Answer:
a) P(A∩B) = 0.29
b) P1 = 0.1
c) P = 0.35
Step-by-step explanation:
Let's call A the event that the motorist stop at the first signal, and B the event that the motorist stop at the second signal.
From the question we know:
P(A) = 0.39
P(B) = 0.54
P(A∪B) = 0.64
Where P(A∪B) is the probability that he stop in the first, the second or both signals. Additionally, P(A∪B) can be calculated as:
P(A∪B) = P(A) + P(B) - P(A∩B)
Where P(A∩B) is the probability that he stops at both signals.
So, replacing the values and solving for P(A∩B), we get:
0.64 = 0.39 + 0.54 - P(A∩B)
P(A∩B) = 0.29
Then, the probability P1 that he just stop at the first signal can be calculated as:
P1 = P(A) - P(A∩B) = 0.39 - 0.29 = 0.1
At the same way, the probability P2 that he just stop at the second signal can be calculated as:
P2 = P(B) - P(A∩B) = 0.54 - 0.29 = 0.25
Finally, the probability P that he stops at exactly one signal is:
P = P1 + P2 = 0.1 + 0.25 = 0.35
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!
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 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.
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
The weight of male babies less than months old in the United States is normally distributed with mean pounds and standard deviation pounds. Answer the following.
Required:
a. What proportion of babies weigh more than 12 pounds?
b. What proportion of babies weigh less than 15 pounds?
c. What proportion of babies weigh between 9 and 13 pounds?
d. Is it unusual for a baby to weigh more than 18.1 pounds?
Answer:
a. P ( X > 12 ) = 0.5254
b. P ( X < 15 ) = 0.7172
c. P ( 9 < X < 13 ) = 0.3179
d. Not unusual
Step-by-step explanation:
Solution:-
- We will define our random variable X as follows:
X: The weights of the male babies less than 2 month old in USA ( lb )
- The distribution given for the random variable ( X ) is defined to follow normal distribution.
- The normal distribution is identified by two parameters mean ( u ) and standard deviation ( σ ). The distribution is mathematically stated or expressed as:
X ~ Norm ( u , σ^2 )
- The parameters for the normal distribution followed by the random variable ( X ) are given. Hence,
X ~Norm ( 12.3 , 4.7^2 )
- We will use standard normal tables to determine the following probabilities:
a) What proportion of babies weigh more than 12 pounds?
- To use the standard normal tables we need to standardized our limiting value of the required probability by finding the corresponding Z-score value.
- The formula used to compute the Z-score value is given below:
[tex]Z-score = \frac{x - u}{sigma}[/tex]
- We are requested to compute the probability p ( X > 12 ). the limiting value is 12 pounds. We will use the conversion formula and compute the Z-score:
[tex]Z-score = \frac{12 - 12.3}{4.7} \\\\Z-score = -0.06382[/tex]
- The standard normal table gives the probabilities of Z-score values in "less than ". So to determine the required probability we look-up:
P ( X > 12 ) = P ( Z > -0.06382 ) = ...
P ( Z > -0.06382 ) = 1 - P ( Z < -0.06382 )
Use standard normal look-up table:
P ( X > 12 ) = 1 - 0.4746
P ( X > 12 ) = 0.5254 ... Answer
Answer: The proportion of babies that weigh more than 12 pounds is the probability of finding babies weighing more than 12 pounds among the total normally distributed population. The proportion is 0.5254
b) What proportion of babies weigh less than 15 pounds?
- We are requested to compute the probability p ( X < 15 ). the limiting value is 12 pounds. We will use the conversion formula and compute the Z-score:
[tex]Z-score = \frac{15-12.3}{4.7} \\\\Z-score = 0.57446[/tex]
- The standard normal table gives the probabilities of Z-score values in "less than ". So to determine the required probability we look-up:
P ( X < 15 ) = P ( Z < 0.57446 )
P ( X < 15 ) = 0.7172
Answer: The proportion of babies that weigh less than 15 pounds is the probability of finding babies weighing less than 15 pounds among the total normally distributed population. The proportion is 0.7172
c) What proportion of babies weigh between 9 and 13 pounds?
- We are requested to compute the probability p ( 9 < X < 13 ). the limiting value are 9 and 13 pounds. We will use the conversion formula and compute the Z-score:
[tex]Z_1 = \frac{9-12.3}{4.7} = -0.70212\\\\Z_2 = \frac{13-12.3}{4.7} = 0.14893\\[/tex]
- The standard normal table gives the probabilities of Z-score values in "less than ". So to determine the required probability we look-up:
P ( 9 < X < 13 ) = P ( -0.70212 < X < 0.14893 )
P ( -0.70212 < X < 0.14893 ) = P ( X < 0.14893 ) - P ( X < -0.70212 )
Use standard normal look-up table:
P ( 9 < X < 13 ) = 0.5592 - 0.2413
P ( 9 < X < 13 ) = 0.3179 ... Answer
Answer: The proportion of babies that weigh less than 13 pounds but greater than 9 pounds is the probability of finding babies weighing less than 13 pounds and more than 9 pounds among the total normally distributed population. The proportion is 0.3179
d)
Is it unusual for a baby to weigh more than 18.1 pounds?
- We are requested to compute the probability p ( X > 18.1 ). the limiting value is 18.1 pounds. We will use the conversion formula and compute the Z-score:
[tex]Z-score = \frac{18.1-12.3}{4.7} \\\\Z-score = 1.23404[/tex]
The standard normal table gives the probabilities of Z-score values in "less than ". So to determine the required probability we look-up:
P ( X > 18.1 ) = P ( Z > 1.23404 )
P ( X > 18.1 ) = 0.1086
Answer: The proportion of babies that weight more than 18.1 pounds are 0.1086 of the total babies population. We can say that the proportion of babies that weigh more than 18.1 pounds are significant because the proportion lies is significant. Not enough statistical evidence to be classified as "unusual".
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
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.
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.
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
I have k quarters, five less quarters than nickels and one more than twice as many dimes as quarters. Find the value of the coins in cents in terms of k.
Answer:
(35k + 20) cents
Step-by-step explanation:
First of all, let us have the value of each unit:
1 quarter = 25 cents
1 nickel = 5 cents
1 dime = 10 cents
Given that number of quarter = k
Quarters are 5 lesser than Nickels, so number of nickels = k+5
One more than twice as many dimes as quarters:
k = 2 [tex]\times[/tex] Number of Dimes + 1
So, number of dimes = [tex]\frac{1}{2}(k-1)[/tex]
Value of quarters = [tex]25 \times k[/tex] cents
Value of nickels = [tex]5 \times (k+5) = (5k+25)\ cents[/tex]
Value of dimes = [tex]\frac{1}{2}(k-1) \times 10 = (5k-5)\ cents[/tex]
So, total value of coins =
[tex]25k + 5k +25 +5k-5\\\Rightarrow (35k+20)\ cents[/tex]
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:
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
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!
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 horizontal force of 480 n is applied to a stationary wooden box in one direction and a 600 n horizontal force is applied in the opposite direction. What is the additional force is needed for the box to remain stationary
Answer:
Step-by-step explanation:
In a static position, the sum of the forces is always 0.
so:
F1 = 480 N
F2 = -600 N
F3 = ?
F1 + F2 + F3 = 0
480 - 600 + F3 = 0
F3 = 120 N (the answer is positive, so the force acts in the same direction as F1)
Write the equation of each line in slope-intercept form.
(If possible please show work)
Answer:
[tex]\displaystyle y = -\frac{2}{3}\, x - 9[/tex].
Step-by-step explanation:
The slope-intercept form of a line on a cartesian plane should be in the form:
[tex]y = m\, x + b[/tex],
where:
[tex]m[/tex] is the slope of the line, while [tex]b[/tex] is the [tex]y[/tex]-coordinate of the point where the line intersects the [tex]y[/tex]-axis.The question states that the slope of this line is [tex]\displaystyle -\frac{2}{3}[/tex]. In other words, [tex]\displaystyle m = -\frac{2}{3}[/tex]. The next step is to find the value of [tex]b[/tex]. That could be done using the information that the point [tex](-6,\, -5)[/tex] is on this line.
Note that the slope-intercept form of a line [tex]y = m\, x + b[/tex] is essentially an equation about [tex]x[/tex] and [tex]y[/tex]. For a point [tex](x_0,\, y_0)[/tex] to be on that line, [tex]x = x_0[/tex] and [tex]y = y_0[/tex] should satisfy its equation. In other words, it must be true that [tex]y_0 = m\, x_0 + b[/tex].
For the point [tex](-6,\, -5)[/tex], [tex]x_0 = -6[/tex] and [tex]y_0 = -5[/tex]. The equation would be:
[tex]\underbrace{-5}_{y_0} = m \times \underbrace{(-6)}_{x_0}+ b[/tex].
Besides, the slope of this line is already known to be [tex]\displaystyle m = -\frac{2}{3}[/tex]. Therefore, this equation would become:
[tex]\displaystyle \underbrace{-5}_{y_0} = \underbrace{\left(-\frac{2}{3}\right)}_{m} \times \underbrace{(-6)}_{x_0}+ b[/tex].
Solve this equation for [tex]b[/tex]:
[tex]b = -9[/tex].
Hence, the slope-intercept form ([tex]y = m\, x + b[/tex]) of this line would be:
[tex]\displaystyle y = -\frac{2}{3}\, x - 9[/tex].
help!! its algebra..
Answer:
The correct answer to this is "Change in Y over Change in X"
Step-by-step explanation:
Change in Y over Change in X is the basis of the saying "rise over run". When you divide the rise by the run you get the slope.
I hope this helps you out!
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
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]
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
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..
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.
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
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
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]
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
A professor gives a statistics exam. The exam has 100 possible points. The scores for the students in the second classroom are as follows:
88 88 92 88 88 72 96 88 84
Calculate the sample size, n, and the sample mean, M n = M =
While grading the exam, the professor realizes that one of the questions covered material that was not yet covered in the lectures. This question was worth 20 points, so he decides to add 20 points to everyone's score.
Calculate the new n and M.
Answer:
N = 9
M = 87.11
Step-by-step explanation:
According to the situation, the data provided and the solution are as follows
The scores for the student in the classroom is
= 88 88 92 88 88 72 96 88 84
The different student's number of scores is 9
The solution of new n and M is shown below:-
Sample size (n) = 9
Sample mean (m) is
[tex]= \frac{Sum\ of\ all\ data\ values}{Sample\ size}[/tex]
= [tex]\frac{88 + 88 + 92 + 88 + 88 + 72 + 96 + 88 + 84}{9}[/tex]
[tex]= \frac{784}{9}[/tex]
= 87.11
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
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.
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