The term for breaking a number into smaller sections and multiplying these numbers is factorization.
What is factorization?This is a common method used in math that implies breaking a big number into smaller ones and then multiplying the numbers. This multiplication should lead you to the original number.
What is an example of factorization?120 can be broken as 12 and 10, then 12 × 10 = 120
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If joe travels 434 miles in 7 hours, how far will he travel in 10 hours at the same speed?
He travels 620miles at the same speed.
Given that joe travels 434 miles in 7 hours.
An object's speed is determined by how quickly it moves. It is the distance a body travels in one unit of time.
Firstly, we will find the speed when the distance is 434 miles and the time is 7 hours by using the formula
Speed=Distance/Time
Substitute the values in the formula, we get
Speed=434miles/7 hours
Speed=62 miles/hour
Now, we will find the distance when time is 10 hours, we get
62=distance/10
Multiply both sides by 10, and we get
62×10=(distance/10)×10
620miles=distance.
Hence, in 10 hours at the same speed, he travels when joe travels 434 miles in 7 hours is 620miles.
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[tex]\sqrt{x}[/tex][tex]\sqrt{x}[/tex]4-[tex]\sqrt{x}[/tex][tex]\sqrt{x}[/tex]7 -[tex]\sqrt{x}[/tex][tex]\sqrt{x}[/tex]4+[tex]\sqrt{x}[/tex]7 +[tex]\sqrt{x}[/tex]2
[tex]4x - 7x - 4x + 7 \sqrt{x} + \sqrt{x} [/tex]
[tex] - 7x + 8 \sqrt{x} [/tex]
When the mean and standard deviation of the process are operating such that the upper and lower control limits are acceptable relative to the upper and lower specification limits, we say the process is
The process is Capable.
According to statement
When the mean and standard deviation of the process are operating such that the upper and lower control limits are acceptable relative to the upper and lower specification limits
and when these conditions are fulfilled then the process is to be called CAPABLE.
So, The process is Capable.
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Kevin was asked to determine the length of side XZ. His work is shown.
Triangle X Y Z is shown. Angle Y Z X is 90 degrees and angle Y X Z is 34 degrees. The length of hypotenuse X Y is 18.
cos(34°) =
(XZ)cos(34°) = 18
XZ =21.7
Which error did Kevin make?
He has the side lengths in the wrong place in the cosine ratio.
He multiplied both sides by the length of XZ instead of dividing by XZ.
He should have used the sine ratio.
He should have used the tangent ratio.
Answer:
The answer is A) He has the side lengths in the wrong place in the cosine ratio.
Answer:
A. He has the side lengths in the wrong place in the cosine ratio.
Step-by-step explanation:
got it right on edge23
Consider a standard deck of playing cards. If 5 cards are selected randomly without replacement from this deck then what is the probability that all of these are red
The probability that all of the cards drawn are red is 0.0253.
How can we find the probability?A standard deck of playing cards has 52 cards.
Of the 52 cards, 26 of the cards are red cards.
When we draw the first card, the probability of getting red is 26/52.
When we draw the second card, the probability of getting red is 25/51.
When we draw the third card, the probability of getting red is 24/50.
When we draw the fourth card, the probability of getting red is 23/49.
When we draw the fifth card, the probability of getting red is 22/48.
Therefore, the probability of drawing 5 red cards without replacement is
= [tex]\frac{26}{52}* \frac{25}{51}* \frac{24}{50} *\frac{23}{49}* \frac{22}{48}[/tex]
= 26*25*24*23*22/52*51*50*49*48
= 0.0253
Therefore, we have found that the probability that all cards drawn are red is 0.0253.
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Using the sine rule, calculate the length y. Give your answer to 2 s.f.
Answer:
y = 9.84 mm
Step-by-step explanation:
Sine rule:Law of sine:
[tex]\sf \boxed{\bf \dfrac{a}{Sin \ A}=\dfrac{b}{Sin \ B}= \dfrac{c}{Sin \ C}}[/tex]
a = y
A = 31°
b = 17 mm
B = 117°
[tex]\sf \dfrac{y}{Sin \ 31^\circ}=\dfrac{17}{Sin \ 117^\circ}\\\\[/tex]
[tex]\sf y = \dfrac{17}{Sin \ 117^\circ}*Sin \ 31^\circ\\\\ y = \dfrac{17}{0.89}*0.515\\\\y = 9.84 \ mm[/tex]
Given: ABCD is a rectangle.
Prove: ABCD has congruent diagonals.
Rectangle A B C D is shown.
Identify the steps that complete the proof.
♣ =
♦ =
♠ =
By SAS property, ABC ≅ DCB.
How to prove the deductionsIn this question we have to proof ABCD has congruent diagonal. By SAS property and reflexive property it can be proved as follows:
Given:
ABCD is a rectangle.
Prove:
Diagonal AC ≅ Diagonal BD
From the question,
As we can see that, ABCD is a rectangle, it is also a parallelogram.
Thus, ABCD is a parallelogram, opposite sides of a parallelogram are congruent.
⇒ AB ≅ DC
⇒ BC ≅ BC (Reflexive Property of Congruence)
Hence, ∠ABC and ∠DCB are right angles by the definition of rectangle.
∠ABC ≅ ∠DCB (all right angles are congruent)
Therefore, by SAS property, ABC ≅ DCB.
⇒ segment AC ≅ segment BD
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Answer:
♣ = parallelogram side theorem
♦ = SAS
♠ = CPCTC
(Correct On Edgen)
The number of bagels sold daily for two bakeries is shown in the table.
Bakery A Bakery B
53 34
52 40
50 36
48 38
53 41
47 44
55 40
51 39
Based on these data, is it better to describe the centers of distribution in terms of the mean or the median? Why? Select the correct answer below. (5 points)
Group of answer choices
A) Mean, because there are no outliers to affect the data
B) Mean, because the distribution is perfectly symmetric for both bakeries
C) Median, because the distribution for Bakery B is not symmetric
D) Median, because there are outliers that affect both data sets
The correct statement based on the data is: A. Mean, because there are no outliers to affect the data.
What are Outliers?Outliers are data point that appears extreme from other data values of a data distribution. When there is an outlier in a data distribution, the median is a better measure of center, while the mean is best when outliers are absent.
From the data distribution for both bakeries, no data seem extreme from the rest of the data, therefore, the mean is a better measure of center.
The answer is: A. Mean, because there are no outliers to affect the data.
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Sarita showed the steps to solving the equation. 5 (x minus 3) 7 (x 4) = 73 steps sarita’s solution sarita’s verification 1 5 x minus 15 7 x 28 = 73 5 (5 minus 3) 7 (5 4) = 73. 5 (negative 2) 7 (9) = 73. negative 10 63 = 73. 53 not-equal-to 73. 2 (5 7) x (negative 15 28) = 73 3 12 x 13 = 73 4 12 x 60 5 x = 5 when sarita tried to verify her answer, she found it was wrong. which explains her mistake? sarita’s solution is correct. she made an error in her verification. sarita was supposed to add the 5 and 7 in the first step. sarita added 13 instead of negative 13 in the fourth step. sarita was supposed to use the division property of equality in the third step.
This enables us to conclude that Sarita's solution is accurate, but her verification was flawed. ( 5 - 3 [tex]\neq[/tex] 2 ).
What is linear equation?
When the greatest power of the variable is consistently 1, an equation is considered to be linear. A one-degree equation is another name for it.
Given the following equation:
5(x-3) + 7(x+4) = 73
The steps to solve it are:
Apply the Distributive property:
5x - 15 + 7x + 28 = 73
12x + 13 = 73
Subtract 13 from both side
12x + 13 - 13 = 73 -13
12x = 60
Divide both side by 12
12x/12 = 60/12
x = 5.
To verify it, put the x = 5 in to the equation:
5(5 - 3) + 7(5 + 4) = 73
After solving it, we get
5(2) + 7(9) = 73
10 + 63 = 73
73 = 73
This enables us to conclude that Sarita's solution is accurate, but her verification was flawed. ( 5 - 3 [tex]\neq[/tex] 2 ).
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A scientist observes the bacteria’s growth. In the first observation, there were 12 bacteria, 24 in the second observation, 48 in the third and so on. How many bacteria will be there in the 8th observation? Use the explicit formula.
1,536
28
126
27
Answer:
Step-by-step explanation:96 in the fourth since they are adding the answer itself two times before you get the other like 12 bacteria and then 24 so that means 12 + 12 is 24 and the third one 48 so 24 +24 =48
fourth 48 + 48=96
fifth 96+96=192
sixth 192+192=384
seventh 384+384=768
last but not least 768+768 = 1536
so your answer is 1,536
How many three-digit numbers use only the digits 0,1 and 5
The number of three digit numbers which use only the digits 0,1, and 5 is; 18.
How many three digit numbers use 0,1 and 5?Since, it follows from the task content that three digit numbers are to be considered, Hence, it follows that the choice for the first digit is between 1 and 5, for the second number and third number, the choice lies within all three numbers.
On this note, we have;
= 2× 3 × 3.
= 18.
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Sample response: there is a common ratio of 2/3 between the height of the ball at each bounce. so, the bounce heights form a geometric sequence: 27, 18, 12. two-thirds of 12 is 8, so on the fourth bounce, the ball will reach a height of 8 feet. what did you include in your response? check all that apply. there is a common ratio between bounce heights. multiply 12 by 2/3. the height on the fourth bounce is 8 feet.
Answer:
Step-by-step explanation:
A Geometric sequence can be used:
To Model this sequence you need to use this formula
A (subscript n) = Ar(n-1)
a = value of the first term
n = the # of the term you want to find (For example, if you want to find the term number 3, it is 12)
r = the common ratio, this is obtained by dividing the second term in the sequence by the first.
So the value of r is = 2/3 because 27 times 2/3 = 18 which is the second term
n = 4 since you want to find the 4th term in the sequence
Plug it in and the results are
4th term = 27(2/3)^(4-1) = 8
The answer is 8
In the 30-60-90 triangle below, side s has a length of
length of
30
90°
S
60
OA. 16√3, 5
B. 4√2, 4√2
OC. 4, 4√3
OD. 8.5, 16
OE. 16√3, 16√3
OF. 4, 8√3
and side q has a
Answer:
4, 4√3
Step-by-step explanation:
In a 30-60-90 triangle:
The leg opposite of the 30-degree angle is 1/2 of the hypotenuse: 8/2 = 4
The longer leg is √3 times the shorter leg: 4*√3 = 4√3
Check work: 4^2+(4√3)^2 = 8^2 --> 16+48 = 64 --> 64 = 64
Mediciones recientes del fondo del mar que se extiende a lo largo de las crestas a medio océano muestran que la deriva continental es del orden de 4 cm. Suponga que este valor ha sido constante a través del tiempo y considere la distancia actual entre Sudamérica y África como 5000 millas. ¿Cuánto tarda Aproximadamente pangea en fragmentarse?
Usando proporciones, hay que la pangea tardra aproximademente 20,116,750 años para fragmentar-se.
¿Qué es una proporción?Una proporción es una fracción de la cantidad total, e puede ser encontrada aplicando una regla de três.
La deriva continental es del orden de 4 cm al año. La distancia actual entre Sudamérica y África es de 5000 millas. En cm, esta distancia es la seguiente:
5000 millas = 5000 x 160934 cm = 80,467,000 cm.
Asi, el tiempo que levará para la pangea fragmentar-se es:
t = 80,467,000/4 = 20,116,750 años
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Diamond went to lunch with her friends. The total bill came to $32.20. If Diamond tipped 19%, how much tip did she leave?
$6.12
Step-by-step explanation:A percentage is some portion of a whole number. Multiple methods can be used to find percentages.
Multiplication to Find Percentages
One of the easiest ways to find percentages is to multiply the original number by a decimal. To do this, one first needs to turn the percentage into a decimal.
For example,
19% = 0.19To convert a percentage to a decimal, just move the decimal point 2 places to the left.
Then, multiply this decimal by the whole number, and the answer, in this case, will be the tip.
19% of $32.20
Now, to solve we can just multiply.
0.19 * 32.20 = 6.118The exact answer is 6.118. However, since we are using money, we are going to round to the nearest hundredth place. This gives the final answer of $6.12.
Evaluate 5 - 3(a3 – b2)2 when a = 3 and b = 5.
Answer:
Step-by-step explanation:
Evaluate 5 - 3(a3 – b2)2 when a = 3 and b = 5.
5 - 3 × (a³-b²)² a=3 and b=5
5 - 3 × (3³ - 5²)² =
5 - 3 × (27 - 25)² =
5 - 3 × (2)² =
5 - 3 × 4 =
5 - 12 =
-7
Which of the following are like terms?
3x and 5x²
4xy and 2x²y
6x and -3x
7x and 7y
At the trial of a contract dispute, the plaintiff has offered to testify to what she heard the defendant say in a private conversation between the two of them, which the plaintiff secretly recorded on an audiotape that she did not offer in evidence. Is the plaintiff's testimony admissible
The plaintiff's testimony is admissible because plaintiff as personal knowledge of the statement of a party-opponent.
How to illustrate the information?The recording is coincidental with firsthand knowledge. The person could testify based upon firsthand knowledge and could also lay the foundation under Article 9 to authenticate the tape.
In this case, the tape is not required as a matter of the original writing rule, giving the proponent options to offer testimony from memory, and/or the opportunity to corroborate the in-court testimony by a demonstrative exhibit
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find the smallest number by which 29160 should be divided so that the quotient becomes a perfect cube
The smallest number by which 29160 should be divided so that the quotient becomes a perfect cube is 5
Perfect cube quotient of a division
The given number is 29160
Note that:
29160 can be factored into 5832
That is, 29160 = 5832 x 5
Take the cube of 5832:
[tex]\sqrt[3]{5832}=18[/tex]
Since it has been confirmed that 5832 is a perfect cube, the smallest number by which 29160 should be divided so that the quotient becomes a perfect cube is 5
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Solve the system of equations.
2x+y = 7
x - 2y = 6
Put your answer as a coordinate point, or use "no solution" or "infinitely many solutions"(aka "the set of all real numbers").
Answer:
Ans: (4,-1)
Step-by-step explanation:
Lets keep:
2x+y=7 --- equation 1
x - 2y=6 ----- equation 2
equation 2 x 2: 2x - 4y=12 -------equation 3
now subtract equation 1 from equation 3
2x - 4y = 12
(-) 2x + y = 7
----> -5y = 5 [ Divide both sides by -5 ]
------> y= -1
Substitute y= -1 into eqaution 1
----> 2x + -1 = 7 [ add 1 to both side]
----> 2x = 8 [Divide by 2 on both sids]
----> x=4
Ans: (4,-1)
(17,-13),(17,8) finding slope from two points
Hi! ❄
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There are really two ways to solve this problem. One of them is the slope formula. You can familiarise yourself with this formula
[tex]\sf{\dfrac{y2-y1}{x2-x1}}[/tex]
SUBSTITUTE the values
[tex]\sf{\dfrac{-13-8}{17-17}}[/tex]
[tex]\sf{\dfrac{-21}{\bf{0}}[/tex] (notice the zero was in bold-face)
Dividing by zero is an operation we cannot do.
So the slope of this particular line is not defined.
The other way is looking at the first co-ordinates of the points given
Notice that they are exactly the same. Whenever that happens, the slope of that line is not defined.
Hope that made sense !!
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[tex]\star\tiny\pmb{\tt{calligraphy}}\star[/tex]
A compound inequality is shown below.
x ≤ 3 and x ≥ 0
Which graph represents the solution of the inequality?
Answer:
b
Step-by-step explanation:
edge
Jim is driving to Denver. Suppose that the distance to his destination (in miles) is a linear function of his total driving time (in minutes). Jim has 61 miles to his destination after 41 minutes of driving, and he has 42.3 miles to his destination after 63 minutes of driving. How many miles will he have to his destination after 81 minutes of driving
Jim has to travel 26.82 miles more to reach Denver.
What is the equation of a line?
Let the first point be = (x₁ , y₁)
Let the second point be = (x₂ , y₂)
m(slope) = (y₂ - y₁) / (x₂ - x₁)
Equation of line = (y - y₁) = m(x - x₁)
Let the no. of miles be plotted on X-axis
Let the driving time be plotted on Y-axis
First point = (61 , 41)
Second point = (42.3 , 63)
Slope of the linear function = (63 - 41)/(42.3 - 61) = -1.17
Equation of the line = (y - 41) = -1.17(x - 61)
Given time of driving = 81 min
Number of miles = (81 - 41) = -1.17(x - 61)
40/-1.17 = x - 61
-34.18 + 61 = x
x = 26.82
Hence, Jim has to travel 26.82 miles more to reach Denver.
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There are 5,280 feet in a mile. Gary walked 220 feet to the bus stop, and the bus took him a quarter of a mile to school. What is the ratio of his distance walking to.the distance he rode the bus
The ratio of distance travelled by walking to distance travelled by bus is 1 : 6.
What is ratio?When two quantities of the same units are compared, the ratio is what shows how much of one quantity is included in the other.
Total no. of Feet in a Mile = 5280
Distance Gary walked to the bus stop = 220 feet
Distance travelled by bus = 1/4 mile = (1 / 4)*5280 = 1320 feet
Ratio of distance walking to distance by bus = 220 / 1320 = 1 : 6
Hence, the ratio of distance travelled by walking to distance travelled by bus is 1 : 6.
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Which equation gives the lines show on Graph y= 2x+4
y= -1/2x-4
y=1/2x+4
y=2x-4
Label the midpoint of PQ as point S, the midpoint of QR as point T, and the midpoint of RP as point U. Next, draw PT, QU, and RS. Which statements are true
The statements that are true based on the midpoint given in the question include:
m∠P + m∠Q + m∠R = 180°PT, QU, and RS intersect at the same point.What is midpoint?In geometry, the midpoint simply means the middle point of a line segment. The midpoint is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints.
Also, it should be noted that the midpoint bisects the segment.
In this case, m∠P + m∠Q + m∠R = 180°. This is because the sum of the angles in a triangle will be equal to 180°. Also, PT, QU, and RS intersect at the same point.
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Complete question:
Label the midpoint of PQ as point S, the midpoint of QR as point T, and the midpoint of RP as point U.
Next, draw PT, QU, and RS.
Which statements are true?
m∠Q = m∠R
The length of QU is half the length of RP.
m∠P + m∠Q + m∠R = 180°
QU ≅ RS
PT, QU, and RS intersect at the same point.
The sum of the lengths of QU and RS is equal to the length of PT.
Olivia is making 15 bead bracelets for her friends what is the proportional relationship?
5 minutes per bracelet.
because 15/3 = 5 mins.
To find the constant of proportionality in minutes per bracelet, divide the total time by the number of bracelets:
constant of proportionality =15/3= 5 minutes.
Now, we're going to consider an example of a proportional relationship in our everyday life: When we put gas in our car, there is a relationship between the number of gallons of fuel that we put in the tank and the amount of money we will have to pay. In other words, the more gas we put in, the more money we'll pay.
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A local pizza parlor has the following list of toppings available for selection. The parlor is running a special to encourage patrons to try new combinations of toppings. They list all possible three-topping pizzas (3 distinct toppings) on individual cards and give away a free pizza every hour to a lucky winner. Find the probability that the first winner randomly selects the card for the pizza topped with ham, artichoke hearts, and pepperoni.
The probability that the first winner randomly selects the card for the pizza topped with ham, artichoke hearts, and pepperoni is 1/560 given that there are 16 toppings to choose from. This can be obtained by finding the total number of all possible three-topping pizzas (3 distinct toppings) using combination formula and finding the probability.
What is the required probability?Given that there are 16 toppings,
the total number of all possible three-topping pizzas,
ⁿCₓ = [tex]\frac{n!}{x!(n-x)!}[/tex] = 16!/[3!(16-3)!] = 16!/[3!(13)!] = 14×15×16/3×2 =560
Probability of choosing pizza topped with ham, artichoke hearts, and pepperoni,
P(ham, artichoke hearts, pepperoni) = 1/560
Hence the probability that the first winner randomly selects the card for the pizza topped with ham, artichoke hearts, and pepperoni is 1/560 given that there are 16 toppings to choose from.
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Complete the system that models the heights of the ball and the receiver’s hands over time. h = -16t² 14t h = -16t² t
Answer: The height of the ball at time t is given as h = -16t² + 14t + 6 while the height of the receiver hand at time t is given as h = -16t² + 10t + 8
What is an equation?
An equation is an expression that shows the relationship between two or more variables and numbers.
A quarterback throws a football toward a receiver from a height of 6 ft. The initial vertical velocity of the ball is 14 ft/s. At the same time that the ball is thrown, the receiver raises his hands to a height of 8 ft and jumps up with an initial vertical velocity of 10 ft/s.
The height of the ball at time t is given as h = -16t² + 14t + 6 while the height of the receiver hand at time t is given as h = -16t² + 10t + 8
Answer:
6
10
8
Step-by-step explanation:
A restaurant uses rectangular napkins where the length, l, is twice as long as the width. the length of the napkin along the diagonal is x. what is x in terms of l? replace a and b with the correct values.
The value of x in terms of l is.
[tex]x=\sqrt{5l^{2} }[/tex]
What is Pythagoras Theorem?A fundamental relationship in Euclidean geometry between a right triangle's three sides is known as the Pythagorean theorem, or Pythagoras' theorem. The area of the square whose side is the hypotenuse is said to be equal to the total of the areas of the squares on the other two sides.
given data:length = [tex]l[/tex]
width= [tex]2l[/tex]
diagonal = [tex]x[/tex]
We would get a right angle triangle if we were to cut a part across the diagonal. The Pythagoras Theorem can be used to solve the right angle triangle.
[tex]x^{2} =a^{2} +b^{2}[/tex]
using this formula substituting the value:
[tex]x^{2} =l^{2} +2l^{2}[/tex]
[tex]x^{2} =l^{2} +4l^{2} \\x^{2} =5l^{2} \\x=\sqrt{5l^{2}} \\[/tex]
from the above calculation we have:
[tex]x=\sqrt{5l^{2} }[/tex]
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