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.
16y5+4y5-12y3+15y3?
What is the simplified form?
Answer:
[tex]20y^5+3y^3[/tex]
Step-by-step explanation:
[tex]16y^5 + 4y^5 -12y^3 + 15y^3[/tex]
All we can do here is combine like terms (add those that have the same the same exponent)
[tex]20y^5+3y^3[/tex]
Good luck!
Answer:
[tex]20y^{5} +3y^{3}[/tex]
Step-by-step explanation:
[tex]16y^{5} +4y^{5} =20y^{5}[/tex] and [tex]-12y^{3} +15y^{3} =3y^{3}[/tex]
So [tex]20y^{5} +3y^{3}[/tex]
A repair man charges $75.00 to come to the house as a service fee. The repairman charges $150 dollars per hour. Which equation best represents the total cost, c, of the repairs?
A. c = 150f + 2.75
B. c = 150-75f
C. c = 150f + 75
D. c = 225f
Jared bakes 2 apple pies. He cuts the two pies into pieces. Each piece is 1/8 of a pie. Enter the number of pie Jared cuts.
Answer:
16 pieces
Step-by-step explanation:
Please give me brainliest
this is so emaruballos can be marked brainliest and yes the answer is 16
what is the answer for this( 7 3 x ∛27 - 2) x 1 5 + √81
Answer:
5208
Step-by-step explanation:
(73 x ³√27 - 2) x 15 + √81
(73 x 3 - 2) x 15 + 9
(219 - 2) x 24
217 x 24
5208
What’s 3/8 OF 5 as a mixed number
Answer:
Step-by-step explanation:
2 3;8
Answer:
1 7/8.
Step-by-step explanation:
5 * 3/8
= 15/8
= 1 7/8.
Suppose ALI was told that relative to the other scores on a NTS test, his score was the 95th percentile i.e., his percentile score is 95. How do we interpret it?
Translate into a variable expression.
18 added to Z
Answer:
z + 18 or z+18
if you want i can even put it in word form.
Answer:
zjsjsjwjs1 balducci howbto
Step-by-step explanation:
hendrickson
Which is equivalent to (x+3)(x-5)
Answer:
x^2 -2x -15
Step-by-step explanation:
by multiplying the 2 brackets
x^2
-5x + 3x = -2x
3 * -5= -15
!!!!!!!!!!!!!!!!!! help
Answer:
option 1
Step-by-step explanation:
It's given in the question that
a (first term of an A.P.) = 14
d (common difference between terms of A.P.) = -3
So,
2nd term will be = a + d = 14 + (-3) = 11
3rd term = a + 2d = 14 + 2×(-3) = 8
4th term = a + 3d = 14 + 3×(-3) = 5
All these terms are matching with option 1. So, option 1 is the correct option
SHOW
YOUR
WORK!!
X -
-67 V6 ²-4ac
2a
The
equation d = n²-12n + 43
models the number of defective
items a produced in a manufacturing process where there are
workers in a restricted
area
a) solve for
n
When
d=30
INTL
DLL
Answer:
1.20, 10.8
Step-by-step explanation:
d = n^2 - 12n + 43
d = 30
30 = n^2 - 12n + 43
0 = n^2 - 12n + 13
now solve for n using quadratic formula:
a=1, b=-12, c=13
n = (-b +- sqrt( b^2 -4ac))/2a
two answers ( one for + the square root, one for - the square root)
n = 1.20, n = 10.8
Please help, solve a and b
Answer:
AE and BD use the same lines for both triangles so the angles for C are the same. this means that all the angles are congruent between both triangles.
Step-by-step explanation:
Answer:
The distance across the river d=175ft
Step-by-step explanation:
As◇ ABC& ◇ EDC are similar, BC/CD=AB/ DE
4x/7x=100/d
d=100×7/4=175
24 coloring books,60 crayons, and 84 markers can be packaged into at most how many Identical packages? How many will each package contain?
Answer:
there can be 12 identical packages at most. each package will contain:
- 2 coloring books
- 5 crayons
- 7 markers
Step-by-step explanation:
Given that 1 inch = 2.54 cm, how many centimeters are there in 5 feet?
Answer: 152.4 cm
Step-by-step explanation:
True or False: Receipts are a way to document or keep track of your expenses.
Answer:
True
Step-by-step explanation:
I hope this is correct and have a great day
Answer:
True
Step-by-step explanation:
People save receipts to keep track of their previous purchases and expenses.
I hope this helps
please help me step by step
Answer:
should be just be like doubling everytime
Step-by-step explanation:
6 water and 4 powder
12 water 8 powder
18 water 12 powder
it's the same ratio so it should taste the same, like 3 water and 2 powder is going to taste the same as 18 water and 12 powder
solve the following equation-7x-4y=-4 -9x-5y=-6
Answer:
[tex]\boxed{x = 4~~and~~ y = -6}[/tex]
.
Step-by-step explanation:
-7x - 4y = -4 (times 5) -35x - 20y = -20
-9x - 5y = -6 (times 4) -36x - 20y = -24
.
Eliminate both equations
[tex]-35x - 20y = -20[/tex]
-36x - 20y = -24
[tex]x = 4[/tex]
.
Substitute the value of x to one of equations
[tex]-7x - 4y = -4[/tex]
[tex]-7(4) - 4y = -4[/tex]
[tex]-28 - 4y = -4[/tex]
[tex]-4y = - 4 + 28[/tex]
[tex]-4y = 24[/tex]
[tex]y = \frac{24}{-4}[/tex]
[tex]y = -6[/tex]
Step-by-step explanation:
ib2j2nwj wjwjw wjw w wiw w akwbysks soshsiw sksns sks sos sisIyah lah s ais ssj sj
A school is selling t-shirts and hoodies to raise money. Cara bought a t-shirt and 2 hoodies for $60. Jack bought 3 t-shirts and one hoodie for $60. How much is one t-shirt and one hoodie?
what is the percent of change from 300,000 to 30,000 its 90
Answer:
-90%
Step-by-step explanation:
83, 15, 50, 28, 52, 96 - What is the mean? What is the mode? What is the median?
Answer: mean-54 mode-1 median-50
Step-by-step explanation:
Please answer i don't have muc time
PLEASE HELP ME OUT FAST MULTIPLE CHOICE IF YOU DOMT KNOW PLEASE DONT RIGHT ANYTHING!
Answer:
B
Step-by-step explanation:
When you are finding the solution of two lines on a graph, you look at the intersection point and that is the answer. On the given graph, both lines intersect at (4, -3). Thus, that is the solution.
Best of Luck!
HELP ME PLZ
A figure is shown in the image. What is the measure of the
highlighted angle?
А. 30
В. 60
С. 120
D. 65
Answer:
c is the correct answer i my guest
8 pencils for 14 dollars
Answer:
1 pencil will be for 1.75 $
Answer:
$1.75 for each pencil.
Step-by-step explanation:
if you're asking the price for each pencil then its 1,75 for each because 8 multiplied by 1.75 is 14 :))
Axis of symmetry: x = -0.5; Vertex: (-0.5, 0.75); f(x) = x2 + x + 1
Axis of symmetry: x = -0.5; Vertex: (-0.5, -0.75); f(x) = x2 - x + 1
Axis of symmetry: x = -0.5; Vertex: (-0.5, 0.75); f(x) = -x2 + x
Axis of symmetry: x = -0.5; Vertex: (-0.5, 0.75); f(x) = x2 + 2x + 1
Graph of the question is missing so I have attached it
Answer:
Option A: Axis of symmetry: x = -0.5; Vertex: (-0.5, 0.75); f(x) = x2 + x + 1
Step-by-step explanation:
1) The axis of symmetry of quadratic graph is the vertical line that divides the graph curve into two congruent halves. In this case, it is: x = -0.5
2) Vertex is the point at which the graph curve changes direction or simply coordinates of the crest or trough of the curve.
The graph given has a trough with the coordinates: x = -0.5, y = 0.75. This is (-0.5, 0.75)
3) The roots of a quadratic equation are the points where the curve crosses the x-axis. In this case, it doesn't cross and so we have imaginary roots.
Now, formula for line of symmetry is; x = -b/2a
Thus; -b/2a = -0.5 or -b/2a = -1/2
Thus, b = 1 and a = 1
Our first and second terms will now be;
x² + x
Looking at the options, the only one with x² + x as it's first 2 terms is option A.
Thus, the complete equation will be x² + x + 1
Please answer this correctly fast!! What type of triangle is this?
Options:
- SSS
- SAS
- ASA
- AAS
- HL
- Not Possible
Answer:
Not possible
Step-by-step explanation:
These triangles are not congruent
A well known pharmaceutical manufacturer is manufacturing a newly developed vaccine, and is concerned about variability in the immune response of the recipients. They claim the variance in the immune response is 1.9. It is known that the immune responses follow a normal distribution. A random sample of 30 individuals were given the vaccine and their immune response recorded. It was found that they had a sample variance of 0.9. At the 5% significance level, test the hypothesis that the population variance of the immune response is equal to 1.9 against the two-sided alternative, that it is not. a. State the null and alternative hypothesis. b. Perform the hypothesis test. (You may use any of the methods we discussed that are appropriate for the problem.) c. State your decision. d. State your conclusion in full sentences.
Answer:
a
The null hypothesis is [tex]H_o : \ \sigma^2 = 1.9[/tex]
The alternative hypothesis is [tex]H_a : \ \sigma^2 \ne 1.9[/tex]
b
[tex]X^2 = 13.74[/tex]
c
The decision rule is
Reject the null hypothesis
d
The conclusion is
There is no sufficient evidence to conclude that the variance of the immune response is equal to 1.9.
Step-by-step explanation:
From the question we are are told that
The variance is [tex]\sigma ^2 = 1.9[/tex]
The sample size is n = 30
The sample variance is [tex]s^2 = 0.9[/tex]
The level of significance is [tex]\alpha = 0.05[/tex]
The null hypothesis is [tex]H_o : \ \sigma^2 = 1.9[/tex]
The alternative hypothesis is [tex]H_a : \ \sigma^2 \ne 1.9[/tex]
Generally the test statistics is mathematically represented as
[tex]X^2 = \frac{ (n- 1 ) * s^2 }{ \sigma^2 }[/tex]
=> [tex]X^2 = \frac{ (30 - 1 ) * 0.9 }{1.9 }[/tex]
=> [tex]X^2 = 13.74[/tex]
Generally from the degree of freedom is mathematically represented as
[tex]df = n- 1[/tex]
=> [tex]df = 30 - 1[/tex]
=> [tex]df = 29[/tex]
Generally from the chi distribution table the critical value of [tex]\frac{\alpha}{2} \ and \ 1 - \frac{ \alpha }{2}[/tex] at a degree of freedom of [tex]df = 29[/tex] is
[tex]X^2 _{ \frac{\alpha }{2} , df } = X^2 _{ \frac{0.05 }{2} , 29 } = 45.7[/tex]
=> [tex]X^2 _{ 1 - \frac{\alpha }{2} , df } = X^2 _{1 - \frac{0.05 }{2} , 29 } = 16.0 5[/tex]
Gnerally from the values obtained we see that
[tex]X^2 < X^2 _{ 1 - \frac{\alpha }{2} , df }[/tex] hence
The decision rule is
Reject the null hypothesis
The conclusion is
There is no sufficient evidence to conclude that the variance of the immune response is equal to 1.9.
3. (03.01 LC) The domain of the following relation: R: {(-4, 8), (8, 10), (5, 4), (1, 6), (5, -9)} is (1 point) {8, 10, 4, 6, -9) {-4, 1, 5, 8) O {-4, 8, 5, 1, 5} No domain exists
Answer:
{-4, 1, 5, 8}
Step-by-step explanation:
The domain of a relation are all of the inputs (or x-values) of it.
Identify the x-values shown.
{(-4, 8), (8, 10), (5, 4), (1, 6), (5, -9)}
{-4, 1, 5, 8} is the domain of the relation.
Hope this helps.
Help me with this I need help
Simplify this problem :
2 5/8 - 1 1/3
Answer:
-1 1/24
Step-by-step explanation:
Answer:
31/24 is the simplified answer
Step-by-step explanation:
ILL GIVE BRAINLEST
Answer:
the 4th one
Step-by-step explanation:
Answer:
147/2
Step-by-step explanation:
Hi! y=k/x
y=21/4 and x=14 so k=147/2
Please mark brainliest and let me know if you have any more questions!