Jason is 10 years older than Alex. Mark is 11 years younger than Alex. If the total of their ages is 68, how old is the youngest of them?

The 100th term of the sequence is 2130.

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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Answer:

I think its $4 I'm not sure tho

Step-by-step explanation:

Answer:

[tex] \large{ \star{ \boxed{ \tt \: answer : \: \$ \: 3.28 }}}[/tex]

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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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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

Answer:

y = 4 x - 1

Step-by-step explanation:

hope this helps you.

.......

Answer:

.

Step-by-step explanation:

The scatter plot showing Troy's data is given at the end of the answer.

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:

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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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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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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The number of uniforms the Spartan Basketball team purchased was 13.

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.

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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Answer:

No.

Step-by-step explanation:

Rational numbers can be written as a fraction.

Answer:yes

Step-by-step explanation:

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.

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

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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The number of movies that will give same cost is 14 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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The change in distance between you and your friend from the beginning of the race is 8 7/24.

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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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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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).

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.

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.

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Answer:

5.49x=35

Step-by-step explanation:

the x is the number of markers

Using relations in a right triangle, it is found that the length of y is given by:

[tex]y = 2\sqrt{6}[/tex]

The relations in a right triangle are given as follows:

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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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

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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The dimensions of the rectangle =  6 ft

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.

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.

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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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.

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? _____

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.

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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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.

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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Answer:

No solutions.

Step-by-step explanation:

We are given the inequality 6(x+3) < 3(2x+6), and we want to solve the inequality for x.

We 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.