We reject the null hypothesis since the p-value is less than the significance level of 0.05.
what is null hypothesis ?The null hypothesis in statistics is a claim that presupposes there is no statistically significant distinction among the two or even more variables be compared. The antithesis of the alternative hypothesis, it is frequently denoted as H0 (Ha). While conducting statistical studies, the null is often evaluated to see if there is sufficient proof against it or not. The default assumption is typically the null hypothesis, and it serves as a benchmark for comparison of the statistical analysis's findings. A statistically significant distinction between the variables under comparison is said to exist if the statistical analysis yields sufficient data to refute a null hypothesis.
given
To test the hypothesis, we can utilise a z-test. This is the test statistic:
[tex]z = (x - E) / σ[/tex]
where x is the observed percentage of patients whose conditions are getting better. x = 820 * 0.52 = 426.4 is the result. Therefore:
z = (426.4 - 393.6) / 0.026 = 1245.98
P(Z > z) = 1 - P(Z z) is the p-value for this one-tailed test, where Z is a normal standard variable. By using a typical table or calculator, we discover:
P(Z > 1245.98) < 0.0001
We reject the null hypothesis since the p-value is less than the significance level of 0.05.
We have enough data to draw the conclusion that the percentage of patients whose conditions are improving is more than 0.48.
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Please help studying for next grade.
98+107÷(82-12)x122
Answer:
284.06
Step-by-step explanation:
To solve this expression using the order of operations (PEMDAS), we must first perform the operations inside the parentheses: 82-12 equals 70. Next, we must perform the multiplication and division from left to right: 107 divided by 70 equals approximately 1.53, and 1.53 times 122 equals approximately 186.06. Finally, we add 98 to get our answer. Therefore, the expression 98+107÷(82-12)x122 simplifies to approximately 284.06.
Answer:
284.06
Step-by-step explanation:
got it right on edge
Construct a polynomial function with the following properties: third degree, only real coefficients, −1 and 4+i are two of the zeros, y-intercept is −17 .
The polynomial function with the given properties is:[tex]f(x) = x^3 - 7x^2 + 9x - 17[/tex]
What do you mean by polynomial function?A polynomial function is a function that contains only non-negative integer powers or only positive integer exponents in the equation, such as a quadratic equation, a cubic equation, etc. For example, 2x + 5 is a polynomial whose exponent is 1.
Since the polynomial has real coefficients and one of its zeros is complex, the complex conjugate of 4+ i, which is 4-i, must also be zero. So the three zeros of the polynomial are -1, 4+i and 4-i. To form a polynomial with these zeros, we start by writing the factors of the polynomial:
(x + 1) (x - 4 - i) (x - 4 + i)
We can simplify this expression by multiplying the factors:
[tex](x + 1) (x^2 - 8x + 17)[/tex]
Expanding this, we get:
[tex]x^3 - 7x^2+ 9x - 17[/tex]
Thus, the polynomial function with the given properties is:
[tex]f(x) = x^3 - 7x^2 + 9x - 17[/tex]
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The polynomial function is p(x) = (-17/5)x³ + (34/5)x² + (33/5)x - 16
What do you mean by polynomial function?A polynomial function is a function that contains only non-negative integer powers or only positive integer exponents in the equation, such as a quadratic equation, a cubic equation, etc. For example, 2x + 5 is a polynomial whose exponent is 1.
If -1 is a zero of the polynomial function, then x+1 is a factor of the polynomial. Similarly, if 4+i is a zero, then 4-i is also a zero, because complex roots always occur in conjugate pairs. Therefore, (x+1) and (x - 4 - i)(x - 4 + i) = (x - 4)² + 1 are factors of the polynomial. We can then construct the polynomial function by multiplying these factors:
p(x) = A(x+1)(x - 4 - i)(x - 4 + i)
where A is a constant that we need to determine, and p(x) is the desired third-degree polynomial function.
To determine A, we can use the y-intercept given in the problem. The y-intercept is the value of p(0), so:
p(0) = A(0+1)(0 - 4 - i)(0 - 4 + i) = A(17+4i)
But we also know that p(0) = -17, so:
-17 = A(17+4i)
Solving for A:
A = -17/(17+4i) = (-17/5) + (68/5)i
Therefore, the polynomial function we seek is:
p(x) = [(-17/5) + (68/5)i](x+1)(x - 4 - i)(x - 4 + i)
Expanding the product and simplifying, we get:
p(x) = (-17/5)x³ + (34/5)x² + (33/5)x - 16
This is a third-degree polynomial with only real coefficients, -1 and 4+i are two of the zeros, and the y-intercept is -17.
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50 Points! Multiple choice algebra question. Use the value of the discriminant to determine the number and type of roots for the equation x^2-3x+7=0. Photo attached. Thank you!
The correct option A: 2 complex roots will be obtained from the given quadratic equation.
Explain about the discriminant:The quadratic formula's section under square root is the discriminant.
The number of solutions to the given quadratic equation depends on the discriminant, which can be positive, zero, or negative.
A quadratic equation with a positive discriminant has two unique real number solutions.A repeating real number solution to the quadratic equation is indicated by a discriminant of zero.Both of the answers are not real numbers, according to a negative discriminant.Given quadratic equation:
x² - 3x + 7 = 0 ..eq 1
standard form of quadratic equation:
ax² + bx + c = 0 ..eq 2
On comparing eq 1 and eq 2
a = 1, b = -3 and c = 7
Check the value of discriminant:
D = b² - 4ac
D = (-3)² - 4*1*7
D = 9 - 28
D = - 19
D < 0 (No real roots)
As, rational as well as irrational both are real number, so only option that satisfy the obtained condition is:
A: 2 complex roots.
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Angle & segment relationship
Area & Arc Length
An entomologist writes an article in a scientific journal which claims that fewer than 20 in ten thousand male fireflies are unable to produce light due to a genetic mutation. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is to reject the null hypothesis, state the conclusion in nontechnical terms. Be sure to address the original claim.
a) There is sufficient evidence to support the claim that the true proportion is less than 20 in ten thousand.
b) There is not sufficient evidence to support the claim that the true proportion is less than 20 in ten thousand.
c) There is not sufficient evidence to support the claim that the true proportion is greater than 20 in ten thousand.
d) There is sufficient evidence to support the claim that the true proportion is greater than 20 in ten thousand.
* (3) Find the area of the shaded area 2 of each rectangle. 7 cm 8 cm 12 cm
The area of the shaded region is 73.65 cm².
We have,
The shaded region is a triangle.
Base = x
Height = y
Now,
Using the Pythagorean theorem,
y² = 12² + 10²
y² = 144 + 100
y² = 244
y = √244
And,
x² = 8² + 5²
x² = 64 + 25
x² = 89
x = √89
Now,
Area of the shaded region.
= 1/2 x √89 x √244
= 1/2 x 9.43 x 15.62
= 73.65 cm²
Thus,
The area of the shaded region is 73.65 cm².
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HELP ASAP if ur good with non-linear and increasing lines and choose 2 of the letter A,B,C,D,E
(Please see the picture!)
Extra points nd brainlist!
Answer:
B and D
Step-by-step explanation:
A and C are linear because they are going in a straight line. E is going downwards, so it is decreasing. That leaves B and D, which have exponential growth.
Someone please answer this question
Some forms of cardiovascular disease involve the buildup of plaque on the inside walls of blood vessels. The buildup can put added stress on the heart and vessels, reducing or preventing blood flow to vital organs of the body.
Imagine that the diagram is a circular cross section of a blood vessel. What is the area of the inside of the blood vessel (i.e., the yellow part) in square units? Round your answer to the nearest tenth. The equation for the area of a circle is A = πr2, where A is area, π ≈ 3.14, and r is the radius. Recall that the radius is half of the diameter.
Answer:
153.94 cm2
Step-by-step explanation:
Circle area = π * r² = π * 49 [cm²] ≈ 153.94 [cm²]
π ≈ 3.14159265 ≈ 3.14
d = r * 2 = 7 [cm] * 2 = 14 [cm]
MARK AS BRAINLIEST PLS I TOOK 3 HOURS THINKING ABOUT THIS
For each of the figures write an absolute value equation to satisfy the given solution set -5 and -1
the given solution set {-5, -1} can be obtained by substituting either of the possible solutions into the absolute value equation and verifying that it holds.
what is an equation ?
In mathematics, an equation is a statement that asserts the equality of two mathematical expressions. An equation typically consists of two expressions separated by an equal sign, with the expression on the left side of the equal sign equal to the expression on the right side of the equal sign.
In the given question,
To write an absolute value equation that satisfies a given solution set, we need to consider the definition of absolute value. The absolute value of a number is its distance from zero the number line. Therefore, an absolute value equation can be written as follows:
|expression| = distance
where the expression is the quantity whose absolute value is being taken, and distance is a non-negative value representing the distance from zero. The equation is satisfied if and only if the expression has a distance from zero that matches the given distance.
For the solution set {-5, -1}, we can write the following absolute value equations for the given figures:
A number line with -5 and -1 marked as solutions:
|x + 3| = 2
This equation is satisfied when x = -5 or x = -1, because |-5 + 3| = 2 and |-1 + 3| = 2.
A number line with -5 and -1 equidistant from zero:
|x| = 5
This equation is satisfied when x = -5 or x = 5, because |-5| = 5 and |5| = 5.
Note that for both figures, the given solution set {-5, -1} can be obtained by substituting either of the possible solutions into the absolute value equation and verifying that it holds.
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A restaurant owner orders new plates and spoons based on the information below. • plates are sold in spoons are sold in packages of 9 packages of 12 The restaurant owner orders an equal number of plates and spoons. What is the least number of packages of plates and packages of spoons she should order to have an equal number of plates and spoons?
The least number of packages of plates and spoons will be 12 and 9 respectively so she should order to have an equal number of plates and spoons.
What is inequality?
It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.
Given that, a restaurant owner will use the data below to place new orders for plates and spoons. Packages of nine plates and twelve spoons are available for purchase. Equal quantities of plates and spoons are ordered by the restaurant owner.
For the inequality, we have to apply the arithmetic operation in which we do the multiplication of x and apply the inequality for the given data.
If the plates are sold in packages of 9 and there are 12 packages the number of plates will be 108.
If the plates are sold in packages of 12 and there are 9 packages the number of plates will be 108.
Thus, the least number of packages of plates and spoons will be 12 and 9 respectively so she should order to have an equal number of plates and spoons.
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15 POINTS!!!! PLEASE, I'M BEGGING. 15 POINTS!!!!
Which investment choice has the potential for the greatest rate of return?
Corporate bonds
Government bonds
Common stocks
Preferred stocks
Answer:
mark me as brainliest
Step-by-step explanation:
common stocks
If ƒ (x) = 3x²+1 — 1, what is the value of f(−1), to the nearest ten-thousandth (if necessary)?
Answer:
To find the value of f(-1), we need to substitute -1 for x in the given function:
f(x) = 3x² + 1 - 1
f(-1) = 3(-1)² + 1 - 1
f(-1) = 3(1) + 0
f(-1) = 3
Therefore, f(-1) is equal to 3.
Is (-5, 3) a solution to this system of equations?
y = X-6
y = -2x - 7
yes
no
Answer:
No
Step-by-step explanation:
to determine if (- 5, 3 ) is a solution substitute the x- coordinate into both equations and if the value of y is equal to the y- coordinate then the point is a solution to the system.
y = x - 6 = - 5 - 6 = - 11 ≠ 3
y = - 2x - 7 = - 2(- 5) - 7 = 10 - 7 = 3
since both equations are not satisfied , then
(- 5, 3 ) is not a solution to the system
please help me solve the bonus question
Answer: a = 5 and k = 1/2
Step-by-step explanation:
We are given that the function is defined by:
f(x) = 16 + a(3^(kx))
We need to find the real numbers a and k such that f(0) = 21 and f(4) = 61. Using the given values of f(0) and f(4), we can form a system of two equations:
f(0) = 16 + a(3^(k(0))) = 21
f(4) = 16 + a(3^(k(4))) = 61
Simplifying the first equation, we get:
16 + a(3^0) = 21
16 + a = 21
a = 5
Substituting this value of a into the second equation, we get:
16 + 5(3^(4k)) = 61
5(3^(4k)) = 45
3^(4k) = 9
We know that 3^2 = 9, therefore
4k = 2
=> k = 2/4
=> k = 1/2
Therefore, the real numbers a and k that satisfy the given conditions are a = 5 and k = 1/2. So the function is:
f(x) = 16 + 5(3^(x/2))
The solution to the equation give us an approximate that x = 1.55.
What is the solution to the equation?To solve this equation, we can start by subtracting 4 from both sides to isolate the exponential term:
3.5^x + 4 - 4 = 11 - 4
This simplifies to:
3.5^x = 7
Next, we can take the logarithm of both sides with base 3.5 to eliminate the exponent:
log(3.5^x) = log(7)
Using the property of logarithms that log(a^b) = b*log(a), we can rewrite the left side as:
x*log(3.5) = log(7)
Now, we can solve for x by dividing both sides by log(3.5):
x = log(7) / log(3.5)
Plugging in the values, we get:
x = 0.84509804001 / 0.54406804435
x = 1.55329475566
x ≈ 1.55.
Answered question "Solve the equation 3.5^x + 4 = 11"
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Find measure of angle MNO
The measure of an inscribed angle of a circle is 1/2 the measure of its intercepted arc. In this case, arc OM is the intercepted arc, and 1/2 of 120 degrees is 60 degrees.
a fully inflated basketball has a radius of 12 cm. Your basketball is only inflated halfway. How many more cubic centimeters air does your ball need to fully inflate? Express your answer in terms of pi
Therefore, the basketball needs an additional 2,016π cubic centimeters of air to be fully inflated.
What is volume?In physics and mathematics, volume refers to the amount of space occupied by a three-dimensional object or region of space. The volume of a solid object can be calculated using various formulas, depending on the shape of the object. The concept of volume is used in many areas of science and engineering, including physics, chemistry, architecture, and manufacturing. It is particularly important in fields such as fluid mechanics and thermodynamics, where the flow and behavior of liquids and gases are often analyzed in terms of their volume and the changes in volume that occur during various processes.
Here,
The volume of a fully inflated basketball is given by the formula V = (4/3)πr³, where r is the radius of the ball. In this case, the radius is 12 cm, so the volume of a fully inflated basketball is:
V = (4/3)π(12 cm)³
V = (4/3)π(1728 cm³)
V = 2,304π cm³
To find the volume of a basketball that is only inflated halfway, we need to find the radius of the half-inflated ball. Since the volume of a sphere is proportional to the cube of its radius, we can use the following proportion:
(Volume of half-inflated ball) / (Volume of fully inflated ball) = (Radius of half-inflated ball)³ / (Radius of fully inflated ball)³
Let Vh be the volume of the half-inflated ball, then:
Vh / 2,304π cm³ = (6 cm)³ / (12 cm)³
Simplifying this equation, we get:
Vh = (1/8) * 2,304π cm³
Vh = 288π cm³
Now we can find the additional volume of air needed to fully inflate the ball:
Volume of fully inflated ball - Volume of half-inflated ball = Additional volume of air needed
2,304π cm³ - 288π cm³ = 2,016π cm³
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What is the volume of a rectangular prism that is 120 centimeters by 2 meters by 1.5 meters in cubic centimeters? 3,600,000 cm 3 3,600 cm 3 36,000 cm 3 3.6 cm 3
The volume of the rectangular prism in cubic centimeters is 3,600,000
What is the volume of the rectangular prismFrom the question, we have the following parameters that can be used in our computation:
Dimension = 120 centimeters by 2 meters by 1.5 meters
The volume of the rectangular prism is the product of the dimensions
i.e.
Volume = Length * width * height
Substitute the known values in the above equation, so, we have the following representation
Volume = 120 * 2 * 1.5
Convert to cm
Volume = 120 * 200 * 150
Evaluate
Volume = 3600000
Hence, the volume in cubic centimeters is 3,600,000
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Find the circumference of a child swimming pool that has a radius of 3 feet
The circumference of a child swimming pool is 6π.
What is circumference?
The circumference of a circle or ellipse in geometry is its perimeter. That is, if the circle were opened up and straightened out to a line segment, the circumference would be the length of the arc. The curve length around any closed figure is more often referred to as the perimeter.
Here, we have
Given: A child swimming pool that has a radius of 3 feet.
We have to find the circumference.
The circumference is diameter x π
The diameter is twice the radius
c = 2πr
c = 2π(3)
= 6π
Hence, the circumference of a child swimming pool is 6π.
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Mrs. Harris is making a fruit salad for the 6th grade picnic. She wants each person to get 25 of a cup of fruit. She made a total of 31 cups of fruit salad. Part A: How many complete servings of fruit salad will be served with the amount Mrs. Harris made? Part B: Each cup of fruit salad contains 14 of a banana. How many bananas does Mrs. Harris need to buy for the fruit salad?
Part A: Number of servings is 1.24 servings/person
What is the servings?Part A: To determine the number of complete servings of fruit salad, we need to divide the total amount of fruit salad Mrs. Harris made (31 cups) by the amount she wants each person to get (25 cup/person). Using the formula:
Number of servings = Total amount of fruit salad / Amount per serving
Number of servings = 31 cups / 25 cups/person
Number of servings = 1.24 servings/person
Since we cannot have a fraction of a serving, we round down to the nearest whole number, as we cannot serve a fraction of a fruit salad. Therefore, Mrs. Harris will be able to serve 1 complete serving of fruit salad with the amount she made.
art B:
If each cup of fruit salad contains 1/4 cup of fruit and each serving is 1/4 cup, then each serving contains 1 cup of fruit.
To calculate the number of bananas Mrs. Harris needs, we first need to determine how many cups of bananas are in 31 cups of fruit salad:
31 cups × 1/4 cup of banana per cup of fruit salad = 7.75 cups of bananas
Since each cup of banana contains 14 of a banana, we can multiply the number of cups of bananas by 14 to find the total number of bananas needed:
7.75 cups of bananas × 14 bananas per cup = 108.5 bananas
So Mrs. Harris needs to buy approximately 109 bananas for the fruit salad.
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Given the functions, f(x) = −x+2, and g(x)=5x². Find:
i. f.g(x)
ii. g(f(x))
iii. ƒ.(g(x))²
iv. 8(x-1)
For the functions, f(x) = −x+2, and g(x)=5x²,
a) f∘g(x) = 5x² + 2
b) g(f(x)) = 5x² -20x + 20
c) f∘(g(x))² = 25x⁴
d) g(x - 1) = 5x² - 10x + 5
Here, the functions are: f(x) = −x+2, and g(x)=5x²
a) f∘g(x)
We know that composite function f∘g(x) means f(g(x))
For function f(x) substitute x = g(x)
i.e., f(g(x)) = -(g(x)) + 2
= -(5x²) +2
= 5x² + 2
b) g(f(x))
For function g(x) substitute x = f(x)
i.e., g(f(x)) = 5x²
= 5(-x + 2)²
= 5(x² -4x + 4)
= 5x² -20x + 20
c) f∘(g(x))²
First we find the (g(x))²= (5x²)²
= 25x⁴
Now the composite function f∘(g(x))² would be,
f∘(g(x))² = f((g(x))²)
= -(g(x))²+ 2
= -(g(x))² + 2
d) g(x - 1)
Substitute x = x -1 in function g(x)
g(x - 1) = 5(x - 1)²
= 5(x² - 2x + 1)
= 5x² - 10x + 5
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HELP! Showing all work, solve for x and y and round to nearest tenth
Answer:
x = 67.4°
y = 22.6°
Step-by-step explanation:
The tangent ratio is a trigonometric ratio that relates the ratio of the length of the side opposite an angle in a right triangle to the length of the side adjacent to that angle.
[tex]\boxed{\begin{minipage}{7 cm}\underline{Tangent trigonometric ratio} \\\\$\sf \tan(\theta)=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle.\\\end{minipage}}[/tex]
Angle xThe side opposite angle x is 7.2, and the side adjacent angle x is 3.
Use the tangent trigonometric ratio to find the measure of angle x:
[tex]\begin{aligned}\tan(x)&=\dfrac{7.2}{3}\\x&=\tan^{-1}\left(\dfrac{7.2}{3}\right)\\x&=\vphantom{\dfrac12}67.380135...^{\circ}\\x&=67.4^{\circ}\;\sf (nearest\;tenth)\end{aligned}[/tex]
Therefore, x = 67.4°.
Angle yThe side opposite angle y is 3, and the side adjacent angle y is 7.2.
Use the tangent trigonometric ratio to find the measure of angle y:
[tex]\begin{aligned}\tan(y)&=\dfrac{3}{7.2}\\y&=\tan^{-1}\left(\dfrac{3}{7.2}\right)\\y&=\vphantom{\dfrac12}22.6198649...^{\circ}\\y&=22.6^{\circ}\;\sf (nearest\;tenth)\end{aligned}[/tex]
Therefore, y = 22.6°.
4(x-1)-2x<6-5(x+2) so love and graph the inequality
The vertical line at x=0 represents the boundary of the inequality, and the shaded region to the left of the line represents the solution set of the inequality, x < 0.
Explain the term inequality
Inequality refers to the unequal distribution of resources, opportunities, and rewards among individuals or groups within a society. It can be based on factors such as race, gender, income, education, and social status, leading to disparities in outcomes and experiences.
According to the given information
Start by simplifying the inequality using the distributive property and combining like terms:
4(x-1) - 2x < 6 - 5(x+2)
4x - 4 - 2x < 6 - 5x - 10
2x - 4 < -5x - 4
2x + 5x < 4 - 4
7x < 0
x < 0
So the solution to the inequality is x < 0.
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PLEASE HELP FOR 100 POINTS Polygon KLMN is drawn with vertices at K(0, 0), L(5, 2), M(5, −5), N(0, −3). Determine the image vertices of K′L′M′N′ if the preimage is rotated 270° clockwise.
K′(0, 0), L′(−2, 5), M′(5, 5), N′(3, 0)
K′(0, 0), L′(−2, −5), M′(−5, 5), N′(−3, 0)
K′(0, 0), L′(−5, −2), M′(5, −5), N′(3, 0)
K′(0, 0), L′(−5, −2), M′(−5, −5), N′(0, 3)
Answer: a
Step-by-step explanation:
Suppose the odds for a bet are 11: 1. Your friend tells you that he thinks the odds are too generous. Select all of the odds that are less generous.
Answer
Select all that apply.
19:1
14:1
15:1
4:1
Answer:
The odds that are less generous are 19:1, 14:1, and 15:1.
Step-by-step explanation:
You have to see which numbers are greater than 11.
if k(x) = 3x, then f'(x)=? A. x³Ln3 B. 3xLn3 C. 3x/Lnx D. 3/3xLn3
The closest answer is 3xLn3 which is (B).
Solving the differential equationIf k(x) = 3x, then f(x) can be expressed as the integral of k(x) with respect to x:
f(x) = ∫ k(x) dx = ∫ 3x dx = (3/2)x² + C
where C is the constant of integration.
To find f'(x), the derivative of f(x) with respect to x, we simply differentiate the expression for f(x):
f'(x) = d/dx [(3/2)x² + C] = 3x
What is differential equation?A differential equation is a mathematical equation that relates a function and its derivatives. Specifically, a differential equation describes how a quantity changes as a function of its own rate of change.
Differential equations are commonly used in physics, engineering, and other sciences to model and analyze natural phenomena.
For example, the motion of a simple pendulum can be described using a differential equation that relates the position and velocity of the pendulum to its acceleration and the forces acting upon it.
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8.05 Tides Model Project
*100 points!!!*
Please fill out each slide here are the steps of what type of math you should be doing. There is more info in the link that has the slideshow you need to fill out.
-Determine the amplitude of a sinusoidal function from a graph.
-Determine the equation of the midline of a sinusoidal function from a graph.
-Determine the maximum value of a sinusoidal function from a graph.
-Determine the minimum value of a sinusoidal function from a graph.
-Determine the period of a sinusoidal function from a graph.
-Sketch the graph of a trigonometric function, given a description of the situation it r-represents.
-Graph a sinusoidal function, given characteristics of the function.
-Graph a trigonometric function, given its equation in any form.
-Determine the trigonometric function equation that represents a mathematical or real-world situation.
THANK YOU!!!
It should be noted that to determine the amplitude of a sinusoidal function from a graph:
Identify the highest point (peak) and the lowest point (valley) of the graph of the sinusoidal function.
Find the vertical distance between the peak and the midline of the graph (the line halfway between the highest and lowest points).
The amplitude of the sinusoidal function is half of this vertical distance.
To determine the equation of the midline of a sinusoidal function from a graph:Identify the highest point (peak) and the lowest point (valley) of the graph of the sinusoidal function.
Find the vertical coordinate of the midline of the graph (the line halfway between the highest and lowest points).
Write the equation of the midline as y = the vertical coordinate of the midline.
To determine the maximum value of a sinusoidal function from a graph:
Identify the highest point (peak) of the graph of the sinusoidal function.
The maximum value of the sinusoidal function is the vertical coordinate of this peak.
To determine the minimum value of a sinusoidal function from a graph:
Identify the lowest point (valley) of the graph of the sinusoidal function.
The minimum value of the sinusoidal function is the vertical coordinate of this valley.
To determine the period of a sinusoidal function from a graph:
Identify two consecutive peaks or valleys of the graph of the sinusoidal function.
Find the horizontal distance between these two points.
The period of the sinusoidal function is twice this horizontal distance.
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Find the degree of the monomial. -3q4rs6
Therefore, the degree of the given monomial is 11.
What is monomial?In algebra, a monomial is an expression consisting of a single term. A term can be a constant, a variable, or the product of a constant and one or more variables. In other words, a monomial is a polynomial with only one term. The degree of a monomial is the sum of the exponents of its variables.
Here,
The degree of a monomial is the sum of the exponents of its variables.
For the monomial -3q⁴rs⁶, the degree would be:
4 + 1 + 6 = 11
Therefore, the degree of the monomial -3q⁴rs⁶ is 11.
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anyone know what the area of triangle ABC is?
The area of triangle ABC is 6cm²
What is a triangle?A triangle is a three-sided polygon that consists of three edges and three vertices. It is also known as the trigon and has special names such as the hypotenuse (opposite the right angle) and legs (the other two sides). It can also refer to a percussion instrument consisting of a rod of steel bent into the form of a triangle open at one angle.
The area of the triangle is given as
Area= 1/2absinC
But the CosB = Adj/Hypo
Cos60 = Adj/12
1/2 = Adj/12
corss and multiply to have
2A = 12
Therefore Adj = 6
Therefore base = 6*2 = 12
Applying the formula we have Area= 1/2acsinB
Area = 1/2* 12*12*Cos60
Area = 12*1/2 =6cm²
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The table shows Gillian’s Net worth. Assets are shown as positive numbers, and liabilities are shown as negative numbers. Gillian’s net worth is $90,500. Based on the information in the table, what is the number of money Gillian owes for student loan?
Answer:
Step-by-step explanation:
Angle & segment relationship
Area & Arc Length
Answer:
x = 81.5°
Step-by-step explanation:
the secant- tangent angle x is half the difference of the measures of the intercepted arcs.
the sum of the arcs in a circle = 360°, then
unknown intercepted arc = 360° - (215 + 93)° = 360° - 308° = 52°
then
x = [tex]\frac{1}{2}[/tex] (215 - 52)° = [tex]\frac{1}{2}[/tex] × 163° = 81.5°