Yes, ∠2 and ∠3 are postulate or theorem that proves the condition is identified as supplementary.
∠1 and ∠2 are supplementary (Linear Pair Theorem)
m∠1 + m∠2 = 180◦ (Definition of supplementary ∠s)
∠1 ≈ ∠3 (Given)
m∠1 = m∠3 (Definition of ≈)
m∠3 + m∠2 = 180◦( Subst . prop . of ≈)
∠2 and ∠3 are supplements (Definition of supplementary ∠s)
An unsubstantiated claim that is assumed to be true is referred to as a postulate. A provable true assertion is referred to as a theorem. A line has at least two points, according to postulate 1. A plane has at least three noncollinear points, according to postulate 2.
Hence, postulate or theorem that proves j∥k and also ∠2 and ∠3 are supplementary.
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Determine how long it will take for a principal amount of $1,500 to become double its initial value when deposited into an account paying interest at a rate of 13%, continuously compounded.
A.
5.33 years
B.
6.32 years
C.
11.25 years
D.
14.33 years
c is incorrect
Use only the commutative property of addition to complete the statement.
2x + 21=
Based on the commutative property of addition, 2x + 21 = 21 + 2x.
What is the Commutative Property of Addition?The commutative property of addition states that when we change the order of arrangement of the addends, the value of the sum remains the same.
For example, 3 + 4 = 4 + 3.
Also, given the statement 2x + 21, we can state that:
2x + 21 = 21 + 2x
Therefore, based on the commutative property of addition, 2x + 21 = 21 + 2x.
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If y and x vary directly and
y=1.4when x=3.2, what is x when y=2.6? Round to two decimal places. Show your work
If y and x vary directly, the value of y=2.6 then value of x is 1.14.
The tenths place is represented by the initial digit following the decimal. The hundredths place is denoted by the digit that followed the decimal. Up until there are no additional digits, the remaining ones keep the place values filled in the quantity.
For example, 2.84620364 can be round to two decimal places as 2.85, and 0.8035 can be round to two decimal places as 0.80.
Here x and y vary directly,
So , x/y = k
Therefore K is constant
For x = 3.2 and y = 1.4
Then x/y = k
3.2/1.4 = k
K = 1.6/0.7
If y = 2.6 what is x
y = 2.6 and k = 1.6/0.7
2.6/x = 1.6/0.7
1.6x = 18.2
X = 1.1375.
Hence, the Round to two decimal places of x is 1.14
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Evaluate the expression when c = -4 and x=7.
-5x+c
Answer:
-39
Step-by-step explanation:
Hello, to do this problem, we need to use substitution.
c=-4 and x=7
-5x+c
-5(7)+-4
-35-4
=-39
Hope that helps
:D
Answer:
c = -4
x = 7
- 5 (7) + (- 4)
- 35 + (- 4)
= - 39
Hope this helps :)
The patient recovery time from a particular surgical procedure is normally distributed with a mean of 3 days and a standard deviation of 1.6 days.
(a) X is distributed normally.
(b) The median recovery time is 3 days.
(c) The z score of the patient who takes 4.2 days to recover is 0.75.
(d) The probability of spending more than 2.3 days in recovery is 66.64 %.
(e) The probability of spending between 3.7 and 4.2 days in recovery is 10.7 %.
(f) The 85th percentile for recovery times is 5.24 days.
(a) We are informed that a certain surgical procedure's recuperation time for patients is typically distributed. As a result, X is distributed normally.
(b) The median will be equal to the mean because the patient recovery time has a normally distributed distribution. The median is therefore 3 days.
(c) The formula for z score is given as:
z = X - μ / σ
Now, we have the mean μ = 3 days.
Standard deviation, σ = 1.6 days
The observed value, X = 4.2 days
Therefore,
z = ( 4.2 - 3) / 1.6
z = 1.2 / 1.6
z = 0.75
(d) When X = 2.3 days
Then the z score will be:
z = X - μ / σ
z = 2.3 - 3 / 1.6
z = - 0.7 / 1.6
z = - 0.4375
The corresponding area for z = 0.4375 is 0.3336.
In order to determine the likelihood for a period longer than 2.3 days, we must look at the region to the right, which we can locate by deducting 0.3336 from 1.
Therefore, the probability will be:
p = 1 - 0.3336
p = 0.6664
p = 66.64 %
(e) Now, for the probability between X = 3.7 days and 4.2 days.
z₁ = (3.7 - 3) / 1.6 = 0.7/1.6 = 0.4375
z₂ = (4.2 - 3) / 1.6 = 1.2 / 1.6 = 0.75
The area for a z score of 0.4375 is 0.1664 and the area to left for a z score 0.75 is 0.2734.
Then the probability between 3.7 days and 4.2 days will be:
p = 0.2734 - 0.1664
p = 0.107
p = 10.7 %
(f) For the 85th percentile:
For 0.85 the z score from the table is 1.4.
So, z = 1.4
z = X - μ / σ
1.4 = ( X - 3) / 1.6
(1.4)(1.6) = X - 3
2.24 = X -3
X = 2.24 + 3
X = 5.24 days
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The complete question is mentioned below:
The patient recovery time from a particular surgical procedure is normally distributed with a mean of 3 days and a standard deviation of 1.6 days. Let X be the recovery time for a randomly selected patient. Round all answers to 4 decimal places where possible.
a. What is the distribution of X?
b. What is the median recovery time? __________days
c. What is the Z-score for a patient that took 4.2 days to recover?
d. What is the probability of spending more than 2.3 days in recovery?
e. What is the probability of spending between 3.7 and 4.2 days in recovery?
f. The 85th percentile for recovery times is _________days.
A probability experiment consists of rolling a 6-sided die. Find the probability of the event bel
rolling a number less than 5
The probability is
(Type an integer or decimal rounded to three decimal places as needed.)
The probability of rolling a number less than 5 is 0.667.
Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event asked. The value is expressed from zero to one. An outcome is a value we can obtain.
As we are given a 6-sided dice therefore,
Total possible outcomes = 6
Favorable outcomes (that is less than 5) = 4 [that are; 1, 2, 3, 4]
probability = number of favorable outcomes/number of possible outcomes
probability = 4/6
4/6 = 2/3
= 0.6666666666666
To round the value to three decimal places, we need to see if the fourth value after decimal is more than 5 or not. If it is more than 5, preceding digit is increased by 1. therefore, by applying the rule to the value we get
= 0.667 [rounded to three decimal places as needed]
therefore, the probability of the event given, that is rolling a number less than 5 is 0.667.
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PLEASE! Need help for question 12&14
Answer:
12. BC = 8
14. JL = 18
Step-by-step explanation:
You want to apply the Segment Addition theorem to two problems.
The segment addition theorem tells you the whole is the sum of the parts. The equation for each problem reflects this fact. When given values are substituted, the answer becomes clear.
12.AB +BC = AC
7 +BC = 15
BC = 8 . . . . . . . . subtract 7
14.JK +KL = JL
8 +10 = JL = 18
__
Additional comment
It often helps to draw a diagram.
can someone help me with this ?
The height of the ball is given as 7.74 ft.
How to find the height of the ballWe have the value of h(X) to be
-[tex]-\frac{44x^{2} }{v^{2} } +x+6[/tex]
The initial velocity is given as v which is = 26
v = 26² = 676
the value of x is given as 2
We have to put these values in the formula
[tex]-\frac{44(2)^{2} }{676 } +2+6[/tex]
= 44 * 4/676 + 2 + 6
= -0.26 + 2 + 6
= 7.74
Hence we can say that the height of the ball is given as 7.74 ft.
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HELPPPP PLEASE John walks away from his house down a straight street. The graph shows John's distance from his house over time. Describe his trip. Find John's speed on each section of the walk.
John's speed on each section of the walk are 4 km per hour, 0 km per hour and 1.5 km per hour
How to find John's speed on each section of the walk?On the first section, we have the following points
(x, y) = (0, 0) and (1.5, 6)
The speed is calculated as
Speed = (y2 - y1)/(x2 - x1)
This gives
Speed = (6 - 0)/(1.5 - 0)
Evaluate
Speed = 4
On the second section, we have the following points
(x, y) = (1.5, 6) and (2, 6)
The speed is calculated as
Speed = (y2 - y1)/(x2 - x1)
This gives
Speed = (6 - 6)/(2 - 1.5)
Evaluate
Speed = 0
On the third section, we have the following points
(x, y) = (2, 6) and (6, 0)
The speed is calculated as
Speed = (y2 - y1)/(x2 - x1)
This gives
Speed = (0 - 6)/(6 - 2)
Evaluate
Speed = -1.5
Hence, John's speed on each section of the walk are 4 km per hour, 0 km per hour and 1.5 km per hour
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What value of x is in the solution set of 2(3x - 1) ≥ 4x - 6?
-10
-5
-3
-1
Answer:
-1
Step-by-step explanation:
[tex]2(3x-1) \geq 4x-6 \\ \\ 6x-2 \geq 4x-6 \\ \\ 2x \geq -4 \\ \\ x \geq -2[/tex]
Answer:
-1 is the answer
Step-by-step explanation:
Jorge wants to divide 3x2−x−2 by x + 4 using synthetic division. Which answer shows the correct process? Synthetic division problem with divisor negative four, and the dividends are three, negative one, and negative two. Under the negative one is negative twelve, and under the negative two is forty-four. Under the equals line are the numbers three, eleven, and forty-two. Image with alt text: Synthetic division problem with divisor negative four, and the dividends are three, negative one, and negative two. Under the negative one is negative twelve, and under the negative two is forty-four. Under the equals line are the numbers three, eleven, and forty-two. Synthetic division problem with divisor negative four, and the dividends are three, negative one, and negative two. Under the negative one is negative twelve, and under the negative two is fifty-two. Under the equals line are the numbers three, negative thirteen, and fifty. Image with alt text: Synthetic division problem with divisor negative four, and the dividends are three, negative one, and negative two. Under the negative one is negative twelve, and under the negative two is fifty-two. Under the equals line are the numbers three, negative thirteen, and fifty. Synthetic division problem with divisor four, and the dividends are three, negative one, and negative two. Under the negative one is twelve, and under the negative two is negative forty-four. Under the equals line are the numbers three, negative eleven, and negative forty-six. Image with alt text: Synthetic division problem with divisor four, and the dividends are three, negative one, and negative two. Under the negative one is twelve, and under the negative two is negative forty-four. Under the equals line are the numbers three, negative eleven, and negative forty-six. Synthetic division problem with divisor four, and the dividends are three, negative one, and negative two. Under the negative one is twelve, and under the negative two is negative fifty-two. Under the equals line are the numbers
The graph that shows the correct synthetic division process is given at the end of the answer.
How does synthetic division works?In synthetic division, the coefficients of a polynomial are each divided by a value.This value is the zero of the divided polynomial, which goes into the far left box.For this problem, we have that:
The divisor is: 3x² - x - 2, hence the coefficients are: 3, -1, -2.The dividend is: x + 4, hence the bottom left term is -4.Then, from the graph, we have that:
The first coefficient, 3 is pushed to the bottom of the table.Then, each bottom term is multiplied with -4(3 x -4 = -12) and added with the next coefficient to get the result.-1 - 12 = -13, -13 x -4 = 52.-2 + 52 = 50.Hence, the result of the division of 3x² - x - 2 by (x + 4) is 3x - 13 with a remainder of 50.
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Magic Mirror has $428,210 in capital and $87,498 in
liabilities. Find the assets.
The total asset of Magic mirror is $515,708
How to find the asset of magic capital?Magic Mirror has $428,210 in capital and $87,498 in liabilities.
The capital is also know as the equity which means the company's net worth.
Liabilities are everything a business owes, now and in the future.
Assets are everything a business owns. Assets may be current or fixed assets
Therefore,
Total Assets - Total Liabilities = Capital
Where
Total Liabilities = $87,498Total assets = ?Capital = $428,210Hence,
Total Assets = $87,498 + $428,210
Total Assets = $515,708
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Which equation represents the ellipse with vertices located at (3,-3) and (3,-13) and foci at (3,-5) and (3,-11)?
Check the picture below, so the ellipse looks more or less like so.
[tex]\textit{ellipse, vertical major axis} \\\\ \cfrac{(x- h)^2}{ b^2}+\cfrac{(y- k)^2}{ a^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h, k\pm a)\\ c=\textit{distance from}\\ \qquad \textit{center to foci}\\ \qquad \sqrt{ a ^2- b ^2} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\begin{cases} h=3\\ k=-8\\ a=5 \end{cases}\implies \cfrac{(x-3)^2}{b^2}+\cfrac{(y-(-8))^2}{5^2}=1 \\\\\\ \stackrel{\textit{we also know that}~\hfill }{c=3\hspace{3.5em} 3=\sqrt{5^2 - b^2}} \implies 3^2=5^2-b^2\implies b=\sqrt{5^2-3^2} \implies \boxed{b=4} \\\\\\ \cfrac{(x-3)^2}{4^2}+\cfrac{(y-(-8))^2}{5^2}=1\implies \cfrac{(x-3)^2}{16}+\cfrac{(y+8)^2}{25}=1[/tex]
what’s the measure of angle SQT?
Joanna's vegetable garden covers an area of 16 of a square mile. If the garden is 14 mile wide, how long does the garden stretch?
112 mile
1 over 12 mile
512 mile
5 over 12 mile
23 mile
2 thirds mile
34 mile
The length of the rectangular garden given the area and width is 8/7 miles
Area of rectangleA rectangle is a form of quadrilateral having opposing sides parallel and four right angles. The area of a rectangle can be calculated by multiplying the length by width.
Width of the rectangular garden = 14 mileLength of the rectangular garden = x mileArea of the garden = 16 square milesArea of a rectangular garden = length × width
16 = x × 14
16 = 14x
divide both sides by 14x = 16 / 14
x = 8/7 miles
Therefore, the length of the rectangular garden given the area and width is 8/7 miles.
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Written as a simplified polynomial in standard form, what is the result when
(2x + 5)2 is subtracted from 10?
what are two different operations with at least four numbers that equal 12
Answer:
3+3+3+3=12
48-12-12-12=12
Step-by-step explanation:
common sense :)
A carpet is made with a blend of wool and other fibers. If the concentration of wool in the carpet is 75% and the carpet weighs 169 lb, how much wool is in the carpet?
lb
Answer:
Hope the picture will help you
At a workshop , each of the 100 participants hugs each other participants once. Find the total number of hugs?
Answer:
10000
Step-by-step explanation:
100 hugs x 100 hugs
= 10,000 hugs.
How to do this problem in the picture 8th grade math
Answer:
4.69 x 10⁵
Step-by-step explanation:
Step 1
To find a, take the number and move a decimal place to the right one position.
Original Number: 469,000
New Number: 4.69000
Step 2
Now, to find b, count how many places to the right of the decimal.
New Number: 4 . 6 9 0 0 0
Decimal Count: 1 2 3 4 5
There are 5 places to the right of the decimal place.
Step 3
Building upon what we know above, we can now reconstruct the number into scientific notation.
Remember, the notation is: a x 10b
a = 4.69 (Please notice any zeroes on the end have been removed)
b = 5
Now the whole thing:
4.69 x 10⁵
Step 4
Check your work:
105 = 100,000 x 4.69 = 469,000
Answer: [tex]4.61 \times 10^5[/tex]
Reason:
The original number is 461,000 or 461000
Place a decimal point between the first two nonzero values. Erase the zeros and we get 4.61
To get back to 461000, we need to move the decimal point 5 spaces to the right. This is the exponent for the [tex]10^5[/tex] portion.
So [tex]461,000 = 4.61 \times 10^5[/tex]
Cynthia Besch wants to buy a rug for a room that is 19 ft wide and 33 ft long. She wants to leave a uniform strip of floor around the rug. She can afford to buy 275 square feet of carpeting. What dimensions should the rug have?
The dimensions of the rug that Cynthia Besch should buy are 11 ft wide and 25 ft long, which gives an area of 275 ft².
How are the dimensions determined?The dimensions of the rug include the width and the length.
Cynthia is budget-constrained to buy 275 ft² only.
When we factorize 275, we have 1, 5, 11, 25, 55, and 275.
The possible combinations of width and length to get 275 ft² and also ensure that a uniform strip of the floor is left around the rug are 11 ft and 25 ft. This width and length are less than the room's width and length and satisfy the requirement for a uniform strip.
The strip from the room's width and length must be 8 ft each (from all sides).
Data and Calculations:Width of room = 19 ft
Length of room = 33 ft
Area of room = 627 ft²
Dimensions:Width of rug = 11 ft(19 - 8)
Length of rug = 25 ft (33 - 8)
Area = 275 ft² (11 x 25)
Thus, the dimensions of the rug that Cynthia Besch should buy are 11 ft wide and 25 ft long.
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Elimination method.
A warehouse store sells 3.5-ounce cans of tuna in package of 3. A package of 3 cans costs $3.99. The store also sells 6.5-ounce cans in packages of 4 cans for $6.48. Which package is the best buy
which of the following number lines shows the solution to the inequality given below? 3x + 1 <_ -11 or 4x - 3 > 9
The number line which shows the solution to the inequality is option C
Number lines which shows the solution to the inequality3x + 2 ≤ -11
or
4x - 3 > 9
3x + 2 ≤ -11
substract 2 from both sides3x ≤ -11 - 2
3x ≤ -13
divide both sides by 3x ≤ -13/3
x ≤ -4.33
or
4x - 3 > 9
Add 3 to both sides4x > 9 + 3
4x > 12
divide both sides by 4x > 12 / 4
x > 3
Ultimately, the answer to the inequalities is x ≤ -4.33 and x > 3
Therefore, the number line which shows the solution to the inequality is option C
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What percent of 332.5 is 66.5?
After calculation the percentage, we have come to find that 66.5 20% percent of 332.5 .
What is percentage?A percentage is a number or ratio in mathematics that could be expressed as a fraction of 100. If we need to calculate a percentage of a number, divide it by 100. As a result, the percentage denotes a part out of a hundred. The word % means "per 100." The symbol for it is "%."
Percentages can also be expressed as decimals or fractions, for example, 0.6%, 0.25%, and so on. Academic grades are calculated in terms of percentages. Ram, for example, received a 78% on his final exam. As a result, this percentage is calculated based on Ram's total marks across all subjects.
To find out percentage, We multiply the fraction of given numbers with 100
= 66.5/332.5 × 100
= 1/5 × 100
= 20%
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Anna has 55 coins in her piggy bank. She notices that she only has dimes and pennies. If she has exactly
four times as many pennies as dimes, how many pennies are in her piggy bank?
Answer: 44 Pennies
Step-by-step explanation: The ratio of pennies to dimes is 4:1. Add both numbers up to get 5 and divide 55 by 5 to get 11. multiply 4 and 1 from the ratio by 11 to get 44 and 11. This is the number of pennies and dimes.
NEEEEEDDDD HELPPPPPP PLEASE...........
Solve for [x]. Each figure is a trapezoid.
Answer:
11
Step-by-step explanation:
Opposite sides of a trapezoid are parallel. So, by the same-side interior angles theorem,
[tex]-16x+10x+86=180 \\ \\ 10x+70=180 \\ \\ 10x=110 \\ \\ x=11[/tex]
Fiona spent of her money on a dress and $39 on a bag. If she had $121 left, how much money did she have at first?
Answer:
She had $160 at first
Step-by-step explanation:
Fiona spent of her money on a dress and $39 on a bag. If she had $121 left, how much money did she have at first?
In order to find how much she had at first
we have to add how much she spent plus how much she has left with her
➟ $121 + $39
➟ $160
∴ She had $160 at first
the expanded form for 300,648 can be written with only 4 addends . explain how this is possible for a number with 6 digits
Answer:
The expanded form of 300684 can be written with only 4. Add ends, explain how this is possible for a number with 6 digits. When we look at this number, we want to write that in expanded form, which means we want to write the value of each digit. So i look at the value the 4 in the one's place, so its value is 4 actually 4. The 8 is in the tense place, so its value is 810 point. The 6 is in the hundreds place, so its value is 600 point. The 0 is, in the thousands place, that's 0. Thousands. This 0 is in the 10000 point, so we have 010000 and i'm running out of room. So this 3 is in the 100000. Place of its value is 3 times 100000. It just think of it like money, you have 810 dollar bills, 600 dollar bills, etcetera. So if you have 41 dollar bills, you have 4 dollars. If you have 810 dollar bills, you have 80 dollars: 600 dollar bills. You have 600 dollars now. If you have 0 thousands and 010000, you don't have any money in this, so you don't need to write that down. So now i have 300 dollar bills. Some got a value of 300000 point, so they could leave me only 4 digits that i'm adding together reason being this was 0, so there was no value there.
Solve for x and show work
[tex] \longrightarrow \: - 4 + \frac{x + 4}{3} - 2 = 2(x + 1) \\ \longrightarrow \: { -4} + \frac{x}{3} + \frac{4}{3} - {2} = 2x + 2 \\ \longrightarrow \: { - 4}+ \frac{4}{3} - {2} - 2 = 2x - \frac{x}{3} \\ \longrightarrow \: -4 - 2 - 2 + \frac{4}{3} = 2x - \frac{x}{3} \\ \longrightarrow \: - 8 + \frac{4}{3} = 2x - \frac{x}{3} \\ \longrightarrow \: \frac{ - 20}{3} = \frac{5}{3} x \\ \longrightarrow \:\frac{ - 20}{3} \times \:3\: = 5x \\ \longrightarrow \:-20 = 5x\\\longrightarrow \:\frac{-20}{5} = x \\\longrightarrow \:x = - 4[/tex]
