Answer:
Definition. Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles. If two or more figures have the same shape, but their sizes are different, then such objects are called similar figures.
Final exam scores in a mathematics course are normally distributed with a mean of 71 and a standard deviation of 12. Fill in the missing information
Percentile: 99.87
Z-score: ?
Exam score: ?
Answer:
See below
Step-by-step explanation:
99.87-71 = 28.81 this is 28.81/12 = z-score = +2.4
corresponding to .9918 ( from z-score table) = a score of 99.18%
brunette college offers 444 math classes, 222 science classes, 333 language classes, and 555 art classes. sylvia needs to sign up for exactly one class in each subject. how many different combinations of classes does sylvia have to choose from?
The total number of different combinations is 120.
What is combination and permutation?
Combination and permutation are two alternative strategies in mathematics to divide up a collection of components into subsets. The subset's components can be listed in any order when combined. The components of the subset are listed in a permutation in a certain order.We are to find the number of different combinations of classes does Sylvia have to choose from.
We will be using the following formula for number of combinations of n elements taken r (r is less than or equal to n) at a time:
nCr = n!/r!( n - r )!
Since Sylvia needs to sign up for exactly one class in each subject, so the total number of different combinations from which she has to choose will be
⁴C₁ * ²C₁ * ³C₁ * ⁵C₁
= 4!/1!( 4 - 1 )! × 2!/1! ( 2 - 1 )! × 3!/1! ( 3 -1)! × 5!/1! ( 5 - 1 )!
= 4 × 2 × 3 × 5
= 120
Thus, the total number of different combinations is 120.
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PRACTICE Describe the domain and range of each function using inequality or set-builder notation.
In the picture there are 4 graphs.
1st graph we get domain as (-∞,+∞) and range as (-∞,+∞).
2nd graph we get domain as [-4,4] and range as [3,-1].
3rd graph we get domain as [-4,1] and range as [1,-4].
4th graph we get domain as (-∞,4] and range as (-∞,-2].
Given that,
In the picture there are 4 graphs.
We have to find the domain and range of the each function using inequality or set-builder notation.
A function's domain is the set of values that we are allowed to enter into our function.
This set consists of the values of the x-axis for a function like f. (x).
The range of values that can be used as input for a function is called this. The values in this set hence, once we input an x value, the function returns. The y values are those.
1st graph we get domain as (-∞,+∞) and range as (-∞,+∞).
2nd graph we get domain as [-4,4] and range as [3,-1].
3rd graph we get domain as [-4,1] and range as [1,-4].
4th graph we get domain as (-∞,4] and range as (-∞,-2].
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Conditional Statement: If the object has a remote, then it is a television.
Part A: Write the converse to the conditional statement.
Part B: Write a biconditional statement from the conditional statement.
Part C: Validate the biconditional statement from Part B. Use details to support your answer.
For given conditional statement 'If the object has a remote, then it is a television.'
Part A: converse to the conditional statement
'If it is a television, then the object has a remote.'
Part B: a biconditional statement
'The object has a remote if and only if it is a television.'
Part C: validation of biconditional statement
The biconditional statement is true because the conditional statement and the converse are true.
In this question, we have been given a conditional statement: 'If the object has a remote, then it is a television.'
Part A:
We need to write the converse to the conditional statement.
The converse of given conditional statement would be:
'If it is a television, then the object has a remote.'
Part B:
We need to write a biconditional statement from the conditional statement.
A biconditional statement of the given conditional statement would be:
'The object has a remote if and only if it is a television.'
Part C:
We need to validate the above biconditional statement.
The biconditional statement is true because the conditional statement and the converse are true.
Therefore, for given conditional statement 'If the object has a remote, then it is a television.'
Part A: converse to the conditional statement
'If it is a television, then the object has a remote.'
Part B: a biconditional statement
'The object has a remote if and only if it is a television.'
Part C: validation of biconditional statement
The biconditional statement is true because the conditional statement and the converse are true.
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(3, 9), (1, 1) write in standard form
last month a manufacturing company shipped 452 boxes of ball bearings each box contains 48 ball bearings how many ball bearings sis the company ship last month
Answer:
answer is B
Step-by-step explanation:
Sorry if this is incorrect
20 pointsssss
HELPPPPPPPPP
The coordinates of the point X are (1 + 2, 6 - 1.25) = (3,4.75).
The segments, PX and XQ, have lengths in a ratio of 1: 2.
What is meant by partition segment?A line segment is partitioned when it is divided into equal parts according to a specified ratio. The total number of partitions of the line segment must be equal to the sum of the two values in the ratio.
Suppose you have a line segment PQ on the coordinate plane, and you need to estimate the point on the segment 1/3 of the way from P to Q.
Where P exists at the origin and line segment is a horizontal one.
The length of the line exists 6 units and the point on the segment 1/3 of the way from P to Q would be 2 units away from P, 4 units away from Q and would be at (2, 0).
The segment exists not a horizontal or vertical line:
The components of the directed segment PQ exists (6, 3) and we require to estimate the point, say X on the segment 1/3 of the way from P to Q. Then, the components of the segment PX exists [tex]$\left\langle\left(\frac{1}{3}\right)(6),\left(\frac{1}{3}\right)(3)\right\rangle=\langle 2,1\rangle$[/tex].
Since the initial point of the segment exists at origin, the coordinates of the point X exists given by (0+2, 0+1) = (2, 1).
where neither P nor Q exists at the origin.
Use the end points of the segment PQ to estimate the components of the directed segment.
[tex]$\left\langle\left(x_2-x_1\right),\left(y_2-y_1\right)\right\rangle=\langle(7-1),(2-6)\rangle[/tex]
= (6,-4)
The components of the segment PX where X exists a point on the segment 1 / 3 of the way from P to Q are
[tex]$\left\langle\left(\frac{1}{3}\right)(6),\left(\frac{1}{3}\right)(-4)\right\rangle=(2,-1.25)$$[/tex]
To estimate the coordinates of the point X add the components of the segment PX to the coordinates of the initial point P.
Therefore, the coordinates of the point X exists (1+2,6-1.25) = (3, 4.75).
The segments, PX and XQ, have lengths in a ratio of 1: 2.
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A line passes through the points (−6, −3) and (6, −3). Which of the following points is also on the line? A. (−3, 0) B. (6, 0) C. (0, −3) D. (−6, 0)
Answer:
C
Step-by-step explanation:
Since the y-coordinates of both points are -3, the equation is [tex]y=-3[/tex].
The only option with a y-coordinate of -3 is option C.
A contractor purchases 3 dozen pairs of padded work gloves for $43.56 incorrectly calculates the unit price as $14.52 per pair for the expense report. What is the correct unit price?What is the error?
Answer: I think the answer is $1.21
Step-by-step explanation: Instead of 3 pairs it says 3 dozen. A dozen is 12.
3 x 12 = 36
Then you should do 43.56 / 36
For one pair of gloves it should be $1.21
The contractor got $14.52 because he did a dozen (12) divided by 43.56.
I hope that helps! ^^
A(-3, 13), B(4, -15) Find the slope
In Exercises 5 and 6, use the translation (x,y) → (x + 1, y - 3) to find the image
of the given point.
5. Q(5,9)
6. M(-3,-8)
After using translation the image of the given points will be at Q( 6 , 6 ) and M( -2 , -11 ).
What is translation ?
The linear movement of a point relative to its initial position is known as translation. The horizontal position is labeled first and the vertical position is labeled second when describing a point's coordinates with respect to the origin of an x-y coordinate plane.
The translation is given to be (x,y) → (x + 1, y - 3)
The tow points are Q(5,9), M(-3,-8)
using translation we get,
Q( 5 , 9 ) → (5 + 1, 9 - 3) = Q( 6 , 6 )
M( -3 , -8 ) → (-3+ 1, -8- 3) = M( -2 , -11 )
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What is the circumference of a circle with a radius of 14 feet using pie?
Answer:
Circumference 87.92 ft
Step-by-step explanation:
You have a radius of 14 so u multiply by 2 to get the diameter, then u mulptiply by pie (3.14) thats how u get the circumference.
14×2=28
28×3.14=87.92
5. Below is a model of the infield of a baseballstadium. How long is each side of the infield?oth a perfectquare rootnumbers?A= 81 in.?
We have that the area of the infield is 81 in2.
This area is a square, which means it has equal sides, and its area is:
[tex]\text{Area}=side^2[/tex]If the area of the square is 81 in2, we have that:
[tex]\begin{gathered} \text{side}^2=81 \\ \text{side}=\sqrt{81} \\ \text{side}=9\text{ in} \end{gathered}[/tex]So the side of the infield is 9 inches.
Work out the circumference of this circle. Take n to be 3.142 and write down all the digits given by your calculator. 10 cm
The circumference of the circle will be given by 62.84 cm.
A circle is a closed figure having a fixed point known as center of the circle and the distance from the center to any point on the boundary of circle is known as the radius of the circle. Circumference is the total length of the boundary of the circle. The circumference of the circle is given by the formula
C = 2πr where r is the radius of the circle and the value of π is given as 3.142.
Now, according to question r = 10cm
C = 2×3.142×10
C = 20×3.142
=> C = 62.84 cm
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If x+y =8 and x^2+y^2=36 find x-y
in the usa, the cost of a phone is $1200. in the uk a phone is £920. using the exchange rate £1 = $1.36, work out the difference in cost of the phones in the usa and the uk
The difference between of the cost of the phones in the USA and the UK is $51. 2
What is exchange rate?Exchange rate can be defined as the price of the unit of foreign currency in terms of the home currency.
It is also known as the rate at which a currency is exchanged to another currency
From the information given, we have that;
The cost of a phone in the USA is $1200The cost of a phone in the UK is £920We also have that;
The exchange rate is expressed as;
£1 = $1.36
Now, let's convert the cost from dollars to euros, we have;
If £1 = $1.36
Then, £920 = $x
cross multiply, we have;
x = 920 × 1. 36
x = $1251. 36
Now, let's find the difference between the cost in the USA and UK, we have;
= $1251. 36 - $1200
= $51. 2
Hence, the difference is $51. 2
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Can someone explain how to do this to me!! Please thanks
Answer:
MP = 19
Step-by-step explanation:
MP = MN + NO + OP
we require to find OP and MN before we can evaluate MP
NO + OP = NP , that is
8 + OP = 15 ( subtract 8 from both sides )
OP = 7
and
MN + NO = M0 , that is
MN + 8 = 12 ( subtract 8 from both sides )
MN = 4
Then
MP = MN + NO + OP = 4 + 8 + 7 = 19
Line AB is a straight
line.
9
1. m∠AOB = ____
Statement
1. ________
Reason
2. m∠AOE+m∠EOF+m∠FOB=m∠____ 2. ________
3. x + ____ +20° = ____ 3. Substitution
4. x = ____ 4. Algebra
The two column proof of the given angles are;
Statement 1; m∠AOB = 180°
Reason 1; Sum of angles on a straight line sums up to 180°
Statement 2; m∠AOE + m∠EOF + m∠FOB = m∠AOB
Reason 2; Opposite angles
Statement 3; x + 3x + x + 12 = 152
Statement 3; Substitution
Statement 4; x = 28°
Reason 4; Algebra
How to solve two column proof?From the attached image, we can complete the two column proof as follows;
Statement 1; m∠AOB = 180°
Reason 1; Sum of angles on a straight line sums up to 180°
Statement 2; m∠AOE + m∠EOF + m∠FOB = m∠AOB
Reason 2; Opposite angles
Statement 3; x + 3x + x + 12 = 152
Statement 3; Substitution
From statement 3, we can use algebra to find x as;
x + 3x + x + 12 = 152
5x + 12 = 152
5x = 152 - 12
5x = 140
x = 28°
Thus;
Statement 4; x = 28°
Reason 4; Algebra
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get it down give u more points for the rest of the questions
Kali just started a new sales floor job to save for college. She earns $15.75 per hour plus a flat fee of $50 per week. She wants to earn between $200 and $400 per week. The following inequality represents her earning potential: 200 ≤ 15.75x + 50 ≤ 400 Solve the inequality.
The solution set of the given inequality is:
9.52 ≤ x ≤ 22.22
Or [9.52, 22.22] if we write this as an interval.
How to solve the inequality?Here we have the inequality:
200 ≤ 15.75x + 50 ≤ 400
Which represents Kali's earning potential.
To solve the inequality we need to isolate the variable in the middle, if we subtract 50 in the 3 sides we get:
200 - 50 ≤ 15.75x + 50 - 50 ≤ 400 - 50
150 ≤ 15.75x ≤ 350
Now we need to divide both all by 15.75, so we get:
150/15.75 ≤ 15.75x/15.75 ≤ 350/15.75
9.52 ≤ x ≤ 22.22
This is the solution of the inequality, the solution set written as an interval will be [9.52, 22.22]
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What is 4y - 9x + 3y - 2x when simplified?
Answer:
A. -11x + 7y
Step-by-step explanation:
4y - 9x + 3y - 2x
4y + 3y = 7y
-9x - 2x = -11x
-11x + 7y
I hope this helps!
Write an inequality that represents the fact that while making your product you can’t exceed this spending limit.
I'm making figures for $100 and selling them for $150, my spending limit is $200
The inequality which correctly represents the fact that the spending limit cannot be exceeded as described in the task content is; 100x ≤ 200.
Which inequality represents the fact that the spending limit cannot be exceeded?It follows from the task content that the inequality which correctly represents the spending limit as described be determined.
Since the given spending limit is; $200.
Let, x = the number of figures made.
Therefore, the cost of making x number of figures can be written algebraically as; 100x.
Hence, since it costs $100 to make each figure, it follows that the required inequality is;
100x ≤ 200.
This follows from the fact that each figure costs $100 to make.
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Translate this phrase into an algebraic expression.
Nine less than the product of 18 and Jose's age
Use the variable j to represent Jose's age.
Answer:
J(18)-9
Step-by-step explanation:
j times 18 minus 9
Multiply 3.2x and 4x.
12.8x2
7.2x2
12.8x
7.2x
Answer: 12.8x2
Step-by-step explanation:
Based on the given task content; the solution to the Multiplication of 3.2x and 4x is 12.8x².
The correct answer option is option a.
Multiplication of numbersThis is a process of computing the sum of a number with itself in a specified number of times. Multiplication is also called product and it is represented by the sigh ×. The product of a and b means ab.
For instance, from the task which is given above;
3.2x and 4x
= 3.2x × 4x
= 12.8x²
In this answer above,
12.8 is the coefficient and
x² is the variable.
In conclusion, 3.2x × 4x will give the result 12.8x².
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In triangle OPQ, m/O = (2x - 5)°, m/P = (3x − 8)°, and m/Q = (10x - 17)°. What is the value of x?
The value of x is 14 °
What is angle sum property of triangle?The sum of the interior angles in a triangle is supplementary. In other words, the sum of the measure of the interior angles of a triangle equals 180°. So, the formula of the triangle sum theorem can be written as, for a triangle ABC, we have ∠A + ∠B + ∠C = 180°.
In ΔOPQ,
∠O = (2x- 5)°
∠P = (3x-8)°
∠Q= (10x- 17)°
Thus by angle sum property of triangle we know:
∠O+ ∠P + ∠Q = 180
thus 2x - 5 + 3x - 8 + 10x - 17 = 180
15x - 30 = 180
= 15 x = 180 + 30
= 15 x = 210
= x= 210 / 15
= x = 14 .
Thus ∠O = (2x- 5)° = 2X 14 - 5 = 23 °
∠P = (3x-8)° = 3× 14 - 8 = 44°
∠Q= (10x- 17)° = 10 × 14 - 17 = 123°
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What’s x-5=1
Please please please help
If the vertical component of velocity for a projectile is 7.3 meters/second, find its hang time. a. 1.5 seconds b. 2.5 seconds c. 5.6 seconds d. 6.7 seconds e. 7.1 seconds
The hang time is calculated to be a. 1.5 seconds if the vertical component of velocity for the projectile is 7.3 meters/second.
The formula for the height of the projectile can be used to calculate the hang time as follows;
h = ut - 0.5at²
here;
h is the height of the projectile
u is the velocity = 7.3 m/s
a is the acceleration due to gravity
The standard value of acceleration due to gravity is equal to 9.81 m/s²
The height will be zero both the times when t=0 and when the journey has been completed
Now adding these values to the formula;
h = ut - 0.5at²
0 = 7.3t - 0.5(9.81)t²
Solving for t;
4.905t² = 7.3t
4.905t² / t = 7.3
4.905t = 7.3
t = 7.3 / 4.905
t = 1.49 ≈ 1.5
Therefore; the hang time is calculated to be 1.5 seconds.
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If A intersects B, B intersects C, C is parallel to D, and D intersects E, which is not true?
Following the descriptions of the relationship existing between the lines the option that is not true is the last option which is b || d which is read as b is parallel to d
What are parallel lines?Some set of lines are said to be parallel if the lines are equally spaced apart. This ensures that such line will never meet . Parallel lines is very useful in the field of geometry as it the foundation of many postulates and theorem.
Also, when two lines are being connected by a line. Say line x and line y and the connecting line is z. If the lines x and y makes similar angle with line z then line x and line y is said to be parallel.
Considering the descriptions given in the question. line b is tether perpendicular to line d. Hence saying that line b is parallel to line d is not true and the correct answer to the question.
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a forest trail is 607 feet long. a person biked from one end to the other and back again 6 times in the past 5 weeks. how far the person bike over the past 5 weeks
The distance that the person bike over the past 5 weeks is 7284 feet.
How to illustrate the expression?Distance is the sum of an object's movements, regardless of direction. Regardless of an object's starting or ending position, distance can be defined as the amount of ground it has covered. Distance is a measurement of how far apart two things or points are, either numerically or occasionally qualitatively.
From the information, the forest trail is 607 feet long and a person biked from one end to the other and back again 6 times in the past 5 weeks.
Therefore, the distance that the person covered will be:
= 2 × 6 × 607
= 7284 feet.
The distance is 7284 feet.
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Between 10 pm and 7:45 am the water level in a swimming pool decreased by 3/16 inches
The rate of change of the level of the swimming pool is -0.019 inches per hour.
How to get the rate of change in the level of the swimming pool?
The rate of change will be given by the quotient between the change in the level of the water (-3/16 inches) and the time in which that change happens.
We know that the change happens between 10 pm and 7:45pm, so the number of hours is:
2 hours + 7 hours + 45 min
Where:
1 hour = 60 min
45 min = 45/60 hours = 0.75 hour
Then the total time is:
2h + 7h + 0.75h = 9.75h
Then the rate of change is:
R = (-3/16 inches)/(9.75 h) = -0.019 inches per hour.
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