Answer:
-3x+y=0
Step-by-step explanation:
Standard form= Ax+Bx=C
Add -3x both sides, answer -3x+1y=0
Find the length of AG
Answer:
[tex]AG=22[/tex]
Step-by-step explanation:
Follow the next steps:
[tex]\frac{A-B}{A-E} =\frac{B-C}{E-F} =\frac{C-D}{F-G} =\frac{A-C}{A-F} =\frac{B-D}{E-G} =\frac{A-D}{A-G}[/tex]
Let:
[tex]\frac{A-B}{A-E} =\frac{B-C}{E-F}\\ \\\frac{4}{A-E} =\frac{5}{10x}\\ \\Solving\hspace{3}for\hspace{3}A-E\\\\A-E=8x[/tex]
Now:
[tex]\frac{C-D}{F-G} =\frac{A-C}{A-F} \\\\\frac{2}{F-G} =\frac{9}{18x} \\\\Solving\hspace{3}for\hspace{3}F-G\\\\F-G=4x[/tex]
Hence:
[tex]A-G=(A-E)+(E-F)+(F-G)=22x[/tex]
Finally:
[tex]\frac{B-D}{E-G} =\frac{A-D}{A-G}\\\\\frac{A-D}{B-D} =\frac{A-G}{E-G}\\[/tex]
[tex]\frac{11}{7} =\frac{22x}{14x} \\\\\frac{11x^{2} }{7} -\frac{11}{7} =0\\\\[/tex]
Hence:
[tex]x=1\\x=-1[/tex]
Since it would be absurd for [tex]x=-1[/tex], the real solution is [tex]x=1[/tex]
Therefore:
[tex]AG=22[/tex]
5/9 + (1/9 + 4/5)=×
Answer:
22/15I hope it helps :)Step-by-step explanation:
[tex]\frac{5}{9}+\left(\frac{1}{9}+\frac{4}{5}\right)=x\\x=\frac{5}{9}+\left(\frac{1}{9}+\frac{4}{5}\right)\\\mathrm{Remove\:parentheses}:\quad \left(a\right)=a\\x=\frac{5}{9}+\frac{1}{9}+\frac{4}{5}\\\mathrm{Compute\:a\:number\:comprised\:of\:factors\\\:that\:appear\:in\:at\:least\:one\:of\:the\:following:}\\9,\:9,\:5\\=3\times \:3\times\:5\\\mathrm{Multiply\:the\:numbers:}\:3\times \:3\times \:5=45\\\frac{5}{9}=\frac{5\times \:5}{9\times \:5}=\frac{25}{45}\\[/tex]
[tex]\frac{1}{9}=\frac{1\times \:5}{9\times \:5}=\frac{5}{45}\\\\\frac{4}{5}=\frac{4\times \:9}{5\times \:9}=\frac{36}{45}\\\\x=\frac{25}{45}+\frac{5}{45}+\frac{36}{45}\\\\\mathrm{Since\:the\:denominators\:are\:equal,\\combine\:the\:fractions}:\\\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}\\\\x=\frac{25+5+36}{45}\\\\x=\frac{66}{45}\\\\x=\frac{22}{15}[/tex]
Find the slope of the line passing through the points (8,-4) and (4, -8).
Answer:
1
Step-by-step explanation:
We can find the slope using
m= ( y2-y1)/(x2-x1)
= ( -8 - -4)/( 4 - 8)
= ( -8 +4)/( 4 - 8)
= -4 / -4
= 1
Answer:
slope equals 1
Step-by-step explanation:
To do this you would need to do an equation that is [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex] so in this case -8 would be y2 and -4 would be y1 and 4 would be x2 and 8 would b e x1 so if you plug it into the equation we would get [tex]\frac{-8-(-4)}{4-8}[/tex] and if we simplify we get [tex]\frac{-4}{-4}[/tex] which simplifies to 1 so the slope would equal 1
The gas mileage for a certain vehicle can be approximated by m=−0.05x2+3.5x−49, where x is the speed of the vehicle in mph. Determine the speed(s) at which the car gets 9 mpg. Round to the nearest mph.
Answer:
14mphStep-by-step explanation:
Given the gas mileage for a certain vehicle modeled by the equation m=−0.05x²+3.5x−49 where x is the speed of the vehicle in mph. In order to determine the speed(s) at which the car gets 9 mpg, we will substitute the value of m = 9 into the modeled equation and calculate x as shown;
m = −0.05x²+3.5x−49
when m= 9
9 = −0.05x²+3.5x−49
−0.05x²+3.5x−49 = 9
0.05x²-3.5x+49 = -9
Multiplying through by 100
5x²+350x−4900 = 900
Dividing through by 5;
x²+70x−980 = 180
x²+70x−980 - 180 = 0
x²+70x−1160 = 0
Using the general formula to get x;
a = 1, b = 70, c = -1160
x = -70±√70²-4(1)(-1160)/2
x = -70±√4900+4640)/2
x = -70±(√4900+4640)/2
x = -70±√9540/2
x = -70±97.7/2
x = -70+97.7/2
x = 27.7/2
x = 13.85mph
x ≈ 14 mph
Hence, the speed(s) at which the car gets 9 mpg to the nearest mph is 14mph
1. What are the formulas that help determine the equation of a circle? 2. How are the center, radius and a point on the circle expressed algebraically? 3. What do you need to know in order to use the ellipse equation formulas?
Answer: see below
Step-by-step explanation:
1) The equation of a circle is: (x - h)² + (y - k)² = r² where
(h, k) represents the center of the circler represents the radius of the circle.2) If you are given a point on the circle and the center (h, k)
you can input those points into the equation of a circle to find r².
Then input (h, k) and r² to identify the equation of that particular circle.
3) If you divide each term in the equation of a circle by r², you will get:
[tex]\dfrac{(x-h)^2}{r^2}+\dfrac{(y-k)^2}{r^2}=1[/tex]
(h, k) is the center of the circler is the x-radius and y-radiusThe difference between a circle and an ellipse is that an ellipse is in the shape of an oval. In other words, the x-radius and y-radius are different.
The equation of an ellipse is:
[tex]\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1[/tex]
(h, k) is the center of the ellipsea is the x-radiusb is the y-radiust-7= -1 what is t in this equation
Answer:
t=6
Step-by-step explanation:
t-7=-1
6-7=-1
t - 7 = -1
t = 7 -1
t = 6
t is equals 6
A P E X!!!! URGENT :The annual interest rate of Belinda's savings account is 8.6% and simple interest is calculated quarterly. What is the periodic interest rate of Belinda's account?
Answer:
The answer is 2.15%
Step-by-step explanatio
2. The first and last term of an AP are 1 and 121 respectively. If the sum of the
series is 671, find a) the number of terms in) in the AP b) the common
difference between them.
Step-by-step explanation:
since you provided 1st and the last terms
the equation can be nth term
n/2 × ( a + l) = nth sum
n/2 × ( 1 + 121) = 671
n/2 × 122 = 671
61 n = 671
n = 11
a) so there are 11 terms
then,
so as 11th term is 121
let's find common diff
a + ( n-1) d = nth term
1 +( 11-1) d= 121
10d = 121 -1
10d = 120
common difference = 12
A compressive uniform stress distributed on a rectangular areas of sides. located on the two opposite vertical/radial faces of step. If Force = 1.87kN and stress = 0.987MPa calculate the h * t in m^2
Answer:
Area = 0.019 m²
Step-by-step explanation:
stess = applied Force over Area
since stress = 0.987 MPa
and the force = 1.87 Kn
then Area = h * t
Q = F / (h * t)
0.987 mPa = 1.87 kN / (h* t)
since h * t = Area then 1.87 / 0.987
Area = 1.89 x 0.01 =
Area = 0.019 m²
The volume of wine in liters produced by a parcel of vineyard every year is modeled by a Gaussian distribution with an average of 100 and a variance of 9. Find the probability that this year it will produce 115 liters of wine
Answer:
0.99865
Step-by-step explanation:
The question above is modelled by gaussian distribution. Gaussian distribution is also known as Normal distribution.
To solve the above question, we would be using the z score formula
The formula for calculating a z-score
z = (x-μ)/σ,
where x is the raw score
μ is the population mean
σ is the population standard deviation.
In the above question,
x is 115 liters
μ is 100
σ is the population standard deviation is unknown. But we were given variance in the question.
Standard deviation = √Variance
Variance = 9
Hence, Standard deviation = √9 = 3
We go ahead to calculate our z score
z = (x-μ)/σ
z = (115 - 100) / 3
z = 15/ 3
z score = 5
Using the z score table of normal distribution to find the Probability of having a z score of 5
P(x = 115) = P(z = 5) =
0.99865
Therefore the probability that this year it will produce 115 liters of wine = 0.99865
i neeed help thanksssss
Answer:
Volume: 366.6
Surface Area: 314.2
Explanation (look at below)
Step-by-step explanation:
Volume:
The radius of this sphere is 5 (half of 10). The equation will be [tex]\frac{4}{3} \pi[/tex]5^3
When you calculate that, it will become: 366.6<-- rounded to the nearest tenth.
Surface Area:
4[tex]\pi[/tex]5^2
=100Π
=314.2<-- rounded to the nearest tenth.
314.2 is the nearest tenth digit no.
Improving the quality of high-value decision making by an executive will save an organization far more money than improving the quality of lesser-value decisions made at a lower level.
A. True
B. False
Answer:
A. True
Step-by-step explanation:
Since it is lesser, it will also bring in lesser profit :)
Select the correct answer. Consider matrices A, B, and C:
Answer:
i think it is c. i may be incorrect, i am sorry!
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
I did the math
Ashley has 500 songs in his music player. Every week he adds 10 songs to his collection. How many songs will he have in his music player after 20 weeks ?
At the end of n weeks, the number of songs is given by the function
f(n) =500 +10n
Or
f(n) = 10 +20b
The output of the function is 700
or
600
when the input is 20.
Answer:
700
Step-by-step explanation:
500+10*20=700
it's f(n) = 500+10n
Solve the system using multiplication for the linear combination method. 6x – 3y = 3 –2x + 6y = 14 What is the solution to the system
Answer:
work is shown and pictured
Answer:
2/3
Step-by-step explanation:
got right n edg 2021
Find the zeros of g(x) = x3 + x2 – 9x – 9
Answer: The zeros are -1,-3, and 3
Hope this helps
Answer:
let g[x]=0
then0=x3−x2-9x+9
rewrite it as x3−x2−9x+9=0
by factorising it becomes
(x−1)(x+3)(x−3)=0
therefore
either x-1=0 OR x+3=0 OR x-3=0
which becomes
x=1 OR x=-ve3 OR x=3
are the zeroes of the polynomial
hope this helps
For the functions f(x)=8 x 2 +7x and g(x)= x 2 +2x , find (f+g)(x) and (f+g)(3)
Answer:
(f+g)(x)= 9x² + 9x
(f+g)(3) = 108
Step-by-step explanation:
f(x)=8x² +7x
g(x)= x² +2x
(f+g)(x) = f(x) + g(x) = 8x² +7x +x² +2x = 9x² + 9x
(f+g)(x)= 9x² + 9x
(f+g)(3)= 9*3² + 9*3 = 108
How many times would a coin have to show heads in 50 tosses to have an experimental probability of 20% more than the theoretical probability of getting heads? Which of the following represents a function
Answer: The required number of heads = 30
Step-by-step explanation:
Given, Total tosses = 50
The theoretical probability of getting head = [tex]\dfrac{1}{2}[/tex]
As per given,
Experimental probability = Theoretical probability + 20% of Theoretical probability
= [tex]\dfrac{1}{2}+\dfrac{20}{100}\times\dfrac{1}{2}[/tex]
= [tex]\dfrac{1}{2}+\dfrac{1}{10}=0.5+0.1=0.6[/tex]
Required number of heads = (Experimental probability) x (Total tosses )
= 0.6 x 50
= 30
Hence, the required number of heads = 30
A relation is said to be a function if each input value corresponds to a unique output value.For example: {(1,2), (3,4), (2,3), (4,1))}
Answer:
35 is the Answer
Find the value of the chi-square test statistic for the goodness-of-fit test. You wish to test the claim that a die is fair. You roll it 48 times with the following results. Number 1 2 3 4 5 6Frequency 5 10 12 9 4 8Observed frequency (O) 5,10,12,9,4,8Expected frequency (E) 8,8,8,8,8,8What is the value of the 2 test statistic?a. X2 = 3.538b. X2 = 4.182c. X2 = 5.75d. X2 = 7.667
Answer:
The value of Chi-square test statistic is χ² = 5.75.
Step-by-step explanation:
The Chi-square Goodness of fit test will be used to determine whether the die is fair or not.
The hypothesis can be defined as follows:
H₀: The die is fair.
Hₐ: The die is not fair.
The Chi-square test statistic is given by:
[tex]\chi^{2}=\sum\limits^{n}_{i=1}{\frac{(O_{i}-E_{i})^{2}}{E_{i}}}[/tex]
Consider the table attached below.
The value of Chi-square test statistic is χ² = 5.75.
The state of CT claims that the average time on death row is 15 years. A random survey of 75 death row inmates revealed that the average length of time on death row is 17.8 years with a standard deviation of 5.9 years. Conduct a hypothesis to test the state of CT's claim. What type of test should be run? t-test of a mean z-test of a proportion The alternative hypothesis indicates a right-tailed test left-tailed test two-tailed test Calculate the p-value. What is the decision? We reject the claim that the average time on death row is 15 years We fail to reject the claim that the average time on death row is 15 years
Answer:
a)The calculated value t = 4.111 > 1.9925 at 5 % level of significance
Null hypothesis is rejected
The claim that the average time on death row is not 15 years
b) The p-value is 0.000101<0.05
we reject Null hypothesis
The claim that the average time on death row is not 15 years
Step-by-step explanation:
Step(i):-
Sample size 'n' =75
Mean of the sample x⁻ = 17.8
standard deviation of the sample (S) = 5.9
Mean of the Population = 15
Null hypothesis:H₀:μ = 15 years
Alternative Hypothesis :H₁:μ≠15 years
Step(ii):-
Test statistic
[tex]t = \frac{x^{-} -mean}{\frac{S}{\sqrt{n} } }[/tex]
[tex]t = \frac{x^{-} -mean}{\frac{S}{\sqrt{n} } }=\frac{17.8-15}{\frac{5.9}{\sqrt{75} } }[/tex]
t = 4.111
Degrees of freedom
ν = n-1 = 75-1=74
t₀.₀₂₅ = 1.9925
The calculated value t = 4.111 > 1.9925 at 5 % level of significance
Null hypothesis is rejected
The claim that the average time on death row is not 15 years
P-value:-
The p-value is 0.000101<0.05
we reject Null hypothesis
The claim that the average time on death row is not 15 years
Which describes the graph in words?
A. All numbers less than -10 and less than or equal to 8.
B. All numbers greater than -10 and less than 8
C. All numbers greater than or equal to -10 and less than or equal to 8
D. All numbers greater than -10 and less than or equal to 8.
D. All numbers greater than -10 and less than or equal to 8
Question 15 of 25
What is the solution to this equation?
X + 8 = -3
Answer:
x=-11
Step-by-step explanation:
x+8=-3
x=-3-8 :- collect like term
since we are adding two negative numbers, we will let the number be negative but add them.
x=-11
Hope it helps :)
Answer:
x=-11
Step-by-step explanation:
x+8=-3
collect like terms;
x=-3-8
x=-11
Which choice is equivalent to 4 square root 8
Answer:
A
Step-by-step explanation:
............................ ....
A loudspeaker converts electrical energy into the kinetic energy of the speaker. This kinetic energy is transferred to air, and the motion of the air is the sound that people hear. An illustration of speaker with a wide arrow away from it labeled electrical energy 100 J and it splits into 3 arrows labeled sound energy 80 J, thermal energy ? J, and friction 5 J. How much thermal energy is put out by the speaker? 5 J 15 J 80 J 100 J
Answer:
15 J
Step-by-step explanation:
There is a total of 100 J of energy being used which is then converted into sound energy, thermal energy, and friction. This means the total amount must equal 100 J.
1. Set up the equation
80 + x + 5 = 100
2. Simplify
x + 85 = 100
3. Solve for x by subtracting 85 from both sides
x = 15
Answer:
The correct answer is 15J which is B.
Consider this quote: "In a recent survey, 65 out of 100 consumers reported that they preferred plastic bags instead of paper bags for their groceries. If there is no difference in the proportions who prefer each type in the population, the chance of such extreme results in a sample of this size is about .03. Because .03 is less than .05, we can conclude that there is a statistically significant difference in preference." Give a numerical value for each of the following.
a. The p-value.
b. The level of significance, α.
c. The sample proportion.
d. The sample size.
e. The null value.
Answer:
Step-by-step explanation:
The p value (probability of obtaining results as extreme the z score if null is true) is usually the value derived to make a conclusion and in this case the p value is 0.03
The level of significance is the value usually compared with the p value which is 0.05
The sample promotion is 65 out of 100 = 65/100 = 0.65
The sample size is the total number of consumers which is 100
The null value is usually the default value. The null value would assume that there is no difference in the proportions who prefer each type in the population. There are two preferences: 100/2 = 50- 0.5 for each preference.
when Charles eats Oreos , he likes to dunk 2 out of every 5 cookies in a cold glass of milk. if he eats a total of 15 Oreos , how many will he dunk ? how many will ge eat without dunking?
Answer: 6 with milk, 9 without
Step-by-step explanation:
2/5 of the cookies he eats are dunked. Thus, simply do 2/5, or .4*15 to get that 6 cookies are dunked, and 15-6 to get that 9 cookies are not dunked.
Hope it helps <3
In a random sample of 40 refrigerators, the mean repair cost was $150. Assume the population standard deviation is $15.50. Construct a 99% confidence interval for the population mean repair cost. Then change the sample size to n = 60. Which confidence interval has the better estimate?
Answer: ($143.69, $156.31)
Step-by-step explanation:
Confidence interval to estimate population mean :
[tex]\overline{x}\ \pm z\dfrac{\sigma}{\sqrt{n}}[/tex]
, where [tex]\sigma[/tex] = population standard deviation
n= sample size
[tex]\overline{x}=[/tex] Sample mean
z= critical value.
As per given,
n= 40
[tex]\sigma[/tex] = $15.50
[tex]\overline{x}=[/tex] $150
Critical value for 99% confidence level = 2.576
Then, 99% confidence interval for the population mean:
[tex]150\pm(2.576)\dfrac{15.50}{\sqrt{40}}\\\\\Rightarrow\ 150\pm6.31 \ \ (approx)\\\\\Rightarrow(150-6.31,150+6.31)=(143.69,156.31)[/tex]
Hence, the required confidence interval : ($143.69, $156.31)
The marginal cost (dollars) of printing a poster when x posters have been printed is given by the following equation. C'(x)=x^-3/4 Find the cost of printing 142 more posters when 18 have already been printed.
The cost of printing 142 more posters when 18 have already been printed is $________.
(Round to the nearest cent as needed.)
Answer:
The cost of printing 142 more posters when 18 has already been printed is $5.57.
Step-by-step explanation:
We are given that the marginal cost (dollars) of printing a poster when x posters have been printed is given by the following equation C'(x)=x^-3/4.
The given equation is: [tex]C'(x) = x^{\frac{-3}{4} }[/tex]
The cost of printing 142 more posters when 18 have already been printed is given by;
Integrating both sides of the equation and using the limits we get;
[tex]\int_{a}^{b} C'(x) dx=\int_{18}^{142} x^{\frac{-3}{4}}dx[/tex]
As we know that [tex]\int\limits {x}^{n} \, dx = \frac{x^{n+1} }{n+1}[/tex] , so;
= [tex]\frac{x^{\frac{-3}{4}+1 } }{\frac{-3}{4}+1 } ]^{142} __1_8[/tex]
= [tex]\frac{x^{\frac{1}{4} } }{\frac{1}{4} } ]^{142} __1_8[/tex]
= [tex]4[x^{\frac{1}{4} } } ]^{142} __1_8[/tex]
= [tex]4[(142)^{\frac{1}{4} }- (18)^{\frac{1}{4} }} ][/tex]
= $5.57
Hence, the cost of printing 142 more posters when 18 has already been printed is $5.57.
Suppose that any baseball that has a coefficient of restitution that exceeds 0.625 is considered too lively. Based on the available data, what proportion of the baseballs in the sampled population are too lively
Answer:
hello some parts of your question is missing attached below is the missing parts of the question
Answer : The proportion of the baseballs in the sampled population that are too lively
P = x / n = 18 / 40 = 0.450
Step-by-step explanation:
coefficient of restitution > 0.625
Based on available data the proportion of the baseballs that is in the sampled population that are too lively can be calculated using the values below
n = 40
x = n ( p > 0.625 ) = 18
The proportion of the baseballs in the sampled population that are too lively
P = x / n = 18 / 40 = 0.450
Please help with this
Answer: B
Step-by-step explanation:
Because of Supplementary Angles, we know that the two angles in the right side of the equation add up to 90.
Hope it helps <3