Answer: x = 22
Step-by-step explanation: To get x by itself, we divide both sides by 2 and we have x = 22 which is the solution to this equation.
Answer:x=22
Step-by-step explanation:divide 3 by both sides makes x=22
Reflected across the x-axis ? How is look in the figure
Answer:
Well a shape reflecting across the x axis will look like some thing in the image below.
Look at both images.
A camera shop stocks eight different types of batteries, one of which is type A76. Assume there are at least 30 batteries of each type.
Required:
a. How many ways can a total inventory of 30 batteries be distributed among the eight different types.
b. How many ways can a total inventory of 30 batteries be distributed among the eight different types if the inventory must include at least four A76 batteries?
c. How many ways can a total inventory of 30 batteries be distributed among the eight different types if the inventory includes at most three A7b batteries?
Answer:
a. 10295472 ways
b. 4272048 ways
c. 6023424 ways
Step-by-step explanation:
Given that:
Camera shop stocks ----- 8 different types of batteries
one of which is ---- A76
Assume that there are ------ at least 30 batteries of each type.
a.
How many ways can a total inventory of 30 batteries be distributed among the eight different types.
The number of ways a total inventory of 30 batteries be distributed is :
[tex]= \left \{ {{30+8-1} \atop {30}} \right. \}[/tex]
[tex]= \left \{ {{37} \atop {30}} \right. \}[/tex]
[tex]=\dfrac{37!}{30! *7!}[/tex]
[tex]= \dfrac{37*36*35*34*33*32*31*30!}{30!*7*6*5*4*3*2*1}[/tex]
[tex]= \dfrac{37*36*35*34*33*32*31}{7*6*5*4*3*2*1}[/tex]
= 10295472 ways
b.
How many ways can a total inventory of 30 batteries be distributed among the eight different types if the inventory must include at least four A76 batteries?
If we must include 4 A76 batteries; then the number of ways a total inventory of 30 batteries can be distributed among eight different types of batteries will be:
30 - 4 = 26 batteries
Now;
[tex]= \left \{ {{26+8-1} \atop {26}} \right. \}[/tex]
[tex]= \left \{ {{33} \atop {26}} \right. \}[/tex]
[tex]=\dfrac{33!}{26! \ \ 7!}[/tex]
[tex]=\dfrac{33*32*31*30*29*28*27*26!}{26! \ * \ 7*6*5*4*3*2*1}[/tex]
[tex]=\dfrac{33*32*31*30*29*28*27}{ \ 7*6*5*4*3*2*1}[/tex]
= 4272048 ways
c. If we must include at most three A7b batteries. the number of ways that a total inventory of 30 batteries can be distributed among eight different types of inventory is:
[tex]= \sum \limits ^3 _{x=0} \left \{ {{(30-x)+7-1} \atop {30-x}} \right. \} \\ \\ \\ = \sum \limits ^3 _{x=0} \left \{ {{(30-0)+7-1} \atop {30-0}} \right. \} = (^{36}_{30})+(^{35}_{29})+ (^{34}_{28})+ (^{33}_{27})[/tex]
[tex]= \dfrac{36!}{30! * 6!} + \dfrac{35!}{29! * 6!} + \dfrac{34!}{28! * 6!} + \dfrac{33!}{27! * 6!}[/tex]
= 1947792 + 1623160 + 1344904 + 1107568
= 6023424 ways
is lmn congruent to opq if so name the postulate
Answer:
Option (A)
Step-by-step explanation:
Given:
LM ≅ OP
MN ≅ PQ
∠M ≅ ∠P
To Prove:
ΔLMN ≅ ΔOQP
Statements Reasons
1). LM ≅ OP 1). Given
2). MN ≅ PQ 2). Given
3). ∠P ≅ ∠M 3). Given
4). ΔLNM ≅ ΔOQP 4). By the SAS postulate of congruence.
[Side - Angle - Side]
Therefore, Option (A) will be the answer.
Factor by grouping 5x^3+6x^2+25x+30
Answer:
(5x + 6) (x² + 5)
Step-by-step explanation:
5x³ + 6x² + 25x + 30
= x² (5x + 6) + 25x + 30 -- Group 5x³ and 6x²
= x² (5x + 6) + 5 (5x + 6) -- Group 25x and 30
= (5x + 6) (x² + 5) -- Both terms have a common factor of 5x + 6
The quick ratio, Q, is calculated using the formula Q= CA-I-P/ CL, where CA is the value of the company’s current assets, I is inventory, P is prepaid expenses, and CL is current liabilities. Rearrange the formula for current assets
Answer:
CA = Q·CL +I +P
Step-by-step explanation:
Multiply by the denominator, then add the opposite of all terms that are not CA.
[tex]Q=\dfrac{CA-I-P}{CL}\\\\Q\cdot CL=CA-I-P\\\\Q\cdot CL+I+P=CA\\\\\boxed{CA=Q\cdot CL+I+P}[/tex]
Assume that the helium porosity (in percentage) of coal samples taken from any particular seam is normally distributed with true standard deviation 0.78.
Requried:
a. Compute a 95% CI for the true average porosity of a certain seam if the average porosity for 20 specimens from the seam was 4.85.
b. Compute a 98% CI for true average porosity of another seam based on 16 specimens with a sample average of 4.56.
c. How large a sample size is necessary if the width of the 95% interval is to be 0.40?
d. What sample size is necessary to estimate the true average porosity to within 0.2 with 99% confidence?
Answer:
a) The 95% CI for the true average porosity is (4.51, 5.19).
b) The 98% CI for true average porosity is (4.11, 5.01)
c) A sample size of 15 is needed.
d) A sample size of 101 is needed.
Step-by-step explanation:
a. Compute a 95% CI for the true average porosity of a certain seam if the average porosity for 20 specimens from the seam was 4.85.
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.95}{2} = 0.025[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.025 = 0.975[/tex], so [tex]z = 1.96[/tex]
Now, find the margin of error M as such
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 1.96*\frac{0.78}{\sqrt{20}} = 0.34[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 4.85 - 0.34 = 4.51
The upper end of the interval is the sample mean added to M. So it is 4.35 + 0.34 = 5.19
The 95% CI for the true average porosity is (4.51, 5.19).
b. Compute a 98% CI for true average porosity of another seam based on 16 specimens with a sample average of 4.56.
Following the same logic as a.
98% C.I., so [tex]z = 2.327[/tex]
[tex]M = 2.327*\frac{0.78}{\sqrt{16}} = 0.45[/tex]
4.56 - 0.45 = 4.11
4.56 + 0.45 = 5.01
The 98% CI for true average porosity is (4.11, 5.01)
c. How large a sample size is necessary if the width of the 95% interval is to be 0.40?
A sample size of n is needed.
n is found when M = 0.4.
95% C.I., so Z = 1.96.
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
[tex]0.4 = 1.96*\frac{0.78}{\sqrt{n}}[/tex]
[tex]0.4\sqrt{n} = 1.96*0.78[/tex]
[tex]\sqrt{n} = \frac{1.96*0.78}{0.4}[/tex]
[tex](\sqrt{n})^{2} = (\frac{1.96*0.78}{0.4})^{2}[/tex]
[tex]n = 14.6[/tex]
Rounding up
A sample size of 15 is needed.
d. What sample size is necessary to estimate the true average porosity to within 0.2 with 99% confidence?
99% C.I., so z = 2.575
n when M = 0.2.
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
[tex]0.2 = 2.575*\frac{0.78}{\sqrt{n}}[/tex]
[tex]0.2\sqrt{n} = 2.575*0.78[/tex]
[tex]\sqrt{n} = \frac{2.575*0.78}{0.2}[/tex]
[tex](\sqrt{n})^{2} = (\frac{2.575*0.78}{0.2})^{2}[/tex]
[tex]n = 100.85[/tex]
Rounding up
A sample size of 101 is needed.
For the data set represented by this box plot, what is the value of the maximum? maximum:
Answer:
140
Step-by-step explanation:
The maximum is the furthest the line that goes out the furthest, the minimum would be about 83-84
Answer:
the other person is correct!
Step-by-step explanation:
Each of 100 students in the Allen School can only take 1 CSE class each, between the four classes CSE 311, CSE 312, CSE 331, and CSE 332. Each student (independently of others) takes CSE 311 with probability 0.3, CSE 312 with probability 0.4, CSE 331 with probability 0.1, and CSE 332 with probability 0.2. What is the probability that exactly 31 sign up for CSE 311, 39 sign up for CSE 312, 7 sign up for CSE 331, and 23 sign up for CSE 332
Answer:
[tex]P(a=31,b=39,c=7,d=23) = 0.000668[/tex]
Step-by-step explanation:
Sample space, n = 100
Let the number of students signed up for CSE 311 = a
Let the number of students signed up for CSE 312 = b
Let the number of students signed up for CSE 331 = c
Let the number of students signed up for CSE 332 = d
Probability of taking CSE 311, [tex]P_a[/tex] = 0.3
Probability of taking CSE 312, [tex]P_b[/tex] = 0.4
Probability of taking CSE 331, [tex]P_c[/tex] = 0.1
Probability of taking CSE 332, [tex]P_d[/tex] = 0.2
[tex]P(a,b,c,d) = \frac{n!}{a! b! c! d!} p_a^{a} p_b^{b} p_c^{c} p_d^{d} \\P(a=31,b=39,c=7,d=23) = \frac{100!}{31! 39! 7! 23!} * 0.3^{31} * 0.4^{39} * 0.1^{7} 0.2^{23}\\P(a=31,b=39,c=7,d=23) = \frac{4.58*10^{111}}{2.13*10^{56}* 5040 }* (1.57*10^{-55})\\P(a=31,b=39,c=7,d=23) = 0.000668[/tex]
Simplify The square root of 5 (6-4 the square root of 3)
Answer:
7.75
Step-by-step explanation:
6-4=2
2 times the square root of 3=3.46410161514
square root of 5 times 3.46410161514=7.74596669242
to 2dp=7.75
9/3 *[(18-10)-2^2]
36
12
0.25
0.75
Answer:
12
Step-by-step explanation:
Use the PEMDAS
there is a parenthesis and exponents
9/3{(8) - 4)}
Multiply and divide 9/3= 3
Also subtract 8-4 = 4
3{8-4}
3(4)= 12
Sphere A has a diameter of 2 and is dilated by a scale factor of 3 to create sphere B. What is the ratio of the volume of sphere A to sphere B? 2:6 4:36 1:3 1:27
Answer:
1:27 (D)
Step-by-step explanation:
Given:
Sphere A has a diameter of 2
Sphere A is dilated to create sphere B
Scale factor = 3
Volume of a sphere = 4/3 πr³
Radius = r = diameter/2 = 2/2
r = 1
Volume of sphere A = 4/3 ×π(1)³
Volume of sphere A = 4/3 × π
Volume of sphere B = 4/3 πR³
Since the diameter was dilated, the diameter of B = diameter of A × scale factor
diameter of B = 2×3 = 6
Radius of B = R = diameter/2 = 3
Volume of sphere B = 4/3 × π(3)³
Volume of sphere B = (4/3)(27)π
Ratio of the volume of sphere A to volume of sphere B
= [4/3 ×π]: [(4/3)(27)π]
= (4π/3)/[(4π/3)×27] = 1/27
= 1:27
Answer: 1:27
Step-by-step explanation:
The original volume * scale factor cubed = new volume.
The scale factor is 3 and 3^3 is 27, so the ratio is 1:27
A 7 cm x 5 cm rectangle sits inside a circle with radius of 6 cm. What is the area of the shaded region? Round your final answer to the nearest hundredth. Please answer fast!
Answer:78.14cm^2
Step-by-step explanation:
There are members on the board of directors for a certain non-profit institution. a. If they must elect a chairperson, first vice chairperson, second vice chairperson, and secretary, how many different slates of candidates are possible? b. If they must form an ethics subcommittee of four members, how many different subcommittees are possible?
Answer: a. 1320
b.495
Step-by-step explanation:
Complete question is provided in the attachment.
Total members on the board = 12
a. Persons to chose : chairperson, first vice chairperson, second vice chairperson, and secretary
i.e. Total 3 posts in an order.
Number of ways to choose 3 persons from 12 in an order = [tex]^{12}P_3[/tex] [By permutation]
[tex]=\dfrac{12!}{(12-3)!}\\\\=\dfrac{12!}{7!}\\\\=12\times11\times10\\\\=1320[/tex]
hence, 1320 different slates of candidates are possible .
b. number of ways to choose 4 members out of 12 ( order not matters)=[tex]^{12}C_{4}[/tex] [By combinations]
[tex]=\dfrac{12!}{4!8!}\\\\=\dfrac{12\times11\times10\times9}{24}\\\\=495[/tex]
Hence, the number of different subcommittees are possible =495
You buy a 33-pound bag of flour for $9 or you can buy a 1- pound bag for $0.39. Compare the per pound cost for the large and small bag. How much is the pounds per dollar
Answer:
see below
Step-by-step explanation:
9 dollars / 33 lbs = .272727 dollars per lb
.39 / 1 lbs = .39 per lb
The large bag is less expensive
Step-by-step explanation:
33lb bag = $9.00
1lb = $0.39
$9.00 bag per pound is $.0.27 per pound
If I bought 33, 1 pound bags it would cost $12.87
cheaper by $ 3.87 to buy the 9lb bag.
PLEASE HELPP! f(x)= -3x + 3
Which of the graphs represent the inverse of the function F??
Answer:
Answer is Y
Step-by-step explanation:
Which statement best describes the function below?
f(x)=x2-x2-9x+9
Answer:
B. It is a many-to-one function.
Step-by-step explanation:
To find what the function below is, you can use the Function Grapher and Calculator from Math is Fun to graph the function.
As you can see, the graph passes the vertical line test, since each x-value has exactly one y-value.
According to the diagram below, the function will be a many-to-one function, since there are y-values that have three different x-values.
So, your answer will be B. it is a many-to-one function.
Hope this helps!
Simplify e^ln4
A. 1/4
B. 4
C. 1n4
D. E^4
Answer:
The answer is option B.
4Step-by-step explanation:
Using the expression
[tex] {e}^{ ln(x) } = x[/tex]
[tex] {e}^{ ln(4) } = 4[/tex]
Hope this helps you
Tom takes a cancer test and the test is advertised as being 99% accurate: if you have cancer you will test positive 99% of the time, and if you don't have cancer, you will test negative 99% of the time. If 1% of all people have cancer and Tom tests positive, what is the prob that Tom has the disease
Answer:
99% chance tommy has it
Step-by-step explanation:
cuz do da math
6 out of 9 pairs of your jeans are blue. What percentage of you
jeans are NOT blue?
Answer:
33.333333%
Step-by-step explanation:
If 6/9 (66.66666666%) of the jeans are blue it means that 3/9 of the jeans are not blue. 3/9 as a percentage is 33.333333%
Answer:
33.3%
Step-by-step explanation:
6 ÷ 9 = 66.66666667%
100% - 66.66666667% = 33.3% (Or you can put 33.33333333)
Hope this helped! :)
Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Enter a number. Round your answer to four decimal places.) μ = 24; σ = 4.2 P(x ≥ 30) = ?
Answer:
Step-by-step explanation:
x is a random variable. Since we are assuming that x has a normal distribution, then we would apply the formula,
z = (x - µ)/σ
Where
x = sample mean
µ = population mean
σ = standard deviation
From the information given,
µ = 24
σ = 4.2
The indicated probability to be determined is P(x ≥ 30)
P(x ≥ 30) = 1 - P(x < 30)
For P(x < 30),
z = (30 - 24)/4.2 = 1.43
Looking at the normal distribution table, the probability corresponding to the z score is 0.9236
Therefore,
P(x ≥ 30) = 1 - 0.9236 = 0.0764
For what value of the variable: 1. are the values of the expressions 2m−13 and m+3 equal? 2. is the value of 2x+1 twenty greater than 8x+5? 3. is the value of 9−y twice as much as the value of y?
Answer:
1.- m = 13
2.- [tex]x<-\frac{2}{3}[/tex]
3.- y = 3
Step-by-step explanation:
In all cases we need to start with an equation or an inequality and slove for the variable:
Case 1. : 2 m - 13 = m + 3
[tex]2m-13=m+3\\2m-m=3+13\\m=16[/tex]
Case 2. : 2 x + 1 > 8 x + 5 + 20
[tex]2x+1>8x+25\\1-25>8x-2x\\-24>6x\\-4 >x\\x<-4[/tex]
Case 3. : 9 - y = 2 y
[tex]9-y=2y\\9=2y+y\\9=3y\\y=3[/tex]
A pet store has 32 more dogs than cats. If there are a total of 144 dogs and cats altogether, then how many cats does the pet store have?
PLZ ANSWER ASAP THANKS
Answer:
56 cats
88 dogs
Step-by-step explanation:
x=cats
x+32=dogs
x+x+32=144
2x=144-32
2x=112
x=112/2
x=56 (56 cats)
x+32=88 (88 dogs)
Answer:
56
Step-by-step explanation:
In order to solve this question you need to subtract 32 by 144 then divide that answer by 2.
So we know that they're 32 more dogs then cats and there is 144 dogs and cats all together.
[tex]144 - 32 = 112[/tex]
Divide it in half
[tex]112 \div2=56[/tex]
[tex]56+32 = 88[/tex]
[tex]= 56[/tex]
Therefore they're 56 cats in the pet store.
Hope this helps.
Write an equation in point-slope form for each line.
(If possible please show work)
Answer:
y= -2x+3
Step-by-step explanation:
Point slope form= y=mx+b
The m is the slope.
So, we have an incomplete equation right now: y= -2x+b
We want to find b. We can do that by plugging in values for the x and y coordinates. Fortunately, we do have a set of coordinates, (1, 1)!
We plug them in:
1= -2(1)+b
1= -2+b
b=3
So, since we have the slope and the b, also called the y-intercept, we can form an equation!
y= -2x+3
When testing for current in a cable with sixsix color-coded wires, the author used a meter to test threethree wires at a time. How many different tests are required for every possible pairing of threethree wires?
Answer:
20 tests
Step-by-step explanation:
There are six different wires, and for each test the author picks three, this means that each test is a combination of three out of six wires (₆C₃) . The number of total combinations possible is given by:
[tex]_6C_3=\frac{6!}{(6-3)!3!}\\_6C_3=\frac{6*5*4}{3*2*1}\\_6C_3=20[/tex]
20 tests are required to verify every possible pairing of three wires.
Please answer this correctly
Answer:
0
Step-by-step explanation:
The probability of picking a even number is 1/3
If u don’t replace it then the probability of picking an even number is 0/3
Multiply and u get 0/9 or 0
Hope this helps
Answer:
0
Step-by-step explanation:
The number 2 is even.
The probability of picking an even number is 1/3.
You don't put the first card back.
1 and 3 are odd.
1/3 × 0 = 0
What are the characteristics of a socialist economy? What are the pros and cons of this type of economy?
Answer:
The pro is Political Control, the cons, however, are many.
Step-by-step explanation:
However, A Socialist Economy cons outweigh its pros. The only thing that is a PRO is you dictating it, preventing people from success. Wanna know the cons? The Cons are more Regulations, to which chokes more businesses of their money, they function, & motive. To which it has a chain reaction of: The Businesses not employing people, more people are out of work, which means more people ain't buying stuff to support the businesses, which means the businesses are out of business, they shut down.
The Economy ain't something that you can stop, or go, & it ain't statistics. An Economy is just.. people, that's it. It's just people, they are the ones that work, run businesses & factories, they are the ones that buy N' sell. They create, craft, invent, innovate, etc.
Here's a quote that I have: "The more you choke it from breathing in, the less it breathes out". That's my stance on regulation & Socialism, to which Socialism is just Voluntary Communism, & A Permanent Ideological belief that Big government Involvement is the way to go.
To which, it's not!
What is the measure of angle ABC? Please answer quickly!
Answer:
ABC = 88
Step-by-step explanation:
Angle Formed by Two Chords = 1/2( sum of Intercepted Arcs)
ABD = 1/2 ( 131+ 53)
ABD = 1/2 (184)
=92
ABC = 180 -ABD
ABC = 88
Find value of z and simplify completely.
Answer:
3√10Given:
A right triangle in which an altitude is drawn from the right angle vertex
To find: value of X
We have leg rule in similarity in right triangle as:
[tex] \frac{leg}{part} = \frac{hypotenuse}{leg} \\ [/tex]
Plugging the given values,
[tex] \frac{z}{3} = \frac{3 + 27}{z} \\ z \times z = 3(3 + 27) \: \: (cross \: multiplication) \\ {z}^{2} = 9 + 81 \\ {z}^{2} = 90 \\ z = \sqrt{90} \\ z = 3 \sqrt{10} [/tex]
Hope this helps...
Good luck on your assignment..
If the area to the left of x in a normal distribution is 0.187, what is the area to the right of x? (Enter an exact number as an integer, fraction, or decimal.)
Answer:
Area to the right is 0.813
Step-by-step explanation:
Since the area under the full normal distribution should render "1" (one), then the area to the right of x should be:
1 - area to the left of x = 1 - 0.187 = 0.813
The area to the right of x in this normal distribution will be 0.813.
What is a normal distribution?The majority of the observations are centered around the middle peak of the normal distribution, which is a continuous probability distribution that is symmetrical around its mean.
The probabilities for values that are farther from the mean taper off equally in both directions. Extreme values in the distribution's two tails are likewise rare.
Not all symmetrical distributions are normal, even though the normal distribution is symmetrical.
We know that the total area described in a normal distribution is 1.
Given, that the area to the left of x in a normal distribution is 0.187.
So, the area to the right of x will be,
1 - 0.187.
= 0.813.
learn more about normal distribution here :
https://brainly.com/question/15103234
#SPJ2
Which parent function is f(x) = x^2?
O A. An exponential parent function
OB. The linear parent function
C. The absolute value parent function
D. The quadratic parent function
Answer:
D. Quadratic parent function.
Step-by-step explanation: