3/8 + 2/5 in simplest form

The number of two point basket is equal to 31 two point basket.

The number of three point basket is equal to 6 three point baskets.

In order to write an equation that model this situation, we would assign variables to the number of two point basket and the three point basket respectively, and then translate the word problem into algebraic equation as follows:

Next, we would translate the word problem into an algebraic equation based on the fact that they made a total of 80 points in a game and a total of 37 two point and three point baskets as follows;

x + y = 37

2x + 3y = 80

By solving the system of equations simultaneously, we have:

2(37 - y) + 3y = 80

74 - 2y + 3y = 80

74 + y = 80

y = 6 three point baskets.

x = 37 - 6

x = 31 two point basket.

Read more on two point  here: https://brainly.com/question/15158320

#SPJ1

Answer:

Step-by-step explanation:

To determine how much a decimal was multiplied, you need to find how many places the decimal moved.

In this case we can see the decimal moved once. How many times the decimal moved can be represented by the zeros in the number. So 10 = 1

100 = 2     1,000 = 3 and it keeps going.

So since the decimal moved 1 time, the answer to question one is 10

Now question 2.

Both 8.4 ÷ 2.1 and 84 ÷ 21 will give the exact same answer. It is just easier to solve. So solve which one is easier for you. I did 84 ÷ 21.

84 ÷ 21 = 4

We can verify our answer by multiplying the the divisor by the quotient

21 * 4 = 84

So 4 is the answer to question 2

the greatest common factor of the given expressions is -5xy.

To find the greatest common factor of the given expressions, we need to factor them first.

\(-15x^2y - 10xy^3 + 5xy^4 = -5xy(3x^2 + 2y^2 - y^3)\\5xy = 5xy(1)\\5x^2y^4 = 5xy^4(x^2)\\5xy^2 = 5xy^2(1)\)

xy = xy(1)

Now, we can find the common factors by taking the minimum exponent of each variable in the factors:

The common factors are:5xy

Therefore, the greatest common factor of the given expressions is -5xy.

Learn more about factor here

https://brainly.com/question/29128446

#SPJ1

The chance of the event B is 0.4 when using the probability for the two independent two event formula.

In the given question, if a and b are independent events with p(a) = 0.65 and p(a ∩ b) = 0.26, then we have to find the value of p(b).

Events classified as independent do not depend on other events for their occurrence.

Event A's likelihood of happening is P(A)=0.65.

The likelihood of the two events A and B intersecting is P(A∩B)=0.26.

Given that the likelihood of the two independent events is:

P(A∩B) = P(A)⋅P(B)

Then the probability of the event B will be,

P(B) = P(A)/P(A∩B)

P(B) = 0.65/0.26

P(B) =0.4

To learn more about independent events link is here

brainly.com/question/13488890

#SPJ4

Answer:

B)

Step-by-step explanation:

4+5*(3^2-9)/3^2=4+5*0/9=4

Answer:

the answer is c and the entire equation means that the tickets each cost $15 and the service fee is $12

The only point that lies on both lines is (-4,5).

To determine which of the points (−4,5), (4,3), and (1,2) lie on both the lines −x1−4x2=−16 and −3x1−5x2=−13, we need to check if the coordinates of each point satisfy both of the equations.

For the first line, we can rewrite it as x2 = (-x1 + 16)/4 and for the second line, we can rewrite it as x2 = (-3x1 + 13)/5.

Substituting the coordinates of each point into these equations, we get:

For the point (-4,5):

-4(2) + 16/4 = -4 + 4 = 0, and

-3(-4) + 13/5 = 12/5 + 13/5 = 25/5 = 5.

Therefore, (-4,5) satisfies both equations.

For the point (4,3):

4(2) + 16/4 = 8 + 4 = 12, and

-3(4) + 13/5 = -12 + 13/5 = -47/5.

Therefore, (4,3) does not satisfy both equations.

For the point (1,2):

-1(2) + 16/4 = -2 + 4 = 2, and

-3(1) + 13/5 = -3 + 13/5 = 2/5.

Therefore, (1,2) does not satisfy both equations.

Therefore, the only point that lies on both lines is (-4,5).

When given two equations, the solution can be found by solving the system of equations. To solve a system of equations, one should find the values of x and y that satisfy both equations. The solution to the system is the point (x,y) that satisfies both equations.

Know more about "equations":-

https://brainly.com/question/14114409#

#SPJ11

To be 94% confident that the true mean IQ is within 2 points of the sample mean, you must obtain a sample of at least 199 individuals.

To determine how large a sample must be obtained to be 94% confident that the true mean IQ is within 2 points of the sample mean, we will use the following terms: confidence level, margin of error, and standard deviation. We will also need the z-score corresponding to the desired confidence level.

Step 1: Identify the confidence level, margin of error, and standard deviation
Confidence level: 94%
Margin of error: 2 points
Standard deviation (σ): Since it's not provided, we will use a common value for IQ, which is 15 points.

Step 2: Find the z-score corresponding to the 94% confidence level
A 94% confidence level has a z-score of approximately 1.88 (you can find this value in a z-score table or using a calculator).

Step 3: Use the formula for sample size
n = (z * σ / E\()^2\)
n = (1.88 * 15 / 2\()^2\)
n = (28.2 / 2\()^2\)
n = \((14.1)^2\)
n ≈ 198.81

Step 4: Round appropriately
Since we can't have a fraction of a person in a sample, round up to the nearest whole number. In this case, the sample size should be 199.

To know more about "IQ" refer here:

https://brainly.com/question/30762833#

#SPJ11

The expressions have, the first expression has degree 5, end behavior to ± infinite terms , zeros are h = 0, -1/2 , -1/2, 11 , 11 and 2 multiplicity -1/2 and 11 and sketch is drawn in image 1. And second expression has degree 4, end behavior to + infinite terms , zeros are x = 0,0, 3,-3. , 2 multiplicity of 0 and sketch is drawn in image 2.

An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.

Given that the expression ;

T(h) = h (2h + 1)²(h - 11)² and D(x) = 3x⁴ - 27x²

Now for the first expression T(h) = h (2h + 1)²(h - 11)²

Simplifying, the expression;

T(h) = h (2h + 1)²(h - 11)²

Degree of the highest polynomial of above expression is 5.

To find end behavior, we will find the factors of expression;

T(h) = h (2h + 1)²(h - 11)²

Here, h = 0,  (2h + 1)² = 0 , (h - 11)²= 0

h= 0 , h = -1/2 , -1/2 and h = 11 , 11

Multiplicity of -1/2 is 2 and 11 is 2.

End behavior, given expression has 2 pair of repeated roots.

And  (2h + 1)² ≥ 0 , (h - 11)²≥ 0

So the expression behavior depends on the term h alone.

And also it is an even polynomial.

So the graph of expression varies to infinity term for both positive and negative.

Zeros of the polynomial are  h = 0, -1/2 , -1/2, 11 , 11.

Sketch 1,

Now for the second expression D(x) = 3x⁴ - 27x²

Simplifying, the expression;

D(x) = 3x⁴ - 27x²

Degree of the highest polynomial of above expression is 4.

To find end behavior, we will find the factors of expression;

D(x) =3x²(x+3)(x−3)

Here, x = 0,0, 3,-3.

Multiplicity of 0 is 2.

End behavior, it is an odd polynomial. So the graph of expression varies to positive infinity.

Sketch 2,

Therefore, the first expression has degree 5, end behavior to ± infinite terms , zeros are h = 0, -1/2 , -1/2, 11 , 11 and 2 multiplicity -1/2 and 11 and sketch is drawn in image 1. And second expression has degree 4, end behavior to + infinite terms , zeros are x = 0,0, 3,-3. , 2 multiplicity of 0 and sketch is drawn in image 2.

To learn more about the Polynomials;

https://brainly.com/question/11536910

#SPJ1

The area of the irregular shape is 84 ft square.

The diagram is a trapezium. A trapezium is a quadrilateral. Therefore, the area of the trapezium can be found as follows:

area of the trapezium = 1 / 2 (a + b)h

where

Therefore,

a = 10 ft

b = 18 ft

c = 6 ft

area of the trapezium = 1 / 2 (10 + 18)6

area of the trapezium = 1 / 2 (28)6

area of the trapezium = 168 / 2

area of the trapezium = 84 ft²

learn more on area here: https://brainly.com/question/29297809

#SPJ1

Answer:

Step-by-step explanation:

(12x + 19) + (22x - 9) = 180

34x + 10 = 180

34x = 170

x = 5

Answer:

m=9/7

Step-by-step explanation

I dont think its right but i hope it helps!

Answer:

a) P = 26 m

b) A = 30 m^2

Step-by-step explanation:

Given:

x = 10 m

y = 3 m

a) P = 2x + 2y (since there are 2 sides that have x length, and 2 that have y lenght)

P = 2 × 10 + 2 × 3 = 20 + 6 = 26 (m)

b) A = x × y

A = 10 × 3 = 30 (m^2)

ANSWER and EXPLANATION

a) To simplify the radical, we have to:

1) First, express the number inside the radical as a product of a perfect square and a number that is not a perfect square.

2) Next, we separate the numbers into two radicals and find the square root of the perfect square.

3) Finally, we find the product of the number and the remaining radical.

B) Following the steps above:

STEP 1

STEP 2

STEP 3

The total amount to be paid at the end of the 10-year period is $24,465. The correct answer is option d. To calculate the total amount to be paid, we need to consider the compounded interest on the borrowed amount.

The nominal interest rate of 12% compounded quarterly means that interest is added to the principal four times a year. Using the formula for compound interest, we can calculate the future value of the loan. The formula is given as:

Future Value = Principal * (1 + (Nominal Interest Rate / Number of Compounding Periods))^Number of Compounding Periods * Number of Years

In this case, the principal is $7,500, the nominal interest rate is 12% (or 0.12), the number of compounding periods per year is 4 (quarterly), and the number of years is 10.

Plugging in these values into the formula, we get:

Future Value = $7,500 * (1 + (0.12 / 4))^(4 * 10) = $24,465

Therefore, the total amount to be paid at the end of the 10-year period is $24,465. The correct answer is option d.

Learn more about principal here: brainly.com/question/27870032

#SPJ11

About 195 students at Nikhil's middle school would have atleast one sibling.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

We can use proportion to estimate the number of students at Nikhil's middle school who have at least one sibling.

If 13 out of 20 students surveyed have at least one sibling, we can assume that the same proportion applies to the entire school.

So, we can set up a proportion as follows:

13/20 = x/300

where x is the number of students in the entire school who have at least one sibling.

Solving for x, we can cross-multiply and get:

13 * 300 = 20 * x

x = (13 * 300)/20

x = 195

Therefore, about 195 students at Nikhil's middle school would have at least one sibling.

To learn more about Algebraic expression from given link.

brainly.com/question/953809

#SPJ1

Answer:

16

Step-by-step explanation:

x^2 = whole * part

x^2 = (6+2) * 2

x^2 = 8*2

x^2 = 16

Answer:

16

Step-by-step explanation:

Hope this helps.

If you find answers that say 48 for this same problem, they are incorrect.  Please disregard them.

The alternating series test states that if the terms of a series alternate in sign and decrease in absolute value, then the series converges.

Let's first rewrite the given power series as an alternating series. We can do this by multiplying and dividing each term by (-1)^n, which will alternate the sign of the terms:

[infinity]∑ (-1)^n(x-5)^n / (2^n n^2) n=1

Now, we can apply the alternating series test to this series to verify convergence at certain values of x. To use the alternating series test, we need to show that the terms decrease in absolute value. We can do this by taking the absolute value of the terms and comparing them to the next term:

|(-1)^n(x-5)^n / (2^n n^2)| = |(x-5)^n| / (2^n n^2)

To simplify the comparison, we can take the ratio of the absolute values of consecutive terms:

|(x-5)^(n+1) / ((n+1)^2 2(x-5)^n)| = |(x-5) / (2(n+1)^2)|

Now, we need to find values of x for which the series converges. The radius of convergence is given as 2, which means the series converges for |x-5| < 2.

Checking each option:

a. x=6: |6-5| = 1, which is less than 2, so the series converges at x=6.

b. x=4: |4-5| = 1, which is not less than 2, so we cannot use the alternating series test to verify convergence at x=4.

c. x=2: |2-5| = 3, which is not less than 2, so we cannot use the alternating series test to verify convergence at x=2.

d. x=0: |0-5| = 5, which is not less than 2, so we cannot use the alternating series test to verify convergence at x=0.

e. x=-1: |-1-5| = 6, which is not less than 2, so we cannot use the alternating series test to verify convergence at x=-1.

Therefore, we can only use the alternating series test to verify convergence at x=6.

learn about alternating series,

https://brainly.com/question/31584140

#SPJ11

Answer:

what are the other dimensions ?

Step-by-step explanation:

Triangle properties include triangle inequality, angle sum, congruence, exterior angle theorem, and isosceles triangle theorem.

1. Triangle Inequality: The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

2. Angle Sum of a Triangle: The sum of the angles of a triangle is always equal to 180°.

3. Congruence of Triangles: If two triangles have all three sides equal, then they are congruent (the same size and shape).

4. Exterior Angle Theorem: The measure of an exterior angle of a triangle is equal to the sum of the measures of the two interior angles that are not adjacent to it.

5. Isosceles Triangle Theorem: If two sides of a triangle are equal in length, then the angles opposite those sides are also equal in measure.

Learn more about triangle here

https://brainly.com/question/2773823

#SPJ4

The five properties of triangle is listed below.

The term triangle is defined as the polygon with three angle, sides and vertices.

Here we have to list down the properties of triangle.

The basic five properties of triangle are as follows:

1) in geometry, total amount of space inside the triangle is called the area of a triangle. And it is measured by square units.

2) The property of perimeter of a triangle is equal to the sum of all three sides of the triangle.

3) And the another property states that sum of the length of the two sides of a triangle is greater than the length of the third side.

4) according to the angle, the property states that sum of the angles of a triangle is always 180 degrees.

5) If angles of an equilateral triangle are equal and has a measure of 60⁰ each.

To know more about Triangle here.

https://brainly.com/question/8587906

#SPJ4

Step-by-step explanation:

csc(Theta) = 1/sin(Theta) = 3.2362

Answer:

C. 3.2362

Explanation:

a.) The number of pounds of empty cans needed by the class is 200 pounds.

b.) The number of empty cans needed by the class to collect are 5486 cans.

The books will cost a total amount of $ 50.

If $ 0.25 per pound is the current price for aluminium at the recycling centre, the number of pounds the class will have to collect is found by dividing the total amount needed by cost per pound is,

⇒ 50/0.25 = 200

b.) Six empty cans weigh 3.5 ounces.

1 pound = 16 ounces

200 pounds = 200 × 16 = 3200 number of ounces

3200/3.5 = 914.29

914.29 × 6 = 5485.7 cans ≈ 5486 cans

To know more about pounds:

https://brainly.com/question/22701996

#SPJ4

Answer:

Look Below

Step-by-step explanation:

The formula for a circle is πr².

Therefore, we can divide the area of the circle by 3.14, and then square root it. 490.63/3.14=156.25... If you square root that, you get 12.5. Same thing with the other circle. 219.45/3.14=69.888... If you square root that, you get 8.36. Now that we have the radius, we can multiply that by two to find the diameter. And we're done.

Feel free to tell me if I did anything wrong! :)

The height of the actual building, given the height of the model, can be found to be 1, 455 feet

The model is such that every inch of the building on the model is 75 feet of the actual building.

This means that if the height of the building in the model is 19 ² / ₅ inches, then the height of the actual building would be:

= Height of building in model x Scale factor per inch

= 19 ² / ₅  x 75

= 97 / 5 x 75

= 1, 455 feet

Find out more on height at https://brainly.com/question/22574157

#SPJ1

Answer:

50%

Step-by-step explanation:

(V2−V1)|V1|×100

=(7.5−5)|5|×100

=2.55×100

=0.5×100

=50%change

=50%increase

To determine whether the sequence {an} = 5n/4n + 1 is convergent or divergent, we can analyze its behavior as n approaches infinity.

First, let's rewrite the expression for the nth term of the sequence:

an = 5n / (4n + 1)

As n approaches infinity, the denominator 4n + 1 becomes dominant compared to the numerator 5n. Therefore, we can simplify the expression by neglecting the term 5n:

an ≈ n / (4n + 1)

Now, we can consider the limit of the sequence as n approaches infinity:

lim(n→∞) n / (4n + 1)

To evaluate this limit, we can divide both the numerator and denominator by n:

lim(n→∞) (1 / 4 + 1/n)

As n approaches infinity, the term 1/n approaches zero, leaving us with:

lim(n→∞) 1 / 4 = 1/4

Since the limit of the sequence is a finite value (1/4), we can conclude that the sequence {an} = 5n/4n + 1 is convergent.

In other words, as n gets larger and larger, the terms of the sequence {an} get closer and closer to the limit of 1/4. This indicates that the sequence approaches a fixed value and does not exhibit wild oscillations or diverge to infinity. Therefore, we can say that the sequence is convergent.

To learn more about  convergent click here:

brainly.com/question/31756849

#SPJ11

Answer:

  1/10

Step-by-step explanation:

The fraction 3/5 can be rewritten as one that has 10 as its denominator.

  \(\dfrac{7}{10}+\left(-\dfrac{3}{5}\right)=\dfrac{7}{10}-\dfrac{6}{10}=\dfrac{7-6}{10}=\boxed{\dfrac{1}{10}}\)

Answer:

48w +2

Step-by-step explanation:

Perimeter of a rectangle=2( length+width)

=2(15w-1+9w+2)

=2(24w+1)

=48w+2

2x + 17 grows no faster than 3x as x approaches infinity.

To show that 2x + 17 is O(3x), we need to find two positive constants, C and k, such that:

|2x + 17| <= C|3x| for all x > k

We can start by simplifying the left-hand side:

|2x + 17| = 2x + 17 (since x is always non-negative)

Next, we can simplify the right-hand side:

|3x| = 3x

Now, we need to find C and k that satisfy the inequality:

2x + 17 <= C*3x for all x > k

Dividing both sides by 3x, we get:

(2/3) + (17/3x) <= C for all x > k

Since (2/3) is a constant, we only need to find a value of k such that (17/3x) is less than some other constant. Let's choose k = 1, then:

(17/3x) < 6 for all x > 1

So, we can choose C = 6 and k = 1. Therefore, we have shown that:

|2x + 17| <= 6|3x| for all x > 1

This satisfies the definition of 2x + 17 being O(3x), which means that 2x + 17 grows no faster than 3x as x approaches infinity.

Learn more about big O notation

brainly.com/question/13257594

#SPJ11

Answer:

48=3b+v

Step-by-step explanation:

384=24b+8v

b standing for bus

v standing for vam

to simplify the equations you would divided by eight since all numbers are multiples

48=3b+v