Write 3.16 as a mixed number in lowest terms
The pie below is cut into 6 equal slices. Show shade2/3 of this pie
A soccer ball is kicked into the air from the ground. If the ball reaches a maximum height of 25 ft and spends a total of 2.5 s in the air, which equation models the height of the ball correctly? Assume that acceleration due to gravity is –16 ft/s2.
Jesse was ranked 11th in his graduating class of 180 students. At what percentile is Jesse's ranking? (Round your answer to the nearest whole number.)
A principal of $1,000 is invested in an account paying an annual interest rate of 4% using the formula A=P(1+r/n) ^nt
find the amount in the account after 2 years if the account is compounded annually
Solve the system using the elimination method.
2x + 2y + 5z =−1
2x − y + z =2
2x + 4y − 3z =14
What x,y, and z?
Find a + b, 2a + 3b, |a|, and |a − b|. a = 5i + j, b = i − 3j
solve the equation 0.4+0.5=-4.7-0.6z
a tour bus cost $75 plus $6 for each passenger. write and evaluate an expression to find the total cost for 25 passengers. then. make a table showing the cost for 26, 30, 35, 40 passengers
Simplify the expression 16 − x2 as much as possible after substituting 4 sin θ for x. (assume 0° < θ < 90°.)
The value of the expression [tex]16 - x^{2}[/tex] is 16 cos^2θ
Here,
The expression is [tex]16 - x^{2}[/tex]
We have to find the value of expression after substitute 4 sinθ for x.
What is substitution method?
Substitution method is algebraic method to solve the linear equations.
Now,
The expression is [tex]16 - x^{2}[/tex]
By putting x = 4 sinθ in above equation, we get;
[tex]16 - x^{2}[/tex] = 16 - ( 4 sinθ)^2
= 16 - 16 sin^2θ
= 16 ( 1 - sin^2θ )
= 16 cos^2θ
Since, 1 - sin^2θ = cos^2θ
Hence, The value of the expression [tex]16 - x^{2}[/tex] is 16 cos^2θ
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To simplify the expression 16 - x² after substituting 4 sin θ for x, you end up with 16 cos² θ, using the Pythagorean trigonometric identity.
Explanation:To simplify the expression 16 - x² after substituting 4 sin θ for x, where 0° < θ < 90°, we follow these steps:
Substitute 4 sin θ into the expression for x.Simplify the resulting expression.The substitution gives us 16 - (4 sin θ)².
To further simplify:
Calculate the square of 4 sin θ, which is 16 sin² θ.Subtract 16 sin² θ from 16, giving us 16 - 16 sin² θ.Factor out the common factor of 16, resulting in 16(1 - sin² θ).Recognize that (1 - sin² θ) is equal to cos² θ due to the Pythagorean identity.Finally, the simplified expression is 16 cos² θ.Simplify the expression and eliminate any negative exponent(s). Assume that all letters denote positive numbers.
√s√s^9
The temperature in Minneapolis changed from -7°F at 6 AM to 7°F at noon. how much did the temperature increase?
For a school assembly, students sit in chairs that are arranged in 53 rows. There are 12 chairs in each row. About how many students can be seated?
A soccer ball is kicked from the ground. After traveling a horizontal distance of 35m, it just passes over a 1.5m tall fence before hitting the ground 37m from where it was kicked. How far has the ball travelled horizontally to reach the maximum height?
Answer:
18.5 meters
Step-by-step explanation:
As the maximum height ona projectile motion that starts from the ground and finishes at the ground is simmetric, the maximum height of the projectile will be found exactly at half of the distance tranveled horizontally, so the exact half of the total distance traveled horizontally is 18.5 meters, since distance is 37 meters and divided by 2 is 18.5.
The ball will travel 18.5 meters to reach its maximum height.
What's S divided by 8=2 ?.....Answer needed ASAP.
Which is greater, the greatest whole number with 4 digits or the least whole number with 5 digits?
What is the greatest whole number that rounds to 54,300
When determining slope, data points do not usually fall within a straight line, so you need to draw a _____ line, with as many points above and below the line as possible.
accurate
precise
best fit
correct
Answer:
The correct option is 3.
Step-by-step explanation:
If a straight line passes through some of the points, none of the points, or all of the points of a scatter plot and best represents the data, then it is called a best fit line.
Best fit line minimizes the squared distance of each point. Some points of the scatter plot lie above and below the best fit line.
When determining slope, data points do not usually fall within a straight line, so you need to draw a best fit line, with as many points above and below the line as possible.
Therefore the correct option is 3.
The denominator of a fraction is 1 more than the numerator. If both the numerator and denominator are decreased by 3, the resulting fraction is equal to 4/5. Find the fraction
Find the area of the region bounded by the parabola y = x2, the tangent line to this parabola at the point (2, 4), and the x-axis.
The area of the region is [tex]\(\frac{64}{3}\)[/tex] square units.
To find the area of the region bounded by the parabola \(y = x^2\), the tangent line at the point (2, 4), and the x-axis, we'll first determine the points of intersection.
The tangent line at (2, 4) has the same slope as the derivative of the parabola at x = 2. The derivative of [tex]\(y = x^2\)[/tex] is [tex]\(2x\)[/tex], so at x = 2, the slope is [tex]\(2 \times 2 = 4\)[/tex]. Thus, the equation of the tangent line is [tex]\(y - 4 = 4(x - 2)\)[/tex].
Now, let's find the points of intersection between the parabola and the tangent line:
[tex]\[x^2 = 4(x - 2) + 4\][/tex]
Solving for x, we get [tex]\(x^2 - 4x = 0\)[/tex], which factors to [tex]\(x(x - 4) = 0\)[/tex]. So, [tex]\(x = 0\)[/tex] and [tex]\(x = 4\)[/tex].
Now, integrate the absolute difference of the functions from 0 to 4 to find the area:
[tex]\[A = \int_0^4 |x^2 - (4x - 4)| \,dx.\][/tex]
Evaluate the integral:
[tex]\[A = \int_0^4 (x^2 - 4x + 4) \,dx = \frac{1}{3}x^3 - 2x^2 + 4x \Big|_0^4 = \frac{64}{3}.\][/tex]
Therefore, the area of the region is [tex]\(\frac{64}{3}\)[/tex] square units.
The answer is: [tex]\frac{8}{3}[/tex].
The area of the region bounded by the parabola [tex]\( y = x^2 \)[/tex], the tangent line to this parabola at the point (2, 4), and the x-axis is given by the integral of the difference between the parabola and the tangent line from [tex]\( x = 0 \) to \( x = 2 \)[/tex].
First, we need to find the equation of the tangent line to the parabola at the point (2, 4). The slope of the tangent line is the derivative of the parabola's equation at \( x = 2 \). The derivative of [tex]\( y = x^2 \)[/tex] is [tex]\( y' = 2x \).[/tex] At[tex]\( x = 2 \)[/tex], the slope is [tex]\( 2 \cdot 2 = 4 \)[/tex].
Using the point-slope form of a line,[tex]\( y - y_1 = m(x - x_1) \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( (x_1, y_1) \)[/tex] is a point on the line, we get the equation of the tangent line as follows:
[tex]\[ y - 4 = 4(x - 2) \][/tex]
[tex]\[ y = 4x - 8 + 4 \][/tex]
[tex]\[ y = 4x - 4 \][/tex]
Now, we will find the area under the parabola and above the tangent line from [tex]\( x = 0 \) to \( x = 2 \)[/tex]. The integral of [tex]\( x^2 \)[/tex] from 0 to 2 is:
[tex]\[ \int_{0}^{2} x^2 \, dx = \left[ \frac{x^3}{3} \right]_{0}^{2} = \frac{2^3}{3} - \frac{0^3}{3} = \frac{8}{3} \][/tex]
The integral of the tangent line \( y = 4x - 4 \) from 0 to 2 is:
[tex]\[ \int_{0}^{2} (4x - 4) \, dx = \left[ 2x^2 - 4x \right]_{0}^{2} = (2 \cdot 2^2 - 4 \cdot 2) - (2 \cdot 0^2 - 4 \cdot 0) = (8 - 8) - (0 - 0) = 0 \][/tex]
The area between the parabola and the tangent line is the difference between these two integrals:
[tex]\[ \text{Area} = \int_{0}^{2} x^2 \, dx - \int_{0}^{2} (4x - 4) \, dx \][/tex]
[tex]\[ \text{Area} = \frac{8}{3} - 0 \][/tex]
[tex]\[ \text{Area} = \frac{8}{3} \][/tex]
Therefore, the area of the region bounded by the parabola [tex]\( y = x^2 \)[/tex], the tangent line at the point (2, 4), and the x-axis is [tex]\( \boxed{\frac{8}{3}} \)[/tex] square units.
which undefined using the undefined terms point más line?
A angle
B circle
C parallel lines
D ray
Select the expression that has a quitiont greater than 1. Explain your reasoning.
4 2/3 divided by 5 1/4= 3 1/8 divided by 2 2/5=
1 6/7 divided by 2 1/3= 5 3/4 divided by 7 3/8=
Final answer:
To find the expression with a quotient greater than 1, we convert the mixed numbers into improper fractions and perform the division for each expression. The expression that gives a quotient greater than 1 is 5 3/4 divided by 7 3/8.
Explanation:
To find the expression that has a quotient greater than 1, we need to divide the given fractions. Let's examine each expression:
4 2/3 divided by 5 1/4: To divide mixed numbers, we convert them into improper fractions and then perform the division. In this case, the quotient is less than 1.
3 1/8 divided by 2 2/5: Similar to the first expression, we convert the mixed numbers into improper fractions and divide. The quotient is also less than 1.
1 6/7 divided by 2 1/3: Again, convert the mixed numbers into improper fractions and perform the division. The quotient is less than 1.
5 3/4 divided by 7 3/8: Convert the mixed numbers into improper fractions and divide. The quotient is greater than 1, so this is the expression we're looking for.
Therefore, the expression with a quotient greater than 1 is 5 3/4 divided by 7 3/8.
Problem Page A science fair poster is a rectangle 48 inches long and 24 inches wide. What is the area of the poster in square feet?
48/12 = 4 feet
24/2 = 2 feet
4 *2 = 8 square feet
Answer:
8 feet squared
The distribution of the amount of money spent by students for textbooks in a semester is approximately normal in shape with a mean of 235andastandarddeviationof235andastandarddeviationof 20. according to the standard deviation rule, how much did almost all (99.7%) of the students spend on textbooks in a semester?
In a certain grocery store, strawberries cost $5.92 per pound ( 5.92 dollars/lb ). what is the cost per ounce? express your answer numerically to the hundredths place.
.002 is 1/10 of what
.002 is 1/10 of 0.02. To find this, we multiply .002 by 10. This is seen as moving the decimal point to the right once because we are multiplying by a power of ten.
Explanation:The student asked: ".002 is 1/10 of what". To find the answer to this question, we can set up a simple equation where we multiply .002 by 10 because we know that if .002 is 1/10 of a number, then multiplying it by 10 will give us that whole number.
So the equation is:
.002 x 10 = 0.02Therefore, .002 is 1/10 of 0.02.
This can also be understood by recognizing that when dividing by powers of 10, you move the decimal to the left by the number of zeros in the power of ten. So, in the reverse process, when we want to find a number that is ten times larger (i.e., 1/10 of the original), we move the decimal one place to the right.
please help 13(3+2x)−1=10
Solve for q 8r-5q=3
94.99 in expanded form
the table represents a linear function?
Answer: 5
Step-by-step explanation:
In the given picture we have a table representing two columns as x and y.
We know that the slope of the function is given by :-
[tex]k=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Using points (0,4) and (2,14) from the table , we get the slope of the function will be :-
[tex]k=\dfrac{14-4}{2-0}\\\\\\=\dfrac{10}{2}=5[/tex]
Therefore, the slope of the given function in the table = 5