Answer:
The probability that the person will not be a senior
P(E⁻) = 1 - P(E)
= [tex]1- \frac{5}{9} = \frac{4}{9}[/tex]
Step-by-step explanation:
Explanation:-
Given A high school club has 10 members who are seniors and 8 members who are juniors
n(S) = 10 + 8 = 18
If a member is randomly selected to be the club president
Let 'E' be the event that the person will be a senior
The probability that the person will be a senior
[tex]P(E) = \frac{n(E)}{n(S)}[/tex]
[tex]P(E) = \frac{n(E)}{n(S)} = \frac{10}{18} = \frac{5}{9}[/tex]
The probability that the person will not be a senior
P(E⁻) = 1 - P(E)
= [tex]1- \frac{5}{9} = \frac{4}{9}[/tex]
1.)
a^2b^3
---------- <-----write in expanded form.
cd
2.)what is the exact solution to the equation 4^5x=3^x-2
Please show all work I've been struggling to understand these questions!!!! thank you so much <3
Answer:
1. Expanded form of [tex]a^{2} . b^{3}[/tex] = (a.a).(b.b.b)
2.Exact solution x = -0.376
Step-by-step explanation:
Solution:
First we have to write the Expanded Form of [tex]a^{2} . b^{3}[/tex], Let's do it.
1) [tex]a^{2} . b^{3}[/tex] = (a.a).(b.b.b)
Hence,
Expanded form of [tex]a^{2} . b^{3}[/tex] = (a.a).(b.b.b)
2) [tex]4^{5x} = 3^{x-2}[/tex]
Now, we have to find out the exact solution of the above equation:
In order to equate the exponents, we need to make sure the bases are same. Or we simply can use logarithm to solve the above equation.
So,
We are using logarithm to solve this equation.
Let's break this down:
[tex]4^{5x} = 3^{x-2}[/tex]
Taking log on both sides.
log[tex]4^{5x}[/tex] = log[tex]3^{x-2}[/tex]
[tex]5xlog(4)[/tex] = [tex](x-2)log(3)[/tex]
Dividing both sides by log(4)
[tex]5x[/tex] = (x-2) [tex]\frac{log(3)}{log(4)}[/tex]
value of log(3) = 0.4771
value of log(4) = 0.6020
[tex]5x[/tex] = (x-2) [tex]\frac{log(0.4771)}{log(0.6020)}[/tex] =
5x = (x-2)0.792
5x = 0.792x - 1.584
by rearranging the equation, we get:
0.792x - 5x = 1.584
x(0.792 - 5) = 1.584
x(-4.208) = 1.584
x = -1.584/4.208
x = -0.376
Exact solution x = -0.376
What are some things to be aware of that can lead to higher than expected totals when making a purchase or checking out
Answer:
taxes
Step-by-step explanation:
Taxes, shipping (if checkout is online), and false advertisements.
Please someone help:)
Answer:
Im lost to lol mark brainlest imagine
Please help me. Thank you...
9514 1404 393
Answer:
V = (x)(10-2x)² . . . . factored form
V = 4x³ -40x² +100x . . . . standard form
Step-by-step explanation:
A square with corners cut out has no volume. It is a plane figure.
__
We presume you are interested in the volume of the open-top box obtained by folding up each "ear" of the cut figure. The length of each side of its square bottom is 10-2x. The depth of the box is x. So, the volume is ...
V = LWH = (10-2x)(10-2x)(x)
V = x(10 -2x)²
_____
The graph shows the volume is a maximum when x = 1 2/3 cm.
Jake organizes 48 marbles into packs. He places the same number of marbles into each pack. How
could he arrange the marbles?
Answer:
10 to 12
Step-by-step explanation:
12 times 4 is 48
ben made 14 field goal he made about 74% how many did he try
can u pls help me with this question asap
Answer:
.
Step-by-step explanation:
Answer:
0.0025
Step-by-step explanation:
HELP FAST!!!! Please
A plane passes through this three-dimensional figure parallel to its base. Which shape represents the cross section that is created.
Answer:
c
Step-by-step explanation:
hope it helpp
Combine like terms to simplify the expression:
2/5k-3/5+1/10k
Answer:
1/2k-3/5
Step-by-step explanation:
Answer:
Step-by-step explanation:
2/5 k - 3/5 + 1/10 k
like denominators
4/10 k + 1/10 k - 3/5
5/10k - 3/5
1/2k - 3/5
Translate the shape by the vector { -1 }
5
Answer:
Step-by-step explanation:
Coordinates of the given rectangle are,
A → (3, 3)
B → (6, 3)
C → (6, 1)
D → (3, 1)
Translation of the given rectangle by the vector [tex]\binom{-1}{5}[/tex] means, shifting of rectangle by 1 unit to the left and 5 units up.
So the rule which defines the translation of the vertices by the given vector is,
(x, y) → (x - 1, y + 5)
By this rule, after translation vertices of image rectangle will be,
A(3, 3) → A'(2, 8)
B(6, 3) → B'(5, 8)
C(6, 1) → C'(5, 6)
D(3, 1) → D'(2, 6)
What is the constant of proportionality for the table? What does it represent? Reminder: k= y/x
Answer:
The constant of proportionality is 5. It represents the cups of yellow paint needed for 1 cup of blue paint.
Premium gasoline costs $4.33 per gallon. Noni's car holds 11.6 gallons of gas. What is the estimated cost of filling the tank of Noni's car?
A. $12
B. $48
C. $56
D. $60
Answer:
It is (B) $48
Step-by-step explanation:
I just finished the unit test and got it right :D
Can someone answer this?:(( I really need it
Answer:
What lesson in math is this?
Step-by-step explanation:
So that I can search it and then help you
Xinran walks 3 mi/h uphill, 4 mi/h on flat land and 5 mi/h downhill. If he walks one mile uphill, then one mile on flat land and then returns by the same route to his starting point, how many minutes does he walk?
Given :
Xinran walks 3 mi/h uphill, 4 mi/h on flat land and 5 mi/h downhill.
To Find :
If he walks one mile uphill, then one mile on flat land and then returns by the same route to his starting point, how many minutes does he walk.
Solution :
Time taken to walk one mile uphill is :
[tex]t_1 = \dfrac{1}{3}\ hours[/tex]
Time taken to walk two mile on flat land( one on going and one or returning ) is :
[tex]t_2 = \dfrac{2}{4}\ hours\\\\ t_2 = \dfrac{1}{2}\ hours[/tex]
Time taken to walk one mile downhill is :
[tex]t_3 = \dfrac{1}{5}\ hours[/tex]
Total time taken :
[tex]T = t_1 + t_2 + t_3 \\\\T = \dfrac{1}{3} + \dfrac{1}{2}+\dfrac{1}{5}\\\\T = \dfrac{10 + 15 + 6}{30} \\\\T = \dfrac{31}{30}\ hours = \dfrac{31}{30}\times 60 \ minutes\\\\T = 62\ minutes[/tex]
Therefore, time taken un 62 minutes.
A population is of size 5,500 observations. When the data are represented in a relative frequency distribution, the relative frequency of a given interval is 0.15. The frequency in this interval is equal to:
Answer:
825
Step-by-step explanation:
Calculation for what The frequency in this interval is equal to:
Using this formula
Frequency=Population size*Relative frequency interval
Let plug in the formula
Frequency=5,500 observations*0.15
Frequency=825
ThereforeThe frequency in this interval is equal to:825
The frequency in this interval is equal to 825.
Given
A population is of size 5,500 observations.
When the data are represented in a relative frequency distribution, the relative frequency of a given interval is 0.15.
Frequency;The frequency is defined as the product of population size and relative frequency interval.
The following formula is used to calculate frequency in this interval is;
[tex]\rm Frequency= Population\ size\times Relative\ frequency \ interval\\\\[/tex]
Substitute all the values in the formula;
[tex]\rm Frequency= Population\ size\times Relative\ frequency \ interval\\\\Frequency= 5500\times 0.15\\\\Frequency= 55\times 15\\\\Frequency= 825[/tex]
Hence, the frequency in this interval is equal to 825.
To know more about relative frequency click the link given below.
https://brainly.com/question/8972639
Which expression is equivalent to 9 + 8?
A. 3 to the power of 3 + 2 to the power of 4
B. 3 to the power of 2 + 2 to the power of 3
C. 3 to the power of 2 + 2 to the power of 3
D. 3 to the power of 3 + 2 to the power of 3
Answer:
i think it is A
Step-by-step explanation:
Katie's deli can make 60 sandwiches in 4 hours. Stacy's can make double that in the same amount of time. How many sandwiches can Stacy's deli make in 6 hours
Answer:
Step-by-step explanation:
Answer: 150 sandwhiches
Step-by-step explanation: 60 sandwhiches in 4 hours. 15 sandwhiches per hour so you add 30 to the doulbe of 60 which is 120 then you add 30
Need help pls will put u brainliest
Use slopes to determine whether the lines AB and CD are parallel, perpendicular, or neither. SHOW WORK
A(-10, 8) and B (-9,4).
C (-5, 12) and D (2,9).
Answer:
Neither
Step-by-step explanation:
Slope for AB is -4
Slope for CD is -3/7
in order to find the slope use this formula attached
AB -9-(-10) / 4-8 = -4 your y2 is 4 your y1 is 8 / x2 is -9 x1 is -10
CD 9-12 / 2-(-5) your y2 is 9 your y1 is 12 / x2 is 2 x1 is -5
Answer: The lines will be neither
Line A is Purple dot
Line B is Blue dot
Line C is Red dot
Line D is Green dot
PLS HELP ME ILL MARK BRAINLIST IF SOMEONE CAN HELP ME WITH THESE 2 QUESTIONS!!
1. Andrew grew 1 3/4 inches last year. This year he grew 2 2/3 inches. What was his total growth for the two years?
-
2. Abbey rode her bike for 1 3/4 hours on Saturday and 1 5/8 hours on Sunday. What is the total amount of time she rode her bike on these two days ?
Answer:
1. Andrew grew 4 5/12 inches in 2 years
2. Abbey rode her bike for 3 3/8 hours in 2 days.
Step-by-step explanation:
When adding fractions you must have a common denominator for both of them.
First make the mixed fraction, improper fractions.
1 3/4 = 7/4
2 2/3 = 8/3
7/4 x 3/3 = 21/12
8/3 x 4/4 = 32/12
21 + 32 = 53
53/12 = 4 5/12
1 3/4 = 7/4
1 5/8 = 13/8
7/4 x 4/4 = 28/16
13/8 x 2/2 = 26/16
26 + 28 = 54
54/16 = 3 3/8
I hope this helped and if it did I would appreciate it if you marked me Brainliest. Thank you and have a nice day!
3/2 as a mixed number
Answer:
Divide using long division. The whole number portion will be the number of times the denominator of the original fraction divides evenly into the numerator of the original fraction, and the fraction portion of the mixed number will be the remainder of the original fraction division over the denominator of the original fraction.
1 1/2
Step-by-step explanation:
not eleven one and 1 half
Answer:
0 whole 3 upon 2
0[tex]\frac{3}{2}[/tex]
What is the product?
3.[ 1 -4 5 -7]
a. [3 -12 15 -21]
b. [4 -1 8 -4]
c. [3 12 15 21]
d. [4 -12 8 -21]
Answer:
(a) [3 -12 15 -21]
Step-by-step explanation:
Given;
3.[ 1 -4 5 -7]
The product of the function is calculated as;
3.[ 1 -4 5 -7] = [1 x 3 -4x3 5x3 -7x3]
= [3 -12 15 -21]
Therefore the correct option is "a" [3 -12 15 -21]
how to tell if your answer is reasonable
Answeri dont now
Step-by-step explanation:
10. The Johnson family purchased a new television that had a 62 inch diagonal. The height of the television was 30 inches. Approximately how wide is the new television? show work
Answer:
Width = 54.3 inches
Step-by-step explanation:
We solve this question using the Pythagoras Theorem
Width² + Height² = Diagonal²
From the above question
Width= ??
Height = 30 inches
Diagonal = 62 inches
Width² + 30² = 62²
Width² = 62² - 30²
Width = √62² - 30²
Width =✓2944
Width = 54.258639865 inches
Approximately
Width = 54.3 inches
Hence, the new television was 54.3 inches wide.
Kevin Durant's free throw
percentage is about 88%. If he
shoots 75 free throws at
practice, how many would you
expect him to make?
Answer:
66
Step-by-step explanation:
88% of 75
66
What is the rate of change And initial value for the linear relationship that includes the points shown in the table
Answer:
Multiply them and then add them altogether
so
Step-by-step explanation:
2x3=6
4x5=20
6x7=42
8x9=72
6+20+42+72= 140
6+20=26
26+42=68
68+72= 140
Solve for x.
14 + 3x = 2 + 9x
You don’t have to do an explanation
Answer:
x=2
Step-by-step explanation:
Answer:
X=2
Step-by-step explanation:
Melissa is 13 years old. Becky is 12 years old. Daniel is 10 years old. Melissa, Becky and Daniel share £42 in the ratio of their ages. Becky decided to save a third of her share. How much will Becky have to spend?
Answer: Becky will have to spend £ 9.6 .
Step-by-step explanation:
The ratio of their ages will be:
Melissa : Becky : Daniel = 13 : 12 : 10
Total amount share = £42
Share of Becky = [tex]\dfrac{12}{12+13+10}\times42[/tex]
[tex]=\dfrac{12}{35}\times42\\\\= 14.4[/tex]
Hence, Becky's share = £14.4
Becky decided to save a third of her share.
Then, Amount she spend = [tex]14.4-\dfrac13 \times 14.4[/tex]
[tex]=14.4-4.8\\=9.6[/tex]
hence, Becky will have to spend £ 9.6 .
2x - 4
——— =4
5
Pls solve
Step-by-step explanation:
cross multiply
2x - 4 = 4 × 5
2x - 4 =20
collect like terms (CLT)
2x = 20 + 4
2x=24
divide both sides by 2
x=12
Solve the system by substitution.
x - 5y = 1
- 2x + 9y = -1
what is the solution?
Answer:
x = − 4 .y = − 1
Step-by-step explanation: