Answer:
x= 2
y= 7
z= 4
Step-by-step explanation:
Equation 1: x+y+z=13
Equation 2: x-z= -2
Equation 3: -2x+y=3
Add equation 2 and 1
(x+y+z)+(x-z)= 13 -2
2x+y= 11
Add this to equation 3
(-2x+y)+(2x+y)= 11+3
2y= 14
y= 7
Plug in y= 7 to equation 3
-2x+(7)= 3
-2x+7=3
-2x= -4
x= 2
Plug x=2 into equation 2
2-z= -2
4 = z
what is the image point of (8,-7) after a translation right 1 unit and up 4 units?
Answer:
It is (9,-3) because x increased by 1 unit and y increased by 4 units.
Answer:
\((9,-3)\)
Step-by-step explanation:
\((8,-7)\)
If it moves right, add the value to the x-coordinate. If it moves left, subtract the value from the x-coordinate. In this case, because the point was translated 1 unit right, we add 1 to the x-coordinate 8.
\((9,-7)\)
If it moves up, add the value to the y-coordinate. If it moves down, subtract the value from the y-coordinate. In this case, because the point was translated 4 units up, we add 4 to the y-coordinate.
\((9,-3)\)
I hope this helps!
Please help!!
What is the formula that is used for DISCOUNT SALES?
Answer:
discounted price = original price ( 1 - discount rate)
Step-by-step explanation:
Of 94 adults selected randomly from one town, 67 have health insurance. Find a 90% confidence interval for the true proportion of all adults in the town who have health insurance. Use Interval Notation with decimal rounded to the thousandths,
The required confidence interval is,
⇒ CI = (0.628, 0.797)
According to the given information,
We can use a formula to calculate the confidence interval,
⇒ CI = p ± z (√(p(1-p)/n))
Where,
p = sample proportion = 67/94 = 0.7128
z = z-score corresponding to a 90% confidence level = 1.645 (you can find this value on a z-table)
n = sample size = 94
So put the values, we get,
⇒ CI = 0.7128 ± 1.645 (√((0.7128 (1 - 0.7128))/94))
Simplifying this formula, we can get,
⇒ CI = 0.7128 ± 0.0846
Therefore, the 90% confidence interval for the true proportion of all adults in the town who have health insurance is,
⇒ CI = (0.6282, 0.7974)
In Interval Notation with decimal rounded to the thousandths,
⇒ CI = (0.628, 0.797)
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37. Briefly explain how the use of credit helped increase the average
American's standard of living in the 20th century.
Answer: If a person has a better credit, they have better chances of getting the job they had applied for. Getting the job means they get a stable income. Having a stable income helps a person to buy all essential needs.
Step-by-step explanation:
A popular 24-hour health club, Get Swole, has 29 people using its facility at time t=0. During the time interval 0≤t≤20 hours, people are entering the health club at the rate E(t)=−0.018t 2
+11 people per hour. During the same time period people are leaving the health club at the rate of L(t)=0.013t 2
−0.25t+8 people per hour. a.) Is the number of people in the facility increasing or decreasing at time t=11 ? Explain your reasoning. b.) To the nearest whole number, how many people are in the health club at time t=20. c. At what time t, for 0≤t≤20, is the amount of people in the health club a maximum? Justify your answer.
a) The rate of people leaving the health club, L(t), can be calculated as:
L(11) = 0.013(11)^2 - 0.25(11) + 8
b) To find the number of people, we integrate the net rate of change over the time interval:
Number of People at t=20 = Integral of (E(t) - L(t)) dt, from t=0 to t=20
c) This can be done by finding the critical points of the net rate of change and evaluating them to determine whether they correspond to maximum or minimum values.
To determine whether the number of people in the facility is increasing or decreasing at time t=11, we need to compare the rates of people entering and leaving the health club at that time.
a) At time t=11 hours:
The rate of people entering the health club, E(t), can be calculated as:
E(11) = -0.018(11)^2 + 11
Similarly, the rate of people leaving the health club, L(t), can be calculated as:
L(11) = 0.013(11)^2 - 0.25(11) + 8
By comparing the rates of people entering and leaving, we can determine if the number of people in the facility is increasing or decreasing. If E(t) is greater than L(t), the number of people is increasing; otherwise, it is decreasing.
b) To find the number of people in the health club at time t=20, we need to integrate the net rate of change of people over the time interval 0≤t≤20 hours.
The net rate of change of people can be calculated as:
Net Rate = E(t) - L(t)
To find the number of people, we integrate the net rate of change over the time interval:
Number of People at t=20 = Integral of (E(t) - L(t)) dt, from t=0 to t=20
c) To determine the time t at which the number of people in the health club is a maximum, we need to find the maximum value of the number of people over the interval 0≤t≤20.
This can be done by finding the critical points of the net rate of change and evaluating them to determine whether they correspond to maximum or minimum values.
Let's calculate these values and solve the problem.
Note: Since the calculations involve a series of mathematical steps, it would be best to perform them offline or using appropriate computational tools.
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draw an unordered stem and leaf diagram
The stem and leaf for the data values is
0 | 3 8
1 | 2 2 4
2 | 0 1 3 6
3 | 4
How to draw a stem and leaf for the data valuesFrom the question, we have the following parameters that can be used in our computation:
Data values:
3 8 12 12 14 20 21 23 26 34
Sort in order of tens
So, we have
3 8
12 12 14
20 21 23 26
34
Next, we draw the stem and leaf as follows:
a | b
Where
a = stem and b = leave
number = ab
Using the above as a guide, we have the following:
0 | 3 8
1 | 2 2 4
2 | 0 1 3 6
3 | 4
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an independent random sample is selected from an approximately normal population with unknown standard deviation. find the degrees of freedom and the critical t-value (t*) for the given sample size and confidence level.
a) The critical value 90% is 1.833
b) The critical value for 98% is 2.528
c) The critical value of 90% is 1.645
d) 3.169 is the critical value of 99%.
What is meant by critical value?The critical probability (p*) = 1 - (α / 2), where α equals 1 - (confidence level / 100).
Given that an independent random sample is drawn from a population with an essentially normal standard deviation.
To calculate the degrees of freedom and crucial t-value for a given sample size and confidence level.
n-1 degrees of freedom
Critical t can be obtained from the internet's t table.
a) degree of liberty = 5
The critical 90% is 1.833
b) degree of freedom is 20.
The critical value for 98% is 2.528
c) degree of freedom =28
The critical value of 90% is 1.645
d) degree of freedom =10.
3.169 is the critical value of 99%.
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At which points are the equations y = x- + 3x + 2 and y = 2x + 3 approximately equal?
Select all the correct locations on the graph. At which points are the equations y = x2 + 3x + 2 and y = 2x + 3 approximately equal? 2.
Answer:
The equations are approximately equals at the points (0.618,4.236)(0.618,4.236) and (-1.618,-0.236)(−1.618,−0.236)
what's the value of
\( \frac{2 {}^{2} }{ {5}^{2} } \)
Answer:
your answer will be 4/25
Step-by-step explanation:
.....
\( \sf Q) \frac{2 {}^{2} }{ {5}^{2} } = {?} \)
\( \sf \implies \frac{2 {}^{2} }{ {5}^{2} }\)
\( \sf \implies \frac{4}{25}\)is the required answer.
A man walks 4km from point x due east of point Y. The bearing of a flag point x and y are due N80°W and N40°E respectively. Find the distance of the flag pole from point y
The distance of the flag pole from point Y is 0.8 km and it is placed at an bearing of N40°E
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Sine rule shows the relationship between the sides and angles of a triangle.
The triangle formed has angles A = 10°, B = 50°, C = 120°, c = 4 km, a = distance from point y.
Hence:
a / sinA = c / sinC
a / sin(10) = 4 / sin(120)
a = 0.8 km
The distance of the flag pole from point Y is 0.8 km and it is placed at an bearing of N40°E
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2 1/4 + 3 1/2 = ???
Answer:
\(5\frac{3}{4}\)
Step-by-step explanation:
You need to set bot denominators equal so multiply the second fraction by two for both the top and bottom.
\(2\frac{1}{4} +3\frac{1}{2} \\ =2\frac{1}{4} +3\frac{2}{4}\\\\ =5\frac{3}{4}\)
Can yall please put the formula as well x
Answer:
x = 10°
Step-by-step explanation:
(3x + 88) + (x + 36) + (2x -4) = 180°
6x + 120 = 180°
6x = 60°
x = 10°
a diver was collecting water samples from a lake. he collected a sample at every 3m, starting at 5m below water surface. the final sample was collected at a depth of 35m.how many sample did he collected
The diver collected water samples at every 3 meters, starting from 5 meters below the water surface, up to a final depth of 35 meters.
We can find the number of samples collected by dividing the total depth range by the distance between each sample and then adding 1 to include the first sample.
The total depth range is:
35 m - 5 m = 30 m
The distance between each sample is 3 m, so the number of samples is:
(30 m) / (3 m/sample) + 1 = 10 + 1 = 11
Therefore, the diver collected a total of 11 water samples.
Name a fraction that is equivalent to three twelfths and also has a denominator that is less than 12. Explain how you found your answer.
Please.
Answer:
3/12 is equals to 1/4
I know this because 4*3=12
500TH MATH QUESTION LETS GO!!!
Hope This Helps!!!
Help please fast geometry surface area!
Answer:
SA=2πrh+2πr2=2·π·12·3+2·π·122≈282.7cm2
Given angle EFG has angle bisector FH, where EF = GF, find the value of y if EH = 5y + 10 and HG = 28 - y.
Answer:
y = 3
Step-by-step explanation:
*As seen in the photo, the fact that EF = GF and the bisector being there makes EH = HG.
5y + 10 = 28 - y
*Add y to both sides.
6y + 10 = 28
*Subtract 10 from both sides.
6y = 18
*Divide both sides by 6.
y = 3
In triangle EFG, with angle bisector FH and equal lengths for EF and GF, the value of y is 3.
Use the concept of a triangle defined as:
A triangle is a 3-sided polygon, which has three vertices and three angles which has a sum of 180 degrees.
Given that,
Angle EFG has an angle bisector FH.
EF = GF (the lengths of the corresponding sides of triangle EFG are equal).
EH = 5y + 10 (length of segment EH).
HG = 28 - y (length of segment HG).
To find the value of y,
Start by applying the angle bisector theorem in triangle EFG.
According to the theorem,
The ratio of the lengths of the segments formed by the angle bisector to the corresponding sides should be equal.
Since EF = GF,
Set up the following equation:
EH / HG = EF / FG
Substituting the given values, we have:
\(\dfrac{(5y + 10)}{ (28 - y)} = \dfrac{1} { 1}\)
Cross-multiplying, we get:
5y + 10 = 28 - y
Combining like terms, we have:
6y = 18
Dividing both sides by 6, we find:
y = 3
Therefore, the value of y is 3.
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What’s 50.272 to 1 decimal place
TRUNCATED to one decimal place, it's 50.2
ROUNDED to one decimal place, it's 50.3
The round-off of 50.272 to 1 decimal place using rules of rounding
numbers are 50.3.
Rounding off numbers means making a number simpler by adjusting it to its nearest place according to certain rules.
Rounding a number to one decimal place means keeping only the first digit after the decimal point and neglecting the rest. In this case, the digit in the second decimal place is 7, which is greater than or equal to 5. As per the rounding rules, if the digit is greater than 5, the preceding digit is increased by 1.
So, 50.272 becomes 50.3 when rounded to one decimal place.
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Which of the lines have a slope of 2?
Answer:
Im 99% sure it is D but the graphs are hard to see
Step-by-step explanation:
A fair coin is flipped twice If both flips come up heads, you lose $7 If at least one flip comes up tails, you win $1. Let X be the random variable that corresponds to your winnings in dollars. Ex X2 if you win $2 and X-2 if you lose S2. What is the expected value of X?
This is the complement of both flips coming up heads, so the probability is 3/4. The expected value of X is -$1.
To find the expected value of the random variable X, we need to calculate the weighted average of its possible outcomes based on their probabilities.
Given:
If both flips come up heads, X = -7 (loss of $7)
If at least one flip comes up tails, X = 1 (win of $1)
Let's calculate the probabilities of each outcome:
Both flips come up heads:
The probability of getting a head on a fair coin flip is 1/2.
Since the flips are independent events, the probability of getting two heads in a row is (1/2) * (1/2) = 1/4.
At least one flip comes up tails:
This is the complement of both flips coming up heads, so the probability is 1 - 1/4 = 3/4.
Now, let's calculate the expected value of X:
E(X) = (-7) * P(X = -7) + (1) * P(X = 1)
E(X) = (-7) * (1/4) + (1) * (3/4)
= -7/4 + 3/4
= -4/4
= -1
Therefore, the expected value of X is -$1.
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Help me please!!!!!!!!!!!!!!
The equation of the table of values is f(x) = 2x
Representing the equation of the tableFrom the question, we have the following parameters that can be used in our computation:
The table of values
On the table of values, we can see that
The x values are multiplied by 2 to get the y values
When represented as a function. we have
f(x) = 2 * x
Evaluate the product
f(x) = 2x
Hence, the function equation is f(x) = 2x
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A pizza was cut into 12 pieces. After lunch, 5/12 of a pizza was left over. Then Santa ate 1/4 of a pizza. What part of the pizza was left when Santa finished eating?
To answer this question, we have to substract 1/4 (which is the part of the pizza Santa ate) from 5/12 (the part of the pizza that was left over).
\(\frac{5}{12}-\frac{1}{4}=\frac{20-12}{48}=\frac{8}{48}=\frac{1}{6}\)1/6 of the pizza was left when Santa finished eating.
A tool box has the dimensions of 8 in by 5 in by 4 in. If Danny plans to double all three dimensions to build a larger tool box, he believes he would double the volume of the tool box. Is he correct? 1) Is Danny correct about doubling all three dimensions to build the larger tool box? Why or why not? :) Is Danny correct about doubling all three dimensions? If he doubles all three dimensions, the new volume will be the volume of the original tool box. Yes less than double exactly double No more than double
Danny's belief that doubling all three dimensions would double the volume of the tool box is incorrect.A tool box has the dimensions of 8 in by 5 in by 4 in.
If Danny plans to double all three dimensions to build a larger tool box, he believes he would double the volume of the tool box. Danny is incorrect about doubling all three dimensions to build the larger tool box. If he doubles all three dimensions, the new volume will not be exactly double the volume of the original tool box.
Let's calculate the volume of the original tool box:
Volume = Length x Width x Height
Volume = 8 in x 5 in x 4 in
Volume\(= 160 in³\)
Now, if Danny doubles all three dimensions, the new dimensions would be:
Length = 2 * 8 in = 16 in
Width = 2 * 5 in = 10 in
Height = 2 * 4 in = 8 in
The volume of the larger tool box would be:
Volume = Length x Width x Height
Volume = 16 in x 10 in x 8 in
Volume \(= 1280 in³\)
Therefore, the volume of the larger tool box is not double the volume of the original tool box\((160 in³)\), but rather\(1280 in³\). So, Danny's belief that doubling all three dimensions would double the volume of the tool box is incorrect.
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The answer
I don’t know how to do it
The values of a, b, c, and d, based on the given equation are:
\(a = 10\\b = 3\\c = -6\\d = -5\)
Let's calculate the values of a, b, c, and d based on the given table:
Using the equation \(y = x^2 - 4x - 2\), we can substitute the values of x and find the corresponding values of y:
For x = -3:
\(y = (-3)^2 - 4(-3) - 2 = 9 + 12 - 2 = 19\)
For x = -2:
\(y = (-2)^2 - 4(-2) - 2 = 4 + 8 - 2 = 10\)
For x = -1:
\(y = (-1)^2 - 4(-1) - 2 = 1 + 4 - 2 = 3\)
For x = 0:
\(y = (0)^2 - 4(0) - 2 = 0 - 0 - 2 = -2\)
For x = 1:
\(y = (1)^2 - 4(1) - 2 = 1 - 4 - 2 = -5\)
For x = 2:
\(y = (2)^2 - 4(2) - 2 = 4 - 8 - 2 = -6\)
For x = 3:
\(y = (3)^2 - 4(3) - 2 = 9 - 12 - 2 = -5\)
Now let's match these values with the table:
\(x , y = x^2 - 4x - 2\)
\(\[\begin{align*}(-3, 19) \\(-2, a) \\(-1, b) \\(0, -2) \\(1, -5) \\(2, c) \\(3, d) \\\end{align*}\]\)
From the given table, we have:
\(a = 10\\b = 3\\c = -6\\d = -5\)
Certainly! Here's a 100-word explanation of the given data:
The data provided consists of pairs of values, where the first column represents the x-values and the second column represents the y-values. Each row in the table corresponds to a data point. For instance, when x is \(-3\), the corresponding y-value is \(19\). Similarly, when x is \(-2\), the y-value is denoted as '\(a\)', and when \(x\) is -\(1\), the \(y\)-value is denoted as 'b'.
The pattern continues for the remaining data points, with specific values assigned to \(x \ and \ y\). This data set allows for the representation and analysis of relationships between the variables \(x \ and \ y\).
Therefore, the values of a, b, c, and d are:
\(a = 10\\b = 3\\c = -6\\d = -5\)
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What equation can you use to find the
distance of the orange grove from the hive?
Distance between hive and flower bed is 2250 feet.
Distance=Speed *time
What is a hive?
A freak flies at 20 bases per alternate directly to a flower bed from its hive
so, forward speed is
canvases directly back to the hive at 12 bases per alternate
so, backward speed is
It's down from the hive for 20 twinkles total
so,
total time = forward time backward time stay time
The freak stays at the flower bed for 15 twinkles,
20 = tb 15
Now, we can change it into seconds we know that
distance between hive and flower bed will remain Let's assume
forward time = x
So,
We know that
Distance = speed * time
Now, we can plug value now, we can plug values
Both distances are same
Now, we can break above equations and find x
Add both sides 12x
Now, we can find distance
So, distance between hive and flower bed is 2250feet.
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On a map 1 centimeter represents 200 meters Ridge trail 850 meters long how long is Ridge trail on the map ?
Answer:
4.25cm
Step-by-step explanation:
1cm=200m
given ridge Trail=850m
so,200m=1cm
1m=1/200cm
850m=1/200×850=4.25cm ans
Hope it will help u
a house is drawn to the scale of 1/4in = 5 ft. Its rectangular kitchen measures
4.5 inches by 6.5 inches on the blueprints. What is the actual length and width of the kitchen?
Find the actual area of the kitchen.
Answer:
1 : 4 1/2 :: 8 1/5 : x proportion
x = (4 1/2)(8 1/5) product of means/extremes
x = (9/2)(41/5) change improper fraction
x = 369/10 multiply
x = 36.9 change to decimal
what is 48 - 36 and then divided by 36
Answer
The result of 48 - 36 is 12. Then, if you divide 12 by 36, the result is 0.3333 or 1/3.
Step-by-step explanation:
HI, i need help. im not sure how to do this. apparently people did it in 5th grade but.. i dont know
Answer:
Yeah people did not do this in 5th grade just to let you know
and just do the numbers pointing to the other numbers top to bottom
Step-by-step explanation:
8. [9 points) Consider the function f(:r) = 2x3 - 6x² + 7, (a) find f'(x) and critical value(s). (b) Determine intervals where f(x) is increasing and intervals where it is decreasing. (c) Find local
the critical values are x = 0 and x = 2. f(x) is increasing for x < 0 and x > 2, and decreasing for 0 < x < 2. There is a local maximum at x = 0 and a local minimum at x = 2.
(a) The derivative of f(x) is f'(x) = 6x² - 12x.
To find the critical values, we set f'(x) equal to zero and solve for x:
\(6x² - 12x = 0\)
Factor out 6x:
\(6x(x - 2) = 0\)
Setting each factor equal to zero, we have:
\(6x = 0 -- > x = 0\)
\(x - 2 = 0 -- > x = 2\)
So, the critical values are x = 0 and x = 2.
(b) To determine the intervals where f(x) is increasing or decreasing, we can use the first derivative test. We evaluate the sign of f'(x) in the intervals between and outside the critical values.
For x < 0, we choose x = -1 as a test point:
\(f'(-1) = 6(-1)² - 12(-1) = 6 + 12 = 18\)
\(Since f'(-1) > 0, f(x) is increasing for x < 0.\)
For 0 < x < 2, we choose x = 1 as a test point:
\(f'(1) = 6(1)² - 12(1) = 6 - 12 = -6\)
\(Since f'(1) < 0, f(x) is decreasing for 0 < x < 2.\)
For x > 2, we choose x = 3 as a test point:
\(f'(3) = 6(3)² - 12(3) = 54 - 36 = 18\)
\(Since f'(3) > 0, f(x) is increasing for x > 2.\)
(c) To find the local extrema, we examine the sign changes of f'(x) around the critical values.
For x < 0, f'(x) is always positive, so there is no local extremum.
At x = 0, f'(x) changes sign from positive to negative, indicating a local maximum.
For 0 < x < 2, f'(x) is always negative, so there is no local extremum.
At x = 2, f'(x) changes sign from negative to positive, indicating a local minimum.
For x > 2, f'(x) is always positive, so there is no local extremum.
In summary, the critical values are x = 0 and x = 2. f(x) is increasing for x < 0 and x > 2, and decreasing for 0 < x < 2. There is a local maximum at x = 0 and a local minimum at x = 2.
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(0.9)+'
What is the approximate rate of decay in the exponential function f (t)
?
A
0.02
B.
0.1
С
0.11
D
0.9
Answer:
soooo u do dis and dat and OPE lookit the time
Dum Step-by-step explanation:
looks like its time to act dum ayy friend me. im givin out free points every weekday. if its friday, i do it every hour, called free point friday. check me out.