Answer:
see below
Step-by-step explanation:
Part A: (72)^x = 1
Take the log base 72 of each side
log72(72^x) = log 72(1)
We know log a^b = b log a
x log72(72) = log72(1)
x = log72(1)
x = 0
Part A: (70)^x = 1
Take the log base 70 of each side
log70(70^x) = log70(1)
We know log a^b = b log a
x log70(70) = log70(1)
x = log70(1)
x = 0
There are two machines available for cutting corks intended for use in wine bottles. The first produces corks with diameters that are normally distributed with mean 3 cm and standard deviation 0.08 cm. The second machine produces corks with diameters that have a normal distribution with mean 3.04 cm and standard deviation 0.03 cm. Acceptable corks have diameters between 2.9 cm and 3.1 cm.
What is the probability that the first machine produces an acceptable cork? (Round your answer to four decimal places.)
What is the probability that the second machine produces an acceptable cork? (Round your answer to four decimal places.)
Please explain the math behind your answer so I am able to understand!(:
Answer:
0.7888 = 78.88% probability that the first machine produces an acceptable cork.
0.9772 = 97.72% probability that the second machine produces an acceptable cork.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
First machine:
Mean 3 cm and standard deviation 0.08 cm, which means that [tex]\mu = 3, \sigma = 0.08[/tex]
What is the probability that the first machine produces an acceptable cork?
This is the p-value of Z when X = 3.1 subtracted by the p-value of Z when X = 2.9. So
X = 3.1
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{3.1 - 3}{0.08}[/tex]
[tex]Z = 1.25[/tex]
[tex]Z = 1.25[/tex] has a p-value of 0.8944
X = 2.9
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{2.9 - 3}{0.08}[/tex]
[tex]Z = -1.25[/tex]
[tex]Z = -1.25[/tex] has a p-value of 0.1056
0.8944 - 0.1056 = 0.7888
0.7888 = 78.88% probability that the first machine produces an acceptable cork.
What is the probability that the second machine produces an acceptable cork?
For the second machine, [tex]\mu = 3.04, \sigma = 0.03[/tex]. Now to find the probability, same procedure.
X = 3.1
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{3.1 - 3.04}{0.03}[/tex]
[tex]Z = 2[/tex]
[tex]Z = 2[/tex] has a p-value of 0.9772
X = 2.9
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{2.9 - 3.04}{0.03}[/tex]
[tex]Z = -4.67[/tex]
[tex]Z = -4.67[/tex] has a p-value of 0
0.9772 - 0 = 0.9772
0.9772 = 97.72% probability that the second machine produces an acceptable cork.
The in center is the center of the circle of a triangle
1) circumscribed
2) centralized
3) cocentric
4) inscribed
Answer:
inscribed
Step-by-step explanation:
For any given triangle, the circle inside of it is called the Inscribed circle
Hello please help me solve this inequality shown in the graph, thank you so much!
Please help I will give you Brainlyest
Answer:
below
Step-by-step explanation:
Clare's mistake was the writing of 4000 in standard form
he wrote 4 ×10²
instead of 4 ×10³
Answer:
Step 1
Step-by-step explanation:
I believe Claire's mistake is when she tries to simplify 4000
She says that 4000 = 4 × 10²
4000 is actually equal to 4 ×10³
Write the word sentence as an inequality.
3.2 less than a number t is at most 7.5
t-3.2 ≤ 7.5
"at most" means less than or equal to
Please help me please !!
convert 6 miles to meters
Answer:
9656.06 meters
Step-by-step explanation:
evaluate the expression when f=6 12f+3
Answer:
75
Step-by-step explanation:
Substitute 6 for f
12f+3=
12*6+3=
72 + 3 = 75
Answer:
12f+3 = 75 when f = 6
Step-by-step explanation:
12f+3
Let f = 6
12*6+3
Multiply
72 +3
Add
75
Alexander is collecting aluminum cans for charity. One empty 355 ml can weighs about 17 g. It takes 59 cans to get about 1 kg of 100% recyclable aluminum.
Over one month, he collected 1297 cans.
What is the mass, in kilograms, of these cans?
Answer:
22 kg
Step-by-step explanation:
1297 cans * (17 grams)/(1 can) * (1 kg)/(1000 g) = 22.049 kg
Answer: 22 kg
Olivia randomly samples 50 students attending a basketball game and asks what grade they are in. Of the studets surveyed, 19 were in the seventh grade. I
there are 200 students attending the basketball game, based on the sample, how many of them are in seventh grade?
Answer:
76
Step-by-step explanation:
19 out of 50 are in 7th grade.
200/50 = 4
Multiply both numbers in the ratio by 4.
19 out of 50 = 76 out of 200
Answer: 76
The number of arrivals per minute at a bank located in the central business district of a large city was recorded over a period of 200 minutes with the results shown in the table below.
Complete parts (a) and (b)
Arrivals Frequency
0 21
1 46
2 40
3 36
4 25
5 20
6 8
7 3
8 1
a. Compute the expected number of arrivals per minute.
μ=___( please type as an integer or a decimal)
b. Compute the standard deviation
σ=___(please round to three decimal places as needed)
Answer:
a. μ = 25
b. σ = 16.496
Step-by-step explanation:
Note: See the attached excel for the calculation of Mean and Deviation from Mean.
Let: N = Number of observation = 9
F = Frequency
Therefore, we have:
a. Compute the expected number of arrivals per minute. μ=___( please type as an integer or a decimal)
From the attached excel file, we have:
Total F = 200
Therefore, we have:
μ = Mean = Total of F / (N - 1) = 200 / (9 - 1) = 25
b. Compute the standard deviation σ=___(please round to three decimal places as needed)
From the attached excel file, we have:
Total (F - μ)^2 = 2,177
σ = Standard deviation = (Total of (F - μ)^2 / (N - 1))^0.5 = (2,177 / (9 - 1))^0.5 = 16.496
Find the surface area of a square pyramid with side length 4 yd and slant height 6 yd.
Answer:
112 yd²
Step-by-step explanation:
Surface area of the square pyramid = area of base + perimeter of base × slant height
Area of base = s²
s = 4 yd
Area = 4² = 16 yd²
Perimeter = 4(s)
Perimeter = 4(4) = 16 yd
Slant height = 6 yd
Surface area of the square pyramid = 16 + 16 × 6
= 16 + 96
= 112 yd²
Find the midpoint of the equation y = 4x - 6 between the x-intercepts and the y-intercepts.
Step-by-step explanation:
y int
x=0
y=4(0)-6
y=-6
0;-6
x int
y=0
0=4x-6
6=4x
6/4=x
3/2=x
3/2;0
Answer:
Below in bold.
Step-by-step explanation:
y = 4x - 6
Find y-intercept:
y = 4(0) - 6 = -6
Y intercept is at (0, -6)
x-intercept:
4x - 6 = 0
4x = 6
x = 6/4 =1.5.
x intercept is at (1.5, 0)
Midpoint is at ((0+1.5)/2, (-6 + 0)/2)
= (0.75, -3)
What is the slope formula?
Answer:
(y2-y1)/(x2-x1)
Step-by-step explanation:
The slope is the change in y over the change in x
(y2-y1)/(x2-x1)
where ( x1,y1) and (x2,y2) are two points on the line
Answer:
O A. [tex]\frac{y2-y1}{x2-x1}[/tex]
Step-by-step explanation:
This is just about how the Slope-Formula works
ok so you get two points off a graph then you use it to plot it in the Slope-Formula like this
for example imma go with (-2, 5) and (3, 7)
I need to subtract 7 - 5 / 3 - -2. so...
m = slope
m = [tex]\frac{y2-y1}{x2-x1}[/tex]
m = [tex]\frac{7-5}{3--2}[/tex] Only add the denominators when there's 2 - signs together
m = [tex]\frac{2}{5}[/tex]
Solve the inequality 5u≤8u−21 and write the solution in interval notation
Answer:
Step-by-step explanation:
[tex]5u\leq 8u-21[/tex]
Subtract 8u from both sides
[tex]-3u\leq -21[/tex]
Divide by -3 on both sides
[tex]u\geq 7[/tex]
Interval notation: [greater/less than or equal to], (greater or equal to)
[7,∞)
The solution to the inequality is u ≥ 7, which means that u is greater than or equal to 7. In interval notation [ 7, ∞).
What is inequality?In mathematics, an inequality is a remark that two values or expressions are not equal. An inequality uses one of the comparison symbols: "<" (less than), ">" (greater than), "≤" (less than or equal to), "≥" (greater than or equal to), or "≠" (not equal to).
Here,
To solve the inequality 5u ≤ 8u - 21, we can start by isolating u on one side of the inequality. We can do this by subtracting 5u from both sides:
5u ≤ 8u - 21
-3u ≤ -21
Divide both sides by -3. Note that dividing by a negative number will reverse the direction of the inequality:
u ≥ 7
Therefore, the solution to the inequality is u ≥ 7, which means that u is greater than or equal to 7. In interval notation [ 7, ∞).
Learn more about inequality here:
brainly.com/question/14098842
#SPJ2
For numbers 6-10, how long does it take to travel:
11. A car travels 200 kilometers in 8 hours. Calculate the average speed of the car in:
a. Kilometer per hour
b. Kilometers per minute
This question have no choices specify your answers only
Answer:
A
Step-by-step explanation:
You divide distance over time so 200 divided by 8.
What is the length of u and v in this 30-60-90 triangle
Answer:
option 2
Step-by-step explanation:
Using trigonometric ratio:
[tex]Cos \ 60 = \frac{adjacent } {hypotenuse} \\\\\frac{1}{2} = \frac{4}{u}\\\\1 \times u = 2 \times 4 \\\\u = 8[/tex]
Now using Pythagoras theorem we will find v
[tex]8^2 = 4^2 + v^2\\\\64 = 16 + v^2\\\\v^2 = 64 - 16 \\\\v = \sqrt{48} = \sqrt{16 \times 3} = \sqrt{4^2 \times 3 } = 4\sqrt{3}[/tex]
By using trigonometric relations, we will see that v = 4*√3 and u = 8
How to get the missing lengths?
Here we have a right triangle, we can use trigonometric relations to find the missing sides.
We can see that v is the opposite cathetus of the 60° angle, then we can use the relation:
tan(a) = (opposite cathetus)/(adjacent cathetus)
Replacing what we know, we get:
tan(60°) = v/4
4*tan(60°) = v = 4*√3
To get the value of u, we use:
cos(a) = (adjacent cathetus)/(hypotenuse).
cos(60°) = 4/u
u = 4/cos(60°) = 2*4 = 8
Then we have:
v = 4*√3
u = 8
If you want to learn more about triangles, you can read:
https://brainly.com/question/17972372
Zeus Computer Chips, Inc., used to have major contracts to produce the Centrino-type chips. The market has been declining during the past three years because of the quad-core chips, which it cannot produce, so Zeus has the unpleasant task of forecasting next year. The task is unpleasant because the firm has not been able to find replacement chips for its product lines. Here is demand over the past 12 quarters:
Two Years
Ago Last Year This Year
I 4800 I 3500 I 3,200
II 3500 II 2700 II 2100
III 4300 III 3500 III 2700
IV 3,000 IV 2,400 IV 1700
Use the decomposition technique to forecast demand for the next four quarters.
Answer:
1st quarter := 2488.23
2nd quarter = 1646.50
3rd quarter = 1893.98
4th quarter = 1152.93
Step-by-step explanation:
Forecast demand in the next four quarters
intercept ( a ) = 3116.67 - (- 168.25 * 6.5 ) = 4210.29
Slope ( b ) = ( 219041.15 ) - ( 12 * 6.5 * 3,116.67 ) / 650 - ( 12 * ( 6.5)^2 )
= -24059.11 / 143 = -168.25
Forecast demand = a + bt = 4210.29 + 168.25t
1st quarter := 2488.23
2nd quarter = 1646.50
3rd quarter = 1893.98
4th quarter = 1152.93
Values calculated using data from table attached below ( table 2 )
Which values for A and B will create many solutions for this system of equations? 4x-Ay=15 -4x+6y=B
Answer:
A = 6; B = -15
Step-by-step explanation:
To have an infinite number of solutions, both equations must be the same.
4x - Ay = 15
-4x + 6y = B
The only coefficient we see in both equations is the coefficient of the x term. We have -4x and 4x. Multiply both sides of the second equation by -1.
4x - Ay = 15
4x - 6y = -B
For the equation to be equal, we need each term of one equation to be equal to the corresponding term of the other equation.
4x and 4x are equal.
-Ay must equal -6y
-Ay = -6y
-A = -6
A = 6
15 must equal -B
-B = 15
B = -15
Answer: A = 6; B = -15
Which inequality is true?
А. Зп > 9
B. 7 + 8< 11
C. 27 -1 < 5
D. 2 > 2
SUBMIT
< PREVIOUS
9514 1404 393
Answer:
А. Зп > 9
Step-by-step explanation:
The inequality of A may or may not be true. (It is true only if n > 3.) All of the others are definitely false.
help please quick please
Answer:
the answer is 3.5
Step-by-step explanation:
(0.020(5/4) + 3 ((1/5) – (1/4)))
Answer:
- 0.125
Step-by-step explanation:
Given the equation :
(0.020(5/4) + 3 ((1/5) – (1/4)))
0.020(5/4) = 0.025
3((1/5) - (1/4)) = 3(1/5 - 1/4) = 3(-0.05) = - 0.15
0.025 + - 0.15 = 0.025 - 0.15 = - 0.125
(2 1
2
-
4
-
5
) ÷
3
-
4
Answer:
[tex]63\frac{6}{9}[/tex]
Step-by-step explanation:
[tex](212-4-5)[/tex] ÷ [tex]3-4=[/tex]
[tex]203[/tex] ÷ [tex]3-4=[/tex]
[tex]67\frac{6}{9}-4=[/tex]
[tex]=63\frac{6}{9}[/tex]
Hope this helps
Recounting Rectangles
How many rectangles are
there in the figure below?
Answer:
gimme a second, I'll comment
PLEASE HURRY i need an answer now please help
Answer:
2 hours
Step-by-step explanation:
10/50 * 10 = 2
Find the surface area of the regular pyramid.
Answer:
B
Step-by-step explanation:
Base area = side^2 = 3^2 = 9 m^2
Base perimeter = side x 4 = 3 x 4 = 12 m
LA = (base perimeter x slant height)/2 = (12 x 5)/2 = 30 m
SA = base area + LA = 9 + 30 = 39 m^2
HELP I will give brainliest I am begging you only a few questions
Answer:
Graph A: (0,10) Graph B: (0,20)
Graph A: Height (feet) Graph B: Hight (feet)
Graph A: 138 Graph B: 120
Graph A: 32.6 Graph B: 43
Step-by-step explanation:
The smaller text was really blurry but I tried my best. Hope this helps!
Answer:
Step-by-step explanation:
I just pointed the answers, but quality of picture is poor: it's impossible to indicate the numbers on y-axis, and tell exact number on x-axis.
answer the following questions
1. 2 2/3 divided by 1 1/6.
2. 6 2/3 divided by 2 6/7.
3. 4 1/6 divided by 10.
4. 6 1/2 divided by 3/4.
5. 3 3/4 divided by 5 5/8
Answer:
1. [tex]2 \frac{2}{7} [/tex]
2. [tex]2 \frac{1}{3} [/tex]
3. [tex] \frac{5}{12} [/tex]
4. [tex]8 \frac{2}{3} [/tex]
5. [tex] \frac{2}{3} [/tex]
Step-by-step explanation:
[tex]1. \: \: 2 \frac{2}{3} \div 1 \frac{1}{6} [/tex][tex] \frac{8}{3} \div \frac{7}{6} [/tex]
[tex] \frac{8}{3} \times \frac{6}{7} [/tex]
[tex]8( \frac{2}{7} )[/tex]
[tex] \frac{8 \times 2}{7} [/tex]
[tex] \frac{16}{7} [/tex]
[tex]2 \frac{2}{7} [/tex]
[tex]2. \: \: 6 \frac{2}{3} \div 2 \frac{6}{7} [/tex][tex] \frac{20}{3} \div \frac{20}{7} [/tex]
[tex] \frac{20}{3} \times \frac{7}{20} [/tex]
[tex] \frac{1}{3} \times 7[/tex]
[tex] \frac{7}{3} [/tex]
[tex]2 \frac{1}{3} [/tex]
[tex]3. \: \: 4 \frac{1}{6} \div 10[/tex][tex] \frac{25}{6} \div \frac{10}{1} [/tex]
[tex] \frac{25}{6} \times \frac{1}{10} [/tex]
[tex] \frac{5}{6} \times \frac{1}{2} [/tex]
[tex] \frac{5}{6 \times 2} [/tex]
[tex] \frac{5}{12} [/tex]
[tex]4. \: \: 6 \frac{1}{2} \div \frac{3}{4} [/tex][tex] \frac{13}{2} \div \frac{3}{4} [/tex]
[tex] \frac{13}{2} \times \frac{4}{3} [/tex]
[tex]13( \frac{2}{3} )[/tex]
[tex] \frac{13 \times 2}{3} [/tex]
[tex] \frac{26}{3} [/tex]
[tex]8 \frac{2}{3} [/tex]
[tex]5. \: \: 3 \frac{3}{4} \div 5 \frac{5}{8} [/tex][tex] \frac{15}{4} \div \frac{45}{8} [/tex]
[tex] \frac{15}{4} \times \frac{8}{45} [/tex]
[tex] \frac{1}{4} \times \frac{8}{3} [/tex]
[tex] \frac{2}{3} [/tex]
Hope it is helpful...At the grocery store, Diego has narrowed down his selections to 4 vegetables, 8 fruits, 6 cheeses, and 4 whole grain breads. He wants to use the Express Lane, so he can only buy 15 items. In how many ways can he choose which 15 items to buy if he wants all 6 cheeses
Answer:
Diego can choose the 15 items in 128 different ways.
Step-by-step explanation:
Since at the grocery store, Diego has narrowed down his selections to 4 vegetables, 8 fruits, 6 cheeses, and 4 whole grain breads, and he wants to use the Express Lane, so he can only buy 15 items, to determine how many ways can he choose which 15 items to buy if he wants all 6 cheeses the following calculation must be performed:
4 x 4 x 8 = X
16 x 8 = X
128 = X
Therefore, Diego can choose the 15 items in 128 different ways.
Why is android sound louder then iPhone???
Answer ASAP
Cause my volume isn’t as loud as android and my speakers work fine and so does the volume?
Answer:
There are many outcomes or data that needs to be collected... like does the iPhone and android share the same speaker? or are your speaker grills blocked out by something? or is your iPhone old, because they do change the speaker each gen.
