Answer:
Proof below
Step-by-step explanation:
Irrational and Rational Numbers
We need to use the basic property of logarithms:
[tex]log_b\ a=x\ \ \Rightarrow b^x=a[/tex]
We are given:
[tex]log_3\ 7[/tex]
And we will prove it's an irrational number, i.e., it's not a rational number.
Recall a rational number can always be expressed as a fraction a/b, where a and b are integer numbers. Thus, if the expression was a rational number, then:
[tex]\displaystyle log_3\ 7=\frac{a}{b}[/tex]
Applying the property:
[tex]\displaystyle 3^{\frac{a}{b}}=7[/tex]
Raising to the power of b:
[tex]3^a=7^b[/tex]
It's not possible to find two integers a and b that satisfy the condition above. That contradiction comes from the assumption that [tex]log_3\ 7[/tex] is rational, thus, it's proven [tex]log_3\ 7[/tex] is irrational.
Carla packed this box with 1-centimeter cubes. What is the volume of the box?
Answer:
60 cm 2
Step-by-step explanation:
Answer:
60 cubic cm
Step-by-step explanation:
i just multiplied 3 x 4 x 5 and that gave me 60 and cubic cm
hoped it helped :)
- 14b + 38 = 108
b = [?]
Answer:
b = -5
Step-by-step explanation:
[tex] - 14b + 38 = 108[/tex]
[tex] = > - 14b = 108 - 38 = 70[/tex]
[tex] = > b = \frac{70}{ - 14} = - 5[/tex]
What is the value of x?
ans is 21
Step-by-step explanation:
you see the right angle plus 15 degree angle equal to the 5x angle
so the quation is
90+15=5x
105=5x
21=x
Why are whole numbers rational numbers? Use 15 as an example.
Answer:
Every whole number n can be written as a fraction of integers.
Step-by-step explanation:
Every whole number n can be written as a fraction of integers: x=x/1.
If we use 15 as an example, it would be 15 = 15/1. 15/1 is 15.
So whole numbers are rational
Whole numbers are rational numbers because all whole numbers can be expressed in the form a/b. Hence, 15 can be expressed as a rational fraction thus 15/1
When a number can be expressed in the form a/b ; such that the value of the denominator, b ≠ 0 ; then the number is said to be rational. Whole numbers are positive integer values and as such, they are not decimals. Every whole number can be expressed such that the denominator is 1 ; hence, they can be expressed in the form a/b.15 as a whole number can be rewritten as 15/1. Hence, all whole numbers are rational.
Learn more : https://brainly.com/question/18109354
If cos a= 0.93. Sin 0 =0.26, and tan ß = 0.84, find a + B + 0.
Answer:
77°
Step-by-step explanation:
From the question given above, the following data were obtained:
Cos α = 0.93
Sine θ = 0.26
Tan β = 0.84
α + β + θ =?
Next, we shall determine the value of α. This can be obtained as follow:
Cos α = 0.93
Take the inverse of Cos
α = Cos¯¹ 0.93
α = 22°
Next, we shall determine the value of θ. This can be obtained as follow:
Sine θ = 0.26
Take the inverse of Sine
θ = Sine¯¹ 0.26
θ = 15°
Next, we shall determine the value of β. This can be obtained as follow:
Tan β = 0.84
Take the inverse of Tan.
β = Tan¯¹ 0.84
β = 40°
Finally, we shall determine the value of α + β + θ . This can be obtained as follow:
α = 22°
θ = 15°
β = 40°
α + β + θ = 22 + 40 + 15
α + β + θ = 77°
What is 15% of 80kg i am
Really not sure
Answer:
12 kg
Step-by-step explanation:
15×80/100
15×8/10
120/10
12 kg
Answer:
12kg
Step-by-step explanation:
When finding 15% of something you can set it up like this
? 15
--- ----
80 1000
to figure out what the '?' is you need to multiply diagonally and divide the neighbor
80 x 15 = 1200
1200 / 100 = 12
Hence, your answer is 12 kg
Hope this helps <3
Many track runners believe that they have a better chance of winning if they start in the inside lane that is closest to the field. For the data below, the lane closest to the field is Lane 1, the next lane is Lane 2, and so on until the outermost lane, Lane 6. The data lists the number of wins for track runners in the different starting positions. Calculate the chi-square test statistic to test the claim that the number of wins is uniformly distributed (equally likely) across the different starting positions. The results are based on 240 races.
This question is incomplete, the complete question is;
Many track runners believe that they have a better chance of winning if they start in the inside lane that is closest to the field. For the data below, the lane closest to the field is Lane 1, the next lane is Lane 2, and so on until the outermost lane, Lane 6. The data lists the number of wins for track runners in the different starting positions. Calculate the chi-square test statistic to test the claim that the number of wins is uniformly distributed (equally likely) across the different starting positions. The results are based on 240 races.
starting position: 1 2 3 4 5 6
Number of wins : 44 33 50 32 45 36
options
a) 15.541
b) 9.326
c) 6.750
d) 12.592
Answer:
the chi-square test statistic is 6.75
Option c) 6.750 is the correct answer
Step-by-step explanation:
Given that;
starting position: 1 2 3 4 5 6
Number of wins : 44 33 50 32 45 36
Given that we have 240 races
Using x² test.
we have to calculate the expected frequency
so
E(1) = 240 × 1/6 = 40
E(2) = 240 × 1/6 = 40
E(3) = 240 × 1/6 = 40
E(4) = 240 × 1/6 = 40
E(5) = 240 × 1/6 = 40
E(6) = 240 × 1/6 = 40
Now we know that,
x²_cal = [∑( Oi - Fi)²] / Fi
so
x²_cal = (44-40)²/40 + (33-40)²/40 + (50-40)²/40 + (32-40)²/40 + (45-40)²/40 + (35-40)²/40
= 0.4 + 1.225 + 2.5 + 1.6 + 0.625 + 0.4
= 6.75
Therefore the chi-square test statistic is 6.75
Option c) 6.750 is the correct answer
1. A force of 30N is applied to a screwdriver to pry the lid off of a can of paint. The
screwdriver applies 90N of force to the lid. What is the MA of the screwdriver?
Answer:
I would have to guess that the MA of the screwdriver is 120N.
Step-by-step explanation:
I think this because you are adding 30 and 90, since there are two forces being acted on the same place in the same direction.
#teamtrees #WAP (Water And Plant)
#teamtrees #WAP (Water And Plant)
Suppose you run a bookstore, and have ratings (1 to 5 stars) of books. Your collaborative filtering algorithm has learned a parameter vector for user j, and a feature vector for each book. You would like to compute the "training error", meaning the average squared error of your system’s predictions on all the ratings that you have gotten from your users. Which of these are correct ways of doing so (check all that apply)For this problem, let m be the total number of ratings you
have gotten from your users. (Another way of saying this is
that m=∑nmi=1∑nuj=1r(i,j)). [Hint: Two of the four options below are correct.]
a) 1m∑(i,j):r(i,j)=1((θ(j))Tx(i)−r(i,j))2
b) 1m∑nmi=1∑j:r(i,j)=1(∑nk=1(θ(j))kx(i)k−y(i,j))2
c) 1m∑(i,j):r(i,j)=1((θ(j))Tx(i)−y(i,j))2
d) 1m∑nuj=1∑i:r(i,j)=1(∑nk=1(θ(k))jx(k)i−y(i,j))2
A right triangle has a hypotenuse that is 9
inches long and one leg that is 4 inches long.
What is the perimeter of the triangle?
Answer:
sqrt65+17
Step-by-step explanation:
a^2+b^2=c^2
a^2+4^2=9^2
a=sqrt65
perimeter = sqrt65+97
Hope this helps plz hit the crown :D
Indicate whether the following congruence statement is true or false.
50 points
Step-by-step explanation:
Since line NL is not necessarily congruent to MQ (labelled with different congruent marks), triangle NLM is not congruent to triangle MQP.
Instead, triangles NLM and QPM are congruent.
This could true because of the markings of the triangles' sides and angles are in the same location.
But the statement labeled the lines wrong which makes them False
What is the sum of the fractions?
Answer:
It is 6/7 because the denometere is sMe
x-axis =____
y-axis =____
y= x ____
y= -x____
Answer:
x-axis = (2, -3)
y-axis = (-2, 3)
y = x (3, 2)
y= -x (-3, -2)
Step-by-step explanation:
x-axis = (2, -3) The point is below the x-axis.
y-axis = (-2, 3) The point is left of the y-axis
y = x (3, 2) Plot the line y = x. The point is on the other side of the line.
y= -x (-3, -2) Plot the line y = -x. The point is on the other side of the line.
-2/7x - 11 + 4/7x - 7
Answer:
2/7x - 18
Step-by-step explanation:
-2/7x - 11 + 4/7x - 7
rearrange the expression so it's easier to add, optional
-2/7x + 4/7x - 11 - 7
2/7x - 18
PLEASE HELP ME IM TAKING TIMED TEST I WILL MARK YOU AS BRAINLEST!!
Answer:-4.5, -0.5, 0.3, 0.7, 2.3
Step-by-step explanation:
Helpppppppppppppp asappppp
Answer:
[tex]B.\ 3[/tex]
Step-by-step explanation:
Given
[tex]x^3 + \frac{1}{3}x^3 +6x + 5[/tex]
Required
Power of term with coefficient of 1
First, we need to identify the variable in the given polynomial
The variable is x
Each term has the following format:
[tex]mx^n[/tex] where [tex]n \ge 0[/tex] and m is the coefficient
In this case, we are to look for n where m = 1
Looking at each term of the polynomial, we have the following match:
[tex]mx^n = x^3[/tex]
Substitute 1 for m
[tex]1 * x^n = x^3[/tex]
[tex]x^n = x^3[/tex]
By comparison:
[tex]n = 3[/tex]
Hence, the solution to this question is (B)
The terminal point of Dis ( 1/2,3/2). What is cos 0?
O A. V 3
B. V3
Coc.
o D. V
SUBMIT
Answer:
(c). [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
The cosine is the "x" coordinate of the terminal point on the unit circle.
Thus the answer is (c). [tex]\frac{1}{2}[/tex]
If I had 1 banana then I ate that banana how many of the banana would I have hint the peal First person gets brainliest
1 peal 0 banana
eeeeeeeeeeeeee
Answer quickly for brainliest!!!
Answer:
Subtract 5 from both sides.
Step-by-step explanation:
Answer:
C. subtract 5 from both sides.
Step-by-step explanation:
when solved, its y=7
Need HELP ASAP!!
Please help me
Check over my math please.
Answer:
It looks like everything is correct :)
Step-by-step explanation:
What’s 4/5 of 3 And what’s 2/9 of 20
Answer:
4/5 of 3 = 12/5
2/9 of 20 = 40/9
Step-by-step explanation:
Answer:
1. 2.4
2. 4.444
Step-by-step explanation:
First, let's look at 4/5 of 3. We can set it up like this:
[tex]3 * \frac{4}{5}[/tex]Next, multiply the 3 by the 4 to get this:
[tex]\frac{12}{5}[/tex]Then, if a calculator is permitted, we get the answer of 2.4.
The next thing to do would be to repeat the steps for 2/9 of 20.
[tex]20 * \frac{2}{9}[/tex]
[tex]\frac{40}{9} = 4.444[/tex]
Hope this helps!!
- Kay :)
I need help please but if you can give me the step by step it would be helpful thank you
Answer: (x^2 -6x +10)(x - 2)
All the steps are shown in the picture below:
4x-3y=24 in slope-intercept form
Answer:
y=(4/3)x-8
Step-by-step explanation:
Slope-intercept form: y=mx+b
4x-3y=24
3y=4x-24 (isolating the 3y)
y=(4/3)x-8 (dividing both sides by 3)
Hope this helps!
In a right triangle, the tangent of angle A is 9/12 and the cosine of angle a is 12/15 based on these values what is the sine of angle a
a. 9/15
b 15/16
c 1, 1/15
d 1. 11/20
Answer:
option A 9/15
im srry i suck at math
write 5,020,700 in expanded form
5,000,000+20,0000+700
84.637-28.56 solve this for me and show work
Answer:
56.077
Step-by-step explanation:
84.637
- 28.560
56.077
Answer:
56.077
Step-by-step explanation:
Work is shown in picture above
Find the number between 100 and 999 such that
the sum of the three digits is 12.
the hundreds digit equals the sum of the tens digit and the ones digit.
the hundred digit equals one greater than the tens digit.
The owner of a small local bakery wants to determine how many fruit-filled pastries she should bake each day. Each pastry costs $.60 to make and sells for $1.00 each. Each pastry that is not sold at the end of the day is sold the next day for $.30 as day-old merchandise. She has determined that her average daily sales of this type of pastry are 193, with a daily standard deviation of 41. Flag this Question Question 114 pts What is the value of Co
This question is incomplete, the complete question is;
The owner of a small local bakery wants to determine how many fruit-filled pastries she should bake each day. Each pastry costs $.60 to make and sells for $1.00 each. Each pastry that is not sold at the end of the day is sold the next day for $.30 as day-old merchandise. She has determined that her average daily sales of this type of pastry are 193, with a daily standard deviation of 41. Flag this Question Question 114 pts
-What is the value of Co
-What is the value of Cu
Answer:
- the value of the cost overage Co is $ 0.3
- the value of the cost shortage Cu is $ 0.40
Step-by-step explanation:
Given that;
Revenue per unit R = $ 1.00
Cost per Unit C = $ 0.60
Salvage value per unit S = $ 0.30
Mean Demand μ = 193
Standard Deviation of demand σ = 41
-To get the value of our cost overage Co;
we simply say
Co = Cost per Unit C - Salvage value per unit S
Co = 0.6 - 0.30 = 0.30
therefore the value of the cost overage Co is $ 0.30
- To find the value of Cost Shortage Cu;
Cu = Revenue per unit R - Cost per Unit C
Cu = 1.00 - 0.60 = 0.40
therefore the value of the cost shortage Cu is $ 0.40
It is suspected that calcium in blood platelets may be related to blood pressure. As part of a study of this relationship, researchers recruited 30 subjects whose blood pressure was normal (i.e., not abnormally elevated). For each subject two measurements were made: pressure (average of systolic and diastolic measurements) and calcium concentration in the blood platelets. The sample size is n = 30, and the sample correlation is r = 0.4. Is there evidence that blood pressure and platelet calcium are linearly related? State the hypothesis and test it at 5% level of significance. What is your conclusion?
Answer:
Step-by-step explanation:
The null and the alternative hypothesis are:
[tex]\mathbf{ H_o: \rho = 0} \\ \\ \mathbf{H_1: \rho \ne 0}[/tex]
The test statistics is as follows:
[tex]t = \dfrac{r\sqrt{n-2} }{\sqrt{1-r^2}}[/tex]
[tex]t = \dfrac{0.4 \sqrt{30-2} }{\sqrt{1-0.4^2}}[/tex]
[tex]t = \dfrac{0.4 \sqrt{28} }{\sqrt{0.84}}[/tex]
t = 2.3094
The critical value
[tex]t_{\alpha/df} = t_\ \{0.05/2 \ , \ 30-2 \} } \\ \\ = t_{0.025,28} = \pm 2.048 ( from \ the \ t-tables)[/tex]
Decision rule:
To reject [tex]H_o[/tex] if t > [tex]t_{\alpha/df}[/tex].
So since t > [tex]t_{\alpha/df}[/tex]. we reject [tex]H_o[/tex] at ∝ = 0.05
Conclusion: There is sufficient evidence to conclude that blood pressure and patient calcium are linearly related.
