Answer:
A. 5 < AC < 10
Step-by-step explanation:
We are given the ∆ABC
To solve for the sides of ∆ABC , we make use of Pythagoras Theorem
Pythagoras Theorem states that:
AB² = AC² + BC²
Where AB = Longest side, hence its length is always more that AC and BC.
In the above Question, we are given the values of AB and BC
AB = 10
BC = 5
Inputting these values into the Pythagoras Theorem,
10² = AC² + 5²
100 = AC² + 25
AC² = 100 - 25
AC² = 75
AC = √75
AC = 8.6602540378
According to the above calculation, we can see that the expression that is always true = Option A "5 < AC < 10"
According to the National Center for Health Statistics, in 1990, 28% of babies in the United States were born to parents who were not married. Throughout the 1990s, this increased by approximately 0.6% per year. If this trend continues, in which year will 49% of babies be born out of wedlock
Answer:
2029
Step-by-step explanation:
We can write an equation:
0.28+0.006x=0.51
A few things explained:
The constant 0.28 comes from the fact in 1990, 28% of babies were born to parents who were not married. 28%=0.28
0.006 represents 0.6% and x represents the number of years will pass until 49% of babies will be born out of wedlock
0.51 represents 51%. 51% represents the percentage of babies who will be born to parents not married (100% - 49%=51%). You want to use 51% instead of 49% because the right side represents the babies born to parents not married.
We can solve the equation:
0.28+0.006x=0.51
0.006x=0.23
x=38.33
Since you can't have 38.3333 years, we'll say that 39 will pass until 49% of babies are born out of wedlock.
So, we add 39 years to 1990.
1990+39=2029
Hope this helps!
Does anyone know this? Need it ASAP
Answer:
D) P = 80 feet, A = 360 square feet
Step-by-step explanation:
Perimeter=15+20+17+8+20=80 feet
Area=(15*20)+(1/2*8*15)=300+60=360 square feet
Perform the operation. (Write fractional answers in simplest form.) 4x/5 + x/7
Answer:
simplest form:
[tex]\frac{33 x}{35}[/tex]
Express 4/5 in
a) percentage
b) decimal
c)decimal
Answer:
4/5 = 80/100 = 80%
4/5 = 0.8
Miguel runs 7 miles in 60 minutes. At the same rate, how many miles would he run in 24 minutes?
Answer:
We use the rule of three
7 miles ---------------> 60 minutes
So x ------------------> 24 minutes
So x= (24 minutes × 7 miles )/60 minutes .
We simplify by 《minutes》 because it's in the numerator and the denominator .
So x= (24×7 miles )/60
x = 168 miles /60
x=2,8 miles
So Miguel runs 2,8 miles in 24 minutes.
A model plane has a scale of 1 in: 6 yd. If
the model plane is 3 in tall then how tall is
the real plane?
Answer:
18 yards
Step-by-step explanation:
Let's set up a proportion using the following setup.
inches / yards = inches / yards
We know the scale is 1 inch to 6 yards.
1 inch / 6 yards = inches / yards
We know the model plane is 3 inches tall, but we don't know how tall the real plane is. Therefore, we can it is 3 inches to x yards.
1 inch / 6 yards= 3 inches / x yards
1 /6= 3/x
Cross multiply. Multiply the numerator of the first fraction by the denominator of the second. Then, multiply the denominator of the first by the numerator of the second.
1*x= 6*3
1x= 6*3
x= 6*3
x=18
x= 18 yards
The real plane is 18 yards.
what is 4 3/7 as a decimal.
A complicated mechanical system contains 8 components. If there is a 18% chance that each component will fail during processing, and components fail independently of each other, then
(a) What is the probability that fewer than 3 components will fail?
(b) What is the meet likely number of failures?
Answer:
(a) The probability that fewer than 3 components will fail is 0.8392.
(b) The mean likely number of failures is 1.44.
Step-by-step explanation:
We are given that a complicated mechanical system contains 8 components. If there is an 18% chance that each component will fail during processing, and components fail independently of each other.
Let X = Number of components fail during processing
The above situation can be represented through the binomial distribution;
[tex]P(X=r) = \binom{n}{r}\times p^{r} \times (1-p)^{n-r} ;x=0,1,2,.....[/tex]
where, n = number of samples (trials) taken = 8 components
r = number of success = fewer than 3 components will fail
p = probability of success which in our question is the probability
that each component will fail during processing, i.e. p = 18%
SO, X ~ Binom(n = 8, p = 0.18)
(a) The probability that fewer than 3 components will fail is given by = P(X < 3)
P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)
= [tex]\binom{8}{0}\times 0.18^{0} \times (1-0.18)^{8-0}+ \binom{8}{1}\times 0.18^{1} \times (1-0.18)^{8-1}+ \binom{8}{2}\times 0.18^{2} \times (1-0.18)^{8-2}[/tex]
= [tex]1 \times 1 \times 0.82^{8}+ 8 \times 0.18^{1} \times 0.82^{7}+28 \times 0.18^{2} \times 0.82^{6}[/tex]
= 0.8392
(b) The mean likely number of failures is given by the following formula;
Mean of X, E(X) = n [tex]\times[/tex] p
= [tex]8 \times 0.18[/tex] = 1.44
Hence, the mean likely number of failures is 1.44.
20 points, I HAVE SCHOOL IN 1 HOUR PLEASE HELP, ONLY 2 QUESTIONS,
1. use distributive property to simplify the expression 7(6x + 1)
2. Simplify the expression 4 + ( 14 + x )
Answer:
[tex]\Huge \boxed{42x+7} \\ \\ \\ \Huge \boxed{x+18}[/tex]
Step-by-step explanation:
Part 1:
[tex]7(6x + 1)[/tex]
Distribute 7 to the terms in the brackets.
[tex]7(6x)+7(1)[/tex]
[tex]42x+7[/tex]
Part 2:
[tex]4+(14+x)[/tex]
Removing brackets.
[tex]4+14+x[/tex]
Combining like terms.
[tex]18+x[/tex]
$325.50 of 30% what is the price
A rectangle is 6 ft long and 11 ft wide. What is the length of the diagonal of the
rectangle?
Answer:
sqrt(157) ft is the length of the diagonal
Step-by-step explanation:
We can use the Pythagorean theorem to find the length of the diagonal
a^2 + b^2 = c^2
6^2 + 11 ^2 = c^2
36+ 121 = c^2
157 = c^2
Take the square root of each side
sqrt(157) = sqrt(c^2)
sqrt(157) = c
Answer:
sqrt(157) ft is the length of the diagonal
Step-by-step explanation:
We can use the Pythagorean theorem to find the length of the diagonal
a^2 + b^2 = c^2
6^2 + 11 ^2 = c^2
36+ 121 = c^2
157 = c^2
Take the square root of each side
sqrt(157) = sqrt(c^2)
sqrt(157) = c
8-|21 - 13 - 9| -| -4|
Answer:
8-1-4=8-1-4=3
Step-by-step explanation:
Order of operations: solve inside the absolute value first. 21-13-9=8-9=-1. The absolute value of -1 is 1.
write each ratio statement as a fraction and reduce to lowest terms if possible.(i)18 to 24 (ii)5 to 15 (iii)14:42 (iv) 15 cents to 18 cents.
Answer:
i) 3/4
ii) 1/3
iii) 1/3
iv) 5/6 cents
Step-by-step explanation:
Any ratio can be written as a fraction.
For example 3:4 can be writen as 3/4 or 14:42 as 14/42.
After you convert them to fractions you then simplify them by finding their highest common factor (HCF) and then divide both numerator and denominator by the HCF. When you cant simplify the fraction anymore, that is the fraction in its lowest terms.
Simplify the equation 5(3m-2)+4m
Answer:
19m - 10
Step-by-step explanation:
Order of Operation: BPEMDAS
Step 1: Write out equation
5(3m - 2) + 4m
Step 2: Distribute parenthesis
15m - 10 + 4m
Step 3: Combine like terms
19m - 10
A. 3^2+2x8
—————
16-11
B. (32x1/2+6)-(4-1)
C. ((8-10.3)+2^3-5)
Answer:
=3²+2×8
=9+2×8
=9+16
=25
PROVED!!
Steve rides his bike at a rate of 1760 feet per minute. What is his rate in miles per hour?
Answer:
The answer is 19.36 miles per hoursStep-by-step explanation:
this problem is a unit conversion problem
In this problem, we are expected to convert from feet/min to miles per hour
given that the rate is 1760 feet per minute
from tables, we are given that
1 foot per minute is 0.011 miles per hour hence
1760 feet per minutes will give x miles per hour
cross multiplying we have
x= 1760*0.011
x= 19.36 miles per hours
15.2, 3,6,11,18, ...
Describe the pattern. Then write the next three numbers
Answer:
27, 38, and 51
Step-by-step explanation:
3, 6, 11, 18, ...
We increase the first number by 3. Then 5. Then 7.
The pattern is that the difference increases by 2.
That means this is a quadratic sequence.
y = x² + 2, where x = 1, 2, 3, etc.
The next three numbers are 27, 38, and 51.
At the market, Joey buys 3 avocados for $0.40 each and 5 lemons for $0.40 each. The cashier in training rings up 3 × 0.40 and then 5 × 0.40 to get the total. The experienced cashier says to add the 3 plus 5 in his head and then ring up 8 × 0.40.
What property says that these two totals would be the same?
multiplicative identity
associative property of multiplication
distributive property
commutative property of multiplication
Answer:
Distributive property
Step-by-step explanation:
3*$0.40 + 5*$0.40 = (3+5)*$0.40
Distributive law, in mathematics, the law relating the operations of multiplication and addition, stated symbolically, a(b + c) = ab + acAccording to distributive property multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.answer is distributive property
Step-by-step explanation:
hope this answer helps :)
Solve equation
56=-8d+8
Answer:
d = - 6
Step-by-step explanation:
56 = -8d +8
-8 . -8
48 = -8d
__ . __
-8 -8
-6 = d
Combine the like terms to create an equivalent expression: \large{-4p+(-2)+2p+3}−4p+(−2)+2p+3
Answer:
-2p+1
Step-by-step explanation:
-4p+2p+(-2)+3
-2p+1
The equivalent expression of the expression {-4p+(-2)+2p+3}−4p+(−2)+2p+3 is -4p+2.
What is expression?An expression is a combination of numbers, variables, function, indeterminants, symbols like addition, multiplication, subtraction and division. It is not usually present in equal to form.
How to create equivalent expression?We have been given one expression {-4p+(-2)+2p+3}−4p+(−2)+2p+3 and we have to find the equivalent expression by solving the expression.
First we need to put appropriate signs by solving brackets and the expression will look like after opening brackets and after opening of brackets the signs may change:
=-4p-2+2p+3-4p-2+2p+3
=-4p+2p-4p+2p-2+3-2+3
=-4p+2
Hence the equivalent expression of {-4p+(-2)+2p+3}−4p+(−2)+2p+3 is -4p+2.
Learn more about expressions at https://brainly.com/question/723406
#SPJ2
Caleb has worked hard and is offered a salaried position with the same company. He is offered $28,000, but will be expected to work 44 hours per week with no overtime pay. How much would he be paid per year if he remained in his present job and worked 44 hours per week, and was paid for the overtime? (Caleb makes $11.15 an hour and gets time and a half for overtime.)
Answer:
$7.50 (paid per hour) times 70 hours (times 2 of 35 hours) = $525 gross pay
Step-by-step explanation:
525 is the gross pay.
Hello there! :D
We know that Caleb has two options:
Let's say that Option A is taking the new job, and Option B is solving for the new one. We know that Option A will leave him with $28,000. Let's do some math to see how much he would make with Option B.
We can do this by calculating how many ours he would work in one year and multiplying that by $11.15.
So, we have 44 hours a week. There are 52 weeks in a year.
52*44= 2288
Now, we can mutltiply that by his hourly wage.
2288*11.15=$25,511.2
Let's see how much time it would take to make the same amount of money since he is allowed to work overtime at half price:
Subtract the amount he makes in Option A by Option B:
28,000-25,511.2= 2488.8
Now we need to divide his hourly wage in half, because he gets paid half as much for overtime (I am assuming the wording is weird here).
11.15/2= 5.575
Now we can find out how many hours he needs to do per year to make the same amount.
2488.8/5.575=432.834 hours
Per week that is 8.3 extra hours! (Sounds like a lot of work)
If I was Caleb, I would take the new job offer, because it is unlikely that he will make much more in his current job.
I hope this helped you and that you have a wonderful day,
Kai xx
During each summer, many families spend part of their vacation time at a beach along the East or West Coast. Due to the popularity of movies like Jaws and The Shallows, and publicity about recent shark attacks on surfers, swimmers, snorkelers, and spearfishermen, Americans have become increasingly concerned about water activities. Research suggests that 58% of all shark attacks involve surfers. One thousand records of shark attacks are selected, and each is categorized by the victim group. Identify the population, sample, and variable for the study.
Answer:
a
POPULATION : The population is the surfers , swimmers, snorkelers and spear-fishermen in America
SAMPLE : The 1000 records of shark attacks selected
VARIABLE FOR STUDY: 580 surfers
Step-by-step explanation:
Generally the population is the surfers , swimmers, snorkelers and spear-fishermen in America
This is because it is the entire pool from which a statistical sample is drawn
Generally the sample is the 1000 records of shark attacks selected
This is because this the number drawn from the population for statistical testing also this contain the characteristics of the population
Generally the variable for study is 58% of 1000 = 580 surfers
This is because the this 580 surfer is the major focus of the Researchers study
A school newspaper decides to survey all the students enrolled in a gym class to determine the percentage of these students who are
also on the football team. What is the population of this study?
A. students who take gym class
B. students who take gym class and are on the football team
C. all students in the school
D. students who are on the football team
Answer:
A sudents who take gym class
Step-by-step explanation:
the survey only asks for all the students enrolled in a gym class so they can compare with the data for all the students enrolled in the football team
Answer:
a
Step-by-step explanation:
19
Write
as a mixed number.
7
Answer:
2 5/7
Step-by-step explanation:
Set up the division problem in long division format. Divide 19 by 7. Place this digit in the quotient on top of the division symbol. Multiply the newest quotient digit (2) by the divisor 7. Subtract 14 from 19. Then you have your answer of 2 5/7.
hope this helps :3
How much money did she earn?
Answer:
$160, basic multiplication ^^
Step-by-step explanation:
20×8=160
Answer:
$20 x 8
=$160
Multiplication
Hope it helped u if yes mark me BRAINLIEST pzllzllzl
36 1 3 2. 13 = 20
Order of operations
Answer: (36 - 1) ÷ (3 + 2) + 13 = 20
Step-by-step explanation:
PEMDAS rule calls for parenthesis to be solved first, then exponents, then multiplication or division then addition or subtraction depending on which comes first in the equation.
Using the PEMDAS rule the 20 can be gotten to if the equation is expressed as follows;
(36 - 1) ÷ (3 + 2) + 13 = 20
The parenthesis will be solved first;
35 ÷ 5 + 13 = 20
The division will be done first;
7 + 13 = 20
Then the addition;
7 + 13 = 20
The position of an object in circular motion is modeled by the given parametric equations. Describe the path of the object by stating the radius of the circle, the position at time t = 0, the orientation of the motion (clockwise or counterclockwise), and the time t that it takes to complete one revolution around the circle.
x = 4 cos 3t, y = 4 sin 3t
How do you get to that solution?
Answer:
4 units ; counter clockwise ; 2.09 units
Step-by-step explanation:
Given the following :
x = 4 cos 3t
y = 4 sin 3t
The Radius (r) could be obtained using Pythagoras:
R = √(x^2 + y^2)
R = √[(4cos3t)^2 + (4sin3t)^2]
R = √[16cos^(2)3t + 16sin^(2)3t]
Recall : cos^2θ + sin^2θ = 1
Therefore, cos^(2)3t + sin^(2)3t= 1
Where, 3t stands for θ
R = √[16cos^(2)3t + 16sin^(2)3t]
Factorizing:
R = √16[cos^(2)3t + sin^(2)3t)]
R = √16[1]
R = √16
R = 4 units
Position at time t = 0
x = 4 cos 3(0)
x = 4 cos 0
x = 4 * 1 = 4 units
y = 4 sin 3t
y = 4 sin 3(0)
y = 4 * sin 0
y = 0
Position at t = 0;
(x, y) = (4, 0) = counterclockwise
Time taken to complete 1 complete revolution:
2π/3 = 6.2831853 /3 = 2.0943951
= 2.09
Which numbers are factors of 42? Check all that apply.
1
2
3
6
8
Answer:
1, 2, 3, 6
Step-by-step explanation:
Select the correct answer.
What are the domain and range of this function?
(x + 3)² - 5
A Domain: (0o,00)
Range (-00,00)
Domain: (-5,00)
Range: (-5,00)
C. Domain: (-0,00)
Range: (-5,00)
D. Domain: (-5,00)
Range: (-00,00)
Reset
Next
Answer:
Domain: [tex](-\infty,\infty)[/tex]
Range: [tex][-5,\infty)[/tex]
C
Step-by-step explanation:
Please refer to the graph.
Recall that the domain is the span of x-values covered by the graph, while the range is the span of y-values covered by the graph.
So we have the equation.
[tex]y=(x+3)^2-5[/tex]
This is a quadratic.
The domain of a quadratic is all real numbers. If you look at the graph, we can also see that the x-values will go on infinitely in both direction.
In interval notation, this is:
[tex](-\infty,\infty)[/tex]
For the range, note that the lowest the parabola goes is y=-5.
Therefore, our range is all values greater than or equal to -5.
In interval notation, this is:
[tex][-5,\infty)[/tex]
Note that we use brackets for the -5 because it is included in our range.
So, our answer is C
Answer:
Step-by-step explanation:
the domain and range of y = (x+3)^2 - 5
Doman: (-∞,∞). {x|x∈R}
Range:{-5,∞),{y|y≥-5}
the solution is C
7/9 x 1/2 =
what’s the answer guys
Answer:
0.388
Step-by-step explanation:
7/9 x 1/2 = 0.388