9=(1/27)^a+3 find a
-11/3
-7/3
7/3
11/3
Step-by-step explanation:
I think you made some mistakes in the problem definition.
I guess you mean
9 = (1/27)^(a+3)
let's think about how to create 9 out of 1/27 just by using exponents.
we note that 27 is 3³. and therefore the cubic root of 27 is 3.
so,
(1/27)^(1/3) = 1/3
because the exponent 1/3 means "cubic root". an exponent 1/2 means square root. and so on.
making the exponent negative means 1/...
so,
(1/27)^(-1/3) = 3
and now, with what exponent operation can we turn 3 into 9 ?
by squaring it.
so,
((1/27)^(-1/3))² = 9
putting an exponent on an exponent means to multiply the exponents during simplification.
therefore,
((1/27)^(-1/3))² = (1/27)^(-2/3) = 9
that means
a + 3 = -2/3
a = -2/3 - 3 = -2/3 - 9/3 = -11/3
so, the first answer option is correct.
Slope of line that passes through (3,6) and (8,2
Answer:
-4/5
Step-by-step explanation:
To find the slope of a line with two points, we do y2-y1/x2-x1.
y2 is 2. y1 is 6.
2-6 = -4
x2 is 8. x1 is 3
8-3 = 5
-4/5 is the answer meaning it is the slope.
Answer:
Slope of this line = -4/5.
Step-by-step explanation:
The formula is
Slope = (y2-y1)/(x2-x1) where (x1, y1) and (x2, y2) are the 2 points.
So here we have:
(6-2)/(3-8)
= -4/5.
A statement of an employee's biweekly earnings is given below. earnings deductions week ended regular fed. soc. med state with. with. care. with. net pay 8/18 $_____ $62.00 $45.06 $10.54 $12.40 $596.80 what is the employee's gross pay? a. $703.86 b. $714.40 c. $716.26 d. $726.80 please select the best answer from the choices provided a b c d
The amount of the gross pay of the employee is 726.80 dollars. Then the correct option is D.
What is addition?Taking two or more numbers and adding them together, or the entire amount of two or more numbers in addition.
A statement of an employee's biweekly earnings is given below. earnings deductions week ended regular is shown below.
$62.00, $45.06, $10.54, $12.40, $596.80
Then their sum will be
→ $62.00 + $45.06 + $10.54 + $12.40 + $596.80 = 726.80
More about the addition link is given below.
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Need help asap
6. Choose a number that will produce an irrational answer when added to 7/8
Answer:
√7
Step-by-step explanation:
√7 is the only irrational number because it has the radical sign
√
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5+2√3 / 7+4√3 = a-6√3
please answer this
[tex]~~~~\dfrac{5+2\sqrt 3}{7+4\sqrt 3} = a- 6\sqrt 3\\\\\\\implies a= \dfrac{5+2\sqrt 3}{7+4\sqrt 3}+6\sqrt3 \\\\\\\implies a=\dfrac{\left(5+2\sqrt 3 \right) \left( 7-4\sqrt 3\right)}{\left(7+4\sqrt 3 \right) \left(7-4\sqrt 3 \right)}+6\sqrt 3\\\\\\\implies a = \dfrac{35-20\sqrt 3+14\sqrt 3-24}{7^2 - \left(4\sqrt 3 \right)^2}+6\sqrt 3\\\\\\\implies a=\dfrac{11-6\sqrt 3}{49-48}+6\sqrt 3\\\\\\\implies a=11-6\sqrt 3+6\sqrt 3\\\\\\\implies a = 11[/tex]
Please show the figure in a piece of paper
Step-by-step explanation:
If you have any dout you can ask me.
A university decides to accept only the top 15% of
the applicants applying. Their acceptance is based on
performance on an entrance exam. If the mean was 70 and
the standard deviation was 8, then what is the minimum
score needed to be accepted to the university?
The minimum score needed to be accepted in the university when it takes only top 15% performers where performace had mean 70 score and standard deviation of 8 is found being 78.32 approx.
How to get the z scores?If we've got a normal distribution, then we can convert it to standard normal distribution and its values will give us the z score.
If we have
[tex]X \sim N(\mu, \sigma)[/tex]
(X is following normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] )
then it can be converted to standard normal distribution as
[tex]Z = \dfrac{X - \mu}{\sigma}, \\\\Z \sim N(0,1)[/tex]
(Know the fact that in continuous distribution, probability of a single point is 0, so we can write
[tex]P(Z \leq z) = P(Z < z) )[/tex]
Also, know that if we look for Z = z in z tables, the p value we get is
[tex]P(Z \leq z) = \rm p \: value[/tex]
For this case, suppose that:
X = the score a student gets in the considered university's entrance exam.
Then, we have:
[tex]X \sim N(\mu = 70, \sigma = 8)[/tex]
Let X = x be the score such that scores bigger than x is 15% of all the scores applicants get.
That means, P(X > x) = 15% of the total area the distribution of X have under its normal distribution. Or, we can say that there is 15% chance of getting scores above X = x
Now, we can rewrite this statement as:
[tex]1 - P(X \leq x) = 0.15[/tex]
Converting X to Z (standard normal variate), we get:
[tex]1 - P(X \leq x ) = 0.15\\\\1 - P\left(Z \leq z = \dfrac{x - 70}{8} \right) =0.15\\\\P(Z \leq z = (x-70)/8) = 0.85[/tex]
The value Z = z for which the p-value is approx 0.85 is found from the z-tables as:
Thus, we get:
[tex]z = \dfrac{x-70}{8}\\x = 8z + 70\\x \approx 8 \times 1.04 + 70 = 78.32[/tex]
Thus, the minimum score needed to be accepted in the university when it takes only top 15% performers where performace had mean 70 score and standard deviation of 8 is found being 78.32 approx.
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I need help with #1 & #2
Answer:
2. Letter B, see the attachment?
and also, I can't answer the #1 because I can't read it. I'm sorry
Already done #1 in your other question.
#2
2x-y=4y=2x-4Comapre to slope intercept form
slope=m=2Parallel lines have equal slope
Equation in point slope form
y+11=2(x+3)y+11=2x+6y=2x-5In order to better decide how to market a new line of clothing, mary is researching the demographics of the customers of a certain clothing store. she counted the number of customers who visited the store over the course of a month, and found out how many of the customers were high school students. her collected data is in the table below. week 1 2 3 4 customers 2,848 3,141 3,861 3,911 students 2,033 1,937 2,076 1,721 mary predicts that the store will see 4,238 customers next week. approximately how many high school students should the store expect next week? a. 1,865 b. 2,392 c. 2,446 d. 3,025
Number of high school students which should the store expect next week, Mary predicts that the store will see 4,238 customers next week is 2392.
What is expected value?The expected value is the long term average of the data or the mean of the data.
In order to better decide how to market a new line of clothing, Mary is researching the demographics of the customers of a certain clothing store.
She counted the number of customers who visited the store over the course of a month, and found out how many of the customers were high school students.
Her collected data is in the table below.
Week 1 2 3 4 Customers 2,848 3,141 3,861 3,911 Students 2,033 1,937 2,076 1,721Mary predicts that the store will see 4,238 customers next week.
From using the long term mean value calculator for the provided data, the predicted value of the next week we get as 2392.
Hence, the number of high school students which should the store expect next week, Mary predicts that the store will see 4,238 customers next week is 2392.
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Answer:
B
Step-by-step explanation:
B because the of the is the cool make of giga chad braincells :)
Maggie made 3 withdrawals of $30 each from her bank account. She also wrote a check for $50. What change did these transactions have on her bank account balance? F $80 g-$80 H $140 j-$140
There are 20 machines at the gym and Manuel wants to perform exercises on 5 different machines while he is there. How many different ways can he select the machines to use?
31008
1860480
100
15504
Selection of machines is persons choice and not arranged specifically, thus we will use Combination.
⇒ 20C5
⇒ 20!/5!(20-5)!
⇒ 15504
Use combination
total ways
[tex]\\ \rm\dashrightarrow ^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]
[tex]\\ \rm\dashrightarrow ^{20}C_5[/tex]
[tex]\\ \rm\dashrightarrow \dfrac{20!}{5!15!}[/tex]
[tex]\\ \rm\dashrightarrow \dfrac{20(19)(18)(17)(16)(15!)}{5(4)(3)(2)(15!}[/tex]
[tex]\\ \rm\dashrightarrow 15504[/tex]
The length of the hypotenuse, line segment ac, in right triangle abc is 25 cm. the length of line segment bc is 15 cm. which is the approximate measure of angle acb? 31.0° 36.9° 53.1° 59.0°
The approximate measure of angle acb in right triangle abc in which the length of the hypotenuse, line segment ac is 25 cm is 53.1 degrees.
What is right angle triangle property?In a right angle triangle, ratio of the adjacent side to the hypotenuse side is equal to the cosine angle between them.
[tex]\cos\theta=\dfrac{b}{c}[/tex]
Here, (a) is the adjacent side, (c) is the hypotenuse side and θ is the angle made between them.
The right triangle abc is given, in which,
The length of the hypotenuse, line segment ac, in right triangle abc is 25 cm. The length of line segment bc is 15 cm.According to the right angle triangle property,
[tex]\cos(acb)=\dfrac{bc}{ac}\\\cos(acb)=\dfrac{15}{25}\\\angle acb=\cos^{-1}(0.6)\\\angle acb=53.1^o[/tex]
Hence, the approximate measure of angle acb in right triangle abc in which the length of the hypotenuse, line segment ac is 25 cm is 53.1 degrees.
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Answer:
53.1 degrees.
Step-by-step explanation:
I DONT DO MATHHHHH?????
A medical center conducted a study to investigate cholesterol levels in people who have had heart
attacks. A random sample of 16 people was obtained from the names of all patients of the medical
center who had a heart attack in the previous year. Of the people in the sample, the mean cholesterol level was 264.70 milligrams per deciliter (mg/dL) with standard deviation . Assuming all conditions for inference were met, which of the following is a 90 percent confidence interval for the mean cholesterol level, in, of all patients of the medical center who had a
heart attack in the previous year?
Using the t-distribution, as we have the standard deviation for the sample, it is found that the 90% confidence interval is (246.6, 282.8).
What is a t-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The critical value, using a t-distribution calculator, for a two-tailed 90% confidence interval, with 16 - 1 = 15 df, is t = 1.7531.
Researching the problem on the internet, the standard deviation was of 42.1 mg/dL, hence the parameters are as follows:
[tex]\overline{x} = 264.7, s = 41.2, n = 16[/tex]
Thus, the bounds of the interval are given by:
[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 264.7 - 1.7531\frac{41.2}{\sqrt{16}} = 246.6[/tex]
[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 264.7 + 1.7531\frac{41.2}{\sqrt{16}} = 282.8[/tex]
The 90% confidence interval is (246.6, 282.8).
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Need some help with math
Answer:
Question 6 answer is 35
Step-by-step explanation:
using pythagoras theorem, hypotenuse²= opposite²+ adjacent²
since it is said that we're looking for the hypotenuse then the values given are for opposite and adjacent.
therefore, hyp²= 21²+28²
hyp²= 1225 take square root of both sides to eliminate square and find hypotenuse
hyp= 35
Quick help please it will mean a lot if you help me :)
Answer:
Green heart is 2 and blue shape is 8.
Step-by-step explanation:
We know 1 purple drop equals 3.
So 3+3 = 6
The total weight is 16 so we can do 16-6 = 10
We have 10 left. Since we need the weight to be balanced the green heart must be 2.
Because then it would be 8 on 1 side (2 purples equals 6 and 1 heart equals 2, so 6+2=8) and 8 on the other side (8+8=16).
Question 5 of 5
Roshaun kept track of the number of hours that he spent
playing his saxophone each week for several weeks. He
spent 8 25 10 and 5 hours.
What is the range of the data set?
O A 10 hours
B. Shours
C. 5 hours
OD 6 hours
SUBMIT
PREVIOUS
There is a bag filled with 4 blue and 5 red marbles.
A marble is taken at random from the bag, the colour is noted and then it is replaced.
Another marble is taken at random.
What is the probability of getting 2 that are different in colour?
Answer:
50% chance
Step-by-step explanation:
obviously
Which table contains only the points that lie on the line represented by y=5/4x-3
Answer:
A table that represents a linear equation should be your answer. This means your slope should be constant/straight not like a parabola or absolute function.
Step-by-step explanation:
When you're trying to solve something using slope-intercept you can graph it or plug numbers for (x,y).
Graph:
Start at (0,-3)
Then plot the point since that is your Y-Intercept
Then go 5 up and 4 over to find your next point.
Once done, you should connect the dots to form a slope or a linear equation.
189.939360828 to 4 decimal places.
Answer:
189.9394
Step-by-step explanation:
Since 6 is >= 5, the 3 thurns into a 4
Bradley owns 2 surfboards and 4 wet suits. If he takes one surfboard and one wet suit to the beach, how many different combinations can he choose?
Answer:
The answer is eight
Step-by-step explanation:
4*2=8
help w this !!!!!!!!!!
Answer:
1. BC = 24
Perimeter of ABCD = 96
3. PT = 9
ST = 7
Step-by-step explanation:
Question 1
All the side lengths of a rhombus are equal.
Therefore, BC = AB = 24
So the perimeter of ABCD = 24 × 4 = 96
Question 3
The diagonals of a rhombus bisect each other at right angles.
Bisect means to divide into two equal parts.
Therefore, PT = TR so PT = PR ÷ 2
As PR = 18 then PT = 18 ÷ 2 = 9
QT = ST so ST = QS ÷ 2
As QS = 14 then ST = 14 ÷ 2 = 7
Who’s in 10th grade and who’s in 9th? I’m doing a poll for math?
Answer:
I'm in 10th
hope that would help, lol
I need help with is question please.
can some help me with this one question pls
Answer:
turn it
Step-by-step explanation:
30 point question if you answer!
Find the volume of the shaded region of the figure. Round answer to the nearest hundredths place.
Answer:
Step-by-step explanation:
Cylinder
Start by finding the volume of the cylinder as though the spheres were not there.
Volume of a cylinder = pi r^2 h
r = 6 inches
h = 25 inches. Put the givens in the formula
Volume = pi 6^2 * 25
Volume = pi * 36 * 25
Volume = 900 pi
One sphere
Don't try and find the volume of both spheres. Just do one and double it.
V = pi * (4/3) * r^3
r = 6 inches
V = pi * (4/3) * 6^3
V = pi * 288 Cubic inches
Two spheres
Total volume spheres = 2 * 288 pi
Total Volume of spheres = 576 pi
Volume of the shaded region.
The following will act as a formula for the answer to the question
V_shade = Volume of the cylinder - volume of the 2 spheres
Substitute values into formula
Volume shade = 900 * pi - 576* pi Take out common factor (pi)
Volume shade = pi * (900 - 576 )
Volume of the shaded area
Volumne shade = pi *324
pi = 3.14
Volume shade = 1017.36
Answer:
volume of the shaded region = 1018
Step-by-step explanation:
What is the completely factored form of f(x) = x3 – 2x2 – 5x 6? f(x) = (x 2)(x – 3)(x 6) f(x) = (x 2)(x – 3)(x – 6) f(x) = (x – 2)(x 3)(x – 1) f(x) = (x 2)(x – 3)(x – 1)
[tex]x^3-2x^2-5x +6\\\\=x^3-x^2-x^2+x-6x+6\\\\=x^2(x-1)-x(x-1)-6(x-1)\\\\=(x-1)(x^2 -x -6)\\\\=(x-1)(x^2 -3x +2x -6)\\\\=(x-1)\textbf{[} x(x-3) +2(x-3)\textbf{]}\\\\=(x-1)(x-3)(x+2)[/tex]
The requried, factored form of the given expression is (x - 1)(x - 3)(x + 2).
What are the factors?A number or algebraic expression that evenly divides another number or expression—i.e., leaves no remainder—is referred to as a factor.
To factor the polynomial f(x) = x³ – 2x² – 5x + 6 completely, we can use a combination of the rational root theorem and synthetic division.
We can use synthetic division to test each possible root and see if it is a factor of the polynomial. Starting with x = 2, we have:
2 | 1 -2 -5 6
| 2 0 -10
|_____________
1 0 -5 -4
Since the remainder is not zero, x = 2 is not a factor of the polynomial. Continuing with the other possible roots, we find that x = 1 and x = 3 are roots, but x = -1, x = -2, x = -3, and x = -6 are not roots.
Therefore, we can factor the polynomial as follows:
f(x) = x² – 2x² – 5x + 6
= (x - 1)(x - 3)(x + 2)
So the completely factored form of f(x) is f(x) = (x - 1)(x - 3)(x + 2).
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Consider the line y=-7x+8. -- Find the equation of the line that is perpendicular to this line and passes through the point (8. -3). Find the equation of the line that is parallel to this line and passes through the point (8. –3).
Equation of perpendicular line:
Equation of parallel line:
Answer:
Step-by-step explanation:
Perpendicular formula
m1 * m2 = - 1
Givens
m1 = - 7
m2 = ??
Solution
-7 * m2 = -1
m2 = 1/7
y = 1/7 x + b
x = 8
y = -3 Substitute these values into y = 1/7 x + b
-3 = (1/7)*8 + b
-3 = 8/7 + b Subtract 8/7 from both sides
-3 - 8/7 = b
-4 1/7 = b
Answer (perpendicular line) y = (1/7) x - 4 1/7 or
Answer (perpendicular line) y = (1/7) x - 4.14
Parallel line
Nothing changes except you have a different y intercept.
y = -7x + b
x = 8
y = -3 Substitute these values into y = -7x + b
-3 = -7*8 + b
-3 = - 56 + b
-3 + 56 = b
b = 53
Equation Parallel line: y = -7x + 53
The bowling team at Lincoln High School must choose a president, vice president, and secretary. If the team has 20 members, how many ways could the officers be chosen?
Using the permutation formula, as the order is important, it is found that the officers can be chosen in 6840 ways.
Each "position" is a different role(president, vice president and secretary), hence the order is important.
What is the permutation formula?The number of possible permutations of x elements from a set of n elements is given by:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
In this problem, 3 people will be chosen from a set of 20, hence:
[tex]P_{20,3} = \frac{20!}{17!} = 6840[/tex]
The officers can be chosen in 6840 ways.
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