Required algebraic expression is (t+30).
What is algebraic expression?
An algebraic expression is a mathematical phrase that contains variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. It may also contain brackets or parentheses to indicate the order of operations.
Algebraic expressions can be written using letters or symbols to represent variables, and they are used to represent mathematical relationships or formulas. For example, the expression "3x + 4" represents the sum of three times a variable x and the constant 4.
Let's represent the amount of time that Jill spends watching television as the variable j. We know that she watches 30 minutes more than Bill, so we can write:
j = t + 30
This algebraic expression says that Jill's time j is equal to Bill's time t, plus 30 additional minutes.
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A 4-sided die, labeled 1–4 is rolled twice. Which outcome is not part of the sample space?
Answer: Let the experienced one help you out! Read the explanation down below! Brainliest?
Step-by-step explanation:
The sample space for rolling a 4-sided die twice consists of all possible pairs of outcomes, where each outcome is a number from 1 to 4. To find which outcome is not part of the sample space, we can list all the possible outcomes and then look for a number pair that does not appear.
Possible outcomes:
(1,1), (1,2), (1,3), (1,4)
(2,1), (2,2), (2,3), (2,4)
(3,1), (3,2), (3,3), (3,4)
(4,1), (4,2), (4,3), (4,4)
There are 16 possible outcomes, so one of the numbers from 1 to 16 is not part of the sample space. The missing outcome is (3,4) or (4,3), depending on the order in which the dice are rolled.
if 4-sided die, labeled 1–4 is rolled twice then 5,3 is not part of the sample space because the outcomes 5 and 3 are not part of the sample space.
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
A sample space is a collection or a set of possible outcomes of a random experiment.
The sample space of rolling a 4-sided die twice can be represented by all possible ordered pairs of the outcomes, which can be listed as follows:
{(1,1), (1,2), (1,3), (1,4), (2,1), (2,2), (2,3), (2,4), (3,1), (3,2), (3,3), (3,4), (4,1), (4,2), (4,3), (4,4)}
Therefore, if 4-sided die, labeled 1–4 is rolled twice then 5,3 is not part of the sample space because the outcomes 5 and 3 are not part of the sample space.
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Is 40, –40, 16, or –16 the solution of the equation 28=d−12?
Answer:
To check whether 40, -40, 16, or -16 is the solution of the equation 28 = d - 12, we can substitute each value into the equation and see if it results in a true statement.
When we substitute 40 into the equation, we get:
28 = 40 - 12
Simplifying, we get:
28 = 28
This is a true statement, so 40 is a solution of the equation.
When we substitute -40 into the equation, we get:
28 = -40 - 12
Simplifying, we get:
28 = -52
This is not a true statement, so -40 is not a solution of the equation.
When we substitute 16 into the equation, we get:
28 = 16 - 12
Simplifying, we get:
28 = 4
This is not a true statement, so 16 is not a solution of the equation.
When we substitute -16 into the equation, we get:
28 = -16 - 12
Simplifying, we get:
28 = -28
This is not a true statement, so -16 is not a solution of the equation.
Therefore, the only solution of the equation 28 = d - 12 is d = 40.
A package is weighed at 11 kg to the nearest kg. Find the largest possible weight for the package.
Answer:11.4999...
Step-by-step explanation:
Any number when rounding that starts with 1, 2, 3 4 will be rounded down. All numbers above will be rounded up. Therefore, you find the largest number that will still round down.
Please I’ll give brainliest
A Ferris wheel reaches a maximum height of 60 m above the ground and takes twelve minutes to complete one revolution. Riders have to climb a m staircase to board the ride at its lowest point.
(a) [4 marks] Write a sine function for the height of Emma, who is at the very top of the ride when t = 0.
(b) [2 marks] Write a cosine function for Eva, who is just boarding the ride.
(c) (2 marks] Write a sine function for Matthew, who is on his way up, and is at the same height as the central axle of the wheel.
If Riders have to climb a m staircase to board the ride at its lowest point.
a. sine function for the height of Emma, who is at the very top of the ride when t = 0 is: h(t) = 60 sin(π/6 t).
b. a cosine function for Eva, who is just boarding the ride is: h(t) = m + 60 cos(π/6 t).
c. a sine function for Matthew is: h(t) = 30 sin(π/6 t).
What is the sine function for the height of Emma?(a) Let's assume that the Ferris wheel completes one full revolution in 12 minutes. The height of the Ferris wheel can be modeled by a sine function as it moves up and down periodically. When the Ferris wheel completes one revolution, it returns to its original position, so the period of the sine function is 12 minutes.
The maximum height of the Ferris wheel is 60 m, so the amplitude of the sine function is 60 m. When t = 0, Emma is at the very top of the ride, which means she is at the maximum height of the Ferris wheel. Therefore, the sine function for Emma's height, h(t), can be written as:
h(t) = 60 sin(2π/12 t)
Simplifying this equation, we get:
h(t) = 60 sin(π/6 t)
(b) Eva is just boarding the ride, which means she is at the lowest point of the ride when t = 0. The cosine function is ideal for modeling this situation, as it starts at its maximum value and reaches its minimum value after one-fourth of the period. Therefore, the cosine function for Eva's height, h(t), can be written as:
h(t) = m + 60 cos(2π/12 t)
Simplifying this equation, we get:
h(t) = m + 60 cos(π/6 t)
where m is the height of the staircase that Eva has to climb to board the ride.
(c) Matthew is at the same height as the central axle of the Ferris wheel, which means he is halfway between the maximum and minimum height of the ride. Therefore, the sine function for Matthew's height, h(t), can be written as:
h(t) = 30 sin(2π/12 t)
Simplifying this equation, we get:
h(t) = 30 sin(π/6 t)
Therefore sine function for the height of Emma, who is at the very top of the ride when t = 0 is: h(t) = 60 sin(π/6 t).
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$2000 are invested in a bank account at an interest rate of 5 percent per year.
Find the amount in the bank after 7 years if interest is compounded annually.
Find the amount in the bank after 7 years if interest is compounded quaterly.
Find the amount in the bank after 7 years if interest is compounded monthly.
Finally, find the amount in the bank after 7 years if interest is compounded continuously.
The amount in the bank after 7 years increases as the compounding frequency increases, and it is highest when interest is compounded continuously.
Simple interest calculation.
Using the formula A = P(1 + r/n)^(nt), where:
A = the amount in the account after t years
P = the principal (initial amount)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
a) If interest is compounded annually:
A = 2000(1 + 0.05/1)^(1*7) = $2,835.08
b) If interest is compounded quarterly:
A = 2000(1 + 0.05/4)^(4*7) = $2,888.95
c) If interest is compounded monthly:
A = 2000(1 + 0.05/12)^(12*7) = $2,905.03
d) If interest is compounded continuously:
A = Pe^(rt) = 2000e^(0.05*7) = $2,938.36
Therefore, the amount in the bank after 7 years increases as the compounding frequency increases, and it is highest when interest is compounded continuously.
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Aeronautical researchers have developed three different processes to pack a parachute. They want to compare the different processes in terms of time to deploy and reliability. There are 1,200 objects that they can drop with a parachute from a plane. Using a table of random digits, the researchers will randomly place the 1,200 items into three equally sized treatment groups suitable for comparison. Which design is the most appropriate for this experiment
- Randomly number each item with 1, 2, or 3. Assign the items labeled 1 to the process 1 group, assign the items labeled 2 to the process 2 group, and assign the items labeled 3 to the process 3 group.
- Number each item from 1 to 1,200.
Reading from left to right from a table of random digits, identify 800 unique numbers from 1 to 1,200. Assign the items with labels in the first 400 numbers to the process 1 group. Assign the items with labels in the second 400 numbers to the process 2 group. Assign the remaining items to the process 3 group.
- Number each item from 0000 to 1199.
Reading from left to right on a random number table, identify 800 unique four-digit numbers from 0000 to 1199. Assign the items with labels in the first 400 numbers to the process 1 group. Assign the items with labels in the second 400 numbers to the process 2 group. Assign the remaining items to the process 3 group.
- Select an item, and identify the first digit reading from left to right on a random number table. If the first digit is a 1, 2, or 3, assign the item to the process 1 group.
If the first digit is a 4, 5, or 6, assign the item to the process 2 group. If the first digit is a 7, 8, or 9, assign the item to the process 3 group. If the first digit is a 0, skip that digit and move to the next one to assign the item to a group. Repeat this process for each item.
Answer: The most appropriate design for this experiment is the third option:
- Number each item from 0000 to 1199.
- Reading from left to right on a random number table, identify 800 unique four-digit numbers from 0000 to 1199. Assign the items with labels in the first 400 numbers to the process 1 group. Assign the items with labels in the second 400 numbers to the process 2 group. Assign the remaining items to the process 3 group.
This design ensures that the groups are equally sized and selected randomly without any biases. The use of a random number table to assign the groups helps to avoid any systematic patterns or preferences that might arise from numbering or labeling the items directly.
Step-by-step explanation:
The length of the altitude of an equilateral triangle is 4 square root of 3 . Find the length of a side of the triangle.
[tex]\textit{height of an equilateral triangle}\\\\ h=\cfrac{s\sqrt{3}}{2}~~ \begin{cases} s=\stackrel{length~of}{a~side}\\[-0.5em] \hrulefill\\ h=4\sqrt{3} \end{cases}\implies 4\sqrt{3}=\cfrac{s\sqrt{3}}{2} \\\\\\ 8\sqrt{3}=s\sqrt{3}\implies \cfrac{8\sqrt{3}}{\sqrt{3}}=s\implies 8=s[/tex]
Clare lives in Iowa and pays 6% in sales tax. She just bought $135 in groceries, but $40 worth of those groceries were not taxable. What is the total amount that Clare paid for the groceries, including sales tax?
Answer:
$140.70
Step-by-step explanation:
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Angel made a table runner that has an area of 80 square inches. The length and width of the table runner are whole numbers. The length is 5 times greater than the width. What are the dimensions of the table runner?
the dimensions of the table runner are [tex]20[/tex] inches in length and [tex]4[/tex] inches in width.
What are the dimensions?Let's denote the width of the table runner as "w" inches. Since the length is 5 times greater than the width, the length would be 5w inches.
The area of a rectangle is calculated by multiplying its length by its width. Given that the area of the table runner is 80 square inches, we can set up the following equation:
Length × Width = Area
[tex](5w) \imes w = 80[/tex]
Simplifying further:
[tex]5w^2 = 80[/tex]
Dividing both sides by 5:
[tex]w^2 = 16[/tex]
Taking the square root of both sides:
w = ±4
Since the width cannot be negative in this context, we discard the negative value. Therefore, the width (w) of the table runner is [tex]4[/tex] inches.
Substituting this value back into the equation for length:
Length [tex]= 5w = 5 \times 4 = 20[/tex] inches
So, the dimensions of the table runner are [tex]20[/tex] inches in length and 4 inches in width.
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One hundred adults were asked to name
their favorite sport, and the results are
shown in the circle graph. What percent of
adults preferred soccer or baseball?
Volleyball, 3
Other, 4
Golf, 7
Soccer. 11.
Baseball, 14
Football,39
Basketball, 22
Total percentage of adults who preferred soccer or baseball: is 25%
what is percentage ?
Percentage is a way of expressing a number as a fraction of 100. It is often denoted by the symbol "%". For example, 50% means 50 out of 100, or 50/100 as a fraction.
In the given question,
The circle graph shows the percentage of adults who preferred each sport. To find the percentage of adults who preferred soccer or baseball, we need to add the percentages for soccer and baseball.
Soccer: 11%
Baseball: 14%
Total percentage of adults who preferred soccer or baseball: 11% + 14% = 25%
Therefore, 25% of adults preferred soccer or baseball.
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helpppppppp plsssssssss
I think it might be:
Between 1754 and 1885 European imperialism was global. Nations like Britain, France, and Spain grew their Empires in the Americas, on the continent of Africa, and in parts of Asia. Their colonies created power and wealth for European businesses and governments. Eventually, many European countries held a meeting to decide how to divide up the world to avoid wars and conflict between themselves. This meeting was called the Conference.
Please help me, I am confused on how to do this problem.
Find the exact value, cos(-pi/12). Use the half angle strategy.
Using the half angle formula, cos(-π/12) = ±√[2 + √3]/4]
What is the half angle formula?The half angle formula for cosine is cosФ/2 = ±√[(1 + cosФ)/2]
Since we want to find the value of cos(-pi/12) using the half angle formula, we have that cosФ/2 = cos(-π/12)
⇒ Ф/2 = -π/12
⇒ Ф = -π/12 × 2
⇒ Ф = -π/6
So, substituting this into the equation, we have
cosФ/2 = ±√[(1 + cosФ)/2]
cos(-π/6)/2 = ±√[(1 + cos(-π/6))/2]
= ±√[(1 + cos(π/6))/2]
Now, we know that cos(π/6) = √3/2
So, substituting this into the equation, we have that
cos(-π/6)/2 = ±√[(1 + cos(π/6))/2]
cos(-π/12 = ±√[(1 + cos(π/6))/2]
= ±√[(1 + √3/2)/2]
= ±√[[2 + √3]/2)/2]
= ±√[[2 + √3]/2 × 2]
= ±√[2 + √3]/4]
So, cos(-π/12) = ±√[2 + √3]/4]
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What is a solution to the system of equations that includes quadratic function f(x) and linear function g(x)?
(x is -2,-1,0,1,2 and g(x) is 1,3,5,7,9?
f(x) = 2x^2 + x + 4
We see that f(-1) = g(1) = 5. Therefore, the solution to the system of equations is x = -1.
Describe System of equation?A system of equations is a set of two or more equations that are to be solved simultaneously. Each equation in the system represents a relationship between variables, and the solution to the system is the set of values for the variables that satisfy all of the equations in the system.
One way to solve a system of equations is by substitution. We can solve one of the equations for one of the variables in terms of the other variable, and then substitute that expression into the other equation to get an equation in one variable. We can then solve that equation for the variable, and use that value to find the value of the other variable.
Another way to solve a system of equations is by elimination. We can add or subtract the equations in the system to eliminate one of the variables, and then solve for the other variable. We can then use that value to find the value of the eliminated variable.
To find a solution to the system of equations that includes the quadratic function f(x) and the linear function g(x), we need to find the value of f(x) for each value of x and compare it to the corresponding value of g(x). If f(x) and g(x) are equal for any value of x, then that value is a solution to the system.
Substituting each value of x into the quadratic function f(x), we get:
f(-2) = 2(-2)² + (-2) + 4 = 10
f(-1) = 2(-1)² + (-1) + 4 = 5
f(0) = 2(0)² + 0 + 4 = 4
f(1) = 2(1)² + 1 + 4 = 7
f(2) = 2(2)² + 2 + 4 = 14
Comparing these values to the corresponding values of g(x), we see that f(-1) = g(1) = 5. Therefore, the solution to the system of equations is x = -1.
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Part of the proceeds from a garage sale was $290 worth of $5 and $20 bills. If there were 8 more $5 bills than $20 bills, find the number of each denomination.
Answer:
18 5-dollar bills
10 20-dollar bills
I need help in like 5 minutes please
Answer: 3/2 or 1 1/2 or 1.5
Step-by-step explanation:
9/8 times 2 is 2.25 or 9/4
9/4-6/8= 3/2 or 1 1/2 or 1.5
Determine if the function below is continuous.
A. not continuous at x = 5
B. not continuous at x = 0
C. continuous
D. not continuous x = -2
Is the function above continuous: B. not continuous at x = 0.
What is a continuous function?In Mathematics and Geometry, a continuous function can be defined as a type of function in which there is no discontinuities or breaks between the intervals for the points plotted on a graph.
What is a discrete function?In Mathematics and Geometry, a discrete function can be defined as a type of function in which the ordered pair of values on the x-axis and y-axis are separate from each other and unconnected.
By critically observing the graph shown above, we can reasonably infer and logically conclude that it represents a discrete function because it is not continuous at x is equal to 0 i.e x = 0.
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Miss Wu's class made 36
paper flowers. One half of the
flowers were red. One third of
the flowers were yellow. The
rest were blue. What fraction
of the flowers were blue?
Answer:
1/6 of flowers were blue
Point B(5,-2) is translated 4 units right and 2 units down and then dilated by a factor of 2 using the origin as the center of dilation what is the resultant point?
the the coordinates of the resulting point are (18, -8). of the resulting point are (18, -8).
What is center of dilation?
The center of dilation is a fixed point in the plane.
Starting with point B(5, -2), if we move it 4 units to the right and 2 units down, we get:
B'(9, -4)
Next, we need to dilate the point by a factor of 2, using the origin as the center of dilation. This means we need to multiply both the x-coordinate and y-coordinate of B' by 2.
So, doubling the x-coordinate of B' gives:
2 × 9 = 18
And doubling the y-coordinate of B' gives:
2 × (-4) = -8
Therefore, the coordinates of the resulting point are (18, -8).
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A rectangle has an area of 108 square
centimeters. Its width is 9 centimeters.
What is the perimeter of the
rectangle?
Therefore, the perimeter of the rectangle is 42 centimeters.
What is area?The concept of area is used in many areas of mathematics, science, and everyday life. It is used in geometry to calculate the area of various shapes, such as triangles, circles, and polygons. It is also used in physics to calculate the amount of surface area of an object that is exposed to air or water, and in architecture and engineering to determine the amount of material needed to construct a building or structure.
Here,
To find the perimeter of a rectangle, we need to know its length and width. We are given that the width of the rectangle is 9 centimeters, and the area of the rectangle is 108 square centimeters.
We can use the formula for the area of a rectangle:
Area of rectangle = length x width
Plugging in the values we have:
108cm² = length x 9cm
Solving for the length, we can divide both sides by 9cm:
length = 108cm² / 9cm
length = 12cm
So, the length of the rectangle is 12 centimeters.
To find the perimeter of the rectangle, we can use the formula:
Perimeter of rectangle = 2 x (length + width)
Plugging in the values we have:
Perimeter of rectangle = 2 x (12cm + 9cm)
Perimeter of rectangle = 2 x 21cm
Perimeter of rectangle = 42cm
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the 3rd and 6th term in fibonacci sequence are 7 and 31 respectively find the 1st and 2nd terms of the sequence
Answer:
Step-by-step explanation:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89,144,233,377,610,987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, 514229, ... Can you figure out the next few numbers?
the area of Rectangle is 112 in sq. if the height is 8 in, what is the base length
Answer:
14cm
Step-by-step explanation:
112÷8=14
base length=14cm
Answer:
To find the base length of a rectangle, given its area and height, you can use the formula for calculating the area of a rectangle, which is:
Area = Length x Width
In this case, you are given that the area is 112 square inches and the height is 8 inches. Let's denote the base length as "x" inches.
So, the equation for the area of the rectangle becomes:
112 = x * 8
To solve for "x", you can divide both sides of the equation by 8:
112 / 8 = x
x = 14
Therefore, the base length of the rectangle is 14 inches.
Fill in the blanks to make the statement true.
Pi the ratio of the (choose your answer...) of a circle to its ( choose your answer....)
Pi is the ratio of the circumference of a circle to its diameter.
Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options.
The radius of the circle is 3 units.
The center of the circle lies on the x-axis.
The center of the circle lies on the y-axis.
The standard form of the equation is (x – 1)² + y² = 3.
The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
The x-axis is where the circle centre is located. Three units make up the circle's radius. This circle's radius coincides with the radius of the circle whose equation is x² + y² = 9.
What is the circle's equation when its centre is on the x-axis?The y coordinate of a circle's centre will be 0 if the circle's centre is on the x-axis. The circle's equation will therefore have the generic form x2 + y2 + 2gx + c = 0, where g and c are constants.
Circle's standard equation is written as:
x²+y²+2gx+2fy+C=0
Centre is (-g, -f)
radius = √g²+f²-C
Given a circle whose equation is : x²+y²-2x-8=0
Get the centre of the circle
2gx = -2x
2g = -2
g = -1
Similarly, 2fy = 0
f = 0
Centre = (-(-1), 0) = (1, 0)
This demonstrates circle's centre is on the x-axis.
r = radius = √g²+f²-C
radius = √1²+0²-(-8)
radius =√9 = 3 units
The circle has a radius of three units.
For the circle x²+y²=9, radius is expressed as:
r² = 9
r = 3 units
As a result, this circle's radius matches that of the circle whose equation is x² + y² = 9.
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Can someone tell me what 2.72 as a fraction?
Answer:
68/25
Step-by-step explanation:
Round your answer to the nearest tenth of a degree
Answer:
57.8°
Step-by-step explanation:
SohCahToa
use sin^1 to get angle
sin^1(11/13)=57.7957725
to the nearest tenth=57.8°
11. Triangles can be classified by their side lengths or by their angle measures. Sometimes triangles are classified using both classifications (side length and angle measure) but these can be redundant and unnecessary. Give an example of a classification based on both side length and angle measure that is unnecessary and explain why.
By answering the presented question, we may conclude that As a result, adding the isosceles triangle categorization is superfluous and redundant in this circumstance.
What is triangle?A triangle is a polygon since it has three sides and three vertices. It is a basic geometric shape. Triangle ABC refers to a triangle with the vertices A, B, and C. In Euclidean geometry, a single plane and triangle are obtained when the three points are not collinear. If a triangle has three sides and three corners, it is a polygon. The triangle's corners are the spots where the three sides meet. The sum of three triangle angles equals 180 degrees.
An isosceles triangle has two sides of equal length, but a right triangle has one angle that measures 90 degrees. As a result, an isosceles right triangle is one with two equal-length sides and one 90-degree angle.
The Pythagorean theorem states that in any right triangle, the two legs (the sides next to the right angle) are always of equal length. Hence, if we know that a triangle has one 90-degree angle and two equal-length sides, we already know that it is a right triangle and that the two legs are equal. As a result, adding the isosceles triangle categorization is superfluous and redundant in this circumstance.
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The reflector of a flashlight is in the shape of a paraboloid of revolution. Its diameter is 8 centimeters and its depth is 4 centimeters. How far from the vertex should the light bulb be placed so that the rays will be reflected parallel to the axis?
Answe: The distance of light bulb can be calculated using equation of parabola. The parabola is a plane curve which is U-shaped.
Step-by-step explanation:
An average newspaper contains at least 9 pages and at most 46 pages. How many newspapers must be collected to be certain that at least two newspapers have the same number of pages?
We need to collect 46 newspapers to be certain that at least two newspapers have the same number of pages.
What is the minimum number of newspapers needed to guarantee that two newspapers have the same number of pages?According to the Pigeonhole Principle, if we have n+1 pigeons and n holes, then there must be at least one hole with two or more pigeons. Similarly, if we have n+1 newspapers with n possible page counts, then there must be at least one page count that appears in two or more newspapers.
In this case, we have a range of 38 possible page counts (46 - 9 + 1), so we need at least 39 newspapers to guarantee that each possible page count appears in at least one newspaper.
However, to guarantee that at least two newspapers have the same number of pages, we need one more newspaper than the number of possible page counts, so we need a total of 46 newspapers. Therefore, if we collect 46 newspapers, we can be certain that at least two of them have the same number of pages.
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!!ILL GIVE BRAINLIST!!
Set up a proportion and use your proportion to solve for x.
Answer:
do how to do this is 16 x 16=256 and 8 x 8 =64 so 256+64=320
Factor completely. 5x ^2-5y ^2
In this expression, the GCF is 5. Therefore, we can factor out a 5 to get 5(x² - y²).
What is difference of squares formula?The difference of squares formula states that the difference of two squares can be factored into the product of two terms, one of which is the sum of the terms and the other is the difference of the terms.
When factoring polynomials, it is important to factor out the greatest common factor (GCF).
In this expression, the GCF is 5.
Therefore, we can factor out a 5 to get 5(x² - y²).
Now, we can expand the parentheses and factor out the remaining terms. Since both terms are perfect squares, we can factor them using the difference of squares formula:
5(x² - y²) = 5(x + y)(x - y)
In this case, the terms are x and y, resulting in the factorization of 5(x² - y²) into 5(x + y)(x - y).
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