The area of a rectangle is given by the formula:
[tex]A=lw[/tex]Where
A is area
l is length
w is width
We find the expression for the area by multiplying the two "lengths" given:
[tex]\begin{gathered} A=2y(9y-4) \\ A=18y^2-8y \end{gathered}[/tex]The answer is:
[tex]A=18y^2-8y[/tex]Would 2(3 + X) - 2x make 4x?
Given that,
2(3 + X) - 2x, we have to verify whether the solution results in 4x. For that, solve the equation
2(3+x) - 2x
=> 6 + 2x - 2x
=> 6
Hence, it does not make 4x.
what is the reflexive property of equality?
The reflexive property of equality states that every element is equal to itselft, for example, 3 = 3, or a = a. In algebra is often applied for numbers. In geometry is applied to sides or angles, for example, side A
USE THE NORMAL CURVE TABLE TO DETERMINE THE PERCENT OF DATA SPECIFIED.A) TO THE LEFT OF z = 1.62B) BETWEEN z = -1.53 AND z = -1.82
SOLUTION:
Using a normal distribution table, we find that;
a. The area to the left of z = 1.62 is;
[tex]P(z<1.62)=0.9474[/tex]b. The area between z = -1.53 and z = -1.82, this is;
[tex]P(-1.82Data concerning the time between failures (in hours of operation) for a computer printer have been recorded, and the first quartile equals 36 hours, the second quartile equals 65 hours, and the third quartile equals 74 hours.The value for the lower inner fence equals
1) Let's remind ourselves of what is the Lower Fence.
2) So, let's calculate the Lower Fence given that the Quartiles have been given and the Interquartile Range can be found like this:
[tex]IQR=Q_3-Q_1=74-36=38[/tex]3) So now, we can write down the formula for the Lower Fence as well as plug into that the given data:
[tex]undefined[/tex]Your favorite music artist is inside Best Buy signing autographs. If you are at the back of a single fileline that is 2 miles out the door, how many people are ahead of you? Each person takes up 18 inches.
there are 7372 people ahead of you
The first thing we will do is state the parameters we are given:
Your location is 2miles from the door.
Each person takes 18inches.
To know the number of people ahead, we will find how many inches make up a mile.
1 mile = 66360inches
[tex]\begin{gathered} 2\text{ miles = 2}\times66360\text{ } \\ =\text{ 132720 inches} \end{gathered}[/tex]Since 1 person = 18inches, the number of persons on that line would be:
[tex]\begin{gathered} =\text{ }\frac{132720}{18} \\ =\text{ 7373 approxi}mately \end{gathered}[/tex]There are 7373 people on the line.
The number of people ahead of you = 7373-1 = 7372
But, there are 7372 people ahead of you
Expand and simplify (a^2+b)^8
For this exercise, we must use the binomial theorem. The formula of this theorem is described as follows
[tex](a+b)^n=\sum_{i\mathop{=}0}^nnCi(a^{n-i})(b^i)[/tex]Where nCi represents the combinatory of n between i. For our case,
[tex]a=a^2\text{ y }b=b[/tex]Replacing the values you have in the formula
[tex]\begin{gathered} (a^2+b)^8=\sum_{i\mathop{=}0}^88Ci(a^2)^{8-i}(b^i) \\ =\frac{8!}{0!(8-0)!}(a^2)^{8-0}b^0+\frac{8!}{1!(8-1)!}(a^2)^{8-1}b^1+\frac{8!}{2!(8-2)!}(a^2)^{8-2}b^2+....+\frac{8!}{8!(8-8)!}(a^2)^{8-8}b^8 \\ =\frac{8!}{8!}(a^2)^8+\frac{8!}{1(7)!}(a^2)^7b^1+\frac{8!}{2(6)!}(a^2)^6b^2+....+\frac{8!}{8!}(a^2)^5b^8 \\ =a^{16}+8a^{14}b+28a^{12}b^2+56a^{10}b^3+70a^8b^4+56a^6b^5+28a^4b^6+8a^2b^7+b^8 \end{gathered}[/tex]Thus,the expansion and simplification is as follows
[tex](a^2+b)^8=\placeholder{⬚}+8a^{14}b+28a^{12}b^2+56a^{10}b^3+70a^8b^4+56a^6b^5+28a^4b^6+8a^2b^7+b^8[/tex]Find the area of the circle if the square has an area of 900 in.² to give your answer in terms of
Diameter of circle = length of each side of the square
The formula for calculating the area of a square is
Area = l^2
where l is the length of each side
From the information given,
Area = 900
900 = l^2
l = √900
l = 30
diameter = 30
radius = diameter/2 = 30/2
radius = 15
The formula for calculating the area of a circle is
Area = πr^2 = π * 15^2
Area of circle = 225π in^2
Marcus para sailing in Florida. The angle of depression from his line of sight to the boat is 41 °. if the cable attaching Mark to the boat is 500 ft long how many feet is Mark above the water
As you can see, a right triangle is formed in the situation that the statement describes. So to solve the exercise you can use the trigonometric ratio sin(θ):
[tex]\sin (\theta)=\frac{\text{opposite side}}{\text{hypotenuse}}[/tex]Graphically
So, in this case, you have
[tex]\begin{gathered} \theta=41\text{\degree} \\ \text{Opposite side = Mark's height above water } \\ \text{Hypotenuse = 500 ft} \\ \sin (\theta)=\frac{\text{opposite side}}{\text{hypotenuse}} \\ \sin (41\text{\degree})=\frac{\text{Mark's height above water }}{500ft} \\ \text{Multiply by 500ft from both sides of the equation} \\ \sin (41\text{\degree})\cdot500ft=\frac{\text{Mark's height above water }}{500ft}\cdot500ft \\ \sin (41\text{\degree})\cdot500ft=\text{Mark's height above water } \\ 328.03ft=\text{Mark's height above water } \end{gathered}[/tex]Therefore, Mark is 328.03 feet above the water.
A line shaft rotating at 250 rpm is connected to a grinding wheel by the pulley assembly shown in the diagram. If the grinder shaft must turn at 1200 rpm, what size pulley should be attached to the line shaft?
A line shaft rotating at 250 rpm is connected to a grinding wheel by the pulley assembly shown in the diagram. If the grinder shaft must turn at 1200 rpm, what size pulley should be attached to the line shaft?
grinder shaft
the radius is r=5/2=2.5 in ------> given
Find out the circumference
C=2*pi*r
C=2*pi*2.5 ------> C=5pi in
one revolution is 5pi in
so
1200rpm is
1200*5pi=6,000pi in per minute
step 2
pulley assembly
Diameter x
250 rpm
circumference is equal to -----> C=xpi in
so
xpi*250=6,000pi
simplify
250x=6,000
x=24 in
the diameter of the pulley assembly is 24 inchesFor any positive number b not equal to 1 and any number or variable n, evaluate the following expression. logb (b^n) = ?
The logarithm is the inverse function of the exponentiation, and viceversa. The property of the logarithms and exponents tells us:
[tex]\log_b(b^n)=n[/tex] Thus, the correct answer is option A. nin how many ways can six players be assigned to six positions on a baseball team assuring there any player can play any position
Imagine htat each position is a box numbered from 1 to 6. You have the following
We will first find all posibilitied by simply calculating all possibilities for each box if we fill them in order.
For the first box, since we haven't chosen any player, we have 6 possibilities.
For the second box, since we have already filled box 1, we have 5 possibilites.
In the same manner, for box 3 we have 4 possibilites.
For box 4 we have 3 possibilities
For box 5 we have 2 possibilites.
Finally, for box 6 we will have only 1 possibility
So, the total number of possibilites is simply the product of all possibilites for each box
That is
[tex]6\cdot5\cdot4\cdot3\cdot2\cdot1=6!=720[/tex]so there are 720 possiblilites.
Solve the following system of equations by using elimination: 3x - y = -1 x + y = 13
Solution
For this case we have the following system of equations:
3x-y =-1 (1)
x +y= 13 (2)
Solving x from the (2) equation we have:
x=13-y (3)
Replacing (3) into (1) we got:
3(13-y) -y= -1
Solving for y we have:
39 -3y -y = -1
4y = 40
y= 10
And solving for x we got:
x= 13-10 = 3
Find the conjugate of the following binomial ^15t-^5
The conjugate is formed by changing the sign between the terms of the binomial:
[tex]\begin{gathered} \sqrt{15}t-\sqrt{5} \\ \uparrow\downarrow conjugate \\ \sqrt{15}t+\sqrt{5} \end{gathered}[/tex]In this case, the sign is negative, then the sign of its conjugate is positive.
Answer: [tex]\sqrt{15}t+\sqrt{5}[/tex]A full 275 L tank contains a 20% saline solution. How many litres must be replaced with a 100% saline solution to produce a full tank with a 45% saline solution? Round your final answer to 1 decimal place if necessary.
Let x be the volume of 20% solution in the tank after the given process
Let y be the volume of 100% solution used.
The sum of x and y needs to be equal to the final volume 275L:
[tex]x+y=275[/tex]The amount of substance (salt) in each solution is calculated by multipliying the volume by the concentration (in decimals); then, the amount of salt in 20% solution is 0.2x, in 100% solution is 1y and in the final solution (45%) is 0.45(275).
Sum amount in 20% solution with amount in 100% solution to get the amount in final solution:
[tex]\begin{gathered} 0.2x+y=0.45\left(275\right) \\ 0.2x+y=123.75 \end{gathered}[/tex]Use the next system of equations to answer the question:
[tex]\begin{gathered} x+y=275 \\ 0.2x+y=123.75 \end{gathered}[/tex]1. Solve x in the first equation:
[tex]x=275-y[/tex]2. Use the value of x (step 1) in the second equation:
[tex]0.2\left(275-y\right)+y=123.75[/tex]3. Solve y:
[tex]\begin{gathered} 55-0.2y+y=123.75 \\ 55+0.8y=123.75 \\ 0.8y=123.75-55 \\ 0.8y=68.75 \\ y=\frac{68.75}{0.8} \\ \\ y=85.93 \end{gathered}[/tex]The volume of 100% solution that needs to be used is 85.9 Litres.
Then, the litres that must be replaced with 100% solution to produce a full tank with 45% saline solution is 85.9What are the characteristics of a t-distribution? (Give at least 3characteristics).
Given,
T-distribution.
T-distribution: The T-distribution, also known as the student's t-distribution, is a type of probability distribution that is similar to the normal distribution with its bell shape but has heavier tails.
There are 3 characteristice of the distribution:
shape, central tendency and variability.
How much medicine is to be taken in each dose
All changes saved1. (07.01 MC)The moon forms a right triangle with the Earth and the Sun during one of its phases, as shown below:EarthSunMoonA scientist measures the angle x and the distance y between the Earth and the moon. Using complete sentences, explain how the scientist can use only thesetwo measurements to calculate the distance between the Earth and the Sun.
Notice that we can use the trigonometric function tangent to find the distance between the Earth and the Sun with the following expression:
[tex]\begin{gathered} \tan x=\frac{y}{ES} \\ \Rightarrow ES=\frac{y}{\tan x} \end{gathered}[/tex]then, if the scientist only have the measure of the distance between the earth and the moon and the angle that forms between the earth and the moon in the sun, we can find out the distance between the Earth and the Sun
From the diagram below, if AC is a tangent line, and if PD = 9 and DC = 32, find the length of BC.
Solution:
Given the circle;
From the circle theorem, triangle PBC is a right triangle.
[tex]\begin{gathered} PB=PD=9 \\ \\ PC=PD+DC=9+32 \\ \\ PC=41 \end{gathered}[/tex]Using the Pythagorean theorem;
[tex]\begin{gathered} BC=\sqrt{PC^2-PB^2} \\ \\ BC=\sqrt{41^2-9^2} \\ \\ BC=\sqrt{1600} \\ \\ BC=40 \end{gathered}[/tex]CORRECT OPTION: C
please choose all answers that best matches the question provided thank you
ANSWER
• Quadrilateral
EXPLANATION
In a parallelogram, opposite sides are parallel and congruent - they have the same length.
A rectangle is like a parallelogram, but all interior angles are right angles.
A square has four congruent sides, as well as a rhombus.
If a trapezoid is isosceles, then the non-parallel legs are congruent. If it is not isosceles, then all sides have different lengths and two opposite sides are parallel.
We know that this is a quadrilateral because it has 4 sides.
What is the area of this parallelogram? (HINT: Use Pythagorean Theorem) 28 in 17 in lih 15 in X. 238in? b. 224in? < 112in? 210 in?
using pythagorean theorem we can get h
[tex]17^2=15^2+h[/tex][tex]h=\sqrt[]{64}\text{ =8}[/tex]so we get h as 8.
A=bxh
h=8 b= 28
so,A=224in
Question 4 The graph of f(x) is shown. For what values of x does f(x) = 0 ? Select all that apply. MU 0 2 3
Question 4 The graph of f(x) is shown. For what values of x does f(x) = 0 ? Select all that apply. MU 0 2 3
___________________________________
Can you see the updates?
Give me two minutes to point out the points on your graph
__________________________________
Answer
x= 2, -1, -3
____________________________________
Do you have any questions regarding the solution?
Determine the type of triangle that is drawn below. W 5.57 50° X 80° 7.13 5-57 50° V
Given the triangle VWX
AS shown:
[tex]\begin{gathered} m\angle V=m\angle W=50 \\ m\angle X=80 \end{gathered}[/tex]So, the three angles are less than 90, which mean it is an acute triangle
And there are two congruent angles, which mean it is an isosceles triangle
so, the type of the triangle is an acute isosceles triangle
Identify two similar triangles in the figure below, and complete the explanation of why they are similar. Then find AB. B A С C 4 D ZA = (select) and ZABD = (select), so AABD - ACB by the select) Triangle Similarity Theorem. AB=
we know that
If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent
so
In this problem
Question 12 of 15 What is the midpoint of a line segment with endpoints at (-1,-1) and (3, 3)?
To find the midpoint, we will use the formula;
(Xm, Ym) = [ x₁+x₂ /2 , y₁+y₂ /2]
x₁=-1 y₁=-1 x₂=3 y₂=3
substitute the values into the formula
(Xm , Ym) = [ -1+3 /2 , -1+3 /2]
(Xm , Ym) = (1, 1)
The midpoint is : (1, 1)
A teacher asks students to determine the accuracy of this statement.A reflection over the x-axis and then over the y-axis results in the same transformation as a 180° rotation about the originof the original figure.Kwame's explanation of the accuracy of the statement is shown below.Step 1: Choose the vertices of a pre-image: (1, 2), (1, 4), (2, 3).Step 2: Reflect the pre-image over the x-axis: (1, -2), (1, -4), (2, -3).Step 3: Reflect the figure from step 2 over the y-axis: (-1,2), (-1, 4), (-2, 3).Step 4: Rotate the pre-image 180°:(-1, -2), (-1,-4), (-2, -3).Step 5: Compare the reflected figure to the rotated figure. The vertices are not located in the same place, therefore thestatement made by the teacher is inaccurate.Which best explains Kwame's solution?
(Reminder: To find the reflection over the x-axis, we just need to switch the signal of the y-coordinate of the points.
To find the reflection over the y-axis, we just need to switch the signal of the x-coordinate of the points)
Kwame's solution has a mistake in step 3:
The figure from step 2 is:
(1, -2), (1, -4), (2, -3).
Then, when reflecting these points over the y-axis, the result is:
(-1, -2), (-1, -4), (-2, -3)
At this point Kwame wrote (-1,2), (-1, 4), (-2, 3), which is incorrect.
Step 4 is correct, then when comparing the images in step 5, the vertices will be located in the same place, therefore the statement made by the teacher is accurate.
1.75,____,6.75,9.25,11.75
Answer:
This looks like an addition (summation is the technical term) series. Here we need to figure out the difference between each number in the series. The difference between 6.75 and 9.25 is 2.5 (You can subtract the larger number from the smaller number to find out). So, 6.75-2.5=4.25.
So the correct answer in the blank is 4.25, and the rule is +2.5.
Step-by-step explanation:
s Southern New Ham... t: This question is similar to Example 4 in "1-3 Reading and Participation Ac blications" in Module One. You can check your answers to part c and d to make right track. rectangle has perimeter 86 cm and its length is 1 cm more than twice its width. 1 the dimensions of a rectangle given that its perimeter is 86 cm and its leng e its width. ip your solution using the variables L for the length. W for the width, and P for the perimeter
You have that a rectangle has a perimeter of 86cm and its length is 1cm more than twice its width.
If W is the width and L is the length you can write the previous situation as follow:
part a:
2W + 2L = 86 perimeter of the rectangle
part b:
L = 2W + 1
replace the expression for y into the equation 2x + 2y = 86, just as follow:
2W + 2(2W + 1) = 86 expand the parenthesis
2W + 4W + 2 = 86 subtract 2 both sides and simplify like terms
6W = 86 - 2
6W = 84
W = 84/6
W = 14
L = 2W + 1 = 2(14) + 1 = 28 + 1 = 29
part c:
The length is 29 cm
part d:
The width is 14 cm
420, 84, 16.8, 3.36,... What is the explicit rule for this sequence? An =___ *(____)^n-1
Answer:
[tex]a_n=420\ast(0.2)^{n-1}[/tex]Explanation:
The explicit formula for a geometric sequence is always given in the form;
[tex]a_n=a_1\ast(r)^{n-1}[/tex]where an = the nth term of the sequence
a1 = the 1st term of the sequence
r = the common ratio of the sequence
From the given sequence, we can see that the 1st term, a1, is 420.
We can find the common ratio, r, by dividing any number of the sequence with its preceding number;
[tex]\begin{gathered} r=\frac{84}{420}=0.2\text{ or 16.8/84 = 0.2} \\ \therefore r=0.2 \end{gathered}[/tex]Substituting the above values into our formula above, we'll have;
[tex]a_n=420\ast(0.2)^{n-1}[/tex]Solve sin(x) = 0.23 on 0 ≤ x < 2T.There are two solutions, A and B, with A
Given -
sin(x) = 0.23 on 0 ≤ x < 2π
To Find -
Two solutions, A and B =?
Step-by-Step Explanation -
[tex]0.23\text{ = }\frac{23}{100}[/tex]So, the two solutions will be -
[tex]\begin{gathered} \sin^{-1}(\frac{23}{100})\text{ and }\pi\text{ - }\sin^{-1}(\frac{23}{100}) \\ \\ So,\text{ }\sin^{-1}(\frac{23}{100})\text{ = 0.232} \\ \\ Also,\text{ }\pi\text{ - }\sin^{-1}(\frac{23}{100})\text{ = 3.141 - 0.232 = 2.909} \end{gathered}[/tex]Now, Since A < B
So,
A = 0.232
B = 2.909
Final Answer -
A = 0.232
B = 2.909
Watch help video Find the length of the third side. If necessary, write in simplest radical form. 4V3 8 oc Submit Answer Answer
SOLUTION
Using Pythagoras theorem,
[tex]\begin{gathered} 8^2\text{ = ( 4}\sqrt[]{3})^2+h^2 \\ 64=48+h^2 \\ h^2\text{ = 64 - 48} \\ h^2\text{ = 16} \\ \text{square root both sides , we have :} \\ h\text{ = 4} \end{gathered}[/tex]