Answer:
x=2 y=4
Step-by-step explanation:
y = 2x
y = –x + 6
Set the two equations equal to each other
2x = -x+6
Add x to each side
2x+x =-x+x+6
3x = 6
Divide each side by 3
3x/3 = 6/3
x =2
Now find y
y = 2x
y =2(2)
y = 4
The Empire State Building weighs about 7.3×108pounds. The One World Trade Center building weighs about 88,200,000 pounds. What is the total weight, in pounds, of these two buildings? Expressing your answer in scientific notation in the form a×10b, what are the values of a and b?
Answer:
[tex]8.182X10^8 $pounds[/tex]
a=8.182 and b=8
Step-by-step explanation:
Weight of the Empire State Building =[tex]7.3X 10^8[/tex] pounds.
Weight of the One World Trade Center building= 88,200,000 pounds.
=[tex]8.82 X 10^7[/tex]
The addition of the two:
[tex]=7.3X 10^8+8.82 X 10^7\\$To make it easier to add, express both as powers of 8\\=7.3X 10^8+0.882 X 10^8\\=(7.3+0.882)X10^8\\=8.182X10^8 $ pounds[/tex]
Comparing with the form: [tex]aX10^b[/tex]
a=8.182 and b=8
simplify [tex]\sqrt{.49x^{18} }[/tex] where x<0
Answer:
-7x⁹
Step-by-step explanation:
[tex]\sqrt{49x^{18}} = \sqrt{(7^2)(x^9)^2} =\sqrt{(7x^{9})^2} = |7x^9|[/tex]
Since x < 0 ,then |7x⁹| = -7x⁹
A data set with a mean of 34 and a standard deviation of 2.5 is normally distributed
According to the Empirical Rule, what percent of the data is in each of the following ranges? Round to the nearest tenth of a percent if necessary.
Between
34 and 39
Less than
31.5
Between
29 and 36.5
Percentage
%
%
Answer:
a) [tex] z= \frac{34-34}{2.5}= 0[/tex]
[tex] z= \frac{39-34}{2.5}= 2[/tex]
And we want the probability from 0 to two deviations above the mean and we got 95/2 = 47.5 %
b) [tex] P(X<31.5) [/tex]
[tex] z= \frac{31.5-34}{2.5}= -1[/tex]
So one deviation below the mean we have: (100-68)/2 = 16%
c) [tex] z= \frac{29-34}{2.5}= -2[/tex]
[tex] z= \frac{36.5-34}{2.5}= 1[/tex]
For this case below 2 deviation from the mean we have 2.5% and above 1 deviation from the mean we got 16% and then the percentage between -2 and 1 deviation above the mean we got: (100-16-2.5)% = 81.5%
Step-by-step explanation:
For this case we have a random variable with the following parameters:
[tex] X \sim N(\mu = 34, \sigma=2.5)[/tex]
From the empirical rule we know that within one deviation from the mean we have 68% of the values, within two deviations we have 95% and within 3 deviations we have 99.7% of the data.
We want to find the following probability:
[tex] P(34 < X<39)[/tex]
We can find the number of deviation from the mean with the z score formula:
[tex] z= \frac{X -\mu}{\sigma}[/tex]
And replacing we got
[tex] z= \frac{34-34}{2.5}= 0[/tex]
[tex] z= \frac{39-34}{2.5}= 2[/tex]
And we want the probability from 0 to two deviations above the mean and we got 95/2 = 47.5 %
For the second case:
[tex] P(X<31.5) [/tex]
[tex] z= \frac{31.5-34}{2.5}= -1[/tex]
So one deviation below the mean we have: (100-68)/2 = 16%
For the third case:
[tex] P(29 < X<36.5)[/tex]
And replacing we got:
[tex] z= \frac{29-34}{2.5}= -2[/tex]
[tex] z= \frac{36.5-34}{2.5}= 1[/tex]
For this case below 2 deviation from the mean we have 2.5% and above 1 deviation from the mean we got 16% and then the percentage between -2 and 1 deviation above the mean we got: (100-16-2.5)% = 81.5%
4. Find the zeros for 0 = x2 + 6x + 9.
a. X= 3
b. x = -3
C. X = 3 and x = -3
d. x = 1 and x = 9
Answer:
b. x = -3
Step-by-step explanation:
0 = x^2 + 6x + 9
Factor
0 = (x+3) (x+3)
Using the zero product property
x+3 = 0 x+3 =0
x = -3
log 10(x + 3) – log 10(x-3) = 1
Answer:33/9
Step-by-step explanation:
Log10(x+3)-Log10(x-3)=1
Log10((x+3)/(x-3))=1
(x+3)/(x-3)=10^1
(x+3)/(x-3)=10
Cross multiply
x+3=10(x-3)
Open brackets
x+3=10x-30
Collect like terms
10x-x=30+3
9x=33
Divide both sides by 9
9x/9=33/9
x=33/9
Grace is going to a carnival that has games and rides. Each game costs $1.50 and each ride costs $2.50. Grace spent $16.50 altogether at the carnival and the number of games she played is twice the number of rides she went on. Write a system of equations that could be used to determine the number of games Grace played and the number of rides Grace went on. Define the variables that you use to write the system.
Answer:
g=games; r=rides1.5g +2.5r = 16.5g = 2rStep-by-step explanation:
Let g and r represent the numbers of games played and rides ridden, respectively. Then the system can be written ...
1.50g +2.50r = 16.50 . . . . . total amount spent
g = 2r . . . . . . . . . . . . . . . . . . relationship of games to rides
Answer:
# of Rides: 3
# of Games: 6
Step-by-step explanation:
First try any possible combinations of games *2 more than rides.
Ex: 1&2, 2&4, 3&6, 4&8
2.50*3 = $7.50
1.50*6 = $9.00
7.50 + 9 = $16.50
If # of rides = r and # of games = g, equation:
16.50 = 2.50r + 1.50g
Oil is leaking from an oil tanker, and an expanding circle of oil is spreading on the ocean. The radius, r, of
modeled by the function r(s)=315, where sis time in seconds.
The area of the spill when s=5 seconds is
1 square inches.
Reset
Reset
Next
Next
Answer:
[tex]45\pi$ square inches[/tex]
Step-by-step explanation:
The radius, r of the expanding circle of oil is modeled by the function:
[tex]r=3\sqrt{s}[/tex] , where s is time in seconds.
When s=5
Radius [tex]r(5)=3\sqrt{5}$ inches[/tex]
Area of a circle [tex]=\pi r^2[/tex]
Therefore, the area of the oil spill when s=5 seconds
[tex]=\pi* (3\sqrt{5})^2\\=45\pi$ square inches[/tex]
The area of the spill when s=5 seconds is 45pi square inches.
The complement of 20°17' is
Answer:69°43'
Step-by-step explanation:
Complementary angles add up to 90
Let them complement be y
y+20°17`=90°
Collect like terms
y=90-20°17' 20°17'=1217/60
y=90-1217/60
y=(60x90 -1 x 1217)/60
y=(5400-1217)/60
y=4183/60
y=69°43'
Unlike most packaged food products, alcohol beverage container labels are not required to show calorie or nutrient content. An article reported on a pilot study in which each of 58 individuals in a sample was asked to estimate the calorie content of a 12 oz can of beer known to contain 153 calories. The resulting sample mean estimated calorie level was 193 and the sample standard deviation was 88. Does this data suggest that the true average estimated calorie content in the population sampled exceeds the actual content
Answer:
We conclude that the true average estimated calorie content in the population sampled exceeds the actual content.
Step-by-step explanation:
We are given that an article reported on a pilot study in which each of 58 individuals in a sample was asked to estimate the calorie content of a 12 oz can of beer known to contain 153 calories.
The resulting sample mean estimated calorie level was 193 and the sample standard deviation was 88.
Let [tex]\mu[/tex] = true average estimated calorie content in the population sampled.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] [tex]\leq[/tex] 153 calories {means that the true average estimated calorie content in the population sampled does not exceeds the actual content}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 153 calories {means that the true average estimated calorie content in the population sampled exceeds the actual content}
The test statistics that would be used here One-sample t test statistics as we don't know about the population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean estimated calorie level = 193 calories
s = sample standard deviation = 88
n = sample of individuals = 58
So, the test statistics = [tex]\frac{193-153}{\frac{88}{\sqrt{58} } }[/tex] ~ [tex]t_5_7[/tex]
= 3.462
The value of t test statistics is 3.462.
Since, in the question we are not given the level of significance so we assume it to be 5%. Now, at 0.05 significance level the t table gives critical value of 1.6725 at 57 degree of freedom for right-tailed test.
Since our test statistic is more than the critical value of t as 3.462 > 1.6725, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.
Therefore, we conclude that the true average estimated calorie content in the population sampled exceeds the actual content.
The altitude of an airplane is decreasing at a rate of 44 feet per second. What is the change in altitude of the airplane over a period of 34 seconds?
Answer:
1320 feet
Step-by-step explanation:
All we have to do is multiply the rate of change of altitude by the time it took the altitude to change.
The altitude of an airplane is decreasing at a rate of 44 feet per second. After 30 seconds, the change is altitude is:
44 * 30 = 1320 feet
The altitude of the airplane has changed by 1320 feet.
Rewa Delta Union RugbyCEOhas become concerned about the slow pace of the rugby gamesplayed inthe current union rugby, fearing that it will lower the spectator attendance. The CEOmeets with the union rugbymanagers and refereesanddiscusses guidelines for speeding upand makingthe gamesmore interesting and lively. Before the meeting, the mean duration of the15-sided rugbygame timewas 3 hours, 5 minutes, that is, 185 minutes.This includes all the breaks and injury times during the game. A random sample of 36 of the 15-sided rugbygames after themeeting showed a mean of 179 minutes with a standard deviation of 12 minutes.Testing at the 1% significance level, can you concludethat the mean duration of 15-sided union rugbygames has decreased after the meeting?
Answer:
Check the explanation
Step-by-step explanation:
Kindly check the attached image below to see the step by step explanation to the question above.
What is the Surface Area of the figure below?
A
60 units2
B
60 units3
C
104 units2
D
104 units3
Answer:
D
Step-by-step explanation:
I'm really sry if it's wrong!
The scatter plot for which type of data is most likely to suggest a linear association between
the two variables?
ages and heights of a group of dogs
time working out and strength of muscles
level of water in a reservoir each day and the day's date during one month
number of books returned to the library each day and the day's date over a period of one week
Plzzzz help
Answer:
level of water in a reservoir each....
Step-by-step explanation:
The scatter plot
A scatter plot is like a scatter chart or graph that uses the dots for representing the values of two different numeric variables. The horizontal value indicates the individual point data. Thus is used for observing the realtisohips between the variables.
This the answer is level of the water in a dam each day and date during 1 month.
The scatter plot can tell you the values for the set of data. The points may be given in different sizes, colors, and shapes. The data is displayed in points. The values are shown on the vertical axis. The relationship of the data can positive, negative, and neutral. The scatter plot can display a mosaic and a fluctuational diagram.Hence the option C is correct.Learn more about the which type of data.
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g We are told that the data is representative of the two populations (U.S. males aged 20-29 years and U.S. males aged 75 years), and we will assume that researchers collected random samples. The samples are very large; therefore, the conditions are met for use of the T-test. Using StatCrunch, we find a T-score of 5.3 and a P-value of "< 0.0001." What can we conclude
Answer:
Step-by-step explanation:
With a T-score of 5.3 and a P-value of "< 0.0001." we can conclude that there is sufficient statistical evidence to prove that the data provided is not a representative of the two populations as the p value is less.
1. Solve the system of equations
-x+y=0
4x - 3y=-3
I
=
Answer:
x = -3
y = -3
Step-by-step explanation:
To solve this system of equations, you can use the elimination method, which is to have one of the variables match, but be the opposite sign of the other:
- x + y = 0
4x - 3y = -3
The easier one to match is the 1st equation, and to make it match oppositely, you multiply the whole equation by 4:
4(-x + y = 0)
-4x + 4y = 0
4x - 3y = -3
-4x and 4x cancel each other out:
4y = 0
-3y = -3
_______
y = -3
Then plug in -3 for y, into one of the equations:
- x + y = 0
- x - 3 = 0
Add 3 to both sides:
- x = 3
Divide both sides by -1:
x = -3
In the right triangle shown DF=EF=3. How long is DE?
Answer:
4.24
Step-by-step explanation:
To solve this, use the Pythagorean therom. A^2 + b^2 = C^2
in this case a = 3 and b = 3
so 9 + 9 = sqrt 18
4.24
Answer:3√(2)
Step-by-step explanation:
DF=3
EF=3
DE=√(3^2 + 3^2)
DE=√(3x3 + 3x3)
DE=√(9+9)
DE=√(18)
DE=√(2 x 9)
DE=√(2) x √(9)
DE=√(2) x 3
DE=3√(2)
For the functions f(x)=6x−4 and g(x)=2x2+5, find (g∘f)(x).
Answer:
72x^2-96x+37
Step-by-step explanation:
Solve SA = πrs + π r2 for s A) -r B) SA + r C) SA π2r3 D) SA - πr2 πr
Answer:
(SA - π r^2)/πr = s
Step-by-step explanation:
SA = πrs + π r^2
Subtract π r^2 from each side
SA - π r^2 = πrs + π r^2-π r^2
SA - π r^2 = πrs
Divide each side by πr
(SA - π r^2)/πr = πrs/πr
(SA - π r^2)/πr = s
Answer:
D
Step-by-step explanation:
SA = πrs + πr²
SA - πr² = πrs
s = (SA - πr²)/πr
What number should be added to both sides of the equation to complete the square? x2 – 10x = 7
Answer:
25
Step-by-step explanation:
x^2 – 10x = 7
Take the coefficient of x
-10
Divide by 2
-10/2 = 5
Square it
5^2 = 25
Add this to both sides
x^2 – 10x+25 = 7+25
Express the inequality x≤−0.12 using interval notation.
Answer:
(0.12,∞)
Step-by-step explanation:
The inequality x>0.12 means "all numbers greater than 0.12." There is no upper end to the solution to this inequality. In interval notation, we express x>0.12 as (0.12,∞). Notice that the parenthesis symbol shows that the endpoint of the inequality, 0.12, is not included.
The inequality x ≤ - 0.12 is written in interval notation as,
⇒ x ∈ (- ∞, - 0.12 ]
What is Inequality?A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
The inequality is,
⇒ x ≤ - 0.12
Now, We can write the inequality in interval notation as;
⇒ x ≤ - 0.12
⇒ x ∈ (- ∞, - 0.12 ]
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Is an estimate of 28,000 over under the actual peoduct of 360 68? How can you tell
Answer:
Over Estimate of the actual product.
Step-by-step explanation:
360*68= 24,480
The estimate of 28,000 is larger than the actual product 360 and 68 which is 24480, which means that the estimate is an over estimate (an over estimate means that the number you estimated is bigger than the actual number, and an under estimate is when the estimate is smaller than the actual number, Just FYI)
Ollivanders stuffed bear shop has 456 bears in stock exactly half of them Are made from wool how many wool does Mr.oillvander have in stock
Answer:
228 of them are made from wool, but there is no enough information to determine how many would he has in stock.
Step-by-step explanation:
Mr Ollivander's stuffed bear shop has 456 bears in stock, and exactly half of them are made from wool, this means that 1/2 of 456 are made from wool
1/2 of 456 = 1/2 × 456 = 456/2 = 228.
That is 228 of them are made from wool.
However, nothing tells us that this is all he has in his stock. There is no information available to determine how many would he has in stock.
A movie theater decreased the size of its popcorn bags by 20%. If the old bags held 15 cups of popcorn, how much do the new bags hold
Answer:
Your answer will be [tex]12[/tex] cups of popcorn.
Step-by-step explanation:
To find out how much the new bags hold, you need to find out the discount.
[tex]\frac{20}{100 } = .2[/tex]
[tex]15 * .2 = 3[/tex]
We know that the discount is [tex]3[/tex].
To figure out how much the new bags hold, subtract by the old bags.
[tex]15 - 3 = 12[/tex]
The new bags hold 12 cups of popcorn.
Greatest common factor for 30 abd 42
Answer:
6
Step-by-step explanation:
Because you are familiar with your times tables, you know that ...
30 = 6·5
42 = 6·7
The greatest common factor is 6.
Which phrase represents this expression?
(47−17)×4
A. 4 times the difference of 47 and 17
B. 4 times the difference of 17 and 47
C. the difference of the product of 4 times 17 and 47
D. the difference of 47 and the product of 4 times 17
Answer:
I think its A
Step-by-step explanation:
AB=
Round your answer to the nearest hundredth.
pleaseee
Answer:
[tex]c = \frac{2}{0.42} [/tex]
Step-by-step explanation:
AB = c
[tex] \frac{a}{sin \: A} = \frac{c}{sin \: C} \\ \frac{2}{sin \: 25} = \frac{c}{sin \: 90} \\ \frac{2}{0.42} = \frac{c}{1} \\ 0.42 \: c = 2 \\ c = \frac{2}{0.42} [/tex]
Answer:
4.73
Step-by-step explanation:
which expresion has a valume of 7/12
Answer:
1/1 x 7/1 x 1/12
Is there any options?
Step-by-step explanation:
Answer:6/8 adding 1/4
Step-by-step explanation: Because im right probably
Consider the triangle.
Which statement is true about the lengths of the sides?
45°
Each side has a different length.
Two sides have the same length, which is less than the
length of the third side.
D. The three sides have the same length.
D. The sum of the lengths of two sides is equal to the
length of the third side.
45°
Answer:
Assuming this is a 45 - 45 - 90 right triangle, The answer would be B) Two sides have the same length, which is less than the length of the third side
Hence statements stated true false along with reason
What is triangle?A triangle is a three-sided polygon with three edges and three vertices in geometry. The sum of a triangle's interior angles equals 180 degrees is the most significant feature of a triangle.
Triangle of Isosceles: Triangle with Obtuse Angle
Triangle Inequality in the Scalene Triangle
Triangle Surface Area: Triangle with Sharp Angle
Triangle with Right Angles: Triangle Form of Pascal...
How to solve?Given a triangle and statements related to it let's check
Each side has a different length.
-This statement can't always be true as in equilateral triangle all sides are equal
Two sides have the same length, which is less than the
length of the third side.
-this statement is correct but when it is a right angles triangle where other two anges are 45degrees each then this can't be true.
The three sides have the same length.
-this statement is true for equilateral triangle
D. The sum of the lengths of two sides is equal to the
length of the third side.-
-This statement is true when we talk of only right angled triangle
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Bob, Paula and Sam invest $50000 in a business. Bob invests $4000 more than Paul does and Paul invests $5000 more than Sam does. If the total profit was $70000, select the correct answer. Note that the profit is distributed proportionally based on the respective amount each invested. A. The ratio of the investment of Bob, Paula and Sam is 11:15:10. B. The ratio of the investment of Bob, Paula and Sam is 12:17:21. C. The ratio of the investment of Bob, Paula and Sam is 12:5:4. D. The profit of Paula was $23,800
Answer:
D
Step-by-step explanation:
since sam invest the least, let a be the amount invested by sam
sam = a
paul = a + 5000
bob = a + 5000 + 4000
3a + 14000 = 50000
3a = 36000
a = 12000
thus sam is 12000, paul is 17000 and Bob is 21000
therefore the ratio of B:P:S is 21:17:12
profit by paula is 17/50 x 70000 = 23800
The profit by Paula is 17/50 x 70000 = 23800.
We have given that Bob, Paula and Sam invest $50000 in a business. Bob invests $4000 more than Paul does and Paul invests $5000 more than Sam does. If the total profit was $70000
Since sam invest the least, let a be the amount invested by sam
Therefore we get,
sam = a
What is the investment of Paul?
The investment of Paul = a + 5000
Bob = a + 5000 + 4000
3a + 14000 = 50000
3a = 36000
divide both sides by 3 so we get,
a=36000/3
a = 12000
Therefore, sam is 12000,
paul =5000+12000=17000 and
Bob =12000+9000= 21000
Therefore the ratio of B:P:S is 21:17:12
The profit by Paula is 17/50 x 70000 = 23800.
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PLEASE HELP!!! WILL MARK AS BRAINLIEST!!!
A colony of 300 bacteria doubles in size every 22 minutes can be represented by the exponential function y=300(2)x. If you want to know how many bacteria will be present about 66 minutes, what should you plug in for x?
Answer:
[tex] y = 300 (2)^x[/tex]
Where x represent the number of period of times of 22 minutes. If we want to know the value of the population after 66 minutes we need to find the value of x on this way:
[tex] x = 66 minutes *\frac{1period}{22 minutes}= 3[/tex]
So then we need to replace the value of x =3 and we got:
[tex] y= 300 (2)^3 = 2400[/tex]
Step-by-step explanation:
For this case we have the following function:
[tex] y = 300 (2)^x[/tex]
Where x represent the number of period of times of 22 minutes. If we want to know the value of the population after 66 minutes we need to find the value of x on this way:
[tex] x = 66 minutes *\frac{1period}{22 minutes}= 3[/tex]
So then we need to replace the value of x =3 and we got:
[tex] y= 300 (2)^3 = 2400[/tex]
