 16. b = 192.

Anika’s work:

StartFraction 12 Over b EndFraction = 16. b = 192.

Step-by-step explanation:

Answer:

  [tex]\dfrac{y^2+3y}{y^2-6y+9}[/tex]

Step-by-step explanation:

When we write this using appropriate math symbols, it is easier to see the solution. To evaluate this, we multiply by the inverse of the denominator fraction.

  [tex]\dfrac{2y}{y - 3}\div \dfrac{ 4 y - 12}{2 y + 6}=\dfrac{2y}{y-3}\cdot\dfrac{2y+6}{4y-12}\\\\=\dfrac{4y(y+3)}{4(y-3)^2}}=\boxed{\dfrac{y^2+3y}{y^2-6y+9}}[/tex]

Answer:

d

Step-by-step explanation:

Jill owns approximately 60,000 acres of land.

Let's first find out how many trees Jill has per acre based on the information given.

Jill has 150 peach trees on 1/2 of her land, which means she has 300 peach trees on her entire land. If there are 5 trees for every 1,000 square feet of land, we can calculate the total square feet of land that Jill owns:

[tex]\[ \text{Total trees} = \text{Trees per acre} \times \text{Total acres} \]\[ 300 = \frac{5}{1000} \times \text{Total acres} \][/tex]

Solving for the total acres:

[tex]\[ \text{Total acres} = \frac{300}{\frac{5}{1000}} \]\[ \text{Total acres} = \frac{300 \times 1000}{5} \]\[ \text{Total acres} = \frac{300000}{5} \]\[ \text{Total acres} = 60000 \][/tex]

Now, we can convert the total acres from square feet to acres using the conversion factor given:

[tex]\[ \text{Total acres in square feet} = 60000 \times 43560 \]\[ \text{Total acres} = \frac{60000 \times 43560}{43560} \]\[ \text{Total acres} = 60000 \][/tex]

So, Jill owns approximately 60,000 acres of land.

Jill owns approximately 1.38 acres of land.

To find out how many acres of land Jill owns, we first need to determine the total number of peach trees on all her land.

Since she counts 150 peach trees on half of her land, we can assume there are 300 peach trees in total (since half of her land has 150 trees and the other half will also have 150 trees).

Now, if there are 5 trees for every 1,000 square feet of land, we can set up a proportion to find out how many square feet of land these 300 trees occupy:

[tex]\( \frac{5 \text{ trees}}{1000 \text{ square feet}} = \frac{300 \text{ trees}}{x \text{ square feet}} \)[/tex]

Cross-multiplying, we get:

[tex]\( 5x = 300,000 \)[/tex]

Dividing both sides by 5:

[tex]\( x = 60,000 \)[/tex]

So, Jill's 300 peach trees occupy 60,000 square feet of land.

To convert this to acres, we use the conversion factor provided: [tex]1 acre = 43,560 square feet.[/tex]

[tex]\( \text{Number of acres} = \frac{60000}{43560} \)[/tex]

[tex]\( \text{Number of acres} = 1.38 \)[/tex]

Complete correct question:

Jill counts 150 peach trees on 1/2 of the land she owns. She determines that there are 5 trees for every 1,000 square feet of land. About how many acres of land does Jill own? [tex]1 acre= 43,560 square feet.[/tex]

Answer:

$9

Step-by-step explanation:

set up a proportion where 20% is represented as 20/100 and set it equal to 1.80/x

cross multiply and you should get 180=20x

divide by 20 to solve for x

you then get 9, which is the amount you were looking for

Answer:

c

Step-by-step explanation:

Answer:

Question

Select the correct answer. Which expression is equivalent to x + y + x + y + 3(y + 5)? A. 2x + 5y + 5 B. 2x + y + 30 C. 2x + 5y + 15 D. 2x + 3y + 10 Reset          Answer C.

Step-by-step explanation:

Answer:Yes

Step-by-step explanation:A=16 B=30 C=34

16*16= 256 30*30=900 34*34=1156

256+900=1156

Answer:

let's check first is it Right Triangle because we can do it using Pythagorean theorem:

let's sides 16 and 30 be legs, and 34 hypotenuse

1156=1156...so, this is true and your triangle IS Right Triangle

but, it is also a scalene triangle with a right angle

Step-by-step explanation:

Answer:

B) 112 cm²; 336 cm²

Step-by-step explanation:

The lateral area would be without the bases. In this case, the bases are the top and the bottom

Lateral Area

(2)(2.54)(8) = 40.64

(2)(2.54)(14) = 71.12

Add together and get 111.76 cm²

Surface Area

LA + Bases

Bases

(2)(14)(8) = 224

Add with lateral area and get 335.76 cm²

The requried volume of the cylinder is approximately 1017.9 cubic meters.

The volume of a cylinder can be calculated using the formula:

Volume = π * (diameter/2)² * height

where π (pi) is a mathematical constant approximately equal to 3.14159, diameter is the base diameter of the cylinder, and height is the height of the cylinder.

In this case, the height is 9m and the base diameter is 12m. We need to first calculate the radius, which is half of the diameter:

Radius = diameter/2 = 12m/2 = 6m

Now we can substitute the values into the formula and calculate the volume:

Volume = π * (6m)² * 9m

Volume ≈ 1017.88 cubic meters

Rounding to the nearest tenth place, the volume of the cylinder is approximately 1017.9 cubic meters.

Learn more about the volume of the cylinder here:

https://brainly.com/question/16134180

#SPJ3

Final answer:

The volume of a cylinder with a height of 9m and a base diameter of 12m is approximately 9160.9 cubic meters when rounded to the nearest tenth.

Explanation:

The student is asking for the volume of a cylinder with a given height and base diameter, which is a common problem in mathematics related to geometry and measurements. To find the volume, we use the formula for the volume of a cylinder V = πr²h, where V is the volume, r is the radius of the base, and h is the height of the cylinder. Given that the diameter is 12 meters, the radius (r) is half of that, which is 6 meters. We then substitute these values into the formula:

V = π(6m)²(9m)

V = 3.1416 × 36m² × 9m

V = 3.1416 × 324m² × 9m

V = π × 2916m³

V = 9160.88m³

After calculating, we round the volume to the nearest tenths place, obtaining V ≈ 9160.9m³.

Answer:

2/3

Step-by-step explanation:

Well, it supplied the formula, so let's start from there.

    P(A or B) = P(A) + P(B) - P(A and B)

Let A = the probability that the red die shows a number larger than three

Let B = the probability that the green die shows a number less than three

I'm assuming they both have 6 numbers on them, like a regular die.

    So there are 3 possibilities that are larger than 3 (4, 5, and 6) and 6 total possibilities, so A = 3/6.

    There are 2 possibilities that are less than 3 (1 and 2) and 6 total possibilities, so B = 2/6.

Plug that into the formula.

    P(A or B) = 3/6 + 2/6 - P(A and B)

Now we have to subtract the probability that both A and B happen, which is 3/6 * 2/6 = 6/36 = 1/6.

    P(A or B) = 3/6 + 2/6 - 1/6

    P(A or B) = 4/6 = 2/3

Answer:

-45

Step-by-step explanation:

I think it means that you just solve it.

Answer: False.

Step-by-step explanation:

There does not exist a "quarter circle" as a circle with a radius of 4 units, the only notable circle that does exist is the unit circle, that is the circle where the radius is equal to 1, represented by the equatin x^2 + y^2 = 1

The term "quarter circle" actually does refer to a fourth part of a circle, not to a circle of radius 4.

So the statement is false

Answer:

I believe it is about 47.63 meters squared

Leave a comment if you'd like a step-by-step explanation

Answer:

(2,-1)

Step-by-step explanation:

Multiply everything by 1/3:

6*1/3=2

-3*1/3=-1

This makes it smaller, so you know what the dilation is.

Answer:

first person is correct

Step-by-step explanation:

Answer: can u help me with an equation then I will help you?

Step-by-step explanation:

Answer:

Dilation

Step-by-step explanation:

Dialation-A dilation is a transformation that produces an image that is the same shape as the original, but is a different size

Answer:

1:12

Step-by-step explanation:

Answer:

18.75%

Step-by-step explanation:

The probability of the coin is 1/2, because it only has two options (tail or head).

Now, in the case of roulette, it has a total of 8 options, and the red region has 3 parts, that is, of the 8 options, roulette 3 is red, therefore the probability is 3/8

Now the final probability is the multiplication of the probability of both events:

(1/2) * (3/8) = 0.1875 s 18.75%

In other words, the probability of these two events happening, that the tail comes out and is red, i

Answer:

Use what you used for the first one and you should get the right answer.

Step-by-step explanation:

Answer:

3.88

4n + 0.24 = 15.76

     - 0.24   - 0.24

______________

4n            = 15.52

4n = 15.52

__    ____

4         4  

n = 3.88

After 4 hours: 60 ng/mL, After 8 hours: 30 ng/mL, After 12 hours: 15 ng/mL, After 16 hours: 7.5 ng/mL.

The half-life of a drug is the time it takes for the concentration of the drug in the body to reduce by half. In this case, the half-life of the drug is 4 hours. When a patient discontinues taking the medication, the concentration of the drug decreases exponentially over time.

The initial concentration is given as 120 ng/mL. After the first 4 hours, which is one half-life, the concentration reduces to 60 ng/mL. Subsequent half-lives continue to halve the concentration. After 8 hours, it becomes 30 ng/mL, after 12 hours it's 15 ng/mL, after 16 hours it's 7.5 ng/mL.

This exponential decrease reflects the nature of drug elimination from the body, with each half-life reducing the concentration by half. The rounded values in the table represent the decreasing drug concentrations at different time intervals after the patient stops taking the medication.

Answer and Step-by-step explanation:

First, you want to graph the line of x = -1. This line is simply a vertical line running through (-1, 0).

The coordinates of each of the points are:

G(5, 9)

F(8, 9)

D(5, 6)

E(8, 6)

When we reflect point G over the line x = -1, we will get a point with the same y-coordinate, but with a different x-coordinate. Since 5 is 6 units away from -1, when you reflect G, the new x-coordinate will be -1 - 6 = -7. So, the new point for G is (-7, 9).

By similar reasoning for all the other points, we have:

F'(-10, 9)

D'(-7, 6)

E'(-10, 6)

Finally, just graph the points G'(-7, 9), F'(-10, 9), D'(-7, 6), and E'(-10, 6), and that's your new shape.

Hope this helps!

Answer:

D': (-7,6)

E': (-10,6)

F': (-10,9)

G': (-7,9)

Step-by-step explanation:

D: (5,6)

E: (8,6)

F: (8,9)

G: (5,9)

After reflection in x = -1

D': (-1-6,6)

E': (-1-9,6)

F': (-1-9,9)

G': (-1-6,9)

D': (-7,6)

E': (-10,6)

F': (-10,9)

G': (-7,9)

The number of unit cubes in one layer may vary depending on the type of cubic lattice structure. In a simple cubic lattice, there is one atom per unit cell. However, without specific dimensions or the exact structure type, the exact number of cubes per layer cannot be determined.

When we talk about the number of unit cubes in one layer, we must understand the geometry of the structure we are discussing. In a simple cubic lattice, each layer is made up of unit cubes that sit next to each other on each side. If the structure is in fact a simple cubic unit cell, then according to Figure 10.49 which describes this as having an atom at each of its eight corners and being shared by eight unit cells, there would be a total of one atom per unit cell.

In the context of a body-centered cubic structure mentioned, which is depicted in Figure 10.51, atoms in a specific layer do not touch each other, making the calculation of unit cubes in a single layer less straightforward; the cubes in the layers above and below touch the atom at the center.

Without specific dimensions or the type of cubic structure (simple cubic, face-centered cubic, or body-centered cubic), the exact number of unit cubes per layer cannot be determined. If we consider a cube made up of smaller unit cubes with a known side length, such as the polystyrene cube measuring 10 cm per side as mentioned, the number of unit cubes per layer would simply be the area of the cube's face divided by the area of one unit cube face. For a 10 cm cube, if each unit cube is 1 cm3, then there would be 10 x 10 = 100 unit cubes per layer.

Answer:

24 candies originally

Step-by-step explanation:

Add the 4 to how many you had left, then think about that number, 16, and what goes into 16 evenly 2 times? 8 and originally she gave away 1/3 of the box and if you were to add another 8 to the box it would be 24 divided by 1/3, -,-4,= 12.

Answer:

13

Step-by-step explanation:

Answer: 1,833,615

Step-by-step explanation:

Hi, to answer this question we have to apply an exponential growth function:

A = P (1 + r) t  

Where:

p = original population

r = growing rate (decimal form)

t= years

A = population after t years

Replacing with the values given:

A = 800,000 (1+ 5/100)^17

A = 1,833,615  

Feel free to ask for more if needed or if you did not understand something.

Answer:uh look up a video?

Step-by-step explanation:

Answer:

$7.58

Step-by-step explanation:

Think about it, (S+C), each flavor costs $3.97 per carton, and there's 2 cartons. $3.79 x 2 = $7.58

Answer

Step-by-step explanation:The fine schedule for overdue books at the county library is modeled by the values in the table.

Library Fines for Overdue Books

Days overdue

Amount of fine

0

0 ¢

2

5 ¢

4

10 ¢

6

15 ¢

8

20 ¢

10

25 ¢

Which equation best models the fine schedule for overdue books?

y = five-halves x, where x is the cost in cents for a book that is y days overdue

y = five-halves x, where y is the cost in cents for a book that is x days overdue

y = 5 x, where x is the cost in cents for a book that is y days overdue

y = 5 x, where y is the cost in cents for a book that is x days overdue

Answer:

Givens

[tex]m \angle BAC=63\°[/tex]

[tex]m(BE)=96\°[/tex]

[tex]DE[/tex] is secant.

[tex]DG[/tex] is tangent.

Remember that the arc subtended by a central angle is equal to it. That means

[tex]m(BC)=m\angle BAC = 63\°[/tex]

Now, by sum of arcs, we know

[tex]m(EBC)=m(EB)+m(BC)=96\° +63\°=159\°[/tex]

By definition, the total arc of a circle is 360°, so

[tex]m(EFC)=360\°-m(EBC)=360\° - 159\°=201\°[/tex]

We know that the external angle formed by a secant and a tanget is one half of the difference between the intercepted arcs, so

[tex]\angle D=\frac{1}{2}(m(EFC)-m(BC))=\frac{1}{2} (201\° - 63\°)=\frac{1}{2} (138\°)=69\°[/tex]

So, the angle D is 69°.

Answer:

Volume of the cube is [tex]64x^9[/tex].

Step-by-step explanation:

Given:

Volume of the cube [tex]V = L^3[/tex]

where [tex]L[/tex] ⇒ side length

side length [tex]L =4x^3[/tex]

We need to find the Volume of the cube.

Solution:

Now we know that;

Volume of the cube [tex]V = L^3[/tex]

But side length [tex]L =4x^3[/tex]

So we will substitute the value of L in above equation we get;

Volume of the cube [tex]V = L^3=(4x^3)^3[/tex]

Now by using Law of indices which states [tex](a^m)^n=a^{mn}[/tex]

So we can say that;

Volume of the cube [tex]V = L^3=(4x^3)^3=4^3x^{3\times3}=64x^9[/tex]

Hence Volume of the cube is [tex]64x^9[/tex].

Answer:

166 2/13 deg

Step-by-step explanation:

The sum of the measures of the interior angles of a convex polygon of n sides is 180(n - 2).

A hexagon has 6 sides, so n = 6.

sum of measures of angles = 180(n - 2) = 180(6 - 2) = 180(4) = 720

4x + 5x + 6x + 7x + 8x + 9x = 720

39x = 720

x = 720/39

x = 240/13

The largest angle has measure 9x.

9x = 9 * 240/13 = 2160/13

2160/13 = 166 2/13

Answer: 166 2/13 deg