Answer:
The system of equations is consistent and independent
Step-by-step explanation:
Given system of equations :
\(y=x+4\\y= -x-4\)
Consistent : For a two variable system of equations to be consistent the lines formed by the equations have to meet at some point or they have to be parallel.
Inconsistent :If the system of equations is not consistent then it is inconsistent.
Dependent:A dependent system of equations has infinite solutions
Independent :An independent system has a single solution.
Plot the lines on graph
y=x+4 --- Blue line
y=-x+4 ---- Green line
Refer the attached graph
The lines formed by the equations intersect at one point
So the lines are consistent
Now the given system of equations has single solution . So, it is independent
So, Option C is true
Hence The system of equations is consistent and independent
ar A starts in Sacramento at 11am. It travels along a 400 mile route to Los Angeles at 30 mph. Car B starts from Los Angeles at noon and travels to Sacramento along the same route at 75 mph. The route goes past Fresno which is 150 miles along the route from Los Angeles. How far from Fresno are the cars when they meet
Therefore, the distance between Car A and Car B when they meet is 150 miles (distance from Fresno to Los Angeles) - 90 miles (distance covered by Car A) = 60 miles. Thus, they meet 60 miles away from Fresno, which is 200 miles away from Fresno along the entire route.
To determine the distance from Fresno where the cars meet, we need to consider the relative speeds and the time it takes for each car to travel. Car A starts in Sacramento and travels at a speed of 30 mph, while Car B starts in Los Angeles and travels at a speed of 75 mph.
Car A starts one hour earlier than Car B, so it has a head start. In that one hour, Car A would have traveled 30 miles (30 mph x 1 hour). The remaining distance between Car A and Fresno would be 400 miles - 30 miles = 370 miles.
Now, we need to calculate the time it takes for Car B to travel from Los Angeles to Fresno, which is 150 miles. Using the formula Time = Distance / Speed, the time taken by Car B would be 150 miles / 75 mph = 2 hours.
Since Car B starts at noon, it will take 2 hours to reach Fresno, which means it will arrive at Fresno at 2pm. At that time, Car A would have been traveling for 3 hours (11am to 2pm). Given that Car A's speed is 30 mph, it would have covered a distance of 30 mph x 3 hours = 90 miles.
Therefore, the distance between Car A and Car B when they meet is 150 miles (distance from Fresno to Los Angeles) - 90 miles (distance covered by Car A) = 60 miles. Thus, they meet 60 miles away from Fresno, which is 200 miles away from Fresno along the entire route.
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(PLEASE HELP)(THIS IS MIDDLE SCHOOL LEVEL EASY!) What is the surface area of the box
Answer:
C) 42 square cm
Step-by-step explanation:
each rectangle 2x3 = 6
each square 3x3 =9
4 rectangles 4x6 = 24
2 squares 2x9=18
24+18 = 42
The measure of one of the smaller base angles of an isosceles trapezoid is $60^\circ$. The shorter base is 5 inches long and the altitude is $2 \sqrt{3}$ inches long. What is the number of inches in the perimeter of the trapezoid?
Answer:
22
Step-by-step explanation:
If cos(x) = 3/5 and sin x < 0, find sin(2x) as a fraction in simplest terms.
sin(2x) =
Answer:
NOT 24/25 and NOT -4/5
Step-by-step explanation:
took the quiz
If cos(x) = 3/5 and sin x < 0, sin(2x) is equal to -24/25 as a fraction in simplest terms.
To find sin(2x), we can use the double-angle formula for sine:
sin(2x) = 2 * sin(x) * cos(x)
Given:
cos(x) = 3/5
sin(x) < 0
We need to determine sin(x) based on the given information.
Using the Pythagorean identity, sin^2(x) + cos^2(x) = 1:
\((sin(x))^2 + (cos(x))^2 = 1\\(sin(x))^2 + (3/5)^2 = 1\\(sin(x))^2 + 9/25 = 1\\(sin(x))^2 = 1 - 9/25\\(sin(x))^2 = 16/25\)
sin(x) = -4/5
Now we can the values into the double-angle formula for sine:
sin(2x) = 2 * sin(x) * cos(x)
sin(2x) = 2 * (-4/5) * (3/5)
sin(2x) = (-8/5) * (3/5)
sin(2x) = -24/25
Therefore, sin(2x) is equal to -24/25 as a fraction in simplest terms.
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-hello10olleh (hello)
Answer: The slope of the line is b. 3
Answer:b
Step-by-step explanation:
Four times a number added to twelve is divided by seven times a different number minus twenty-eight. Convert this to math symbols using x and y for the variables. *
Answer:
\(=\frac{4x+12}{7y-28}\)
Step-by-step explanation:
Four times a number (let's call this x) is added to twelve. In other words, this is:
\(4x+12\)
Now, this entire thing is divided by seven times a different number (let's use y) minus twenty-eight. So:
\((4x+12)\div (7y-28)\)
Let's put it into a fraction to simplify. Remember that dividing something by something else is the same as putting it over fraction. Thus:
\(=\frac{4x+12}{7y-28}\)
And we're done!
Answer:
12 + 4x
7y - 28
Step-by-step explanation:
Here we have 4 times a number is added to 12. So let's say that number is "x". Now we have 4x plus the 12 to get 4x + 12 And that is divided by 7 times a different number minus 8.
So 7 times a different number "y" is the same as 7y and put in that minus 28 to get 7y - 28 and don't forget the dividing!
It'll end up being;
12 + 4x
7y - 28
Hope this helps and have a great day!
Assume that the sample is a random sample from a distribution that is reasonably normally distributed and that we are doing inference for a population mean. Find the area in a t-distribution to the right of 2.6 if the sample has size n
The area to the right of 2.6 in a t-distribution with n degrees of freedom is 0.9082, assuming the sample is a random sample from a distribution that is reasonably normally distributed and that we are doing inference for a population mean.
We can use a t-distribution table or a statistical software program to find the area to the right of 2.6. Here, I'll show you how to use a t-distribution table:
Determine the degrees of freedom (df) for the t-distribution. This is equal to n - 1.
Look up the t-value that corresponds to a one-tailed probability of 0.05 and df.
Multiply the t-value by -1 to get the positive value for the right tail. In other words, we need the value for the right tail, so we flip the sign of the t-value.
Add 0.5 to the result to account for the area to the left of 2.6. This gives us the cumulative probability from negative infinity to 2.6.
Subtract the result from 1 to get the area to the right of 2.6.
For example, suppose we have a sample of size n = 10. Then, the degrees of freedom for the t-distribution would be df = 10 - 1 = 9. Using a t-distribution table, we can look up the t-value that corresponds to a one-tailed probability of 0.05 and df = 9:
t-value = 1.833
Since we need the positive value for the right tail, we multiply by -1 to get:
t-value = -1.833
Adding 0.5 to account for the left tail gives:
t-value + 0.5 = -1.333
Finally, subtracting this result from 1 gives us the area to the right of 2.6:
Area to the right of 2.6 = 1 - 0.0918 = 0.9082
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can someone please help me with this.
Answer:
BC = 25units
Step-by-step explanation:
The image indicates that:
∡ABC = ∡BCA
then this triangle is a isosceles triangle
then:
AB = AC
4x + 4 = 6x - 14
4 + 14 = 6x - 4x
18 = 2x
x = 18/2
x = 9
then:
BC = 2x + 7
BC = 2*9 + 7
BC = 18 + 7
BC = 25 Units
Help me please because i'm confused
Answer:
She does have enough turkey for the recipe. She has enough because 4.35 is greater then 4 1/3. 4 1/3= 4.3333... and 4.35 is greater then 4.3333...
Step-by-step explanation:
18. (5 points) Determine \( \int 9 \cos \theta d \theta \).
The integral of 9cos(θ) with respect to theta is 9sin(θ) + C.
We start with the integral of 9cos(θ) with respect to θ:
∫ 9cos(θ) dθ
To integrate cos(θ), we can use the trigonometric identity:
∫ cos(θ) dθ = sin(θ) + C
where C is the constant of integration.
Now, we have the integral in the form:
∫ 9cos(θ) dθ
Since 9 is a constant, we can pull it out of the integral:
9∫ cos(θ) dθ
Now, we can substitute the integral of cos(θ) with sin(θ):
9sin(θ) + C
Therefore, the integral of 9cos(θ) with respect to θ is given by:
∫ 9cos(θ) dθ = 9sin(θ) + C
In this expression, 9sin(θ) represents the antiderivative of 9cos(θ), and C represents the constant of integration. The constant of integration arises because when we take the derivative of a constant, it becomes zero. Therefore, when we perform an indefinite integral, we add a constant term to account for all possible functions that have the same derivative.
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A certain ore contains 21 percent gold. How much ore (in tons) is needed to obtain 882 tons of gold?
Answer:
it would be 4200 ore
Step-by-step explanation:
because 882/.21
7, 3, -1, -5, what is the sequence
Answer:
-4
Step-by-step explanation:
7-4=3
3-4=-1
-1-4=-5
There are about 10^23 atoms of gold in 1 ounce of gold. Copy and complete the table by finding the number of atoms of gold for the given amounts of gold (in ounces).
The number of atoms in an element is a constant, and can be calculated using Avogadro's number, which is approximately 6.022 x 10³ atoms/mole. This number is used to convert between mass and number of atoms.
What does Avogadro’s number represent?Amedeo Avogadro, an Italian scientist, is commemorated with Avogadro's number/constant. The number of particles (atoms, ions, or molecules) contained in one mole of a substance is known as Avogadro's number. It is commonly designated as N or N0.
Avogadro's number is 6.02 x 10²³.
Given that,
10²³ atoms of gold in 1 ounce of gold.
The number of atoms in an element is a constant, and can be calculated using Avogadro's number, which is approximately 6.022 x 10³ atoms/mole. This number is used to convert between mass and number of atoms.
Here is the completed table ↓↓↓
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What is 16 divided by 4 1/2
Answer:
3 5/9
Step-by-step explanation:
how many positive integers of 3 digits may be made from the digit 1,2,3,4,5, each digit may be used just once
60 positive integers of 3 digits may be made from the digit 1,2,3,4 and 5 if the digits are not repeated.
According to the question,
We have the following information:
3 digits integers are to be made from 1,2,3,4 and 5
So, we will use permutation to find the possible number of digits that can be made if we apply all the given conditions.
Now, we have:
Total number of digits = 5
Number of digits to be made = 3
So, we have:
\(^{5} P_{3}\)
Solving this expression:
5*4*3
60
Hence, 60 positive integers of 3 digits may be made from the digit 1,2,3,4 and 5 if the digits are not repeated.
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Students held a carnival to raise funds for the school. Adult tickets sold for $6 and children's tickets
sold for $3. A total of $384 was raised. If twice as many children attended the carnival as adults, how
many adults attended?
a. 16 adults
b. 64 adults
c. 32 adults
d. 12 adults
Answer: 16
Step-by-step explanation:
multiply 6 by the answers below until you get 1/3 of 384.
what is the eccentricity of an infinitely long ellipse?
Answer:
1
Step-by-step explanation:
Given \(a\), half the length of the major axis, and \(b\), half the length of the minor axis for an ellipse, its eccentricity is \(\displaystyle e=\sqrt{1-\frac{b^2}{a^2}}\), which tells us how close the ellipse is to the shape of a circle or how flat and round it is. An infinitely long ellipse would have an infinitely long major axis, so the greater the \(a\) value, the eccentricity gets infinitely closer to 1.
rectangular swimming pool is 6 ft deep. One side of the pool is 4.5 times longer than the other. The amount of water needed to fill the swimming pool is 2700 cubic feet. Find the dimensions of the pool.
Answer: length = 12 feet, width = 54 feet and depth = 6 feet.
the life of light bulbs is distributed normally. the standard deviation of the lifetime is 15 hours and the mean lifetime of a bulb is 530 hours. find the probability of a bulb lasting for between 557 and 561 hours. round your answer to four decimal places.
The probability of a bulb lasting for between 557 and 561 hours is roughly 0.0382 or 3.82%
Able to utilize the standard ordinary dissemination to discover the likelihood of a bulb enduring for between 557 and 561 hours. To do this, we ought to standardize the values utilizing the equation:
z = (x - μ) / σ
where x is the bulb lifetime we're fascinated by
, μ is the cruel(mean) lifetime,
and σ is the standard deviation.
For 557 hours:
z1 = (557 - 530) / 15 = 1.8
For 561 hours:
z2 = (561 - 530) / 15 = 2.07
Employing a standard ordinary conveyance table or a calculator with a typical dissemination work, we are able to discover the probabilities corresponding to these z-scores:
P(z1 < Z < z2) = P(1.8 < Z < 2.07)
This speaks to the likelihood of a bulb enduring between 557 and 561 hours, where Z could be a standard ordinary variable.
Employing a standard ordinary dispersion table or a calculator, we discover:
P(1.8 < Z < 2.07) ≈ 0.0382
Therefore, the likelihood of a bulb enduring for between 557 and 561 hours is roughly 0.0382 or 3.82% (adjusted to four decimal places).
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Find the difference between the two. Thanks!
4a –3b +2c and –6a +4b –2c –2
Answer: 10a - 7b + 4c + 2
Step-by-step explanation:
To find the difference between the two, we will subtract –6a +4b –2c –2 from 4a –3b +2c.
Expression:
4a –3b +2c - (–6a +4b –2c –2)
Distribute the negative ("change the sign"):
4a - 3b + 2c + 6a - 4b + 2c + 2
Reorder terms:
4a + 6a - 3b - 4b + 2c + 2c + 2
Combine like terms:
10a - 7b + 4c + 2
in conducting your test for question 1, you assumed equal variances. complete a test to determine whether the variances are equal – use the "folded" or "right-tail" test.
A. To determine whether the variances are equal, conduct a right-tail test using appropriate statistical methods.
B. To test the equality of variances, we can use a right-tail test, also known as a folded test.
This test compares the variances of two samples to assess whether they are statistically different or not.
Here are the steps to conduct the right-tail test for equal variances:
1. State the null and alternative hypotheses:
- Null hypothesis (H0): The variances of the two samples are equal.
- Alternative hypothesis (H1): The variances of the two samples are not equal.
2. Choose an appropriate significance level (e.g., α = 0.05) to determine the critical value.
3. Calculate the test statistic.
There are different tests available, such as the F-test or Bartlett's test, depending on the nature of the data and assumptions.
The test statistic measures the ratio of the variances and follows a specific distribution under the null hypothesis.
4. Determine the critical value corresponding to the chosen significance level.
This critical value helps determine whether to reject or fail to reject the null hypothesis.
5. Compare the test statistic with the critical value.
If the test statistic exceeds the critical value, we reject the null hypothesis, indicating that the variances are significantly different.
If the test statistic does not exceed the critical value, we fail to reject the null hypothesis, suggesting that there is not enough evidence to conclude a significant difference in variances.
By following these steps and conducting the appropriate test, you can determine whether the variances of the samples are equal or not.
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The amount of sales tax on a new car
varies directly to the purchase price of
the car. If a $25,000 car pays $1,750 in
sales taxes, what's the purchase price
of a new car with $3,500 in sales tax?
New Purchase Price = [?]
Enter
Answer:
$50,000
Step-by-step explanation:
Let :
sales tax = t
Purchase price = p
Sales tax α purchase price
t = kp
Where. K is the constant of proportionality
When p = $25000 ; t = 1750
Using this we can obtain the value of k
1750 = 25000k
k = 1750/25000
k = 0.07
Purchase price of car with $3500 sales tax;
3500 = 0.07p
p = 3500 / 0.07
p = $50,000
Charlie bought shares worth £7000.
a) After one month, their value had increased by 12%. How much were
they worth after one month?
b) After two months, this new value had decreased by 15%. How much
were they worth after two months?
Give your answers in pounds
Answer:
a) After one month, the value of the shares increased by:
£7000 x 12/100 = £840
Therefore, the shares were worth:
£7000 + £840 = £7840
b) After two months, the value of the shares decreased by:
£7840 x 15/100 = £1176
Therefore, the shares were worth:
£7840 - £1176 = £6664
i. The uniform probability distribution's shape is a rectangle. ii. The uniform probability distribution is symmetric about the mode. iii. In a uniform probability distribution, P(x) is constant between the distribution's minimum and maximum values. Multiple Choice (ii) and, (iii) are correct statements but not (i). (i). (ii), and (iii) are all false statements. (i) is a correct statement but not (ii) or (iii). (i) and, (iii) are correct statements but not (ii).
The correct option is: (i) and (iii) are correct statements but not (ii).
The correct answer is:
(i) The uniform probability distribution's shape is a rectangle.
(ii) The uniform probability distribution is symmetric about the mode.
(iii) In a uniform probability distribution, P(x) is constant between the distribution's minimum and maximum values.
Therefore, the correct option is: (i) and (iii) are correct statements but not (ii).
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Which of the following is NOT a limitation of the model?
A size of sun
B size of the planets
C distances between planets
D number of planets
Answer:
the answer to this question is option D mark me as brainliest
A bag contains 4 red, 2 blue, 6 green, and 8 white marbels. Round anwsers to the nearest tenth. What is the probibility of selecting a green marble, replacing it, and then selecting a red marble. Answers: 6.3% 6.0% 4.5% 4.7%
Answer:6.3% 6.0% 4.5% 4.7%
Step-by-step explanation:
What is the value of x?
A. X=45
B. X=65
C. x= 70
D. X=115
B. X = 65
Hope its helpful to you
PLZ HELP!!! ASAP!!!PLZ!!!
Answer: 150 cm2
Step-by-step explanation:
60x5 divided by 2 its pretty easy.
Which formula below is used to find the volume of a shape?
length + width + height
length × width × height
length ÷ width ÷ height
length − width − height
Answer:
Option B : Length × Width × Height
- How did you know it's option B ?
Since we know the unit of volume of unit cube so if we multiply length , width and height , we'll get the answer in unit cube so this is how I predicted the answer.-------------HappY LearninG <3 ----------
Answer:length × width × height
Step-by-step explanation:
*97 POINTS*
Use the numerals representing cardinalities in the Venn diagram, shown on the right, to give the cardinality of the set
A' ∩ B' ∩ C. '
n(A' ∩ B' ∩ C')= ___________
Answer:
19
Step-by-step explanation:
A' represents everything out A
B' represents everything out B
C' represents everything out C
So only the outside is left hope this helps