Answer:A point can represent a piece of data or an (x,y) value.
Step-by-step explanation:
⎧
21x+7y=42
−5x+5y=10
Answer:
(1, 6.71)
Step-by-step explanation:
I'm assuming that you need to solve this by substitution or elimination since you didn't include any context in your question, just the equations.
To solve this by elimination, first, decide on a variable you want to get rid of / cancel out. I chose y. To do this, you need to find the least common multiple (LCM) of 7 and 5, which is 35. Now, multiply the top equation, 21x + 7y = 42, by -5. Multiply the bottom equation, -5x + 5y = 10, by 7. Make sure when you multiply that you either make the 5 or the 7 negative so you can cancel out y. I chose to make 5 negative.
After you multiply by the -5 and the 7, rewrite your new equations:
-105x - 35y = -210
-35x + 35y = 70
Now, add the two equations together. When you do this, the y's cancel out and you're left with -140x = -140. Now, divide both sides by -140, and you're left with x = 1. Plug the value of x into one of your original equations. I chose the bottom equation, -5x + 5y = 10.
-5(1) + 7y = 42 -----> -5 + 7y = 42.
Add -5 to both sides, which gives you 7y = 47. Divide both sides by 7, which gives you y = 6.71.
The last step is to put the values of x and y into a point: (1, 6.71).
Hope this helps!
Use the figure to the right to find the value of PT. T is the midpoint of PQ.
PT = 4x + 5 and TQ = 8x-7
Answer:
PT = 17
Step-by-step explanation:
Since T is the midpoint of PQ, then
PT = TQ , substitute values
4x + 5 = 8x - 7 ( subtract 4x from both sides )
5 = 4x - 7 ( add 7 to both sides )
12 = 4x ( divide both sides by 4 )
3 = x
Thus
PT = 4x + 5 = 4(3) + 5 = 12 + 5 = 17
Answer:
17
Step-by-step explanation:
since T is mid point of PQ
PT=TQ
\(4x + 5 = 8x - 7 \\ 5 + 7 = 8x - 4x \\ 12 = 4x \\ x = 12 \div 4 \\ x = 3 \\ \)
so
\(pt = 4x + 5 \\ = 4(3) + 5 \\ = 12 + 5 \\ pt = 17\)
Which represents the solution(s) of the system of equations, y = x2 – 6x 8 and y = –x 4? determine the solution set by graphing.
The solution set of the given system of equations is {(4, 0), (2, 4)}.
The given system of equations is: y = x² – 6x + 8 and y = –x + 4
To solve the given system of equations, we need to solve both the equations simultaneously.
We can solve the equations by the following method:
First Equation:
y = x² – 6x + 8
Rewriting in vertex form, we get:
y = (x – 3)² – 1
This is a parabola that opens upward and its vertex is at (3, –1).
Second Equation:
y = –x + 4
This is a line that passes through (0, 4) and (4, 0).
Now, we can find the solution of the given system of equations by plotting the graph of both the equations on the same graph.
We can observe from the graph that the two graphs intersect at (4, 0) and (2, 4).
Therefore, the solution of the given system of equations is: x = 4, y = 0, x = 2, y = 4
So, the solution set of the given system of equations is {(4, 0), (2, 4)}.
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what will the equation be for this "Ryan is saving money to buy a skateboard that costs $85. He has already saved $40. He plans to save the same amount each week for three weeks. Let "x" represent the amount he saves each week. Write and solve an equation to represent this situation."
Answer:
weir
Step-by-step explanation:
Richard’s Supplies sold 100 calculators in the month of August. Joseph’s Deals sold 30 calculators in the first week of October. A business consultant concluded that Richard's Supplies sells more calculators than Joseph's Deals. Explain why the statistic is misleading
The statistic that "Richard's Supplies sells more calculators than Joseph's Deals" based solely on the information given is misleading because it compares the total sales of one business for an entire month with the sales of another business for only one week.
What should be the most acceptable way to make the sales comparison in statistic?It's possible that Joseph's Deals could sell more calculators than Richard's Supplies in a given week or even in the entire month of October, despite the fact that they only sold 30 calculators in the first week but we don't have enough information to compare the sales of these two businesses accurately.
In addition, we don't know if Richard's Supplies and Joseph's Deals are similar businesses with similar customer bases, pricing strategies, and marketing efforts. These factors could also affect their respective sales numbers.
In conclusion, to draw a meaningful comparison between the sales of these two businesses, we would need to gather more data about their sales over a longer period of time and under similar conditions.
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the mean monopotassium phosphate content of a popular athletics drink is listed as 133 mg in a 32-oz bottle. analysis of 38 bottles indicates a sample mean of 132.4 mg. (a) state the hypotheses for a two-tailed test of the claimed monopotassium phosphate content. h0: μ
In this case, H0 represents the null hypothesis, which assumes that the claimed mean monopotassium phosphate content is true.
The hypotheses for a two-tailed test of the claimed monopotassium phosphate content would be as follows:
H0: The true mean monopotassium phosphate content of the athletics drink is equal to 133 mg (μ = 133 mg)
Ha: The true mean monopotassium phosphate content of the athletics drink is not equal to 133 mg (μ ≠ 133 mg)
In this case, H0 represents the null hypothesis, which assumes that the claimed mean monopotassium phosphate content is true.
Ha represents the alternative hypothesis, which suggests that the true mean monopotassium phosphate content differs from the claimed value.
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Justin jogged for four days in a row. He jogged 2 miles the first day. On the second day, he jogged 75% of the distance he jogged the first day. On the third day, he jogged 1.5 miles more than the distance he jogged the first day. If Justin jogged a total distance of 9.25 miles, how many miles did he jog on the fourth day?
Answer:
2.75 miles jogged on the fourth day
Step-by-step explanation:
Justin jogged 2 miles on the first day.
On the second day he jogged 75% of 2 miles. To find 75% of 2 miles we need to divide by 100 and multiply by 75.
2 / 100 = 0.02 x 75 = 1.5 miles jogged on the second day. (3.5 miles jogged in total so far)
On the third day he jogged 1.5 miles more than the last day:
1.5 + 1.5 = 3 (6.5 miles jogged so far)
9.25 total miles were jogged, meaning that we will need to subtract 6.5 from 9.25 to get the answer:
9.25 - 6.5 = 2.75 miles jogged on the fourth day
A uniform E-field of magnitude E and directed horizontally fills a region of space. Points A through D are all inside the uniform field and form a rectangle with horizontal side d as shown. 1 씽 - -- Two particles, 1 and 2, with equal masses and charges q1 = +Q and q2 = +2Q are placed in the field at points B and D respectively and are initially held at rest. Particle 1 is released and allowed to move from B to A under the influence of the E-field only. Particle 2 is moved by an external force (call it "us") from D to C so that it both starts at rest and ends at rest. Which of the following statements about particles 1 and 2 are TRUE? You may select more than one. a. The net work done on particle 1 by the field is zero. b. The Coulomb force exerted on both particles by the source of the E-field increases as they move fro start to finish. c. Particle 1 loses electrical potential energy from start to finish. The electrical potential energy of particle 2 does not change from start to finish. d. The net work done on particle 2 by the field and by us is zero. e. Both particles lose electrical potential energy from start to finish. f. The E-field at point A when particle 1 is at point A has less magnitude than the E-field at point C when particle 2 is at point C. g. Both particles are at rest when they reach points A and C respectively. h. Both particles move through the same potential difference from start to finish. i. The Coulomb force exerted on particle 2 by the source of the E-field is larger in magnitude that the Coulomb force exerted on particle 1 by the source of the E-field.
In the given problem regarding electric charge, we conclude that options 1, 3, 4, and 6 are correct and true.
In the 1st statement,
it says both particles will be at rest when they reach A and C, which is true as they are addressed towards A and C under a uniform field and will be moving by the force of the electric field (F=QE) but we are applying for Work on it, so it ends at rest.
The 2nd statement is false as
the electric field is uniform and is not changing.
The 3rd statement is true because the forces are different as the Coulomb Force exerted on Particle two by the source of electrical is larger due to the difference in charges.
The 4th Statement is true due to the fact that both of the particles will move through, the same potential difference from start to finish.
The 5th Statement is false, coloumbic force will not increase and will remain constant.
The 6th Statement is true as Both the particles are positive, they are approaching the negative, so potential energy will be decreasing.
The 7th statement is false as the net work done on Particle two by the field and by us is zero but it is not zero.
The 8th statement is false, the electric potential energy of particles does not change from start to finish.
The 9th statement is also false, net work done is not zero due to the reason that electric force is conservative and here we are not coming back to the starting point.
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A cube made of an unknown material has a height of 9 cm. The mass of this cube is 3,645 grams. Calculate the density of this cube given this information. Hint: a cube has equal sides
Answer:
Step-by-step explanation:
Volume of the cube = s^3
s = 9cm
V = 9 * 9 * 9
V = 729 cm^3
d = mass / volume
d = 3645 / 729
d = 5 grams / cm^3
3. Mel has a bag of 8 marbles: 2 red, 3 yellow, and 3 green. She draws a marble from the bag,
writes down the color, replaces it, and draws again. She repeats this process for 40 trials and
records drawing a yellow marble 12 times. How does the experimental probability of selecting
a yellow marble compare to the theoretical probability? Explain.
We can see that the experimental probability is smaller than the theoretical one.
How do the probabilities compare?The theoretical probability is equal to the quotient between the number of yellow marbles and the total number, so here we have:
T = 3/8 = 0.375
The experimental probability is equal to the quotient between the number of times that Mel got a yellow marble and the total number of trials, so here we have:
E = 12/40 = 0.3
So the experimental probability is smaller than the theoretical one.
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The model is shaded to represent the remaining one-half of a cake. Three friends will
each receive an equal amount of the remaining cake until it is all gone.
Cake
Which equation can be used to determine the fraction of the whole cake each friend
will receive?
Answer:
jsjshshshhsgdhshdhdhddhshggzggzgzhshsggggghzhgzgzgdgxgshdhdhgd
Step-by-step explanation:
h
Answer:
h
Step-by-step explanation:
choose each digit of a 5 digit number at random from digits 1, . . . , 9. compute the probability that no digit appears more than twice.
The probability that no digit appears more than twice is 0.648.
What is probability?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Here,
We will choose each digit of 5-digit numbers at random from digits 0,1,2,..,9.
We have to compute the probability that no digit appears more than twice.
So, we have to form a five-digit number say "abcde".
Now, for 'a' we have 10 choices.
For 'b' we have again 10 choices because a digit can appear at most two.
For 'c' we have 9 choices because the digit in 'a' can not be chosen as a digit can appear at most two.
For 'd' we have again 9 choices by a similar argument.
Finally, for 'e' we have 8 choices because the digit chosen previously can not be repeated more than twice.
The total number of such 5-digit numbers is = 10*10*9*9*8 = 64800.
Now, a total number of 5-digit numbers = 10*10*10*10*10 = 100000.
Hence, the probability that no digit appears more than twice is given by,
= 64800/ 100000
= 0.648
Hence, the probability that no digit appears more than twice is 0.648.
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Sam bought three folders and one notebook from the office store and spent $8.25. he went back the next day and bought two more folders and three more notebooks and spent $16. if the prices did not change between the days, find the cost of one folder
The cost of one folder is $1.23.
Let x be the cost of one folder and y be the cost of one notebook. From the given information, we can form two equations:
3x + y = 8.25 ---(1)
2x + 3y = 16 ---(2)
To solve for x, we can use the elimination method. Multiplying equation (1) by 2 and subtracting equation (2) from it, we get:
6x + 2y = 16.50
- (2x + 3y = 16)
-----------------
4x - y = 0.50
Similarly, multiplying equation (2) by 3 and subtracting equation (1) from it, we get:
6x + 9y = 48
- (3x + y = 8.25)
------------------
3x + 8y = 39.75
Now, we can solve these two equations simultaneously to get the value of x:
4x - y = 0.50
3x + 8y = 39.75
Multiplying the first equation by 8 and adding it to the second equation, we get:
35x = 43
Therefore, x = 1.23
The cost of one folder is $1.23.
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Aster sold 18 oranges. If these are 12% of her total oranges are not sold
answer is 132
because the whole amount of the oranges is 150 so the unsold 82 percent will be 132
What is the value of the angle marked with x?
Answer:
x = 146°
Step-by-step explanation:
The given shape is a Rhombus. In rhombus, adjacent angles are supplementary.
x + 34 = 180°
Subtract 34 from both sides,
x = 180 - 34
x = 146°
Indira makes a graph to show how many pages of her graphic novel she can
illustrate each day.
a. What is the constant of proportionality for the relationship between
pages and days?
b. Write an equation to show the relationship between pages and days.
Answer:
a). k = 0.75
b). y = 0.75x
Step-by-step explanation:
a). Graph is showing the relation between number of pages (P) illustrated by Indira and number of days taken (D).
P ∝ D
P = kD
Where 'k' is the proportionality constant.
k = \(\frac{P}{D}\)
From the graph attached,
For a point with ordered pair (2, 1.5),
k = \(\frac{1.5}{2}\)
k = 0.75
b). Equation representing the relation between number of pages and number of days will be,
P = 0.75D
y = 0.75x
What is the range of this data?
{3, 3, 0, 8, 7, 10, 2, 6, 12, 0}
Subtract the minimum data value from the maximum data value to find the data range. In this case, the data range is \(12-0=12\).
\(\bold{12}\)
The probability that house sales will increase in the next 6 months is estimated to be 0.25. The probability that the interest rates on housing loans will go ip in the same period is estimated to be 0.74. The probability that house sales or interest rates will go up during the next 6 motnhs is estimated to be
The probability that either house sales or interest rates will increase in the next 6 months is estimated to be 0.79.
To find the probability that either house sales or interest rates will go up in the next 6 months, we can use the concept of union in probability theory. The union of two events A and B, denoted as A ∪ B, represents the event that either A or B or both occur.
Given the probabilities that house sales will increase (0.25) and interest rates on housing loans will go up (0.74), we need to calculate the probability of the union of these two events. However, we must consider that the events are not mutually exclusive, meaning that it is possible for both house sales to increase and interest rates to go up simultaneously.
To calculate the probability of the union, we can use the formula: P(A ∪ B) = P(A) + P(B) - P(A ∩ B), where P(A) represents the probability of event A, P(B) represents the probability of event B, and P(A ∩ B) represents the probability of both events A and B occurring.
Substituting the given probabilities into the formula, we have P(A ∪ B) = 0.25 + 0.74 - P(A ∩ B). Since we do not have the information regarding the joint probability of both events occurring (P(A ∩ B)), we cannot determine the exact probability of the union. However, we can say that the probability of either house sales or interest rates going up is estimated to be 0.79, assuming that the joint probability is not significant.
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What is the measure of arc BEC in circle D?
134°
150°
209°
210°
The measure of arc BEC is 134°. The correct option is the first option 134°
Circle GeometryFrom the question, we are to determine the measure of arc BEC
In the given diagram,
Measure of angle C = 1/2 (measure of arc AB)
Reason: The measure of an inscribed angle is half the measure of the intercepted arc
∴ Measure of angle C = 1/2 (76°)
Measure of angle C = 38°
m∠A + m∠B + m∠C = 180° (Sum of angles in a triangle)
m∠A + 75° + 38° = 180°
m∠A + 113° = 180°
m∠A = 180° - 113°
m∠A = 67°
Measure of arc BEC = 2 × m∠A (Angle at the center is twice the angle at the circumference)
Measure of arc BEC = 2 × 67°
Measure of arc BEC = 134°
Hence, the measure of arc BEC is 134°. The correct option is the first option 134°
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2x^2-5x-3=0 ? im working on factoring and im not sure how to solve this
Answer:
\(x = - \frac{1}{2} \)
\(x = 3\)
Step-by-step explanation:
hope it helps you
have a wonderful day
does this graph represent a function? why or why not?
Answer:
D. Yes, because it passes the vertical line test
Step-by-step explanation:
the vertical line test is a test you do by drawing a vertical line through the graph of the function if more than one point from the function lies on the line it does not represent a function
in this graph at any part if you draw a vertical line it passes through one point only
Answer:
Okay so what you need to know here is for a graph to be considered a function it has to pass the vertical line test. This means that if a vertical line is moved across the graph and touches the graph at only one point, then it is considered a function. But if the vertical line touches the graph at more than one point, then it is not considered a function.
Step-by-step explanation:
But for this graph, I know it wouldn't be A, B, or C...... This is because this and it touches the graph at only one point. We know the graph has to pass the vertical line test to be a function. But we can see here that it does because on the graph it only touches one point as you can see in that attachment. So, It would be D.... I'm pretty sure it is D though. Sorry if it's wrong. I tried to do what I could bcs I'm not really good at math lol
Please mark as brainliest pls and I have attached of graphs that pass the vertical line test to help you understand it better!
Triangle DEF is shown below.
E
110°
135°
D
F
X
+
Use the drop-down menus to explain how to determine the angle measures of any triangle that is
similar to triangle DEF. Click the arrows to choose an answer from each menu.
degrees, an angle
A triangle similar to DEF will have an angle that measures Choose...
that measures Choose... degrees, and an angle that measures
Choose...
degrees.
Answer:
70
45
180-115
Step-by-step explanation:
An isosceles triangle has two congruent sides of length 15 inches. The remaining side has a length of 6 inches. Find the angle that a side of 15 inches makes with the 6-inch side.
The angle that a side of 15 inches makes with the 6-inch side is approximately 78.46 degrees.
c²= a² + b² - 2ab cos(C)
In this case, we know that the lengths of the two congruent sides are both 15 inches, and the length of the remaining side is 6 inches. So we have:
15² = 6² + 15² - 2(6)(15)cos(x)
225 = 261 - 180cos(x)
180cos(x) = 36
cos(x) =\(\frac{36}{180}\)
cos(x) = 0.2
Now we can use the inverse cosine function (\(cos^{-1}\)) to find the value of "x" in degrees:
x = \(cos^{-1}\)(0.2)
x ≈ 78.46 degrees
An angle is a geometric figure formed by two rays with a common endpoint, called the vertex. The rays are known as the sides of the angle. The measure of an angle is usually expressed in degrees, and it represents the amount of rotation needed to rotate one of the sides of the angle onto the other. A full rotation around a point is 360 degrees, so an angle measuring 180 degrees is called a straight angle.
Angles can be classified according to their measure. An acute angle is an angle measuring less than 90 degrees. A right angle is an angle measuring exactly 90 degrees. An obtuse angle measures more than 90 degrees but less than 180 degrees. A reflex angle measures more than 180 degrees but less than 360 degrees.
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evaluate the following function is f(x)=3x-2 and g(x)=5x+1 what is -2•f(4)+3•g(1)
Answer:
work is shown and pictured
Suppose a store examines a sample of n =100 purchases and observes 48 customers used a debit card. what is the probability of a sample proportion of 0.48 or less if the true population proportion is 0.60?
There is a 45.22% chance that a randomly selected sample proportion of 100 purchases will be 0.48 or less.
To find the probability of a sample proportion of 0.48 or less if the true population proportion is 0.60, we can use the sampling distribution of the sample proportion and the z-score.
Given:
Sample size (n) = 100
Observed sample proportion ) = 0.48
True population proportion (p) = 0.60
To find the probability, we need to standardize the observed sample proportion using the z-score formula:
z = ( - p) / √(p * (1 - p) / n)
Substituting the values:
z = (0.48 - 0.60) / √(0.60 * (1 - 0.60) / 100)
= -0.12 / √(0.24 / 100)
= -0.12 / √0.0024
= -0.12 / 0.049
Using a standard normal distribution table or a statistical calculator, we can find the probability associated with the z-score.
The probability of a sample proportion of 0.48 or less, given a true population proportion of 0.60, is the probability to the left of the z-score obtained.
P ≤ 0.48) = P(z ≤ -0.12)
Using a standard normal distribution table, we find that the probability of z ≤ -0.12 is approximately 0.4522.
Therefore, the probability of a sample proportion of 0.48 or less, given a true population proportion of 0.60, is approximately 0.4522 or 45.22%.
This means that there is a 45.22% chance that a randomly selected sample proportion of 100 purchases will be 0.48 or less, if the true population proportion is 0.60.
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2. Write the expression 2 3/5 as a radical.
Answer:
A
Step-by-step explanation:
The 5 goes on outside and the 3 with the 2 under the radical sign
sin² x + cos²x = 1
Which Trigonometric Identity is given above?
- Pythagorean Identity
- Lagrange's Trigonometric Identity
- Angle Sum and Difference Identity
- Tangent Identity
The Trigonometric Identity sin² x + cos²x = 1 is: A. Pythagorean Identity.
What is Pythagorean Identity?The Pythagorean Identity which tend to asserts that for every angle x, the sum of the squares of the sine and cosine of x is equal to one is known as or called a trigonometric identity.
The Pythagorean identity can be expressed as:
sin² x + cos² x = 1
This identity is crucial to understanding trigonometry and tend to have several uses in numerous branches of science and engineering.
Therefore the correct option is A.
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A recipe for a loaf of bread calls for 2/3 of a cup of flour. If milo used 12 cups of flour, how many loaves of bread did he prepare?
A.18
B.16
C.15
D.12
E.8
Answer:
15
Step-by-step explanation:
no
John has 4 milligrams of copper and 0.76 milligram of lead.
How much more copper does he have than lead?
A
3.24 milligrams
B 32.4 milligrams
C 4.76 milligrams
Answer:
A 3.24 milligrams
Step-by-step explanation:
4 milligrams of copper - 0.76 milligrams of lead = 3.24 milligrams.
brainliest please. . . .
The measures of both
Answer:
m<EAD=29°
m<CAB=119°
Solution,
< CAE+<EAD+90°=180°( angles on a straight line)
61+<EAD+90°=180°
<EAD=180-(90+61)
=180-151
=29°
<CAB+<FAB=180°( Linear pair)
<CAB+61°=180°
<CAB=180°-61°
<CAB=119°
hope this helps ..
Good luck on your assignment..