For a 4-units class like Statistics, students should spend average of 12 hours studying for the class. A survey was done on students, and the distribution of total study hours per week is bell-shaped with a mean of 15 hours and a standard deviation of 3 hours. a) 95% of the students have study hours that are between_____and_____hours.
b) What percentage of the students have study hours that are above 12?

x is 45° (45 degrees.)

To find this out, we first need to understand the properties of a rectangle. A rectangle has opposite sides that are equal, but more importantly, all 4 interior angles of a rectangle are right angles, meaning they are all 90 degrees. These can also be denoted by 4 square boxes in each corner.

When a rectangle is cut diagonally, the rectangle becomes two right triangles, but when joined together, of course make a rectangle. When they are cut diagonally, the triangles are congruent triangles by the Hypotenuse-Leg (HL) Congruence property.

To find the missing x in this angle, we must know that x is apart of a right angle, and if 45 is next to it, x must also be 45 degrees (90-45 = 45)

Hope this helped!

Answer:

A. -7

Step-by-step explanation:

Answer:

1.) & 2.) BC and AD are congruent and parallel because in parallelogram opposite sides are equal and parallel

4.) <BCE≅<DAF because they are alternating interior angles bisected by line CA

5.) & 6.) The line BE/DF which bisects the <B/<D iS perpendicular to diagonal CA which forms the right angle

7.) Because sum of any two adjacent angles are 180
8.) This follows ASA Postulate which means that if 2 pair of angles is congruent given that they share a same side, the triangle formed will also be congruent.

Step-by-step explanation:

Take the side CA as the same side of both triangles. This side also participates on the aforementioned angles on the given. The angles <BCE≅<DAF shares the side CA which makes the angles <DFA and <BEC congruent to each other. Therefore, the two right triangles are congruent

Answer:

38%

Step-by-step explanation:

2.3/5.98 x 100

= 0.38 x 100

= 38%

Hello,

8(6x-7) <5(9x - 4)

48x - 56 < 45x - 20

48x - 45x < -20 + 56

3x < 36

x < 36/3

x < 12

Answer:

AB - Diameter

DA - Tangent

BC - Chord

OA - Radius

CAB - Inscribed Angle

The different ways that the students can elect a president and a vice president will be 13110.

The chances of an event occurring are defined by probability. Probability has several uses in games, in business to create probability-based forecasts,

Given data;

Total no of students =  115

The total number of ways to elect a president = 115

If one person is elected as the president the total number of ways to elect a president  = 114

The different ways that the students can elect a president and a vice president are found as;

⇒ 115 ways × 114 ways

⇒ 13110 ways

Hence the different ways that the students can elect a president and a vice president will be 13110.

To learn more about probability, refer to the link;

https://brainly.com/question/11234923

#SPJ1

Using translation concepts, the vertices of the rectangle after the translation about the origin by 180° will be as follows:

E'(-4,3), F'(7,-5) and G(-2,-8).

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

The rule for a rotation of 180º about the origin is:

(x,y) -> (-x,-y).

Hence, for triangle EFG, the vertices after the translation will be given as follows:

E'(-4,3), F'(7,-5) and G(-2,-8).

More can be learned about translation concepts at https://brainly.com/question/4521517

#SPJ1

Answer:

Step-by-step explanation:

Answer:

16c² + 32c + 16

Step-by-step explanation:

(4c+4)² =

(4c+4)(4c+4) =

16c² + 16c + 16c + 16 =

16c² + 32c + 16

I think this is the answer you are looking for.

Hope this helped and have a good day

[tex]\huge\boxed{8\ \text{bags of oranges}}[/tex]

Let's first find how many ounces the basket can hold.

1 pound is equal to 16 ounces. Multiply that to find how many ounces the basket can hold.

[tex]6\cdot16=96[/tex]

Now, divide the weight held by the basket by the weight of each bag of oranges.

[tex]96\div12=\boxed{8}[/tex]

[tex]f(1)=1^2+4\cdot1+6=1+4+6=11\\f(5)=5^2+4\cdot5+6=25+20+6=51[/tex]

Answer:

  (c)  x plus b over 2 times a equals plus or minus the square root of the quantity b squared minus 4 times a times c all over the square root of 4 times a squared

Step-by-step explanation:

The next step is to take the square root of both sides of the equation. It can help to show the intermediate steps.

The last step shown in the derivation so far is ...

  [tex]x^2+\dfrac{b}{a}x+\dfrac{b^2}{4a^2}=-\dfrac{4ac}{4a^2}+\dfrac{b^2}{4a^2}[/tex]

The left side of the above expression can be written as a square, and the right side can be written over one denominator. Then the square root is taken as the next step.

  [tex]\left(x+\dfrac{b}{2a}\right)^2=\dfrac{b^2-4ac}{4a^2}\\\\\sqrt{\left(x+\dfrac{b}{2a}\right)^2}=\sqrt{\dfrac{b^2-4ac}{4a^2}}\\\\\boxed{x+\dfrac{b}{2a}=\pm\dfrac{\sqrt{b^2-4ac}}{\sqrt{4a^2}}}\qquad\text{"next step"}[/tex]

Answer: [tex]x+\frac{b}{2a}=\pm \frac{\sqrt{b^2 - 4ac}}{\sqrt{4a^2}}[/tex]

Step-by-step explanation:

We can rewrite the left hand side as a perfect square, more specifically

[tex]\left(x+\frac{b}{2a} \right)^2[/tex]

So, taking the square root of both sides,

[tex]x+\frac{b}{2a}=\pm \frac{\sqrt{b^2 - 4ac}}{\sqrt{4a^2}}[/tex]

Answer: Circumcenter

Step-by-step explanation: The circumcenter is the point where all perpendicular bisectors of a triangle meet. The 3 perpendicular bisectors of the 3 sides of the triangle meet at the point which is labeled in this triangle as H.

[tex]\huge\boxed{y-5&=-\frac{1}{3}(x+9)}[/tex]

First, we'll find the slope of the new line. The first line has a slope of [tex]3[/tex]. Take the negative reciprocal of this (Flip the numerator and denominator, then multiply by [tex]-1[/tex]) to get [tex]-\frac{1}{3}[/tex] for the new slope.

Then, we'll use the point-slope form to make the new equation, where [tex]m[/tex] is the slope and [tex](x_1,y_1)[/tex] is a point on the line:

[tex]\begin{aligned}y-y_1&=m(x-x_1)\\y-5&=-\frac{1}{3}(x-(-9))\\y-5&=-\frac{1}{3}(x+9)\end{aligned}[/tex]

The growth of the lily pad is in geometric progression, and it covers half the pond in 29 days.

In the question, we are given that the size of the lily pad doubles itself every day.

If we assume the size of the lily pad on the first day as a, then on the second day its size will be 2a, on the third day it will be 2(2a) = 4a, and on the fourth day, it will be 2(4a) = 8a, and so on.

This makes a geometric progression, with the first term as a, and the constant ratio as 2.

We are given that on the 30th day, the size of the lily pad, covers the entire pond.

The size on the 30th day can be shown as the 30th term of this geometric progression

Therefore, size of the  pond = a(2)³⁰⁻¹ = a.2²⁹. {Using the formula, aₙ = arⁿ⁻¹, where aₙ is the n-th term, a is the first term, and r is the constant ratio}.

We are asked the day on which the pond is half covered.

The size of the pond in this case = (a.2²⁹)/2 = a.2²⁸.

The day can be calculated as follows:

a.2ⁿ⁻¹ = a.2²⁸,

or, 2ⁿ/2 = 2²⁸,

or, 2ⁿ = 2²⁹,

or, n = 29.

Thus, the lily pad covers half the pond on the 29th day.

Learn more about geometric progression at

https://brainly.com/question/24643676

#SPJ4

See below for the demonstration of (e) graphing a line using x- and y-intercepts

To solve this question, we make demonstrate (e) graphing a line using x- and y-intercepts

At the end of this exercise, you should be able to graph a line using x- and y-intercepts

A linear equation is represented as:

Ax + By = C

Where:

This means that we plot the points (0,C/B) and (C/A, 0) on a graph and then connect the points using a straight line.

Once this is done, the line has been graphed.

For instance, a line parallel to 3x + 8y = 16 will have a slope of -3/8

Plot the graph of the following equation using the intercepts

2x + 4y = 10

We have:

2x + 4y = 10

Set x = 0 to determine the y-intercept

4y = 10

Divide by 4

y = 2.5

Set x = 0 to determine the x-intercept

2x = 10

Divide by 2

x = 5

So, we have:

(5, 0) and (0, 2.5)

Plot the above points and connect the points (see attachment for graph)

Plot the graph of the following equation using the intercepts

3x + 6y = 18

We have:

3x + 6y = 18

Set x = 0 to determine the y-intercept

6y = 18

Divide by 6

y = 3

Set x = 0 to determine the x-intercept

3x = 18

Divide by 3

x = 6

So, we have:

(6, 0) and (0, 3)

Plot the above points and connect the points (see attachment for graph)

Read more about linear equations at:

https://brainly.com/question/14323743

#SPJ1

By constructing and solving the profit equation for the cuckoo clock sales, we conclude that the sales of 30 clock will make a profit of $ 4250

The profit (P) is the result of subtracting costs from sales (S). Cost (Cp) is the sum of rent (C) and production cost (C'). Now we proceed to create and solve the expression:

P = S - C - C'

P = 500 · x - 275 · x - 2500

P = 225 · x - 2500

P = 225 · 30 - 2500

P = 4250

By constructing and solving the profit equation for the cuckoo clock sales, we conclude that the sales of 30 clock will make a profit of $ 4250.

To learn more on profits: https://brainly.com/question/13716014

#SPJ1

Answer:

137,131

Step-by-step explanation:

The two pairs of polar coordinates for the given point (3, -3) with 0° ≤ θ < 360° are (3√2, 135°) and (3√2, 315°).

A polar coordinate is a two-dimensional coordinate system, wherein each point on a plane is typically determined by a distance (r) from the pole (origin) and an angle (θ) from a reference direction (polar axis).

Next, we would determine the distance (r) and angle (θ) as follows:

r = √(3² + (-3)²)

r = √(9 + 9)

r = 3√2.

θ = tan⁻¹(-3/3)

θ = tan⁻¹(-1)

θ = 3π and 7π/4 (second and fourth quadrants).

Converting to degrees, we have:

θ = 135° and 315°.

Read more on polar coordinates here: https://brainly.com/question/3875211

#SPJ1

Complete Question:

Determine two pairs of polar coordinates for the point (3, -3) with 0° ≤ θ < 360°

Simple

Sum of all three

Sum of first two

Divide by

Yes Verified

Lou Ann needed 25 packages that contains all the 150 invitations.

Lou Ann needed to mail 150 invitations to her school play. The invitations came 6 to a package.

The statistic is the study of mathematics which deal with relations between comprehensive data.

Here, 1 package contains 6 invitation
so 1 package = 6 invitations
total invitation= 150 invitations
now number of packages = Total invitation/ 6 invitation = 150/6
=25

Thus the required number of packages is 25.

Learn more about Statistics here:
https://brainly.com/question/23091366

#SPJ1

Answer:

the top one as highlighted

Step-by-step explanation:

y=Mx+c is the equation for a straight line

C is the intercept as it is at 0 it can be dropped from the expression as adding or taking away 0 makes no difference to the end value.

m is the slope

Answer:

(f + g)(x) = x - 7

Step-by-step explanation:

(f + g)(x)

= f(x) + g(x)

= - 3x - 5 + 4x - 2 ← collect like terms

= x - 7

Answer:

[tex]\sqrt{16} = 4\\[/tex]

Step-by-step explanation:

the distance formula for graph = [tex]\sqrt{x^{2} + y^{2} }[/tex]

(simplified version)

[tex]\sqrt{0^{2} + (-4)^{2} } \\\\\\\sqrt{0 + 16} \\\\\\\sqrt{16}\\\\= 4[/tex]

I hope its right TT I just looked it up here:

https://byjus.com/maths/distance-between-two-points-formula/

you should double check here as well

Answer:

x = 1 19/21 the one is in front of the 19/21

Step-by-step explanation:

Exact form: x = 40/21

Decimal form: x = 1.90476190

Mixed number form: x = 1 19/21.

Answer:

Let's solve your equation step-by-step.

[tex]\tt{ 14 = \dfrac{3}{5}\left( 7x + 10 \right) }[/tex]

Step 1: Simplify both sides of the equation.

[tex]\tt{ 14 = \dfrac{3}{5}\left( 7x + 10 \right) }[/tex]

[tex]\tt{ 14 = \dfrac{3}{5}(7) + \dfrac{3}{5}(10)}[/tex]

(Distribute)

[tex]\tt{ 14 = \dfrac{21}{5} x + 6 }[/tex]

Step 2: Flip the equation.

[tex]\tt{ \dfrac{21}{5} x + 6 = 14}[/tex]

Step 3: Subtract 6 from both sides.

[tex]\tt{ \dfrac{21}{5} x + 6 - \blue{6} = 14 - \blue{6}}[/tex]

[tex]\tt{ \dfrac{21}{5} = 8}[/tex]

Step 4: Multiply both sides by 5/21.

[tex]\tt{ \left( \dfrac{5}{21}\right) \times \left(\dfrac{21}{5}x \right) = \left(\dfrac{5}{21}\right) \times (8)}[/tex]

[tex]\\[/tex]

[tex]\large\tt\purple{ x = \dfrac{40}{21}}[/tex]

━━━━━━━━━━━━━━━━━━━━━

The rational expression that satisfies x = y +-2 is 2xy/(x + y)(x² - 4).

It should be noted that non permissible value is the value of the variable which make the denominator of the rational expression equal to zero.

Based on the information, x + y gives x - y = 0.

x = 2 gives x - 2 = 0

x = -2 gives x + 2 = 0

Ths denominator according to the condition illustrated will be (x - y)(x - 2)(x + 2) = (x - y)(x² - 4)

Then, the rational expression can be written by taking the numerator and denominator. An example will be 2xy/(x + y)(x² - 4).

Learn more about rational expression on:

brainly.com/question/1928496

#SPJ1