✎Question:Amirah is 4 years elder than Priya and Shirley is 2 years younger than Priya. If the sum of their ages is 47, find their respective ages ✔
Answer:
Priya's age = 15
Amirah's age = 19
Shirley's age = 13
Step-by-step explanation:
Let x be the age of Priya.
According to the question,
Amirah's age = x + 4
Shirley's age = x - 2
Their sum is 47.
So,
x + 4 + x + x - 2 = 47
3x + 2 = 47
3x = 47 - 2
3x = 45
x = 45/3
x = 15
So,
Priya's age = 15
Amirah's age = 15 + 4 = 19
Shirley's age = 15 - 2 = 13
Answer:
Priya is 15 years old
Amirah is 19 years old and
Shirley is 13 years old
Step-by-step explanation:
let Amirah =x
let Priya = y
let Shirley = s
so we have
x= 4+y
s=y-2
x+y+s =47
we have x= 4+y
4+y+y+s=47
4+2y+s=47
2y+s=43
s-y=-2 (MULTIPLY BY NEGATIVE 1)
y-s =2
2y+s= 43
by solving simultaneously we get
3y= 45
y=15
x= 4+y
x=19
s=y-2
s= 13
so Priya is 15 years old
Amirah is 19 years old and
Shirley is 13 years old
Please help with this
Answer:
[tex]S_{25}=555[/tex]
Step-by-step explanation:
Given that,
In an AP, the 6th term is 39 i.e.
[tex]a_6=a+5d\\\\39=a+5d\ ....(1)[/tex]
In the same AP, the 19th term is 7.8 i.e.
[tex]a_{19}=a+18d\\\\7.8=a+18d\ ......(2)[/tex]
Subtract equation (1) from (2).
7.8 - 39 = a+18d - (a+5d)
-31.2 = a +18d-a-5d
-31.2 = 13d
d = -2.4
Put the value of d in equation (!).
39 = a+5(-2.4)
39 = a- 12
a = 39+12
a = 51
The sum of n terms of an AP is given by :
[tex]S_n=\dfrac{n}{2}[2a+(n-1)d][/tex]
Put n = 25 and respected values,
[tex]S_{25}=\dfrac{25}{2}[2(51)+24(-2.4)]\\\\=555[/tex]
Hence, the sum of first 25 terms of the AP is equal to 555.
Prove that the sum of three successive even integers is always a multiple of 6.
Answer:
if you see three consecutive numbers you can figure out that at least one of them is divisible by 6
Step-by-step explanation:
you can use mathematical induction by proving it mathematically. for a number to be divisible by 6, it should be divisible by 2. Since all are even numbers the number will be divisible by 2.
Beryllium is an extremely lightweight metal that is used in many industries, such as aerospace and electronics. Long-term exposure to beryllium can cause people to become sensitized. Once an individual is sensitized, continued exposure can result in chronic beryllium disease, which involves scarring of the lungs. In a study of the effects of exposure to beryllium disease, which involves scarring of the lungs. In a study of the effects of exposure to beryllium, workers were categorized by their duration of exposure (in years) and by their disease status (diseased, sensitized, or normal.) The results were as follows:
Duration of Exposure
< 1 1 to < 5 >= 5
Diseased 12 10 18
Sensitized 14 18 13
Normal 66 142 210
Required:
a. Compute the expected frequencies of diseased workers.
b. Compute the expected frequencies of sensitized workers.
c. How many degrees of freedom are there?
Answer:
1. Has been answered below
2. Degree of freedom is 4
Step-by-step explanation:
Row 1: 12+10+18 = 40
Row 2: 14+18+13 = 45
Row 3: 66+142+210 = 418
Grand total = 40+45+418 = 503
Column 1 : 12+14+66 = 92
Column 2: 10+18+142 = 170
Column 3: 18+13+210 = 241
Total = 92+170+241 = 503
Expected frequencies of diseased workers
92x40/503 = 7.316
170x40/503 = 13.52
241 x 40/503 = 19.165
Expected frequencies of sensitized workers
92x45/503 = 8.23
170x45/503 = 15.20
241x 45/503 = 21.56
2.
Degree of freedom
= (Number of row -1)(number of column - 1)
= 3-1 * 3-1
= 2x2
= 4
How many time does 217.39 go into 5000
Answer is in the photo. I can't attach it here, but I uploaded it to a file hosting. link below! Good Luck!
tinyurl.com/wpazsebu
which is the following is true about the graph of linear inequalities?
a.)it is a line
b.)it is a parabola
c.)it os a curve
d.)it is a half-plane
Answer:
d.) half-plane..
Reason:
A linear inequality divides the coordinate plane into two halves by a boundary line where one half represents the solutions of the inequality. The boundary line is dashed for > and < and solid for ≤ and ≥. The half-plane that is a solution to the inequality is usually shaded.
Tyler has to savings accounts that his grandparents opened for him . One of the accounts Pay 8% annual interest Where as the other pay 10% annual interest. If you have $700 more invested at 10% then you invested at 8%, how much do you have invested in each account If the total amount of interest You earn in a year is $106?
Tyler invested $___at 8%, and $___at 10%
What is the area of the triangle in the diagram?
theres no diagram given
If the polygon is translated 3 units down and 4 units left, what will the coordinates of the new image be? Use prime notation in expressing the new coordinates.
Answer:
A' (-2,-4) B' (-3,-7) C' (-1,-8) D' (1,-6)
Step-by-step explanation:
Just take it one point at a time and move each point down 3 and 4 left. Prime notation just means to put this little sign ' so it indicates that this is the new coordinate. So A was (2,-1) and A' (the new one) is (-2,-4)
Triangle RST reflectid over the x-and then translated 4 unita to the right What are the coordinates of the final image in its new position?
Answer:
R" (0,3)
S" (1,1)
T" (4,2)
Step-by-step explanation:
The reflection of the point (x, y) across the x-axis is the point (x, -y).
Translate right 4- add 4 to the x coordinate
R ( -4, -3 ) R' ( -4 , 3) R" ( 0 , 3)
S ( -3, -1) S' (-3 , 1) S" ( 1 , 1)
T ( 0 , -2) T' (0, 2) T" ( 4 , 2)
free BRAINLESS it could be youea
Anastasia went shopping for birthday gifts and bought three of the same board game. She also spent $9.75 on birthday cards. Anastasia spent a total of $69.60. What was the price of each board game?
Identify as indicating a linear function or quadratic function. f (x) = ax^2 + bx +c
Dan is randomly selecting an outfit to wear to school. He can choose from 3 shirts: blue striped, red striped, or white. He
can choose from 3 pairs of shorts: tan, blue, or plaid.
Determine whether each statement is true or false.
Select True or False for each statement.
The probability that Dan chooses a striped shirt and a pair of tan shorts is
O True
o
False
There are 6 possible outcomes in the sample space.
O
True
O
False
The probability that Dan chooses a striped shirt and a pair of blue shorts is
o
True
O False
There are 2 ways to choose a red striped shirt and a pair of tan shorts.
O True
O False
Answer:i dont know :(
Step-by-step explanation:
im sorry :(
Answer:
1. true
2. false
3. false
4. false
Step-by-step explanation:
hope this helps
please mark brainiest
please give 5 stars
thank you
Write an algebraic expression that illustrates the additive identity.
Answer:
Step-by-step explanation:
I hope this helped
A store manager decides to clear out
school supplies to make room for new
inventory. Now a $20 bookbag will be
on sale for only $9. What is the
discount, as a percentage?
A:55%
B:40%
C:45%
D:50%
Answer:
it would be A:55%
Step-by-step explanation
For percent, to make it easier try to turn it into a 100.
20x5=100
do the same to the 9.
9x5=45.
Now subtract 45 from 100.
100-45=55.
There was a discount of 55%.
need help please look at attachment
Answer:
y = 1/2x + 2
Step-by-step explanation:
Perpendicular slope = 1/2
( -2, 1)
y - y1 = m(x - x1)
y - 1 = 1/2(x + 2)
y - 1 = 1/2x + 1
y = 1/2x + 2
Answer:
y1=+/2/5+1
y1+/15
/1=+5/36
-2=1/-/12
I will give you b if your answer is correct I only mark first answer so please help me
Answer:
b
Step-by-step explanation:
Write the left side of the identity in terms of sine and cosine. Rewrite the numerator and denominator separately. (Do not simplify.) Simplify the fraction from the previous step such that both the fractions have the common denominator The expression from the previous step then simplifies to using what? A. Addition and a Reciprocal Identity B. Addition and a Pythagorean Identity
Answer:
[tex](a)[/tex] [tex]\frac{2}{cos\theta}/\frac{1}{sin\theta} + \frac{4sin\theta}{cos\theta} =6tan\theta[/tex]
[tex](b)[/tex] [tex]\frac{2sin\theta}{cos\theta} + \frac{4sin\theta}{cos\theta} =6tan\theta[/tex]
(c) Addition and Quotient identity
Step-by-step explanation:
Given
[tex]\frac{2sec\theta}{csc\theta} + \frac{4sin\theta}{cos\theta} =6tan\theta[/tex] --- The expression missing from the question
Solving (a): Write the left hand side in terms of sin and cosine
In trigonometry:
[tex]sec\theta = \frac{1}{cos\theta}[/tex]
and
[tex]csc\theta = \frac{1}{sin\theta}[/tex]
So, the expression becomes:
[tex]\frac{2 * \frac{1}{cos\theta}}{\frac{1}{sin\theta}} + \frac{4sin\theta}{cos\theta} =6tan\theta[/tex]
[tex]\frac{\frac{2}{cos\theta}}{\frac{1}{sin\theta}} + \frac{4sin\theta}{cos\theta} =6tan\theta[/tex]
Rewrite as:
[tex]\frac{2}{cos\theta}/\frac{1}{sin\theta} + \frac{4sin\theta}{cos\theta} =6tan\theta[/tex]
Solving (b): Simplify
[tex]\frac{2}{cos\theta}/\frac{1}{sin\theta} + \frac{4sin\theta}{cos\theta} =6tan\theta[/tex]
Change / to *
[tex]\frac{2}{cos\theta}*\frac{sin\theta}{1} + \frac{4sin\theta}{cos\theta} =6tan\theta[/tex]
[tex]\frac{2sin\theta}{cos\theta} + \frac{4sin\theta}{cos\theta} =6tan\theta[/tex]
Solving (c): The property used
To do this, we need to further simplify
[tex]\frac{2sin\theta}{cos\theta} + \frac{4sin\theta}{cos\theta} =6tan\theta[/tex]
Take LCM
[tex]\frac{2sin\theta+ 4sin\theta}{cos\theta} =6tan\theta[/tex]
Add the numerator
[tex]\frac{6sin\theta}{cos\theta} =6tan\theta[/tex]
Apply quotient identity
[tex]\frac{sin\theta}{cos\theta} = tan\theta[/tex]
This gives
[tex]\frac{6sin\theta}{cos\theta} = 6tan\theta[/tex]
Hence, the properties applied are:
Addition and Quotient identity
Which mode of transportation did you choose? Why?
Answer:
land
Step-by-step explanation:
because,bus are more comfortable and easier other transportation are dangerous than land transportation ❤️
hope i helped u
STD 10
maths
If the roots of the equation 9x2 – (2k – 5)x – 25 = 0 are additive inverse ( opposite),
then k = ………… .
(a) 0 (b) 1 (c) -5/2 (d) 5/2
Answer:
k = 5/2
Step-by-step explanation:
.....................
On Joe’s business trip, he spent $258.14 during the 5 day trip on meals. How much did he spend per day on meals, round to the nearest penny?
Answer:
$51.63
Step-by-step explanation:
Joe spent 5 days on the trip and spent $258.14 total on food. To find the cost for each day, divide 258.14 by 5.
258.14 / 5 ≈ 51.63
Need help please thanks
Answer:
6.
Just count the x's on the graph...
i have been struggling with this question for 30mins. if you answer it can you please show work? thank you
Answer:
a)22
Step-by-step explanation:
which situation shows a constant rate of change?
Answer: option D
Step-by-step explanation: just did it
C was wrong and showed option D was the correct answer
e)
2 Before you calculate these answers, first estimate the
a) 30 870 ÷49
b) 221 340 ÷17
c) 100 719÷ 279
d) 75 640 ÷310
Step-by-step explanation:
1.) 630
2.) 13020
3.) 361
4.) 244
Help Me Please.............................(7)
Answer:
Step-by-step explanation:
The first step contains the error.
2x - 10 = 22 Add 10 to both sides
+ 10 +10
2x = 32 Divide by 10
2x/2 = 32/2
x = 16
Robin weighs her math textbook and finds that it is 2 kilograms. How many grams does her textbook weigh?
Answer:
2000
Step-by-step explanation:
1 kilogram is 100 grams therefore 2 kilo grams is equal to 2000 grams
The word kilo means thousand in Greek and i think French
:)
Answer:
2,000 grams :)
Which expression is equivalent to -6(3x-3)?
O 2x+4
2
-3X-6
O 3 6
-18.X+ 12
- 15x+4
a person invests 6500 dollars in a bank. the bank pays 6.75% interest compounded semi-annually. to the nearest tenth of a year, how long must the person leave the money in the bank until it reaches 15700 dollars?
A = P(1+r/n)^nt
Answer:
t=13.28382 ≈ 13.3 years
It takes 13.3 years to amount $15700 from the principal $6500.
Given that, a person invests 6500 dollars in a bank. the bank pays 6.75% interest compounded semi-annually.
What is the compound interest?Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.
The formula used to find the compound interest = A = P(1+r/n)^nt
Now, 15700 =6500(1+6.75/2×100)^2t
⇒ 15700/6500=(1+6.75/200)^2t
⇒ 15700/6500=1.03375^2t
⇒ 2.415=1.03375^2t
Take the logarithm of both sides of the equation to remove the variable from the exponent.
Exact Form:
t=ln(2.415)/2ln(1.03375)
Decimal Form:
t=13.28141707
≈ 13.3 years
Therefore, it takes 13.3 years to amount $15700 from the principal $6500.
To learn more about the compound interest visit:
https://brainly.com/question/14295570.
#SPJ2