To find the simultaneous solution of two equations, we need to find the values of x and y that satisfy both equations at the same time.
Let's substitute the given values of x and y in each option and see which option satisfies both equations simultaneously:
a. x = -1, y = -2
Substituting these values in the first equation:
3x + 4y = 10
3(-1) + 4(-2) = -3 - 8 = -11
Substituting these values in the second equation:
5x + 4y = 14a
5(-1) + 4(-2) = -5 - 8 = -13
Option a does not satisfy both equations simultaneously.
b. x = 2, y = 1
Substituting these values in the first equation:
3x + 4y = 10
3(2) + 4(1) = 6 + 4 = 10
Substituting these values in the second equation:
5x + 4y = 14a
5(2) + 4(1) = 10 + 4 = 14
Option b satisfies both equations simultaneously.
c. y=2x
Substituting y = 2x in the first equation:
3x + 4y = 10
3x + 4(2x) = 3x + 8x = 11x
Substituting y = 2x in the second equation:
5x + 4y = 14a
5x + 4(2x) = 5x + 8x = 13x
Since 11x is not equal to 13x for any value of x, option c does not satisfy both equations simultaneously.
d. x=y
Substituting x = y in the first equation:
3x + 4y = 10
3x + 4(x) = 7x
Substituting x = y in the second equation:
5x + 4y = 14a
5x + 4(x) = 9x
Since 7x is not equal to 9x for any value of x, option d does not satisfy both equations simultaneously.
e. x=1,y=2
Substituting these values in the first equation:
3x + 4y = 10
3(1) + 4(2) = 3 + 8 = 11
Substituting these values in the second equation:
5x + 4y = 14a
5(1) + 4(2) = 5 + 8 = 13
Option e satisfies both equations simultaneously.
Therefore, the simultaneous solution of the given equations is option b, which is x = 2 and y = 1.
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Evaluate the following
expression using x = 6:
8(3x + 1)
Anyone know the answer
Answer:
152
Step-by-step explanation:
Substitute the given value for x.
\(8(3(6)+1)\\8(18+1)\\8(19)\\152\)
Answer:
152
Step-by-step explanation:
8(3x+1)
Let x = 6
8(3*6+1)
Multiply inside the parentheses
8(18+1)
Add inside the parentheses
8(19)
Multiply
152
Which of the following means a study used a bivariate correlational design?
a. presence of measured variables
b. use of correlational stats
c. inclusion of quantitative variables
d. depiction of bar graph
among the given options, the use of correlational statistics OPTION B is the most reliable indicator that a study employed a bivariate correlational design.
A bivariate correlational design is characterized by the examination of the relationship between two quantitative variables. In this context, the use of correlational statistics is a key indicator of this design. Correlational statistics, such as correlation coefficients (e.g., Pearson's r), are employed to assess the strength and direction of the relationship between the variables under investigation.
The presence of measured variables, inclusion of quantitative variables, or depiction of a bar graph are not definitive indicators of a bivariate correlational design. Measured variables can be present in various study designs, including experimental ones. Similarly, quantitative variables can be utilized in different types of studies, such as experimental, quasi-experimental, or observational designs. The depiction of a bar graph, which is commonly used to illustrate categorical data, does not inherently imply the use of a bivariate correlational design.
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Thirty cards, marked with the even numbers from 2 to 60 inclusive, are shuffled and one card
is withdrawn at random and then replaced. The random variable X takes the value of the
number on the card each time the experiment is repeated.
(a) What must be assumed about the cards if the distribution of X is modelled by a discrete
uniform distribution?
(1 mark)
(b) Making this modelling assumption, find the expectation and the variance of X.
(5 marks)
The variance of X is 55, and the expectation of X is 31.
(a) If the distribution of X is modeled by a discrete uniform distribution, then we must assume that each of the 30 cards has an equal probability of being chosen at random and that the outcomes are mutually exclusive and collectively exhaustive.
(b) Since the distribution of X is modeled by a discrete uniform distribution, the probability of X taking any value between 2 and 60 (inclusive) is the same, i.e., 1/30. Therefore, the expected value of X can be calculated as:
E(X) = (2 + 4 + ... + 60)/30 = 31
To calculate the variance of X, we first need to find the variance of a single trial, and then multiply it by the number of trials (which is 30 in this case). The variance of a single trial can be calculated using the formula:
\(Var(X) = E(X^2) - [E(X)]^2\)
where E(X^2) is the expected value of \(X^2\). Since the distribution of X is uniform, the expected value of \(X^2\) can be calculated as:
\(E(X^2) = (2^2 + 4^2 + ... + 60^2)/30 = 1234\)
Substituting this and the value of E(X) into the formula for variance, we get:
\(Var(X) = 1234 - 31^2 = 55\)
Therefore, the variance of X is 55, and the expectation of X is 31.
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A relation contains the points (1, 2), (2, -1), (3, 0), (4, 1), and (5, -1). Which statement accurately describes this relation?
Answer:
J The relation represents y as a function of x, because each value of x is associated with a single value of y.
Step-by-step explanation:
I'm sure of this
Answer:
H
Step-by-step explanation:
i think so i’m not one hundred percent sure though ! Tell me if i’m wrong
wHaTs Ur FaV tYlEr ThE cReAtOr SoNg? DoNt RePoRt Me BuT mY fAv SoNg iS eArFqUaKe :P
Answer:
so u jus gon bring me a birthday gift on my birthday to my birthday party on my birthday wit a birthday gift ?
Step-by-step explanation:
Answer:
Uh
Step-by-step explanation:
I dont know any of his songs
Ms. Salazar’s car averages 25 miles per gallon of gasoline. She filled the 10-gallon tank with gasoline before traveling 200 miles on a trip. Which graph BEST represents this situation?
Step-by-step explanation:
2524 ÷ 23 = 24a6u= 7
bengek hyung
Jason bought 10 of the 30 raffle tickets for a drawing. Assuming that he chooses the winning ticket each time, what is the probability that Jason will win all 3 of the prizes if once a raffle ticket wins a prize, the ticket is thrown away?
StartFraction 6 over 203 EndFraction
StartFraction 1 over 27 EndFraction
StartFraction 3 over 29 EndFraction
StartFraction 1 over 9 EndFraction
The probability that all three of these things will happen is A)6/203.
What is probability?
Probability is a way of calculating how likely something is to happen. It is difficult to provide a complete prediction for many events. Using it, we can only forecast the probability, or likelihood, of an event occurring. The probability might be between 0 and 1, where 0 denotes an impossibility and 1 denotes a certainty.
For the first drawing, there are 30 tickets altogether, and Jason
has 10 of them. The probability that one of his tickets will win is
=>10 / 30 .
For the second drawing, there are 29 tickets altogether, and Jason
has 9 of them. The probability that one of his tickets will win is
=> 9 / 29 .
For the third drawing, there are 28 tickets altogether, and Jason
has 8 of them. The probability that one of his tickets will win is =>8 / 28 .
The probability that all three of these things will happen is => (10/30) x (9/29) x (8/28) = 720 / 24,360 = 6/203.
Hence the correct option is A) 6/203.
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2. Paige's sock drawer has 3 pairs of black socks, 6 pairs of green socks, and 1 pair of white
socks. If she picks a pair at random, what is the probability she will pick a green pair?
Help!
AnsweGreen socks
Step-by-step explanation: the is more green socks then black and even if she put in the green socks first the is a 90% chance of getting a black sock.
Answer:
1/10
Step-by-step explanation:
ok byeeee
(Chapter 13) The curve r(t)= <0, t^2, 4t> is a parabola
We can see that the first component of the vector equation is always zero, so the parabola lies in the xz-plane.
Moreover, the second component is a quadratic function of t, which gives us a vertical parabola when plotted in the yz-plane. The third component is a linear function of t, so the curve extends infinitely in both directions. Therefore, we have a vertical parabola in the xz-plane.
This statement is referring to a specific vector-valued function, which we can write as:
f(t) = (0, t^2, ct)
where c is a constant.
The second component of this vector function is t^2, which is a quadratic function of t. When we plot this function in the yz-plane (i.e., we plot y = t^2 and z = 0), we get a vertical parabola that opens upward. This is because as t increases, the value of t^2 increases more and more quickly, causing the curve to curve upward.
The third component of the vector function is ct, which is a linear function of t. When we plot this function in the xz-plane (i.e., we plot x = 0 and z = ct), we get a straight line that extends infinitely in both directions. This is because as t increases or decreases, the value of ct increases or decreases proportionally, causing the line to extend infinitely in both directions.
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PLEASE HELP
Translate N( 1,-5) to the right 4 units and down 6 units
Answer:
( 6, -11 )
Step-by-step explanation:
do it on a graph called desmos
A trough is 14 ft long and its ends have the shape of isosceles triangles that are 4 ft across at the top and have a height of 1 ft. If the trough is being filled with water at a rate of 9 ft3/min, how fast is the water level rising when the water is 7 inches deep
The water level is rising at a rate of 0.16 ft/min when the water is 7 inches deep.
To determine how fast the water level is rising, we need to find the rate of change of the volume of water with respect to time. The trough can be divided into two parts: the rectangular base and the two isosceles triangle ends.
The volume of the rectangular base can be calculated by multiplying the length, width, and height: 14 ft * 4 ft * 7/12 ft = 16.33 ft³.
The volume of each isosceles triangle end can be calculated by multiplying the base, height, and width: 1/2 * 4 ft * 7/12 ft = 1.17 ft³. Since there are two triangle ends, the total volume contributed by the triangle ends is 2 * 1.17 ft³ = 2.34 ft³.
The total volume of the trough is the sum of the volume of the rectangular base and the volume of the triangle ends: 16.33 ft³ + 2.34 ft³ = 18.67 ft³.
Now, we can find the rate of change of the volume with respect to time by differentiating the volume equation: dV/dt = 9 ft³/min.
To find the rate at which the water level is rising, we need to find the rate of change of the height (h) with respect to time (t). We can rearrange the volume equation to solve for h: V = lwh. Since the trough is rectangular, the width (w) remains constant at 4 ft. Differentiating the volume equation with respect to time, we get: dV/dt = lw(dh/dt).
Now, we can solve for dh/dt: dh/dt = (dV/dt)/(lw). Plugging in the values, we get: dh/dt = (9 ft³/min)/(14 ft * 4 ft) = 0.16 ft/min.
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if is a real number, then the vectors are linearly independent precisely when , where , , and .
The vectors are linearly independent precisely when the determinant of the matrix formed by the vectors is non-zero.
Let's denote the given vectors as v1, v2, and v3, where v1 = [a, b, c], v2 = [d, e, f], and v3 = [g, h, i]. To determine if these vectors are linearly independent, we need to check the determinant of the matrix formed by these vectors:
| a b c |
| d e f |
| g h i |
If the determinant of this matrix is non-zero, then the vectors are linearly independent. On the other hand, if the determinant is zero, the vectors are linearly dependent.
In summary, the vectors are linearly independent precisely when the determinant of the matrix formed by the vectors is non-zero. This condition ensures that no scalar multiples of the vectors can add up to the zero vector, indicating independence.
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PLEASE HELP!!!
Problem #1
A groundskeeper needs grass seed to cover a circular field, 580 feet in diameter.
A store sells 100-pound bags of grass seed. One pound of grass seed covers about 800 square feet of field. What is the smallest number of bags the groundskeeper must buy to cover the circular field? Explain or show your reasoning.
Step1: Find the area of the circular field.
Step2: Find how many square feet covers a 100-pound bag(1pound covers 800 sq. ft)
Step 3: Find how many bags are needed to cover the entire area found on step1?
Step 4: Make sure to tell the number of bags that you need to cover the entire area of the field.
(Is this question not too complex)
Ask the questions one-by-one.
In ΔEFG, g = 34 inches, e = 72 inches and ∠F=21°. Find the area of ΔEFG, to the nearest square inch.
The area of triangle EFG, to the nearest square inch, is approximately 1061 square inches.
To find the area of triangle EFG, we can use the formula:
\(Area = (1/2) \times base \times height\)
In this case, the base of the triangle is FG, and the height is the perpendicular distance from vertex E to side FG.
First, let's find the length of FG. We can use the law of cosines:
FG² = EF² + EG² - 2 * EF * EG * cos(∠F)
EF = 72 inches
EG = 34 inches
∠F = 21°
Plugging these values into the equation:
FG² = 72² + 34² - 2 * 72 * 34 * cos(21°)
Solving for FG, we get:
FG ≈ 83.02 inches
Next, we need to find the height. We can use the formula:
height = \(EF \times sin( \angle F)\)
Plugging in the values:
height = 72 * sin(21°)
height ≈ 25.52 inches
Now we can calculate the area:
\(Area = (1/2) \times FG \times height\\Area = (1/2)\times 83.02 \times 25.52\)
Area ≈ 1060.78 square inches
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Write an inequality to describe all the points on the coordinate plane above y=-4?
Answer: y > -4
Step-by-step explanation: i believe this is your answer because i think you are asking for the range more or less. when you do this, you have to just ask yourself what points would be acceptable (any y point above -4) so the answer would be any y value more than -4, y > -4
The inequality for all the points of y above 4 is y > -4.
What is an inequality and what are it's types ?An inequality is comparison between two non-equal quantitates.
Inequalities are of four types.Less than,less than or equal to,greater than and greater than or equal to.If a is greater than be it is written as a>b.
For a is greater than or equal o b it is written as a ≥ b and for the other two types in equality will switch it's direction.
According to the given question we have to describe an inequality that describes all the points on the co-ordinate plane above y = -4.
This can be represented as y > -4 the range of the points can be defined as (-4,∞).
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Can someone please help me I’ll mark you as brainlist
A=
B=
Answer:
A = 14
B = 4
Step-by-step explanation:
You want to know the values of A and B consistent with ∆EFG being congruent to ∆HJI, given that EF=14B-15, FG=9A-28, HJ=7B+13, JI=7A.
CongruenceCorresponding sides of congruent triangles have the same measure, so we have ...
FG = JI
9A -28 = 7A
2A = 28 . . . . . . add 28-7A
A = 14 . . . . . divide by 2
and ...
FE = JH
14B -15 = 7B +13
7B = 28 . . . . . . . . add 15-7B
B = 4 . . . . . . divide by 7
The values of A and B are 14 and 4, respectively.
Please help I need an answer ASAP!!!!!!!
Answer:
A its the mos resonable one
I need helped really need this question to be answer!
Answer:
the answer for your question is b
Wyatt buys a one-quart bottle of juice for $4.80. How many fluid ounces of juice did Wyatt buy?
Answer:
Step-by-step explanation:
Unit rate per fluid ounce = $0.15
Step-by-step explanation:
Given that:
Cost of one quart bottle of juice = $4.80
We know that:
One quart = 32 ounces
Unit rate is the rate in which two quantities are compared and one of them is one.
Unit rate =
Unit rate = $0.15 per fluid ounce
Hence,
Unit rate per fluid ounce = $0.15
Answer:
Wyatt bought 32 fluid ounces.
Step-by-step explanation:
If Wyatt bought a 1 quart bottle of juice, (which you would need to convert into fluid ounces) but every 0.1 quarts of juice would be 3.2 fluid ounces. And if 0.5 quarts of juice is 16 ounces we could do 16 + 16 (fluid ounces) and we would get 32 fluid ounces in total.
And that's how you get the answer! :)
Solve for x 12 + x = 27
Answer:
15
Step-by-step explanation:
subtract 12 on both sides and you get
x=27-12
x=15
Answer:
I think your answer is 15
Step-by-step explanation:
Hope this helped you
A doctor advises a patient not to consume more than 8.5 × 10−2 kg of sugar per day. Coca cola
contains 110 g/L sugar. How many 12 oz cans of Coca cola can the patient consume? Show your work.
The patient can consume approximately 2 cans of 12 oz Coca Cola without exceeding the advised sugar limit.
To determine the number of 12 oz cans of Coca Cola the patient can consume, we need to convert the sugar limit provided by the doctor into grams and then calculate the amount of sugar in a 12 oz can of Coca Cola.
Provided:
Sugar limit: 8.5 × 10^(-2) kg
Coca Cola sugar content: 110 g/L
Volume of a 12 oz can: 12 oz (which is approximately 355 mL)
First, let's convert the sugar limit from kilograms to grams:
Sugar limit = 8.5 × 10^(-2) kg = 8.5 × 10^(-2) kg × 1000 g/kg = 85 g
Next, we need to calculate the amount of sugar in a 12 oz can of Coca Cola:
Volume of a 12 oz can = 355 mL = 355/1000 L = 0.355 L
Amount of sugar in a 12 oz can of Coca Cola = 110 g/L × 0.355 L = 39.05 g
Now, we can determine the number of cans the patient can consume by dividing the sugar limit by the amount of sugar in a can:
Number of cans = Sugar limit / Amount of sugar in a can
Number of cans = 85 g / 39.05 g ≈ 2.18
Since the number of cans cannot be fractional, the patient should limit their consumption to 2 cans of Coca Cola.
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PLEASE HELP PLEASE HELP PLEASE HELP IM BEGGING PLEASE HELP PLEASE HELP!!!
Answer:
a) 390
b) 239
c) 151
Step-by-step explanation:
a) 30 + 15 + 45 + 300 = 390
b) 160 + 30 + 9 + 40 = 239
c) 390 (income) - 249 (expenses) = 151 pounds (profit)
help mah easy lol ... :^
whats the volume of 9cm 7cm 6cm
Answer:
The combined volume of 9cm, 7cm, and 6cm is 378cm³ if a rectangular prism or cube
Step-by-step explanation:
To find the volume of a 3-dimensional prism or cube you need to find the Area of the Base and Height and multiply them.
Equation = Bh
Since there are only 3 different numbers you just need to multiply them together.
I hope this was helpful!
Select an answer and submit. For keyboard navigation, use the up/down arrow keys to select an answer. a 366.67 b 373.33 с 333.33 d 350 e 379.15
For keyboard navigation, use the up/down arrow keys to select an answer is (b) 373.33
What is keyboard navigation to select an answer?By letting users know where they are while they use the keyboard to browse a page, keyboard focus aids keyboard accessibility. Even those who have trouble using a touchpad or mouse can use a computer thanks to keyboard navigation.
The sequence in which interactive objects acquire keyboard focus is crucial for keyboard users navigating the page. The order of the keyboard navigation must be reasonable and obvious by default. This typically means that it moves from left to right and from top to bottom of the page.
This typically means that the header appears first, followed by the main navigation, page navigation, and finally the footer. The web page's source code determines this navigation order as well as the reading order for screen readers.
For keyboard navigation, use the up/down arrow keys to select an answer is (b) 373.33
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which equation is the vertex form of y = 2x^2 + 16x + 26
Answer:
y = 2(x + 4)² - 6
General Formulas and Concepts:
Order of Operations: BPEMDASCompleting the SquareStep-by-step explanation:
Step 1: Define function
y = 2x² + 16x + 26
Step 2: Find vertex form
Factor GCF: y = 2(x² + 8x + 13)Complete the Square: y = 2(x² + 8x + 4² + 13 - 16)Simplify: y = 2((x + 4)² + 13 - 16)Combine like terms: y = 2((x + 4)² - 6)Simplify: y = 2(x + 4)² - 6The National Assessment of Educational Progress (NAEP) periodically administers tests on different subjects to high school students. In 2000, the grade 12 students in the sample averaged 301 on the mathematics test; the SD was 30. The likely size of the chance error in the 301 is about ______. a) Can you fill in the blank if a cluster sample of 1,000 students was tested? If so, what is the answer? If not, why not? b) Can you fill in the blank if a simple random sample of 1,000 students was tested? If so, what is the answer? If not, why not?
The average score of 301, for a simple random sample of 1,000 students, is approximately 0.95.
a) To determine the likely size of the chance error in the average score of 301 for a cluster sample of 1,000 students, we need additional information about the cluster sampling design.
The cluster sampling method involves dividing the population into clusters, selecting a subset of clusters, and then sampling all individuals within the selected clusters.
The likely size of the chance error depends on the within-cluster variability and the between-cluster variability.
Without information about the variability at each level, we cannot accurately estimate the size of the chance error in this specific scenario.
Therefore, we cannot fill in the blank without more details regarding the cluster sampling design and the variability present in the clusters.
b) If a simple random sample of 1,000 students was tested, we can estimate the likely size of the chance error in the average score of 301. Since a simple random sample implies that each student has an equal chance of being selected, we can use the standard error of the mean formula to estimate the size of the chance error.
The standard error of the mean (SE) is calculated as the standard deviation (SD) divided by the square root of the sample size (n):
SE = SD / √n
Given that the SD is 30 and the sample size (n) is 1,000, we can calculate the standard error:
SE = 30 / √1000 = 30 / 31.62 ≈ 0.95
Therefore, the likely size of the chance error in the average score of 301, for a simple random sample of 1,000 students, is approximately 0.95.
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What's the answer to this?
Answer:
Step-by-step explanation:is 10
A cell phone company wants to determine the average amount of data that their smart phone customers use each month. which group would best represent a sample of the population?
The group that would best represent a sample of the study population is: C: one thousand of their customers with a current smart phone data plan.
What is a Representative Sample of a Population?A sample that best represents a population under study is a sample that is a subset of the entire population, that is, research subjects that are drawn as samples should reflect the general characteristics of the entire population without leaving out any part of the population. Also, a good sample should enable a researcher make generalization.
A sample that is a subset of a population and reflects the characteristics of the general population would not be biased.
Given the situation above, the population of the study are smart phone customers that use dat in the cell phone company. So, a sample that would better represent this general population would be customers that currently have a smart phone plan, since the average amount of data they use is what the cell pone company wants to ascertain.
Therefore, the group that would best represent a sample of the study population is: C: one thousand of their customers with a current smart phone data plan.
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For each row with a quadratic expression below, select an equivalent expression.
Explanation
Step 1
\(x^2+6x-7\)The middle number is 6 and the last number is -7.
Factoring means we want something like
\(\mleft(x+a_{}\mright)\mleft(x+b_{}\mright)\)We need two numbers that...
Add together to get 6
Multiply together to get -7
c