Answer:
1. timely
2. measurable
3. specific
Step-by-step explanation:
In triangle ABC, the side lengths are AB = 13, AC = 21, and BC = x. Write a compound inequality that represents the range of possible values for x.
Answer:
7 < x < 34
Step-by-step explanation:
The answer must be greater than 7, else the two sides are less than or equal to the third. That triangle is impossible. The answer must also be less than 34, because then the two other sides would equal the third, making an impossible triangle.
Answer:
7 < x < 34
it just is
Find the interquartile range (IQR) of the data in the dot plot below. chocolate chips 0 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10. Number of chocolate chips. Chocolate chips in different cookies in a package
*The dot plot is shown in the attachment below
Answer:
2
Step-by-step explanation:
Interquartile range is the difference between the upper median (Q3) and the lower median (Q1).
First, let's write out each value given in the data. Each dot represents a data point.
We have:
2, 3, 3, 4, 4, 4, 4, 5, 5, 6, 7
=>Find the median:
Our median is the middle value. The middle value is the 6th value = 4
==>Upper median Q3) = the middle value of the set of data we have from the median to our far right.
2, 3, 3, 4, 4, |4,| 4, 5, [5], 6, 7
Our upper median = 5
==>Lower median(Q1) = the middle value of the data set we have from our median to our far left.
2, 3, [3], 4, 4, |4,| 4, 5, 5, 6, 7
Lower median = 3
==>Interquartile range = Q3 - Q1 = 5-3 = 2
Answer:
2
Step-by-step explanation:
Steve Fossett is approaching the shores of Australia on the first successful solo hot air balloon ride around the world. His balloon, the Bud LightTM Spirit of Freedom, is being escorted by a boat (directly below him) that is 108 meters away. The boat is 144 meters from the shore. How far is Fossett's balloon from the shore?
Answer:
180 meters
Step-by-step explanation:
Distance from the balloon to the boat = 108 meters
Distance from the boat to the shore = 144 meters
Since the boat is directly below the balloon, the problem forms a right triangle in which the distance from the balloon to shore is the hypotenuse.
Let the length of the hypotenuse = l
Using Pythagoras Theorem
[tex]l^2=108^2+144^2\\l^2=11664+20736\\l^2=32400\\l=\sqrt{32400} \\l=180$ meters[/tex]
The distance from Fossett's balloon to the shore is 180 meters.
Fossett's balloon is 180m from the shore
data;
escort boat to the ballon = 108mboat from the shore = 144mdistance between the ballon and the shore = xPythagoras TheoremTo solve this problem we can assume this is situation forms a right angle triangle and we can solve this using pythagoras theorem.
[tex]x^2 = y^2 + z^2\\[/tex]
Let's substitute the values and solve
[tex]x^2 = y^2 + z^2\\x^2 = 108^2 + 144^2\\x^2 = 32400\\x = \sqrt{32400} \\x = 180m[/tex]
Fossett's balloon is 180m from the shore
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Help please........please
Answer:
58, 38 and 76
Step-by-step explanation:
(a)
The median is represented by the vertical line inside the box
median = 58
(b)
The interquartile range is the difference between the upper quartile and the lower quartile.
The upper quartile is the value at the right of the box, that is 72
The lower quartile is the value at the left of the box, that is 34
Interquartile range = 72 - 34 = 38
(c)
The range is the difference between the largest and smallest value
max value is the value at the right of the data, that is 86
min value is the value at the left of the data, that is 10
Range = 86 - 10 = 76
Find dy/dx of (3 - 2x)-1/2
Answer:
Step-by-step explanation:
To evaluate the derivative of this function you need the chain rule. The pattern I teach to my calculus students is to find
u =
u' =
f(u) =
f'(u) =
First pick your "u". u will be the inner function, the one inside the parenthesis.
u' will then be the derivative of u.
f(u) is the function in terms of u, and
f'(u) is the derivative of the function in terms of u.
The derivative then, finally, will be u' * f'(u). Let's begin.
Our u, or the part of the function inside the parenthesis is 3 - 2x; hence,
u = 3 - 2x
The derivative, u', then is
u' = -2
f(u) is the function in terms of u, so
f(u) = [tex]u^{-\frac{1}{2}[/tex] and the derivative in terms of u is
f'(u) = [tex]-\frac{1}{2}u^{-\frac{3}{2}[/tex]
u' * f'(u) then is
[tex]-\frac{1}{2}u^{-\frac{3}{2}*(-2)[/tex] Simplify that by subbing back in for u and multiplying -2 by -1/2 to get
[tex]y'=(3-2x)^{-\frac{3}{2}[/tex]
Given that y is directly proportional tox, and when y = 8 when x=
10.
(a) Write down the equation of y in terms of x.
(b) Find the value of y when x = 25.
8
(c) Find the value of x when y==
25
Answer:
see explanation
Step-by-step explanation:
(a)
Given that y is directly proportional to x then the equation relating them is
y = kx ← k is the constant of proportion
To find k use the condition y = 8 when x = 10. then
8 = 10k ( divide both sides by 10 )
0.8 = k
y = 0.8k ← equation of proportion
(b)
when x = 25, then
y = 0.8 × 25 = 20
(c)
when y = 25, then
25 = 0.8x ( divide both sides by 0.8 )
x = 31.25
If x, y, z, are integers such that 2^x*3^y*7^z=329, Then what is x, y, and z? PLZZZZ HELP THANK YOU
Answer:
I just answered this question lol but the answer is 2^0*3^0*7^47=329. Hope this helps!!
Step-by-step explanation:
Can someone explain how to answer this question please
Plz help similarity in right triangle
Answer:
similar triangles have there corresponding sides proportional and corresponding angles equal
Find the ordered pairs for the x- and y- intercpets of the equations 3x-2y=18 and select the appropriate option below
Answer:
ordered pairs for the
x-intercept : (6,0)
y- intercepts :(0,9)
Step-by-step explanation:
Given equation : 3x-2y=18
X- intercept on coordinate plane is point where the line intersect the x- axis.
The coordinate of point y is 0 for x-intercept.
Based on this let the coordinate of X- intercept be (x,0)
we will plug this value in equation 3x-2y=18, to find value of x and hence we will get x-intercept
3x-2y=18
3x -2*0 =18
=> 3x = 18
=> x = 18/3 = 6
Thus, coordinate of x-intercept is (6,0)
________________________________________________
Y- intercept on coordinate plane is point where the line intersect the y- axis.
The coordinate of point x is 0 for y-intercept.
Based on this let the coordinate of X- intercept be (0,y)
we will plug this value in equation 3x-2y=18, to find value of y and hence we will get y-intercept
3x-2y=18
3*0 -2y =18
=> 2y = 18
=> y = 18/2 = 9
Thus, coordinate of y-intercept is (0,9)
find the perimiter of this shape
Answer:
The perimeter of the shape is (7x²+10x+81) inches.
Step-by-step explanation:
When finding the perimeter of a shape, you have to add up all the side lengths :
[tex]p = 31 + (4 {x}^{2} + 8x) + (3 {x}^{2} - 5x + 20) + (7x + 30)[/tex]
[tex]p = 31 + 4 {x}^{2} + 8x + 3 {x}^{2} - 5x + 20 + 7x + 30 [/tex]
[tex]p =( 7 {x}^{2} + 10x + 81) \: inches[/tex]
Wendy is creating a large soup based on a recipe. Her recipe calls for of a pint of milk, but she only has of a pint of milk, so she can only make a portion of her soup. Wendy can only make _____ of her recipe with the amount of milk that she has.
Answer:
She can only make 5/6 of her recipe with the amount of milk that she has.
Step-by-step explanation:
Some data of this problem is missing, the data missing is:
Her recipe calls for 3/4 of a pint of milk and she only has 5/8 of a pint of milk.
Now, to know what's the portion she can do with that amount we need to divide the amount of milk she has by the total amount she needs:
[tex]\frac{5}{8}[/tex] ÷[tex]\frac{3}{4}[/tex]
When we divide we turn the second fraction upside down (the numerator becomes the denominator and viceversa) and multiply, thus:
[tex]\frac{5}{8}[/tex]÷[tex]\frac{3}{4}=\frac{5}{8}[/tex]×[tex]\frac{4}{3} =\frac{20}{24}[/tex]
If we simplify this last expression we have:
[tex]\frac{20}{24}=\frac{10}{12} =\frac{5}{6}[/tex]
Thus, she can only make 5/6 of her recipe with the amount of milk that she has.
Note: In case the data missing is different, you can apply this same procedure with the fractions you have.
1
Select the correct answer.
The edges of a cube are 5 centimeters each and the diagonal of a face is approximately 7 centimeters. What is the approximate area of the cross
section passing through the diagonals of opposite faces of this cube?
OA. 12 square centimeters
OB.
25 square centimeters
O C. 35 square centimeters
OD
49 square centimeters
Answer:35 square
Step-by-step explanation:
I've attached the question in the picture below.
at a map scale of 1:1500, 12 centimeters on the map is equivalent to 1.8 kilometers on the ground.
step-by-step
since the scale is 1 to 15,000 you simply multiply it by the 12 cm
12cm × 15,000 = 180,000
but you still have to convert it to kilometers (the measurement on the ground).
to go from centimeters to kilometers move the decimal 5 place values to the left.
final answer
1.8 kilometers
Emanuel was charged $32 for a 14 2/9km taxi ride What was the cost per kilometer?
Simplify : (-7/18 × 15/-7) - (1 × 1/4) + (1/2 × 1/4)
Answer:
17/24
Step-by-step explanation:
This expression simplifies to the following:
-7 15 1 1
---- * ----- - ----- + -----
18 -7 4 8
Reducing the product, we get
15 1
-------- - -----
18 8
and this simplifies further:
5 1
----- - -----
6 8
The LCD is 24. Thus, we have:
20 3 17
------ - ----- = -----
24 24 24
Nick, Paul and krutika share £80 in a ratio 1:1:2 how much money does each person get
Answer:
£20
Step-by-step explanation:
First you add 1 ,1 ,2 which =4
Next you divide 80 by 4 which give you the answer 20.
Serena wants to wrap ribbon around the edge of the picture frame represented in the drawing. Which is the simplified form of the expression representing the length of ribbon Serena will need? A. 9x – 13.2 B. 4.5x – 6.6 C. 9x – 14.8 D. 2(3.5x – 7) + 2(x + 0.4)
Answer:
A.9x – 13.2
Step-by-step explanation:
2*(3.5x-7+x+0.4)=2*(4.5x-6.6)=9x-13.2
Answer:
It is A
Step-by-step explanation:
HELP NOW PLZ 20-30 POINTS FOR BRAINLIEST LOOK AT MY PROFILE FOR THE SAME QUESTION WITH MORE POINTS Step 1: Write a quadratic equation in standard form choosing your own coefficients and constant! (Recall: Standard Form of a quadratic equation is Ax^2 + Bx + C ). You need to choose a value for A, B, and C that satisfies each of the following conditions. You can use a value of 0 for B for no more than 1 of the 5 questions! Step 2: Solve each of the equations you create. YOU MUST SHOW YOUR WORK TO RECEIVE CREDIT FOR THIS STEP! Write your Exact answer in simplest form AND if necessary, round your estimate to the nearest tenth. 1) Equation 1 should represent a parabola that opens up and has a negative y-intercept. Equation 1: ____________________________________________________________ What strategy are you using to solve this equation and why? ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ Show your work and solution for solving this equation: 2) Equation 2 should represent a parabola that opens down and has a negative y- intercept. Equation 2:___________________________________________________________________ What strategy are you using to solve this equation and why? ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ Show your work and solution for solving this equation: 3) Equation 3 should represent a parabola that is a vertical stretch of the parent function and has a y-intercept greater than 3 and opens down. Equation 3:___________________________________________________________________ What strategy are you using to solve this equation and why? ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ Show your work and solution for solving this equation: 4) Equation 4: You decide what type of parabola you would like to create by answer the following questions: Does your parabola open up or down? _______________ Is there a vertical stretch or vertical compression? _______ What is the y-intercept? __________ Equation 4: ____________________________________________________________________ What strategy are you using to solve this equation and why? ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ ______________________________________________________________________________ Show your work and solution for solving this equation: 5) Write a quadratic equation that can only be solved using the quadratic formula. Equation 4: _________________________________________________________________ Show your work for how you use the quadratic formula to solve this equation:
Answer:
This is equation 1.
Step-by-step explanation:
Step 1: Write a quadratic equation in standard form choosing your own coefficients and constant.
Conditons that need to be satisfied: B can be 0 in only one question, parabola should open up and have a negative y intercept.
1. The parabola should open upwards: a> 0
2. [tex]3x^2+7x-6[/tex] (a>0), y-int is negative (0s for x's)
3(0)^2 + 7(0) -6
y= -6
Step 2:
1. Factor the original equation: (3x-2)(x+3)
x=2/3, -3
2. Strategy used (factor by grouping)
If z is a standard normal variable, find the probability.
P(Z < 0.97)
0.1660
0.8340
0.8315
0.8078
Answer:
the correct option is A
Step-by-step explanation:
hope this helps
Using the standard normal distribution table, the probability of having a Zscore less than 0.97 would be 0.8340
To obtain the probability z P(Z < 0.97) ; we use a standard normal distribution table or a Z probability calculator ;
Using a normal distribution table :
P(Z < 0.97) = 0.8339Therefore, the most appropriate option is 0.8340
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: Write the equation of the line in Point-Slope Form given the information below. Slope=-2 Point=(1,-1)
Answer: y+1=-2(x-1)
Step-by-step explanation:
The point-slope formula is [tex]y-y_{1}=m(x-x_{1})[/tex]. Since we know the coordinate and slope, we can directly plug them in.
[tex]y-(-1)=-2(x-1)[/tex]
[tex]y+1=-2(x-1)[/tex]
The inverse of G(x) is a function.
Answer:
This is False.
Step-by-step explanation:
I hope this helped you! :)
Answer: false
Step-by-step explanation:
Leonardo wrote an equation that has an infinite number of solutions. One of the terms in Leonardo's equation is missing, as shown below. Negative (x minus 1) + 5 = 2 (x + 3) minus box Which could be the missing term that Leonardo put into the box? x 3x 1 5
Answer:
The missing term is 3x
Step-by-step explanation:
Given
-(x - 1) + 5 = 2(x + 3) - _
Required
Find _
For proper identification of the parameters, represent _ with Z
So, the equation becomes
-(x - 1) + 5 = 2(x + 3) - Z
Open bracket (start from the left hand side)
-x + 1 + 5 = 2(x + 3) - Z
-x + 1 + 5 = 2x + 6 - Z
Solve like terms
-x + 6 = 2x + 6 - Z
Subtract 6 from both sides
-x + 6 - 6 = 2x + 6 - 6 - Z
-x = 2x - Z
Subtract 2x from both sides
-x - 2x = 2x - 2x - Z
-3x = -Z
Multiply both sides by -1
-3x * -1 = -Z * -1
3x = Z
Reorder
Z = 3x
Hence, the missing term is 3x
Answer:
answer is 3x
Step-by-step explanation:
Is the function f(x) =(4)^x -2 an exponential function. If so, identify the base. If not, why not?
Answer:
Yes.
Base: 4
Step-by-step explanation:
Since we have 4 to the power of x, we do indeed have an exponent. The -2 just signifies vertical movement down.
X^4+9 which pattern can we use to factor the expression?
Answer:
[tex]\left(x^2+3i\right)\left(x^2-3i\right)[/tex]
Step-by-step explanation:
[tex]x^4+9[/tex]
[tex]x^4+9[/tex] can be written as [tex]x^4--9[/tex].
Apply the formula for the difference of two squares.
[tex](a^2-b^2)=(a+b)(a-b)[/tex]
[tex]-9=3i^2[/tex]
[tex]x^4=(x^2)^2[/tex]
[tex](x^2)^2-(3i)^2=(x^2+3i)(x^2-3i)[/tex]
Answer:
(x^2 - 3i) ( x^2 +3i)
Step-by-step explanation:
X^4+9
x^4 - -9
This is the difference of squares (a^2 - b^2) = (a-b)(a+b)
(x^2) ^2 - ( 3i)^2
(x^2 - 3i) ( x^2 +3i)
On a nearby pond, black and white ducks are swimming in groups of 3. James wants to find the experimental probability of two white ducks and one black duck swimming together. Design a simulation using a coin flip and explain why it is the best choice for James.U Will get BRAINLIEST
Answer:
The answer is below
Step-by-step explanation:
Given that, there are only two available choices, which are a black or white duck, this can be represented using a coin: H→White duck, T→Black Duck
Hence, to represent a set of possible outcomes, the coin has to be tossed three times.
Thus, we assume that, at the minimum we have total number of Ducks = 3 Black + 3 White = 6 Ducks
Total Favorable Outcome = 2 White + 1 Black
Total Possible Outcome = Selecting 3 Ducks (2 White +1 Black) from 6 Ducks
Formula to Calculate Probability
= Total favourable outcome ÷ Total possible outcome
Use ,C(n,r)= n! / (n - r)! r!
Therefore, the Probability of two white ducks one black duck swimming together
= ³C² * ³C¹ ÷ 6C3 = 9/20
To use Simulation Coin Flip, we have the following:
H→White duck, T→Black Duck
HHH→Three White Ducks Swimming together
TTT→Three black ducks Swimming together
HHT→Two white duck and a Black Duck swimming together
HTH→Two white duck and a Black Duck swimming together
THH→Two white duck and a Black Duck swimming together
TTH→Two Black duck and a White Duck swimming together
THT→Two Black duck and a White Duck swimming together
HTT→Two Black duck and a White Duck swimming together
Finally, to find the probability, divide the observed desired outcomes by the total number of trials.
Answer:
There are only two choices, a black or white duck, so a coin is the best choice. To represent a set of possible outcomes, toss the coin three times. Repeat the experiment multiple times. To find the probability, divide the observed desired outcomes by the total number of trials.
Step-by-step explanation:
edg2020
Mrs. Boiler is three times as old as her son, William. Mr. Boiler is 4 years older than his wife. If William's age will be x years old in 5 years, express the sum of their current ages, in terms of x.
Answer:
william's age=x-5, mrs boiler=3 (x-5), mr boiler=4+3 (x-5) the sum=7x-31
help me please :) thanks
Answer: B
Step-by-step explanation: graph b
Given: ∆KLM, KL ≅ LM A∈ KM , B ∈ KM AK ≅ BM Prove:△AKL ≅ △BML ΔALB is isosceles
Answer:
ΔAKL is congruent to ΔBML by the Side Angle Side rule of congruency and ΔALB is isosceles as two of its sides [tex]\overline {AL}[/tex] and [tex]\overline {BL}[/tex] are congruent
Step-by-step explanation:
The given parameters are;
The given triangle ΔKLM has sides [tex]\overline {KL}[/tex] ≅ [tex]\overline {LM}[/tex], Given
ΔKLM is isosceles Δ (two equal segments), Definition of isosceles Δ
∠LKM ≅ ∠LMK, Base ∠s of isosceles Δ are ≅
Point A is on segment [tex]\overline {KM}[/tex], Given
Point B is also on segment [tex]\overline {KM}[/tex], Given
Segment [tex]\overline {AK}[/tex] ≅ segment [tex]\overline {BM}[/tex], Given
ΔAKL ≅ ΔBML, SAS rule of congruency
Segment [tex]\overline {AL}[/tex] ≅ segment [tex]\overline {BL}[/tex], CPCTC
ΔALB is isosceles (two equal segments), Definition of isosceles Δ
Where:
SAS = Side Angle Side
CPCTC = Congruent parts of congruent triangles are congruent.
Answer:
m∠AKL=m∠BML | Base Angle Theorem (Base ∠ TH.)
Step-by-step explanation:
KL=LM | Given
A ∈ KM | Given
B ∈ KM | Given
AK=BM | Given
m∠AKL=m∠BML | Base ∠ TH.
Choose one of the theorems about chords of a circle and state it using your own words. Create a problem about chords that uses the theorem that you explained. Choose a problem that a classmate has posted, and explain how to solve it. Note: If you do not see any other responses, explain how to solve the problem that you posted. Please number your responses to the questions as they are shown (1, 2, and 3).
Answer:
Step-by-step explanation:
1. A given chord on a circle is perpendicular to a radius through its center, and it is at a distance less that the radius of the circle.
2. A circle of center O has a radius of 13 units. If a chord AB of 10 units is drawn at a distance, d, to the center of the circle, determine the value of d.
3. From question 2, the radius = 13 units, length of chord = 10 units and distance of chord to center of the circle is d.
A radius that meet the chord at center C, and divides it into two equal parts.
So that;
AC = CB = 5 units
Applying Pythagoras theorem to ΔOCB,
OC = d, CB = 5 units and OB = 13 units
[tex]13^{2}[/tex] = [tex]5^{2}[/tex] + [tex]d^{2}[/tex]
169 = 25 + [tex]d^{2}[/tex]
169 - 25 = [tex]d^{2}[/tex]
144 = [tex]d^{2}[/tex]
⇒ d = [tex]\sqrt{144}[/tex]
= 12 units
Therefore, the chord is at a distance of 12 units to the center of the circle.
A chord is a straight line joining 2 points on the circumference of a circle.
The line that connects any two points of the circumference of a circle is known as a chord.
Theorem: A radius or diameter that is perpendicular to a chord divides the chord into two equal parts and vice versa.
Converse: The perpendicular bisector of a chord passes through the center of a circle.
Problem: In the given figure the radius of the circle is 5 cms. what is the length of the chord?
Solution:
Given to us,
radius of the circle, r = 5 cms,
RA = 1 cm,
Radius, r = OA = OP = OQ = 5 cms.
Also, OR = OA - OR = 4 cms.
In ΔOPQ,
According to Pythagorus theorum,
OP² = OR² + RP²
5² = 4² + RP²
RP² = 25 -16 = 9
RP = 3,
We know,
A radius or diameter that is perpendicular to a chord divides the chord into two equal parts and vice versa.
A radius (OA) that is perpendicular to a chord divides the chord into two equal parts(RP = RQ).
Therefore, chord = RP + RQ = 3+3 = 6 cms.
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