Answer:
The required numbers are 30 and 54.
Step-by-step explanation:
Let 'x' be the smaller numberLet 'y' be the larger numberGiven that one number is 24 more than the other, so
[tex]y = x + 24[/tex]
Given that the sum of the numbers is 84, so
[tex]x + y = 84[/tex]
so we have two equations
[tex]\begin{bmatrix}y=x+24\\ x+y=84\end{bmatrix}[/tex]
Arrange equation variables for elimination
[tex]\begin{bmatrix}y-x=24\\ y+x=84\end{bmatrix}[/tex]
subtracting the equartions
[tex]y+x=84[/tex]
[tex]-[/tex]
[tex]\underline{y-x=24}[/tex]
[tex]2x=60[/tex]
now solve 2x = 60 for x
[tex]2x=60[/tex]
Divide both sides by 2
[tex]\frac{2x}{2}=\frac{60}{2}[/tex]
Simplify
[tex]x=30[/tex]
For y - x = 24 plug in x = 30
[tex]y-30=24[/tex]
Add 30 to both sides
[tex]y-30+30=24+30[/tex]
Simplify
[tex]y=54[/tex]
Thus, the required numbers are 30 and 54.
Verification:
Given that one number is 24 more than the other, so
[tex]y = x + 24[/tex]
substitute x = 30
y = 30 + 24
y = 54
Thus, y is 24 more than x.
Given that the sum of the numbers is 84, so
[tex]x + y = 84[/tex]
sustitute x = 30 and y = 54
30 + 54 = 84
84 = 84
L.H.S = R.H.S
Thus, the sum of the numbers is indeed 84.
Find the solutions of each equation on the interval [0, 2π)
Answer/Step-by-step explanation:
Factor this. GCF=2
2(2cos2x+cos x-1)=0
2(2cos x -1)(cos x+1)=0 Set each factor equal to zero and solve
2cos x -1=0 Add 1 to both sides
2cos x =1 Divide by 2
cos x =1/2
x=π/3
x=5π/3
cos x+1=0 Subtract 1 from both sides
cos x=-1
x = π
Write an equation in slope-intercept form that describes the relationship between the number of minutes, x, and the amount charged, y.
Answer:
y = 1/20x + 6
Step-by-step explanation:
The number of minutes is your x-value. The amount charged is your y-value.
Let's convert the numbers in the table into coordinates.
(30, 7.5)
(120, 12)
(220, 17)
Now, we will take two points and use the slope formula to plug into the slope-intercept equation: y = mx + b
I chose the first and last points given. All three points do not lie on the same line, but using the first and last point should be closer to the line of best fit.
(30, 7.5) & (220, 17)
m = (y₂ - y₁) / (x₂ - x₁)
m = (17 - 7.5) / (220 - 30)
m = (9.5) / (190)
m = 0.05 = 5/100 = 1/20
m = 1/20
Plug m into your equation.
y = 1/20x + b
To find b, plug in a point for x and y.
17 = 1/20(220) + b
17 = 11 + b
b = 6
Plug b into your equation.
y = 1/20x + 6
Hope this helps!
10 Which value of x makes the inequality 3x+3 > 15
true?
A x= 5
B. x = 2
C. x= 3
D. x = 4
Answer:
A, x=5
Step-by-step explanation:
By simplifying the inequality we get:
The only answer that is greater than 4 is A.
Answer:
yes
Step-by-step explanation:
HELP EMERGANCY FAST ANSWERS TIME LIMIT
Assume Sheila's nominal salary increases from $42,000 in 2003 to $69,000 in 2004.
If the Deflator increased from 106 in 2003 to 109 in 2004 and the CPI increased
from 184 in 2003 to 190 in 2004, what was Sheila's percentage increase in real
income?
6
Answer:
E)
Step-by-step explanation:
1 - (69,000 / 42,000) = .64285 * 100% = 64.3%
find the highest common factor using prime factorization for 27y and 54y³
Given:
27y and 54y³
To find:
The highest common factor (HCF) using prime factorization.
Solution:
We have,
27y and 54y³
Using the prime factorization, we get
[tex]27y=3\cdot 3\cdot 3\cdot y[/tex]
[tex]54y^3=2\cdot 3\cdot 3\cdot 3\cdot y\cdot y\cdot y[/tex]
Now, the common prime factors are 3, 3, 3 and y. So,
[tex]HCF=3\cdot 3\cdot 3\cdot y[/tex]
[tex]HCF=27y[/tex]
Therefore, the highest common factor of the given terms is 27y.
Mark the best answer.
1. The grid map shows the location of
some places on a college campus.
What are the coordinates of the
dormitory? (8-1)
Library
Gymnasium
12 Student
Center
5 4 3 2
Dormitory
I.XI
10
2013
Academic
Hall
A (2.1)
B 12)
CK1-2)
D (2.1)
Answer:
it makes sense
Step-by-step explanation:
In a school,2/15 of the students are boys and the rest are girls .If the number of girls is 1950,Find 5he number of boys
Answer:
300
Step-by-step explanation:
A regular price bathing suit is $89.99. What is the new price if it on sale for 25% off the regular price?
Answer:
$67.49 and 1/4 of a cent
Step-by-step explanation:
25% of 89.99 = 224975
89.99-22.4975=67.4925
Answer:
25%=1/4 1/4 of 90= 22.5 90-22.5=67.5
Step-by-step explanation:
What is 36divided by 6.
Answer:
6
Step-by-step explanation:
It is six because 6x6=36
Cameron combined peanuts, cashews and walnuts to make a trail mix. The expression 16p+24c+32w represents the total number of nuts in the mix. Cameron wants to divide the trail mix into equal servings, but he does not know how many. Use factoring to write expressions that will help Cameron divide the trail mix into 4 servings or 8 servings.
72 nuts mix the trail 4 ➕ 8
Answer:
Step-by-step explanation:
How many points are needed to determine a straight line?
A. only one point
B. at least two points
C. at least three points
D. more than three points
Answer:
b
Step-by-step explanation:I hope this helps
Order this set of numbers from greatest to least. Then explain the order, referring to the number line in your explanation,
-1.79, 2 1/4, 2.54,-4
Write an equation in slope-intercept form of a line that has a slope of -2/3 and a y-intercept of 6.
respondo por qué el juego me lo diste 2+24
Answer:
y = -2/3x + 6Step-by-step explanation:
Equation in slope-intercept form:
y = mx + bSubstitute values:
y = -2/3x + 6Fionn observed that 91\%91%91, percent of the background checks he processes are for potential employees who have already interviewed. Let BBB be the number of background checks Fionn processes to get his first background check for a potential employee who has not yet interviewed for the job. Assume that the interview statuses are independent. Find the probability that the 8^{\text{th}}8 th 8, start superscript, start text, t, h, end text, end superscript background check that Fionn processes is the first for which the potential employee has not yet interviewed.
Answer:
0.05
Step-by-step explanation:
checked via khan academy
Rounding to the nearest hundredth, 0.06 = 6% probability that the first new customer places the 5th order.
What is probability?
Probability is the extent to which an event is likely to occur, measured by the ratio of the favourable cases to the whole number of cases possible.
We want to find that the first order placed by a new customer is the 5th.
We have that:
8% = 0.08 probability that an order is placed by a new customer.
1 - 0.08 = 0.92 = 92% probability that an order is placed by an old customer.
Probability that the first order placed by a new customer is the 5th:
First four all old, each with 0.92 probability.
Firth new, with 0.08 probability. So
[tex]p=(0.94)^4\times 0.08=0.0573[/tex]
Rounding to the nearest hundredth, 0.06 = 6% probability that the first new customer places the 5th order.
To know more about probability follow
https://brainly.com/question/24756209
#SPJ2
I NEED HELP PLSSSSSSS
'थूकेंगे' शब्द का वर्ण-विच्छेद कीजिए।
Answer:
English pls
Step-by-step explanation:
अन्यथा बहस करें, शिकायतें पकड़ें।
Plz help with the problem in the picture. Thanks
Answer: x(0,0)y(0,0) tell me more I don't really understand it
x=3.4
Step-by-step explanation:
8/15-1/5
For points or brainliest
Answer:
1/3
Step-by-step explanation:
The answer is 1/3 to find out how look at the picture above!
3) A sample of 42 grams of an unknown substance has a half-life of 1,300 years.
(a) Write an equation to determine the amount of substance, S, left after t years.
(b) Approximately how long will it take for 0.2 grams of substance to remain (to the nearest year)?
Answer:
a) [tex]S(t) = 42(0.9995)^t[/tex]
b) It will take 10,692 years.
Step-by-step explanation:
Exponential function to determine the amount of substance:
An exponential function to determine the amout of substance after t years is given by:
[tex]A(t) = A(0)(1-r)^{t}[/tex]
In which A(0) is the initial amount and r is the decay rate, as a decimal.
(a) Write an equation to determine the amount of substance, S, left after t years.
Half-life of 1300 years means that [tex]A(1300) = 0.5A(0)[/tex].
We use this to find r. So
[tex]A(t) = A(0)(1-r)^{t}[/tex]
[tex]0.5A(0) = A(0)(1-r)^{1300}[/tex]
[tex](1-r)^{1300} = 0.5[/tex]
[tex]\sqrt[1300]{(1-r)^{1300}} = \sqrt[1300]{0.5}[/tex]
[tex]1 - r = 0.9995[/tex]
[tex]r = 0.0005[/tex]
Sample of 42 grams means that [tex]A(0) = 42[/tex]. So
[tex]A(t) = A(0)(1-r)^{t}[/tex]
Replacing A by S, just for notation purposes
[tex]S(t) = 42(0.9995)^t[/tex]
(b) Approximately how long will it take for 0.2 grams of substance to remain (to the nearest year)?
This is t when [tex]S(t) = 0.2[/tex]. So
[tex]S(t) = 42(0.9995)^t[/tex]
[tex]0.2 = 42(0.9995)^t[/tex]
[tex](0.9995)^t = \frac{0.2}{42}[/tex]
[tex]\log{(0.9995)^t} = \log{\frac{0.2}{42}}[/tex]
[tex]t\log{0.9995} = \log{\frac{0.2}{42}}[/tex]
[tex]t = \frac{\log{\frac{0.2}{42}}}{\log{0.9995}}[/tex]
[tex]t = 10692[/tex]
It will take 10,692 years.
Write an equation that shows the relationship 40% of 140 is x
Answer:
x=140times0.4
Step-by-step explanation:
then subtract your anser from 140
An elementary school class ran 1 mile in an average of 11 minutes with a standard deviation of 3 minutes. Rachel, a student in the class, ran 1 mile in 8 minutes. A junior high school class ran 1 mile in an average of 9 minutes, with a standard deviation of 2 minutes. Kenji, a student in the class, ran 1 mile in 8.5 minutes. A high school class ran 1 mile in an average of 7 minutes with a standard deviation of 4 minutes. Nedda, a student in the class, ran 1 mile in 8 minutes.
Required:
a. Why is Kenji considered a better runner than Nedda, even though Nedda ran faster than he?
b. Who is the fastest runner with respect to his or her class? Explain why.
Answer:
Step-by-step explanation:
a.
Kenji ran faster than the class average by 0.25 of a standard deviation while Nedda was slower than the average in her class.
b.
Rachel: average - 1st deviation
Kenji: average - 0.25 standard deviation
Nedda: slower than average so it's definitely not her.
Since Rachel is faster than the average and differs by the most standard deviations compared with Kenji,
So, Rachel is the faster one.
x + 5 x < -2 4 – x2 -2
x2 < −6x − 26
x < -x2/6 - 13/3
a bottle of orange juice holds for 4/6 quarts of juice. a bottle of pineapple juice holds 2/3 quarts of juice. which bottle has more juice
Answer:
the orange juice has more ounces than the pineepple juice
Step-by-step explanation:
Kaitlin has four and two-thirds berry pies. She is going to share it equally among 12 people. How much pies will each person get?
Answer:
7/18
Step-by-step explanation:
4 2/3=14/3
(14/3)/12=14/36
reduces to
7/18
please tell fast plzzzzzz
Answer:
72 degrees
Step-by-step explanation:
let the ratio be 2x and 3x
2x + 3x =180° ( co interior angles )
5x = 180°
x = 180 ÷ 5
x = 36°
And the smaller angle = 2 × 36° = 72°
Directions: Find each product. Show your solution. .
1) 0.35 x 24 =
2) 0.59 x 29 =
3) 2.45 x 5 =
4) 0.84 x 3 =
5) 0.45 ~ 63=
6) 3.54 x 0.59=
7) 5.28 x 1.18 =
8) 4.37 x 0.58 =
9) 7,05 * 0.52 =
10) 2.36 x 1.28=
[tex]0.35 \times 24 = [/tex]
Answer:
.
1) 0.35 x 24 =8.4
2) 0.59 x 29 =17.11
3) 2.45 x 5 =12.25
4) 0.84 x 3 =2.52
5) 0.45 ×63=28.35
6) 3.54 x 0.59=2.0886
7) 5.28 x 1.18 =6.2304
8) 4.37 x 0.58 =2.5346
9) 7.05 * 0.52 =3.666
10) 2.36 x 1.28=3.0208
[tex]0.35 \times 24 = [/tex]=8.4
Answer:
1) 8.4
2) 17.11
3) 12.25
4) 2.52
5) 28.35 (if numbers are multiplied)
6) 2.0886
7) 6.2304
8) 2.5346
9) 3.666
10) 3.0208
234.2 in expanded form
Answer:
Expanded Notation Form:
234.2
=
200
+
30
+
4
+
0.2
Expanded Factors Form:
234.2
=
2 ×
100
+
3 ×
10
+
4 ×
1
+
2 ×
0.1
Expanded Exponential Form:
234.2 =
2 × 102
+
3 × 101
+
4 × 100
+
2 × 10-1
Word Form:
234.2 =
two hundred thirty-four and two tenths
Milo has 5 rocks in his rock collection. He finds 40 rocks outside that he wants to put in his collection. If he places the rocks into boxes of 9, how many boxes of rocks will he have in his collection?
Answer:
puto el que lo lea
Step-by-step explanation:
jajajaja lol no
Answer:
5
Step-by-step explanation:
40+5=45. 45/9=5
Will mark Brainlyist help me fill out the chart
Answer:
The working is done in the image attached.
what is the Multiplicative of -12
multiplicative would be ;
-12 ------> 1/-12