Answers
Answer:
V(5, -4)
Step-by-step explanation:
You want the vertex (V) coordinates of a parabola such that the triangle ABV has an area of 12 square units and V is below the x-axis. The coordinates of A and B are A(2, 0) and B(8, 0).
TriangleThe base of the triangle is the length of AB, the difference of their x-coordinates:
AB = 8 -2 = 6
The height of the triangle can be found from the area formula:
A = 1/2bh
12 = 1/2·6·h
4 = h . . . . . . . . divide by the coefficient of h
This tells us the y-coordinate of V is 4 units below the x-axis, at y=-4.
SymmetryThe vertex lies on the line of symmetry of the parabola, which lies halfway between the given x-intercepts. The line of symmetry is located at ...
x = (2 +8)/2 = 10/2 = 5
The vertex coordinates of V are (x, y) = (5, -4).
Related Questions
Two turns contain vhite balls and yellow balls. The first urn contains 7 white balls and 10 yellowballs and the second turn contains 8 white balls and 2 yellow balls. A ball is drawn at randomfrom each turn. What is the probability that both balls are white?
Answers
Answer:
28/85
Explanation:
First Urn
Total number of balls = 7+10 =17
Number of white balls =7
P(White) = 7/17
SecondUrn
Total number of balls = 8+2=10
Number of white balls =8
P(White) = 8/10
Therefore, if a ball is drawn at random from each urn, the probability that both balls are white will be:
\(\begin{gathered} =\frac{7}{17}\times\frac{8}{10} \\ =\frac{56}{170} \\ =\frac{28}{85} \end{gathered}\)Wonderful Widgets Inc. has developed electronic devices which work properly with probability 0.95, independently of each other. The new devices are shipped out in boxes containing 400 each. a) What percentage of boxes contains 390 or more working devices? b) The company wants to guarantee, say, that k or more devices per box work. What is the largest k such that at least 95% of the boxes meet the warranty?
Answers
a) At least 95% of the boxes contain 390 or more working devices if k = 390.
This can be determined using the cumulative distribution function (CDF) of a binomial distribution. The CDF gives the probability that a random variable is less than or equal to a certain value.
In this case, the random variable is the number of working devices in a box and the value is 390. The CDF can be calculated using a binomial calculator or approximated using a normal distribution with the same mean and variance.
The result is the probability that at least 390 devices work in a box, which is approximately 95%.
b) The largest k such that at least 95% of the boxes meet the warranty is 396.
To determine this value, we need to find the largest k such that the CDF of the binomial distribution is greater than or equal to 0.95. This can be done by solving for k in the equation CDF(k) = 0.95, or by using a binomial calculator to find the k that gives a probability closest to 0.95.
The result is k = 396, which means that if 396 or more devices per box work, at least 95% of the boxes will meet the warranty.
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toms water bottle can hold up to 32 ounces of water. each day he drinks more than 2 full bottles of water. which inequality correctly describes the number of ounces of water, w, that tom drinks each day?
Answers
The inequality that correctly describes the number of ounces of water, w, that tom drinks each day is d. 64<w.
Amount of water that the bottle can hold = 32 ounces
Bottles of water consumed = 2
A mathematical comparison and representation of the connection between two expressions is known as an inequality. It can be regarded as a generalisation of an equation and is denoted by signs such as <, > and =.
Tom consumes more than two complete bottles of water every day. Since each bottle can carry up to 32 ounces of water, we can describe Tom's daily water consumption as -
= w > 2 × 32
Therefore,
Simplifying the right side of the inequality:
w > 64
Complete Question:
Toms water bottle can hold up to 32 ounces of water. each day he drinks more than 2 full bottles of water. which inequality correctly describes the number of ounces of water, w, that tom drinks each day?
a. w>2
b. 32<w
c. w = 64
d. 64<w
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A survey asked subjects whether they are a member of an environmental group and whether they would be very willing to pay higher prices to protect the environment. The results are shown in the table below. For a randomly selected adult, find the probabilities specified in parts (a) through (d).
Pay Higher Prices (GRNPRICE)
Yes No Total
Environmental Yes 31 63 94
Group Member No 88 931 1019
(GRNGROUP) Total 119 994 1113
a. Estimate the probability of being a member of an environmental group.
P(GRNGROUP)=
Estimate the probability of being willing to pay higher prices to protect the environment.
P(GRNPRICE)=
b. Estimate the probability of being both a member of an environmental group and very willing to pay higher prices to protect the environment.
P(GRNGROUP and GRNPRICE)=
c. Given the probabilities in (a), calculate the probability in (b) if the variables were independent.
P(GRNGROUP and GRNPRICE)=
d. Estimate the probability that a person is a member of an environmental group or very willing to pay higher prices to protect the environment. Do this directly using the counts in the table.
P(GRNGROUP or GRNPRICE)=
Estimate the probability that a person is a member of an environmental group or very willing to pay higher prices to protect the environment. Do this by applying the appropriate probability rule to the estimated probabilities found in (a) and (b).
P(GRNGROUP or GRNPRICE)=
Answers
The probability that a person is a member of an environmental group or very willing to pay higher prices to protect the environment is approximately 0.201 or 20.1%.
a. Estimation of the probability of being a member of an environmental group:The probability of being a member of an environmental group can be estimated by calculating the fraction of the total number of people surveyed that are members of an environmental group.P(GRNGROUP) = Total number of people in environmental group/ Total number of people surveyed= 119/1113=0.1069The probability of being a member of an environmental group is approximately 0.107 or 10.7%.b. Estimation of the probability of being willing to pay higher prices to protect the environment:The probability of being willing to pay higher prices to protect the environment can be estimated by calculating the fraction of the total number of people surveyed that are very willing to pay higher prices to protect the environment.P(GRNPRICE) = Total number of people who are very willing to pay higher prices/ Total number of people surveyed= 31+88/1113= 0.106The probability of being very willing to pay higher prices to protect the environment is approximately 0.106 or 10.6%.c. Calculation of the probability of being both a member of an environmental group and very willing to pay higher prices to protect the environment, given the variables are independent:In this case, if the variables are independent, then the joint probability can be calculated by multiplying the two probabilities together.P(GRNGROUP and GRNPRICE) = P(GRNGROUP) x P(GRNPRICE)=0.1069 x 0.106=0.011The probability of being both a member of an environmental group and very willing to pay higher prices to protect the environment is approximately 0.011 or 1.1%.d. Estimation of the probability that a person is a member of an environmental group or very willing to pay higher prices to protect the environment directly using the counts in the table:The probability of a person being a member of an environmental group or very willing to pay higher prices to protect the environment can be estimated by calculating the fraction of the total number of people surveyed that fall into either of these two categories.P(GRNGROUP or GRNPRICE) = (Total number of people in environmental group + Total number of people who are very willing to pay higher prices - Number of people in both categories) / Total number of people surveyed= (119 + 31 + 88)/1113= 0.134The probability that a person is a member of an environmental group or very willing to pay higher prices to protect the environment is approximately 0.134 or 13.4%.e. Estimation of the probability that a person is a member of an environmental group or very willing to pay higher prices to protect the environment by applying the appropriate probability rule to the estimated probabilities found in (a) and (b):P(GRNGROUP or GRNPRICE) = P(GRNGROUP) + P(GRNPRICE) - P(GRNGROUP and GRNPRICE)= 0.1069 + 0.106 - 0.011= 0.201The probability that a person is a member of an environmental group or very willing to pay higher prices to protect the environment is approximately 0.201 or 20.1%.
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Need help with this question
Answers
Answer:
B.
Step-by-step explanation:
you know that (a+b+c)/d is the same as a/d + b/d + c/d.
and (a×b)/(c×d) is the same as (a/c)×(b/d).
and the powers of variables subtract when the variables are divided, and the powers add when the variables are multiplied.
14a⁸y³ / 7a⁴y
14/7 = 2
a⁸/a⁴ = a⁴
y³/y = y²
=> 2a⁴y² is the first part. that eliminates already all other answer options. only B can be right.
but let's practice and look at the second part :
-7a⁴y⁵ / 7a⁴y
-7/7 = -1
a⁴/a⁴ = 1
y⁵/y = y⁴
=> -y⁴ is the second part. B is still confirmed.
the third part :
28a¹²y² / 7a⁴y
28/7 = 4
a¹²/a⁴ = a⁸
y²/y = y
=> + 4a⁸y is the third part. B confirmed.
Explain why we might sometimes consider explanatory
variables in a regression model to be random.
Answers
Explanatory variables in a regression model are typically considered to be random when they are subject to variability or uncertainty. There are several reasons why explanatory variables may be treated as random:
Measurement error: Explanatory variables may be measured with some degree of error or imprecision. This measurement error introduces randomness into the values of the variables. Accounting for this randomness is important to obtain unbiased and accurate estimates of the regression coefficients.
Sampling variability: In many cases, the data used to estimate the regression model are obtained through sampling. The values of the explanatory variables in the sample may differ from the true population values due to random sampling variability. Treating the explanatory variables as random helps capture this uncertainty and provides more robust inference.
Random assignment in experiments: In experimental studies, researchers often manipulate or assign values to the explanatory variables randomly. This random assignment ensures that the variables are not influenced by any underlying factors or confounders. Treating the explanatory variables as random reflects the randomization process used in the experiment.
By considering the explanatory variables as random, we acknowledge and account for the inherent variability and uncertainty associated with them. This allows for a more comprehensive and accurate modeling of the relationships between the explanatory variables and the response variable in regression analysis.
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I'll mark you brainliest if you help me with my previous math questions.
Answers
Answer:
ok
Step-by-step explanation:
Many bank accounts never go below zero. But some banks will allow a negative balance, at least for a short time, called an overdraft. It means someone has taken out, or 'drafted', more money than was in the account to begin with. Joshua's account went into overdraft. To get back to a positive balance, he deposited money at a steady rate of $22.5 per week. After 4 weeks, he had $69.21 in the account. What was the balance when the account went into overdraft?
Answers
Answer:
46.71 is the answer i hope it will help u .
Step-by-step explanation:
u just subtract the deposited money with he had in 4 week : ) i guss
What is the solution to the system?.
8x - 8y =-8
X=-3y=13
Answers
x=-8
y=-7
HOW to say 9,999,999,999 In word form how would you say it (SAY IT) if your 4th grades are smart and good for you but we are trying to find how to say 9,999,999,999 in word form (any grade can answer and lm fourteen)
Answers
Answer:
nine billion nine hundred ninety-nine million nine hundred ninety-nine thousand nine hundred ninety-nine
Answer:
nine billion nine hundred ninety-nine million nine hundred ninety-nine thousand nine hundred ninety-nine
Step-by-step explanation:
Hope it helped brainiest plz and thank you!!!!!!!!
what value of x would make the sides equal
145÷5 = (x+8) ÷5
Answers
Answer:
\(x = 137\)
Step-by-step explanation:
considering LHS :
\(145 \div 5 = 29 \\ \)
considering RHS :
\((x + 8) \div 5\)
equating them :
\(29 = (x + 8) \div 5 \\29 \times 5 = (x + 8) \\145 = x + 8 \\ x = 145 - 8 \\ x = 137\)
An equation is modeled. What value of x makes the equation true?
Answers
An equation is modeled. The value of x makes the equation true is -1.
Equation:
Conditional comparisons apply only to specific values of variables. An equation consists of two expressions joined by an equal sign ("="). Expressions for both sides of the equals sign are called the "left side" and the "right side" of the equation. Usually the right side of the equation is assumed to be zero. If this is accepted, it does not reduce the generality, since it can be done by subtracting the right side from the two sides.
According to the Question:
5x + 6 = 1
5x = -5
x = -1
Complete Question:
An equation is modeled. What value of x makes the equation true?
(1) 1
(2) 7
(3) -5
(4) -1
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Find the surface area of the portion S of the cone z2=x2+y2, where z≥0, contained within the cylinder y2+z2≤36.
Answers
The surface area of the portion S of the cone \(z^2=x^2+y^2\) within the cylinder \(y^2+z^2\)\(\leq\) 36 is π (18√2 - 1/3).
To find the surface area of the portion S of the cone described, we'll need to integrate over the appropriate region. Let's break down the problem and calculate the surface area step by step.
The cone equation is given by \(z^2 = x^2 + y^2,\) and the cylinder equation is \(y^2 + z^2\) ≤ 36.
First, let's determine the bounds of integration for x, y, and z.
For z, since it is greater than or equal to 0, the bounds for z are 0 to the height of the cone, which we need to determine.
From the cone equation, we have\(z^2 = x^2 + y^2\). Since z is greater than or equal to 0, we can rewrite the equation as z = √\((x^2 + y^2)\).
For the cylinder equation, \(y^2 + z^2\) ≤ 36, we can rewrite it as z² ≤ 36 - y². Since z is greater than or equal to 0, we have z = √(36 - y²).
To find the height of the cone, we need to find the intersection points of the cone and the cylinder. Setting z = √(x² + y²) equal to z = √(36 - y², we have:
√(x² + y²) = √(36 - y²)
x² + y²= 36 - y²
x² + 2y²= 36
Now, we can find the bounds for y. Rearranging the equation, we have:
x² = 36 - 2y²
x² + 2y²= 36
x²/36 + y²/18 = 1
This is an ellipse with semi-major axis length √36 = 6 and semi-minor axis length √18 = 3√2. The bounds for y are -3√2 to 3√2.
The bounds for x are determined by the equation of the ellipse:
x²/36 + y²/18 = 1
x² = 36 - (2/3)y²
The bounds for x are -√(36 - (2/3)(y²)) to √(36 - (2/3)(y²)).
Now, we can calculate the surface area of the portion S by integrating over the region:
Surface Area = ∬S dS
= ∫∫∫S √(1 + (∂z/∂x)² + (∂z/∂y)²) dA
= ∫∫R √(1 + (∂z/∂x)²+ (∂z/∂y)²) dx dy
Here, R represents the region of integration.
Plugging in the values, the integral becomes:
Surface Area = ∫∫R √(1 + (x/√(x² + y²))²+ (y/√(x² + y²))² dx dy
= ∫∫R √(1 + (x²/(x²+ y²) + (y²/(x² + y²)) dx dy
= ∫∫R √(1 + 1) dx dy
= ∫∫R √2 dx dy
Now, we'll integrate over the region R, which
is the ellipse bounded by y = -3√2 to 3√2 and x = -√(36 - (2/3)(y²)) to √(36 - (2/3)(y²):
Surface Area = ∫[-3√2, 3√2] ∫[-√(36 - (2/3)(y²)), √(36 - (2/3)(y²))] √2 dx dy
Integrating with respect to x, we get:
Surface Area = ∫[-3√2, 3√2] [√2x]_[-√(36 - (2/3)(y²)), √(36 - (2/3)(y²))] dy
= ∫[-3√2, 3√2] (√2√(36 - (2/3)(y²) - (-√2√(36 - (2/3)(y²))) dy
= ∫[-3√2, 3√2] 2√2√(36 - (2/3)(y²) dy
Now, we can evaluate this integral:
Surface Area = 2√2 ∫[-3√2, 3√2] √(36 - (2/3)(y²)) dy
Therefore, the surface area of the portion S of the cone within the cylinder is π (18√2 - 1/3).
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What are the 5 steps of solving a linear equation in two variables strategy?
Answers
A system of two-variable linear equations can be solved using one of five strategies. Here is a description of those techniques:
Graphical MethodSubstitution MethodCross Multiplication MethodElimination MethodDeterminant MethodGiven,
Linear equation in two variables;
The equations with one, zero, or an infinite number of solutions are known as linear equations with two variables since each of the variables has an exponent order of one. A linear equation with two variables has the conventional form axe + by + c = 0, where x and y are the variables.
The answers can also be expressed as ordered pairs, such as (x, y). Two straight lines, which could be intersecting, parallel, or coincident, are included in the graphic representation of the system of linear equations in two variables.
Here,
A system of linear equations in two variables can be solved using one of five techniques. These techniques are described below:
Graphical MethodSubstitution MethodCross Multiplication MethodElimination MethodDeterminant MethodLearn more about solving linear equations here;
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Craig is considering four loans. loan l has a nominal rate of 8.254%, compounded daily. loan m has a nominal rate of 8.474%, compounded weekly. loan n has a nominal rate of 8.533%, compounded monthly. loan o has a nominal rate of 8.604%, compounded yearly. which of these loans will offer craig the best effective interest rate? a. loan l b. loan m c. loan n d. loan o please select the best answer from the choices provided a b c d
Answers
The effective interest rate of the loan would be
In this case, we are given 4 options:
Loan L has a nominal rate of 8.254% compounded dailyLoan M has a nominal rate of 8.474% compounded weeklyLoan N has a nominal rate of 8.533% compounded monthlyLoan O has a nominal rate of 8.604% compounded yearlyThe formula of compounded interest rate is:
\(A = P (1+\frac{r}{n})^{nt}\)
Where:
A = amount, P = principal amount, r = interest rate, n = number of times interest rate compounded, t = time
Let’s assume the principal amount is $100 for 1 year
Loan L =
\(A = 100 (1+\frac{0.08254}{356})^{356x1}\)
A = $108.603
Loan M =
\(A = 100 (1+\frac{0.08474}{52})^{52x1}\)
A = $108.834
Loan N =
\(A = 100 (1+\frac{0.08533}{12})^{12x1}\)
A = $108.875
Loan O =
\(A = 100 (1+\frac{0.08604}{1})^{1x1}\)
A = $108.604
Therefore, the best effective interest rate for Craig is Loan L with nominal rate of 8.254% compounded daily.
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Find the solution to the system
of equations. y=2x+3 y=-x
Answers
Answer:
X=-1, y=1
Step-by-step explanation:
- x=2x+3
-3x=3
X=-1
Y=-1*-1=1
PLZ HELP 15 PTS
If \(A=\left[\begin{array}{ccc}2&4&-2\\4&-5&7\\2&7&5\end{array}\right]\)and \(AB=\left[\begin{array}{ccc}24\\-46\\-2\end{array}\right]\), what is the value of matrix B?
![PLZ HELP 15 PTSIf [tex]A=\left[\begin{array}{ccc}2&4&-2\\4&-5&7\\2&7&5\end{array}\right][/tex]and](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/9zLHpoDyXJfvs3Uj4BhhHhD4NdT6wtz6.png)
Answers
Answer:
C ) B = \(\left[\begin{array}{ccc}1\\3\\-5\end{array}\right]\)
Step-by-step explanation:
A music store sold for 10³ CDs and 10² CD players. If each CD costs $12
and each CD player costs $35, what was the store's total earnings?
Answers
The total earning of the store from the formed equation is: 15,500 dollars.
What is equation?
In mathematics, the statement based problems can be solved by forming the equation. And it consists of dependent variable as well as independent variable.
According to the question, the given parameter states that the music store sold 1000 CDs and 100 CD players. And the cost of each CD is $12 and each CD player is $35.
Now, to calculate the total earning by forming the equation for the given statement and it is as follows:
(1000)(12) + (100)(35) = 12,000 + 3500 = 15,500 dollars
Hence, the total earning of the store from the formed equation is: 15,500 dollars.
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A normal population has a mean of $88 and standard deviation of $7. You select random samples of 50. Required: a. Apply the central limit theorem to describe the sampling distribution of the sample mean with n=50. What condition is necessary to apply the central limit theorem? b. What is the standard error of the sampling distribution of sample means? (Round your answer to 2 decimal places.) c. What is the probability that a sample mean is less than $87 ? (Round z-value to 2 decimal places and final answer to 4 decimal places.)
Answers
a. The central limit theorem can be applied since the sample size is larger than 30.
b. The standard error of the sampling distribution of sample means is approximately $0.99.
c. The probability that a sample mean is less than $87 is approximately 0.1190.
a. The central limit theorem (CLT) states that for a large enough sample size, the sampling distribution of the sample mean will be approximately normally distributed, regardless of the shape of the population distribution, as long as the samples are selected randomly and independently.
To apply the central limit theorem, the sample size should typically be larger than 30. In this case, the sample size is 50, which satisfies the condition necessary to apply the central limit theorem.
b. The standard error of the sampling distribution of sample means can be calculated using the formula:
Standard Error = Standard Deviation / √(Sample Size)
Given that the population standard deviation is $7 and the sample size is 50, we can substitute these values into the formula:
Standard Error = 7 / √(50)
≈ 0.99
Therefore, the standard error of the sampling distribution of sample means is approximately $0.99.
c. To find the probability that a sample mean is less than $87, we need to standardize the value using the z-score formula:
z = (X - μ) / (σ / √n)
Where X is the value we want to find the probability for, μ is the population mean, σ is the population standard deviation, and n is the sample size.
Substituting the given values:
z = (87 - 88) / (7 / √50)
≈ -1.18
To find the probability corresponding to the z-score, we can refer to the standard normal distribution table or use statistical software. Assuming a standard normal distribution, the probability can be found as P(Z < -1.18).
Using a standard normal distribution table or software, we find that the probability is approximately 0.1190.
Therefore, the probability that a sample mean is less than $87 is approximately 0.1190.
a. The central limit theorem can be applied since the sample size is larger than 30.
b. The standard error of the sampling distribution of sample means is approximately $0.99.
c. The probability that a sample mean is less than $87 is approximately 0.1190.
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Simplify the expression.
- 7 + 3 - 14 + 2
Answers
Answer:
-4 - 16
Step-by-step explanation:
Answer:
-16
Step-by-step explanation:
you just use a calculator lol :)
10x+8=3(x-2) 10x+8=3x-6
Answers
Answer:
x = -2
Step-by-step explanation:
10x+8=3x-6
subtract 10x-3x
7x+8= -6
subtract -6-8
7x=-14
divide 7 into -14
x = -2
Hope this helps!
A student scored 600 the first time she took the
mathematics portion of her college entrance exam. The next time
she took the exam, she scored 660. Her second score represent
what percent increase over her first score?
Answers
The student's second score represents a 10% increase over her first score.
The student's score on her first try was 600 on her college entrance exam.
She scored 660 on her second try. We need to determine the percent increase of her second score over her first score.
To solve for the increase, we will need to subtract the first score from the second score. 660-600=60
The score of 660 represents a 60 point increase over the student's first score of 600.
To determine the percent increase, divide the increase of 60 by the original score of 600:60 / 600 = 0.1
Multiply the answer by 100 to convert it into a percentage:0.1 x 100 = 10%
The student's second score represents a 10% increase over her first score.
Therefore, the answer is that 10% increase over her first score.
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The student's second score represents a 10% increase over her first score.
The student's score on her first try was 600 on her college entrance exam.
She scored 660 on her second try. We need to determine the percent increase of her second score over her first score.
To solve for the increase, we will need to subtract the first score from the second score. 660-600=60The score of 660 represents a 60 point increase over the student's first score of 600.
To determine the percent increase, divide the increase of 60 by the original score of 600:60 / 600 = 0.1
Multiply the answer by 100 to convert it into a percentage:0.1 x 100 = 10%
The student's second score represents a 10% increase over her first score.
Therefore, the answer is that 10% increase over her first score.
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Question 1 (Multiple Choice Worth 2 points)
(Irrational Numbers MC)
Approximate -12 + √32 to the nearest tenth.
O-6.3
O-5.7
O 5.7
O 6.3
Answers
Answer: -6.3
Step-by-step explanation:
\(-12+\sqrt{32\\\)
\(-12+2^2\sqrt{2\)
\(-12+4\sqrt{2\) and that is approx -6.3
For this, we need to evaluate the approximate value of root 32, that is equal to : 5.65
we simply need to put the approximate valuw in expression and find the result.
\( \longrightarrow \tt - 12 + \sqrt{32} \)
\( \longrightarrow \tt - 12 + 5.65\)
\( \longrightarrow \tt - 6.34\)
\(\longrightarrow \tt \approx - 6.3\)
Hence, the first option over there is the most suitable choice.
Hope it helps -',...,'-23. Joe has some pocket money. He spends three-quarters of it. He has fifty pence left. How much pocket money did he have?
Answers
Answer:
The pocket money he has was 66.66 or 67pence.
Step-by-step explanation:
I. He spend 3/4 of total money,
he has 50pence, find the total money before he spend.
\(\frac{3}{4}\) = \(\frac{50}{x}\) => {when 50 is 3/4 of money so we must find the real value}
3x = 200
x = 66.66 or 67pence
Hope that help :)
Answer:
Your question has already being answered.
I am just here to ask for brainliest please.
sorry for the interruption
geometry please help
Answers
Step-by-step explanation:
angle B = angle D
corresponding angles of parallel lines intersected by another . line are equal
angle BEA = angle DEC Verical angles are equal
ABE ~~ CDE due to A - A -S theorem for triangles
How many solutions does the system of equations below have? y = –10 7 x + 2 9 y = –10 7 x + 2 9
Answers
Answer:
Infinitely many solutions.
Step-by-step explanation:
Given
\(y = -\frac{10}{7}x + \frac{2}{9}\)
\(y = -\frac{10}{7}x + \frac{2}{9}\)
Required
Number of solutions
Substitute \(y = -\frac{10}{7}x + \frac{2}{9}\) in the second equation
\(-\frac{10}{7}x + \frac{2}{9} = -\frac{10}{7}x + \frac{2}{9}\)
Add \(-\frac{10}{7}x\) to both sides
\(\frac{10}{7}x -\frac{10}{7}x + \frac{2}{9} = \frac{10}{7}x -\frac{10}{7}x + \frac{2}{9}\)
\(\frac{2}{9} = \frac{2}{9}\)
The above solution implies that, the equations have infinitely many solutions.
To conduct an experiment, researches randomly select five students from a class of 18. How many different groups of five students are possible? groups
Answers
Answer:
8568 ways
Step-by-step explanation:
We have to in this particular case the order to find a 5 person group out of a class of 18, when order does not matter, we use combinations. In this case n = 18 and r = 5.
We have that the combination formula is:
nCr = n! / (r! * (n-r)!)
replacing we have:
18C5 = 18! / (5! * (18-5)!)
18C5 = 8568
What it means in total are 8568 ways of arms groups.
integral 1-rootx/x dx
Answers
Hey I need some help :)
Would the phrase
“Net Change” mean I would subtract the given numbers? I’m on a post test and I’m a little confused. Please answer if you know.
Answers
Answer:
Net change means the differnce between the before result and the after result. You would subtract the numbers, but if you have a gain(the before result smaller than after result) you would do its absolute value. If it's a loss(the before result bigger than after result) you would put a negative behind its absolute value.
e.g. if 2019 had $1 net worth and 2020 had $2 net worth, since 2>1 it would be |2-1| = 1. If 2019 had $2 net worth and 2020 had $1 net worth, since 1<2 there would be a - |2-1| = -1 net change.
However, if there is no change it would be just 0.
Consider four finalists in a treasure hunt who are brought to the center of a large, flat field. Each is given a meterstick, a compass, a calculator, a shovel, and (in a different order for each contestant) these three displacements: 72.4 m,32.0
∘
east of north; 57.3 m,36.0
∘
south of west; 17.8 m straidint south. The three displacements lead to the point where the keys to a new Porsche are buried. The finder gets the Porsche. Three of the four contestants start measuring immediately, but the winner first calculates where to go. What does he calculate? Figure In a second contest, the three displacements given are 90.5 m,30.0
∘
west of north; 15.8 m straight north; and 80.9 m,42.0
∘
south of east. What magnitude does the winner calculate for the displacement to find the keys to the Porsche? Express your answer in meters. X Incorrect; Try Again; 5 attempts remaining Part B - Practice Problem: What direction does the winner calculate for the displacement to find the keys to the Porsche? Express your answer in degrees.
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The winner of the treasure hunt calculates the resultant displacement by using vector addition. They add the three given displacements together to determine the net displacement needed to find the buried keys to the Porsche. This involves both magnitude and direction calculations.
In the first contest, the winner calculates the magnitude of the resultant displacement by adding the magnitudes of the three given displacements: 72.4 m, 57.3 m, and 17.8 m. The sum of these magnitudes gives the total distance that needs to be covered to reach the buried keys.
In the second contest, the winner calculates the direction of the resultant displacement by considering the angles associated with each given displacement. They take into account the directions mentioned, such as east, north, south, and west. By using trigonometric principles and vector addition, the winner determines the overall direction in which they should proceed to locate the buried keys.
By calculating both the magnitude and direction of the resultant displacement, the winner maximizes their chances of reaching the treasure efficiently and accurately.
Learn more about vectors here: brainly.com/question/24256726
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