x = amount of liters of the 15% OJ
y = amount of liters of the 5% OJ
let's recall that
[tex]\bf \begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}[/tex]
so then, the amount of juice in the 15% solution will be (15/100)*x, or 0.15x
and the amount of juice in the 5% solution will be (5/100)*y or 0.05y.
we know our mixture must be 10 liters at 14% or namely 14/100, which will give in juice (14/100)*10 or 1.4 liters or pure juice in the solution with water making the OJ.
[tex]\bf \begin{array}{lcccl} &\stackrel{liters}{quantity}&\stackrel{\textit{\% of }}{juice}&\stackrel{\textit{liters of }}{juice}\\ \cline{2-4}&\\ \textit{15\% OJ}&x&0.15&0.15x\\ \textit{5\% OJ}&y&0.05&0.05y\\ \cline{2-4}&\\ mixture&10&0.14&1.4 \end{array}~\hfill \begin{cases} x+y=10\\ \boxed{y}=10-x\\ \cline{1-1} 0.15x+0.05y=1.4 \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \stackrel{\textit{substituting on the 2nd equation}}{0.15x+0.05\left( \boxed{10-x} \right)}=1.4\implies 0.15x+0.5-0.05x=1.4 \\\\\\ 0.10x+0.5=1.4\implies 0.10x=0.9\implies x=\cfrac{0.9}{0.10}\implies \blacktriangleright x = 9 \blacktriangleleft \\\\\\ \stackrel{\textit{since we know that}}{y=10-x}\implies y=10-9\implies \blacktriangleright y=1 \blacktriangleleft[/tex]
Determine the measure of arc CED.
A. 180°
B. 99°
C. 198°
D. 81°
Answer:
C
Step-by-step explanation:
An angle whose vertex lies on a circle and whose sides are 2 chords of the circle is one half the measure of the intercepted arc.
arc CED is the intercepted arc, hence
arc CED = 2 × 99° = 198°
Answer:
C) 198
Step-by-step explanation:I took the test
The regular octagon has a perimeter of 122.4 cm. Which statements about the octagon are true? Check all that apply.
Answer:
The length of segment XY can be found by solving for a in
[tex]20^2-7.65^2=a^2[/tex]
The measure of the central angle [tex]\angle ZXW[/tex] is [tex]45\degree[/tex].
Step-by-step explanation:
If the regular octagon has a perimeter of 122.4cm, then each side is [tex]\frac{122.4}{8}=15.3cm[/tex]
The measure of each central angle is [tex]\frac{360\degree}{8}=45\degree[/tex]
The angle between the apothem and the radius is [tex]\frac{45}{2}=22.5\degree[/tex]
The segment XY=a is the height of the right isosceles triangle.
We can use the Pythagoras Theorem with right triangle XYZ to get:
[tex]a^2+7.65^2=20^2[/tex]
[tex]a^2=20^2-7.65^2[/tex]
Therefore, the correct options are:
The length of segment XY can be found by solving for a in
[tex]20^2-7.65^2=a^2[/tex]
The measure of the central angle [tex]\angle ZXW[/tex] is [tex]45\degree[/tex].
Answer:3rd and 4th anwser
What is the slope of the line x = 3?
Answer:
1/3 = .33
THE UNIT RATE IS 1 TO 3
Answer:
infinite slope
Step-by-step explanation:
Note that x=3 is simply a vertical straight line that passes through the point (3,y) for all real values of y
Also recall that the slope of a vertical straight line is undefined (or infinite slope)
hence the slope of x=3 is infinite.
Which of the following is the correct notation for -48-89
Answer:
Step-by-step explanation:
Because 48 and 89 have the same sign, that is, the negative sign, their sum takes on that sign:
-48
-89
---------
-137
When solving the proportion x−26=1x+3, Santos first starts by using the Cross Product Property, multiplying the extremes and the means, to get 6=x2+x−6. Then, he subtracts 6 from both sides of the equation 6=x2+x−6 and finds the equation 0=x2+x−12. Part A: What should Santos do next to solve the equation? Part B: What is/are the solution(s) to the proportion? Select one answer for Part A, and select all answers that apply for Part B.
Answer:
A: factor the equation to (x -3)(x +4) = 0
B: solutions are x=-4, x=3
Step-by-step explanation:
A: Santos has the equation in standard form. Several options for solution are available: graphing (see attached), completing the square, factoring, using the quadratic formula. I find factoring to get to the solution most directly. The other methods work just as well.
To factor the equation, Santos needs to find two factors of -12 that have a sum of +1. Those would be +4 and -3. Putting these numbers into the binomial factors, Santos would have ...
(x +4)(x -3) = 0
__
B: The values of x that make the factors zero are ...
x = -4, x = 3
To solve the equation, Santos should first factor the quadratic equation, then use the Zero Product Property to find the solutions, which are x = 3 and x = -4.
Explanation:For Part A, Santos should factor the quadratic equation x2 + x - 12 = 0. This can be done by finding two numbers that add to 1 (the coefficient of x) and multiply to -12 (the constant term). These numbers are 4 and -3. So the factored form of the equation is (x - 3)(x + 4) = 0.
For Part B, to find the solutions to the proportion, he should use the Zero Product Property which states that if the product of two factors is zero, then at least one of the factors must equal zero. This gives us the solutions x - 3 = 0 and x + 4 = 0. Solving for x in each case provides the solutions: x = 3 and x = -4.
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hat is the value of the car two years after Fred buys it? Explain how you got your answer or show your work.
When will the car be worth less than $500,000? Explain or show your work
Answer:
Step-by-step explanation:
Since we don't have the information we need to fit this into an exponential equation, we will do it the simple way, using recursion. We will take the value of the car and subtract from it the depreciation, using the value at the end of one calculation as the initial value of the one following. Here's where it gets tricky, though. If the car's value at the end of a calculation is 80% of its initial value, then it depreciates 20%. Here is what the equation looks like after one year:
2,700,000 - .2(2,700,000) = 2,160,000
We subtracted away 20% of the initial to get the new initial. Now we use that value in the next recursion.
2,160,000 - .2(2,160,000) = 1,728,000
This is the value of the car after 2 years.
If we continue this process, we would find that after the 8th year, the car's value drops below 500,000 (namely, $452,984.83)
Drag the tiles to the boxes to form correct pairs.
Multiply the sets of numbers and match them with their products.
Answer:
[tex](-\frac{3}{4})(\frac{7}{8})[/tex] ↔ [tex]-\frac{21}{32}[/tex]
[tex](\frac{2}{3})(-4)(9)[/tex] ↔ [tex]-24[/tex]
[tex](\frac{5}{16})(-2)(-4)(-\frac{4}{5})[/tex] ↔ [tex]-2[/tex]
[tex](2\frac{3}{5})(\frac{7}{9})[/tex] ↔ [tex]\frac{91}{45}[/tex]
Step-by-step explanation:
The first expression is
[tex](-\frac{3}{4})(\frac{7}{8})[/tex]
On simplification we get
[tex]-\frac{3\times 7}{4\times 8}[/tex]
[tex]-\frac{21}{32}[/tex]
Therefore the product of [tex](-\frac{3}{4})(\frac{7}{8})[/tex] is [tex]-\frac{21}{32}[/tex].
The second expression is
[tex](\frac{2}{3})(-4)(9)[/tex]
On simplification we get
[tex](\frac{2}{3})(-36)[/tex]
[tex]-\frac{72}{3}[/tex]
[tex]-24[/tex]
Therefore, the product of [tex](\frac{2}{3})(-4)(9)[/tex] is [tex]-24[/tex].
Similarly,
[tex](\frac{5}{16})(-2)(-4)(-\frac{4}{5})\Rightarrow (\frac{5}{16})(8)(-\frac{4}{5})=(\frac{5}{2})(-\frac{4}{5})=-2[/tex]
[tex](2\frac{3}{5})(\frac{7}{9})=(\frac{13}{5})(\frac{7}{9})=\frac{91}{45}[/tex]
The sets of numbers are:
(-7)(-1.2) <-> 8.4
(-2 1/2)(-2) <-> 5
(2.5)(-2)<->-5
(7) (-1.2) <-> -8.4
The given expressions involve multiplication and follow the product rule of signs. According to this rule, the product of two numbers with the same sign is positive, while the product of two numbers with different signs is negative.
(-7)(-1.2) = 8.4: Both numbers have the same sign (negative * negative), so the product is positive. The result is 8.4.
(-2 1/2)(-2) = (-5/2)(-2) = 5: Again, both numbers are negative, so the product is positive. The calculation involves multiplying mixed numbers, where -2 1/2 is equivalent to -5/2. The result is 5.
(2.5)(-2) = -5: The numbers have different signs (positive * negative), so the product is negative. The result is -5.
(7)(-1.2) = -8.4: Once more, the numbers have different signs (positive * negative), leading to a negative product. The result is -8.4.
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i rlly hate math, pweaseeee help me asap!!!
Answer:
See explanation.
Step-by-step explanation:
Part C)
[tex]5+(-10)[/tex]
When adding a positive to a negative, the result will be the sign of the larger absolute value. In this case, 10 is greater than 5, so the result will be negative.
Adding a negative is also the same thing as subtracting a positive.
[tex]5+(-10)\\5-10\\-5[/tex]
For your second problem, 5 is larger than 3, so the result will be positive.
[tex]5+(-3)\\5-3\\2[/tex]
-----
When adding a positive to another positive, the result will be positive.
[tex]5+3\\8[/tex]
When adding a number to zero, the answer will always be the number.
[tex]5+0\\5[/tex]
Part D)
When multiplying a positive times a negative, the result will always be negative.
[tex]5*(-10)\\-50[/tex]
[tex]5*(-3)\\-15[/tex]
-----
When multiplying a positive times a positive, the result will always be positive.
[tex]5*10\\50[/tex]
When multiplying a positive or a negative times zero, the result will always be zero.
[tex]5*0\\0[/tex]
Help please!
What is the magnitude of the position vector whose terminal point is (-2, 4)?
Which of the following points lies on the circle whose center is at the origin and whose radius is 10?
Answer:
C.(5 sqrt(2), 5 sqrt(2)
Step-by-step explanation:
The point which lie on the circle is :
[tex](5\sqrt{2},5\sqrt{2})[/tex]
Step-by-step explanation:It is given that the circle is centered at origin and has a radius of 10 units.
We know that if (h, k) represents the coordinate of the center of circle and r is the radius of the circle then the equation of circle is given by:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Here we have:
[tex]h=0\ ,\ k=0\ and\ r=10[/tex]
Hence, the equation of circle is given by:
[tex](x-0)^2+(y-0)^2=10^2\\\\i.e.\\\\x^2+y^2=100------------(1)[/tex]
If we substitute the given point into the equation of the circle and it makes the equation true then the point lie on the circle and if it doesn't make the equation true then the point do not lie on the circle.
a)
[tex](\sqrt{10},0)[/tex]
i.e.
[tex]x=\sqrt{10}\ and\ y=0[/tex]
i.e. we put these points in the equation(1)
[tex](\sqrt{10})^2+(0)^2=100\\\\i.e.\\\\10=100[/tex]
which is a false statement .
Hence, this point do not lie on the circle.
b)
[tex](0,2\sqrt{5})[/tex]
i.e.
[tex]x=0\ and\ y=2\sqrt{5}[/tex]
i.e. we put these points in the equation(1)
[tex](0)^2+(2\sqrt{5})^2=100\\\\i.e.\\\\20=100[/tex]
which is a false statement .
Hence, this point do not lie on the circle.
c)
[tex](5\sqrt{2},5\sqrt{2})[/tex]
i.e.
[tex]x=5\sqrt{2}\ and\ y=5\sqrt{2}[/tex]
i.e. we put these points in the equation(1)
[tex](5\sqrt{2})^2+(5\sqrt{2})^2=100\\\\i.e.\\\\50
+50=100\\\\i.e.\\\\100=100[/tex]
which is a true statement .
Hence, this point lie on the circle.
Bubble wrap sells in sheets, and each sheet has 1 million individual spherical bubbles, each with a diameter of 0.01 m. What is the total volume of air contained in the bubbles of one sheet of bubble wrap? Round to the nearest tenth.
Answer: The total volume of air contained in the bubbles of one sheet of bubble wrap is about 0.5 cubic meters.
Step-by-step explanation:
Volume of sphere :-
[tex]V=\dfrac{4}{3}\pi r^3[/tex], where r is the radius of the sphere.
Given : Diameter of the bubble = 0.01 m
Then Radius of the bubble = [tex]\dfrac{0.01}{2}=0.005\ m[/tex]
Volume of each bubble:-
[tex]V=\dfrac{4}{3}(3.14) (0.005)^3[/tex]
Also, Number of bubbles in each sheet = 1,000,000
Then , the total volume of air contained in the bubbles of one sheet of bubble wrap will be :-
[tex]\dfrac{4}{3}(3.14) (0.005)^3\times1,000,000=0.52333333\approx0.5\ \text{cubic meters} [/tex]
Hence, the total volume of air contained in the bubbles of one sheet of bubble wrap is about 0.5 cubic meters.
Determine the horizontal, vertical, and slant asymptotes: y=x2+2x-3/x-7
Answer:
vertical asymptote: x = 7slant asymptote: y = x+9Step-by-step explanation:
The vertical asymptotes are found where a denominator factor is zero (and there is no corresponding numerator factor to cancel it). Here, that is at x = 7.
There is no horizontal asymptote because the numerator is of higher degree than the denominator.
When you divide the numerator by the denominator, you get ...
y = (x +9) +60/(x -7)
Then when x gets large, the behavior is governed by the terms not having a denominator: y = x +9. This is the equation of the slant asymptote.
The function y = (x^2 + 2x - 3) / (x - 7) has a vertical asymptote at x = 7 and a slant asymptote at y = x. It does not have a horizontal asymptote.
Explanation:
The function given is y = (x^2 + 2x - 3) / (x - 7). When identifying the asymptotes, we need to consider three types: horizontal, vertical, and slant.
For vertical asymptotes, we look for values of x that make the denominator of the function zero. In this case, x = 7 is a vertical asymptote.
For horizontal or slant asymptotes, we compare the degree of the polynomial in the numerator with the degree of the polynomial in the denominator. Since the degree of the numerator (which is 2) is larger than the degree of the denominator (which is 1), there's no horizontal asymptote. However, we have a slant asymptote which is determined by long division of the polynomials or using synthetic division.
The slant asymptote is therefore y = x.
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HELPPPP!!!!!!!!!!!!!!!! (10 points) We want to know the probability that a student selected randomly from her class would have an “A” (90 or above) in her class. Find the probability. Explain HOW to find the probability
Answer:
23 out of 91
around 1/3 of the class
Step-by-step explanation:
the total number of students so around the third part of the class
A student's course grade is based on one midterm that counts as 5% of his final grade, one class project that counts as 15% of his final grade, a set of homework assignments that counts as 35% of his final grade, and a final exam that counts as 45% of his final grade. His midterm score is 75, his project score is 93, his homework score is 78, and his final exam score is 70. What is his overall final score? What letter grade did he earn (A, B, C, D, or F)? Assume that a mean of 90 or above is an A, a mean of at least 80 but less than 90 is a B, and so on.
Answer:
76.5CStep-by-step explanation:
Apply the weights to the scores and add them up:
5% × midterm + 15% × project + 35% × homework + 45% × final
= 0.05(75) +0.15(93) +0.35(78) +0.45(70)
= 76.5
The student has a solid letter grade of C.
The student's overall final score is 76.5 which is between 70 and 79, the students earned a C.
To calculate the student's overall final score, we can use the following formula:
Final grade = (midterm score * midterm weight) + (project score * project weight) + (homework score * homework weight) + (final exam score * final exam weight)
where midterm weight is the percentage of the final grade that the midterm counts for, project weight is the percentage of the final grade that the project counts for, homework weight is the percentage of the final grade that the homework assignments count for, and final exam weight is the percentage of the final grade that the final exam counts for.
In this case, the midterm weight is 5%, the project weight is 15%, the homework weight is 35%, and the final exam weight is 45%. The student's midterm score is 75, his project score is 93, his homework score is 78, and his final exam score is 70.
Therefore, the student's overall final score is calculated as follows:
Final grade = (75 * 0.05) + (93 * 0.15) + (78 * 0.35) + (70 * 0.45)
Final grade = 3.75 + 13.95 + 27.3 + 31.5
Final grade = 76.5
Therefore, the student's overall final score is 76.5.
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A rectangular prism with a volume of 666 cubic units is filled with cubes with side lengths of \dfrac12 2 1 ? start fraction, 1, divided by, 2, end fraction unit. How many \dfrac12 2 1 ? start fraction, 1, divided by, 2, end fraction unit cubes does it take to fill the prism?
Answer:
[tex]48\ cubes[/tex]
Step-by-step explanation:
we know that
The volume of the rectangular prism is equal to
[tex]V=6\ unit^{3}[/tex]
step 1
Find the volume of one cube
The volume of the cube is equal to
[tex]V=b^{3}[/tex]
where
b is the side length of the cube
we have
[tex]b=\frac{1}{2}\ unit[/tex]
substitute
[tex]V=(\frac{1}{2})^{3}[/tex]
[tex]V=\frac{1}{8}\ unit^{3}[/tex]
step 2
To find out the number of cubes needed to fill the prism, divide the volume of the rectangular prism by the volume of one cube
so
[tex]6/(1/8)=48\ cubes[/tex]
Which expression is a sum of cubes?
Answer:
-27a³b⁶+ 8a⁹b¹²
Step-by-step explanation:
In the expression above -27 is a perfect cube of -3, 8 is a perfect cube of 2.
The exponents of a and b in both terms in the expression are divisible by 3.
The cube root of x, that is ∛xⁿ=x∧(n/3) where n is an integer.
ANSWER
[tex]- 27 {a}^{3} {b}^{6} + 8 {a}^{9} {b}^{12} [/tex]
EXPLANATION
When we can write an expression in the form
[tex] {(x)}^{3} + {(y)}^{3} [/tex]
then it is a sum of cubes.
To write a given sum as sum of cubes, then the coefficients of the terms should cube be numbers and the exponents of any power should be a multiple of 3.
This tells us that the first option will be the best choice.
[tex] - 27 {a}^{3} {b}^{6} + 8 {a}^{9} {b}^{12} [/tex]
We can rewrite this as:
[tex] { (- 3)}^{3} {a}^{3} {b}^{2 \times 3} + {2}^{3} {a}^{3 \times 3} {b}^{4 \times 3} [/tex]
We apply this property of exponents:
[tex] ({a}^{m} )^{n} = {a}^{mn} [/tex]
This gives us
[tex] {( - 3a {b}^{2}) }^{3} + {(2{a}^{3} {b}^{4} })^{3} [/tex]
Therefore the correct option is A
Find the value of x. Then find the measure of each labeled angle.
x = 110; the labeled angles are 110º and 70º.
x = 70; the labeled angles are 110º and 70º.
x = 20; the labeled angles are 160º and 20º.
x = 20; the labeled angles are 60º and 20º.
Answer:
x = 70; the labeled angles are 110º and 70º.
Step-by-step explanation:
The full degrees will add up to 180º. There are 2x and +40.
Equation: [tex]2x+40=180[/tex]
Solve: [tex]2x+40=180\\\\180-40=140\\\\2x=140\\\\x=70[/tex]
Since x=70, 70+40 will equal to 110.
Therefore, "x = 70; the labeled angles are 110º and 70º." is correct.
What is this (pic provided) written as a single log?
Answer:
Step-by-step explanation:
when logs are added, they can be multiplied to produce a simplified log.
log_5(4*7) + log_5(2)
log_5(4*7*2)
log_5(56)
Of 1232 people who came into a blood bank to give blood, 397 people had high blood pressure. Estimate the probability that the next person who comes in to give blood will have high blood pressure. Round to three decimal places as needed.
A. 0.241
B. 0.29
C. 0.373
D. 0.322
Answer: D. 0.322
Step-by-step explanation:
Given : Of 1232 people who came into a blood bank to give blood, 397 people had high blood pressure.
Then, the probability that the next person who comes in to give blood will have high blood pressure will be :_
[tex]\dfrac{\text{People had high blood pressure}}{\text{Total people}}\\\\=\dfrac{397}{1232}\\\\=0.32224025974\approx0.322[/tex]
Hence, the estimated probability that the next person who comes in to give blood will have high blood pressure = 0.322
The probability that the next person who comes in to give blood will also have high blood pressure is 0.322, calculated by dividing the number of people with high blood pressure (397) by the total number of people (1232).
Explanation:The question is asking for the probability that the next person to come in and give blood will have high blood pressure based on previous data. We calculate probabilities by dividing the number of successful outcomes by the total number of outcomes. In this case, the successful outcome is a person having high blood pressure, and the total number of outcomes is the total number of people.
Simply divide the number of people with high blood pressure (397) by the total number of people (1232). Doing this gives: 397 / 1232 = approximately 0.322.
Therefore, the estimate of the probability that the next person who comes in to give blood will also have high blood pressure is 0.322.
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What is the solution to the system of equations shown below?
2x + y - 3z = 11
-x + 2y + 4z = -3
x - 5y + 2z = - 18
a. (-1, 1, -4)
b, (1, 3, -2)
c.(3, 8, 1)
d. (2, -3, 0)
Answer:
b. (1, 3, -2)
Step-by-step explanation:
A graphing calculator or scientific calculator can solve this system of equations for you, or you can use any of the usual methods: elimination, substitution, matrix methods, Cramer's rule.
It can also work well to try the offered choices in the given equations. Sometimes, it can work best to choose an equation other than the first one for this. The last equation here seems a good one for eliminating bad answers:
a: -1 -5(1) +2(-4) = -14 ≠ -18
b: 1 -5(3) +2(-2) = -18 . . . . potential choice
c: 3 -5(8) +2(1) = -35 ≠ -18
d: 2 -5(-3) +2(0) = 17 ≠ -18
This shows choice B as the only viable option. Further checking can be done to make sure that solution works in the other equations:
2(1) +(3) -3(-2) = 11 . . . . choice B works in equation 1
-(1) +2(3) +4(-2) = -3 . . . choice B works in equation 2
After substituting the given values from each option into the system of equations, (1, 3, -2) is found to satisfy all three equations. Hence, the correct option is b.
The solution to the system of equations:
2x + y - 3z = 11
-x + 2y + 4z = -3
x - 5y + 2z = -18
can be found using methods such as substitution, elimination, or matrix inversion. In this case, we can find the solution by either of these methods. To check which option is the solution, we can substitute the given (x, y, z) values from each option into the system of equations and see which one satisfies all three equations.
For option a: (-1, 1, -4)
2(-1) + 1 - 3(-4) = -2 + 1 + 12 = 11
-(-1) + 2(1) + 4(-4) = 1 + 2 - 16 = -13
(-1) - 5(1) + 2(-4) = -1 - 5 - 8 = -14
This option does not satisfy the second and third equations.
For option b: (1, 3, -2)
2(1) + 3 - 3(-2) = 2 + 3 + 6 = 11
-(1) + 2(3) + 4(-2) = -1 + 6 - 8 = -3
(1) - 5(3) + 2(-2) = 1 - 15 - 4 = -18
This option satisfies all three equations, hence, it is the correct solution.
Write an equation that could be used to find the measure of angle A
Answer: C
Step-by-step explanation: The numerator is the angle measure, and the denominator is the side length. For angle B, the angle is 47 degrees. The opposite side is b, which is 85. We are finding the angle A, which is the numerator. The side 94 is opposite of angle A.
A recent study claimed that half of all college students "drink to get drunk" at least once in a while. Believing that the true proportion is much lower, the College Alcohol Study interviews an SRS of 14,941 college students about their drinking habits and finds that 7,352 of them occasionally "drink to get drunk". What type of statistical inference is this?
Answer: Hypothesis testing
Step-by-step explanation:
In statistics , Hypothesis testing is a general procedure to check the results of a experiment or a survey to confirm that they have actual and valid results.
Given claim : A recent study claimed that half of all college students "drink to get drunk" at least once in a while. By believing that the true proportion is much lower, the College Alcohol Study interviews an SRS of 14,941 college students about their drinking habits and finds that 7,352 of them occasionally "drink to get drunk".
Here the College Alcohol Study is just testing the results of the survey .
Hence, this is is s a type of Hypothesis testing.
What’s the length of BD ?
Answer:
BD = 4.99
Step-by-step explanation:
You can simply use the trigonometric identity tangent to solve for length BD.
Tan = opposite/adjacent
In this case we have,
Tan 31 = 3/BD
BD = 3/Tan 31
BD = 4.99
The state education commission wants to estimate the fraction of tenth grade students that have reading skills at or below the eighth grade level. in an earlier study, the population proportion was estimated to be 0.23. how large a sample would be required in order to estimate the fraction of tenth graders reading at or below the eighth grade level at the 95% confidence level with an error of at most 0.03? round your answer up to the next integer.
Answer:
The sample size must be greater than or equal to 756
Step-by-step explanation:
The formula to calculate the error of the proportion is the following
[tex]E=z_{\alpha/2}*\sqrt{\frac{p(1-p)}{n}}[/tex]
where p is the proportion, n the sample size, E is the error and z is the z-score for a confidence level of 95%
For a confidence level of 95% [tex]z_{\alpha/2}=1.96[/tex]
We know that for this case [tex]p=0.23[/tex]
We require that the error be 0.03 as maximum
Therefore we solve for the variable n
[tex]z_{\alpha/2}*\sqrt{\frac{p(1-p)}{n}}\leq0.03\\\\1.96*\sqrt{\frac{0.23(1-0.23)}{n}}\leq0.03\\\\\sqrt{\frac{0.23(1-0.23)}{n}}\leq \frac{0.03}{1.96}\\\\(\sqrt{\frac{0.23(1-0.23)}{n}})^2\leq (\frac{0.03}{1.96})^2\\\\\frac{0.23(1-0.23)}{n}\leq (\frac{0.03}{1.96})^2\\\\\frac{0.23(1-0.23)}{(\frac{0.03}{1.96})^2}\leq n\\\\n\geq\frac{0.23(1-0.23)}{(\frac{0.03}{1.96})^2}\\\\n\geq756[/tex]
Answer:
1305
Step-by-step explanation:
HELLLLP!!!!
Type the correct answer in each box.
The equation of a hyperbola is x2 − 4y2 − 2x − 15 = 0.
The width the asymptote rectangle is units, and its height is units.
Answer:
The width the asymptote rectangle is 8 units
The height the asymptote rectangle is 4 units
Step-by-step explanation:
* Lets explain how to solve this problem
- The equation of the hyperbola is x² - 4y² - 2x + 16y - 31 = 0
- The standard form of the equation of hyperbola is
(x - h)²/a² - (y - k)²/b² = 1 where a > b
- The length of the transverse axis is 2a (the width of the rectangle)
- The length of the conjugate axis is 2b (the height of the rectangle)
- So lets collect x in a bracket and make it a completing square and
also collect y in a bracket and make it a completing square
∵ x² - 4y² - 2x - 15 = 0
∴ (x² - 2x) + (-4y²) - 15 = 0
- Take from the second bracket -4 as a common factor
∴ (x² - 2x) + -4(y²) - 15 = 0
∴ (x² - 2x) - 4(y²) - 15 = 0
- Lets make (x² - 2x) completing square
∵ √x² = x
∴ The 1st term in the bracket is x
∵ 2x ÷ 2 = x
∴ The product of the 1st term and the 2nd term is x
∵ The 1st term is x
∴ the second term = x ÷ x = 1
∴ The bracket is (x - 1)²
∵ (x - 1)² = (x² - 2x + 1)
∴ To complete the square add 1 to the bracket and subtract 1 out
the bracket to keep the equation as it
∴ (x² - 2x + 1) - 1 = (x - 1)² - 1
- Lets put the equation after making the completing square
∴ (x - 1)² - 1 - 4(y²) - 15 = 0 ⇒ simplify
∴ (x - 1)² - 4(y)² - 16 = 0 ⇒ add the two side by 16
∴ (x - 1)² - 4(y)² = 16 ⇒ divide both sides by 16
∴ (x - 1)²/16 - y²/4 = 1
∴ (x - 1)²/16 - y²/4 = 1
∴ The standard form of the equation of the hyperbola is
(x - 1)²/16 - y²/4 = 1
∵ The standard form of the equation of hyperbola is
(x - h)²/a² - (y - k)²/b² = 1
∴ a² = 16 and b² = 4
∴ a = 4 , b = 2
∵ The width the asymptote rectangle is 2a
∴ The width the asymptote rectangle = 2 × 4 = 8 units
∵ The height the asymptote rectangle is 2b
∴ The height the asymptote rectangle = 2 × 2 = 4 units
Answer:
[tex]w=8\\h=4[/tex]
Step-by-step explanation:
The given equation is
[tex]x^{2} -4y^{2}-2x-15=0[/tex]
First, we complete squares for each variable to find the explicit form of the hyperbola.
[tex]x^{2} -2x-4y^{2}=15\\x^{2} -2x+(\frac{2}{2} )^{2} -4y^{2} =15+1\\ (x-1)^{2}-4y^{2}=16\\\frac{(x-1)^{2} }{16} -\frac{4y^{2} }{16} =\frac{16}{16}\\\frac{(x-1)^{2} }{16} -\frac{y^{2} }{4}=1[/tex]
Now that we have the explicit form, you can observe that [tex]a^{2}=16 \implies a=4[/tex] and [tex]b^{2}=4 \implies b=2[/tex].
On the other hand, the width of the asymptote rectangle is [tex]2a[/tex] and the height is [tex]2b[/tex].
Therefore, the dimensions are 8 by 4.
[tex]2(4)=8\\2(2)=4[/tex]
Find the coordinates of the orthocenter of ΔYAB that has vertices at Y(3, –2), A(3, 5), and B(9, 1). (JUSTIFY)
Answer:
So (5,1) is the orthocenter.
Step-by-step explanation:
So we have to find the slopes of all three lines in burgundy (the line segments of the triangle). We also need to find the equations for the altitudes with respect from all sides of the triangle (we are looking for perpendicular lines).
The vertical line there is just going to be x=a number so that line is x=3 because all the points on that line are of the form (3,y). x=3 says we don't care what y is but x will always be 3. So the line for AY is x=3.
So the altitude of the triangle with respect to that side (that line segment) would be a line that is perpendicular to is which would be a horizontal line y=1. I got y=1 because it goes through vertex B(9,1) and y=1 is perpendicular to x=3.
So we now need to find the equations of the other 2 lines.
One line has points A(3,5) and B(9,1).
To find the slope, you may use [tex]\frac{y_2-y_1}{x_2-x_1}[/tex].
Or you could just line up the points vertically and subtract then put 2nd difference over 1st difference.
Like this:
(9 , 1)
-(3 ,5)
----------
6 -4
So the slope is -4/6=-2/3.
So a line that is perpendicular will have opposite reciprocal slope. That means we are looking for a line with 3/2 as the slope. We want this line from segment AB going to opposite point Y so this line contains point (3,-2).
Point slope-form is
[tex]y-y_1=m(x-x_1)[/tex] where [tex](x_1,y_1)[/tex] is a point on the line and [tex]m[/tex] is the slope.
So the line is:
[tex]y-(-2)=\frac{3}{2}(x-3)[/tex]
[tex]y+2=\fac{3}{2}x-\frac{9}{2}[/tex]
Subtract 2 on both sides:
[tex]y=\frac{3}{2}x-\frac{9}{2}-2[/tex]
Simplify:
[tex]y=\frac{3}{2}x-\frac{13}{2}[/tex].
Let's find the the third line but two lines is plenty, really. The othorcenter is where that perpendicular lines will intersect.
Now time for the third line.
BY has points (9,1) and (3,-2).
The slope can be found by lining up the points vertically and subtracting, then put 2nd difference over 1st difference:
(9 ,1)
-(3,-2)
---------
6 3
So the slope is 3/6=1/2.
A perpendicular line will have opposite reciprocal slope. So the perpendicular line will have a slope of -2.
We want this line segment to go through A(3,5).
We are going to use point-slope form:
[tex]y-5=-2(x-3)[/tex]
Add 5 on both sides:
[tex]y=-2(x-3)+5[/tex]
Distribute:
[tex]y=-2x+6+5[/tex]
Combine like terms:
[tex]y=-2x+11[/tex]
So the equation of the 3rd altitude line is y=-2x+11.
So the equations we want to find the intersection to is:
y=(3/2)x-(13/2)
y=1
y=-2x+11
I like the bottom two equations so I'm going to start there and then use my third line to check some of my work.
y=1
y=-2x+11
Replacing 2nd y with 1 since y=1:
1=-2x+11
Subtract 11 on both sides:
1-11=-2x
Simplify:
-10=-2x
Divide both sides by -2:
5=x
The point of intersection between y=1 and y=-2x+11 is (5,1).
Let's see if (5,1) is on that third line.
y=(3/2)x-(13/2)
1=(3/2)(5)-(13/2)
1=(15/2)-(13/2)
1=(2/2)
1=1
So (5,1) is the intersection of all three lines.
So (5,1) is the orthocenter.
Can someone help me with this math question
Answer:
The coordinates of D' are (1,-1)
Step-by-step explanation:
The point D in the figure has co-ordinates (2,-2) as shown in the figure.
The figure is dilated by a factor of 1/2
So, multiply the coordinates of D (2,-2) by 1/2
D' = (1/2*2, 1/2*-2)
D' = (1,-1)
So, the coordinates of D' are (1,-1)
Sue graphed the formula for converting temperatures from Fahrenheit to Celsius. If the temperature is 50 degrees Fahrenheit, what is the temperature in Celsius? 5 degrees Celsius 10 degrees Celsius 15 degrees Celsius 20 degrees Celsius
For this case, we have by definition that:
[tex]C = (F-32) * \frac {5} {9}[/tex]
If they tell us that the base temperature is 50 degrees Fahrenheit, then we substitute:
[tex]C = (50-32) * \frac {5} {9}\\C = 18 * \frac {5} {9}\\C = 2 * 5\\C = 10[/tex]
Finally, the temperature equals 10 degrees Celsius.
Answer:
10 degrees Celsius
The temperature in Celsius when it is 50 degrees Fahrenheit is 10 degrees Celsius, calculated using the conversion formula Celsius = (Fahrenheit - 32) × 5/9.
Explanation:To convert a temperature from Fahrenheit to Celsius, we use the formula: Celsius = (Fahrenheit - 32) × 5/9. If the temperature is 50 degrees Fahrenheit, we subtract 32 from 50, giving us 18. Then we multiply 18 by 5/9, resulting in 10. Therefore, the temperature in Celsius is 10 degrees Celsius.
Step-by-step conversion:Start with the Fahrenheit temperature: 50°F.Subtract 32 from the Fahrenheit temperature: 50 - 32 = 18.Multiply by 5/9 to convert to Celsius: 18 × 5/9 = 10°C.Thus, when the temperature is 50°F, it is equivalent to 10°C.
PLEASE HELP ME WITH THIS MATH PROBLEM
Answer:
22π
Step-by-step explanation:
The area formula for a sector is
[tex]A=\frac{\theta }{360}*\pi r^2[/tex]
The angle theta is to be the angle that is a part of the sector for which we are trying to find the area. If we are looking for the area of the larger sector, we are not using 140 as our angle theta, we are using 360 - 140 = 220 as our angle theta since that is the angle for the larger of the 2 sectors. Filling in our formula using r = 6:
[tex]A=\frac{220}{360}*36\pi[/tex]
The easiest way to handle this math is to multiply the 220 by the 36, hit enter on your calculator, then divide that product by 360. When you do that your answer, in terms of pi, is 22π
myra's stamp collection consisted of 120 stamps in october. By the following march, her collection had grown to 138 stamps. By how much did her collection increase between october and march
Answer:
18 stamp increase
15 % increase
Step-by-step explanation:
To find the increase in number , we take the number of stamps in march and subtract the stamps in october
128-120 = 18
To find the percent increase, we take the number of stamps that we gained over the original amount of stamps * 100%
percent increase = 18/120 * 100%
.15 * 100%
15% increase
Myra's stamp collection increased by 18 stamps from October to the following March. This is calculated by subtracting the number of stamps she had in October (120 stamps) from the number she had in March (138 stamps).
To find out by how much Myra's stamp collection has increased between October and March, you simply need to subtract the number of stamps she had in October from the number she had in March. She had 120 stamps in October, and by March, she had 138 stamps.
To calculate the increase, we'll use the following steps:
Take the number of stamps in March: 138 stamps.Subtract the number of stamps she had in October: 120 stamps.The difference will give us the increased number of stamps.Doing the math:
138 stamps (in March) - 120 stamps (in October) = 18 stamps
So, Myra's collection increased by 18 stamps between October and March.