We use the information that $x$, $y$, and $z$ forms a geometric sequence, and that $x + y + z = 18$ and $x^2 + y^2 + z^2 = 612$ to set up two equations in terms of $y$. These can be solved simultaneously to get the value of $y$.
Explanation:The problem involves a geometric sequence and two simultaneous equations in mathematics. Given $x$, $y$, and $z$ are in a geometric sequence, then they can be represented as $x=y/r$, $y=y$, $z=yr$, where $r$ is the common ratio. This sequence gives us the first equation, $ x + y + z = 18 $.
We have another given equation which is $ x^2 + y^2 + z^2 = 612 $. Substituting $x$, $y$ and $z$ with the terms of the geometric sequence in the second equation, we have $y^2(1/r^2+1+r^2)=612$. Now we have two equations: $ y(1/r+1+r)=18 $ and $ y^2(1/r^2+1+r^2)=612 $, which we can solve simultaneously to find the value of $ y $.
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The survey of study habits and attitudes (ssha) is a psychological test that measures the motivation, attitude, and study habits of college students. scores range from 0 to 200 and follow (approximately) a normal distribution with mean 115 and standard deviation 25. you suspect that incoming freshmen at your school have a mean μ which is different from 115 because they are often excited yet anxious about entering college. to test your suspicion, you decide to test the hypotheses h0: μ = 115 versus ha: μ ≠ 115. you give the ssha to 25 incoming freshmen and find their mean score to be 116.2. what is the value of the test statistic?
Final answer:
The value of the test statistic in this scenario is 0.24, calculated using the z-score formula based on the provided sample mean, population mean, standard deviation, and sample size.
Explanation:
The value of the test statistic for a hypothesis testing can be calculated using the formula for the z-score, which is (sample mean - population mean) / (standard deviation / √sample size). In this case, given that the sample mean is 116.2, the population mean is 115, the standard deviation is 25, and the sample size is 25 students, the test statistic can be calculated as follows:
(116.2 - 115) / (25 / √25)
This computation yields a z-score of:
(1.2) / (25 / 5)
(1.2) / 5 = 0.24.
Therefore, the value of the test statistic is 0.24.
Using the given points, determine the slope.
(0, 32) and (100, 212)
The slope is the change in y divided by the change in x.
The slope is the ratio of rise to run.
so:If two tangent segments to a circle share a common endpoint outside a circle, then the two segments are
If two tangent segments to a circle share a common endpoint outside a circle, then the two segments are congruent. This is according to the intersection of two tangent theorem. The theorem states that given a circle, if X is any point within outside the circle and if Y and Z are points such that XY and XZ are tangents to the circle, then XY is equal to XZ.
Final answer:
Two tangent segments to a circle that share a common endpoint outside the circle are congruent, meaning they have the same length. This is a fundamental concept in circle geometry, illustrating the unique properties of tangents and their interactions with circles.
Explanation:
If two tangent segments to a circle share a common endpoint outside a circle, then the two segments are congruent. This means the lengths of the two tangent segments from the common external point to their respective points of tangency on the circle are equal. This concept is important in the study of circle geometry, as it helps in understanding relationships between tangents and circles.
A tangent to a circle is a line that touches the circle at exactly one point, ensuring it does not cross the circle at that touchpoint. This property of tangents being congruent when they share an external point is proven using the properties of right triangles and the fact that tangents from a point outside the circle to the circle are perpendicular to the radius at the point of tangency.
An example of this concept in action is if you draw two tangents from a single point outside of the circle to any two points on the circle's boundary, the segments of these tangents from the external point to the points of tangency will have the same length.
In two or more complete sentences describe how to determine the appropriate model for the set of data, (0,2), (2,3), (5,4), (10,5).
If 7 is added to twice a number and this sum is multiplied by 5 â, the result is the same as if the number is multiplied by 6 and 11 is added to the product. what is theâ number?
(2x+7)*5 = 6x+11
10x+35 = 6x+11
4x+35 =11
4x=-24
x=-6
the number is -6
In rectangle JKLM, angle JML is 3x - 15. Find the value of x.
Find the area of a regular hexagon with a perimeter of 42 feet. Round to the nearest tenth if necessary. Select one: a. 128.1 units2 b. 256.2 units2 c. 42.7 units2 d. 21.35 units2
10 POINTS AND BRAINLIST ANSWER TO FIRST CORRECT ANSWER
Rewrite using standard notation: 2.43 × 104
A: 24,300
B: 2,430
C: 2.43
D: 0.000243
#27 how do I find x?
E to F is 6 F to G is x
and overall distance from e to g is 1.6x
so:
6+x = 1.6x
subtract x from each side
6 = 0.6x
now divide both sides by .6
x = 6/0.6 = 10
x = 10
What is the solution to this system of linear equations?
x + y = 4
x − y = 6
Answer:
x = 5 and y = -1
Step-by-step explanation:
[tex]x + y = 4[/tex]
[tex]x - y = 6[/tex]
To solve for x and y , we use elimination method
In the given equations, the co efficient of y are same with different coefficient
So we add both equations
[tex]x + y = 4[/tex]
[tex]x - y = 6[/tex]
--------------------------------
[tex]2x=10[/tex]
Divide both sides by 2
x= 5
now we plug in x value in first equation
[tex]5 + y = 4[/tex]
Subtract 5 on both sides
y= -1
Find the equation of the linear function which passes through the points (-1, 3) and (4, -2). give your answer in y = mx + b form.
Hello : let
A(-1,3) B(4,-2)
the slope is : (YB - YA)/(XB -XA)
(-2-3)/(4+1) = -1
an equation is : y=ax+b a is a slope
y = -x +b
the line through
point B(4,-2) : -2 = -1(4)+b
b = 2
the equation is : y =-x+2
A person is standing exactly 36 ft from a telephone pole. There is a 30 degree angle of elevation from the ground to the top of the pole. What is the height of the pole?
By using the tangent function in trigonometry, we find that the height of the telephone pole is approximately 20.78 feet. This was calculated using the given angle of elevation and the distance from the pole.
To find the height of the telephone pole, we can use trigonometry, specifically the tangent function. The tangent of an angle in a right triangle is the ratio of the opposite side to the adjacent side.
Given:
Distance from the person to the base of the pole (adjacent side) = 36 ftAngle of elevation from the ground to the top of the pole = 30 degreesWe know that:
tan(30°) = opposite / adjacent
So,
tan(30°) = height / 36 ft
From a trigonometric table or calculator, tan(30°) ≈ 0.5774.
We can set up the equation as:
0.5774 = height / 36 ft
Solving for the height of the pole:
height = 0.5774 * 36 ftheight ≈ 20.78 ftTherefore, the height of the pole is approximately 20.78 feet.
Find the surface area of the figure below. Leave answer in terms of π.
A. 1060π in2
B. 1160π in2
C. 1260π in2
D. 1000π in2
A country population in 1993 was 94 million. In 1999 it was 99 million. Estimate the population in 2005 using the expoetential growth formula. Round your answer to the nearest million
What is the simplified form of the expression?
5(14 - 2)2 ÷ 2
If a and b are positive numbers such that 2b=3a, what's the value of ((a+b)/b)? I know you can plug in numbers for this, but i'm interested in solving this algebraically. Thanks.
NEED AN ANSWER ASAP
Figure ABCD is a rectangle with point A (−2, 5). What rule would rotate the figure 90° clockwise?
A. (x,y)→(y,−x)
B. (x,y)→(y,x)
C. (x,y)→(−y,x)
D. (x,y)→(−y,−x)
Answer:
A. [tex](x,y)\rightarrow (y,-x)[/tex]
Step-by-step explanation:
We have been given that figure ABCD is a rectangle with point A (−2, 5). We are asked to choose the rule that would rotate the figure 90° clockwise.
We know that rule of rotating a figure 90 degrees clockwise is: [tex](x,y)\rightarrow (y,-x)[/tex]
Upon looking at our given choices we can see that option A is the correct choice.
After rotating our given point 90 degree clockwise, the coordinates of point A would be:
[tex](-2,5)\rightarrow (5,--2)=(5,2)[/tex]
a basketball player has already scored 56 points in a game the team record for point a in a game is 72 which equation would allow you to find out how many more points the player needs to tie the record
Answer: The player needs 16 more points to tie the record.
Step-by-step explanation:
Let the number of points the player needs to tie the record be 'x'.
Number of points that a basketball player has already scored = 56
Number of points a team need for record in a game = 72
According to question, it becomes,
[tex]x+56=72\\\\x=72-56\\\\x=16[/tex]
Hence, the player needs 16 more points to tie the record.
The following is an arithmetic sequence.
-3, 3, -3, 3
true false
Joey has a full 40 coins consisting of only quarters and nickels if the total value is $5.00 how many of each does joey have.
In pentagon ABCDE, angle A= 87, angle B=125, angle C= 63, angle D=169. Find angle E
Aunt Mary is 6 times as old as Jane. If Aunt Mary is 72 years old, how old is Jane?
$15 represents 20% of the spending money Arie is saving for camp this summer. What is the total amount of money she hopes to take to camp?
Answer: $75
Step-by-step explanation: i got it right on my quiz
Does anyone know how to do this problem? Thanks.
Choose the correct simplification of (5x3 − 5x − 8) + (2x3 + 4x + 2).
Answer:
7x^3+x+6
Step-by-step explanation:
Its answer choice A on a test.
The perimeter of a rectangular slab of concrete is 24 meters. If the length of the
rectangular slab is 2 meters longer than its width, what is the width of the slab?
Answers:
A) 5 meters
B) 6 meters
C) 7 meters
D) 8 meters
The answer is 5 meters but i don't know how to get that. HELP
The width of the slab is 5 meters which is correct option(A).
What is perimeter of rectangle?Perimeter of rectangle is defined as addition the lengths of the rectangle's four sides.
Let length of slab is L, width is W,
The perimeter of a rectangular slab = 24
2(length) + 2(width) = 2L + 2W = 24
If the length of the rectangular slab is 2 meters longer than its width
= width + 2
So, the equation L = W+2
Now substitute, L= W+2 in equatioin of perimeter,
2(W+2) + 2W = 24
2W + 4 + 2W = 24
4W = 24-4 = 20
W = 20/4 = 5
W = 5
Hence, the width of the slab is 5 meters.
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The word that best describes two acute angles of a right triangle is:
inductive.
supplementary.
vertical.
complementary.
A bicycle lock has a four-digit code. The possible digits, 0 through 9, cannot be repeated. What is the probability that the lock code will begin with the number 5? . What is the probability that the lock code will not contain the number 0? .
The probability that the lock code will begin with the number 5 is:
0.1The probability that the lock code will not contain the number 0 is:
0.6What is Probability?This refers to the use of permutations to find the possible occurrence of events.
The total number of elements is 10
Hence, the total codes is 5040.
P(five)= n(first number)/n(all codes)= 1/10= 0.1
Next,
P(codes without zero)= n(codes without zero)/n(all codes)
(9*8*7*6)/(10*9*8*7)=6/10=0.6
=0.6
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Angle bisectors TX and UY triangle TUV meet at point I. Find all possible values of angleV if angleTIU = 109. As your answer, enter the number of degrees in angleV. If you find more than one possibility, list the possible values in increasing order, separated by commas.