Answer:
n = 7
Step-by-step explanation:
simplify the logs according to their bases
Answer:
n = 7
Step-by-step explanation:
[tex]\sf \log_4(64)^{n+1}=log_5(625)^{n-1}[/tex]
Change 64 to an exponent with base 4 and 625 to an exponent with base 5:
[tex]\implies \sf \log_4(4^3)^{n+1}=log_5(5^4)^{n-1}[/tex]
Using exponent rule [tex](a^b)^c=a^{bc}[/tex]
[tex]\implies \sf \log_4(4)^{3(n+1)}=log_5(5)^{4(n-1)}[/tex]
Using log rule: [tex]\log_a(b^c)=c \log_a(b)[/tex]
[tex]\implies \sf 3(n+1)\log_4(4)}=4(n-1)log_5(5)[/tex]
Using log rule: [tex]\sf \log_a(a)=1[/tex]
[tex]\implies \sf 3(n+1)=4(n-1)[/tex]
[tex]\implies \sf 3n+3=4n-4[/tex]
[tex]\implies \sf 3+4=4n-3n[/tex]
[tex]\implies \sf n=7[/tex]
How many patients had more than 5 cavities?
Answer:
2 patients had more than 5 cavities.
step-by-step explanation:
5 cavities = 26 cavities = 07 cavities = 2Here cavities > 5
so only 2 patients had more than 5 cavities also as had total 7 cavities.
Answer:
2 patients had more than 5 cavities
Step-by-step explanation:
Each dot represents a different patient.
"More than 5" means numbers greater than 5 (so from 6 onwards).
From inspection of the dot plot, there are 2 dots above all the numbers that are greater than 5.
Therefore, there are 2 patients who had more than 5 cavities.
**see annotated dot plot**
The area shaded with a pink rectangle is "more than 5 cavities"
27 is 0.5% of what number
Answer:
54
Step-by-step explanation:
27 is half of what number?
27 x 2 = 54
:)
Answer:
135
Step-by-step explanation:
27 x 0.5 = 135
Hope it helps!!!!!
1
Leslie earned $12 Friday, $20 Saturday, and $56 Sunday selling bracelets. If she sold each bracelet for the same amount of money what is the most she could charge for each bracelet?
Answer:
$4
Step-by-step explanation:
For this, you want to find the greatest common factor
This basically means what number can be divided out of all of these.
So, you can find the factors for all of them and find which one appears in all three numbers and which is the greatest number
for 12:
1, 2, 3, 4, 6, 12
For 20:
1, 2, 4, 5, 10, 20
For 56:
1, 2, 4, 7, 8, 14, 28, 56
The numbers that appear in all of there are:
1, 2, and 4
And since we want to find the greatest amount she can charge for bracelet, the answer is:
$4
find the area of circle o if DCBO is a rectangle and DB measure 10 units
Answer:
[tex]100\pi[/tex]
Step-by-step explanation:
Step 1: Identity the radius.
Since O is the center of the circle, and C and E lie on the circumference, OC and OE are the radii of the circle and thus,
OC=OE.
Step 2: Consider the rectangle.
All diagonals in a rectangle are congruent so this means
DB= OC ( OC is also a diagonal).
Thus, OC= 10 units.
Step 3: Analyze
So this means OE is also 10 units as well.
Since we know the length of the radius, Use the area of circle,
[tex]\pi {r}^{2} [/tex]
[tex]\pi( {10}^{2} ) = 100\pi[/tex]
So the area of a circle is 100 pi.
Answer:
314.2 square units
Step-by-step explanation:
The diagonals of a rectangle are the same length, so segment OC is the same length as segment DB: 10 units. OC is a radius of the circle, which means the circle's radius is 10 units.
The area of a circle is given by ...
A = πr²
A = π(10 units)² = 100π units²
A ≈ 314.2 units²
The area of circle O is about 314.2 square units.
Help me out please I don’t understand
[tex]\\ \sf\Rrightarrow y=-4(x+2)^2-1[/tex]
Compare to the vertex form of parabola
y=a(x-h)^2+kh=-2k=-1So vertex should be at (h,k)=(-2,-1)
Graph attached
Help picture below problem 12
Write an equation for a perpendicular to y = - 2 x 2 and passing through the point (-4,-5)
Y=
[tex]======================================[/tex]
Perpendicular lines have slopes that are opposite reciprocals.
This means we take a number, flop it over, and change its sign.
So the slope of the given line is -2
Flop it over:
-1/2
Change its sign:
1/2
Now, let's write the equation in point-slope form:
y-y1=m(x-x1)
y-(-5)=1/2(x-(-4)
y+5=1/2(x+4)
y+5=1/2x+2
y=1/2x+2-5
[tex]\bold{y=\displaystyle\frac{1}{2} x-3}}[/tex]
[tex]==========================================[/tex]
Notes:-Hope everything's clear.Let me know if you have any questions!Enjoy your Day!Answered by:-~DnomaiD
;)
A culture started with 6000 becteria. after 4 hours it grew to 6600 becteria. Predict how many bacteria will be present after 10 hours. Round your answer to the nearest whole number. p=ae^kt
Answer:
7614
Step-by-step explanation:
The exponential growth of the bacteria culture can be modeled by the equation ...
p = a·b^(t/c)
where 'a' is the initial population, 'b' is the growth factor, and 'c' is the period over which that growth factor applies.
__
modelIn the given scenario, we have ...
a = 6000 bacteriab = 6600/6000 = 1.1 . . . . growth factorc = 4 hoursSo, our model is ...
p = 6000·1.1^(t/4)
__
applicationAfter 10 hours, the population is predicted to be ...
p = 6000·1.1^(10/4) ≈ 7614
We predict 7614 bacteria will be present after 10 hours.
__
Additional comment
If we compare the form we used to the one suggested in the proglem statement, we see
p = 6000·1.1^(t/4)p = 6000·e^(kt)For the bases of the exponential term to be the same, we must have ...
1.1^(t/4) = e^(kt)
(1.1^(1/4))^t = (e^k)^t . . . . . factor t from the exponent
1.1^(1/4) = e^k . . . . . . . match the bases
k = ln(1.1)/4 . . . . . take natural logs
k ≈ 0.0238275
and the equation becomes ...
p = 6000·e^(0.0238275t)
__
In terms of 'a', 'b', and 'c' used above, we find ...
k = ln(b)/c
Tim read 70% of his book containing 230 pages. How many pages does he have left?
Answer:
69
Step-by-step explanation:
To do this, you want to first find how many pages he has read
So, to get that you want to multiply 230 by 70% or 0.7 (70% = 0.7 because to get the percent, you multiply the number by 100)
230 * 0.7 = 161
BUT, since you want to find how many pages he has left, you subtract the amount of pages he has read by how many pagest here are in total like so:
230 - 161 = 69 pages left
If you have any questions feel free to ask in the comments, and if this helped it would be appreciated if you left a brainliest :)
need help please and I have more questions on the same topic like this .
Answer 1 1/4
Step-by-step explanation:
You can get this by finding 3/4 on the line plot and counting the x's. Then you must add the 3 x's which means 3 of 3/4 and sum is your answer. Be sure to change improper to proper fraction. 9/4 to 1 1/4.
Read the question and enter your response in the box prc
How do you write an equivalent expression -1/4(-8x+12y
Need some math help 50pts
Answer:
angle 1 and 3 are 127.3 degrees and angle 2 is 52.7 degrees
Step-by-step explanation:
so angle 2 is also 52.7 degrees because angle 2 and 4 are vertical oppostite angles
so we can look at it now that we have to find angle 1. since we know a line is 180 degrees we make angle 1 plus angle 2 equal to 180
let angle 1 be x
x + 52.7 = 180
x = 180 - 52.7
x = 127.3
Answer:
m∠1 = 127.3°
m∠2 = 52.7°
m∠3 = 127.3°
Step-by-step explanation:
Vertical Angle Theorem: When two straight lines intersect, the opposite vertical angles are always equal to each other.
⇒ m∠1 = m∠3 and m∠2 = m∠4
If m∠4 = 52.7° then m∠2 = 52.7°
Linear pair: Two adjacent angles which sum to 180°.
⇒ m∠1 + m∠2 = 180°
⇒ m∠3 + m∠4 = 180°
⇒ m∠3 + 52.7° = 180°
⇒ m∠3 = 180° - 52.7°
⇒ m∠3 = 127.3°
As m∠1 = m∠3 then m∠1 = 127.3° also.
List and describe the characteristics of a perfectly competitive market.
A market system with perfect competition is one in which there are several buyers and sellers interacting with the same goods.
A perfectly competitive market structure is widely found a market in the Indian economy. This market often accepts prices as a single seller cannot change the market price in the economy. Together with other characteristics, this trait sets this market apart from other types of markets.
Let's discuss the characteristics of the perfectly competitive market in detail which are as follows:
1. Large number of buyers and sellers- A commodity has a high number of buyers and sellers when there is ideal competition. Because there are so many customers, each one only purchases a very little portion of the available supply.
2. Homogeneous Products- Products in this market are homogenous in nature which means the products are identical in nature. This suggests that each company's output, in terms of quantity, quality, colour, size, features, etc., is a perfect substitute for the work of the others. This suggests that consumers don't care about what different companies produce.
3. Free entry and exit of firms- In the economy, there are 2 periods: long run and short run. In the long run, there is completely free entry and exit of firms while in the short run, some factors may contribute to the obstruction of entry and exit of firms. This guarantees that all businesses will ultimately make a regular profit or no economic profit, which evaluates the opportunity cost of the business to either continue operating or close.
4. Perfect Knowledge- In this market structure both the sellers and buyers have perfect knowledge of the market factors like price prevailing in the market because of this feature no seller can charge a higher price in the market to any customer.
5. No transportation cost- The products sold in this market structure are generally sold locally so there incur no transportation cost. Also because the same price is prevailing in the market sellers not require to transport anything.
6. No promotion cost- Homogeneous product is sold and uniform prices prevail so the sellers do not need to incur any selling cost like advterisemt for such a product. So the promotional cost incurred by firms is zero.
7. Price Taker- Firms are generally price takers in this structure of the market as sellers cannot influence the price of the goods so they need to accept the price that is prevailing in the market.
8. Perfect mobility of factors of production- Factors of production like Land, Labour and Capital are perfectly mobile in this market structure. These factors can freely move in and out of industry making demand and supply equal to each other.
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Frank ate 2/8 of the apple pie and
Jose at 3/8 of the cherry pie. How
much pie did Frank and Jose eat
altogether?
Answer:
answer 5/8 because 2/8 + 3/8= 5/8
Evaluate UV if possible.
Answer: B
Step-by-step explanation:
Multiply U and V:
[tex]\begin{pmatrix}-9&1&0\\ \:4&0&2\\ \:0&1&5\end{pmatrix}\begin{pmatrix}2\\ \:-2\\ \:1\end{pmatrix}[/tex]
[tex]\mathrm{Multiply \ the \ rows \ of \ the \ first \ matrix \ by \ the \ columns \ of \ the \ second \ matrix:}[/tex]
[tex]\begin{aligned}&\left(\begin{array}{ccc}-9 & 1 & 0\end{array}\right)\left(\begin{array}{c}2 \\-2 \\1\end{array}\right)=(-9) \cdot 2+1 \cdot(-2)+0 \cdot 1 \\&\left(\begin{array}{ccc}4 & 0 & 2\end{array}\right)\left(\begin{array}{c}2 \\-2 \\1\end{array}\right)=4 \cdot 2+0 \cdot(-2)+2 \cdot 1 \\&\left(\begin{array}{lll}0 & 1 & 5\end{array}\right)\left(\begin{array}{c}2 \\-2 \\1\end{array}\right)=0 \cdot 2+1 \cdot(-2)+5 \cdot 1\end{aligned}[/tex]
[tex]=\begin{pmatrix}\left(-9\right)\cdot \:2+1\cdot \left(-2\right)+0\cdot \:1\\ 4\cdot \:2+0\cdot \left(-2\right)+2\cdot \:1\\ 0\cdot \:2+1\cdot \left(-2\right)+5\cdot \:1\end{pmatrix}[/tex]
[tex]\mathrm{Simplify\:each\:part:}[/tex]
[tex]=\begin{pmatrix}-20\\ 10\\ 3\end{pmatrix}[/tex]
Therefore, the correct answer is B
Ms. Bassie bikes a total of 11/12 mile to get to and from work each day. Write
an expression that can be used to find the total number of miles that Ms.
Bassie bikes to and from work over 5 days. Then evaluate the expression.
Answer:
Step-by-step explanation:
1 day, she travels 11/12 of a mile.
5 days, she travels 5 * 11/12 miles
5*11/12 = 55/12 = 4 7/12 miles.
Solve. 9 m 3 − 27 m 2 − 252 m = 0
Answer:
m = 0
m = 7
m = -4
Step-by-step explanation:
[tex]\sf 9m^3-27m^2-252m=0[/tex]
Divide by 9:
[tex]\sf \implies m^3-3m^2-28m=0[/tex]
Factor out common term m:
[tex]\sf \implies m(m^2-3m-28)=0[/tex]
Factor expression in parentheses:
[tex]\sf \implies m(m-7)(m+4)=0[/tex]
Therefore,
[tex]\sf \implies m=0[/tex]
[tex]\sf \implies m-7=0 \implies m=7[/tex]
[tex]\sf \implies m+4=0 \implies m=-4[/tex]
1. Which of the following is a true statement?
a. A perfect square is a number whose
square root is, an even number.
b. The inverse of squaring a number is to
divide the number by 2.
C. To square a number, multiply the number by
itself.
d. All of the above.
Thank you so much
Answer:
C. To square a number, multiply the number by itself.
Answer:
[C] To square a number, multiply the number by itself.
Step-by-step explanation:
To square a number you multiply it by itself.
Let's go through all answer:
[A] A perfect square is a number whose square root is, an even number.
Explain for [A]:
It incorrect because perfect squares can be odd or even
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
[B] The inverse of squaring a number is to divide the number by 2.
Explain for [B]:
It incorrect because square roots are made by multiplying the number to itself.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
[D] All of the above
Explain for [D]
Know that [A] and [B] is wrong you can know that [D] is 100% wrong.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Lenvy~
The pair of figures to the right are similar. The area of one figure is given. Find the area of the other figure to the nearest whole number.
answer:
148ft²
explanation:
to solve this problem, we must set up a proportion.
[tex]\frac{side (L)}{area(L)} = \frac{side(S)}{area(S)} \\\frac{15}{185} = \frac{12}{x}[/tex]
15x=2220
x=148ft²
--
if this helped, please consider giving brainliest !
Given m \| nm∥n, find the value of x. (7x-10)° (6x-5)°
7x-10=6x-5
We simplify the equation to the form, which is simple to understand
7x-10=6x-5
We move all terms containing x to the left and all other terms to the right.
+7x-6x=-5+10
We simplify left and right side of the equation.
+1x=+5
We divide both sides of the equation by 1 to get x.
x=5
José plotted points on a coordinate plane to represent the vertices of a rectangle. The first
two points José plotted are shown below.
Jose's rectangle must have equal and parallel opposite sides
The coordinates of the other points could be C(7,5) and D(7,1)
How to determine the other points?The coordinates are given as;
A = (2,5).
B = (2,1).
To form a rectangle, each of the remaining points must have the same y-coordinates as points A and B.
So, we have:
C = (x,5)
D = (x,1)
Also, the remaining points must have the same x-coordinates.
i.e.
Cx = Dx
From the list of options, we have:
C(7,5) and D(7,1)
Hence, the coordinates of the other points could be C(7,5) and D(7,1)
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PLEASE HELP PLEASE I WILL GIVE BRAINLIEST
Answer:
143
Step-by-step explanation:
I'm not sure if this is correct but this is what I came up with:
all angles combined must add to 360
125+55+37= 217
360-217=143
if <1 and <2 are vertical angles. If m<1=(5x +12) and m<2=(6x-11), find m<1
Answer:
its 23
Step-by-step explanation:
Help picture below problem 5
Answer:
option A is the correct answer!!
Step-by-step explanation:
mark me brainliest
A) angel OJP
Explanation(name by its vertex, by the three points of the angle (the middle point must be the vertex),
Help me pls
Question 4 Part B (2 points): In part A you factored f(x) = 9m2 + 3m - 2. What are the x intercepts of this function? SELECT ALL THAT APPLY.
A.
m = -1/3
B.
m = 1/3
C.
m = -2/3
D.
m = 2/3
E.
m = 3
F.
m = -3
G.
m = 6
H.
m = -6
We need zeros
[tex]\\ \rm\Rrightarrow 9m^2+3m-2=0[/tex]
[tex]\\ \rm\Rrightarrow 9m^2-3m+6m-2=0[/tex]
[tex]\\ \rm\Rrightarrow 3m(3m-1)-2(3m-1)=0[/tex]
[tex]\\ \rm\Rrightarrow (3m-2)(3m-1)=0[/tex]
m=2/3mm=1/3Moose left a $7.50 tip for his waitress on a $50 restaurant bill. What percent of his bill did he leave as a tip?
Answer:
he left 15 % of his bill as a tip
Step-by-step explanation:
7.5/50 x 100
0.15 x 100
15
Percentage
7.5/50×1000.150(100)15.0%Trigonometric Equations
Solve the equation over the interval [0°, 360°)
2sin^2theta-5sintheta+3=0
Step-by-step explanation:
The solutions are
S
=
{
30
º
,
150
º
,
270
º
}
Explanation:
The equation is
2
sin
2
θ
+
sin
θ
−
1
=
0
We can factorise the LHS
(
2
sin
θ
−
1
)
(
sin
θ
+
1
)
=
0
Therefore,
sin
θ
=
−
1
,
⇒
,
θ
=
270
º
sin
θ
=
1
2
,
⇒
,
θ
=
30
º
,
150
º
Choose the multiplication problem that correctly shows partial products.
A) A
B) B
C) C
Answer:
B) B
Step-by-step explanation:
2 times 4 is 8, so in this case the option is option b as none of the other options show this.
In total,
2 * 4 = 8
60 * 4 = 240
240 + 8 = 248
Jazmine is picking an outfit to wear to a party. She has 5 pairs of pants, 7 shirts, and 4 pairs of shoes to choose from. The number of possibilities Jazmine has to wear to the party is ———- than 120.
xzavier makes a conjecture that the sun of two odd integers is always an even integer which choice is the best proof of his conjecture
PLEASE I NEED THIS NOWWWWWWW
Answer:
2n+1
Step-by-step explanation:
i dont know but i tried to do it in paper and got this