The side lengths and x are x = 5, BC = 8 meters and x = 12
How to determine the side lengths and xValue of x
From the question, we have the following parameters that can be used in our computation:
3x = x + 10
Evaluate
2x = 10
So, we have
x = 5
Length of BC
Here, we have
BC = CD
So, we have
BC = 8 m
Value of x
Here, we have
2x - 3 = x + 9
Evaluate
x = 12
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Please help me with this, quickly.
Answer: That would odd.
evaluate the expression when y= -2 and z = -5
2z/y
Answer:
5 is the answer
Step-by-step explanation:
\( \frac{2 z}{y } \\ = \frac{2 \times ( - 5)}{ - 2} \\ = \frac{ - 10}{ - 2} \\ = 5 \: ans.\)
when \(y = -2\) and \(z = -5\), the value of the expression \(2z/y\) is \(5\).
How to evaluate the expression when y= -2 and z = -5 2z/yTo evaluate the expression \(2z/y\) when \(y = -2\) and \(z = -5\), follow these steps:
1. Substitute the values of \(y\) and \(z\) into the expression:
\(2z/y = 2(-5) / (-2)\)
2. Perform the calculations:
\(2z/y = -10 / (-2) = 5\)
So, when \(y = -2\) and \(z = -5\), the value of the expression \(2z/y\) is \(5\).
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Choose the correct correspondence. 5
a, 6
b, 7
c, 8
Answer:
c
Step-by-step explanation:
What is the probability that a random sample of 12 second grade students results in a mean reading rate of more than 95 words per minute?
The probability that a random sample of 12 second grade students results in a mean reading rate of more than 95 words per minute is 0.4582.
Given that the population mean, \(\mu\) = 90 wpm
The standard deviation of the population ,\(\sigma\) = 10
Sample size, n = 12
Sample mean, \(\bar x\) = 95
The reading rate of students follows the normal distribution.
Let z = \(\frac{\bar x - \mu}{\frac{\sigma}{\sqrt n} }\)
= \(\frac{95 - 90}{\frac{10}{\sqrt 12} }\)
= 1.732
Probability that the mean reading exceeds 95 wpm = P(\(\bar x\) >95)
= P(z>1.732)
= 1- P(z<1.732)
= 0.4582
[The value 0.4582 found from the area under the normal curve using tables].
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the line through (2,1,0) and perpendicular to bothi+j and j+k
find the parametric equation and symmetric equation
The symmetric equation of the line is x - y + z = 1.
We can find the direction vector of the line by taking the cross product of the two given vectors, since the cross product of two vectors is perpendicular to both of them:
(i + j) × (j + k) = (1i - 1j + 1k)
So the direction vector of the line is <1, -1, 1>. We can use this vector and the given point (2, 1, 0) to find the parametric and symmetric equations of the line.
Parametric equation:
x = 2 + t
y = 1 - t
z = t
where t is a parameter.
Symmetric equation:
We can find the symmetric equation of the line by solving for t in each of the parametric equations:
t = z
t = y - 1
t = x - 2
Then we can set the expressions for t equal to each other and simplify:
z = y - 1 = x - 2
We can rewrite this as:
x - y + z = 1
So the symmetric equation of the line is x - y + z = 1.
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Find the length of each arc. Use the exact answer
Answer:
D) 16π/3 ft
Step-by-step explanation:
We solve the above question using the Arc length formula when our central angle is in degrees
The formula is given as:
Arc length = 2πr × θ /360
r = 4 ft
θ = Central angle in degrees = 240°
Hence,
2 × π × 4 × 240/360
8π × 240/360
8π × 20/30
16π/3 ft
Arc length = 16π/3 ft
Option D is the correct option
if Sophia took a bath at 9:36 and finish at 10:30 how much time did she use in taking a bath
Answer:
54 minutes
Step-by-step explanation:
1) There are 60 minutes in an hour. So, you can do 60-36 to find the first value. (24)
2) Add 24 minutes to 30 and get 54 minutes.
Evaluate the expression below if x = -1 and y = 3.
3x^2-y^2
Employee: "We have a promotion that will allow us to beat our competitors' prices and save you money. Did you notice that our competitor is selling that same item for $150.00?
Customer: "Yes"
Employee: "Our price for that item is $120.00, for a savings of __________."10% 15% 20% 30% 40%
Answer:
20%
Step-by-step explanation:
120 / 150 = 0.8 or 80%, so the difference is 20%
The discount percentage is 20%.
Given that the competitor is selling an item for $ 150.00, while the price for that item in the store is $ 120.00, the following calculation must be performed to determine the discount percentage:
150 = 100 120 = X 120 x 100/150 = X 80 = X 100 - 80 = X 20 = X
Therefore, the discount percentage is 20%.
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triangle is an isosceles right triangle in the unit circle. a circle with center a at the origin of an x y plane. explain why . use the pythagorean theorem to explain why .
The Pythagorean Theorem is used to show that the hypotenuse has a length of sqrt(2).
In a unit circle, the radius is always equal to 1 unit. Now, consider an isosceles right triangle with two equal sides of length 1 unit
By the Pythagorean Theorem, the length of the hypotenuse (c) of this triangle can be found as:
\(c^2 = 1^2 + 1^2\)
\(c^2 = 2\)
\(c = sqrt(2)\)
Now, let's consider a circle centered at the origin with a radius of sqrt(2) units. Any point on this circle has coordinates (x, y) such that:
\(x^2 + y^2 = (sqrt(2))^2\)
\(x^2 + y^2= 2\)
This equation represents the unit circle, and any point on the isosceles right triangle we considered earlier also satisfies this equation. Therefore, the isosceles right triangle is inscribed in the unit circle.
In summary, the isosceles right triangle is inscribed in the unit circle because its hypotenuse has a length of sqrt(2) units, which satisfies the equation of the unit circle \((x^2 + y^2 = 1)\). The Pythagorean Theorem is used to show that the hypotenuse has a length of sqrt(2).
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A shipping company uses a formula to determine the cost for shipping a package: c = 2.79 + 0.38p, where c is the cost of shipping and p is the number of pounds. What is the cost of shipping a package that weighs 8 pounds?
Using the formula they gave us:
Cost of shipping = 2.79 + 0.38(8)
Cost of shipping = 2.79 + 3.04
Cost of shipping = 5.83(currency unit)
8 x 10{-3} is how many time greater then 4 x 10{-6}
To find out how many times greater 8 x 10{-3} is than 4 x 10{-6}, we need to divide the larger number by the smaller one. This will give us the ratio of the two numbers.
So, 8 x 10{-3} divided by 4 x 10{-6} can be written as:
(8 / 4) x (10{-3} / 10{-6})
Simplifying this expression, we get:
2 x 10{3}
This means that 8 x 10{-3} is 2,000 times greater than 4 x 10{-6}.
we can break down the process of dividing the two numbers. When we divide 8 by 4, we get 2. Then, when we divide 10{-3} by 10{-6}, we get 10{3}. Multiplying these two results gives us the ratio of 2 x 10{3}. This means that 8 x 10{-3} is 2,000 times greater than 4 x 10{-6}.
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ordered pairs of this equation: f(x)=3-2x
Answer:
Graph in the image
Step-by-step explanation:
Which panda was heavier when born
Answer: The one on the left.
Step-by-step explanation:
There is no file, but the panda on the left is bigger.
What is the vertical shift of the function y = 3x - 8
Answer:
8
-3
___
y
Step-by-step explanation:
Which of the following is a pair of corresponding angles?
Answer:
Step-by-step explanation:
1 and 5
Answer:
The corresponding angles is < 1 & <5Step-by-step explanation:
#stay safeThree of the vertices of a rectangle are located at (5, 2), (8, 2), (5, -5). Find the coordinates of the 4th vertex and then find the area of the rectangle. 4th Vertex (
Question Blank 1 of 2
2,-5
)
Area
Question Blank 2 of 2
type your answer. Units2
Thus, the 4th coordinate of the rectangle with the given coordinates is found as : D(8, -5). Area of the rectangle ABCD = 21 sq. units.
Explain about the distance formula:The Pythagorean theorem serves as the foundation for the distance formula. A line connecting two sites of interest is the hypotenuse of a right triangle, and this particular line connects the two points of interest.
The neighbouring side is obtained by joining the x-coordinates of a two points in a horizontal line, whereas the opposing side is obtained by joining the y-coordinates.
d=√((x2 - x1)²+(y2 - y1)²)
Given data:
vertices of a rectangle ABCD -
A(5, 2), B(8, 2), C(5, -5)
Let the 4 the vertex be D(x,y).
Plot the coordinates on the graph.
Now, we know that - opposite sides of the rectangle are equal.
Thus,
AB = CD
From graph,D(x,y).
x - (5 + 3) = 8
y - (2 - 7) = -5
Thus, the 4th coordinate of the rectangle with the given coordinates is found as : D(8, -5).
Area of the rectangle ABCD = length x breadth
length = 2 + 5 = 7 units
width = 8 - 5 = 3 units
Area of the rectangle ABCD = 7 x 3
Area of the rectangle ABCD = 21 sq. units.
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Triangle RST is given in the coordinate plane. If triangle RST is reflected across
the y-axis, will the corresponding sides of the two triangles be congruent?
No, reflecting triangle RST across the y-axis will not necessarily result in congruent corresponding sides of the two triangles.
What is triangle?
A triangle is a three-sided polygon with three angles. It is a fundamental geometric shape and is often used in geometry and trigonometry.
Reflection across the y-axis involves changing the sign of the x-coordinates of each point in the original triangle. This means that the shape of the triangle will be mirrored across the y-axis, but the lengths of the sides may not remain the same.
To determine if the corresponding sides of the two triangles will be congruent after reflection, you would need to know the specific coordinates of the vertices of triangle RST and perform the necessary calculations.
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150 decreased by 15 percent
Answer:127.5
Step-by-step explanation:
15% of 150 = 22.5
150-22.5=127.5
Answer:
Step-by-step explanation:
3x + 2 – x = 9x – 7x + 5 – 3
Answer:0=0
Step-by-step explanation:
Please help me!
"Explain why this graph shows a function."
Answer:
This graph shows a function because no vertical line passes through more than one point on the graph.
Step-by-step explanation:
GEOMETRY
what method could be used to prove congruency for each of the four triangles? (ASA,SSS,SAS,AAS)
Answer:
ASA, ASA, SAS, SSS
Step-by-step explanation:
i think this is it
Answer:
AsA
Step-by-step explanation:
Estimate ΔyΔy using differentials.
y=cos(5x),=/30,x=0.055
(Give your answer to three decimal places.)
The estimated change in yy using differentials is -0.00679. This means that if xx is increased by 0.005, then yy is estimated to decrease by 0.00679. The differential of yy is dy=-5sin(5x)dxdy=−5sin(5x)dx. We are given that y=cos(5x)=π/30y=cos(5x)=π/30 and x=0.055x=0.055.
We want to estimate ΔyΔy, which is the change in yy when xx is increased by 0.005. We can use the differential to estimate ΔyΔy as follows:
Δy≈dy≈dy=-5sin(5x)dx
Plugging in the values of y, x, and dxdx, we get:
Δy≈-5sin(5(0.055))(0.005)≈-0.00679
Therefore, the estimated change in yy using differentials is -0.00679.
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abc is a right triangle with ab=ac. bisector of <a meets bc at d. prove that bc = 2ad.
Answer:
Let ac=ab=5
With this, bc= 5√2
Step-by-step explanation:
So to find ad, Let ad be x
5√2=(2)(x)
(5√2/2)= x
This proves that bc=2ad
Which expression is equivalent to 1/4(3x+4y) + 3(1/4x+ 2/3y)
The expression is equivalent is 6x/4 + 24y/12
What are algebraic expressions?
Algebraic expressions are described as expressions composed of variables, terms, factors, constants, and coefficients.
These expressions also consisting of mathematical operations, such as;
AdditionParenthesesDivisionSubtractionMultiplicationFloor division, etcGiven the expression;
1/4(3x+4y) + 3(1/4x+ 2/3y)
expand the bracket
3x/4 + 4y/4 + 3/4x + 3/3y
collect like terms
3x/4 + 3/4x + 4y/4 + 3/3y
add like terms
3x + 3x/4 + 12y + 12y /12
add the numerators
6x/4 + 24y/12
Hence, the expression is 6x/4 + 24y/12
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Suppose annual salaries for sales associates from a particular store have a bell-shaped distribution with a mean of $32,500 and a standard deviation of $2,500. Refer to Exhibit 3-3. The z-score for a sales associate from this store who earns $37,500 is
Suppose annual salaries for sales associates from a particular store have a bell-shaped distribution with a mean of $32,500 and a standard deviation of $2,500. Refer to Exhibit 3-3. The z-score for a sales associate from this store who earns $37,500 is
To find the z-score for a sales associate who earns $37,500, we can use the formula:
z = (x - μ) / σ
Where:
x is the value we want to convert to a z-score (in this case, $37,500),
μ is the mean of the distribution (in this case, $32,500), and
σ is the standard deviation of the distribution (in this case, $2,500).
Substituting the given values into the formula, we have:
z = (37,500 - 32,500) / 2,500
z = 5,000 / 2,500
z = 2
Therefore, the z-score for a sales associate who earns $37,500 is 2.
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The z-score for a sales associate earning $37,500 in a system where the mean salary is $32,500 and the standard deviation is $2,500 has a z-score of 2. This score indicates that the associate's salary is two standard deviations above the mean.
Explanation:The z-score represents how many standard deviations a value is from the mean. In this case, the value is the salary of a sales associate, the mean is the average salary, and the standard deviation is the average variation in salaries.
We calculate the z-score by subtracting the mean from the value and dividing by the standard deviation, like so:
Z = (Value - Mean) / Standard Deviation
So, the z-score for an associate earning $37,500 would be:
Z = ($37,500 - $32,500) / $2,500
This gives us a z-score of +2, indicating that a salary of $37,500 is two standard deviations above mean.
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Shama’s age is three times the age of her son Ankit. 10 years ago Shama
was 5 times the age of Ankit. Find the present age of Shama.
Answer:
Step-by-step explanation:
Let sharma age be S and Ankit age be A
S = 3a
(s-10) = 5(a-10)
substitute 1 in 2
3a-10 = 5a -50
40 = 2a
a = 20
s = 3 * 20 = 60
What are the two types of angles that are formed by interacting lines?
In geometry, angles are formed when two lines interact or intersect. There are two main types of angles that are formed by intersecting lines: acute angles and obtuse angles.
Acute angles are angles that measure less than 90 degrees. These angles are smaller in measure than a right angle. They are defined by the point where two lines meet, and the angle formed by the intersection of the lines is acute if the measure of the angle is less than 90 degrees.
Obtuse angles are angles that measure more than 90 degrees. These angles are greater in measure than a right angle. They are defined by the point where two lines meet, and the angle formed by the intersection of the lines is obtuse if the measure of the angle is greater than 90 degrees.
In summary, in geometry, angles are formed when two lines interact or intersect.
There are two main types of angles that are formed by intersecting lines: acute angles which are angles that measure less than 90 degrees, and obtuse angles which are angles that measure more than 90 degrees.
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How many solutions are there to the equation below?
x² = 9
A. O
B. 4
C. 9
D. 1
E. 2
Answer: E. 2
Step-by-step explanation:
x²=9
x=±3 ⇔ since it is square (any value after square will always be positive), the value can be negative or positive.
There are 2 solutions: 3 and -3
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an x-ray test is used to detect a certain disease that is common in 3% of the population the test has the following error 87 per-cent of people who are disease-free to get a positive reaction and 2% of the people who have the disease do get a negative reaction from the test a large number of people are screened at random using the test and those with a positive reaction are further examine what is the probability that a person tested at random indeed has the disease given that the test results shows positive
Let the event D be that a person has the disease.
\(P(D)=\frac{3}{100},P(D^{\prime})=\frac{97}{100}\)Now Let T be positive test and T' be a negative test result.
\(P(T|D^{\prime})=\frac{87}{100},P(T|D)=\frac{13}{100},P(T^{\prime}|D)=\frac{2}{100},P(T^{\prime}|D^{\prime})=\frac{98}{100}\)So the probability that the person has the disease given that the test is positive is given by:
\(\begin{gathered} P(D|T)=\frac{P(D)P(T|D)}{P(D)P(T|D)+P(D^{\prime})P(T|D^{\prime})} \\ =\frac{\frac{3}{100}\times\frac{13}{100}}{\frac{3}{100}\times\frac{13}{100}+\frac{97}{100}\times\frac{87}{100}} \\ =\frac{13}{2826} \\ \approx0.0046 \end{gathered}\)So only 0.46% of the people who tested positive will have the disease.