Answer:
The skeleton is 1150 yrs old.
Step-by-step explanation:
To get this answer you would take 5750 and divide by 5 because the problem say 1/5th. This would give you the equation 5750/5 = 1150.
Find the measure of AngleJ, the smallest angle in a triangle with sides measuring 11, 13, and 19. Round to the nearest whole degree. 30° 34° 42° 47°
Answer:
34°
Step-by-step explanation:
The law of cosines is good for finding angles when only sides are known. We'll use the conventional sides a, b, c, and angles A, B, C. Yes, we know the problem statement calls the smallest angle "J". We trust you can make the translation.
a² = b² +c² -2bc·cos(A) . . . . . for sides a, b, c and angle A
Solving for the angle, we get ...
A = arccos((b² +c² -a²)/(2bc))
Filling in the numbers with "a" being the shortest side, we have ...
A = arccos((13² +19² -11²)/(2·13·19)) = arccos(409/494)
A ≈ 34.113°
The smallest angle, ∠J, is about 34°.
Answer:
b
Step-by-step explanation:
Two different radioactive isotopes decay to 10% of their respective original amounts. Isotope A does this in 33 days, while isotope B does this in 43 days. What is the approximate difference in the half-lives of the isotopes?
Answer:
A. 3 Days
Step-by-step explanation:
Just took the test hope this helps :)
Answer:
the answer on edge is A.3
Help please!Thank you
Answer:
f. 85
Step-by-step explanation:
All triangles add up to 180 degrees
BCE=25
then you need to find DBC, you can do that since ABD is isocilies that means all sides are equal in length and angle so 180 divided by 3 (number of side) is 60
isoceles triangle have 2 sides that are equiangular, cince we know BCA is 25 we also know BAC is 25, leaving angle ABC to be 130 (180-50=130)
we subtract angle ABD from angle ABC to get angle DBC, leaving angle DBC to equal 70 degrees
since 70 (angle DBC) + 25 (Angel BCA)= 95
we just subtrract 95 from 180 to get the answer 85 (:
Answer:
85 degrees
Step-by-step explanation:
if Δ ABD is equilateral then the 3 sides and three angles are equal
sum of angles of Δ=180
180/3=60 degrees (∠A,∠B,∠D)
ΔBCA is isosceles then the two angles A and C are equal = 25
∠B=180-50=130
∠B in Δ BEC=130-60=70
∠E+∠B+∠C in Δ BEC=180
∠E= 180-70-25=85 degrees
what are two ways to solve this equation.
Answer:
x = - [tex]\frac{96}{23}[/tex] or x= 4.1739
Step-by-step explanation:
[tex]\frac{3x}{8}[/tex] - [tex]\frac{4x}{3}[/tex] = 4
I will show two methods of solving this equation
First method
We will follow the steps below:
First find the LCM of 8 and 3
The LCM of 8 and 3 is 24
Next is to multiply through by 24
Our equation becomes
24 ×[tex]\frac{3x}{8}[/tex] - 24× [tex]\frac{4x}{3}[/tex] = 24× 4
3×3x - 8×4x =24×4
9x - 32x = 96
-23x = 96
Divide both-side of the equation by - 23
-23x/-23= 96/-23
x=-[tex]\frac{96}{23}[/tex] or x=4.1739
second method
[tex]\frac{3x}{8}[/tex] - [tex]\frac{4x}{3}[/tex] = 4
[tex]\frac{9x - 32x}{24}[/tex] = 4
multiply both-side of the equation by 24 or cross multiply
9x - 32x = 96
-23x = 96
divide both-side of the equation by -23
x = - [tex]\frac{96}{23}[/tex] or x= 4.1739
Marx and Engels believed that a. people in a good environment would behave unselfishly. b. people should create utopian communities. c. the capitalist system should be destroyed. d. workers should improve conditions by taking political office. Please select the best answer from the choices provided A B C D
Q;- Marx and Engels believed that a. people in a good environment would behave unselfishly. b. people should create utopian communities. c. the capitalist system should be destroyed. d. workers should improve conditions by taking political office. Please select the best answer from the choices provided A B C D
A;- Marx and Engels believed that the capitalist system should be destroyed.
The owner of a music store gathered data from several schools about the number of students in their concert and marching bands. The scatter plot shows the data she gathered and the line of best fit
Answer:
25 students
Step-by-step explanation:
What we need to do here is to do some tracing. We simply need to go to the point on the concert band where we have the value 35.
After sighting this value, we then make a tracing to the line of best fit. Then from this line of best fit, we trace the point on the matching band that correlated with the value 35.
If properly traced, we would arrive at a value of 25 on the marching band
Hey, I need help.
A school has 486 students, and this is an 8% increase from the number of students last year. How many students were in school last year?
Please also show working out, thanks :)
486 ÷ 108
4.5 x 100
450 were there last year
Answer:
The answer is 450Step-by-step explanation:
Let the original number of students be x
Since the number of students increased by 8% we add 8% to 100% making it 108%
108% of the original number of students gave us 486
So we have
108% of x = 486
108 / 100 × x = 486
Multiply through by 100
108x = 48600
Divide both sides by 108
x = 450
So the number of students in the school last year was 450
Hope this helps you
Please answer this in two minutes
Answer:
x = 5.7 units
Step-by-step explanation:
By applying Sine rule is the triangle XYZ,
[tex]\frac{\text{SinX}}{\text{WY}}=\frac{\text{SinY}}{\text{WX}}=\frac{\text{SinW}}{\text{XY}}[/tex]
[tex]\frac{\text{SinX}}{\text{x}}=\frac{\text{SinY}}{\text{y}}=\frac{\text{SinW}}{\text{10}}[/tex]
[tex]\frac{\text{Sin33}}{\text{x}}=\frac{\text{SinY}}{\text{y}}=\frac{\text{Sin107}}{\text{10}}[/tex]
[tex]\frac{\text{Sin33}}{\text{x}}=\frac{\text{Sin107}}{\text{10}}[/tex]
[tex]x=\frac{10\times(\text{Sin33})}{\text{(Sin107)}}[/tex]
x = 5.69
x ≈ 5.7 units
An employee is paid a salary of \$73,840 per year, plus benefits and overtime (time and a half) on hours worked over 40 per week, working as a civil servant. What is the regular time hourly rate of pay for this employee, and what is her total income in a month where she works 40 hours, 44 hours, 43.5 hours, and 40 hours, weekly, in the month?
A.$37.00/hr and \$6,336.25 in total income
B. $35.50/hr and \$6,079.38 in total income
C.$37.50/hr and \$6,421.88 in total income
D.$36.00/hr and \$6,165.00 in total income
Answer:
B. $35.50/hr and \$6,079.38 in total income
Step-by-step explanation:
Given the following :
Total regular pay earning for the year = $73,840
Let basic salary = b
Overtime = 1.5b
Regular earning per week :
Regular year earning / number of weeks per year
$73840 / 52 = $1420
Regular hours = 40
Regular earning per week = $1420
Regular earning per hour = $1420 / 40
Regular earning per hour = $35.50
Number of overtime hours :
4 hours + 3.5hours = 7.5hours
Overtime pay per hour = 1.5 * regular earning
Overtime pay per hour = 1.5 * 35.5 = $53.25
Total overtime pay = Overtime pay per hour * Number of overtime hours
Total overtime pay = $53.25 * 7.5
Total overtime pay = 399.375
Total pay for the month :
160 regular hours + 7.5 overtime hours
(160 * 35.5) + $399.375
$5,680 + 399.375 = $6,079.375
= $6,079.38
En un colegio, dos séptimos de total de los estudiantes asisten al taller de escultura, un décimo al taller de guitarra y dos quintos al taller de computación. ¿Qué fracción del total de los estudiantes no asiste a estos talleres?
Answer:
3/14
Step-by-step explanation:
En esta pregunta, nos preocupa calcular la fracción de los estudiantes que no asisten a los talleres.
Para obtener la fracción que no asiste a los talleres, lo que debemos hacer es sumar las fracciones de cada uno de los talleres y restar el total de 1.
Matemáticamente eso sería;
1- (2/7 + 1/10 + 2/5)
Agregando los términos en el paréntesis, tenemos;
(20+ 7 + 28) / 70 = 55/70 = 11/14
Restando esto de 1, tenemos; 1-11 / 14 = 3/14
A doctor recommends a two-step process to treat a rare form of pancreatic cancer. The first method is successful 80% of the time. If the first method is successful, the second method is successful 90% of the time. If the first treatment is not a success, the second is 25% of the time. What is the probability that both treatments are unsuccessful?
Answer:
The answer is 15%.
Step-by-step explanation:
The probability that:
Both treatments are successful:80% x 90% = 72%
The first method is a success, but the second one is not:80% x (1 - 90%) = 8%
The first method is not successful, but the second one is:(1 - 80%) x 25% = 5%
Both treatments are unsuccessful:1 - (72% + 8% + 5%) = 15%
Solve by completing the square: x^2+4x-5
Answer:
(x + 2)^2-9
How to find answer:
Use the formula (b/2)^2 in order to complete the square.
Hope this helps :)
Sara needs to pack 108 stalks of roses, 81 stalks of lilies, and 54 stalks of orchids into identical baskets so that each type of flower is equally distributed among the baskets. Find the largest number of the basket that can be packed
Answer:
54
Step-by-step explanation:
There are 108 roses, 81 lilies and 54 orchids.
The problem is asking that every basket contain the same number for that type of flower.
So if I put one of each flower in each basket, I will get 54 baskets at the most.
Sounds correct to you?
Please can someone help me with this
Answer:
[tex]\boxed{V = 434.9 \ cm^3 }[/tex]
Step-by-step explanation:
Volume of Sphere = [tex]\frac{4}{3} \pi r^3[/tex]
Where r = 4.7 cm
V = [tex]\frac{4}{3} (3.14)(4.7)^3[/tex]
V = [tex]\frac{4}{3} (3.14)(103.8)[/tex]
V = [tex]\frac{1304.7}{3}[/tex]
V = 434.9 cm³ (Up to 1 dp)
Answer:
Step-by-step explanation:
4/3×22/7×4.7^3=435.1cm
Which of the following is NOT a trig function OR an inverse? a COT b TON c SIN d COS
Answer:
B
Step-by-step explanation:
A nice way to remember the normal trig functions and what they stand for is with SOH CAH TOA, where S represents the Sin, C represents the Cos, and T represents tan. Note: those are only abbreviations of the actual words.
I don't know a way to remember the names of the inverse trig functions, but they are Csc, sec, and cot.
Looking at all of the options, only TON does not fit the bill, so that's the answer.
find the equation of the circle whose center and radius are given center (7,3) radius =7
Answer:
[tex](x-7)^2+(y-3)^2=7^2[/tex]
Step-by-step explanation:
[tex](x-h)^{2}+(y-k)^{2}=r^{2}\\[/tex]
Thus,
[tex](x-7)^2+(y-3)^2=7^2[/tex]
Explain PLEASE:
The legs of a right triangle are lengths x and x√3. The cosine of the smallest angle of the triangle is _____.
a. 1/2
b. √3
c. √3/2
d. 2√3
Answer:
[tex]\frac{\sqrt{3}}{2}[/tex]
Step-by-step explanation:
The quickest way to solve this is to recognize this as a 30-60-90 triangle. The smallest angle is 30 degrees, and the answer is simply cos 30º.
You can also use the pythagorean theorem to find the length of the hypotenuse, then use SOH-CAH-TOA to get the answer.
Find the complex fourth roots of 81(cos(3π/8)+isin(3π/8)). a) Find the fourth root of 81. b) Divide the angle in the problem by 4 to find the first argument. c)Use the fact that adding 2π to the angle 3π/8 produces the same effective angle to generate the other three possible angle for the fourth roots. d) Find all four of the fourth roots of 81(cos(3π/8)+isin(3π/8)). express your answer in polar form.
Answer:
The answer is below
Step-by-step explanation:
Let a complex z = r(cos θ + isinθ), the nth root of the complex number is given as:
[tex]z_1=r^{\frac{1}{n} }(cos(\frac{\theta +2k\pi}{n} )+isin(\frac{\theta +2k\pi}{n} )),\\k=0,1,2,.\ .\ .,n-1[/tex]
Given the complex number z = 81(cos(3π/8)+isin(3π/8)), the fourth root (i.e n = 4) is given as follows:
[tex]z_{k=0}=81^{\frac{1}{4} }(cos(\frac{\frac{3\pi}{8} +2(0)\pi}{4} )+isin(\frac{\frac{3\pi}{8} +2(0)\pi}{4} ))=3[cos(\frac{3\pi}{32} )+isin(\frac{3\pi}{32})] \\z_{k=0}=3[cos(\frac{3\pi}{32} )+isin(\frac{3\pi}{32})]\\\\z_{k=1}=81^{\frac{1}{4} }(cos(\frac{\frac{3\pi}{8} +2(1)\pi}{4} )+isin(\frac{\frac{3\pi}{8} +2(1)\pi}{4} ))=3[cos(\frac{19\pi}{32} )+isin(\frac{19\pi}{32})] \\z_{k=1}=3[cos(\frac{19\pi}{32} )+isin(\frac{19\pi}{32})]\\\\[/tex]
[tex]z_{k=2}=81^{\frac{1}{4} }(cos(\frac{\frac{3\pi}{8} +2(2)\pi}{4} )+isin(\frac{\frac{3\pi}{8} +2(2)\pi}{4} ))=3[cos(\frac{35\pi}{32} )+isin(\frac{35\pi}{32})] \\z_{k=2}=3[cos(\frac{35\pi}{32} )+isin(\frac{35\pi}{32})]\\\\z_{k=3}=81^{\frac{1}{4} }(cos(\frac{\frac{3\pi}{8} +2(3)\pi}{4} )+isin(\frac{\frac{3\pi}{8} +2(3)\pi}{4} ))=3[cos(\frac{51\pi}{32} )+isin(\frac{51\pi}{32})] \\z_{k=3}=3[cos(\frac{51\pi}{32} )+isin(\frac{51\pi}{32})][/tex]
Please Help!!!
Gina wants to take dance classes. She compares two dance studios to determine which has the best deal for her. Dance World charges a rate for each class. Toe Tappers charges a rate for each class plus a one-time registration fee. The system of equations shown models the total costs for taking x classes at each.
Dance World: y = 15x
Toe Tappers: y = 25 + 12.5x
How many classes would Gina need to take for the total cost to be the same at both dance studios?
A: 10
B: 15
C: 100
D: 150
Answer:
The correct answer is A: 10
Step-by-step explanation:
We know that for Dance World the equation is y=15x and for Toe Tapper it is y=25+12.5x
Make a chart with both dance companies and compare the solutions to each equation. Like the one below.
Dance World / Toe Tappers
A:10 $150 / $150
B:15 $225 / $212.5
C:100 $1500 / $1275
D:150 $2250 / $1900
In conclusion, A:10 is the correct answer as both dance companies cost the same for 10 classes.
Sorry if this is really late, this is for the people who have the same question and need an answer too.
Answer:
A 10
Step-by-step explanation:
Set the equations equal to each other:15x = 25 + 12.5x
Solve for x2.5x = 25
x= 10
What is the vertex on the graph of the absolute-value parent function?
Answer:
The highest or the lowest point on the graph is the vertex of an absolute-value function!
Step-by-step explanation:
Please help me it will be greatly appreciated!
Answer:
∠y = 70º, ∠z = 60º, ∠w = 70º
Step-by-step explanation:
i believe the angle measures are the same for both triangles.
so ∠z = 60º, ∠x = 50º
to get ∠w, 180 - (50 + 60) = 70
∠w = 70º
∠w and ∠y would be equivalent
Listed below are speeds (mi/h) measured from traffic on a busy highway. This simple random sample was obtained at 3:30 P.M. on a weekday. Use the sample data to construct a 98% confidence interval estimate of the population standard deviation. 65 62 62 55 62 55 60 59 60 70 61 68
The confidence interval estiamte it __mi/h< o <__mi/h
Answer:
3.0 mi/h < σ < 8.54 mi/h
Step-by-step explanation:
Given:
Sample data: x: 65 62 62 55 62 55 60 59 60 70 61 68
Confidence = c = 98% = 0.98
To find:
Construct a 98% confidence interval estimate of the population standard deviation.
Solution:
Compute Mean:
number of terms in data set = n = 12
Mean = Sum of all terms / number of terms
= 65 + 62 + 62 + 55 + 62 + 55 + 60 + 59 + 60 + 70 + 61 + 68 / 12
= 739/12
Mean = 61.58
Compute standard deviation:
s = √∑(each term of data set - mean)/ sample size - 1
s = √∑([tex]_{x-} {\frac{}{x} }[/tex])²/n-1
= √( 65 - 61.58)² + (62 - 61.58)² + (62 - 61.58)² + (55 - 61.58)² + (62 - 61.58)² + (55 - 61.58)² + (60 - 61.58)² + (59 - 61.58)² + (60 - 61.58)² + (70 - 61.58)² + (61 -61.58)² + (68 - 61.58)² / 12-1
= √(11.6964 + 0.1764 + 0.1764 + 43.2964 + 0.1764 + 43.2964 + 2.4964 + 6.6564 + 2.4964 + 70.8964 + 0.3364 + 41.2164) / 11
= √222.9168/11
= √20.2652
= 4.50168
= 4.5017
s = 4.5017
Compute critical value using chi-square table:
For row:
degree of freedom = n-1 = 12 - 1 = 11
For Column:
(1 - c) / 2 = (1 - 0.98) / 2 = 0.02/2 = 0.01
1 - (1 - c) / 2 = 1 - (1-0.98) / 2 = 1 - 0.02 / 2 = 1 - 0.01 = 0.99
[tex]X^{2} _{1-\alpha/2}[/tex] = 3.053
[tex]X^{2} _{\alpha/2}[/tex] = 24.725
Compute 98% confidence interval of standard deviation:
[tex]\sqrt{\frac{n-1}{X^{2} _{\alpha/2}} } s[/tex] = [tex]\sqrt{\frac{12-1}{24.725} } ( 4.5017)[/tex] = [tex]\sqrt{\frac{11}{24.725} } ( 4.5017)[/tex] = [tex]\sqrt{0.44489}(4.5017)[/tex]
= 0.6670 (4.5017) = 3.0026
[tex]\sqrt{\frac{n-1}{X^{2} _{\alpha/2}} } s[/tex] = 3.0026
[tex]\sqrt{\frac{n-1}{X^{2} _{1-\alpha/2}} } s[/tex] = [tex]\sqrt{\frac{12-1}{3.053} } ( 4.5017)[/tex] = [tex]\sqrt{\frac{11}{3.053} } ( 4.5017)[/tex] = [tex]\sqrt{3.6030} (4.5017)[/tex]
= 1.8982 ( 4.5017) = 8.5449
[tex]\sqrt{\frac{n-1}{X^{2} _{1-\alpha/2}} } s[/tex] = 8.5449
3.0026 mi/h < σ < 8.5449 mi/h
Find the product.
(2xyz) (-4x2yz)
PLEASE HELP!!! ASAP!!!
Answer:
[tex]-16x^{2} y^{2}z^{2}[/tex]
Step-by-step explanation:
Let's calculate the answer to the second parenthesis. Just multiply throughout to get -8xyz. Then, multiply the first parenthesis by the second. Multiply the constants (-8 and 2) first to get -16, multiply the x's together to get x^2, the y's together to get y^2, and the z's together to get z^2. Put it all together to get [tex]-16x^{2} y^{2}z^{2}[/tex].
Answer:
Your correct answer is = −16y2z2
A city counsel has a square lot to place a playground. They plan to place a diagonal of trees to create two distinct play areas. To determine if there is enough money in the budget, they needs to know the distance. If the length of each side of the lot is 45 m, how long is the diagonal?
Answer:
66.63
Step-by-step explanation:
To find the diagonal length, use Pythagorean’s theorem.
Diagonal = √45^2 + 45^2 = √2025+2025 = √4050 = 63.63.
Hope this helps
I really need help with this question, and I would really appreciate it! I will mark brainliest!
Answer:
These are two equilateral triangles and all the sides of an equilateral triangle are equal. The question even says so so that's the answer, all the sides of the equilateral triangles are equal so all the sides equate to each other
Answer two questions about Equations A and B: A. 5x-2+x=x-4 B. 5x+x=x-4 How can we get Equation B from Equation A?
Answer:
The answer is below
Step-by-step explanation:
To be able to get equation B from equation A, we have to compare equation A with equation B. Given that equation A. is 5x-2+x=x-4 and equation B is 5x+x=x-4.
Equation B: 5x+x=x-4.
Equation A: 5x-2+x=x-4.
Simplifying equation A to be in the form of equation B:
5x -2 + x = x - 4
Adding 2 to both sides:
5x + x -2 + 2 = x - 4 + 2
5x + x = x - 4 + (+2)
= equation A + 2
But 5x+x=x-4 = equation A
Therefore Equation B is the same as Equation A + 2
Answer:ADD/SUBTRACT A QUANTITY TO/FROM ONLY ONE SIDE
And part 2: is NO
Help pleaseee! Thank you
Answer:
Step-by-step explanation:
width of a rectangle=11 cm=11*5=55 ft
length of rectangle =8 cm= 8*5=40
Area=55*40=2220 ft²
height=3 cm=3*5=15
base=11 cm=11*5=55
Area of a triangle=base*height/2=15*55/2= ft^2
2220+412.5=2632.5 ft^2
this number is close to 2615 if the square unit on the grid =1 cm
John and 2 friends are going out for pizza for lunch. They split one pizza and 3 large drinks. The pizza cost $14.00. After using a $7.00 gift certificate, they spend a total of $12.10. Write an equation to model this situation, and find the cost of one large drink
Answer:
cost of one drink: $1.70
Step-by-step explanation:
P = price of pizza
L = Price of each large drink
Gift certificate discount =$ 7
Net paid= $12.10
P +3L -7 = 12.10
14 +3L -7 =12.10
7+3L =12.10
3L = 12.10 -7 = 5.10
L = $1.70 for each large drink
hopefully this helped :3
Answer: The equation to model this situation is 3d + $14.00 – $7.00 = $12.10 and the cost of one large drink is $1.7 .
Step-by-step explanation:
As given
John and 2 friends are going out for pizza for lunch.
They split one pizza and 3 large drinks. The pizza cost $14.00. After using a $7.00 gift certificate, they spend a total of $12.10.
let us assume that the numbers of large drinks are represented by d .
Than the equation becomes
Total money spend = Number of drinks × d + Pizza cost - Gift certificate amount .
Putting all the values in the above
12.10 = 3d + 14.00 - 7.00
Simplify the aboves
12.10 = 3d + 14 - 7
12.10 = 3d + 7
12.10 - 7 = 3d
5.1 = 3d
d = $ 1.7
Therefore the equation to model this situation is 3d + $14.00 – $7.00 = $12.10 and the cost of one large drink is $1.7 .
Latoya drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 6 hours. When Latoya drove home, there was no traffic and the trip only took 4 hours. If her average rate was 22 miles per hour faster on the trip home, how far away does Latoya live from the mountains
PLEASSSSEEE HELP ! what number belongs in the box ? y=200+ ? x
Answer:
10
Step-by-step explanation:
It's the $10 that is to be added to the cost for each produced item.