Given: An angle of measure 115 degrees We know that: The supplement of an angle is equal to 180 degrees minus the angle, and the complement of an angle is equal to 90 degrees minus the angle
Now, we need to find the complement of the supplement of an angle measuring 115 degrees.So, let's first find the supplement of the given angle:
Supplement of 115 degrees = 180 - 115= 65 degrees
Now, we need to find the complement of the above angle which is:
Complement of 65 degrees = 90 - 65= 25 degrees Therefore, the complement of the supplement of an angle measuring 115º is 25 degrees.
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What z-score value separates the highest 70% of the scores in a normal distribution from the lowest 30%?
a. z = 0.52
b. z = 0.84
c. z = -0.84
d. z = -0.52
Using the normal distribution, the value that separates the highest 70% of the scores in a normal distribution from the lowest 30% is:
z = -0.52.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The value that separates the highest 70% of the scores in a normal distribution from the lowest 30% is is the 30th percentile, which is Z with a p-value of -0.3, hence z = -0.52.
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If the value of the sample standard deviation increases, what happens to the confidence interval?
If the value of the sample standard deviation increases, the confidence interval becomes wider and is denoted as option A.
What is Confidence interval?This term is used in statistics and refers to the probability that a population parameter will fall between two set values.
it has a direct relationship with standard deviation in which its increase will also lead to the set of values being wider thereby making it the most appropriate choice.
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The options are :
a. It becomes wider
b. It becomes more precise
c. It does not change
d. It narrows
Find the present value of a loan with a maturity value of $15,000 for 9 months at 6%.
Present value of the loan amount is $[tex]27[/tex] with a maturity value of $[tex]15000[/tex] for [tex]9[/tex] months at [tex]6[/tex]%
How to find the present value of loan amount ?
We know that
Maturity value of loan amount [tex]= 15000[/tex]
Time period is [tex]=9[/tex] months
Rate (r)[tex]=6[/tex] %
Present value of loan amount=?
So we can use the formula of maturity level
[tex]MV=PV*(1+r*t)[/tex]
Substitute the values
[tex]15000=PV *(1+6*9)\\15000=PV(55)\\\frac{15000}{55} =PV\\27.27=PV[/tex]
So present value of the loan amount is $[tex]27[/tex] in round figure.
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Write the standard equation of a circle that passes through(-4,0) with center (-1,-4)
The standard equation of the circle is x² + y² + 8x - 9 = 0 if the circle with center at (-1,-4) that passes through the point (-4,0).
According to the question,
The circle with center at (-1,-4) that passes through the point (-4,0).
To find the radius of the circle:
Radius r = √[(-4 - (-1))² + (0- (-4))²]
=√(-4+1)² + (4)²
=√9+16
=√25
=5.
In order to find the standard equation of the circle is
(x - (-4))² + (y - (0))² = (5)²
(x + 4)² + (y )² = 25
x² + 8x + 16 + y² = 25
x² + y² + 8x + 16 = 25
x² + y² + 8x = 25 - 16
x² + y² + 8x = 9
x² + y² + 8x - 9 = 0
Hence, the standard equation of the circle is x² + y² + 8x - 9 = 0.
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What is the minimum point on the graph of the equation y=f(x)+5 ?
Answer:
Step-by-step explanation:
This function will have a minimum point only if f(x) has one.
Examples:
y = x + 5: straight line with no minimum
y = x^2 + 5: parabola that opens up and has vertex at (0, 5); thus, the minimum is (0, 5)
What f(x) did you have in mind? Please share it.
A hypothesis test is conducted at the 0.05 level of significance to test whether or not the population correlation is zero. If the sample consists of 25 observations and the correlation coefficient is 0.60, what conclusion should be drawn
3.60
t = r√n − 2/1 − √r2
= 0.6√25 − 2/√1 − 0.62
= 3.5969 t or about 3.60 rounded to two decimal places.
Hypothesis Testing:
Hypothesis testing is a form of statistical inference that uses data from a sample to draw conclusions about a population parameter or a population probability distribution. First, a tentative assumption is made about the parameter or distribution. This assumption is called the null hypothesis and is denoted by H0.
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Katie has 100 apples, and she plans on eating 2 of them every day.
True or false...the number of apples Katie has left is proportional to the number of days that pass.
Consider the polynomial function of g(x)= -2x^8 +5x^6 -3x^5+50
Answer:
C) as x –> ∞, q(x) –> –∞, and as x –> -∞, q(x) –> –∞
Step-by-step explanation:
use the end behavior chart to figure out the end directions of the graph. remember these
E O
+|↑↑|↓↑
–|↓↓|↑↓
all you need to do is look at the first number of the equation and ask yourself:
1. Is the first number even or odd?
2. is the first number positive or negative?
find where the answers to both meet on the chart.
so, in this question, the first number is even and negative. when using the chart we see that they meet at the ↓↓ which means that the end behavior on both sides is going towards negative infinity.
if three pies require 2 dozen apples, then four bird require ? dozen apples?
The inverse variation equation shows the relationship between wavelength in meters, x, and frequency, y. y = startfraction 3 x 10 superscript 8 baseline over x endfraction what is the wavelength for radio waves with frequency 3 × 109?
The wavelength for radio waves with frequency 3 × 10⁹ Hz is 0.1 m.
What's the relation between frequency and wavelength of electromagnetic waves?For electromagnetic waves travelling in vaccum, the product of frequency and wavelength is the speed of light in vaccum.Mathematically, frequency × wavelength = 3×10⁸ m/s (which is speed of light)So, wavelength= 3×10⁸/ frequencyWhat's the wavelength of radio wave with frequency 3×10⁹ Hz ?Wavelength of the radio wave= 3×10⁸/3×10⁹ = 0.1 m
Thus, we can conclude that the wavelength of the radio wave with frequency of 3 × 10⁹ Hz is 0.1 m.
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Two ways to measure the relationship between the returns of two securities are ______ and blank______.
a. standard deviation
b. variance
c. covariance
d. correlation
Two ways to measure the relationship between the returns of two securities are correlation and covariance. That is options C and D.
What is Correlation?Correlation can be defined as the measure of the difference between two variables in a statistical analysis.
Covariance can be defined as the measure of the relationship between two variables in statistical analysis.
Therefore, Two ways to measure the relationship between the returns of two securities are correlation and covariance.
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As a rule of thumb, the sampling distribution of the sample proportion can be approximated by a normal probability distribution when _____
As a rule of thumb, when each component is selected independently from the same population, the sampling distribution of the sample percentage may be estimated by a regular probability distribution.
Why is it crucial to use the thumb rule?One of our primary, simple-to-learn ways to handle complexity is the rule of thumb. Real thumb rules take into account operating, security, and financial constraints. They inform us of the likely location of a practical solution. Additionally, they reveal which tactics are most prone to failure.What is sampling distribution?A statistic that is obtained by sampled data from a bigger population is known as a sampling distribution. It depicts an array of potential results that may result from a statistic, such as the mean or mode of a certain parameter because there is really a population.Therefore the main solution is- from the identical group, each component is individually chosen.
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Marissa is painting her rectangular patio, with the exception of a bench that does not need to be painted: rectangle with a length of x plus 20 and width of x plus 10 with a rectangle in the bottom right corner labeled bench that has a length of 6 and width of 2 write an equation to determine the area, a, of the patio that will be painted. a = (x 20)(x 10) 12 a = (x 20)(x 10) − 12 a = (x 26)(x 12) a = (x 14)(x 8)
The area of the rectangular patio to be painted is: B. A = (x + 20)(x + 10) - 12.
What is a Rectangle?A rectangle, by definition, is a quadrilateral with two pairs of opposite that have the equal lengths. All four angles of a rectangle are right angles (90 degrees).
What is the Area of a Rectangle?The area of a rectangle = (length of rectangle)(width of rectangle).
Given the following parameters for the patio and the bench:
Length of rectangular patio = x + 20Width of rectangular patio = x + 10Length of rectangular bench = 6Width of rectangular bench = 2Area to be painted = area of rectangular patio - area of rectangular bench
Area of rectangular patio = (x + 20)(x + 10)
Area of rectangular bench = (6)(2) = 12
Area to be painted = (x + 20)(x + 10) - 12
The answer is: B. A = (x + 20)(x + 10) - 12.
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Lola has collected 935 buttons. what is the number of buttons rounded to the nearest ten?
Answer:
940
Step-by-step explanation:
Since there is a 5 in the ones spot we round the number is the tens spot up by 1: 935 --> 940
what is the domain of f(x)=√11-x?
The domain of the function f(x) is:
11 ≥ x
What is the domain of the function f(x)?
Here we have the function:
[tex]f(x) = \sqrt{11 - x}[/tex]
Now, remember that the argument of a square root can only be a number equal to or larger than zero, so the domain of our function is defined by:
11 - x ≥ 0
Then, solving this for x, we get:
11 ≥ x
Concluding, the domain of the function f(x) is:
11 ≥ x
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help please a.-5 b.-1/5 c1/5 d.5
Answer:
-5
Step-by-step explanation:
Slope is rise over run. The graph decreases by 5 units every 1 unit to the right, so the slope is -5.
Find the midpoint of points A(-9, -3) and B(1, 7) graphically.
Plot the line segment AB
Answer: (-4,2)
Step-by-step explanation:
To find the midpoint of AB, we have to find the mean of the x coordinates for the x coordinate of the midpoint and the mean of the y coordinates for the y coordinate of the midpoint
So the midpoint is ((-9+1)/2,(-3+7)/2) = (-4,2)
To plot the line AB, just find the points A and B on the graph and draw a straight line from A to B
Help me:-
Distribute to create an equivalent expression with the fewest symbols possible.
4(5+y) =
Answer:
20 + 4y
Step-by-step explanation:
The 4 multiplies the 5 and the y, i.e., it distributes over the terms of the expression in ( ).
Determine the value of x and y, show calculations
The value for x and y are 140° and 70° respectively.
How to solve Polygon QuestionThere are two ways to solve polygon question. Formula for the sum of interior angle and sum of the exterior angle of regular polygon.
Sum of the interior = (n - 2)180
Sum of the exterior = 360/n
Where n = number of sides of a polygon.
The regular polygon in which x is one of its angle is called decagon
Sum of the interior = (n - 2)180
n = 10
Substitute n into the formula
Sum of the interior angle = (10 - 2)180
Sum of the interior angle = (8)180
Sum of the interior angle = 1440
Each angle = 1400/10
x = 140°
For y, the three angles are similar.
sum of angle in a triangle = 180
Since the each triangle is an isoceles triangle, angle at each base will be y
40 + y + y = 180
2y = 180 - 40
2y = 140
y = 70°
Therefore, the value for x and y are 140° and 70° respectively.
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Find the smallest number by which 1008 must be multiplied to get a perfect square. also, find the square root of the perfect square so obtained
Answer:
7
Step-by-step explanation:
we have 1008=2×2××2×3×3×3
The smallest whole number is 7, by which 1008 should be multiplied so as to get a perfect square.
Now 1008×7=2×2×2×2×3×3×7×7
7056=2×2×3×7
=84
Answer : 7
Answer:
1. 7
2. square root is 84.
Step-by-step explanation:
First find the prime factors:
1008 =2*2*2*2*3*3*7
There's an even number of 2's and 3's but only one 7, so we multiply by 7
Smallest number = 7.
The square number is 1008 * 7
= 7056.
Its square root is 2*2*3*7 = 84.
Which polynomial is a quintic trinomial?
A. -x^4-5x^2
B. x^3+2x^2−8x+16
C. x² + 4
D. 3x^5+7x^2−9x^4
Answer:
D
Step-by-step explanation:
a quintic polynomial is a polynomial of degree 5
A is a polynomial of degree 4 (- [tex]x^{4}[/tex] term )
B is a polynomial of degree 3 (x³ term )
C is a polynomial of degree 2 ( x² term )
D is a polynomial of degree 5 ( 3[tex]x^{5}[/tex] term )
ordenada al origen 6 = paralela a la recta 2x+3y+4=0
La ecuación de la recta que contiene el punto (x, y) = (0, 6) y es paralela a la recta 2 · x + 3 · y + 4 = 0 es igual a 2 · x + 3 · y - 18 = 0.
¿Cómo determinar la ecuación de una recta?
En esta pregunta tenemos que derivar una ecuación de la recta a partir de una recta y un punto. Dos rectas bajo forma implícita son paralelas si y solo si comparten los mismos coeficientes dependientes, entonces tenemos que el coeficiente independiente de la recta es:
2 · 0 + 3 · 6 + k = 0
18 + k = 0
k = - 18
Por tanto, la ecuación de la recta que contiene el punto (x, y) = (0, 6) y es paralela a la recta 2 · x + 3 · y + 4 = 0 es igual a 2 · x + 3 · y - 18 = 0.
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prove that 3+2√5 is irrational
Step-by-step explanation:
To prove that 3 + 2√5 is an irrational number, we will use the contradiction method.
Let us assume that 3 + 2√5 is a rational number with p and q as co-prime integers and q ≠ 0
⇒ 3 + 2√5 = p/ q
⇒ 2√5 = p/ q - 3
⇒ √5 = (p - 3q ) / 2q
⇒ (p - 3q ) / 2 q is a rational number.
However, √5 is an irrational number
This leads to a contradiction that 3 + 2√5 is a rational number.
How many different 4 digit numbers can be formed using only digits 1,2,3 and 4 given that they contain each of these digits as many times as you want?
Answer: 4
Step-by-step explanation:
yeh
Solution
We can start with the pythagorean theorem:
(leg 1)2 + (leg 2)² = (hypotenuse)²
Solve for x.
Substitute the values we know.
18² + x² = 27²
x=0√O
Step-by-step explanation:
324+x²=729
x²=405===> x=√405===> 9√5
The pythagorean theorem (leg 1)2 + (leg 2)² = (hypotenuse)² the values is about 8.5, -8.5.
The Pythagorean theorem is used to find the length of the sides of a right triangle, not for solving equations like x² = 72.
To solve the equation x² = 72, to take the square root of both sides to find the value of x:
√(x²) = √(72)
Since the square root of x² is x (the absolute value of x), the equation simplifies to:
x = √(72)
Now, let's find the approximate value of √(72):
√(72) ≈ 8.49
So, the equation becomes:
x≈ 8.49
Now, remember that the absolute value of x is a positive value, so the equation gives two possible solutions for x:
x= 8.49 → x = 8.49
x = -8.49 → x = -8.49
Rounded to the nearest tenth, the solutions are:
x ≈ 8.5 and x ≈ -8.5
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What equation shows that 9 is a factor of 72?
The equation that shows that 9 is a factor of 72 is given as 9 * 8 = 72
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The equation that shows that 9 is a factor of 72 is given as 9 * 8 = 72
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The diameter of the earth
at the equator is about
8.000 mi.
Based on this figure, how
far is it around the earth?
Answer:
25,132.74 miles
Step-by-step explanation:
Hello!
We are basically asked to find the circumference of the Earth's cross-section.
Circumference: [tex]C = 2\pi r[/tex]
We can replace 2r with the diameter, because the diameter is 2 times the radius.
Multiply the Diameter by pi:
[tex]C = \pi D[/tex][tex]C = 8000\pi[/tex][tex]C = 25,132.7412287183 \approx 25,132.74[/tex]It is around 25,132.74 miles around.
A rectangle's area is given by the expression 6–² -- − n +9. The width of the rectangle is 3n². w = 3n² A = 6n² − n +9
The length of the rectangle = 2 - (1/3n) +(3/n²).
How to estimate the length of a rectangle?
The formula for the area (taking this exists as a rectangle)
Area = length ⋅ width
where A exists the area of the rectangle
l exists the length of the rectangle and w exists the width of the rectangle.
If Area of the rectangle = length ⋅ width
then length of the rectangle = area/ width
Area = 6n² − n +9
width = 3n²
Area = length [tex]*[/tex] width
length = area/ width
= (6n² − n +9)/3n²
= 2 - (1/3n) +(3/n²).
The length of the rectangle = 2 - (1/3n) +(3/n²).
Therefore, the correct answer is option A. 2 - (1/3n) +(3/n²).
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The graphs below have the same shape. What is the equation of the red
graph?
Answer:
[tex]G(x) = x^{3} -1[/tex]
Step-by-step explanation:
The red graph is the blue graph translated 1 unit down, so the answer is A.
y square plus 5y equals to 0
Answer:
y^2 + 5y = 0
y(y + 5) = 0
y = 0, -5
The answer is y = 0 and y = -5.
The given question :
y² + 5y = 0y (y + 5) = 0y = 0, y = -5