The are of the triangle below is 28.8 square centimeters. What is the length of the base?

Answer:

18vw²y^9 + 24v^6w^5

= 6vw²( 3y^9 + 4v^5w³)

Hope this helps.

Answer:

6vw^2(3y^9 + 4v^5w^3)

Step-by-step explanation:

If you were to multiply the equation 6vw^2(3y^9 + 4v^5w^3) then the result would be

18vw^2y^9 + 24v^6w^5

Hope this helps!

Answer:

12 kittens

36 puppies

Step-by-step explanation:

The probability that the medication is effective in 45 of the 50 patients is approximately 0.0204, or 2.04%.

To calculate the probability that the medication is effective in 45 of the 50 patients, we can use the binomial distribution formula. The binomial distribution formula calculates the probability of getting a specific number of successes (in this case, effectiveness) in a fixed number of trials (in this case, patients).

The formula is:

P(X=k) = (n choose k) * p^k * (1-p)^(n-k)

where:

P(X=k) is the probability of getting k successes (45 in this case)

n is the number of trials (50 in this case)

k is the number of successes (45 in this case)

p is the probability of success in each trial (0.8 in this case)

Plugging in the numbers:

P(X=45) = (50 choose 45) * 0.8^45 * (1-0.8)^(50-45)

P(X=45) = (50 choose 45) * 0.8^45 * (1-0.8)^5

P(X=45) = 0.0204

So the probability that the medication is effective in 45 of the 50 patients is approximately 0.0204, or 2.04%.

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Answer:

75m

Step-by-step explanation:

1) The common-difference is -1.2.

2) The 15th term is 40.4.

3)The sum of the first 292 terms is 35,553.6.

1. The first term of an arithmetic sequence is 9, and the sixth term is 3. We need to find the common difference.

Using the formula for the nth term of an arithmetic sequence:

Tn = a + (n - 1)d

We can plug in the values:

T1 = 9

T6 = 3

n = 6

3 = 9 + (6 - 1)d

3 = 9 + 5d

-6 = 5d

d = -6/5

d = -1.2

The common difference is -1.2.

2.The 32nd term of an arithmetic sequence is 14.9, and the common difference is -1.5. We need to find the 15th term.

Using the formula for the nth term of an arithmetic sequence:

Tn = a + (n - 1)d

We can plug in the values:

T32 = 14.9

n = 32

d = -1.5

T32 = a + (32 - 1)(-1.5)

14.9 = a + 31(-1.5)

14.9 = a - 46.5

a = 14.9 + 46.5

a = 61.4

Now we can find the 15th term:

T15 = 61.4 + (15 - 1)(-1.5)

T15 = 61.4 + 14(-1.5)

T15 = 61.4 - 21

T15 = 40.4

The 15th term is 40.4.

3.The first term of an arithmetic sequence is 5, and the common difference is 0.8. We need to find the sum of the first 292 terms.

Using the formula for the sum of an arithmetic sequence:

Sn = (n/2)(2a + (n - 1)d)

We can plug in the values:

a = 5

n = 292

d = 0.8

Sn = (292/2)(2(5) + (292 - 1)(0.8))

Sn = 146(10 + 233.6)

Sn = 146(243.6)

Sn = 35,553.6

The sum of the first 292 terms is 35,553.6.

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1) The common difference in the arithmetic sequence is -1.2.

2) The 15th term of the arithmetic sequence is 40.4.

3) The sum of the first 292 terms of the arithmetic sequence is 28626.4.

4) The balance in the account after 5 years will be $13,760.

5) The balance in the account after 30 months will be $8,474.4.

6) The monthly payment amount will be $137.90

7) The simple annual interest rate charged by The Saver is 415%

Exp:

Question 1:

To find the common difference in an arithmetic sequence, we can use the formula:

common difference = (sixth term - first term) / (6 - 1)

In this case, the first term is 9 and the sixth term is 3. Plugging these values into the formula:

common difference = (3 - 9) / (6 - 1)

common difference = -6 / 5

common difference = -1.2

Therefore, the common difference in the arithmetic sequence is -1.2.

Question 2:

To find the 15th term of an arithmetic sequence, we can use the formula:

nth term = first term + (n - 1) * common difference

In this case, the 32nd term is given as 14.9, and the common difference is -1.5. Plugging these values into the formula:

14.9 = first term + (32 - 1) * (-1.5)

14.9 = first term + 31 * (-1.5)

14.9 = first term - 46.5

first term = 14.9 + 46.5

first term = 61.4

Now we can find the 15th term using the first term and the common difference:

15th term = first term + (15 - 1) * common difference

15th term = 61.4 + 14 * (-1.5)

15th term = 61.4 - 21

15th term = 40.4

Therefore, the 15th term of the arithmetic sequence is 40.4.

Question 3:

To find the sum of the first n terms of an arithmetic sequence, we can use the formula:

sum = (n/2) * (2 * first term + (n - 1) * common difference)

In this case, the first term is 5 and the common difference is 0.8. Plugging these values into the formula:

sum = (292/2) * (2 * 5 + (292 - 1) * 0.8)

sum = 146 * (10 + 233 * 0.8)

sum = 146 * (10 + 186.4)

sum = 146 * 196.4

sum = 28626.4

Therefore, the sum of the first 292 terms of the arithmetic sequence is 28626.4.

Question 4:

To calculate the balance in the account after a certain number of years with monthly interest payments, we can use the formula:

balance = principal * (1 + (interest rate / 100) * (number of months / 12))

In this case, the principal is $8,600, the interest rate is 12% (0.12 as a decimal), and the time is 5 years. Plugging these values into the formula:

balance = 8600 * (1 + (0.12 / 100) * (5 * 12 / 12))

balance = 8600 * (1 + 0.12 * 5)

balance = 8600 * (1 + 0.6)

balance = 8600 * 1.6

balance = 13760

Therefore, the balance in the account after 5 years will be $13,760.

Question 5:

To calculate the balance in the account after a certain number of months with monthly interest payments, we can use the formula:

balance = principal * (1 + (interest rate / 100) * (number of months / 12))

In this case, the principal is $6,284, the interest rate is

14% (0.14 as a decimal), and the time is 30 months. Plugging these values into the formula:

balance = 6284 * (1 + (0.14 / 100) * (30 / 12))

balance = 6284 * (1 + 0.14 * 2.5)

balance = 6284 * (1 + 0.35)

balance = 6284 * 1.35

balance = 8474.4

Therefore, the balance in the account after 30 months will be $8,474.4.

Question 6:

To calculate the monthly payment amount for a loan with a given principal, interest rate, and number of equal monthly payments, we can use the formula:

monthly payment = (principal + (principal * (interest rate / 100) * (number of months))) / number of months

In this case, the principal is $1,709, the interest rate is 182% (1.82 as a decimal), and the number of equal monthly payments is 16. Plugging these values into the formula:

monthly payment = (1709 + (1709 * (1.82 / 100) * 16)) / 16

monthly payment = (1709 + (1709 * 0.0182 * 16)) / 16

monthly payment = (1709 + (1709 * 0.2912)) / 16

monthly payment = (1709 + 497.3848) / 16

monthly payment = 2206.3848 / 16

monthly payment = 137.8993

Therefore, the monthly payment amount will be $137.90 (rounded to two decimal places).

Question 7:

To calculate the simple annual interest rate for a loan with a given principal, monthly payment amount, and number of months, we can use the formula:

interest rate = ((monthly payment * number of months) / principal - 1) * 100

In this case, the principal is $1,000, the monthly payment amount is $859, and the number of months is 6. Plugging these values into the formula:

interest rate = ((859 * 6) / 1000 - 1) * 100

interest rate = (5154 / 1000 - 1) * 100

interest rate = (5.154 - 1) * 100

interest rate = 4.154 * 100

interest rate = 415.4

Therefore, the simple annual interest rate charged by The Saver is 415% (rounded to the nearest whole number).

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Answer:

B) addition property

Step-by-step explanation:

thinking that 3x - 30 - 0 should equal 0.

3x - 30 - 0 = 0

to get rid of numbers on side with variables, we have to add them to both sides (to make it 0 in side with variable.)

3x - 30 - 0 = 0

+30 +0 = +30 +0

3x = 30 <- step 4

The ty plane the hypothesis of theorem are satisfied

The hypothesis of a theorem is a statement or assumption that is made in order to prove a mathematical result.

The hypothesis of the Tychonoff theorem is satisfied in a variety of different spaces, including compact spaces and metrizable spaces.

This theorem is important because it provides a useful tool for understanding the properties of topological spaces, which are spaces that have certain structures that allow for the study of continuous functions and mappings.

In summary, the hypothesis of the Tychonoff theorem is a necessary condition for the theorem to be proven and is satisfied in a variety of different spaces.

Understanding the hypothesis and the spaces in which it is satisfied is crucial for understanding the theorem and its applications in mathematics.

Complete Question:

State where in the ty-plane the hypotheses of Theorem

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Answer:

ur welcoem

Step-by-step explanation:

Answer:

b i think but y are u looking forward to this

As x approaches to infinity y  also approaches to infinity.

In mathematics, a function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range) with the property that each input is related to exactly one output. Formally, a function f from a set A to a set B is defined as a subset of the Cartesian product A × B such that for every element a in A, there is a unique element b in B such that (a, b) belongs to the subset.

A function can be represented using the function notation f(x) = y, where x is the input (or independent variable), y is the output (or dependent variable), and f is the name of the function. The value of f(x) depends on the value of x and the rules of the function.

From the graph

x approaches to infinity

y  also approaches to infinity.

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If the rank of matrix A is equal to the number of columns of A, and the rank of matrix A is equal to the rank of the augmented matrix [A|b], then the system Ax = b will have a unique solution for all choices of b. Otherwise, the system Ax = b will not have a unique solution for all choices of b.

To determine if the system ax = b has a solution for all choices of b, we need to look at the rank of the matrix A and the rank of the matrix formed by appending the vector b to the matrix A.

The rank of a matrix is the number of linearly independent rows or columns in the matrix. If the rank of matrix A is equal to the number of columns in A, then matrix A is full rank and the system Ax = b will have a unique solution for all choices of b. If the rank of matrix A is less than the number of columns in A, then matrix A is not full rank, and the system Ax = b will not have a unique solution for all choices of b.

If the rank of matrix A is equal to the rank of the matrix formed by appending the vector b to matrix A, the system Ax = b will have a unique solution for all choices of b. If the rank of matrix A is less than the rank of the matrix formed by appending the vector b to matrix A, the system Ax = b will not have a unique solution for all choices of b.

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Answer:

17 is added to both numerator and denominator.

Step-by-step explanation:

Given:

Fraction = 1/10

New fraction = 2/3

Find:

Number added to both numerator and denominator.

Computation:

Assume,

a is added to both numerator and denominator.

\(\frac{1+a}{10+a}=\frac{2}{3}\\\\3 + 3a=20+2a\\\\3a-2a=20-3\\\\a=17\)

Therefore, 17 is added to both numerator and denominator.

Answer:

87 people chose soccer

Step-by-step explanation: 39

%

+

22

%

+

10

%

=

71

%

chose a sport other than soccer

→

100

%

−

79

%

=

29

%

chose soccer

29

%

of  

300

people chose soccer

XXX

=

29

100

×

3

00

=

87

people chose soccer

The number of binary strings of length 10 subject to the given restrictions is 2464.

Explanation:

To count the number of binary strings of length 10 subject to the given restrictions, we will use the Principle of Inclusion-Exclusion (PIE). The formula for PIE is:|A∪B|=|A|+|B|-|A∩B|, where A and B are set. Let A be the set of binary strings of length 10 that contain exactly 5 1's.

Let B be the set of binary strings of length 10 that begin with 0. We want to find the number of elements in A∪B. We first find |A|. There are 10 choose 5 ways to choose the 5 positions for the 1's. For the remaining 5 positions, we can use 0 or 1. So, there are 2^5 ways to fill these positions. Hence, |A| = (10 choose 5) × 2^5.

Next, we find |B|. There are 2^9 binary strings of length 9 that can be appended to 0 to form a binary string of length 10 that begins with 0. So, |B| = 2^9.To find |A∩B|, we count the number of binary strings of length 10 that contain exactly 5 1's and begin with 0. The first position must be 0.

Then, there are 9 choose 4 ways to choose the remaining 4 positions for the 1's. For the remaining 5 positions, we can use 0 or 1. So, there are 2^5 ways to fill these positions. Hence, |A∩B| = (9 choose 4) × 2^5.

We can now apply PIE as follows:|A∪B| = |A| + |B| - |A∩B||A∪B| = (10 choose 5) × 2^5 + 2^9 - (9 choose 4) × 2^5|A∪B| = 2464

Therefore, the number of binary strings of length 10 subject to the given restrictions is 2464.

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The median is the best measure of center and equals 11 from box plot

A box plot uses a number line from 6 to 21 with tick marks every one-half unit.

The box extends from 10 to 15 on the number line.

A line in the box is at 11. The lines outside the box end at 7 and 20.

Based on the information provided in the box plot, the best measure of center for the data shown is the median.

The median is represented by the line within the box, which is at 11. Therefore, the best measure of center for the data is the median, and its value is 11.

Hence, the median is the best measure of center and equals 11.

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Answer:

12 hours

Step-by-step explanation:

3 hours landscaping = $36

She still needs to make $224 to meet her requirement.

$224 divided by $19 tutoring = 11.79 hours

224÷19=11.79

Rounded to the nearest whole number: 12

This would mean Makayla worked a total of 15 hours and made $264. Which meets her requirements.

The order of the given numbers with different units of length from biggest to smallest is given by 105cm > 1m > 150mm.

Measurement with different units are,

105cm

1m

150mm

To arrange these measurements in order from biggest to smallest,

Convert all the measurements in the same units.

Convert all of them to meters,

1 meter = 100 centimeter

To convert centimeter to meter divide it by 100 we get,

105 cm

= 105 / 100 m

= 1.05 m

And 1 m = 1 m

1 meter = 100 centimeter

1 centimeter = 10millimeter

⇒ 1meter = 1000 millimeter

To convert millimeter to meter divide it by 1000 we get,

150 mm

= 150 / 1000 m

= 0.15 m

Now, arrange them in order from biggest to smallest we get,

1.05 m, 1 m, 0.15 m

1.05 m > 1 m > 0.15 m

⇒ 105cm > 1m > 150mm

Therefore, the order of the given numbers from biggest to smallest is equal to 105cm > 1m > 150mm.

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The value of the x for the similar triangle ∆UVW is equal to 3.5.

The triangles UVW and RST are similar, this implies that the length VW of the smaller triangle is similar to the length ST of the larger triangle

so;

VW/ST = WU/TR

x/7 = 2/4

x = (2 × 7)/4 {cross multiplication}

x = 14/4

x = 3.5

Therefore, the value of the x for the similar triangle ∆UVW is equal to 3.5..

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Suppose $2000 is deposited in a bank account with an annual compound interest rate of 3%. After two years, we will have accumulated 121.80 in interest on your initial 2000 deposit.

Compound interest is, to put it simply, interest that is earned on interest. Compound interest is interest that is earned on both the initial principal and interest that builds up over time in a savings account.

There may be a difference in the timing of when interest is paid out and compounded. For instance, interest on a savings account may be paid monthly but compounded daily. The account balance plus any interest that has accrued but has not yet been paid out are used by the bank to determine your daily interest earnings.

For the above question:

Account Balance = Principal x (1 + interest rate (decimal))^number of the years. With given information this is:  \(2000 (1.03)^2\) = 2,121.80.  So we will earn 121.80 in interest after the 2 years on your original 2000 deposit.

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a) Rounding this to the nearest whole number, we get an expected number of runs scored in a season of 10,935.

b)  We can assume that the expected number of runs scored in a season of 500 is not achievable with any reasonable batting average.

a. To find the expected number of runs scored in a season for a team with a batting average of 0.235, we substitute 0.235 for x in the regression equation:

y = 9,760 + 5,000x

y = 9,760 + 5,000(0.235)

y = 9,760 + 1,175

y ≈ 10,935

Rounding this to the nearest whole number, we get an expected number of runs scored in a season of 10,935.

b. To find the assumed team's batting average given an expected number of runs scored in a season of 500, we rearrange the regression equation and solve for x:

y = 9,760 + 5,000x

500 = 9,760 + 5,000x

5,000x = -9,260

x = -1.852

This negative value for x doesn't make sense in the context of batting average, so we can assume that the expected number of runs scored in a season of 500 is not achievable with any reasonable batting average.

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Answer (Step-by-step explanation):

so X is horizontal and Y is vertical.  (X,Y) because X comes first and Y comes last and all you need to do is make sure your points are correct and that the best of my ability, you can also try drawing lines to each pin point and you can estimate these (X,Y) because X=? and Y=? so good luck i hope that helps! (:

Answer:

1. "4 dollars" per song and you buy 5 of them is no more than 20 dollars

2. "96 minutes" to write a 1152 letter essay.

Therefore ,the club's president, vice-president, secretary, and treasurer can be chosen in 303600 combinations of different ways as a result.

A permutation is a configuration of objects in a particular order.. Here, the components of sets are arranged in a linear or sequential order. For instance, the set A=1,6 has a permutation of 2, which is 1,6,1.

Here,

given: Number of members: 25

The number of ways to elect the club's president, vice-president, secretary, and treasurer must be determined.

Posts = 4 in total.

The order is important because each member will receive a distinct post.

So, we'll apply permutation here.

P(n, r) is equal to n!/(n-r)!

n = 25

r = 4

the following follows:

=>P(25,4) = 25! / (25-4)!

=> P(25,4) = 25!/21!

=> P(25,4) = 303,600

Therefore ,the club's president, vice-president, secretary, and treasurer can be chosen in 303600 different ways as a result.

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Answer:

0.125

Step-by-step explanation:

\( \frac{1}{2} \div 4\)

\( \frac{1}{2} \times \frac{1}{4} \)

\( \frac{1}{8} \: or \: 0.125\)

Answer:

0.125

Step-by-step explanation:

The equation of a given situation:

                  2x - 157 = 755

Dave Winfield has 465 home runs.

Hank Aaron has 157 runs fewer than twice the runs that Dave Winfield has.

Hank Aaron hits 755 home runs.

Assume that Dave Winfield has X runs.

The equation is 2x - 157 = 755 --------------------------- (1)

solving the equation (1),

    2x - 157 = 755

⇒ 2x = 755 + 157

⇒ 2x = 912

⇒ x = 456

∴ Dave Winfield has 465 home runs.

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Answer: A= 110 B=22.5 C=0

Step-by-step explanation:

Hello,

It is the Fibonacci 's suit.

\(u_1=5\\u_2=4\\u_3=u_1+u_2=5+4=9\\u_4=u_2+u_3=4+9=13\\u_5=u_3+u_4=9+13=22\\u_6=13+22=35\\u_7=22+35=57\\u_8=35+57=92\\u_9=57+92=149\\\\\\\boxed{u_{n+2}=u_{n}+u_{n+1}}\\\)

The approximate area of the trapezoid is determined as  13.95 unit².

The approximate area of the trapezoid is calculated as follows;

Area = ¹/₂(b₁ + b₂)h

Where;

The y-coordinates of the points on the curve at x=3/2 and x=4 is calculated as follows;

y(3/2) = - (3/2)²/2 + 3/2 + 5

y(3/2) = -9/8 + 3/2 + 5

y(3/2) = 5.375

y(4) = -4²/2 + 4 + 5

y(4) = -8 + 9

y(4) = 1

h = 5.375 - 1 = 4.375

The approximate area of the trapezoid is calculated as;

Area = ¹/₂(5.375 + 1) x 4.375

Area = 13.95 unit²

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Answer:

13/3

Step-by-step explanation:

on edug

Answer:

the answer is 13/3

Step-by-step explanation:

did the assignment look below for proof

hope this helps :)