square meter is the SI unit of area.
6 less than six times a number is 42 what is the number
Answer:
x = 8
General Formulas and Concepts:
Pre-Algebra
Equality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityStep-by-step explanation:
Step 1: Define
Identify
6x - 6 = 42
Step 2: Solve for x
[Addition Property of Equality] Add 6 on both sides: 6x = 48[Division Property of Equality] Divide 6 on both sides: x = 8Answer: -6
Step-by-step explanation:
We can create an equation based on the info given.
6-6x=42 Now you solve for x, the unknown number.
-6 -6 Subtract 6 on both sides
-6x=36
/-6 /-6 Divide by -6 on both sides
x=-6
The number is -6.
An individual has a forearm length that places a 25 kg weight 32 cm from the elbow while being held in the hand. The biceps tendon attaches to the radius 4 cm from the elbow. How much force must the flexor group produce to move the weight?
Answer:
Force need F2 = 2000 N
Step-by-step explanation:
Given:
Weight F1 = 25 kg = 25 x 10 = 250 N
Length L1 = 32 cm
Add new length = 4 cm
Net momentum = 0
Find:
Force need F2
Computation:
F2L2 - F1L1 = 0
F2(4) - (250)(32) = 0
F2(4) - 8000 = 0
F2(4) = 8000
F2 = 8000 / 4
F2 = 2000
Force need F2 = 2000 N
Can someone help please
( x - 2 )( x - 8 )( x + 5 ) =
( x^2 - 10x + 16 )( x + 5 ) =
x^3 - 10x^2 + 16x + 5x^2 - 50x + 80 =
x^3 + ( - 10 + 5 )x^2 + ( 16 - 50)x + 80 =
x^3 - 5x^2 - 34x + 80
did from six times a certain number the result is 96 what is the number
Answer:
The number is 16
Step-by-step explanation:
Number : x
Procedure and resolution:
6x = 96
x = 96/6
x = 16
Good Luck!If y = sin 3x, find y" in terms of y.
Answer:
-0.54
Step-by-step explanation:
Hope it helped.
• • •
Find the length of the side CD in the pentagon ABCDE.
A)
4√2 units
B)
12 units
C)
4 units
D)
4√10 units
Answer: A) 4√2 units
Step-by-step explanation:
Use the distance formula to find the distance(d) between Point D and Point C:
[tex]d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]
Point D = (x₁, y₁) = (4, -2)Point C = (x₂, y₂) = (8, 2)[tex]d=\sqrt{(8-4)^{2}+(2-(-2))^{2}}=\sqrt{(4)^{2}+(4)^{2}}=\sqrt{16+16} =\sqrt{32} =4\sqrt{2}[/tex]
What is the domain of the function
v=m***
O x2
O
O O xe3
o
X> 3
ASAP
Answer:
The function will be exist if and only if :
[tex] \frac{ - x + 3}{2} > 0 \\ = > - x + 3 > 0 \\ = > - x > - 3 \\ = > x < 3 \\ \\ \therefore \bf \: domain \: \: \green{x < 3}[/tex]
The mathematics department of a college has 6 male professors, 12 female professors, 14 male teaching assistants, and 11 female teaching assistants. If a person is selected at random from the group, find the probability that the selected person is a teaching assistant or a female.
The probability is ___.
(Type an integer or a fraction. Simplify your answer.)
Answer:
37/43
Step-by-step explanation:
6+12+14+11=43
Males: 6+14=20
Females: 11+12=23
If the selected person is a teaching assistant or a female, then the probability is 11+12+14=37. 37/43
A manufacturer of industrial solvent guarantees its customers that each drum of solvent they ship out contains at least 100 lbs of solvent. Suppose the amount of solvent in each drum is normally distributed with a mean of 101.8 pounds and a standard deviation of 3.76 pounds.
Required:
a. What is the probability that a drum meets the guarantee? Give your answer to four decimal places.
b. What would the standard deviation need to be so that the probability a drum meets the guarantee is 0.99?
Answer:
The answer is "0.6368 and 0.773".
Step-by-step explanation:
The manufacturer of organic compounds guarantees that its clients have at least 100 lbs. of solvent in every fluid drum they deliver. [tex]X\ is\ N(101.8, 3.76)\\\\P(X>100) =P(Z> \frac{100-101.8}{3.76}=P(Z>-0.47))[/tex]
For point a:
Therefore the Probability =0.6368
For point b:
[tex]P(Z\geq \frac{100-101.8}{\sigma})=0.99\\\\P(Z\geq \frac{-1.8}{\sigma})=0.99\\\\1-P(Z< \frac{-1.8}{\sigma})=0.99\\\\P(Z< \frac{-1.8}{\sigma})=0.01\\\\z-value =0.01\\\\area=-2.33\\\\ \frac{-1.8}{\sigma}=-2.33\\\\ \sigma= \frac{-1.8}{-2.33}=0.773[/tex]
Which of the following statements best describes the effect of replacing the graph of y = f(x) with the graph of y = f(x) − 11?
Answer:
the graph would cut the y-axis 11 units below y=f(x)
CAN SOMEONE PLEASE HELL ME WITH THIS PROBLEM? THANK YOU!!!
Answer:
71
Step-by-step explanation:
The reference angle is always the smallest angle with the x-axis.
The nearest x axis is at 0 or another name for 0 is 360
360 -289 = 71
The reference angle is 71
If a seed is planted, it has a 90% chance of growing into a healthy plant.
If 6 seeds are planted, what is the probability that exactly 2 don't grow?
Answer:
[tex]\displaystyle\frac{19,683}{200,000}\text{ or }\approx 9.84\%[/tex]
Step-by-step explanation:
For each planted seed, there is a 90% chance that it grows into a healthy plant, which means that there is a [tex]100\%-90\%=10\%[/tex] chance it does not grow into a healthy plant.
Since we are planting 6 seeds, we want to choose 2 that do not grow and 4 that do grow:
[tex]\displaystyle \frac{1}{10}\cdot \frac{1}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}[/tex]
However, this is only one case that meets the conditions. We can choose any 2 out of the 6 seeds to be the ones that don't grow into a healthy plant, not just the first and second ones. Therefore, we need to multiply this by number of ways we can choose 2 things from 6 (6 choose 2):
[tex]\displaystyle \binom{6}{2}=\frac{6\cdot 5}{2!}=\frac{30}{2}=15[/tex]
Therefore, we have:
[tex]\displaystyle\\P(\text{exactly 2 don't grow})=\frac{1}{10}\cdot \frac{1}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot \binom{6}{2},\\\\P(\text{exactly 2 don't grow})=\frac{1}{10}\cdot \frac{1}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot 15,\\\\P(\text{exactly 2 don't grow})=\boxed{\frac{19,683}{200,000}}\approx 9.84\%[/tex]
Answer:
[tex] {?}^{?} However, this is only one case that meets the conditions. We can choose any 2 out of the 6 seeds to be the ones that don't grow into a healthy plant, not just the first and second ones. Therefore, we need to multiply this by number of ways we can choose 2 things from 6 (6 choose 2):
\displaystyle \binom{6}{2}=\frac{6\cdot 5}{2!}=\frac{30}{2}=15(26)=2!6⋅5=230=15
Therefore, we have:
\begin{gathered}\displaystyle\\P(\text{exactly 2 don't grow})=\frac{1}{10}\cdot \frac{1}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot \binom{6}{2},\\\\P(\text{exactly 2 don't grow})=\frac{1}{10}\cdot \frac{1}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot \frac{9}{10}\cdot 15,\\\\P(\text{exactly 2 don't grow})=\boxed{\frac{19,683}{200,000}}\approx 9.84\%\end{gathered}P(exactly 2 don’t grow)=101⋅101⋅109⋅109⋅109⋅109⋅(26),P(exactly 2 don’t grow)=101⋅101⋅109⋅109⋅109⋅109⋅15,P(exactly 2 don’t grow)=200,00019,683≈9.84%
[/tex]
If r = 0.97, this indicates a ________ correlation. Question 10 options: A) weak negative B) weak positive C) strong negative D) strong positive
Answer:C
Step-by-step explanation:
A correlation of -0.97 is a strong negative correlation while a correlation of 0.10 would be a weak positive correlation
Answer:
C) strong negative.
Step-by-step explanation:
Which of the following equations is written in standard form?
A. 2+3x−6y=0
B. 4x−2y=0
C. −8x+4y=1
D. −3y+x−4=0
Answer:
Choice B.
[tex]4x - 2y = 0[/tex]
Step-by-step explanation:
Has integer coefficients and equal to 0.
Find the missing side round your answer to the nearest tenth
Answer:
x=13.2
Step-by-step explanation:
cos(43)=x/18
x=18×cos(43)
x=13.2
Answered by GAUTHMATH
Trong hệ Oxy cho L là đoạn thẳng từ A(1;−1) đến B(0;2). tìm phương trình L và tính tích phân
Answer:
cannot understand the language man
but please follow
Help please!!!! Im really stuck.
Answer: 275 adults and 130 children
Step-by-step explanation:
First, find the value of one variable by rearranging a equation:
[tex]a+c=405\\c=405-a[/tex]
Substitute it into the other equation and solve for a:
[tex]12a+5c=3950\\12a+5(405-a)=3950\\12a+2025-5a=3950\\12a-5a=3950-2025\\7a=1925\\a=\frac{1925}{7} =275[/tex]
Use the a-value to find b by substituting it into the rearranged equation:
[tex]c=405-a=405-275=130[/tex]
Therefore, the answer would be:
[tex]\left \{ {{a=275} \atop {c=130}} \right.[/tex]
This is a list of the heights ( each nearest cm ) of 12 children
150 134 136 139 131 141
132 134 136 137 150 146
Select the type of the data.PLEASE HELP CHOOSE ONE
Discrete
Continuous
Categorical
Qualitative
Answer:
qualitative
Step-by-step explanation:
bcos it is in quality format
tính công thức Taylo đến x^13
Answer:
أنت مجنون ، هل تعرف ذلك؟
Step-by-step explanation:
بنسلفانيا
If 3(nP2 + 24)=2nP2, find the positive value of n
Answer:
[tex]n = 8[/tex]
Step-by-step explanation:
Given
[tex]3(^nP_2 + 24) = ^{2n}P_2[/tex]
Required
Find n
To do this, we simply apply permutations formula
[tex]nP_r = \frac{n!}{(n -r)!}[/tex]
So, we have:
[tex]3 * [\frac{n!}{(n -2)!} + 24] = \frac{2n!}{(2n -2)!}[/tex]
Expand
[tex]3 * [\frac{n * (n - 1) * (n - 2)!}{(n -2)!} + 24] = \frac{2n * (2n - 1) * (2n - 2)}{2n - 2}[/tex]
[tex]3 * [n * (n - 1) + 24] = 2n * (2n - 1)[/tex]
[tex]3 * [n^2 - n + 24] = 4n^2 - 2n[/tex]
Open bracket
[tex]3n^2 - 3n + 72 = 4n^2 - 2n[/tex]
Collect like terms
[tex]3n^2 - 4n^2- 3n+2n + 72 = 0[/tex]
[tex]-n^2- n + 72 = 0[/tex]
Expand
[tex]-n^2 -9n + 8n + 72 = 0[/tex]
Factorize
[tex]-n(n +9) - 8(n + 9) = 0[/tex]
Factor out n + 9
[tex](-n -8)(n + 9) = 0[/tex]
Split
[tex](-n -8)= 0 \ or\ (n + 9) = 0[/tex]
Solve for n
[tex]n =8\ or\ n = -9[/tex]
The positive value is [tex]n = 8[/tex]
the perimeter of a rectangular field is 346 yards if the length of the field is 95 yards whay is its width
Answer:
78 yards
Step-by-step explanation:
The perimeter of a rectangle is given by
P = 2(l+w)
346 = 2(95+w)
Divide each side by 2
346/2 = 2/2(95+w)
173 = 95+w
Subtract 95 from each side
173-95 = 95+w-95
78 = w
exchange rate for rand is 7 for $1 how any dollars would u receive is u exchange 21 rand
Answer:
$3
Step-by-step explanation:
7 rands for $1
7×3=21
21 rands for $3
Answer:
$3
Step-by-step explanation:
7 rand = 1 dollar
Divide both sides by 7 rand.
1 = (1 dollar)/(7 rand)
Notice that the fraction (1 dollar)/(7 rand) equals 1, so multiplying by it will not change the amount, just the units.
21 rand * (1 dollar)/(7 rand) =
= 21/7 dollar
= 3 dollar = $3
The circle graph above shows the distribution of utility expenses for the Hierra family last year. If the family’s total utility expenses last year were $3,600, what were their expensive go water and sewer.
Water and sewer=X%
Electric=30%
Heating and gas=50%
Answer:
The correct answer is - $720 or 20%.
Step-by-step explanation:
Given:
Total expense = 3600
Electric=30%
Heating and gas=50%
Water and sewer=X%
Solution:
For electric: 3600*30/100 = 1080
for heating and gas: 3600*50/100 = 1800
Left money for expense of water and shower = total - (electric and heating)
= 3600-1880
= 720
Percentage of water and shower = 720*100/3600
= 20%
Answer:
Correct!
Step-by-step explanation:
Thank you this is correct :) I took the test
Of all the people applying for a certain job 75% are qualified and 25% are not. The personnel manager claims that she approves qualified people 80% of the time, she approves unqualified people 30% of the time. Find the probability that a person is qualified if he or she was approved by the manager The probability is:_______.
Type an integer or decimal rounded to four decimal places as needed)
Answer:
The probability is: 0.8889.
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Approved
Event B: Qualified
Probability of a person being approved:
80% of 75%(qualified)
30% of 25%(not qualified). So
[tex]P(A) = 0.8*0.75 + 0.3*0.25 = 0.675[/tex]
Probability of a person being approved and being qualified:
80% of 75%, so:
[tex]P(A \cap B) = 0.8*0.75[/tex]
Find the probability that a person is qualified if he or she was approved by the manager.
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.8*0.75}{0.675} = 0.8889[/tex]
The probability is: 0.8889.
find the missing length indicated
Answer:
192
Step-by-step explanation:
geometric mean theorem :
with p and q being the segments of the Hypotenuse, then
h = x = sqrt(p×q)
p = 144
q = 400-144 = 256
h = x = sqrt(144×256) = 12×16 = 192
A student-faculty committee consisting of 6 members is to be chosen from a pool of candidates consisting of 5 students and 7 faculty members. The committee must have at least 2 student members and at least 1 faculty member. How many possibilities are there
Answer:
[tex]T=812[/tex]
Step-by-step explanation:
From the question we are told that:
No. Committee Members [tex]n=6[/tex]
Pool of : 5 students and 7 faculty members
At least 2 student members and at least 1 faculty member
Generally the committee is mathematically given by
The Total Events are
[tex]T=(^5C_2*^7C_4)+(^5C_3)*(^7C_3)+(^5C_4)*(^7C_2)+(^5C_5)*(^7C_1)[/tex]
[tex]T=350+350+105+7[/tex]
[tex]T=812[/tex]
Please show your work this question what made you come to the conclusion. Thank you
Answer:
B the range, the x- and y-intercept
Step-by-step explanation:
the domain stays the same : all values of x are possible out of the interval (-infinity, +infinity).
but the range changes, as for the original function y could only have positive values - even for negative x.
the new function has a first term (with b) that can get very small for negative x, and then a subtraction of 2 makes the result negative.
the y-intercept (x=0) of the original function is simply y=1, as b⁰=1.
the y-intercept of the new function is definitely different, because the first term 3×(b¹) is larger than 3, because b is larger than 1. and a subtraction of 2 leads to a result larger than 1, which is different to 1.
the original function has no x-intercept (y=0), as this would happen only for x = -infinity. and that is not a valid value.
the new function has an x-intercept, because the y-values (range) go from negative to positive numbers. any continuous function like this must therefore have an x-intercept (again, y = the function result = 0)
[tex] 3 {b}^{x + 1} = 2[/tex]
[tex] {b}^{x + 1} = 2 \div 3[/tex]
[tex] log_{b}(2 \div 3) = x + 1[/tex]
[tex]x = log_{b}(2 \div 3) - 1[/tex]
Suppose that the distribution of snake lengths in a certain park is not assumed to be symmetric. According to Chebyshev's Theorem, at least what percentage of snake lengths are within k =2.9 standard deviations of the mean?
According to Chebyshev,
P(|X - µ| ≤ 2.9σ) ≥ 1 - 1/2.9² ≈ 0.8811
An isosceles right triangle has a hypotenuse that measures 4√2 cm. What is the area of the triangle?
HELP
Answer:
8 cm^2
Step-by-step explanation:
If the triangle is isosceles the sides are the same
Let the sides be x
We know that we can use the Pythagorean theorem
a^2+b^2 = c^2 where a and b are the sides and c is the hypotenuse
x^2+x^2 = (4 sqrt(2))^2
2x^2 =16(2)
2x^2 = 32
Divide by 2
2x^2/ 32/2
x^2 = 16
Taking the square root of each side
sqrt(x^2) = sqrt(16)
x = 4
The area of the triangle is
A =1/2 bh
A = 1/2 (4) (4)
A = 1/2(16)
A = 8
Answer:
8
Step-by-step explanation:
a^2 + b^2 = c^2
c = [tex]4\sqrt{2}[/tex]
[tex]c^{2} = 32[/tex]
a^2 + b^2 = 32
a=b (isosceles triangle)
a=b=4
base = 4
height = 4
area = 1/2 bh = 1/2(4)(4) = 8
Here is data on the percentage of 200 hotels in each of the three large cities across the world on whether minibar charges are correctly posted at checkout are given below.
Hong Kong New York Paris
Yes 86% 76% 78%
No 14% 24% 22%
At the 0.05 level of significance, you want to know if there is evidence of a difference in the proportion of hotels that correctly post minibar charges among the three cities.
Referring to the table above the test will involve _________ degrees of freedom.
Referring to Scenario above, the expected cell frequency for the Hong Kong/Yes cell is _______?
Referring to Scenario above, the critical value of the test is ________. Use degrees of freedom and look at the chi-square distribution table.
Referring to Scenario above, the value of the test statistic is _________.
Answer:
Degree of freedom = 2
Expected frequency = 80%
Critical value, = 5.991
χ² statistic = 3.5
Step-by-step explanation:
Given the data :
Hong Kong New York Paris
Yes 86% 76% 78%
No 14% 24% 22%
The degree of freedom for the Chisquare statistic is given as :
(no of rows - 1) * (number of columns - 1)
Number of rows = 2
Number of columns = 3
. Degree of freedom = (2-1) * (3-1) = 1*2 = 2
Expected frequency = (Row total * column total) / grand total
The expected frequency of Hong Kong / Yes cell :
Row total = (86+76+78) = 240
Column total = (86+14) = 100
Grand total, N = (14+24+22)+240 = 300
Expected frequency = (240*100)/300 = 80%
The critical value :
At α - level = 0.05 ; df = 2
Critical value = 5.991
χ² = Σ(observed - Expected)² / Expected
The expected values :
80 80 80
20 20 20
Hence,
χ² = Σ(86-80)²/80 + (76-80)²/80 + (78-80)²/80 + (14-20)²/20 + (24-20)²/20 + (22-20)²/20
χ² statistic = 3.5
