Answer:
Step-by-step explanation:
p/100* 400=80
*100 *100
400p=8000
:400 :400
p=20
With 5% significant level I think we consider that 22% likes the drink
PLEASE HELP!! 2. Helen and Stephen both simplify the exponential expression .
Helen:
Stephen:
Unfortunately, they both made an error. Identify where each person made his or her error and explain in words what he or she did wrong. Then, correctly simplify the expression.
Answer:
We start with the expression:
exp( (4/3)*ln(2) - 1)
Here we can use that:
exp(ln(x)) = x.
and e^(a + b) = e^a*e^b.
the first step here is:
e^((4/3)*ln(2) - 1) = e^((4/3)*ln(2)*e^(-1)
So the first step of Stephen is correct, but the first step of helen is not, you can not simplify the expression in that way.
now, we have that:
a*ln(x) = ln(x^a)
then we can write:
(4/3)*ln(2) = ln(2^(4/3))
and e^(ln(2^(4/3)) = 2^(4/3)
then we have:
e^((4/3)*ln(2)*e^(-1) = 2^(4/3)/e
now we can write this as:
∛(2^4)/e
here is where stephen makes the mistake, he uses the 4 in the rooth and the 3 in the power.
so the expression actually is:
∛(16)/e
Please answer this correctly
Answer:
1/2
Step-by-step explanation:
The non-even numbers are 1, 3, and 5 on the dice.
3 numbers out of 6.
3/6 = 1/2
Answer:
1/2
Step-by-step explanation:
Total sides of 6-sided die = 6
Numbers not even = 3
Probability of not getting an even = 3/6
=> 1/2
Which of the following is parallel to
2Y = 6X + 4?
A. Y = -3X + 3
B. Y = 3X + 4
C. Y = x + 3
D. Y = -2X - 3
E. Y= 1/2 X + 3
Answer:
B. y = 3x + 4
Step-by-step explanation:
Step 1: Find slope-intercept form of 1st equation
2y = 6x + 4
2y/2 = 6x/2 + 4/2
y = 3x + 2
A parallel line has the same slope but different y-intercept:
y = -3x + 3 (No, different slope)
y = 3x + 4 (Yes, same slope, different y-int)
y = x + 3 (No, different slope)
y = -2x - 3 (No, different slope)
y = 1/2x + 3 (No, different slope)
Vickie buys a pack of 30 folders. She keeps 15 for herself and divides the rest between three of her friends. Which equation will help us find the number of folders each friend gets? *
Answer: 30 folders - 15 folders which she keeps = 15 folders; 15 folders / 3 friends = 5 folders per firend.
Step-by-step explanation:
Answer:
x= (30 -15)/3
Step-by-step explanation:
Number of folders = 30Kept for herself = 15 foldersDivided = the reminderNumber of friends= 3Each friend gets= ?If we call x the number each friend gets, then the equation is:
x= (30 -15)/3Solving this we get:
x= 5Each friend gets 5 folders
If 7 out of 10 people brush thier teeth every night, which of the following represents the percent of people who do not brush thier teeth every night?
Answer: 30 percent of people who do not brush theit teeth every night.
Step-by-step explanation:
Given : 7 out of 10 people brush their teeth every night.
That means 3 out of 10 people do not brush their teeth every night. (7-10=3)
Now, the percent of people who do not brush their teeth every night = [tex]\dfrac{\text{Number of people do not brush their teeth}}{\text{Total people}}\times100\%[/tex]
[tex]=\dfrac{3}{10}\times100\%\\\\=30\%[/tex]
Hence, 30 percent of people who do not brush theit teeth every night.
I need help pleaseee!!
Answer:
(x - [-1])² + (y - [-1])² = [13]
Step-by-step explanation:
If P and Q are the end-points of the diameter PQ, midpoint of the segment PQ will be the center of the circle. (Definition of the center of a circle)
Midpoint of a segment having extreme ends [tex](x_1, y_1)[/tex] and [tex](x_2,y_2)[/tex]
Coordinates of the center = [tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]
Since, extreme ends of the diameter are P(-4, -3) and Q(2, 1)
Center of the circle = [tex](\frac{-4+2}{2},\frac{-3+1}{2} )[/tex]
= (-1, -1)
Radius of the circle = Distance between the center and Q,
Since distance between the two points [tex](x_1, y_1)[/tex] and [tex](x_2,y_2)[/tex] is,
d = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Radius of the circle = [tex]\sqrt{(-1-2)^2+(-1-1)^2}[/tex]
= [tex]\sqrt{9+4}[/tex]
= [tex]\sqrt{13}[/tex]
Equation of the circle will be,
(x - h)² + (y - k)² = r²
Where (h, k) is the center and 'r' is the radius of the circle,
(x - [-1])² + (y - [-1])² = [13]
please simplfy this equation
Answer:
0
Step-by-step explanation:
√12 can be rewritten as √2²·3 = 2√3
√75 can be rewritten as √5²·3 = 5√3
2/5 * 5 = 2
so
2√3 - 2/5 * 5√3 = 2√3 - 2√3 = 0
Answer:
0
Step-by-step explanation:
Transformation of exponential functions
Answer:
first option
Step-by-step explanation:
It's up by 4 units because because the +4 is outside of the exponent and also, it is a +4 not -4 which indicates that the translation is up.
Help me find volume for this given radius please
Answer:
see below
Step-by-step explanation:
The volume of a sphere is given by
V = 4/3 pi r^3
= 4/3 pi ( 7)^3
= 1372/3 pi in^3
Using 3.14 for pi
V =1436.0266666 in^3
Using the pi button
1436.75504 in^3
Try it
Evaluate the function g(x) = -2x² + 3x – 5 for the input values -2, 0, and 3.
g(-2) = -2(-2)2 + 3(-2) - 5
g(-2) = -2(4) - 6-5
g(-2) = ?
g(0) =?
g(3) =?
Answer:
g(-2) = -19g(0) = -5g(3) = -14Step-by-step explanation:
When you have several evaluations to do, it is often convenient to put the formula into a graphing calculator or spreadsheet.
__
If you must evaluate a polynomial by hand, it is often easier if the expression is written in "Horner form":
g(x) = (-2x +3)x -5
Then we have ...
g(-2) = (-2(-2) +3)(-2) -5 = 7(-2) -5 = -19
g(0) = (-2(0) +3)(0) -5 = -5
g(3) = (-2(3) +3)(3) -5 = (-3)(3) -5 = -14
The four-member math team at Pecanridge Middle School is chosen from the math club, which has three girls and five boys. How many different teams made up of two girls and two boys could be chosen?
Answer:
30 ways
Step-by-step explanation:
Given the following :
Number of boys in school (n1) = 5
Number of girls in school (n2) = 3
Total number of team members to be selected = 4
Number of boys required in team(r1) = 2
Number of girls required in team(r2) = 2
How many different teams made up of two girls and two boys could be chosen?
= (2 boys from 5) * (2 girls from 3)
Using combination :
5C2 * 3C2
Recall :
nCr = n! ÷ (n-r)! r!
5C2 = 5! ÷ (5-2)! 2!
5C2 = 5! ÷ 3!2!
5C2 = (5*4) / 2 * 1 = 10ways
3C2 = 3! ÷ (3-2)! 2!
3C2 = 3! ÷ 1!2!
3C2 = (3) / 1 = 3ways
3C2 = 3/1 = 3ways
10 * 3 = 30 ways
Which of the following answer choice is a possible solution to the inequality 4y>10?
A. 7
B. 1/4
C. 2
Please prove your answer.
Answer:
(A) 7
Step-by-step explanation:
[tex] 4y > 10[/tex]
[tex]y > \frac{10}{4} [/tex]
[tex]y > 2.5[/tex]
Since Y is more than 2.5,
the only possible solution is 7, which is (A)
Point C ∈
AB
and AB = 33 cm. Point C is 2 times farther from point B than point C is from point A. Find AC and CB.
Answer:
AC = cm, CB = cm
Answer:
AC: 11 cmCB: 22 cmStep-by-step explanation:
Given:
AC + CB = 33
CB = 2AC
Find:
AC, CB
Solution:
Using substitution, we have ...
AC +2AC = 33
AC = 33/3 = 11
CB = 2·11 = 22
AC = 11 cm; CB = 22 cm.
Solve by completing the square: 5x2 + 20x + 32 = 0
PLEASE ANSWER FAST!! THANK YOU :)
Answer:
option 1 both statements are true
Step-by-step explanation:
Prove by PMI -- Principle of Mathematical Induction
1) n³ + 2n
n= 1 , 1³ +2*1 = 1+2 = 3 = 3*1 ---->divisible by 3
n = 2 ; 2³ + 2*2 = 8+4 = 12 = 3*4 ----> is divisible by 3
Assume that It is valid for n = k ;
[tex]k^{3}+2k[/tex] = 3*m -----(I) , for all m ∈ N
We have to prove for n =k +1 , the statement is true.
n = k+1, [tex](k+1)^{3}+2(k +1) =k^{3}+3k^{2}+3k +1 +2k +2[/tex]
= k³ + 3k² + 3k + 3 + 2k
= k³ + 2k + 3k² + 3k + 3
= 3m + 3 (k² + k + 1)
= 3(3 + [k² + k + 1] ) is divisible by 3
Therefore, this statement is true
2) [tex]5^{2n}-1\\[/tex]
[tex]n=1 ; 5^{2}-1 = 25 -1 = 24 divisible by 24\\\\n = 2 ; 5^{2*2}-1 = 5^{4}-1 = 625 - 1 = 624 divisible by 24[/tex]
This statement is also true
Please answer this correctly
Answer:
2/5
Step-by-step explanation:
Let's find the probability of each condition first.
For P(4), there is only one option: 4. This is 1 out of 5.
For P(even), this includes 4 and 6. However, we already had 4 from our last condition so we can remove this option. This is again 1 out of 5.
Adding them together, we will get 2/5.
The answer is 2/5
What is the answer? ACB ~ EFD
Answer:
y=4solution,
[tex] \frac{ac}{ef} = \frac{cb}{fd} \\ or \: \: \frac{12}{y} = \frac{15}{5} \\ or \: 15 \times y = 12 \times 5( \: cross \: multiplication) \\ or \: 15y = 60 \\ or \: y = \frac{60}{15} \\ y = 4[/tex]
Hope this helps...
Good luck on your assignment..
Answer:
The value of y is 4
Step-by-step explanation:
What is similarity ?
In Euclidean geometry, two objects are similar if they have the same shape, or one has the same shape as the mirror image of the other.
Given,
ΔACB~ΔEFD
The proportional sides are equal.
[tex]\frac{AC}{EF}=\frac{CB}{FD}=\frac{AB}{DE} \\\frac{12}{y}=\frac{15}{5} \\y=12*\frac{5}{15}\\\\ y=4[/tex]
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A human resources specialist is investigating a government claim that the unemployment rate is less than 5%. To test this claim, a random sample of 1500 people is taken and its determined that 61 people are unemployed. The following is the setup for this hypothesis test:
H0:p=0.05
Ha:p<0.05
Find the p-value for this hypothesis test for a proportion and round your answer to 3 decimal places.
The following table can be utilized which provides areas under the Standard Normal Curve:
z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
-1.8 0.036 0.035 0.034 0.034 0.033 0.032 0.031 0.031 0.030 0.029
-1.7 0.045 0.044 0.043 0.042 0.041 0.040 0.039 0.038 0.038 0.037
-1.6 0.055 0.054 0.053 0.052 0.051 0.049 0.048 0.047 0.046 0.046
-1.5 0.067 0.066 0.064 0.063 0.062 0.061 0.059 0.058 0.057 0.056
-1.4 0.081 0.079 0.078 0.076 0.075 0.074 0.072 0.071 0.069 0.068
Answer:
P-value =0.062
At a signficance level of 0.05, there is not enough evidence to support the claim that the unemployment rate is less than 5%.
Step-by-step explanation:
This is a hypothesis test for a proportion.
The claim is that the unemployment rate is less than 5%.
Then, the null and alternative hypothesis are:
[tex]H_0: \pi=0.05\\\\H_a:\pi<0.05[/tex]
The significance level is 0.05.
The sample has a size n=1500.
The sample proportion is p=0.041.
[tex]p=X/n=61/1500=0.041[/tex]
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.05*0.95}{1500}}\\\\\\ \sigma_p=\sqrt{0.000032}=0.0056[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p-\pi+0.5/n}{\sigma_p}=\dfrac{0.041-0.05+0.5/1500}{0.0056}=\dfrac{-0.0087}{0.0056}=-1.5401[/tex]
This test is a left-tailed test, so the P-value for this test is calculated as:
[tex]\text{P-value}=P(z<-1.5401)=0.062[/tex]
As the P-value (0.062) is greater than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that the unemployment rate is less than 5%.
Discuss Mason's notion that you are to be an engineer first and a statistician second. What does that mean to you in terms of how you think about the career you are studying to begin, and how do you think this class might impact a job interview you might ultimately go on later in your studies
Answer:
The answer is explained below
Step-by-step explanation:
What use are statistics if there is no engineer to use them? In other words, a statistician corrects, improves, reinforces, and supports an engineer in building / designing / developing a new product and / or improving an existing product.
The statistician provides a special kind of vision through which I see the same problem in a completely different vision. So you can see the strengths, weaknesses of my product and the promise of improvements that can be made.
Each class of statistics is essential for a student to see and understand a problem in a whole new way where it is much easier to understand information.
What is the area of the triangle?
9 4 12
Answer:
13.636
Step-by-step explanation:
The area can be found using Heron's formula:
A = √(s(s-a)(s-b)(s-c))
where s=(a+b+c)/2.
For the given triangle, ...
a=9, b=4, c=12, s=(9+4+12)/2 = 12.5
A = √(12.5(3.5)(8.5)(0.5)) = √185.9375 ≈ 13.636
The area of the triangle is about 13.636 square units.
Answer:
24 units\
Step-by-step explanation:
Two students use different methods to solve this multiplication problem: 1\3 × −6 3\4 Read each of their methods below and then enter numbers to correctly complete their work. please help will mark the brainliest 12 pt
Answer:
- 2 1/4
Step-by-step explanation:
Methods for solving multiplication problems
I will go into details and give methods to solve with and the final answer.
: 1\3 × −6 3\4 = -1/3 ×( (6*4)+3)/4
1/3 × -6 3/4 = -1/3 ×(24+3)/4
1/3 × -6 3/4 =- 1/3 ×(27/4)
1/3 × -6 3/4 = -27/(3*4)
1/3 × -6 3/4 = -27/(12)
1/3 × -6 3/4 =-( 9/4) * 3/3
1/3 × -6 3/4 = -9/4
1/3 × -6 3/4 =- 2 1/4
OR by direct division
1/3 × -6 3/4 =( -6 3/4)/3
1/3 × -6 3/4 = -6/3 (3/4)/3
1/3 × -6 3/4 = -2 1/4
Do 2b+ b and 3b have the same value for all values of b? explain your reason
Answer:
Yes
Step-by-step explanation:
b is as in 1b so. . .
2 + 1 = 3
We can plug in b or as "b"
2b + b = 3b
So yes in whatever case 2b + b's value will always equal 3b's value
Answer:
yes
Step-by-step explanation:
because you can use any number to put for B and they will have the same value as an example we will use 3 for b so 2b = 6 + b = 9 and 3b = 9
PLEASE HELP!!! How many 2-digit numbers are among the terms of the arithmetic sequence 2, 7, 12, 17, ...?
Step-by-step explanation:
The difference between. Each numbers is 5 so, it's answer is 22 and 27
The shape in the figure is constructed from several identical squares. If the side of each square is 1 unit, what is the area and the perimeter of the shape?
Answer:
Area = 7 square units
Perimeter = 14 units
Step-by-step explanation:
The shape is made up of 7 identical squares and, we are told the side length of each square is 1 unit.
==>Find area of the shape by calculating the area of 1 square, then multiply by the number of square used in the construction.
Thus, area of 1 square = s² = 1² = 1 square units.
Area of shape = 7 × 1 square units = 7 square units
==>Find the Perimeter of the shape by adding all the lengths of the boundary formed by the square to make up the shape.
(Check attachment to understand how we got the measurement of the boundary)
The perimeter = 1 + 1 + 1 + ½ + ½ + 1 + 1 + 1½ + ½ + 1 + 1 + 4 = 14 units
A barrel of crude oil has a volume of 42 gallons, only approximately 45% of which is processed into gasoline. If your car achieves 31 mi/gal, and you drive 36,000 miles in one year, how many barrels of crude oil are required to run your car for a year?
The number of barrels of crude oil required to run the car for a year is 61.4
The information given is as follows;
Percentage of crude oil processed into gasoline = 45%
The distance achieved per gallon by car = 31 mi/gal
Distance driven per year = 36,000 miles
Hence, the number of Gasoline usage in one year,
[tex]\text{Gasoline usage in one year} = \dfrac{\text{Distance drievn per year}}{\text{distance achieve per gallon by car}}[/tex]
[tex]\text{Gasoline usage in one year} = \dfrac{36000 \ \text{miles}}{31\ \text{miles/gallon}}[/tex]
[tex]\text{Gasoline usage in one year} = 1,161 \ \text{gallons}[/tex]
Here, Percentage of crude oil processed into gasoline = 45%
Hence, where 45% of the crude oil produces 1000, the volume of crude, x, from which the gasoline is sourced becomes;
[tex]x \times 45\% = 1161[/tex]
[tex]x \times \dfrac{45}{100} = 1161[/tex]
[tex]45x = 1161\times 100[/tex]
[tex]45x = 1,16,100[/tex]
[tex]x = 2580[/tex] gallons of crude
Since 1 barrel of crude oil is approximately 42 gallons of crude oil.
Hence, we have;
[tex]2580 \ \text{gallons of crude }[/tex] = [tex]\dfrac{2580}{42} \text{ barrels of crude}[/tex]
= [tex]61.4[/tex] [tex]\text{ barrels of crude}[/tex]
Hence the number of barrels of crude oil required to run the car for a year = [tex]61.4[/tex] [tex]\text{ barrels of crude}[/tex]
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Approximately 61.44 barrels of crude oil are required to run your car for a year.
To determine the number of barrels of crude oil required to run your car for a year, we'll need to calculate the total amount of gasoline consumed and then convert that into the equivalent volume of crude oil.
Volume of a barrel of crude oil: 42 gallons
Approximately 45% of crude oil is processed into gasoline
Car fuel efficiency: 31 miles per gallon
Distance driven in a year: 36,000 miles
First, let's calculate the total amount of gasoline consumed in a year. We'll divide the total distance driven by the car's fuel efficiency:
Gasoline consumed = Distance driven / Fuel efficiency
Gasoline consumed = 36,000 miles / 31 miles per gallon
Gasoline consumed ≈ 1161.29 gallons
Next, we need to calculate the equivalent volume of crude oil required to produce this amount of gasoline. Since only approximately 45% of crude oil is processed into gasoline, we'll multiply the gasoline consumed by the reciprocal of 45% (or 0.45) to account for this conversion:
Equivalent volume of crude oil = Gasoline consumed / Conversion factor
Equivalent volume of crude oil = 1161.29 gallons / 0.45
Equivalent volume of crude oil ≈ 2580.64 gallons
Finally, to determine the number of barrels of crude oil required, we'll divide the equivalent volume of crude oil by the volume of a barrel (42 gallons):
Number of barrels of crude oil = Equivalent volume of crude oil / Volume of a barrel
Number of barrels of crude oil = 2580.64 gallons / 42 gallons
Number of barrels of crude oil ≈ 61.44 barrels
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Pls cam someone help me
Extremely confused with both if poss xxxx
Answer:
1. Red red blue blue
2. Red blue red blue
Step-by-step explanation:
A 50 percent chance
The rectangle is three times its width.
If the perimeter of the rectangle is 80in, find its length and width.
Answer:
Length= 30 in
Width= 10 in
Step-by-step explanation:
Let the width of the rectangle be x in.
Length of rectangle
= 3 (width)
= 3x
Perimeter of rectangle= 2(length) +2(width)
80= 2(3x) +2(x)
80= 6x +2x
8x= 80 (simplify)
x= 80 ÷8 (÷8 on both sides)
x= 10
Thus width of rectangle= 10 in
Length of rectangle
= 3(10)
= 30 in
Please answer this correctly
Answer:
60%
Step-by-step explanation:
Total Cards = 5
Even Numbers = 3
P(even) = 3/5
In %age:
=> 60%
Answer:
60%
Step-by-step explanation:
The numbers that are even from the list are 2, 4, and 6.
3 numbers are even out of 5 total numbers.
3/5 = 0.6
P(even) = 60%
PLEASE HELP I’LL MARK BRAINLIEST If 1 equals 1 2/3 how much does 1 1/2 equal?
Answer:
0.9 (9/10)
Step-by-step explanation:
(see picture)
PLEASE HELP ME OUT
Move point b to different locations in the coordinate plane. What do you notice about the relationship between BG and GF? Explain in terms of <BGF
Answer:
BG is always perpendicular to GF. The measure of angle BGF is always 90 degree
Step-by-step explanation:
Answer:
is always perpendicular to . The measure of is always 90°.
Step-by-step explanation:
Plato Awnser