Answer: To find the capacity of the tin can, we can use the formula for the volume of a rectangular prism, which is length x width x height. In this case, the length is 5 cm, the width is 4 cm, and the height is 15 cm. So the volume of the tin can is 5 x 4 x 15 = 300 cubic cm.
To find the capacity of the plastic cylinder, we can use the formula for the volume of a cylinder, which is pi x radius squared x height. The diameter of the circular base is 7 cm, so the radius is half of that, or 3.5 cm. So the volume of the plastic cylinder is pi x (3.5 cm)^2 x 10 cm = 385.4 cubic cm.
So the plastic cylinder has a greater capacity by 385.4 - 300 = 85.4 cubic cm.
Step-by-step explanation:
Write each number as a product using the GCF as a factor in apply to distribute property 14+21
The greatest common factor (GCF) of 14 and 21 is 7.
So we can write 14 and 21 as the product of 7 and their corresponding quotients:
14 = 7 * 2
21 = 7 * 3
Now we can apply the distributive property and combine them:
14 + 21 = 7 * 2 + 7 * 3 = 7 * (2 + 3) = 7 * 5 = 35
The final answer is 35.
Answer:
7(2 + 3)
Step-by-step explanation:
The Greatest Common Factor of 14 & 21 is 7
So, the answer is
7(2 + 3)
Find the length of the third side. If necessary, write in simplest radical form
By using pythagorean theorem, the length of the third side is 3 unit.
What is simplest radical form?In mathematics, a number or an expression is said to be in its simplest radical form if it has no perfect square factors other than 1. For example, the square root of 12 can be simplified to 2√3 because 2 * 2 * 3 = 12, but 2 and 3 are not perfect squares. So the simplest radical form of √12 is 2√3.
what is pythagorean theorem?
The Pythagorean theorem is a fundamental result in Euclidean geometry that states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. It can be written as:
c^2 = a^2 + b^2
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In 1955 a vest sold for $3.50. Twenty years later, the price increased by 95%. How much more did it sell for twenty years later? Round your answer to the nearest cent.
Reason:
An increase of 95% will involve the multiplier 1.95
Think of it like saying 100% + 95% = 1 + 0.95 = 1.95
Therefore,
1.95*3.50 = 6.825 = 6.83 dollars
Copy and complete the table of values for y=x²-3x - 2. What numbers replace A, B and C? X Y -1 A 0 1 2 3 B -4 C — 4
The numbers 2, -2, and -2 can replace the letters A, B, and C respectively in the table of values.
What is a table of valuesWe use table of values when we have to graph out a linear equation. We can make use of the table of values to map out the corresponding values of x and y for a given line equation.
For y = x² - 3x - 2:
when x = -1;
y = (-1)² - 3(-1) -2
y = 1 + 3 - 2
y = 4 - 2
y = 2
when x = 0;
y = (0)² - 3(0) -2
y = 0 - 0 - 2
y = -2
when x = 3;
y = (3)² - 3(3) - 2
y= 9 - 9 - 2
y = 0 - 2
y = -2
Therefore, the values 2, -2, and -2 replace letters A, B, and C respectively in the table of values for y = x² - 3x - 2.
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If g(x)=3x^2-4x+1 what is the value of g(-3)
Answer:
g(-3)= 40
Step-by-step explanation:
g(-3) simply means that where there is X, Substitute -3 into the original equation to find the value.
[tex]g( - 3) = 3( - 3) {}^{2} - 4( - 3) + 1[/tex]
[tex]g( - 3) = 27 + 12 + 1[/tex]
=40.
Answer:
40
Step-by-step explanation:
g(x)=3x^2-4x+1
g(-3)=3x^2-4x+1
g(-3)=3(-3)^2-4(-3)+1
g(-3)=27+12+1
g(-3)= 40
How do insurance companies use math?
Insurance companies use math in several ways to help them assess and manage risk, price their products, and make financial decisions. Some examples include:
Actuarial Science: Actuaries use statistical models and mathematical techniques to calculate the likelihood of future events, such as accidents, illnesses, or natural disasters. They use this information to price insurance policies and estimate the company's potential losses.Risk Management: Insurance companies use mathematical models to assess and manage the risk of potential losses. For example, they may use simulations to estimate the likelihood of different scenarios and the potential impact on their financials.Pricing: Insurance companies use mathematical models to set prices for their products. They take into account a wide range of factors, including the company's overhead costs, the level of risk, and the competition.Underwriting: Underwriters use mathematical models to assess the risk of insuring a particular individual or business. They take into account factors such as the individual's age, health, and occupation when determining the price of the policy.Investment: Insurance companies invest their premiums and reserves in different assets, such as stocks, bonds, and real estate. They use mathematical models to estimate the expected returns and risks of different investments.Fraud Detection: Insurance companies use statistical models and Machine learning algorithms to detect patterns of suspicious behavior that could indicate fraud.Claims Processing: Insurance companies use mathematical models to predict the costs of claims and manage the claims process. They may use data-driven methods to identify patterns in claims data and estimate the costs of claims.Read more about Insurance:
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20+5×9 written in a word expression in a numerical or algebraic expression
Answer:
Step-by-step explanation:
20 = 20 more than
5×9 = 9 times more than 5
So a proper response for a written word expression in a numerical or algebraic expression such as this one here would be:
A number is equal to 20 more than 9 times 5.
What is the LCM for (x+3)2(x-2) and (x+3)(x2-16)? Please explain step by step how to find answer!!
Answer: (x-2)(x+3)^2(x^2-16)
Step-by-step explanation:
(x+3)^2(x-2)
(x+3)(x^2-16)
(x+3)(x^2-16)=(x+3)(x+4)(x-4)
(x+3)^2(x-2)=(x+3)(x+3)(x-2)
LCM: (x+3)^2(x-2)(x^2-16)
Bodens account has a principal of $800 and a simple interest rate 3.8% complete the number line how much money will be in the account after 4 years assuming Boden does not add or take out any money
[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$800\\ r=rate\to 3.8\%\to \frac{3.8}{100}\dotfill &0.038\\ t=years\dotfill &4 \end{cases} \\\\\\ A = 800[1+(0.038)(4)] \implies A = 921.6[/tex]
Divide. Write your answer as a fraction in simplest form. −12÷(−25)
Answer:
4/9 in the simplest form
Step-by-step explanation:
When dividing by a negative number the sign of the quotient changes. so if the quotient is negative when the divisor and dividend have the same sign, it becomes positive when they have opposite sign. In this case -12 and -25 have opposite signs and the quotient will be positive, that's why the negative signs cancel out.
-12 / (-25) = 12/25 = 4/9 in the simplest form
Abby make tie-dyed T-hirt for her cla for her field trip. Each hirt cot 3. 95. For the dye it cot 0. 50 then bought two boxe of alt for 4. 50. If he ha 124. 70 how many can he make?
Abby can make 26 tie-dyed T-shirts.
We can start by setting up a linear equation to represent the total cost of making the tie-dyed T-shirts.
What is a linear equation?
First-order equations include linear equations. In the coordinate system, linear equations are defined for lines. A linear equation in one variable is one in which there is a homogeneous variable of degree 1 (i.e., just one variable).
Multiple variables may be present in a linear equation. Linear equations with two variables, for example, are used when a linear equation contains two variables.
Let x be the number of T-shirts Abby makes
The cost for each T-shirt is $3.95 + $0.50 = $4.45
The cost of the two boxes of salt is $4.50 * 2 = $9
So the total cost for x T-shirts is $4.45x + $9
We know that the total cost is 124.70 and we want to find the value of x, so we can set up the equation as:
$4.45x + $9 = 124.70
Solving for x:
$4.45x = 115.70
x = 115.70 / 4.45
x = 26
Therefore, Abby can make 26 tie-dyed T-shirts.
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which angles are vertical angles?
Answer:angle TSQ and angle UVX
Step-by-step explanation:
A pool i being drained by a pump at a rate of 4 gallon per minute. An identical pump wa added to help drain the pool. How doe the econd pump affect the rate of drainage?
A pool is being drained by a pump at a rate of 4 gallon per minute, then the second pump affect the rate of drainage = 8 minutes
For two identical pumps in parallel the flow rate doubles compared to single pump,
Single pump flow rate = 4 gallons per minute
When two pump act at same time, drain rate will be double,
Drain rate = 8 gallons per minute
The first pump can drain in 8 minutes, therefore:
Rate of the first pump = 1/8
Working together, they can drain the pool in 4 minutes, therefore:
Rate of both pumps = 1/4
Let the time taken by the second pump =t
Rate of the second pump = 1/t.
So,
We can write,
[tex]\frac{1}{8}[/tex] + [tex]\frac{1}{t}[/tex] = [tex]\frac{1}{4}[/tex]
[tex]\frac{1}{t}[/tex] = [tex]\frac{1}{4} -\frac{1}{8}[/tex]
[tex]\frac{1}{t}[/tex] = [tex]\frac{2-1}{8}[/tex]
[tex]\frac{1}{t}[/tex] = [tex]\frac{1}{8}[/tex]
t = 8 minutes
Therefore,
A pool is being drained by a pump at a rate of 4 gallon per minute, then the second pump affect the rate of drainage = 8 minutes
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A group of students was surveyed in a middle school class. They were asked how many hours they work on math homework each week. The results from the survey were recorded.
Number of hours Total number of students
0 1
1 3
2 2
3 5
4 9
5 7
6 3
Determine the probability that a student studied for 1 hour.
1.0
0.9
0.3
0.1
the required probability is 0.1
What is probability?Probability is a measure of the likelihood of an event occurring. The probability formula is defined as the possibility of an event happening is equal to the ratio of the number of favorable outcomes and the total number of outcomes. Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes.
Given here: 3 students study for an hour and total students are 30
Thus P(1 hour) =3/30
=0.1
Hence, the required probability is 0.1
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A+stack+of+30+science+flashcards+includes+a+review+card+for+each+of+the+following:+10+incects,+8+trees,+8+flowers,+and+4+birds+what+is+the+problilty+of+selecting+a+brid&ie=UTF-8&oe=UTF-8
The probability of selecting a bird would be = 2/15
What is probability?Probability is defined as the ability of an outcome to occur by chance or not.
The formula that can be used to calculate the outcome of an event= P(E) = number of favorable outcomes/Total number of outcomes
Where, P(E) is the probability of any event.
Let E be an event of selecting an insect.
According to the given question
We have
Total number of insects = 10
Total number of trees = 8
Total number of flowers = 8
Total number of birds = 4
Now, the total number of outcomes = 10 + 8 + 8 + 4 = 30
Total number of favorable outcomes(birds) = 4
Therefore,
The probability of selecting a bird = 4/30 = 2/15
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Complete question:
A stack of 30 science flashcards includes a review card for each of the
following: 10 insects, 8 trees, 8 flowers, and 4 birds.
What is the probability of randomly selecting a bird.
Which statement about adolecence is false
The statement about adolescence that is false, is D. Teens focus on how to contribute to the world.
What do people do at adolescence ?Young people will navigate puberty and the end of their growth during adolescence. They will also assume sexually dimorphic body shapes, develop new cognitive skills (including the ability to think abstractly), clarify their personal and sexual identities, and reach a certain level of emotional, personal, and financial maturity.
As a result, they can assume bigger responsibilities in the home and community, think through the effects of their choices, and develop their problem-solving and decision-making skills.
They do not focus on contributing to the world just yet.
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Options for this question include:
Teens take on greater responsibilities in the household and community.Teens consider the consequences of their actions.Teens learn to solve problems and make decisions in a mature way.Teens focus on how to contribute to the world.In the triangle below, suppose that mZS= (x+4)°, mZT= (x+4)°, and mU=(5x-3)°.
Find the degree measure of each angle in the triangle.
(5x - 3)
\-(x + 4)*
m Ls =
m2T =
0
0.
m2U = 0.
X
Ś
The measure of angle S = 29 degrees, angle T= 29 degrees, and angle U = 122 degrees.
What are internal angles?A triangle is a straightforward closed curve made up of three-line segments. An angle inside the form is known as an interior angle. The inner angles add up to a constant 180 degrees.
The sum of internal angle of the triangle is 180 degrees.
(x + 4) + (x + 4) + (5x - 3) = 180
7x + 5 = 180
7x = 175
x = 25
Substitute the value of x in each of the angle to find the measure of each angle as follows:
The value of angle S = x + 4 = 25 + 4 = 29 degrees.
The value of angle T = x + 4 = 25 + 4 = 29 degrees.
The value of angle U = 5x - 3 = 125 - 3= 122 degrees.
Hence, the measure of angle S = 29 degrees, angle T= 29 degrees, and angle U = 122 degrees.
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What are the 4 problem-solving methods?
Students must possess both the growth mindset necessary for problem-solving and strong reading skills. Some of the problem-solving methods are described.
Define the 4 problem-solving methods?The capacity to solve math word problems is an essential component of math fluency.
Concentrate on using mathematical key words and phrases.
Putting an emphasis on words and phrases is the first step in assisting students with math word problems. For instance, the terms combined or increased by can refer to addition.Mark this sentence for deletion:
Along with underlining crucial words, students should make an effort to separate important information from irrelevant details. Ask your students to cross out the unnecessary distracting information in the problem to help emphasize what is important.Promote Question-Asking:
During the time you give them to read, give them time to ask questions about what they've read. They will learn what to focus on and what to ignore by asking questions.Sketch the issue.
Allowing your students to draw the issue on graph paper is an entertaining way to aid in their understanding.To know more about the problem-solving methods, here
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A university's freshman class has 5400 students. 48% of those students are majoring
in Economics. How many students in the freshman class are Economics majors?
The number of students that are majoring in Economics is 2592 whose percentage is 48% of the total.
What is the percentage?
In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word percent means per 100. It is represented by the symbol “%”.
Examples of percentages are:
10% is equal to 1/10 fraction.20% is equivalent to ⅕ fraction.25% is equivalent to ¼ fraction.Now,
Total students=5400
Percentage of students doing majoring =48%
Hence,
The number of students that are majoring in Economics
=48/100*5400
=2592
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What is the additive inverse of 4 /- 7?
For the number -(4 / 7), the additive inverse would be (4 / 7).
The additive inverse of a number is the number that when added to the original number, the result is 0. In other words, it is the opposite of the original number.
To see this, let's add -(4 / 7) and (4 / 7) together:
-(4 / 7) + (4 / 7) = 0
This is because the negative sign in front of the fraction indicates that the fraction is the opposite of (4 / 7). So adding the two fractions together cancels out the opposite and results in 0.
In summary, the additive inverse of -(4 / 7) is (4 / 7) because adding the two fractions together results in 0, which is the definition of an additive inverse.
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is a perpendicular bisector of . What is true of any triangle created by points U, V, and any point on other than S
Write an equation, in point-slope form, of the line that is parallel to y=2x+3 and goes through the point (5, -4).
Answer:
The line parallel to y=2x +3 is
y=2x + k---(1)
Since,st.line (1) passes through point (5,-4) then,
-4=2(5)+k
or,k=-4-10
:.k= -14
Putting value of k in eqn(1) we get
y=2x -14
Hence, y=2x -14 is the line parallel to y=2x +3 and passes through point (5,-4)
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the cost of two star bars is the same as the cost of five toffee knobs . one star bar and one toffee knobs together cost 35 p . what do they each cost ?
Answer:
sorry I posted this question and never got and never got an answer
A beaker is considered full when the liquid reaches the fill line showing near the top estimate the amount of water in the beaker by shading The drawing as indicated The first one is done for you
The estimates for the requested shaded parts for 1 fourth is to divide the beaker into four parts and shade an area and 1 third, divide by three parts and shade one part as shown in the diagram.
What are fractions?A fraction is a portion of a larger whole. The number is expressed in arithmetic as a quotient, which is the numerator divided by the denominator. Both are integers in a simple fraction. A complex fraction contains a fraction in either the numerator or the denominator. A proper fraction has a numerator that is less than the denominator.
Proper fractions, improper fractions, and mixed fractions are the three types. Fractions are terms that have a numerator and a denominator. We define its types based on these two terms. One third is considered one part of 3 that makes a whole, one fourth, one part of 4 that makes a whole and so on.
The complete question is:
A beaker is considered full when the liquid reaches the fill line showing near the top estimate the amount of water in the beaker by shading The drawing as indicated The first one is done for you
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Please help me answer all of the questions! I'm sorry that it's so much but thank you to whoever helps me.
The surface areas for each of the cylinders are;
1) S = 10178.8 millimeters squared
2) S = 955.0 inches squared
3) S = 157.1 centimeters squared
4) S = 351 square inches
How to find the surface area of a cylinder?The formula for surface area of a cylinder is;
S = 2πr² + 2πrh
1) We are given;
radius; r = 30 mm
height; h = 24 mm
Thus;
S = 2π(30)² + 2π(30*24)
S = 10178.8 millimeters squared
2) We are given;
radius; r = 8 in
height; h = 11 in
Thus;
S = 2π(8)² + 2π(8*11)
S = 955.0 inches squared
3) We are given;
radius; r = 1 cm
height; h = 9 cm
Thus;
S = 2π(1)² + 2π(1*9)
S = 157.1 centimeters squared
4) We are given;
radius; r = 4 in
height; h = 10 in
Thus;
S = 2π(4)² + 2π(4*10)
S = 351 square inches
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At the grocery store, 7 pints of ice cream cost $6.85. How much would 25 pints of ice cream cost
Answer:
$24.46
Explanation:
$6.85÷7= 1 pint
you times the answer by 25 = $24.46
Answer:
Hi!
We will solve this using proportions, like this:
4 pints cost 10,08
30 pints cost x
__________________
x = (30 * 10,08)/4
x = 302,4/4
x = 75,6
30 pints of ice cream cost 75,6$.
Hope this helps!
Step-by-step explanation:
The point where the graphs of two equations intersect has y-coordinate 0. One equation is y=3x+3. Find the other equation if its graph has a slope of −1. Type the answer in the box below. y=
The equation of the graph is: y = -x.
How to Find the Equation of a Graph?The point where the graphs of two equations intersect has y-coordinate 0. If the y-coordinate is 0, that means that the x-coordinate of the point of intersection is the y-intercept of the equation.
The first equation is y = 3x + 3. Therefore, the slope of this equation is 3, and the y-intercept is 3.
The other equation we are trying to find is y = -1x + b, where b is the y-intercept.
Because the point of intersection has y-coordinate 0, the x-coordinate is the y-intercept of the second equation, which is b.
So, if we substitute 0 for y in the second equation, we get 0 = -1x + b
Therefore, b = 0
so the other equation is y = -1x + 0 which simplifies to y = -1x.
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The mapping diagram represents a relation where x represents the independent variable and y represents the dependent variable. A mapping diagram with one circle labeled x-values containing values negative 8, negative 5, negative 1, 1, and 12 and another circle labeled y values containing values negative 4 and negative 2 and arrows from negative 8 to negative 4, negative 5 to negative 2, negative 1 to negative 2, 1 to negative 2, 12 to negative 4, and 12 to negative 2. Is the relation a function? Explain. Yes, because for each input there is exactly one output Yes, because for each output there is exactly one input No, because for each input there is not exactly one output No, because for each output there is not exactly one input
Is the relation a function: C. No, because for each input there is not exactly one output.
How to determine the relationships that represent functions?In Mathematics, a function is typically used for uniquely mapping an independent value (input variable or domain) to a dependent value (range or output variable).
This ultimately implies that, an independent value represents the value on the x-axis of a cartesian coordinate while a dependent value represents the value on the y-axis of a cartesian coordinate.
Since the independent value (12) is mapped to multiple dependent values (-4 and -2), we can logically deduce that the relation does not represent a function.
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What is quadratic inequality form?
A quadratic inequality is an equation that takes the form of ax^2 + bx + c ≤ 0 or ax^2 + bx + c ≥ 0, where a, b, and c are real numbers and a is not equal to 0.
Solving Quadratic InequalitiesQuadratic inequalities are used to represent a relationship between two variables and can be used to solve a variety of problems. They can be used to find the maximum or minimum value of a function, or to determine the range of values for which a given equation is true. They can also be used to find the number of solutions to an equation and to compare the values of two functions. Quadratic inequalities are used widely in mathematics and other sciences and can help us to understand and solve many real-world problems.
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11. Tionna has $4.00 in dimes and
quarters in her car. She
counts a total of 25 coins.
Define the variables and write
a system of equations that
could be used to find a
solution.
Let [tex]d[/tex] be the number of dimes and [tex]q[/tex] be the number of quarters.
[tex]\begin{cases} 0.10d=4.00 \\ d+q=25 \end{cases}[/tex]