\(7x + 12 = 9x - 6\)
\(7x + 12 - 7x = 9x - 6 - 7x\)
\(12 = 2x - 6\)
\(12 - 6 = 2x -6 - 6\)
\(6 = 2x - 12\)
\(6 + 12 = 2x\)
\(18 = 2x\)
\(18 \div 2 = x\)
\(9 = \bold{ x}\)
In pythagoras, c is the hypotenuse. That is AC. Where a is AB and b is BC.
\( {c}^{2} = {a}^{2} + {b}^{2} \)
\( {(6 x + 5)}^{2} = {(7x + 12)}^{2} + {BC}^{2} \)
\( {((6 \times 9) + 5)}^{2} = {((7 \times 9)}^{2} + 12)^{2} +{BC}^{2} \)
\( {(54 + 5)}^{2} = {(63 + 12)}^{2} + {BC}^{2} \)
\( {59}^{2} = {75}^{2} + {BC}^{2} \)
\(3481 = 5625 + {BC}^{2} \)
\(3481 - 5625 = {BC}^{2} \)
\( - 2144 = {BC}^{2} \)
\( \sqrt{ - 2144} = BC\)
Help pls fast as possible
Answer:
In the middle the narration changes to the inner dialogue of Leamas. We are given the opportunity to be with his thoughts and experience the character for ourselfs
Answer:
The experimental and theoretical probabilities will be completely random because flipping the coin which, of course, has two different sides, the probability is cut perfectly in half.
hope this helps
Step-by-step explanation:
corey bought 2122 start fraction, 1, divided by, 2, end fraction liters of paint for $60\$60$60dollar sign, 60. what was the cost per liter of paint?
Answer:
the cost per liter of the paint is equal to 24 8/liter
Hope this helps :)
Suppose that the antenna lengths of woodice are appróximately normally distributed with a mean of 0.25 inches and a standard deviation of 0.05 inches. What proportion of woodlice have antenna lengths that are more than 0.27 inches? Round your answer to at least four decimal places.
The proportion of woodlice with antenna lengths greater than 0.27 inches is approximately 0.3446 (rounded to four decimal places).
We can use the z-score formula to standardize the value of 0.27 and calculate the corresponding proportion.
z = (x - μ) / σ
where x is the antenna length we are interested in, μ is the mean antenna length, σ is the standard deviation, and z is the standardized score.
Substituting the given values, we get:
z = (0.27 - 0.25) / 0.05 = 0.4
Using a standard normal distribution table or calculator, we can find the proportion of values that fall to the right of z = 0.4. This is equivalent to finding the area under the standard normal curve to the right of z = 0.4.
The table or calculator gives us a value of approximately 0.3446.
Therefore, the proportion of woodlice with antenna lengths greater than 0.27 inches is approximately 0.3446 (rounded to four decimal places).
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PLEASE HELP ITS DUE TMR!!
If M=1,000,P=2.25, and Y=2,000, what is velocity? a. 2.25 b. 4.5 c. 2 d. None of the above is true
Answer:d
Step-by-step explanation:
The answer is d. None of the above is true.
To calculate velocity, we need to use the equation:
Velocity = M * P / Y
Given:
M = 1,000
P = 2.25
Y = 2,000
Plugging in the values:
Velocity = 1,000 * 2.25 / 2,000
Simplifying:
Velocity = 2.25 / 2
The result is:
Velocity = 1.125
Therefore, the correct answer is: d. None of the above is true.
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A student always catches his train if class ends on time. However, 30% of classes run late and then there's a 45% chance he'll miss it. What is the probability that he misses the train today?
The probability that he misses the train today is 0.135 or 13.5%.
P(Class runs late)=30%=0.30
P(Miss train ∣ Class runs late)=45%=0.45
General multiplication rule:
P(A and B)=P(A)×P(B ∣ A)
Using the general multiplication rule, we then obtain (and using that the student always catches his train if the class ends on time) :-
P( Miss train)=P( Miss train and Class runs late)=P(Class runs late)×P(Miss train ∣ Class runs late)
= 0.30×0.45
= 0.135
= or 13.5%.
So, the the probability that he misses the train today is 0.135 or 13.5%.
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the second and fifth terms of an arithmetic sequence are -2 and 7, respectively. find the first term and a recursive rule for the nth term
Answer:
Step-by-step explanation:
a2 = -2
a + d = -2
a + 6d = 7
-5d = -9
d = 9/5
a = -19/5
an = a + ( n-1 ) d
an = -19/5 + ( n-1 ) 9/5
Determine triangle type?
Answer:
scalene right
Step-by-step explanation:
all side are opposite and there is a 90% so that makes it right
john always wears a shirt, pants, socks, and shoes. he owns 12 pairs of socks, 3 pairs of shoes, 5 pairs of pants, and 5 shirts. how many different outfits can john make? PLEASE ANSWER
Answer:
900 outfits
Step-by-step explanation:
You just have to multiply them all together :)
new tables created with the make-table query retain the field ____ of the underlying table(s).
New tables created with the make-table query retain the field data type of the underlying table(s).
What is a table?Tables and graphs are visual representations of data that are used to organize data and reveal patterns and relationships. Tables and graphs are frequently used by researchers and scientists to report research findings.
A make table query retrieves data from one or more tables before loading the results into a new table. That new table can live in the database you're currently working in, or it can be created in a different database. Make table queries are typically used when you need to copy or archive data.
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Help ASAP, Brainliest to whoever answers!
Answer:
these are the ten numbers :
0 8 2 6 9 2 0 8 0 0
Solve the equation to find x:7-3e^x=4
Explanation
\(\begin{gathered} 7-3e^x=4 \\ \end{gathered}\)to solve for x, isolate it
so
Step 1
\(\begin{gathered} 7-3e^x=4 \\ \text{subtract 7 in both sides} \\ 7-3e^x-7=4-7 \\ -3e^x=-3 \end{gathered}\)2y+(4+5y) please answer
Answer:
7y + 4
Step-by-step explanation:
2y+(4+5y)
2y + 4 + 5y
combine y terms:
7y + 4
On the unit circle, where 0 < theta < or equal to 2pi, when is tan theta undefined?
A. Theta=pi and theta=2pi
B. sin theta = cos theta
C. theta = pi/2 and theta=3pi/2
D. sin theta = 1/cos theta
Therefore, the answer is option C: theta = pi/2 and theta = 3pi/2.
To determine when tan(theta) is undefined on the unit circle, we need to remember the definition of the tangent function.
Tangent is defined as the ratio of the sine and cosine of an angle. Specifically, tan(theta) = sin(theta)/cos(theta).
Now, we know that cosine can never be equal to zero on the unit circle, since it represents the x-coordinate of a point on the circle and the circle never crosses the x-axis. Therefore, the only way for tan(theta) to be undefined is if the cosine of theta is equal to zero.
There are two values of theta on the unit circle where cosine is equal to zero: pi/2 and 3pi/2.
At theta = pi/2, we have cos(pi/2) = 0, which means that tan(pi/2) = sin(pi/2)/cos(pi/2) is undefined.
Similarly, at theta = 3pi/2, we have cos(3pi/2) = 0, which means that tan(3pi/2) = sin(3pi/2)/cos(3pi/2) is also undefined.
Therefore, the answer is option C: theta = pi/2 and theta = 3pi/2.
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From the simulation we learned that for a greater than alternative hypothesis, as the true mean gets farther away from the hypothesized value, the probability of a type ii error will?
As the true mean moves farther away from the hypothesized value, the probability of a Type II error decreases, leading to a higher probability of correctly detecting a true effect or difference.
As the true mean gets farther away from the hypothesized value in a hypothesis test, the probability of a Type II error (also known as a false negative) will decrease.
In a hypothesis test, the null hypothesis assumes that there is no significant difference or effect, while the alternative hypothesis suggests that there is a significant difference or effect.
A Type II error occurs when we fail to reject the null hypothesis when it is actually false. In other words, it is a failure to detect a true effect.
When the true mean is far away from the hypothesized value, the difference between the observed data and the hypothesized value becomes more pronounced.
This increases the likelihood of obtaining a test statistic that falls in the critical region (the region where we reject the null hypothesis). Consequently, the probability of correctly rejecting the null hypothesis (i.e., the probability of not making a Type II error) increases.
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bondable, inc. issued $100,000, 10-year, 9% bonds that pay interest annually on january 1 when the going market interest rate was 10%. the issue (sale) price of the bonds equals
The issue price of Bondable Inc.'s $100,000, 10-year, 9% bonds that pay interest annually on January 1, when the going market interest rate was 10%, was $92,582.
Bond prices are determined by the market interest rates prevailing at the time of issuance. When the market interest rates rise, bond prices fall, and vice versa. In this case, Bondable Inc. issued 10-year bonds with a face value of $100,000 and a coupon rate of 9% that pays interest annually on January 1. However, the market interest rate was 10% at the time of issuance.
To calculate the issue price of the bonds, we need to use the present value formula, which discounts the future cash flows of the bond at the market interest rate. The formula is:
PV = (C / r) x [1 - 1 / (1 + r)^n] + F / (1 + r)^n
Where:
PV = Present value of the bond
C = Annual coupon payment
r = Market interest rate
n = Number of periods
F = Face value of the bond
Using this formula, we can calculate the present value of the bond as follows:
PV = ($9,000 / 0.10) x [1 - 1 / (1 + 0.10)^10] + $100,000 / (1 + 0.10)^10
PV = $59,383.11 + $33,198.44
PV = $92,581.55
Therefore, the issue price of the bonds was $92,582, which is lower than the face value of $100,000. This is because the market interest rate was higher than the coupon rate of the bonds, making them less attractive to investors. The lower issue price compensates investors for the lower interest rate they will receive compared to the market rate.
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list a few factors of 24?
Answer:
1,2,3,4,6,8,12,24
Step-by-step explanation:
which of the following is the correct graph of the linear equation below? y+2=1/5(x-1)
Answer:
See attachment
Step-by-step explanation:
If you see ##### in a cell, you should, A. make the row taller B. retype the number C. type in a different number D. make the column wider
Answer:
D. Make the column wider
Step-by-step explanation:
Suppose that 63% of people own dogs. If you pick two people at random what is the probability that they both own a dog.
Answer: 3.175%
Step-by-step explanation:
(63/100)(2/1)
Cross multiply = 200
Then divide 200÷63= 3.175
Answer:
39.69%
Step-by-step explanation:
\(\frac{63}{100}\) * \(\frac{63}{100}\) = .3969
they were 300 people at a football match and 35% were adults, the rest were children b.how many children were present?
Answer:
35% of 300 is 105
Adults=105 , children=195
195 children were present.
13. find the volume of each composite figure to the nearest whole number
Answer:
Step-by-step explanation:
First, you need to be familiar with the volume equation for the object in question.
The equation is \(v= (\frac{\pi r^2h}{2})\)
For the outer shape we are given the diameter (which is just r*2), making the radius 8
For the the first object the equation becomes\(\frac{\pi(8^2)16}{2}\) which then comes out to 1608.49 which when rounded is 1608
Since we are to assume the shaded object is in the middle, we see that the distance from the shaded object to the other object is 4. So to find the radius of the shaded object we need to subtract 4 from the radius of the bigger object. The radius of the shaded object is 4
Using the same equation above we get that the volume is equal to \(\frac{\pi 4^{2}8 }{2}\) which comes to 201.06 which when rounded is 201
If you need the outer object without the volume of the inner object just subtract 201 from 1608
answer two questions about systems aaa and bbb: system aaa \text{\quad}start text, end text system bbb \begin{cases}x-4y
Two questions about systems aaa and bbb, the given system is:
System aaa: x = -1/3 and y = -7/3
System bbb: x = -1/3 and y = -7/3
To answer two questions about systems aaa and bbb, let's first clarify the given system:
System aaa:
x - 4y = 9
System bbb:
2x + y = -3
Question 1: Solve system aaa.
To solve system aaa, we'll use the method of substitution:
Step 1: Solve one equation for one variable.
From the first equation in system aaa, we can isolate x:
x = 4y + 9
Step 2: Substitute the expression from Step 1 into the other equation.
Substitute the expression for x in the second equation of system aaa:
2(4y + 9) + y = -3
Step 3: Simplify and solve for y.
8y + 18 + y = -3
9y + 18 = -3
9y = -3 - 18
9y = -21
y = -21/9
y = -7/3
Step 4: Substitute the value of y into the expression for x.
Using the first equation in system aaa:
x - 4(-7/3) = 9
x + 28/3 = 9
x = 9 - 28/3
x = (27 - 28)/3
x = -1/3
Therefore, the solution to system aaa is x = -1/3 and y = -7/3.
Question 2: Solve system bbb.
To solve system bbb, we'll use the method of substitution:
Step 1: Solve one equation for one variable.
From the second equation in system bbb, we can isolate y:
y = -2x - 3
Step 2: Substitute the expression from Step 1 into the other equation.
Substitute the expression for y in the first equation of system bbb:
x - 4(-2x - 3) = 9
Step 3: Simplify and solve for x.
x + 8x + 12 = 9
9x + 12 = 9
9x = 9 - 12
9x = -3
x = -3/9
x = -1/3
Step 4: Substitute the value of x into the expression for y.
Using the second equation in system bbb:
y = -2(-1/3) - 3
y = 2/3 - 3
y = 2/3 - 9/3
y = -7/3
Therefore, the solution to system bbb is x = -1/3 and y = -7/3.
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Joel ha brownie. The length of each brownie i 7cm and the width i 5cm find the area of the brownie
If Joel has brownie with length 7cm and width 5cm , then the Area of the brownie is 35 cm² .
The Area of a Rectangle can be determined by multiplying its length(l) and width(w) . that means "Area is = Length × Width" ;
In the case of Joel's brownie, the length of brownie is 7 centimeters and the width of brownie is 5 centimeters.
So , By multiplying these two measurements, we can find the area of the brownie.
Area = 7cm × 5cm = 35 square cm .
Therefore, the area of the brownie is 35 square centimeters.
The given question is incomplete , the complete question is
Joel has brownie. The length of each brownie is 7cm and the width is 5cm find the area of the brownie .
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hELP asap
39.67 + 18.41
Answer:
58.08
Step-by-step explanation:
Answer:
58.08
Step-by-step explanation:
39.67+18.41=58.08
Roger is replacing the liner of a chimney. The length of the liner required is 33 ft. Roger has 400 inches of stainless steel pipe for the liner. Is this enough? Justify your answer.
Roger has enough stainless steel pipe to replace the chimney liner, with a slight surplus remaining.
To determine if Roger has enough stainless steel pipe for the chimney liner, we need to convert the given measurements to a consistent unit of measurement. Since the length of the liner required is given in feet, we need to convert the 400 inches of stainless steel pipe to feet.
There are 12 inches in a foot, so 400 inches is equal to 400/12 = 33.33 feet (approximately).
Comparing this converted length of the stainless steel pipe (33.33 feet) with the length of the liner required (33 feet), we can see that Roger does indeed have enough pipe. In fact, he has slightly more than required.
Since the length of the liner required is 33 feet and Roger has 33.33 feet of stainless steel pipe available, there is a surplus of approximately 0.33 feet (about 4 inches) of pipe. This additional length is more than enough to cover any potential measurement errors or adjustments needed during the installation process.
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if my avg is a 96 and my final exam is a 75 which is 25% of my whole grade what will my final grade be
Step-by-step explanation:
That means the 96 is 75% of your grade
96 (.75) + 75 (.25) = 90.75 final grade
How can you return $0.28 in change using the fewest coins?
A
1 dime, 3 nickels and 3 pennies
B
2 dimes, 1 nickel, and 3 pennies
C
2 dimes and 8 pennies
D
1 quarter and 3 pennies
So
Check option D
3 pennies=0.03$Total
0.25+0.03=0.28$Option D is correct
If z is directly proportional to the product of x and y and if z is 10 when x is 4 and y is 5, then x, y, and z are related by the equation
The equation relating x, y, and z is:
z = 0.5 * x * y.
In the given problem, the relationship between x, y, and z can be expressed by the equation z = k * x * y, where k represents the constant of proportionality. By substituting the values of x = 4 and y = 5, when z is equal to 10, we can determine the value of the constant of proportionality, k, and further define the relationship between the variables.
To find the constant of proportionality, we substitute the known values of x = 4, y = 5, and z = 10 into the equation z = k * x * y. This gives us the equation 10 = k * 4 * 5. By simplifying the equation, we have 10 = 20k. To isolate k, we divide both sides of the equation by 20, resulting in k = 0.5. Therefore, the equation relating x, y, and z is z = 0.5 * x * y, meaning that z is directly proportional to the product of x and y with a constant of proportionality equal to 0.5.
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Consider the data: Yi = β0 + β1 + ei where e1, . . . , en are uncorrelated errors with mean zero and variance σ2 .a) Write this model in the form Y = Xβ + e with β = (β0, β1)T . Specify the matrix X.b) Write down the normal equations. Find a solution to them. Is the solution unique?c) What is the least squares estimate of β0 + β1?d) Is β1 estimable?e) Consider now another observation Y_n+1 = β0 + 2β1 + e_n+1 where e1, . . . , e_n+1 are uncorrelated errors with mean zero and variance σ2 . Write this model in the form Y = Xβ +e and calculate the least squares estimate of β.
The estimates of β0 and β1 depend on both the old and the new observations.
a) The model in matrix form is Y = Xβ + e where Y is an n x 1 vector of responses, X is an n x 2 matrix of predictor variables, β is a 2 x 1 vector of coefficients, and e is an n x 1 vector of errors. We have X = [1 x1; 1 x2; ... ; 1 xn] where xi is the value of the predictor variable for the ith observation.
b) The normal equations are X'Xβ = X'Y, where X' is the transpose of X. Expanding, we get:
(∑1n1 + ∑1nxi^2)β0 + (∑1nxi)β1 = ∑1nYi
(∑1nxi)β0 + (∑1nxi^2)β1 = ∑1nxiYi
Solving these equations for β0 and β1, we get:
β0 = (1/n) ∑1n(Yi - β1xi)
β1 = (∑1nxiYi - (1/n)(∑1nxi)(∑1nYi)) / (∑1nxi^2 - (1/n)(∑1nxi)^2)
The solution is unique since the matrix X'X is invertible.
c) The least squares estimate of β0 + β1 is given by the sum of the estimates of β0 and β1, which is:
(1/n) ∑1nYi
d) β1 is estimable since there is a unique solution for it.
e) The model in matrix form is Y = Xβ + e where Y is an (n+1) x 1 vector of responses, X is an (n+1) x 2 matrix of predictor variables, β is a 2 x 1 vector of coefficients, and e is an (n+1) x 1 vector of errors. We have X = [1 x1; 1 x2; ... ; 1 xn; 1 xn+1] where xi is the value of the predictor variable for the ith observation.The least squares estimate of β is given by:
β = (X'X)^(-1)X'Y
Expanding, we get:
β0 = (1/(n+1)) * (Σ1^n Yi + Yn+1 - 2β1 * Σ1^n xi - 2xn+1β1)
β1 = (∑1nxiYi + xn+1Yn+1 - (1/(n+1))(Σ1^n xi + xn+1)^2) / (∑1nxi^2 + xn+1^2 - (1/(n+1))(Σ1^n xi + xn+1)^2).
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