The cylindrical jar above has a height of 12 centimeters and a radius of 4 centimeters. The jar contains 20 spherical marbles. Each marble has a radius of 0.8 centimeters. Which of the following represents the amount of space in the jar that is not occupied by marbles?
The volume of the cylindrical jar, the total volume of marbles, and then find the volume not occupied by the marbles.
The volume of the jar:
Volume of the cylindrical jar = πr²h = 3.142 × (4 cm)² × 12 cm = 603.168 cm³
The total volume of the marbles:
Total volume of 20 marbles = 20 × (4/3)π(0.8 cm)³ = 214.717 cm³
The volume not occupied by marbles:
Volume not occupied = Volume of the jar - Total volume of marbles = 603.168 cm³ - 214.717 cm³ = 388.451 cm³
Write an equation of the line that has a slope of -7 and y-intercept 6 in slope-intercept form.
y = mx + b solve for m (literal equations)
If quadrilateral ABCD is an isosceles trapezoid, which statements must be true? Check all that apply. (Pick more than one)
[] BC ∥ AD
[] BD ⊥ AC
[] BA ≅ CD
[] BE ≅ ED
[] ∠CBA ≅ ∠BCD
If quadrilateral ABCD is an isosceles trapezoid
The true statements among the given options are written below
BC || AD
So option (1) is correct.
AB ≅ DC
So option (3) is correct
∠CBA ≅ ∠BCD
So option (5) is correct.
In an isosceles trapezoid there is one pair of legs of equal length and a pair of parallel lines.
Given that quadrilateral ABCD is a isosceles trapezoid.
We have to check that out of the given options hold good for the isosceles trapezoid
[] BC ∥ AD
[] BD ⊥ AC
[] BA ≅ CD
[] BE ≅ ED
[] ∠CBA ≅ ∠BCD
In the given trapezoid ABCD
BC || AD ( pair of parallel sides )
So option (1) is correct.
AB ≅ DC ( For an isosceles trapezoid legs are equal)
So option (3) is correct
∠CBA ≅ ∠BCD (According to the property of isosceles trapezoid )
So option (5) is correct.
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Find the value of tan θ given cot θ=5/7.
13 1/2 divided by 2 1/4 please help i will mark brainliest
In buffalo, New York, the temperature was -14F in the morning. If the temperature dropped 7F, what is the temperature now?
The initial temperature in Buffalo was -14°F. After a drop of 7°F, the new temperature would be -21°F.
Explanation:The student asked: In Buffalo, New York, the temperature was -14°F in the morning. If the temperature dropped 7°F, what is the temperature now? To solve this, we need to perform a simple subtraction operation. We begin with the initial temperature of -14°F and subtract the temperature drop of 7°F.
The calculation is as follows:
Initial temperature: -14°F
Temperature drop: -7°F
New temperature: -14°F - 7°F = -21°F
Therefore, after the temperature drop, the new temperature in Buffalo would be -21°F.
After the temperature in Buffalo dropped by 7°F from an initial -14°F, the current temperature is now -21°F.
Explanation:In Buffalo, New York, the temperature was -14°F in the morning. If the temperature dropped 7°F, to find the current temperature, you subtract 7 from -14. This calculation is as follows:
Starting temperature: -14°FTemperature drop: 7°FCurrent temperature: -14 - 7 = -21°FTherefore, the temperature now in Buffalo is -21°F.
What is the probability of pulling out a green marble from a jar containing 5 red, 6 green, and 4 blue?
Dori and Malory are tracking their steps taken as a health goal. Dori leaves her house at 12:00 p.m. and walks at 50 steps per minute. Malory leaves her house at 12:20 p.m. and walks at 90 steps per minute.
At what time will Malory's steps catch up to Dori's steps?
What is the amount of space between two points on a line. It is always expressed as a nonnegative number
The amount of space between two points on a line is a distance.
What is a line segment?In Mathematics and Geometry, a line segment can be defined as the part of a line in a geometric figure such as a triangle, circle, quadrilateral, etc., that is bounded by two (2) distinct points. Additionally, a line segment typically has a fixed length.
In Mathematics and Geometry, the distance between two (2) end points that are on a coordinate plane can be calculated by using the following mathematical equation:
[tex]Distance = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}[/tex]
Where:
x and y represent the data points (coordinates) on a cartesian coordinate.
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How many factors does the algebraic expression 5xy have?
The algebraic expression 5xy has three factors: the number 5 and the variables x and y. Factors are the multiplicative components of an expression, and factoring involves breaking down expressions into these components.
The algebraic expression 5xy has three factors: the number 5, the variable x, and the variable y. A factor is a number, variable, or a product/quotient of numbers and/or variables separated by + or - signs.
When we are factoring, we are essentially reversing the distributive law and turning the expression into its multiple components, which can also be termed as factors or multiples. For instance, expressions like 5px, 5py, or similar expressions are all made up of factors that, when multiplied together, produce the value of the expression.
When addressing expressions that can be factored, such as ax² +2hxy+by² = 0, we look for expressions that, when evaluated, produce the same value. In this particular example, it can be factored into two linear factors and represents two straight lines intersecting at the origin.
Answer:
The algebraic expression [tex]\(5xy\)[/tex] has [tex]\(8\)[/tex] factors.
Explanation:
The algebraic expression [tex]\(5xy\)[/tex] can be factored as [tex]\(5 \times x \times y\)[/tex]. To find the number of factors, we count all the unique combinations of its prime factors:
- For the factor [tex]\(5\)[/tex], we have [tex]\(2\)[/tex] options: [tex]\(5\) or \(1\).[/tex]
- For the factor [tex]\(x\)[/tex], we have [tex]\(2\)[/tex] options: [tex]\(x\) or \(1\).[/tex]
- For the factor [tex]\(y\)[/tex], we have [tex]\(2\)[/tex] options: [tex]\(y\) or \(1\).[/tex]
Therefore, the total number of factors is the product of the options for each factor, which is [tex]\(2 \times 2 \times 2 = 8\)[/tex]. So, the algebraic expression [tex]\(5xy\)[/tex] has [tex]\(8\)[/tex] factors.
Evaluate the expression.
3 x (6^12/6^10)
a) 36
b) 39
c) 92
d) 108
How do you solve 1650÷55
Evaluate a + 6 for a = 10.
a)6
b)16
c)60
In a chemistry course, a student scored 99 on one test, 98 on another test, and 88 on each of the other tests. the student’s test average for the course, where each test is weighted equally, is exactly 91. what is the total number of tests that the student has taken in the course?
The total number of tests that the student has taken in the course will be 7.
What is Mean?The mean is the straightforward meaning of the normal of a lot of numbers. In measurements, one of the markers of focal propensity is the mean. The normal is alluded to as the number-crunching mean. It's the proportion of the number of genuine perceptions to the absolute number of perceptions.
In a chemistry course, a student scored 99 on one test, 98 on another test, and 88 on each of the other tests.
Let 'x' be the total number of tests in which he scored 88. Then the equation is given as,
(99 + 98 + 88x) / (2 + x) = 91
197 + 88x = 182 + 91x
91x - 88x = 197 - 182
3x = 15
x = 5
The total number of tests is given as,
Total tests = 2 + 5
Total tests = 7
The total number of tests that the student has taken in the course will be 7.
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He minimum and maximum temperature for a day in cupcake town can be modeled by the equation below: 3|x − 8| + 15 = 18 what are the minimum and maximum temperatures for this day?
What is the average of all integers from 11 to 35?
The average of all integers from 11 to 35 is determined by summing the first and last integers and dividing by 2. The calculation is (11 + 35) / 2, which equals to 23.
Explanation:Calculating the Average of Integers
To calculate the average of all integers from 11 to 35, you sum up all the integers and then divide by the number of integers. Since the numbers form an arithmetic sequence, we can use the formula for the average, which is: (first term + last term) / 2. Therefore, the average is (11 + 35) / 2.
The calculation would then be 46 / 2, which equals 23. This value represents the mean or average of the integer set from 11 to 35. The concept of finding the average is a fundamental aspect of statistics and general mathematics that is commonly applied in various practical scenarios.
The average of all integers from 11 to 35 is 46.
Explanation:To find the average of all integers from 11 to 35, we first calculate the sum of all the integers from 11 to 35. Then, we divide the sum by the total number of integers (i.e., 35 - 11 + 1 = 25). The sum of the integers from 11 to 35 is (11 + 12 + 13 + ... + 35). We can simplify this sum by using the formula for the sum of an arithmetic series: Sn = (n/2)(a + l), where Sn is the sum of the series, n is the number of terms, a is the first term, and l is the last term. Plugging in the values, we get Sn = (25/2)(11 + 35) = 25(46) = 1150. Now, we can find the average by dividing the sum by the total number of integers: Average = 1150/25 = 46. Therefore, the average of all integers from 11 to 35 is 46.
How do you rewrite y+4=-2(x-1) in slope-intercept form
Algebraic expression of 25 more than a number n
Which functions are symmetric with respect to the y-axis? Check all that apply.
f(x) = |x|
f(x) = |x| + 3
f(x) = |x + 3|
f(x) = |x| + 6
f(x) = |x – 6|
f(x) = |x + 3| – 6
Answer:
The correct options are 1, 2 and 4.
Step-by-step explanation:
The vertex form of an absolute function is
[tex]f(x)=|x-a|+b[/tex]
Where, (a,b) is the vertex of the function and x=a is axis of symmetry.
The function is symmetric with respect to the y-axis. It means the axis of symmetry is x=0. It is possible if the value of a in the vertex form is 0.
In option 1,
[tex]f(x)=|x|[/tex]
Here, a=0 and b=0.
Since the value of a=0, therefore it is symmetric with respect to the y-axis.
In option 2,
[tex]f(x)=|x|+3[/tex]
Here, a=0 and b=3.
Since the value of a=0, therefore it is symmetric with respect to the y-axis.
In option 3,
[tex]f(x)=|x+3|[/tex]
Here, a=-3 and b=0.
Since the value of a≠0, therefore it is not symmetric with respect to the y-axis.
In option 4,
[tex]f(x)=|x|+6[/tex]
Here, a=0 and b=6.
Since the value of a=0, therefore it is symmetric with respect to the y-axis.
In option 5,
[tex]f(x)=|x-6|[/tex]
Here, a=6 and b=0.
Since the value of a≠0, therefore it is not symmetric with respect to the y-axis.
In option 6,
[tex]f(x)=|x+3|-6[/tex]
Here, a=-3 and b=-6.
Since the value of a≠0, therefore it is not symmetric with respect to the y-axis.
Hence the correct options are 1, 2 and 4.
How do I solve 8n= -3m + 1 ; n= -2, 2, 4
what is the expression 13b−13 factored?
Simplify 7a+(-10)-2a+1
What is the product of (3√8)(4√3)? Simplify your answer
PLEASE HELP 20 POINTS
According to the Alternating Interior Angles theorem, which pair of angles is congruent?
∠SQU and ∠SRW
∠UQR and ∠WRT
∠VQR and ∠WRQ
∠TRZ and ∠TRW
According to the Alternating Interior Angles theorem, the pair of angles that are congruent are ∠TRZ and ∠TRW. Here option D is correct.
The Alternating Interior Angles theorem states that when a pair of parallel lines are intersected by a transversal, the alternating interior angles are congruent.
A - ∠SQU and ∠SRW: These angles are not alternate interior angles; they are on the same side of the transversal.
B - ∠UQR and ∠WRT: These angles are not alternate interior angles either; they are corresponding angles.
C - ∠VQR and ∠WRQ: These angles are alternate interior angles, but they are not congruent. They are supplementary, meaning their measures add up to 180 degrees.
D - ∠TRZ and ∠TRW: These angles are alternate interior angles and are congruent according to the Alternating Interior Angles theorem.
So, the correct answer is option D - ∠TRZ and ∠TRW.
Complete question:
According to the Alternating Interior Angles theorem, which pair of angles is congruent?
A - ∠SQU and ∠SRW
B - ∠UQR and ∠WRT
C - ∠VQR and ∠WRQ
D - ∠TRZ and ∠TRW
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Math Help Please!!!
On a team’s opening day, fans in a baseball stadium were asked how many home games they plan to attend this season. The histogram shows the results. How many fans plan on attending fewer than 20 games?
Answer: 25
Step-by-step explanation:
Given : On a team’s opening day, fans in a baseball stadium were asked how many home games they plan to attend this season.
In the given histogram , it can be seen that the number of fans attending fewer than 10 = 8
And the number of fans attending between 10-20=17
Then, the number of fans attending fewer than 20 games =[tex]8+17=25[/tex]
Therefore, 25 fans plan on attending fewer than 20 games
Which would hold more milk- a liter or a quart? by how much?
Based on conversion:
1 liter of milk is equivalent to 1.05669 US liquid quart. (1000mL)
While 1 quart of milk is equivalent to 0.946353 liters. (946.353mL)
This concluded that a liter would hold more milk by 0.053647
liters or 53.647 mL.
But if you are talking about an imperial quart, this will hold more milk than a liter. Because its measures 1136 mL which is 136mL bigger than the liter.
A liter holds more milk than a quart by approximately 0.057.
Explanation:A liter holds more milk than a quart.
1 liter is equivalent to approximately 1.057 quarts. Therefore, a liter holds about 0.057 more milk than a quart.
For example, if a quart can hold 4 cups of milk, a liter can hold approximately 4.23 cups of milk.
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the store employee works 35 hours per week,which inequality can be used to find the dollar value x, of weekly sales that the employee must make to earn more than $400 per week
Answer:
35x>400 can be used to find the value of x
Step-by-step explanation:
Here, we have given the information employee works for 35 hours a week
Let, x be the number of hours employee can work
Here it will become 35 x since, he is working for 35 hours
Employee is earning more than $400 per week
The inequality is formed from the given information as below:
35x>400
x>80/7
Therefore, 35x>400 can be used to find the value of x which is giving value of x>80/7
A line has a slope of 1/2 and contains the points (3, y) and (5, 7). The value of y is
6 or 3
please explain why or how!
Which of the following is always irrational?
A. the sum of two fractions
B. the product of a fraction and a repeating decimal
C. the sum of a terminating decimal and the square root of a perfect square
D. the product of a repeating decimal and the square root of a non-perfect square
Answer:
Correct choice is D
Step-by-step explanation:
Option A. The sum of two fractions is a fraction, a fraction is always rational number.
Option B. The product of a fraction and a repeating decimal can be rational number. For example,
[tex]\dfrac{3}{2}\cdot 0.\overline{3}=\dfrac{3}{2}\cdot \dfrac{1}{3}=\dfrac{1}{2}.[/tex]
Option C. The sum of a terminating decimal and the square root of a perfect square is always rational number, because the terminating decimal is a decimal that ends and the square root of a perfect square is a natural number. The product of decimal that ends and natural number is rational number.
Option D. The product of a repeating decimal and the square root of a non-perfect square is always irrational, because the square root of a non-perfect square is irrational number and when multiplying irrational number by fraction (any repeating decimal can be written as fraction) you get irrational number.