The expressions that have the same value are: b) 3^4 = 81 and e) 9^2 = 81
Selecting all expressions that have the same value.To compare the expressions, we can simplify them using the rules of exponents:
a) 3^3 = 27
b) 3^4 = 81
c) 6^2 = 36
d) 6^3 = 216
e) 9^2 = 81
f) 9^3 = 729
Using the above as a guide, we have the following:
Therefore, the expressions that have the same value are: b) 3^4 = 81 and e) 9^2 = 81
So, options b and e have the same value.
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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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Translate this sentence into an equation.
Answer:
24 + c = 40
C= Chau’s height
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.
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.
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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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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PLS HELP!!
Which expressions are equivalent to log4 (1/4x^2)?
Answer:log₄ 1 /4 + log₄ x²
Step-by-step explanation:
Anthony has decided to purchase a $19,000 car. He plans to put 20% down toward the purchase and to finance the rest at a 6.8% interest rate for 4 years. Find his monthly payment.
Find the total price Anthony paid for his vehicle.
The monthly payment and total price paid by Antony at interest rate of 6.8% for vehicle is $362.59 and $21204.4 respectively.
Cost price of the car Antony decided to purchase = $19,000
Down payment = 20% of purchase value
Interest rate of amount to be finance = 6.8%
Time period of finance amount = 4 years
Down payment = 0.2 × $19,000
= $3,800
Amount that Anthony needs to finance,
Amount to finance = $19,000 - $3,800
= $15,200
The monthly payment , use the formula for the monthly payment on a loan,
M = P × r × (1 + r)ⁿ / ((1 + r)ⁿ - 1)
where M is the monthly payment,
P is the principal the amount to finance
r is the monthly interest rate
n is the total number of payments which is the number of years multiplied by 12
The monthly interest rate is 6.8% / 12 = 0.00567,
and the total number of payments is 4 × 12 = 48.
Substituting these values into the formula, we get,
⇒M = $15,200 × 0.00567 × (1 + 0.00567)⁴⁸ / ((1 + 0.00567)⁴⁸ - 1)
⇒M = $15,200 × 0.00567 × 1.3118 / (1.3118 -1)
⇒M = $15,200 × 0.00567 × 1.3118 / 0.3118
⇒M = 113.056 / 0.3118
⇒M ≈ $362.59
Anthony's monthly payment will be about $362.59
Total price that Anthony paid for his vehicle,
add up the down payment and the total amount of payments over the 4-year period.
Total price = $3,800 + ( $362.59 × 48)
= $21204.4
Therefore, the monthly payment and the total price at interest rate of 6.8% that Anthony paid for vehicle is $362.59 and $21204.4 respectively.
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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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A swim team consists of 7 boys and 7 girls. A relay team of 4 swimmers is chosen at random from the team members. what is the probability that 3 boys are selected for the relay team given that the first selection was a girl? express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
The probability of selecting 3 boys for the relay team given that the first selection was a girl is approximately 0.055945 or 8/143.
What is probability?Probability is a way to gauge how likely or unlikely something is to happen. It is denoted by a number between 0 and 1, with 1 denoting a certain event and 0 denoting an impossibility.
According to question:Let's start by calculating the probability of selecting a girl first. Since there are 7 girls and 14 team members in total, the probability of selecting a girl first is:
P(Girl first) = 7/14 = 1/2
Now, we need to calculate the probability of selecting 3 boys from the remaining 13 team members (6 boys and 7 girls). We can do this using combinations:
Number of ways to select 3 boys from 6 = C(6,3) = 20
Number of ways to select 1 girl from 7 = C(7,1) = 7
Total number of ways to form a relay team of 4 from 13 = C(13,4) = 715
Therefore, the probability of selecting 3 boys from the remaining 13 team members is:
P(3 boys from 13) = (20*7)/715 = 4/143
Finally, we can use conditional probability to calculate the probability of selecting 3 boys given that the first selection was a girl:
P(3 boys | Girl first) = P(3 boys from 13)/P(Girl first)
= (4/143)/(1/2)
= 8/143
= 0.055944...
Rounded to the nearest millionth, the probability is 0.055945.
Therefore, the probability of selecting 3 boys for the relay team given that the first selection was a girl is approximately 0.055945 or 8/143.
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A Norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular window. Find the dimensions of a Norman window of maximum area when the total perimeter is 20 feet.
As a result, when the entire circumference is 20 feet, the Norman window's maximum area measurements are as follows: x = 8 feet, or around 2.546 feet, is the width, Height: 9.087 feet, or about y = 16 - 16/feet.
Define Perimeter.Perimeter is the total distance around the boundary of a two-dimensional shape, such as a polygon, a circle, or a rectangle. It is the sum of the lengths of all sides or edges of the shape.
Define Area.Area is a measure of the size or extent of a two-dimensional surface or region. It is the amount of space enclosed within a closed shape or boundary.
Let's assume that the width of the rectangular part of the window is x and the height is y.
The perimeter of the window is given by:
Perimeter = width + height + semicircle circumference
Perimeter = x + y + πx/2
We are given that the total perimeter is 20 feet, so we can write:
x + y + πx/2 = 20
We can solve for y in terms of x:
y = 20 - x - πx/2
The area of the window is given by:
Area = rectangular part area + semicircle area
Area = xy + πx^2/8
We can substitute the expression we obtained for y into the equation for the area:
Area = x(20 - x - πx/2) + πx^2/8
Simplifying this expression, we get:
Area = 20x - (π/2)x^2 + πx^2/8
Area = 20x - (π/2)x^2/4
To find the maximum area, we can take the derivative of the area function with respect to x and set it equal to zero:
d/dx (Area) = 20 - (π/2)x/2 = 0
Solving for x, we get:
x = 8/π
Substituting this value back into the expression for y that we obtained earlier, we get:
y = 20 - 8/π - π(8/π)/2 = 20 - 4π/π - 16/π = 20 - 4 - 16/π = 16 - 16/π
Therefore, the dimensions of the Norman window of maximum area when the total perimeter is 20 feet are:
Width: x = 8/π feet (approximately 2.546 feet)
Height: y = 16 - 16/π feet (approximately 9.087 feet)
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The dimensions of the Norman window of maximum area when the total perimeter is 20 feet are:
Width: x = 8/π feet (approximately 2.546 feet)
Height: y = 16 - 16/π feet (approximately 9.087 feet)
Define Perimeter.Perimeter is the total distance around the boundary of a two-dimensional shape, such as a polygon, a circle, or a rectangle. It is the sum of the lengths of all sides or edges of the shape.
Define Area.Area is a measure of the size or extent of a two-dimensional surface or region. It is the amount of space enclosed within a closed shape or boundary.
Let's assume that the width of the rectangular part of the window is x and the height is y.
The perimeter of the window is given by:
Perimeter = width + height + semicircle circumference
Perimeter = x + y + πx/2
We are given that the total perimeter is 20 feet, so we can write:
x + y + πx/2 = 20
We can solve for y in terms of x:
y = 20 - x - πx/2
The area of the window is given by:
Area = rectangular part area + semicircle area
[tex]Area = xy + \pi x^{2/8[/tex]
We can substitute the expression we obtained for y into the equation for the area:
[tex]Area = x(20 - x - \pi x/2) + \pi x^{2/8[/tex]
Simplifying this expression, we get:
[tex]Area = 20x - (\pi /2)x^2 + \pi x^{2/8[/tex]
[tex]Area = 20x - (\pi /2)x^{2/4[/tex]
To find the maximum area, we can take the derivative of the area function with respect to x and set it equal to zero:
d/dx (Area) = 20 - (π/2)x/2 = 0
Solving for x, we get:
x = 8/π
Substituting this value back into the expression for y that we obtained earlier, we get:
y = 20 - 8/π - π(8/π)/2 = 20 - 4π/π - 16/π = 20 - 4 - 16/π = 16 - 16/π
Therefore, the dimensions of the Norman window of maximum area when the total perimeter is 20 feet are:
Width: x = 8/π feet (approximately 2.546 feet)
Height: y = 16 - 16/π feet (approximately 9.087 feet)
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Find the missing side
Please help
Answer:
The answer is D. 4(sqrt(5))
Step-by-step explanation:
To find this we use the Pythagorean Theorem a^2+b^=c^2
So making 4 = to a, and 8 = to, and x = to, we do
4^2+8^2= 80
Then we take the square root of 80 to find the missing side, which is equal to 4(sqrt(5)
Good luck!
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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1.montrer que résoudre ce problème revient a résoudre l'inéquation 20x-x²>0
Answer:
sorry I just wanted points
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
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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HELP PLEASE!!
refer to picture!!
The null and alternative hypotheses that apply are as follows:
H0: p ≤ 0.54, which claims that the proportion of pupils finishing class with a grade of A, B, or C in this experimental curriculum is no greater than 54%.
H₁: p > 0.54, according to the alternative hypothesis, asserts that the rate of students concluding the course with an A, B, or C grade in its experimental form must be above 54%.
How to explain the hypothesisThe letter "p" represents the proportion of student grades in the experimental program who reach either A, B, or C levels.
The null hypothesis is that the proportion of pupils finishing class with a grade of A, B, or C in this experimental curriculum is no greater than 54%.
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PLEASE HELP! An ethanol railroad tariff is a fee charged for shipments of ethanol on public railroads. An agricultural association publishes tariff rates for railroad-car shipments of ethanol. Assuming that the standard deviation of such tariff rates is $1200, determine the probability that the mean tariff rate of 400 randomly selected railroad-car shipments of ethanol will be within $80 of the mean tariff rate of all railroad-car shipments of ethanol. Interpret your answer in terms of sampling error. The probability is what?
(Round to three decimal places as needed.) Thanks!
The likelihood that the average tariff rate of 400 shipments of ethanol picked at random will be inside $80 of the average tariff rate of all shipments is roughly 0.789, or 78.9%.
What is probability?The probability that an event will occur or that a proposition is true is quantified by probability theory, a branch of mathematics. A number from zero to one, where 0 approximately indicates how likely the event will happen and 1 generally indicates certainty, is the probability given an occurrence. In mathematics, probability is a measure of how likely an event is to take place. Probability levels can also be expressed as percent between 0 and 100 percent in addition to the numerals 0 to 1. the percentage of all outcomes out of all equally likely alternatives that lead to a specific occurrence, represented as a ratio.
given,
To solve this problem, we need to use the central limit theorem, which states that the distribution of sample means is approximately normal, with mean equal to the population mean and a standard deviation determined by dividing the population's standard deviation by the sample size square root.
We are given that the standard deviation of the population of tariff rates is $1200. Let mu be the population mean tariff rate, and x-bar be the sample mean tariff rate. We want to find the probability that the sample mean is within $80 of the population mean, i.e., |x-bar - mu| <= $80.
Using the formula for the standard error of the mean, we have:
SE = sigma/sqrt(n) = $1200/sqrt(400) = $60
Now, we can standardize the variable z = (x-bar - mu)/SE, and find the probability of |z| <= 80/60 = 4/3 using a standard normal distribution table or calculator.
P(|z| <= 4/3) = 0.7887
Therefore, the probability that the mean tariff rate of 400 randomly selected railroad-car shipments of ethanol will be within $80 of the mean tariff rate of all railroad-car shipments of ethanol is approximately 0.789 or 78.9% (rounded to three decimal places).
Interpretation: Sampling error refers to the natural variation in sample statistics (such as the sample mean) that occurs due to chance, even when the sample is randomly selected and representative of the population. In this case, the probability of the sample mean tariff rate being within $80 of the population mean is high (78.9%), which suggests that the amount of sampling error in estimating the population mean using a sample of 400 observations is relatively small.
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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:
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
The coordinates of the three vertices of a square are (4,14) (10,14) and (4,8). What are the coordinates of the missing vertex
Given that the coordinates of the three vertices of a square are (4, 14), (10, 14), and (4,8).
The missing coordinate will be at (10,8) on the coordinate plane for the given square.
VERTEX: WHAT IS IT?A vertex is a location in geometry where two or more line segments converge. Vertices are the corners of two-dimensional forms such as squares and triangles. Vertices are the places where three or more faces of a three-dimensional shape, such as a cube or a pyramid, meet.
Four of a square's vertices have the coordinates (4,14), (10,14), and (4,8).
The length of one of the square's sides may be determined using the distance formula, and the length can then be used to determine the coordinates of the missing vertex.
We know that one side of the square has a length of 6 units since the distance between (4,14) and (10,14) is 6 units.
We know that the missing vertex must be 6 units away from (4,8) in the y-direction since the square is symmetric.
The missing vertex therefore has the coordinates (10,8).
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The missing coordinate will be at (10,8) on the coordinate plane for the given square.
VERTEX: WHAT IS IT?A vertex is a location in geometry where two or more line segments converge. Vertices are the corners of two-dimensional forms such as squares and triangles. Vertices are the places where three or more faces of a three-dimensional shape, such as a cube or a pyramid, meet.
Four of a square's vertices have the coordinates (4,14), (10,14), and (4,8).
The length of one of the square's sides may be determined using the distance formula, and the length can then be used to determine the coordinates of the missing vertex.
We know that one side of the square has a length of 6 units since the distance between (4,14) and (10,14) is 6 units.
We know that the missing vertex must be 6 units away from (4,8) in the y-direction since the square is symmetric.
The missing vertex therefore has the coordinates (10,8).
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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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The graphs below have the same shape. What is the equation of the blue graph?
Answer:
G(x) = (x - 2)^2 + 1, so A is correct.
The distance between Point A and Point B along a jogging track is 24 Km. Gerald
starts from Point A and jogs at a speed of 6 Km/h. Shaun starts from Point B 30 min
after Gerald but reaches Point A 30 min earlier. What is Shaun's average speed?
Answer: Let's start by finding out the time it takes for Gerald to jog from Point A to Point B. We can use the formula:
distance = rate x time
to do this. Since the distance between Point A and Point B is 24 km and Gerald's speed is 6 km/h, we have:
24 = 6t
where "t" is the time it takes for Gerald to jog from Point A to Point B. Solving for "t", we get:
t = 4
So Gerald takes 4 hours to jog from Point A to Point B.
Now, let's look at Shaun's journey. We know that he starts 30 minutes after Gerald and reaches Point A 30 minutes earlier than Gerald. This means that the time it takes for Shaun to travel from Point B to Point A is 3.5 hours (i.e., 4 hours - 0.5 hours + 0.5 hours).
Using the formula distance = rate x time again, we can find out Shaun's average speed:
24 = rate x 3.5
simplifying, we get:
rate = 6.857 km/h
So Shaun's average speed is 6.857 km/h (or approximately 6.86 km/h rounded to two decimal places).
Answer:
8 km/h
Step-by-step explanation:
You want to know Shaun's average speed on a 24 km jogging track if Gerald jogged at 6 km/h for the distance, while Shaun left half and hour later and arrived half an hour earlier than Gerald.
Gerald's timeThe time it took Gerald to complete the distance is found from ...
time = distance/speed
time = (24 km)/(6 km/h) = (24/6) h = 4 h
Shaun's timeShaun left half an hour later than Gerald, and completed the trip half an hour before Gerald did. Shaun's time was 1 hour less than Gerald's, so was ...
4 h -1 h = 3 h
Shaun's speedShaun's average speed can be found from ...
speed = distance/time
speed = (24 km)/(3 h) = 8 km/h
Shaun's average speed was 8 km/h.
What is the y-intercept for this line?
Y = 2/3 x + 3
A. 2
B. 2/3
C. 3
Answer:
y intercept when x is 0, so the answer is 3
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.
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°
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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15 POINTS MARKING BRAINLIST PLEASE HELP
The length of "ab" is approximately 6 cm (to the nearest hundred)
What do you mean by Right angle triangle and its properties ?If two lines intersect at an angle of 90˚ or are perpendicular to each other, they form a right angle. A right angle is indicated by the symbol ∟Angle is always 90° or a right angle. The opposite angle of 90° is the hypotenuse. The hypotenuse is always the longest side. The sum of the remaining two interior angles is 90°. In a right-angled triangle, the side opposite the 90-degree angle is called the hypotenuse, indicated by the letter "c". The sides adjacent to a 37 degree angle and a right angle are called "ab" and "bc" respectively.
Using trigonometry, we find the length of "ab" as follows:
sin(37) = opposite/hypotenuse = ab/c
ab = sin(37) * c
Substituting the given values we get:
ab = sin(37) × 10 cm
= 3/5 × 10 cm
ab = 6.07 cm
Rounding to the nearest hundred, we get:
ab ≈ 6 cm (nearest hundred)
Therefore, the length of "ab" is approximately 6 cm (to the nearest hundred)
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The central angle of a circle measures 97 degrees and intercepts a minor arc. What is the measure of its major arc?
Answer:
D. 263 degrees
Step-by-step explanation:
We know that central angles are congruent to the arcs they encompass or intercept. So, if the minor arc is 97 degrees, and the total measure of a circle's arcs are 360 degrees, then the major arc is 263 degrees.
Therefore, the answer is D.