Answer:
0.15%
Step-by-step explanation:
red is 3
the total is 20
percentage of red counters = 3 ÷ 20 = 0.15%
1/2(2x squared + 17x + 30)
Answer: 14
Step-by-step explanation:
Answer: x^2 + 17x/2 + 15
Step-by-step explanation:
i promise this is right
Find the exact value of cos (2theta), given tan A = -8/15, and theta lies in Quadrant II.
Please show steps and thank you in advance!
The value of cos (2tetha) is 161/289
What is trigonometric ratio?Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.
sin(tetha) = opp/hyp
cos(tetha) = adj/hyp
tan(tetha) = opp/adj
Therefore if tan(tetha) = -8/15, therefore opposite is 8 and adj is 15
hyp = √8²+15²
= √ 64+225
= √ 289
= 17
therefore cos (tetha) = 8/17 and since theta is in second quadrant, cos tetha will be negative
cos (tetha) = -15/17
cos²(tetha) = 225/289
sin(tetha) = 8/17
sin²(tetha) = 64/289
cos(2tetha) = cos²(tetha) -sin²(tetha)
= 225/289 - 64/289
= 161/289
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Your Stats teacher tells you your test score was the 3rd quartile for the class. Which is true?
I. You got 75% on the test.
II. Youcan'treallytellwhatthismeanswithoutknowingthestandarddeviation.
III. You can't really tell what this means unless the class distribution is nearly Normal.
Simplify with steps shown:(p²+17p+70)/9p³ +63p² * 3/p+10
The simplified formula is therefore [tex](p^2 + 31p - 140) / 9p^3 (p - 10)[/tex] as factor the first fraction's numerator and discover a shared denominator.
what is fraction ?A fraction is a percentage of an entire amount or a ratio of two numbers. It is a means to express a numeric value that is neither a whole number nor an integer. The number at the top of a fraction is called the numerator, while the number at the bottom is called the denominator. The denominator is the entire amount of elements of the entirety or the ratio's divisor, while the numerator is the portion that makes up the entirety or ratio that is being evaluated.
given
We must factor the first fraction's numerator and discover a shared denominator for the two fractions in order to simplify this expression:
(p² + 17p + 70) / 9p³ + 63p² * 3 / (p + 10)
= (p + 10)(p + 7) / 9p³ + 189p² / (p + 10)
= (p + 10)(p + 7); 9p3 + 189p2; (p - 10)/(p + 10); (p - 10)
= 189p2(p - 10)/9p3(p + 7)/9p3(p + 10) (p - 10)
= [(p + 10)(p + 7) + 21p²(p - 10)] / 9p³(p - 10) (p - 10)
= [(p² + 31p - 140) / 9p³(p - 10)]
The simplified formula is therefore [tex](p^2 + 31p - 140) / 9p^3 (p - 10)[/tex] as factor the first fraction's numerator and discover a shared denominator.
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Evaluate the expression for = 0. 6. Write your answer as a decimal or whole number. –20 + 18. 5u =
The expression -20 + 18.5u, when u is 0.6, in a decimal or whole number is equal to -8.9.
To evaluate the expression -20 + 18.5u when u = 0.6, we simply substitute 0.6 in place of u and simplify using the order of operations (PEMDAS).
-20 + 18.5u = -20 + 18.5(0.6) (substitute 0.6 for u)
-20 + 11.1 = -8.9 (simplify using multiplication first and then addition/subtraction)
Therefore, the value of the expression when u = 0.6 is -8.9.
The order of operations is a set of rules that dictate the order in which mathematical operations should be performed to avoid ambiguity and ensure that calculations are carried out correctly. PEMDAS stands for Parentheses, Exponents, Multiplication and Division (performed from left to right), and Addition and Subtraction (also performed from left to right).
In this case, we first multiply 18.5 and 0.6, giving us 11.1. Then, we subtract 20 from 11.1, resulting in -8.9.
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Find the values of c that make f continuous everywhere: x² – ² f(x) CX + 9 smaller c = if < 15 if x > 15 larger c = Use at least 3 decimal places in your answers. Submit Question 2 -5 4 -3 -2 1 2 3 4 5 1 -2 3 -4 -5+ Use the graph of f(x) above to estimate the value of f'(-2) to one decimal place. f'(-2) = Question Help: P Viden 1 d. 6+ 5 4 3 2 1 -6 -5 -4 -3 -2 2 3 4 5 -Z -1 5 6 -2 ده -4 -5 -6+ a In the graph above the slope of the tangent at 2 is
To find the values of c that make f continuous everywhere, Finally, from the graph above, it looks like the slope of the tangent at x = 2 is around 1.
For x < 15, the function is given by x² - c*x + 9. To ensure continuity at x = 15, we need to find the limit of the function as x approaches 15 from both sides:
lim x→15- (x² - c*x + 9) = 15² - c*15 + 9 = 201 - 15c
lim x→15+ (x² - c*x + 9) = 15² - c*15 + 9 = 201 - 15c
For continuity at x = 15, we need these two limits to be equal, so we set them equal to each other:
201 - 15c = 201 - 15c
Solving for c, we get c = 13.4 (rounded to 3 decimal places).
For x > 15, the function is given by x² - c*x + 9. To ensure continuity at x = 15, we need to find the limit of the function as x approaches 15 from both sides:
lim x→15- (x² - c*x + 9) = 15² - c*15 + 9 = 201 - 15c
lim x→15+ (x² - c*x + 9) = 15² - c*15 + 9 = 201 - 15c
For continuity at x = 15, we need these two limits to be equal, so we set them equal to each other:
201 - 15c ≤ 15 Solving for c, we get c ≥ 12.9 (rounded to 3 decimal places).
Therefore, the values of c that make f continuous everywhere are 13.4 ≤ c ≤ 12.9.
To estimate the value of f'(-2), we can look at the slope of the tangent line at x = -2 on the graph. From the graph, it looks like the slope of the tangent at x = -2 is around -2.5. Rounding to one decimal place, we estimate f'(-2) to be -2.5.
Finally, from the graph above, it looks like the slope of the tangent at x = 2 is around 1.
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what is the measure of one exterior angle of a polygon with 26 number of sides? round to one decimal place
Answer: The sum of the exterior angles of any polygon is 360 degrees.
The measure of one exterior angle of a regular polygon with n sides is given by the formula:
360/n
For a polygon with 26 sides, the measure of one exterior angle is:
360/26 = 13.8 degrees (rounded to one decimal place)
Step-by-step explanation:
A store is having a sale, so an employee marks down some coats from $86.88 to $65.16. What is the discount (as a percent)?
Answer:The discount would be 25%.
Step-by-Step explanation:
1.In order for us to find out the discount we need to find how much the original price got cut off.Let’s use 86.88-65.16 the answer would be 21.72.
2.Now for us to find the discount we need to find out what part of a hundred is the discount.Let’s use 86.88/21.72 the answer would be 4.
3.So now we have a fourth of a hundred and a fourth of a hundred would be 25%.
Discount given=25%=21.72
Help I don't understand.
Using the given percentage we can see that the minimum and maximum numbers are:
N- = 967
N+ = 1,150
How to get the minimum and maximum amounts?The total number of students is 3,650, and we know that the average percentage is 29% ± 2.5%
The minimum value is what we get when we use the minus sign:
29% - 2.5% = 26.5%
The 26.5% of 3,650 is:
N- = (0.265)* 3,650 = 967
The maximum value is what we get when we use the plus sign:
29% + 2.5% = 31.5%
The 31.5% of 3,650 is:
N+ = (0.315)*3,650 = 1,150
These are the two values.
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what is your interpretation of the slope?a.on average, for every additional year of age, bone density loss increases by approx 0.41.b.on average, for every additional one point of bone density loss, age increases by approx 0.41.c.on average, for every additional year of age, bone density loss increases by approx 6.9.d.none of the above
The interpretation of the slope is On average, for every additional year of age, bone density loss increases by approximately 0.41. (option a)
To calculate the least squares regression line, the data points are first plotted on a scatter plot. The line of best fit is then drawn through the data points such that the sum of the squared distances between the line and the data points is minimized. The slope of this line can be calculated using the following formula:
slope = (nΣ(xy) - ΣxΣy) / (nΣ(x²) - (Σx)²)
where n is the number of data points, Σ represents the sum of the values, x represents age, y represents bone density loss, and xy represents the product of x and y.
Using this formula, the slope for this data set can be calculated to be approximately 0.41. This means that, on average, for every additional year of age, bone density loss increases by approximately 0.41. In other words, the slope indicates a positive relationship between age and bone density loss, with bone density loss increasing as age increases.
Therefore, the correct answer is (a) On average, for every additional year of age, bone density loss increases by approximately 0.41.
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Complete Question:
Osteoporosis is a condition in which bone density decreases, often resulting in broken bones. Bone density usually peaks at age 30 and decreases thereafter. To understand more about the condition, a random sample of women aged 50 and over were recruited. Each woman's bone loss was recorded and the date is shown in this file. Create a scatter plot of these two variables, with age as the x variable and bone density loss as the y variable. Calculate the least squares regression line. What is your interpretation of the slope?
a. On average, for every additional year of age, bone density loss increases by approx 0.41.
b. On average, for every additional one point of bone density loss, age increases by approx 0.41.
c. On average, for every additional year of age, bone density loss increases by approx 6.9.
d. none of the above
in testing hypotheses, which of the following would tend to be evidence in favor of the alternative hypothesis? a. a large p -value. b. a large level of significance. c. a small level of significance. d. a small p -value.
In testing hypotheses, when p-value ≤ alpha (not is significant region) would be evidence in favor of the alternative hypothesis. So, option( a) is right answer.
Hypothesis testing is a statistical procedure for deciding whether the results of a research study support a particular theory which applies to a population. Steps to do hypothesis testing are
Specify the Null Hypothesis.Specify the Alternative Hypothesis.Set the Significance Level (a)Calculate the Test Statistic and Corresponding P-Value.Drawing a Conclusion.Now, we have to draw condition where the conclusion in favour of alternative hypotheses.
If the p-value is lower than or equal to significance level ( a) then reject the null hypothesis, and make the conclusion that supports the potential change. If the p-value is greater than significance level(a) then we fail to reject the null hypothesis, and the conclusion is that we have to support the null hypothesis.Hence, option(a) is right answer for favour alternative hypothesis.
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Paula comió un tercio de una pizza, Sofia un cuarto y Isabella el sexto. ¿Cuánto queda de pizza para Nicole?
Help on both problems pls
Answer:
DE = √21
x = 10
Step-by-step explanation:
4)
AC is bisected by BX
AC/2 = 8/2 = 4 = AB
BX² + AB² = AX²
3² + 4² = AX²
AX = 5 = radius of the circle
DE² = DX² - EX²
DE² = 5² - 2² = 25 - 4 = 21
DE = √21
6)
x² = (11-5)² + 8² = 36 + 64 = 100
x = √100 = 10
x = 10
B.When the Apollo 11 is directly above a tracking
station, L, the angle of its view of earth is 40°. If
the radius of the earth is about 4000 miles, how far
from the tracking station is the spacecraft to the
nearest tenth of a mile?
We can start by drawing a diagram of the situation:
Five strains of the Staphylococcus aureus bacteria were grown at 35 degrees Celsius for either 24 hours or 48 hours. Here are the resulting bacterial counts for each condition. The value of the correlation between bacterial count after 24 hours and bacterial count after 48 hours
The bacterial count after 48 hours decreases. A correlation coefficient of 0 would indicate no relationship between the two variables.
To find the correlation between the bacterial count after 24 hours and 48 hours, we would need the actual numerical values of the bacterial counts for each strain. Without that information, we cannot calculate the correlation coefficient. However, it is important to note that a positive correlation would indicate that as the bacterial count after 24 hours increases, the bacterial count after 48 hours also increases. A negative correlation would indicate that as the bacterial count after 24 hours increases, the bacterial count after 48 hours decreases. A correlation coefficient of 0 would indicate no relationship between the two variables.
The complete question is-
Five strains of the Staphylococcus aureus bacteria were grown for 24 hours either at 35 degrees Celsius or at 43 degrees Celsius. Here are the resulting bacterial counts for each condition:
24 hr: 66, 71, 93, 102, 62
48hr: 110,123,146,136,113
If we had plotted bacterial count at 35 degrees Celsius on the y-axis instead of the x-axis, the value of the correlation coefficient would be
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The scale factor is applies ____ for linear quantities, _____ for two-dimensional quantities, and ___________ for 3-dimensional quantities.
The scale factor is applied uniformly for linear quantities, quadratically for two-dimensional quantities, and cubically for three-dimensional quantities.
The scale factor is a term used in geometry to describe a number or conversion factor that is used to increase or decrease a figure's size without altering its shape1. It is used to increase or decrease the size of an object1. The scale factor can be calculated if the dimensions of the original figure and the dimensions of the dilated (increased or decreased) figure are known1.
The scale factor is applied uniformly for linear quantities, quadratically for two-dimensional quantities, and cubically for three-dimensional quantities.
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Please help me with these exercises that uses area and surface area
The areas and the surface areas of the figures are calculated below
Calculating the areas and the surface areasThe area of a figure is the amount of space it occupies in a plane, measured in square units.
So, we have
Figure 1
For the first figure, we have
Area = (2a)² - 1/2 * b² * sin(B)
Evaluate
Area = 4a² - b²sin(B)/2
For the second figure, we have
Area = 18 * 10 + 1/2 * 10 * √(4 * 15² + 18²) + 1/2 * 18 * √(4 * 15² + 10²)
Evaluate
Area = 639.53 square units
Figure 2
Here, we have
Area = 2 * 2 * 2.5 + 2 * 1/2 * 3 * √(3² - 2.5²) + 3 * 2
Evaluate
Area = 20.97
Figure 3 (Stairs)
Here, we have
Area = 8 * 4 + 8 * 8 + 8 * 4 + 8 * 8 + 2 * 16 * 4 + 2 * 8 * 4
Evaluate
Area = 384
Figure 3 (Semi-circular)
Here, we have
Area = 4 * 4 * 6 + 6 * 6 + 2 * 1/2 * (22/7 * (6/2)²) + 1/2 * 2 * 22/7 * (6/2) × 6
Evaluate
Area = 216.86
Figure 3 (Cylinder-Hemisphere-Cone)
Here, we have
Area = 2 * 22/7 * (10/2) * 12 + 22/7 * (10/2) * √(8² - 5²) + 2 * 22/7 * (10/2)²
Evaluate
Area = 632.42
Figure 3 (Cylinder-Cylinder)
Here, we have
Area = 2 * 22/7 * 8 * (8 + 3) + 2 * 22/7 * 2 * (2 + 7) - 22/7 * 2²
Evaluate
Area = 653.71
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Prueba de unidad Stacia necesita3 9bombillas para cada3candelabros que ella hace Completa la tabla usando razones equivalentes. Número de bombillas Número de candelabros 39 3 4 10 Informar d
The simplified ratio is 3 light bulbs for every 1 chandelier.
How to explain the ratioIt should be noted that to find equivalent ratios, we need to multiply or divide both the numerator and denominator of the ratio by the same number.
In this case, the ratio is 9 light bulbs for every 3 chandeliers, which can be simplified by dividing both the numerator and denominator by 3:
9 light bulbs ÷ 3 = 3 light bulbs
3 chandeliers ÷ 3 = 1 chandelier
So the simplified ratio is 3 light bulbs for every 1 chandelier.
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Stacia needs 9 light bulbs for every 3 chandeliers she makes Complete the table using equivalent ratios.
a nonlinear system contains the equation of a constant function and the equation of a circle. the system has one solution. describe the relationship between the graphs
The constant function and quadratic function intersect at one point in the nonlinear system.
What is the relationship between the graphs in a nonlinear system with one solution?In a nonlinear system with a constant function and a quadratic function, the two graphs intersect at one point, indicating the solution to the system. The constant function represents a horizontal line, while the quadratic function represents a parabola.
The point of intersection represents the solution where the value of the constant function equals the value of the quadratic function. The relationship between the two graphs is that they intersect at this one point, which is the unique solution to the system
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Please help me area parallelograms
The required area of the given parallelogram is 9yd² respectively.
What is Parallelogram?A parallelogram is a straightforward quadrilateral with two sets of parallel sides in Euclidean geometry.
A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of similar size.
If one of the angles in a parallelogram is a right angle, then all four angles must also be right angles.
A four-sided figure is a trapezoid if it has at least one angle of a different measure in addition to at least one right angle.
So, the formula for the area of a parallelogram is:
A=bh
Now, insert values as follows:
A = bh
A = 9/2 * 2
A = 4.5*2
A = 9yd²
Therefore, the required area of the given parallelogram is 9yd² respectively.
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What is the area of this polygon? Enter your answer in the box. units?
The area of the polygon containing the given triangle and rectangle is 45 square units.
What exactly is a rectangle?
A rectangle is a quadrilateral having four straight sides, four right angles, and parallel and equal-length opposing sides. A rectangle's opposing sides are also congruent, which implies they have the same length.
The formula A = lw gives the area of a rectangle, where A is the area, l is the length, and w is the width. A rectangle's perimeter is determined by the formula P = 2l + 2w, where P is the perimeter.
Now,
To find the area of the polygon containing the triangle and rectangle, we need to find the individual areas of the triangle and rectangle, and then add them together.
The area of a triangle
A = (1/2)bh
where b= base and h = height. Substituting the given values, we get:
A_triangle = (1/2)(9)(6) = 27 square units
The area of a rectangle is
A = lw
where l = length and w = width. Substituting the given values, we get:
A_rectangle = (9)(2) = 18 square units
Therefore, the total area of the polygon is:
A_polygon = A_triangle + A_rectangle
A_polygon = 27 + 18
A_polygon = 45 square units
Therefore, the area of the polygon containing the given triangle and rectangle is 45 square units.
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5x+3(8-1)=30 help me lol
Answer:
1.8
Step-by-step explanation:
5x+3(8-1)=30
5x+24-3=30
5x+21=30
5x=9
x=9/5 or 1 4/5 or 1.8
question 2
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question 5
1/ 3 is the difference in the gierls that have blue eyes and brown eyes
How to solve for the differenceLet's first find the difference in fractions between the number of girls with brown eyes and the number of girls with blue eyes.
Brown eyes: 7/12
Blue eyes: 1/4
To subtract these fractions, we need to find a common denominator, which in this case is 12. So, we'll convert the fractions to have the same denominator:
7/12 - (3/3)*(1/4) = 7/12 - 3/12
Now, subtract the fractions:
(7 - 3)/12 = 4/12
Simplify the fraction:
4/12 = (1/3)*(4/4) = 1/3
So, 1/3 more girls have brown eyes than blue eyes.
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using definition of derivative:lim as h approaches 0f(a+h) - f(a) / h
Using the definition of the derivative, we have:
f'(a) = lim (h -> 0) [(f(a+h) - f(a)) / h]
We're asked to use the definition of the derivative, which includes the terms:
limit, h, f(a+h), f(a), and the fraction f(a+h) - f(a) / h.
The definition of the derivative of a function f(x) at a specific point x=a is given by:
f'(a) = lim (h -> 0) [(f(a+h) - f(a)) / h]
f(a+h) represents the value of the function f(x) at the point (a+h).
f(a) represents the value of the function f(x) at the point a.
f(a+h) - f(a) calculates the difference in the function values at these two points.
h is the small change in the x-coordinate (x-axis) between these two points, and we let h approach 0 to ensure we're finding the instantaneous rate of change.
(f(a+h) - f(a)) / h represents the average rate of change between the points (a, f(a)) and (a+h, f(a+h)).
By taking the limit as h approaches 0, we find the instantaneous rate of change at the point x=a, which is the derivative of the function f(x) at x=a.
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How many teaspoons are there in 6 milliliters?
Hint: 1mL≈0.2tsp
Round your answer to the nearest tenth.
Answer: 1.2
Step-by-step explanation:
0.2 times 6 is 1.2
3. How are the areas of the shaded
triangle and the rectangle related?
Select all that apply.
10 in.
4 in.
A The area of the rectangle is twice
the area of the shaded triangle.
The area of the shaded triangle is
twice the area of the rectangle.
The area of the rectangle is
one-half the area of the shaded
triangle.
The area of the shaded triangle is
one-half the area of the rectangle.
The area of the shaded triangle
is the same as the area of the
rectangle.
Based on the given information, the correct statement is: The area of the rectangle is twice the area of the shaded triangle.
What is the rectangle about?The shaded triangle is a part of the rectangle, as indicated by the given dimensions of 10 in. and 4 in. The shaded triangle is formed by one of the shorter sides of the rectangle and a diagonal line connecting the opposite corner of the rectangle to the midpoint of that shorter side.
Since the area of the rectangle is given by the formula length × width, the area of the rectangle is 10 in. × 4 in. = 40 square inches.
On the other hand, the area of the shaded triangle is given by the formula 1/2 × base × height, where the base is the length of the shorter side of the rectangle (4 in.) and the height is the length of the longer side of the rectangle (10 in.) divided by 2, since the triangle only occupies half of the height of the rectangle.
So, the area of the shaded triangle is 1/2 × 4 in. × (10 in./2) = 1/2 × 4 in. × 5 in. = 10 square inches.
Comparing the area of the rectangle (40 square inches) to the area of the shaded triangle (10 square inches), we can see that the area of the rectangle is indeed twice the area of the shaded triangle. Therefore, the correct statement is "The area of the rectangle is twice the area of the shaded triangle."
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Consider quadrilateral ABCD and it's image. Which statement describes the transformation.
~a.) Rotation of 180° counterclockwise about (0,2)
~b.) Reflection in the line x=2
~c.) Translation along the vector ⟨0,-4⟩
~d.) Reflection in the line y=2
The quadrilateral ABCD has been reflected across the line x=2 to form its image, as can be seen in the provided figure.
what is quadrilateral ?A quadrilateral is a closed object with four successive sides that is referred to as a four-sided polygon in geometry. A quadrilateral's internal angles are always added up to 360 degrees. There are numerous varieties of quadrilaterals, such as: A hexagon with two sets of parallel sides is called a parallelogram. A trapezoid with four sharp angles is a rectangle. a rectangles with four equal sides is referred to as square. A parallelogram with one of the parallel sides is called a trapezium (or a trapezoid in American English). A trapezoid with two adjacent sets of equal-length sides is referred to as a kite.
given
The quadrilateral ABCD has been reflected across the line x=2 to form its image, as can be seen in the provided figure.
Thus, the appropriate answer is: Refraction along the line x=2
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Katte is buying plants and soil for her garden. The soil cost $4
per bag, and the plants cost $10 each. She wants to buy at least
5 plants. She cannot spend more than $100. Write and graph a
system of linear inequalities to model all possible solutions to the situation.
Answer: Hi! Read the explanation below:
Brainliest?
Step-by-step explanation:
Let's use the variables x and y to represent the number of bags of soil and plants, respectively, that Katte will buy.
The cost of x bags of soil is $4x, and the cost of y plants is $10y. Therefore, the total cost of Katte's purchases is:
$4x + $10y
We want to make sure that she doesn't spend more than $100, so we can write:
$4x + $10y ≤ $100
We also want to make sure that she buys at least 5 plants, so we can write:
y ≥ 5
Finally, we want to make sure that both x and y are non-negative, since you can't buy negative bags of soil or plants. Therefore, we can write:
x ≥ 0
y ≥ 0
Putting it all together, the system of linear inequalities is:
4x + 10y ≤ 100
y ≥ 5
x ≥ 0
y ≥ 0
To graph this system, we can start by graphing the boundary lines for each inequality. The boundary for 4x + 10y ≤ 100 is the line 4x + 10y = 100, which we can graph by finding two points on the line:
When x = 0, we have 10y = 100, so y = 10. Therefore, one point on the line is (0, 10).
When y = 0, we have 4x = 100, so x = 25. Therefore, another point on the line is (25, 0).
Plotting these two points and connecting them with a line gives us the boundary for 4x + 10y ≤ 100:
|
11 | o
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10 | o
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9 | o
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8 | o
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7 | o
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6 | o
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5 | o
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--------|-----------------------------
0 25
The boundary for y ≥ 5 is the horizontal line y = 5. We can graph this line by plotting two points on the line:
When x = 0, we have y = 5, so one point on the line is (0, 5).
When x = 100/4 = 25, we still have y = 5, so another point on the line is (25, 5).
Plotting these two points and connecting them with a line gives us the boundary for y ≥ 5:
lua
|
|
|
|
|
|
5 |-----------------------
|
|
|
|
|
--------|-----------------------------
0 25
Finally, the boundaries x ≥ 0 and y ≥ 0 are simply the x and y axes, respectively. We can graph them as:
diff
|
|
|
|
|
|
|
|
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--------|-----------------------------
0 25
Putting it all together, the graph of the system of linear inequalities looks like:
|
11 | o
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10 | o
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9 | o
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8 | o
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7 | o
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4 thumb drives and 1 compact disk have a total capacity of 18 gigabytes. 3 compact disks and 4 thumb drives have a total capacity of 22 gigabytes. Find the capacity of 1 thumb drive (x) and the capacity of 1 compact disk (y)
The capacity of 1 thumb drive is 4 gigabytes and the capacity of 1 compact disk is 2 gigabytes.
What is the capacity of 1 thumb drive and 1 compact disk?The first step is to form the system of equations that represent the information in the question:
4x + y = 18 equation 1
4x + 3y = 22 equation 2
The elimination method would be used to determined the required values.
Subtract equation 1 from equation 2
2y = 4
y = 4/2
y = 2
Substitute for y in equation 1: 4x + 2 = 18
4x = 18 - 2
4x = 16
x = 16/4
x = 4
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a survey is planned to estimate the proportion of voters who support gun control. we want a 90% confidence interval with a margin of error of 3%. we have no information about the proportion of the voters who support gun control. how many people need to be included in the sample? give your answer as a whole number, using 0 decimal places.
For a survey to put an estimate the proportion of voters who support gun control, the minimum sample size is 752 that is minimum 752 people need to be included in the sample.
We have a survey which is planned to estimate the proportion of voters who support gun control. Margin of error, MOE = 3% = 0.03
Confidence level = 90% = 0.90
No information about the proportion of the voters that is p,so let's assume, p= 0.5
Level of significance, α = 1 - CI
= 1 - 0.90 = 0.10
We have to determine the sample size of people. Using the following formula for computes minimum sample size required to estimate population proportion within the required margin of error, [tex]n ≥ p( 1-p) (\frac{z_c}{MOE})²[/tex]
where, n --> sample size
[tex]z_c[/tex]--> critical value of z
using the Z-distribution table, the value of z for 90% confidence interval is 1.64.
Substitute all known values in above formula, [tex]n ≥ 0.5( 1- 0.5) (\frac{1.64}{0.03})²[/tex]
= 751.54 ~ 752( people must be a integer no.)
Hence, required minimum sample size is 752.
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