what is the difference if I take the normal (-1,-1,1)
.
Find an equation of the plane. The plane through the point \( (3,-2,8) \) and parallel to the plane \( z=x+y \) Step-by-step solution Step 1 of 1 人 The plane through the point \( (3,-2,8) \) and par
Answers
The equation of the plane passing through the point (3, -2, 8) and parallel to the plane \( z = x + y \) is \( x + y - z = -5 \).
To find the equation of a plane through a given point and parallel to another plane, we can follow these steps:
Step 1: Determine the normal vector of the given plane.
For the plane \( z = x + y \), the coefficients of \( x \), \( y \), and \( z \) give us the normal vector: \( \mathbf{N_1} = (1, 1, -1) \).
Step 2: Use the normal vector and the given point to form the equation of the new plane.
We have the point \( P_0 = (3, -2, 8) \) on the desired plane.
Let \( \mathbf{N_2} \) be the normal vector of the new plane, which is parallel to the given plane.
Since the two planes are parallel, their normal vectors will be the same, so \( \mathbf{N_2} = (1, 1, -1) \).
Using the point-normal form of the equation of a plane, the equation of the new plane can be written as:
\( \mathbf{N_2} \cdot \mathbf{r} = \mathbf{N_2} \cdot \mathbf{P_0} \),
where \( \mathbf{r} \) represents the position vector (x, y, z).
Substituting the values, we have:
\( (1, 1, -1) \cdot (x, y, z) = (1, 1, -1) \cdot (3, -2, 8) \),
which simplifies to:
\( x + y - z = -5 \).
Therefore, the equation of the plane passing through the point (3, -2, 8) and parallel to the plane \( z = x + y \) is \( x + y - z = -5 \).
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Related Questions
part idek anymore of coin giveaway (yall I'm becoming broke i have like 44 coins left)
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*Brainly points xD I’m late but alright
solve the following recurrence relation. (no, i don’t want to know what all the numbers are, i want you to find a closed-form formula).
a₀ = 7 and aₙ = ( n + 1 )aₙ ₋ ₁, n ≥ 1
Answers
To solve the recurrence relation aₙ = (n+1)aₙ₋₁, we can use iteration to find some terms of the sequence and then look for a pattern.
a₁ = 2a₀ = 2(7) = 14
a₂ = 3a₁ = 3(14) = 42
a₃ = 4a₂ = 4(42) = 168
From these calculations, we might guess that aₙ = (n+1)! * 7 for n ≥ 0. We can prove this by induction.
Base case: a₀ = 7 = (0+1)! * 7 is true.
Inductive step:
Assume that aₙ = (n+1)! * 7 for some arbitrary n ≥ 0.
We want to show that aₙ₊₁ = ((n+1)+1)! * 7.
Using the recurrence relation, we have:
aₙ₊₁ = (n+2)aₙ = (n+2)(n+1)! * 7 = (n+2)! * 7
Therefore, aₙ₊₁ satisfies the formula ((n+1)+1)! * 7, completing the inductive step.
By induction, we have shown that aₙ = (n+1)! * 7 for n ≥ 0. This is the closed-form formula for the given recurrence relation.
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PLEASE HELP ASAP! BRAINLEST
solve all math problems
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I hope that helped.............
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An automatic filling machine is used to fill 2-litre bottles of cola. The machine’s output is known to be approximately Normal with a mean of 2.0 litres and a standard deviation of 0.01 litres. Output is monitored using means of samples of 5 observations.
Determine the upper and lower control limits that will include roughly 95.5 percent of the sample means.
If the means for 6 samples are 2.005, 2.001, 1.998, 2.002, 1.995 and 1.999, is the process in control?
Answers
The upper control limit (UCL) is approximately 2.0018 litres, and the lower control limit (LCL) is approximately 1.9982 litres, which would include roughly 95.5 percent of the sample means.
Now let's check if the process is in control using the given sample means:
To determine the upper and lower control limits for the sample means, we can use the formula:
Upper Control Limit (UCL) = Mean + (Z * Standard Deviation / sqrt(n))
Lower Control Limit (LCL) = Mean - (Z * Standard Deviation / sqrt(n))
In this case, we want to include roughly 95.5 percent of the sample means, which corresponds to a two-sided confidence level of 0.955. To find the appropriate Z-value for this confidence level, we can refer to the standard normal distribution table or use a calculator.
For a two-sided confidence level of 0.955, the Z-value is approximately 1.96.
Given:
Mean = 2.0 litres
Standard Deviation = 0.01 litres
Sample size (n) = 5
Using the formula, we can calculate the upper and lower control limits:
UCL = 2.0 + (1.96 * 0.01 / sqrt(5))
LCL = 2.0 - (1.96 * 0.01 / sqrt(5))
Calculating the values:
UCL ≈ 2.0018 litres
LCL ≈ 1.9982 litres
Therefore, the upper control limit (UCL) is approximately 2.0018 litres, and the lower control limit (LCL) is approximately 1.9982 litres, which would include roughly 95.5 percent of the sample means.
Now let's check if the process is in control using the given sample means:
Mean of the sample means = (2.005 + 2.001 + 1.998 + 2.002 + 1.995 + 1.999) / 6 ≈ 1.9997
Since the mean of the sample means falls within the control limits (between UCL and LCL), we can conclude that the process is in control.
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A 35-kg trunk is dragged 10 m up a ramp inclined at an angle of 12 degrees to the horizontal by a force of 90 N applied at an angle of 20 degrees to the ramp. At the top of the ramp, the trunk is dragged horizontally another 15 m by the same force. Find the total work done.
Answers
Answer:
The total work done is approximately 2,114.308 J
Step-by-step explanation:
The mass of the trunk = 35 kg
The height to which the trunk is dragged, d₁ = 10 m
The inclination of the plane on which the trunk is dragged = 12°
The applied force F = 90 N
The angle of inclination of the force to the ramp = 20°
The distance the trunk is dragged horizontally at the top of the ramp, d₂ = 15 m
Work = Force × Distance
The work done along the inclined plane, W₁ = 90 N × cos(20°) × 10 m ≈ 845.723 J
The work done along the horizontal, W₂ = 90 N × cos(20°) × 15 m ≈ 1,268.585 J
The total work done, W = W₁ + W₂
∴ W = 845.723 J + 1,268.585 J = 2,114.308 J
A quadrilateral has three angles that measure 88°, 82°, and 55°. Find the unknown angle measure.
Answers
Answer: 135° is the unknown angle measure.
Step-by-step explanation: We know a quadrilateral has 4 angles and measure a total of 360°.
To find the unknown angle simply add all the 3 angles and then subtract them from 360°.
Follow the steps:
88° + 82° + 55° = 225°. (Added the 3 angles)
360° - 225° = 135°. (Subtract the sum of the 3 angles from 360 degrees)
What does the number .05 represent in the following: t(58) = 2.001, p < .05?
A)test statistic B)t value C)degrees of freedom D)significance level
Answers
The number .05 is the significance level which indicates the probability of obtaining a result as extreme as the observed one.
The number .05 represents the significance level in the t-test. The significance level is the probability of obtaining a result as extreme as the observed one, given that the null hypothesis is true. In this case, the t-test is measuring the difference between two means and the null hypothesis is that there is no difference between them. The t-value is the test statistic which measures the difference between the groups and the degrees of freedom is the number of observations minus one. The p-value is the probability of obtaining a result as extreme as the observed one, given that the null hypothesis is true. If the p-value is less than .05, this indicates that the result is statistically significant, meaning that the null hypothesis can be rejected and the alternative hypothesis is accepted.
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Someone plz help me :(
A or B?
Answers
Answer:
B
Step-by-step explanation:
just count the blocks it represents 9/8
you drop a ball off a 50 foot roof to see how long it will bounce. Each bounce loses 10% of the height of its previous bounce. after how many bounces will the ball's height be less than 1 foot?
Answers
After 37 bounces, the ball's height will be less than 1 foot.
How many bounces until it is less than 1 foot?The initial height of the ball is 50 feet.
After first bounce, the ball will reach a height of:
= 50 feet * (1 - 10%)
= 45 feet.
After second bounce, it will reach a height of:
= 45 feet * (1 - 10%)
= 40.5 feet.
Height decreases by 10% after each bounce.
We have to set up an equation:
50 feet * (0.9)^n < 1 foot
Simplifying:
0.9^n < 1/50
Taking the logarithm:
n * log(0.9) < log(1/50)
n > log(1/50) / log(0.9)
n > 37.1298771746
n > 37.13.
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the sum of three times x and 4 is 25 what's x
Answers
The solution to linear equation is x = 7 .
Equation can be linear , quadratic , cubic and so on .
Linear Equation : An equation whose degree is 1 . It can be 1 variable , 2 variable and so on .
The given question is of linear equation in 1 variable .
Given : the sum of three times x and 4 is 25
To find : variable x
According to question
3 x + 4 = 25
3 x = 21
x = 7
Hence , the solution to linear equation is 7 .
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Ciara measured the length, x, of each of the insects she found underneath a rock. She recorded the lengths in the table below. Calculate an estimate of the mean length of the insects she found. Give your answer in millimetres (mm). Length (mm) 0≤x≤10 10≤x≤20 20≤x≤30 Frequency 5 6 9
Answers
The estimate of the mean length of the insects Ciara found is 17 millimeters (mm).
To calculate an estimate of the mean length of the insects Ciara found, we need to find the weighted average of the lengths using the given frequencies.
Let's denote the lower limits of the length intervals as L1 = 0, L2 = 10, and L3 = 20.
Similarly, denote the upper limits as U1 = 10, U2 = 20, and U3 = 30.
Next, we calculate the midpoints of each interval by taking the average of the lower and upper limits.
The midpoints are M1 = (L1 + U1) / 2 = 5, M2 = (L2 + U2) / 2 = 15, and M3 = (L3 + U3) / 2 = 25.
Now, we can calculate the sum of the products of the frequencies and the corresponding midpoints.
This gives us (5 \(\times\) 5) + (6 \(\times\) 15) + (9 \(\times\) 25) = 25 + 90 + 225 = 340.
Next, we calculate the sum of the frequencies, which is 5 + 6 + 9 = 20.
Finally, we divide the sum of the products by the sum of the frequencies to find the weighted average, which is 340 / 20 = 17.
Therefore, the estimate of the mean length of the insects Ciara found is 17 millimeters (mm).
Thus, the mean length of the insects Ciara found is approximately 17 millimeters (mm).
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8.68x+ 25.84 - 21.6 = 2.3x +17
Answers
Answer: X = 2
Step-by-step explanation:
8.68x - 2.3x = 17 - 4.24
6.38x = 12.76
x = 2
(a) Three squares have the areas of 7 cm², 17 cm² and 10 cm², (i) Will the squares exactly surround a right angled triangle? (ii) Explain your answer.
Answers
Answer:
(i) This equation is not true, which means that the three squares cannot exactly surround a right-angled triangle.
(ii) It is not always possible for three squares to surround a right-angled triangle. One way to see this is to note that the side lengths of a right-angled triangle satisfy the Pythagorean theorem, which means that they must be in a certain relationship to each other. On the other hand, the areas of three squares can take any values, so it is not always possible to find three squares whose side lengths satisfy the Pythagorean theorem.
Step-by-step explanation:
To determine whether the three squares can exactly surround a right-angled triangle, we need to use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
Let's assume that the three squares have side lengths a, b, and c, with areas of 7 cm², 17 cm², and 10 cm², respectively. Then, we have:
a² = 7 cm²
b² = 17 cm²
c² = 10 cm²
We need to find out whether there exist values of a, b, and c that satisfy the Pythagorean theorem. If such values exist, then the three squares can surround a right-angled triangle.
We can rearrange the equations above to solve for a, b, and c:
a = √7 cm ≈ 2.65 cm
b = √17 cm ≈ 4.12 cm
c = √10 cm ≈ 3.16 cm
Now, we can check whether the Pythagorean theorem holds:
c² = a² + b²
(√10 cm)² = (√7 cm)² + (√17 cm)²
10 cm = 7 cm + 17 cm
This equation is not true, which means that the three squares cannot exactly surround a right-angled triangle.
In general, it is not always possible for three squares to surround a right-angled triangle. One way to see this is to note that the side lengths of a right-angled triangle satisfy the Pythagorean theorem, which means that they must be in a certain relationship to each other. On the other hand, the areas of three squares can take any values, so it is not always possible to find three squares whose side lengths satisfy the Pythagorean theorem.
Choose all the expressions that are equal to 1/6. A. 6÷1 B. 3÷18 C. 2÷ 1/3 D. 1÷6 E. 1/3 ÷ 2
Answers
We can state this by responding to the provided question B, D, and E are expressions the expressions that have values of 1/6.
what is expression ?Mathematical operations include doubling, dividing, adding, and subtracting. A phrase is constructed as follows: Expression, monetary value, and mathematical operation Numbers, parameters, and functions make up a mathematical expression. It is possible to use words and terms in contrast. Every mathematical statement including variables, numbers, and a mathematical operation between them is called an expression, sometimes referred to as an algebraic expression.
We need to simplify each expression to see which ones are equivalent to 1/6:
6. 1/6 is not equivalent to 6/1.
B. 3÷18 = 1/6
C. 2/3 of 2 equals 6 (not equivalent to 1/6)
D. 1÷6 = 1/6
E. 1/3 ÷ 2 = 1/6
B, D, and E are the expressions that have values of 1/6.
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33. DF bisects ZEDG. Find the value of x. The diagram is not to scale.
Answers
From the given diagram, we can identify two right-angled triangles. The triangles are shown below:
Using trigonometric ratios, we can find x as follows
\(\begin{gathered} \sin 28^0\text{ = }\frac{7x\text{ + 15}}{DF} \\ \sin 28^0\text{ = }\frac{10x}{DF} \end{gathered}\)We can equate the expressions for DF as follows:
\(\begin{gathered} DF\text{ = }\frac{7x\text{ + 15}}{\sin 28^0} \\ DF\text{ = }\frac{10x}{\sin 28^0} \end{gathered}\)\(\begin{gathered} \frac{7x\text{ + 15}}{\sin28^0}\text{ = }\frac{10x}{\sin 28^0} \\ \text{Cancelling out sin 28}^0 \\ 7x\text{ + 15 = 10x} \end{gathered}\)Solving for x:
\(\begin{gathered} 7x\text{ - 10x = -15} \\ -3x\text{ = -15} \\ \text{Divide both sides by -3} \\ \frac{-3x}{-3}\text{ = }\frac{-15}{-3} \\ x\text{ = 5} \end{gathered}\)Answer:
x = 5
Sharon wants to switch from cable to satellite TV. She calls Great Vista Satellite to get a quote. After looking at her cable bill, the salesperson explains that they can provide the same 300 channels Sharon has for $0.20 less per channel. If she switches, her monthly satellite bill will come to $180.
Answers
Answer:
If Sharon has 300 channels with her cable service, then her monthly cost is calculated as follows:
300 channels × $0.20 per channel = $60
This means that Sharon's current cable bill is $60 per month. If she switches to Great Vista Satellite, her monthly cost will be $180, which is $120 more than her current bill. This increase in cost can be represented by the equation:
$120 = 300 channels × $0.20 per channel × m
where "m" is the number of months Sharon has to subscribe to the satellite service to break even.
Simplifying the equation, we get:
m = $120 ÷ ($0.20 × 300 channels) = 2
Therefore, Sharon will have to subscribe to the satellite service for 2 months to break even. After that, she will start saving $0.20 per channel per month compared to her cable service.
maya achievements in mathematics were closely related to what other area?
Answers
Maya achievements in mathematics were closely related to astronomy.
How were Maya achievements closely related to astronomy?
The Maya civilization made advancements in both mathematics and astronomy and these two fields were intricately interconnected in their culture. The Maya developed a highly sophisticated numerical system which allowed them to perform complex calculations and create precise astronomical predictions.
They meticulously observed celestial bodies and recorded their movements, developing calendars and astronomical tables that aided in agricultural planning, religious rituals, and governance. By studying the stars, planets and celestial events, the Maya not only expanded their understanding of the universe but also used mathematical principles to navigate time and space.
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4/x + 2/y = 3 is that linear? explain
please help i need it for my final
Answers
Answer:
Yes
Step-by-step explanation:
a function f is given. f(x) = 2 − x2 (a) use a graphing calculator to draw the graph of f.
Answers
To draw the graph of the function f(x) = 2 - x^2 using a graphing calculator, follow these steps: Turn on your graphing calculator and enter the function f(x) = 2 - x^2 into the calculator's equation editor.
Set the viewing window of the calculator to a suitable range, such as -5 ≤ x ≤ 5 and -5 ≤ y ≤ 5, to capture the shape of the graph. Press the "Graph" button to plot the graph of f(x). The graph of f(x) = 2 - x^2 should appear on the screen as a downward-opening parabola centered at the point (0, 2). You can use the arrow keys on the calculator to move around and explore different parts of the graph.
The graph of f(x) = 2 - x^2 will show a symmetric curve that opens downwards. The highest point on the graph will be at (0, 2), and the curve will extend infinitely in both the positive and negative x-directions.
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Any genius want a brainliest :)
Answers
Answer:
1.) q less than a number m times 7 is equal to 23
2.) 3 times a number g plus 8 is equal to 10 less than a number h times 4
3.) 6 more than a number k times 9 is equal to 54
4.) a number f times 7 less than a number of d squared times 6 is equal to a number d times 8 more than a number f squared
5.) a number g times 3 is equal to 45
(I might be wrong, so try to read the equations out loud to see if you agree)
n a given year, there are 10 million unemployed workers and 120 million employed workers in an economy.
Answers
In a given year, an economy has 10 million unemployed workers and 120 million employed workers. This information provides a snapshot of the labor market and indicates the number of individuals who are currently without jobs and those who are employed.
The information states that in the given year, there are 10 million unemployed workers and 120 million employed workers in the economy. This data provides a measure of the labor market situation at a specific point in time.
Unemployed workers refer to individuals who are actively seeking employment but currently do not have a job. The number of unemployed workers can be an important indicator of the health of an economy and its ability to provide job opportunities.
Employed workers, on the other hand, represent individuals who have jobs and are currently working. The number of employed workers indicates the size of the workforce that is actively contributing to the economy through productive activities.
By knowing the number of unemployed and employed workers, policymakers, economists, and analysts can assess factors such as labor market conditions, unemployment rates, and workforce participation rates. This information is crucial for formulating policies, understanding economic dynamics, and monitoring the overall health and functioning of the economy.
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What is a formula for the nth term of the given sequence?
180, -240,320...
Answers
Answer:
Tn=T1+(n-1)*d
Step-by-step explanation:
Tn is the nth term
T1 is the first term of the sequence
n is the nth term as well
d is the common difference
1) 116 = -2x - 3(1 + 5x)
Answers
Answer:
x = -7
Step-by-step explanation:
I hope this helps!
Hi there!
~
\(116 = -2x - 3(1 + 5x)\)
= \(x = -7\)
Hope this helped you!
two angles are vertical. one angles measures 10x - 6, and the other angles measured 8x + 12. find the measure of each angle .
Answers
Answer:
9
Step-by-step explanation:
10x-6 = 8x + 12
so
10x-8x = 12 + 6
so
2x = 18
so x = 18/2 = 9
what is the value of x, in units?
Answers
Answer: 12 units
Step-by-step explanation: see both shapes are the same just one is flipped and its small meaning the first shape without numbers is only double of the shape with numbers so you answer would be 12 units
small shape x 2 gives all your answers to the big shape
TOO
EASY
BYE
Which of the following is the solution set of the
problem?
O (-∞, -3)
(-∞, -3]
O
[-3,00)
O (-3,00)
DONE
Answers
The solution set of the example inequality, 2•x + 3 ≤ -3, is the option;
(-∞, -3]How can the solution set of an inequality be found?A possible inequality that can be used to get one of the options, (the inequality is not included in the question) is as follows;
2•x + 3 ≤ -3Solving the above inequality, we have;
2•x + 3 ≤ -3
2•x ≤ -3 - 3 = -6
2•x ≤ -6
Therefore;
x ≤ -6 ÷ 2 = -3
x ≤ -3
Which gives;
-∞ < x ≤ -3-∞ < x ≤ -3 in interval notation is (-∞, -3]
The solution set of the inequality, 2•x + 3 ≤ -3, is therefore the option;
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To test the effectiveness of a business school preparation course, 8 students took a general business test before and after the course. The results are given below.
Student/ Exam Score Before Course/ Exam Score After Course
1/ 530 / 670
2/ 690 / 770
3/ 910 / 1,000
4/ 700 / 710
5/ 450 / 550
6/ 820 / 870
7/ 820 / 770
8/ 630 / 610
...Questions...
1) What is the calculated test statistic?
2) State the null hypothesis, alternate hypothesis, and decision rule at .05 level of significance.
3) What are the conclusions?
Answers
The null and alternative hypothesis are Null hypothesis : The preparation course not effective H₀ = цₐ > 0
What is null hypothesis?A null hypothesis is a type of statistical hypothesis that proposes that no statistical significance exists in a set of given observations. It is represented as H0 and is used to assess the credibility of a hypothesis by using sample data.
Group Before After
Mean 693.75 743.75
Sd 155.37 143.92
SEM 54.93 50.88
n 8 8
Null hypothesis : H₀ = цₐ > 0 The preparation course not effective.
Alternative hypothesis : H₀ = цₐ > 0The preparation course is effective in improving the exam scores.
(after - before)
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a. The calculated test statistic is given as 2.28
b. The Null hypothesis is μd = 0
The Alternative hypothesis μd ≠ 0
The decision rule at a significance level of 0.05 is a rejection of the hypothesis
c. The conclusion states that there is a significant difference between the scores before and after the course.
How do we calculate?a. The test statistic = Mean difference / (Standard deviation of differences / √(sample size))
Test statistic = 55 / (54.94 / √8)
Test statistic = 2.28
b. Null hypothesis is the mean difference between the scores before and after the course is equal to zero.
Then alternative hypothesis is the mean difference between the scores before and after the course is not equal to zero.
we reject the null hypothesis for the decision rule.
c.
We make a comparison between the calculated test statistic with the critical value of the t-distribution. If the absolute value of the test statistic is greater than the critical value, we reject the null hypothesis and conclude that there is a significant difference between the scores before and after the course.
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What must be true about two objects of heat is flowing between them?
Answers
Answer:
that must mean that either the objects are giving off heat or the heat from one object is transferring to the air
Step-by-step explanation:
Answer:
The objects must be different temperatures.
Step-by-step explanation:
Which list describes the correct order of a common treatment plan for leukemia patients?
radiation therapy Right arrow. healthy cells grow Right arrow. stem cell therapy Right arrow. new cells grow
cancer cells killed Right arrow. blood transfusion Right arrow. bone marrow grows Right arrow. chemotherapy
blood transfusion Right arrow. cancer cells killed Right arrow. radiation therapy Right arrow. bone marrow grows
chemotherapy Right arrow. cancer cells killed Right arrow. stem cell transplant Right arrow. healthy cells grow
Answers
The correct order of a common treatment plan for leukemia patients is:
chemotherapy ➞ cancer cells killed ➞ stem cell transplant ➞ healthy cells grow.
In leukemia treatment, chemotherapy is often used to kill cancer cells. After chemotherapy, a stem cell transplant may be performed to replace the unhealthy cells with healthy stem cells. Following the transplant, the healthy cells grow and repopulate the bone marrow.
In a common treatment plan for leukemia patients, chemotherapy is administered to kill cancer cells. After the chemotherapy, a stem cell transplant is performed to replace the unhealthy cells with healthy stem cells. These transplanted stem cells then grow and develop into healthy cells, helping to restore normal function in the patient's body.
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In its first year of operation, Big Lake Camp had 40 campers. This year’s attendance was 180% of the first year’s. How many campers participated this year?
32
58
64
72
Answers
Answer:
72 campers participated this year
Step-by-step explanation:
Percentages
To determine x% of y, we must calculate x*y/100.
The number of campers that participated in Big Lake Camp during its first year was 40. We now want to know the number of campers that participated this year, if the attendance was 180% of the first year's.
The new attendance is calculated as follows:
40 * 180 / 100 = 72
72 campers participated this year
Answer:
72
Step-by-step explanation: