Answer:
Mark is 12 years old.
Step-by-step explanation:
Let's just define some variables:
J = Jason
A = Alex
M = Mark
Next, let's put the information given in the question into equations.
Since Jason is 10 years older than Alex we can represent it like this:
J = A + 10
Since Mark is 11 years younger than Alex we can represent it like this:
M = A - 11
All of their ages add up to 68 so we can represent that like this:
J + A + M = 68
We can now do some substitutions to the J and M in this equation, like this:
(A + 10) + A + (A - 11) = 68
Combine like terms:
3A - 1 = 68
Solve for A
3A = 69
A = 23
Now that we found that Alex is 23 we can plug that back in to the first equations to find their ages:
J = 23 + 10
J = 33
M = 23 - 11
M = 12
Mark is the youngest out of the siblings being 12 years old.
Check:
23 + 33 + 12 = 68
68 = 68 :)
I hope this helps!!
- Kay :)
there is a dart that lands uniformly randomly in space on a dartboard. the dartboard is 3 concentric circles with radius 1, 2, and 3
There are 160 possibilities for area codes
We are required to find all the combinations for different area codes
It is given to us that the conditions for the tree digit area code are:
first digit could be any number from 4 through 8,
the second digit was either 4 5 6 or 7, and the third digit could be any number except 2 or 7
Using the conditions above, the digits which can be first digit of code = 4 through 8 =4,5,6,7,8
the digits which can be second digit of code= 4,5,6,7
the digits which can be third digit of code = 0,1,3,4,5,6,8,9
number of possibilities for first digit= 5
number of possibilities for second digit=4
number of possibilities for third digit= 8
Therefore, total number of possibilities of code = number of possibilities of first digit x number of possibilities of second digit x number of possibilities of third digit = 5 x 4 x 8=160
Therefore, there are 160 possibilities for area codes
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proof that the span of two noncollinear vectors is the plane containing the origin and the heads of the vectors.
The Span of two noncollinear vectors is the plane containing the origin and the heads of the vectors.
Linear Span of vectors can be represented as
let [tex]x_{1} and x_{2}[/tex] be two non collinear vectors its span be written as [tex]x=a_{1} x_{1} +a_{2} x_{2}[/tex] where [tex]a_{1}, a_{2}[/tex] are arbitrary scalars.
Subspace of vectors : a subset A of a vector space V is called a subspace of V if A is itself a vector space under scalar multiplication and addition defined on V.
The Span of two vectors is a vector space containing two vectors. Hence the span is also a vector space . It is sufficient to notice that any two independent vectors from subspace can be the basis.
Zero vector is the linear combination of these basis vector.
hence it is not possible to have a span of two non collinear vectors that does not contain origin .
Therefore, The span of two noncollinear vectors is the plane containing the origin and the heads of the vectors.
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Is 6.5892 a rational number?
Answer:
No.
Step-by-step explanation:
Rational numbers can be written as a fraction.
Mr. Sowers wants to purchase expo markers for his classroom. He has a budget of $35. A four-pack of markers costs $5.49, including tax. Write and solve an inequality, using x for the variable, to solve for the number of packs of markers Mr. Sowers can purchase.
Answer:
5.49x=35
Step-by-step explanation:
the x is the number of markers
2-124. Troy is a fan of baseball, and his favorite player is Moe Jauer of the Minnesota Triplets. Troy made a table displaying how many home runs Jauer hit during his first five seasons. Graph Troy’s data.
The scatter plot showing Troy's data is given at the end of the answer.
What is a scatter plot, and why it is used in this problem?A scatter plot shows a series of points (x,y), relating the input x to the output y.
For this problem, it is used because we want to graph a discrete function, as:
The input x is the professional year of the baseball player. The output y is the number of home runs hit by the player in the year.Both professional year and home runs are countable amounts, that cannot assume decimal values, hence we have a discrete function and use a scatter plot.
From the table presented in this problem, the points for the scatter plot are given as follows:
(1,6), (2,9), (3,13), (4,7), (5,9).
The scatter plot, labeled and with the points, is shown by the graph at the end of the answer.
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Xio just took a math test with 25 questions, each worth an equal
number of points.
The test is worth 100 points total. If a score of 70
points earns a grade of C, how many questions would Xio need to get
right to get a grade a of C on the test?
Select ALL factors of 24.
Question options:
7
8
4
1
48
16
32
3
2
10
Answer:
1, 2, 3, 4, 8
Step-by-step explanation:
The 8 factors of 24 are:
1, 2, 3, 4, 6, 8, 12, 24
The factor pairs of 24 are:
1 × 24 = 24
2 × 12 = 24
3 × 8 = 24
4 × 6 = 24
can you help me and solve it
Answer:
I think its $4 I'm not sure tho
Step-by-step explanation:
Answer:
[tex] \large{ \star{ \boxed{ \tt \: answer : \: \$ \: 3.28 }}}[/tex]
Please see the attached picture for full solution!:)
-------- HappY LearninG <3 ----
The Spartan basketball team purchased equipment and uniforms for a total cost of $1,860. The equipment that was purchased cost $300, and the uniforms were $120 each. How many uniforms did the school purchase?
The number of uniforms the Spartan Basketball team purchased was 13.
How is the number of uniforms determined?The number of uniforms bought by the Spartan Basketball team can be determined using the mathematical operations of subtraction and division.
In the first place, the cost of equipment is subtracted from the total cost. The remainder is divided by the unit cost of uniforms. The quotient is the number of uniforms bought.
Data and Calculations:Total cost incurred = $1,860
Cost of equipment = $300
Remainder cost = $1,560 ($1,860 - $300)
Unit cost per uniform = $120
The number of uniforms bought = 13 ($1,560/$120)
Thus, the number of uniforms the Spartan basketball team purchased was 13.
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Given the following, what is the length, l?
V = lwh
V = 576, w = 6, h = 12
The value of l is. We use simple substitution of values to find the value of l is 48.
We have been given the equation V=lwh where l is the length, we can say that the given equation is that of volume of a cuboid where l is the length, w is the width and h is the height of the cuboid. We know the values of V,w and h. We have to substitute the values of V,w and h in the equation V=lwh inorder to find the value of l. Substitution method is generally used for solving system of equations where we first solve the value of one variable and then substitute the value in the other equation to find the value of the other variable. Since we only have one equation and we know the value of 3 of the 4 variables we only have to solve for one.
V=lwh
l=V/wh =[tex]\frac{576}{6.12} =\frac{576}{72}[/tex]= 48
Thus we get the value of l to be 48 by substituting the values of V,w and h.
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the area of a rectangle is 21, and the length of the rectangle is 1 less than twice the width. find the dimensions of the rectangle.
The dimensions of the rectangle = 6 ft
Geometry defined as:Along with arithmetic, geometry is among the oldest subfields of mathematics. It is concerned with spatial characteristics like the separation between objects, their shape and size, and their relative positions. Geometer is the term used to describe a mathematician who specializes in geometry.
Why does geometry matter so much?At a fundamental level, geometry is essential to understand because it lays the groundwork for learning more complex mathematical concepts. Raj Valli, the founder of Thinkster Math, notes that algebra and geometry frequently overlap. In science and math classes, it introduces crucial formulas like the Pythagorean theorem.
According to the given information:length = 2w - 1
We know that the area:
Area = length * width
Area = 2w - 1 * width
A= 2w^2 -w = 21
2w^2 - w -21 = 0. Solve for w using quadratic formula.
[-b±√(b2 - 4ac)]/2a
[1± √((-1)^2 - 4*2*(-21))]/(2*2)
[1± √(1+168)]/4
w = 3.5 ft
length = 2w - 1
= 2*3.5 - 1
= 6 ft
The dimensions of the rectangle = 6 ft.
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Suppose your cable company charges its customers $4 to rent a movie. An online membership costs $21 and members pay only $2.50 to rent a movie. For what number of movies is the cost the same?
The number of movies that will give same cost is 14 movies.
How to calculate the number of movies?From the information, the cable company charges its customers $4 to rent a movie and an online membership costs $21 and members pay only $2.50 to rent a movie.
Let the number of movies for same cost be represented by x. This will be:
(4 × x) = 21 + (2.50x)
4x = 21 + 2.50x
Collect like terms
4x - 2.50x = 21
1.50x = 21
Divide
x = 21/1.5
x = 14
The number of movies will be 14
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Please help me please
Answer:
A
Step-by-step explanation:
the big triangle is a bigger version of the smaller triangle, so it had to be a dilation.
Dilations of images are also similar, not congruent, so the answer is A.
what is the monthly difference in median income for a male versus a female when both have a bachelor's degree
Answer: $1,372
Step-by-step explanation:
If using the Labor Statistics Document
A men’s median weekly earning with Bachelor’s degree only is $1,384 * 4 weeks = $5,536
A women’s medium weekly earning with a Bachelor’s degree only is $1,041 * 4 weeks = $4,164
Subtract $5,536 - $4,164 = $1,372
The full sentences are:
The typical monthly salary for women with bachelor's degrees is $3,020.
The typical annual salary for a guy with an associate's degree is $36,432.
What is Mean?The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset. The term "average" is frequently used to describe this measure of central tendency.
Every month has four weeks.
The median monthly income is thus:
Earnings = 4 * $755
Earnings = $3020
As a result, the typical monthly salary for women with bachelor's degrees is $3,020.
The median annual income:
A man with an associate's degree makes $759 each week.
A month has four weeks, while a year has twelve months.
Hence, the annual median income is:
Earnings = 4 x 12 x $759
Earnings = $36,432
Thus, the typical annual salary for a guy with an associate's degree is $36,432.
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Complete question:
3. What is your monthly median income if you are a female with a bachelor's degree? _____
4. What is your yearly median income if you are a male with an associates degree? _____
Solve 6(x+3) < 3(2x+6)
Answer:
No solutions.
Step-by-step explanation:
Pre-Solving GivenWe are given the inequality 6(x+3) < 3(2x+6), and we want to solve the inequality for x.
SolvingWe can first do the distributive property on both sides, where we multiply each term on the left side by 6, and each term on the right by 3.
6(x+3) < 3(2x+6)
6x + 18 < 6x + 18
Solving inequalities is a lot like solving equations; we want to isolate the variable by itself on one side.
First, we can subtract 18 from both sides.
6x + 18 < 6x + 18
-18 -18
____________________
6x < 6x
Now, we can subtract 6x from both sides, to get 6x off the right side.
6x < 6x
-6x -6x
0 < 0
We now have the inequality 0 < 0. This is never true, as 0 is always equal to 0.
Therefore, there are no values of x that will make this true, because no matter what, we will end up with a false statement. The answer is no solutions.
Jackie played the drums in the band if he beat the drum at a rate of 110 beats per minute how many bets would he play in 4 1/2 minutes
Number of beats play by in 4[tex]\frac{1}{2}[/tex] minutes = 495 beats
The number of beats per minute is 110 beats.
The number of beats in 1 minute = 110
The number of beats in 4[tex]\frac{1}{2}[/tex] minute= 110×[tex]4\frac{1}{2}[/tex]
= 110 × 9/2
= 495 beats
Therefore we have total of 495 beats in [tex]4\frac{1}{2}[/tex] minutes.
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I will AWard Brainlist !!! Using your knowledge of special right triangles, find the length of y. Its Math problem Help!!!
thanks alot have good day/night.
Using relations in a right triangle, it is found that the length of y is given by:
[tex]y = 2\sqrt{6}[/tex]
What are the relations in a right triangle?The relations in a right triangle are given as follows:
The sine of an angle is given by the length of the opposite side to the angle divided by the length of the hypotenuse.The cosine of an angle is given by the length of the adjacent side to the angle divided by the length of the hypotenuse.The tangent of an angle is given by the length of the opposite side to the angle divided by the length of the adjacent side to the angle.The hypotenuse of both triangles is found as follows:
sin(60º) = 6/x.
[tex]\frac{\sqrt{3}}{2} = \frac{6}{x}[/tex]
[tex]x = \frac{12}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}}[/tex]
[tex]x = 4\sqrt{3}[/tex]
Hence length y is found as follows:
[tex]\cos{45^\circ} = \frac{y}{4\sqrt{3}}[/tex]
[tex]\frac{\sqrt{2}}{2} = \frac{y}{4\sqrt{3}}[/tex]
[tex]2y = 4\sqrt{6}[/tex]
[tex]y = 2\sqrt{6}[/tex]
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Part A
Fill in the blank question.
SHIPPING The U.S. Department of Commerce regulates how much the actual weight of a package can vary from its labeled weight. A package with a labeled weight of 9.4 pounds can have an actual weight that is plus or minus 0.22 pound.
Part A
Write an absolute value equation to represent the maximum and minimum acceptable weights of the package. Let x be the actual weight of the package.
The simplified value of the maximum weight is 9.62 and the minimum weight is 9.18. Also the function for the maximum and minimum weight is y + x and y - x
Here,
Given that, A package with a labeled weight of 9.4 pounds can have an actual weight plus or minus 0.22 pounds.
Let the weight labeled be y and the actual weight be x
Weight = y ± x
Maximum weight = y + x
Minimum weight = y - x
Weight = 9.4 ± 0.22
Now,
Maximum weight = 9.4 + 0.22 = 9.62 pounds
Minimum weight = 9.4 - 0.22 = 9.18 pounds
Thus, the simplified value of the maximum weight is 9.62 and the minimum weight is 9.18. Also, the function for the maximum and minimum weight is y + x and y - x
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Complete the equation describing how x and y are related.
X 0,1,2,3,4
y -1,3,7,11,15
y = [? ]x + []
Answer:
y = 4 x - 1
Step-by-step explanation:
hope this helps you.
.......
Answer:
.
Step-by-step explanation:
a man walked for five hours. first he walked along a level road, then up a hill; then he returned around and walked back to his starting place along the same route. he walked a constant 4 miles per hour on the level road, 3 mph uphill and 6 mph downhill. how far did the man walk?
When he walked a constant 4 miles per hour on the level road, 3 mph on uphill and 6 mph on downhill, then he walked 20 miles
Given,
A man walked for five hours
First he walked along a level road, then up a hill, then he returned around and walked back to his starting place along the same route.
We know,
Speed = Distance/ Time
Time = Distance / Speed
The speed when he walked on the level road = 4 miles per hour
Distance traveled on the level road = A
Time taken = [tex]\frac{A}{4}[/tex]
The speed when he walked on uphill = 3 miles per hour
Distance traveled on the level road = B
Time taken = [tex]\frac{B}{3}[/tex]
The speed when he walked on downhill = 6 miles per hour
Time taken = [tex]\frac{B}{6}[/tex]
Then he walked level road again
Total time taken = Time taken on level road+ Time taken on uphill+ Time taken on downhill+ Time taken on level road
[tex]\frac{A}{4}+\frac{B}{3}+\frac{B}{6}+\frac{A}{4}=5\\ \frac{3A+4B+2B+3A}{12}=5\\[/tex]
6A+6B=60
2A+2B=20
Hence, when he walked a constant 4 miles per hour on the level road, 3 mph on uphill and 6 mph on downhill, then he walked 20 miles
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give the inverse, contrapositive, and converse for each of the following state- ments: (a) if she finished her homework, then she went to the party. (b) if he trained for the race, then he finished the race. (c) if the patient took the medicine, then she had side effects. 3
The inverse of (a) is If she did not go to the party, then she will not finish her homework.
The inverse of (b) is If he did not finish the race, then he will not have trained for the race.
The inverse of (c) is If she has no side effects then the patient will not take the medicine.
The converse of (a) is if she finished her homework, then she went to the party.
The converse of (b) is if he trained for the race, then he finished the race.
The converse of (c) is if the patient took the medicine, then she had side effects.
The contrapositive of (a) is if she did not finish her homework, then she did not go to the party.
The contrapositive of (b) is if he did not train for the race, then he will not finish the race.
The contrapositive of (c) is if the patient did not take the medicine, then she will not have side effects.
What do you mean by Inverse, Contrapositive, and Converse?Converse: By swapping the hypothesis and the conclusion, a statement can be made to mean the converse. "If two lines don't intersect, then they are parallel" is the inverse of "If two lines overlap, then they are parallel."
Inverse: Each of the original statements is presupposed to be false in an inverted statement. "If it is not snowing" would be the polar opposite of "If it is snowing." "Then it is not chilly" would be the polar opposite of "then it is cold."
Contrapositive: a statement or theorem created by swapping out the hypothesis and conclusion, or the subject and predicate, of a given statement or theorem. The opposite of "if A then B" is "if not-B then not-A."
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A veterinarian is investigating a new type of tick repellant to determine if it reduces the number of ticks on dogs compared to a current popular brand.
Part A: Which of the following design is most appropriate: observational study, experiment, census, or sample survey? Explain your reasoning.
Part B: Explain how you would implement the design you selected in Part A.
Part C: Explain one benefit your design would provide.
The most appropriate design is an experiment (A), this can be applied by having a control and an experimental group (B), and one benefit is that you can identify the effectiveness (C).
Why is the best design an experiment?Different from an observational study, a census or a survey that are used to collect information about people's preferences, an experiment allows you to test the effectiveness of a treatment, which is the main purpose in this case.
How to implement it?The bst is to have a control and an experiment group. For example you select 30 dogs and use the repelant in 15 dogs; then all dogs are exposed to ticks. As a result you can evaluate how effective the repelant is by comparing the two groups.
What benefit will this design provide?You can directly compare the two groups and determine the effectiveness of the repelant.The experiment can be replicated or repeated.Learn more about experiments in: https://brainly.com/question/11256472
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10. Before a race, you start 4 5/8 behind your friend. At the halfway point, you are 3 2/3 ahead your friend. What is the change in distance between you and your friend from the beginning of the race?
The change in distance between you and your friend from the beginning of the race is 8 7/24.
How to calculate the value?It should be noted that before the race, you start 4 5/8 behind your friend and at the halfway point, you are 3 2/3 ahead your friend.
Therefore, the change in distance will be the addition of the fractions given.
= 4 5/8 + 3 2/3
= 4 15/24 + 3 16/24
= 7 31/24
= 8 7/24
Therefore, the change in distance between you and your friend from the beginning of the race is 8 7/24.
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Ria has these two cubes.
The side length of the smaller cube is x cm.
The side length of the larger cube is twice the side length of the
smaller cube.
Write an expression for the side length of the larger cube in
terms of x.
Answer:
2x
Step-by-step explanation:
side length of smaller cube = x
side length of larger cube is two times the side length of smaller cube.
Therefore side length of larger cube = 2x
In an arithmetic sequence, if you are given a3=93 and a5=135, find a=100. Must show work to receive full credit.
The 100th term of the sequence is 2130.
How to calculate the value?a3 = a + 2d = 93
a5 = a + 4d = 135
Compute both equations
(4d - 2d) = (135 - 93)
2d = 42
d = 42/2 = 21
a + 2d = 93
a + 2(21) = 93
a + 42 = 93
a = 94 - 42 = 51
100th term will be:
= a + 99d
= 51 + 99(21)
= 51 + 2079
= 2130
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solve this please and thank you
Answer:
b 45
Step-by-step explanation:
its b ur welcome parallel
Answer:
Its 6x6
Step-by-step explanation:
because you have to count going up and over
Complete the explanation to identify the set of numbers that best describes the situation.
the amount of water in a glass as it evaporates
The amount can be any
number less than 0
, thus it is a
rational
number.
Phaedrus claims that this graph shows a straight
line. Is he correct? Explain why or why not.
Answer:yes
Step-by-step explanation:
ms. wilson draws a model of the factorization of a polynomial with integer factors. her model is partially complete. which equation is represented by ms. wilson’s model? n2 3n 40
n²+13n+40,
This is why;
Observe only the right side. The number is (n+8)(n+5).
Let's elaborate on that using FOIL.
F = When we multiply the first two terms, n and n, we obtain n².
O = outer instructs us to multiply n by 5 to get n*5 or 5n from the outer terms.
I = inner instructs us to multiply the inner expressions 8 by 8 and n by n to obtain 8n.
Since 8 and 5 are multiplied by L, we obtain 8*5 = 40.
Add up the outcomes: n²+5n+8n+40 = n²+13n+40
Observe how the phrase is a little bit simplified by the combination of the like terms (5n and 8n).
This demonstrates how (n+8)(n+5) becomes n²+13n+40, becoming the correct response. For all values of n, none of the other options are valid equations;
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What is the equation of the line?
Answer:
y=-1/3x
Step-by-step explanation:
The line decreasing from left to right. So, the slope of the line is a negative number. The only answer choice that has a negative number for the slope is A. y=-1/3x.
Hope this helps!
Please mark as brainliest if correct!
Answer:
y = 3x
Step-by-step explanation:
To find the equation of a graphed line, find the y-intercept and the slope in order to write the equation in y-intercept (y=mx+b) form. Slope is the change in y over the change in x.