Richard and Teo have a combined age of 21. Richard is 3 years older than twice Teo’s age. How old are Richard and Teo?

Answer:

n > 10 meaning, n is greater than 10

Step-by-step explanation:

Two times a number  :  2n

Less 4  :  -4

2n-4

Greater than the same number :  >n

Plus 6  :  +6

> n+6

2n-4 > n+6

To find n, we have to get n alone and equal to a single number. To do this, we first subtract 6 from both sides.

2n-10 > n

Then, subtract 2n from both sides

-10 > -n

Now, divide by -1

10 < n

So, n is greater than 10

90 yards of fence should be purchased

We have:

Dimensions of the pool: 40 yards by 20 yards

Ratio of the dimensions of the fence to the dimensions of the pool: 3/2

Thus, we can say:

The length of the fence is:

3/2 * 40 yards = 60 yards

The width of the fence is:

3/2 * 20 yards = 30 yards

The total length of the fence is:

60 yards + 30 yards = 90 yards

Therefore, 90 yards of fence should be purchased

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Answer:

I apologize if this was poorly explained. The explanation for each is below the angle.

Since these triangles are in a rectangle, The top and bottom triangles are congruent, and the left and right triangles are congruent. All 4 triangles are also Isosceles. (Two equal sides/angles)

m<1= 59

(Left and right triangles are congruent)

m<2=31

(Top and bottom triangles are congruent)

m<3= 59

(Directly across from the other 59)

m<4=31

(Each of the rectangles corner angles totals to 90 degrees, therefore making this angle 31 degrees.)

m<5=31

(Since the triangles are isosceles, this angle is also 31)

m<6= 59

(Since m<5 is 31, this angle is 59.)

m<7=118

{(Two other angles in the triangle) 31+31= 62 180-62= 118)}

m<8=62

{(Two other angles in the triangle)59+59= 118. 180-118= 62}

m<9=62

(This angle and m<8 are congruent.)

m<10=118

(This angle and m<7 are congruent.)

m<11=31

(Same reason as m<4)

I hope this helps!

Answer: -416/1575

Step-by-step explanation:

\(\frac{4}{5}=\frac{20}{25} \implies \frac{4}{5}+\frac{6}{25}=\frac{26}{25}\\\)

\(\frac{8}{9}=\frac{56}{63}\\\\-\frac{8}{7}=-\frac{72}{63}\\\\\implies \frac{8}{9}-\frac{8}{7}=-\frac{16}{63}\)

\(\frac{26}{25} \times -\frac{16}{63}=-\frac{416}{1575}\)

Answer:

1 and 11/15.

Step-by-step explanation:

To solve, we can separate the integers from the fractions.

(6 - 4) + (2/5 - 2/3)

= 2 + (6/15 - 10/15)

= 2 + (-4/15)

= 1 + 15/15 - 4/15

= 1 + 11/15

= 1 and 11/15

Hope this helps!

Answer: D. 3x +28 > 52

Step-by-step explanation:

Based on the information given, the inequality that Maria can use to find how many more bracelets she needs to sell to make more money than she spent on supplies will be calculated thus:

With the question above, the total sales must be greater than the amount spent on supplies. Let the number of bracelets that needs to be sold be represented by x.

Therefore, (3 × x) + 28 > 52

= 3x + 28 > 52.

We can calculate further

3x > 52 - 28

3x > 24

x > 24/3

x > 8

Therefore, 9 or more bracelets needs to be sold since x is greater than 8.

Therefore, the correct option is D 3x +28 > 52

Answer:

D. 3x + 28 > 52

Step-by-step explanation:

Tukey's procedure, also known as the Tukey-Kramer test, a statistical method used to compare multiple groups and identify significant differences in their means. Tukey's procedure is used to identify differences in the true average bond strengths among the five protocols in Example 10.3.

Tukey's procedure, also known as the Tukey-Kramer test, a statistical method used to compare multiple groups and identify significant differences in their means. In this case, we are applying Tukey's procedure to the data in Example 10.3, which consists of bond strengths measured under five different protocols.

To perform Tukey's procedure, we first calculate the mean bond strength for each protocol. Next, we compute the standard error of the mean for each protocol. Then, we calculate the Tukey's test statistic for pairwise comparisons between the protocols. The test statistic takes into account the means, standard errors, and sample sizes of the groups.

By comparing the Tukey's test statistic to the critical value from the studentized range distribution, we can determine if there are statistically significant differences in the true average bond strengths among the protocols. If the test statistic exceeds the critical value, it indicates that there is a significant difference between the means of the compared protocols.

Using Tukey's procedure on the data in Example 10.3 will allow us to identify which pairs of protocols have significantly different average bond strengths and provide insights into the relative performance of the protocols in terms of bond strength.

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Answer:

The first number (x) = 8

Step-by-step explanation:

Let x = the first number

Let y = the second number

x = 3*y - 4

2x + 3 - 2y = 11        Subtract 3 from both sides

2x - 2y = 11 - 3

2x - 2y = 8              Divide by 2

x - y = 4                   Add y to both sides

x = y + 4                  Now go back to the very first equation. Substitute for x

y + 4 = 3y - 4          Subtract y from both sides

4 = 3y - y - 4

4 = 2y - 4                Add 4 to both sides

4 + 4 = 2y

8 = 2y                     Divide by 2

8/2 = y

y = 4

x = 3y - 4

x = 3*4 - 4

x = 12 - 4

x = 8

(a) To solve the recurrence relation T(n) = T(n-1) + 3, we can expand it recursively:

T(n) = T(n-1) + 3

    = (T(n-2) + 3) + 3

    = T(n-2) + 2*3

    = T(n-3) + 3*3

    = T(n-4) + 4*3

    = ...

    = T(n-k) + k*3

We can observe that T(n-k) = T(1) = 0, as given in the initial condition. So, we have:

T(n) = T(n-k) + k*3

    = 0 + k*3

    = 3k

Therefore, the solution to the recurrence relation T(n) = T(n-1) + 3 with T(1) = 0 is T(n) = 3n.

(b) To solve the recurrence relation T(n) = 3T(n-1) with T(1) = 2, we can expand it recursively:

T(n) = 3T(n-1)

    = 3*(3T(n-2))

    = 3*(3*(3T(n-3)))

    = ...

    = 3^k * T(n-k)

We can observe that T(n-k) = T(1) = 2, as given in the initial condition. So, we have:

T(n) = 3^k * T(n-k)

    = 3^k * 2

Since n = n - k, we can solve for k:

n - k = 1  =>  k = n - 1

Substituting this value of k into the solution, we get:

T(n) = 3^(n-1) * 2

Therefore, the solution to the recurrence relation T(n) = 3T(n-1) with T(1) = 2 is T(n) = 3^(n-1) * 2.

(c) To solve the recurrence relation T(n) = T(n/2) + 2n with T(1) = 1, we can expand it recursively:

T(n) = T(n/2) + 2n

    = (T(n/4) + 2*(n/2)) + 2n

    = T(n/4) + 2*(n/2) + 2n

    = T(n/4) + 3n

    = (T(n/8) + 2*(n/4)) + 3n

    = T(n/8) + 2*(n/4) + 3n

    = T(n/8) + 4n/2 + 3n

    = T(n/8) + 7n/2

    = ...

    = T(n/2^k) + (2^k - 1)n/2

We can observe that T(n/2^k) = T(1) = 1, as given in the initial condition. So, we have:

T(n) = T(n/2^k) + (2^k - 1)n/2

    = 1 + (2^k - 1)n/2

Since n = 2^k, we can solve for k:

2^k = n  =>  k = log2(n)

Substituting this value of k into the solution, we get:

T(n) = 1 + (2^(log2(n)) - 1)n

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The algebraic representation that shows a dilation that is an enlargement is (5/2 x,5/2 y). (Option D)

A dilation is a type of transformation that changes the size of the shape or object.  It refers to a process of changing an object’s size by decreasing or increasing its dimensions by a scaling factor. A dilation produces an image that has the same shape as the original image but is a different size.

A dilation that results in a larger image is called an enlargement while a dilation that generates a smaller image is called a reduction. A dilation is described using the scale factor and the center of the dilation (which is a fixed point in the plane).

For a scale factor > 1, the image is an enlargement; for a scale factor < 1 and  > 0, the image is a reduction; and for a scale factor = 1, the figure and the image are congruent. Hence, for a point (x,y), algebraic representation that shows a dilation that is an enlargement is (5/2 x,5/2 y) as the scale factor is greater than 1. For the remaining options, the scale factor is between 0 and 1, hence they are reduction.

Note: The question is incomplete. The complete question probably is: Which of the following algebraic representation shows a dilation that is an enlargement? A) (1/3 x,1/3 y) B) (0.1x, 0.1y) C) (5/6 x,5/6 y) D) (5/2 x,5/2 y)

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Answer:

28 tickets

Step-by-step explanation:

252/9=28

Answer:

2.08 this is answer

Answer:

It's A

Step-by-step explanation:

Because both triangles have the same side connected to, which means that that side is congruent to each other and because it tells us that JL and JK are congruent and KM and ML are congruent that means that its sss. Also, it is not giving us an angle to find the congruence so it has to be sss.

The probability of customers buying each insurance is 1/24.

Probability is the branch of Mathematics that deals with the measurement of the chance of occurrence of a random event.

The probability of any event always lie in the close interval of 0 and 1 [0,1].

Given that,

Total number of sales is 6.

Total number of customers is 12.

The number of customers interested only in auto insurance is 6.

The number of customers interested only in homeowners insurance is 4.

The number of customers interested only in life insurance is 2.

Now, the probability that two sales are for auto insurance is given as,

2/6 = 1/3

The probability that two sales are for homeowners insurance is given as,

2/4 = 1/2

And,  the probability that two sales are for life  insurance is given as,

2/4 = 1/2

Thus the probability of two sales for each insurance is given as the product of all the three probabilities as,

 1/3 × 1/2 × 1/2 = 1/12

And, the probability of six customers out of 12  buying the sales is,

6/12 = 1/2

Thus, the probability for the given case is,

1/2 × 1/12 = 1/24

Hence, the probability for the given problem is 1/24.

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The minimum vertical distance between the curves y = x^2 + 1 and y = x - x^2 is approximately 0.7937 units.

To find the minimum vertical distance between the lines y = x^2 + 1 and y = x - x^2, we can set these two equations equal to each other and solve for x:

x^2 + 1 = x - x^2

Rearranging, we get:

2x^2 - x + 1 = 0

We can use the quadratic formula to solve for x:

x = [1 ± sqrt(1 - 4(2)(1))]/(2(2))

x = [1 ± sqrt(-7)]/4

Since the discriminant of the quadratic equation is negative, the roots are imaginary and there are no real solutions for x. Therefore, the two curves do not intersect, and the minimum vertical distance between them is the shortest distance between any point on one curve and any point on the other curve.

To find this minimum distance, we can use the perpendicular distance between the curves. The line perpendicular to the curve y = x^2 + 1 at a point (a, a^2 + 1) will have a slope of -1/(2a), since the derivative of the curve at that point is 2a. Therefore, the equation of the perpendicular line is:

y - (a^2 + 1) = (-1/(2a))(x - a)

The intersection of this line with the curve y = x - x^2 will give us the point on the second curve that is closest to the first curve. Substituting y = x - x^2 into the equation of the perpendicular line, we get:

x - x^2 - (a^2 + 1) = (-1/(2a))(x - a)

Simplifying and solving for x, we get:

x = (2a^3 - 2a^2 - a + 1)/(2a^2 + 1)

Substituting this value of x back into the equation y = x - x^2, we get:

y = (2a^3 - 2a^2 - a + 1)/(2a^2 + 1) - (2a^6 - 4a^5 + 2a^4 + 1)/(4a^4 + 2a^2 + 1)

Simplifying, we get:

y = (-2a^7 + 6a^6 - 6a^5 + 3a^4 - a^3 + 2a^2 - a + 1)/(4a^4 + 2a^2 + 1)

Now, we can use calculus to find the minimum value of this expression. Taking the derivative with respect to a and setting it equal to zero, we get:

-14a^6 + 36a^5 - 30a^4 + 12a^3 - 3a^2 + 4a - 1 = 0

This equation has no closed-form solution, but we can use numerical methods to approximate the value of a that minimizes the expression. Solving this equation numerically, we get:

a ≈ 0.3538

Substituting this value of a back into the expression for y, we get:

y ≈ 0.7937

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Answer:

24 would prefer CREST

6 woul NOT prefer Crest

Step-by-step explanation:

4:5=x:30

Answer:

Step-by-step explanation:

See image

-1/7, since parallel lines have equal slopes.

Answer:

12 miles

Step-by-step explanation:

Answer:

12 miles

Step-by-step explanation:

20 * 3 = 60 minutes

4 * 3 = 12 miles

Hope this is helpful:)

The measure of the obtuse angle in the triangle is 108 degrees.

A triangle is a polygon with three sides. The total sum of the angles in a triangle is 180 degrees.

Therefore, the measure of the obtuse angle in the triangle can be found as follows;

An obtuse angle is an angle which is greater than 90° and less than 180°.

Hence, the angles of the triangle are 1x, 3x and 6x.

3x + 1x + 6x = 180

10x = 180

x = 180 / 10

x = 18

Therefore, the obtuse angle of the triangle is 6(18) = 108 degrees.

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Answer:

c) 108 on edgen

Answer:

1st- x=140°

2nd-x=90°

Step-by-step explanation:

The interior angle of a 9 -sided polygon is 140x9=1260

divide by 9

The interior angles of a triangle always add up to 180

90°each

Answer:

Heres the general Idea i Got

Step-by-step explanation:

You can Connect the various shapes into traingles and rectangles . for ex : from -8 to 4 you can form a traingle. and then from B to G you can form a rectangle, From G to H by moving straight along G you can make another traingle and so on You can use your imagination to figure the total area by adding up those small figures you just made !

Case 1: Carter needs a fence with a length of 78.724 yards.

Case 2: Carter needs a grass sod with an area of 178 square yards.

In this problem we find the representation of a backyard, which is a combinations of areas of triangles and rectangles, whose formulas are introduced below:

Rectangle

A = b · h

Triangle

A = 0.5 · b · h

Where:

The perimeter of the backyard is the sum of its sides, where oblique sides are determined by Pythagorean theorem. Now we proceed to compute for each each case:

Case 1 - Carter needs the length of the fence.

p = 8 yd + √[(10 yd)² + (6 yd)²] + 6 yd + 4 yd + 4 yd + 6 yd + 6 yd + √[(7 yd)² + (4 yd)²] + 18 yd + 7 yd

p = 78.724 yd

Case 2 - Carter needs the area of the grass sod.

A = 0.5 · (10 yd) · (6 yd) + (7 yd) · (8 yd) + (13 yd) · (6 yd) + 0.5 · (7 yd) · (4 yd)

A = 178 yd²

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The work required to pump the water out of the spout is 5000ft⋅lb

Given

The volume V=12(4ft)(5ft)(6ft)=60ft3,

Then the weight is w = γV = (62.5lb /ft³) (60ft³) = 3750lb.

Since work is force × distance, you need a distance here, and the appropriate one is the distance you must raise the center of mass to get the H2O out of the spout.

Since the center of mass of a uniform triangular area is 13 of the way from any side, the distance is (4ft)/3 so the work is (3750lb) (4ft)/3=5000 ft-lb.

In calculus, the area of a horizontal section yft from the lowest point is (5ft) × (6ft) × y / (4ft) = 7.5y ft2.

We have to lift that slice 4ft−y, so work is

w = \(\int\limits^4_0\) (62.5)(4 − y) (7.5y)

dy = (62.5)[15y2−2.5y3]40  = 5000ft⋅lb

The work required to pump the water out of the spout is  5000ft-lb

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Step-by-step explanation:

how many times is the money of the elder brother ?

this is the same to ask "how many times do I need to add the money of the younger brother to get the money off the older brother ?"

this is simply done by division : how many times do 56 fit into 280 ?

280 / 56 = 5

so, the elder brother has 5 times the money of the younger brother.

Answer:

56+56+56+56+56

hence

5 times

Answer:

0.2

Step-by-step explanation:

The standard form of the equation of a direct proportion is

y = kx

Substitute x and y with values from one given point, and solve for k.

0.4 = k × 2

2k = 0.4

k = 0.2

Answer: 0.2

Answer:

x

Explanation:

Let cost of leash = y

14.26 - y = x

Hope this helps and have a great day :)

And please mark me brainliest if you can :)

Answer:

2/5, 1/5

Step-by-step explanation: