The diagram below shows all the possible outcomes when spinning two fair four-sided spinners and adding the results together.
What is the probability that the outcome is 10?
Give your answer as a fraction in its simplest form.

The expression where the greatest common factor (GCF) is factored completely is \(2x^3y + 18xy - 10x^2y - 90y = 2y(x^3 + 9x - 5x^2 - 45)\)

The expression completely factored in is

\(2y(x^3 + 9x - 5x^2 - 45) = 2y[x(x^2 - 5) + 9(x^2 - 5)]\\= 2y(x - 5)(x^2 + 9)\)

Please refer below for the remaining answers.

We have,

Part A:

To rewrite the expression 2x³y + 18xy - 10x²y - 90y so that the greatest common factor (GCF) is factored completely, we can factor out the common terms.

GCF: 2y

\(2x^3y + 18xy - 10x^2y - 90y = 2y(x^3 + 9x - 5x^2 - 45)\)

Part B:

To completely factor the expression, we can further factor the quadratic term.

\(2y(x^3 + 9x - 5x^2 - 45) = 2y[x(x^2 - 5) + 9(x^2 - 5)]\\= 2y(x - 5)(x^2 + 9)\)

Now,

Part A:

To determine the length of each side of the square given the area expression (9x² + 24x + 16), we need to factor it completely.

The area expression (9x² + 24x + 16) can be factored as (3x + 4)(3x + 4) or (3x + 4)².

Therefore, the length of each side of the square is 3x + 4.

Part B:

To determine the dimensions of the rectangle given the area expression (16x² - 25y²), we need to factor it completely.

The area expression (16x² - 25y²) is a difference of squares and can be factored as (4x - 5y)(4x + 5y).

Therefore, the dimensions of the rectangle are (4x - 5y) and (4x + 5y).

Now,

f(x) = 2x² - 5x + 3

Part A:

To find the x-intercepts of the graph of f(x), we set f(x) equal to zero and solve for x.

2x² - 5x + 3 = 0

The quadratic equation can be factored as (2x - 1)(x - 3) = 0.

Setting each factor equal to zero:

2x - 1 = 0 --> x = 1/2

x - 3 = 0 --> x = 3

Therefore, the x-intercepts of the graph of f(x) are x = 1/2 and x = 3.

Part B:

To determine if the vertex of the graph of f(x) is maximum or minimum, we can examine the coefficient of the x^2 term.

The coefficient of the x² term in f(x) is positive (2x²), indicating that the parabola opens upward and the vertex is a minimum.

To find the coordinates of the vertex, we can use the formula x = -b / (2a), where a and b are the coefficients of the quadratic equation.

For f(x),

a = 2 and b = -5.

x = -(-5) / (2 x 2) = 5/4

To find the corresponding y-coordinate, we substitute this x-value back into the equation f(x):

f(5/4) = 25/8 - 25/4 + 3 = 25/8 - 50/8 + 24/8 = -1/8

Therefore, the vertex of the graph of f(x) is at the coordinates (5/4, -1/8), and it is a minimum point.

Part C:

To graph f(x), we can start by plotting the x-intercepts, which we found to be x = 1/2 and x = 3.

These points represent where the graph intersects the x-axis.

Next,

We can plot the vertex at (5/4, -1/8), which represents the minimum point of the graph.

Since the coefficient of the x² term is positive, the parabola opens upward.

We can use the vertex and the symmetry of the parabola to draw the rest of the graph.

The parabola will be symmetric with respect to the line x = 5/4.

We can also plot additional points by substituting other x-values into the equation f(x) = 2x² - 5x + 3.

By connecting the plotted points, we can draw the graph of f(x).

The steps to graph f(x) involve plotting the x-intercepts, the vertex, and additional points, and then connecting them to form the parabolic curve.

The answer in part A (x-intercepts) and part B (vertex) are crucial in determining these key points on the graph.

Thus,

The expression where the greatest common factor (GCF) is factored completely is \(2x^3y + 18xy - 10x^2y - 90y = 2y(x^3 + 9x - 5x^2 - 45)\)

The expression completely factored in is

\(2y(x^3 + 9x - 5x^2 - 45) = 2y[x(x^2 - 5) + 9(x^2 - 5)]\\= 2y(x - 5)(x^2 + 9)\)

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ1

Answer:

9

Step-by-step explanation:

2( 3/2 )/ 3/9 =9 Put Substitute 3/2 for m and put into a calculator.

The value of the numerical expression 12 × [6.3 + 3 × (1.9)] will be 144.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The numerical expression is given below.

⇒ 12 × [6.3 + 3 × (1.9)]

Simplify the numerical expression, then we have

⇒ 12 × [6.3 + 3 × (1.9)]

⇒ 12 × [6.3 + 5.7]

⇒ 12 × 12

⇒ 144

The value of the numerical expression 12 × [6.3 + 3 × (1.9)] will be 144.

More about the Algebra link is given below.

https://brainly.com/question/953809

#SPJ1

(a) The set of all nxn singular matrices and (c) the set of all nxn skew symmetric matrices are not subspaces, while (6) the set of all nxn upper triangular matrices is a subspace.

In order for a subset of a vector space to be considered a subspace, it must satisfy three conditions: (1) it must contain the zero vector, (2) it must be closed under vector addition, and (3) it must be closed under scalar multiplication. Let's examine each of the given subsets to see if they satisfy these conditions.
(a) The set of all nxn singular matrices: This subset does contain the zero matrix (since the zero matrix is always singular), and it is closed under scalar multiplication (if A is singular and k is any scalar, then kA is also singular). However, it is not closed under addition: the sum of two singular matrices can be invertible (i.e. not singular), so this subset fails to satisfy condition (2). Therefore, this subset is not a subspace.
(b) The set of all nxn upper triangular matrices: This subset contains the zero matrix (which is upper triangular), and it is closed under both addition and scalar multiplication. To see why it is closed under addition, note that if A and B are upper triangular, then so is A+B (since the sum of two upper triangular matrices is still upper triangular). Similarly, if A is upper triangular and k is any scalar, then kA is also upper triangular. Therefore, this subset satisfies all three conditions and is a subspace.
(c) The set of all nxn skew symmetric matrices: This subset contains the zero matrix (which is skew symmetric), and it is closed under scalar multiplication (if A is skew symmetric and k is any scalar, then kA is also skew symmetric). However, it is not closed under addition: the sum of two skew symmetric matrices need not be skew symmetric, so this subset fails to satisfy condition (2). Therefore, this subset is not a subspace.

To learn more about matrices, refer:-

https://brainly.com/question/30646566

#SPJ11

Answer:

x = infinite amount of solutions

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define Equation

2(x + 4) = 4x + 3 - 2x + 5

Step 2: Solve for x

Here we see that x does indeed equal x.

∴ x = infinite amount of solutions

Answer:

Final temeprature = 29 - 29 = 0c

Step-by-step explanation:

The key to solving this problem is in the statement "the average temperature had fallen by 29c"

This means that the average temperature had reduced by a value of 29c from the initial value, hence we will subtract 29 from the initial temperature

Initial temperature = temperature in July = 29c

in order to find the final temperature, we will subtract 29c from the initial temperature:

Final temperature (temperature in December) = 29 - 29 = 0c

Answer:6.76 cm2

Step-by-step explanation:

You have multiply 2.6 by 2.6 and then you have to square the cm so it will be 6.76 cm2

Answer: A. 6.76 \(cm^2\)

Step-by-step explanation:

Area is just length times width.

The length is 2.6 cm and the width is 2.6 cm, so just multiply the two.

2.6 x 2.6 = 6.76 \(cm^2\)

Make sure you don't forget the squared in questions that ask for area.

Answer:

Therefore, the top of the tree will strike the ground about 17.75 meters away from the foot of the tree.

Step-by-step explanation:

We can solve this problem using the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In this case, the tree trunk and the ground form one leg of the triangle, and the broken off portion of the tree forms the other leg, while the distance the top of the tree falls is the hypotenuse.

Let's call the distance we want to find "x". Then, we can set up the following equation:

x^2 = 18^2 - 3^2

where 18 is the height of the tree, and 3 is the distance from the ground where the tree is broken.

Simplifying the right-hand side of the equation, we get:

x^2 = 315

Taking the square root of both sides, we get:

x = sqrt(315) ≈ 17.75

Answer:

What is x? I will tell you the answer in the comments!! Thank you!!

Answer:

B.

Step-by-step explanation:

51 miles / 3 gallons = 17 miles per gallon

its b i did the test

Answer:

A

Step-by-step explanation:

The distance of a = 1 / 2 pi, b = 1 pi, and c = 3 / 2 pi.

The complete movement of an object, regardless of direction, is referred to as distance. The amount of ground a thing travels from its starting point to its destination is also referred to as distance.

Given:

The time, t = π / 2 sec,

Calculate the distance by using the formula given below,

\(Distance = r\times time\)

So, for distance, a = 1 × π / 2 =  π / 2

for distance, b = 1 × π =  π

for distance, c = 1 × 3 π / 2 =  3 π / 2

Therefore, the distance of a = 1 / 2 pi, b = 1 pi, and c = 3 / 2 pi.

To know more about distance:

https://brainly.com/question/15256256

#SPJ1

(a)The hypothesis' are

    H0: p = 0.81

    H1: p < 0.81

(b) Since np ≥ 10, this condition is satisfied.

(c) The p-value is 0.2814.

    The significance level of 0.10, we fail to reject the null hypothesis.

For(a)

According to the information given,

The null hypothesis H0 would be that the proportion of dentists who recommend Starry Whites toothpaste is still 81%,

While the alternative hypothesis H1 would be that the proportion of dentists who recommend this brand is less than 81%.

We can state the null and alternative hypotheses as,

H0: p = 0.81 (proportion of dentists who recommend Starry Whites toothpaste is still 81%)

H1: p < 0.81 (proportion of dentists who recommend Starry Whites toothpaste is less than 81%)

For(b)

Based on the information given, we can use a Z-test for proportions to conduct the hypothesis test.

To confirm that a Z-test is appropriate, we need to check if the following conditions are met:

   np ≥ 10

n(1-p) ≥ 10

Here,

n = 140 (sample size) and

p = 0.81 (population proportion under the null hypothesis).

⇒ np = 140 x 0.81

         = 113.4 Since

np ≥ 10, this condition is satisfied.

⇒ n(1-p) = 140 x (1-0.81) = 26.2

Since n(1-p) >= 10,

This condition is also satisfied.

Therefore, both conditions are met, and we can use a Z-test for proportions to conduct the hypothesis test.

For(c)

We can perform a Z-test using the formula you provided, which is,

⇒z = (p - p0) /√(p0 x (1 - p0) / n)

where:

p0 is the hypothesized proportion (in this case, p0 = 0.81)

p is the sample proportion (in this case, p = 110/140 = 0.786)

n is the sample size (in this case, n = 140)

Substituting the values, we get,

⇒ z = (0.786 - 0.81) / sqrt(0.81 x (1 - 0.81) / 140)

⇒ z = -0.58

To find the p-value, we need to look up the area under the standard normal distribution curve to the left of z = -0.58.

Using a standard normal distribution table or calculator, we find that the area is 0.2814.

Therefore, the p-value is 0.2814.

Since the p-value is greater than the significance level of 0.10, we fail to reject the null hypothesis.

This means we do not have enough evidence to conclude that the proportion of dentists who recommend Starry Whites toothpaste has decreased.

To learn more about statistics visit:

https://brainly.com/question/30765535

#SPJ4

Answer:

\(\sqrt{21}\), π, \(\sqrt{75}\)

Step-by-step explanation:

this set contains only irrationals

Answer:

The scientist would be able to go to the rain forest for only 2 days.

Step-by-step explanation:

The scientist only has 1,283. You subtract 1,283 by 122 and 499 and you are left with 662. The scientist wants to go to the rain forest again so he spends 122 and 499 with 662. All he has left now is 41. He can't afford it anymore.

Answer:

Consumtion:
  September:7535
  October:16556
  November:9616
  December:13615
Tama po yan
Pa branlies naman po
HOPE IT HELPS ALOT

The sequence of transformations of rectangle A onto rectangle B is

B)  A dilation with a center of dilation at the origin, followed by a translation down and a translation to the left.

The graph's curve "moves to the left/right/up/down," "it expands or compresses," or "it reflects" when a function is transformed. For instance, simply advancing the graph of the function g(x) = x2 by 3 units will yield the graph of f(x) = x2 + 3. Function transformations are very useful for graphing the functions by simply moving, expanding, compressing, or reflecting the curve, as opposed to having to start from scratch with the graphing.

A function transformation "moves," "resizes," or "reflects" the parent function's graph, depending on the case. Function transformations can be broadly divided into three categories:

Learn more about transformation

https://brainly.com/question/28025572

#SPJ9

The fractional exponent means 144^(1/2) equals 12. and  121^(3/2) equals 121.

A fractional exponent represents the concept of taking a root or power of a number. The numerator of the fraction indicates the power to which the number is raised, and the denominator represents the root that is taken.

Let's evaluate the given expressions:

144^(1/2): This means we are taking the square root of 144. The square root of a number is a value that, when multiplied by itself, gives the original number. In this case, the square root of 144 is 12 because 12 * 12 = 144. Therefore, 144^(1/2) equals 12.

121^(3/2): This means we are taking the cube root of 121 and then squaring the result. The cube root of a number is a value that, when multiplied by itself twice, gives the original number. The cube root of 121 is 11 because 11 * 11 * 11 = 121. Squaring 11 gives us 121.

Therefore, 121^(3/2) equals 121.

To summarize: 144^(1/2) = 12 and 121^(3/2) = 121

For more such questions on fractional , Visit:

https://brainly.com/question/78672

#SPJ11

Answer:

A.

Step-by-step explanation:

You simplify the square root until you narrow it down to the square root of 5.

The quotient of expression of √40/√8 is √5 which is correct option (A).

Expressions is the defined as mathematical statements that have a minimum of two terms containing variables or numbers.

Arithmetic operations can also be specified by the subtract, divide, and multiply built-in functions.

The operator that perform arithmetic operation are called arithmetic operators .

Operators which let do basic mathematical calculation

+ Addition operation : Adds values on either side of the operator.

For example 4 + 2 = 6

- Subtraction operation : Subtracts right hand operand from left hand operand.

for example 4 -2 = 2

* Multiplication operation : Multiplies values on either side of the operator

For example 4*2 = 8

/ Division operation : Divides left hand operand by right hand operand

For example 4/2 = 2

Given expression as :

⇒ √40/√8

Factor of √40 = √8×√5

⇒ (√8√5)/√8

Cancel out of√8

⇒ √5

Hence, the quotient of expression of √40/√8 is √5.

Learn more about expression here:

brainly.com/question/13947055

#SPJ2

Answer:

3 23/159

Step-by-step explanation:

Density equals mass divided by volume, which is 5/1.59, which is 3 23/159

If you want it as a decimal is it approximately 3.145

Scenario 1A:

Coinsurance amount is $90

Medicare payment is $360

Provider write-off is $290

Scenario 1B:

Remaining amount for Insurance and patient to pay is $350

Coinsurance amount is $70

Total paid by patient is $170

Medicare payment is $280

Provider write-off is $370

Scenario 1A:

Submitted charge: $650

Medicare participating physician fee schedule (PFS): $450

Coinsurance amount (20% paid by patient): $

Medicare payment (80% of the PFS): $

Provider write-off: $

To calculate the missing amounts, we can use the provided information:

Coinsurance amount (20% paid by patient):

Coinsurance amount = 20% of the Medicare participating physician fee schedule (PFS)

Coinsurance amount = 0.2 * $450 = $90

Medicare payment (80% of the PFS):

Medicare payment = 80% of the Medicare participating physician fee schedule (PFS)

Medicare payment = 0.8 * $450 = $360

Provider write-off:

Provider write-off = Submitted charge - Medicare payment

Provider write-off = $650 - $360 = $290

Scenario 1B:

Submitted charge: $650

Medicare participating physician fee schedule (PFS): $450

Patient pays $100 remaining on their deductible

Remaining amount for Insurance and patient to pay: $

Coinsurance amount (20% of remaining amount): $

Total paid by patient (deductible & 20% of remaining): $

Medicare payment (80% of the remaining amount): $

Provider write-off: $

To calculate the missing amounts, we can use the provided information:

Remaining amount for Insurance and patient to pay:

Remaining amount for Insurance and patient to pay = PFS - remaining deductible

Remaining amount for Insurance and patient to pay = $450 - $100 = $350

Coinsurance amount (20% of remaining amount):

Coinsurance amount = 20% of the remaining amount

Coinsurance amount = 0.2 * $350 = $70

Total paid by patient (deductible & 20% of remaining):

Total paid by patient = remaining deductible + coinsurance amount

Total paid by patient = $100 + $70 = $170

Medicare payment (80% of the remaining amount):

Medicare payment = 80% of the remaining amount

Medicare payment = 0.8 * $350 = $280

Provider write-off:

Provider write-off = Submitted charge - Medicare payment

Provider write-off = $650 - $280 = $370

Learn more about Physician Fee Schedule (PFS) at

brainly.com/question/32491543

#SPJ4

Answer:

B

Step-by-step explanation:

it grows b

Answer:

8

Step-by-step explanation:

switch the denominator by the numerator to raise the power to positive

you'll get 2/1 raised to the power 3 which gives you 8

Answer:

BCA

Step-by-step explanation:

Explanation:

The smallest angle is always opposite the smallest side of a triangle. The largest angle is always opposite the largest side.  

Side AC is the shortest, so angle B is the smallest.

Side BC is the longest, so angle A is the largest

Angle C must be between angles B and A.

In order to determine the coordinates of ABCD, it is necessary to apply the following transformation to figure A'B'C'D':

r(-90°,0)(A'B'C'D')

or, which is equivalent, apply a clockwise rotation of 90°, which is represented as follow:

T(x,y) => (y,-x)

then, for the points A', B', C' and D', you obtain:

A'(2,1) => A(1,-2)

B'(-4,-2) => B(-2,4)

C'(-4,-6) => C(-6,4)

D'(-1,-3) => D(-3,1)

If you hear 100 clicks from a trundle wheel, then you have measured a distance of 100 meters. This is because the wheel has a circumference of 1 meter, so every click indicates that the wheel has traveled 1 meter.

A trundle wheel is a simple tool used to measure distance. It consists of a wheel with a handle attached to it. As the wheel is rolled along the ground, it clicks every time it makes a full revolution. The number of clicks can be used to calculate the distance traveled.

In your example, the wheel has a circumference of 1 meter. This means that it takes 1 meter for the wheel to make a full revolution and click once. If you hear 100 clicks, then you have rolled the wheel 100 times, which means that you have traveled 100 meters.

Trundle wheels are not as accurate as other measuring tools, such as a tape measure or a laser rangefinder. However, they are a simple and easy-to-use tool that can be used to measure distances quickly and easily.

Here are some additional details about trundle wheels:

To know more about distance click here

brainly.com/question/29130992

#SPJ11

Given that the perimeter of the square base is 32 cm, The surface area of the square pyramid is 304 cm².

The surface area of a square pyramid can be calculated using the formula: SA = B + (1/2)Pl, where B is the area of the base, P is the perimeter of the base, l is the slant height, and SA is the total surface area.

Given that the perimeter of the square base is 32 cm, we can divide it by 4 to find the length of each side: 32 cm / 4 = 8 cm.

Now, we can calculate the area of the base by squaring the length of a side: B = (8 cm)² = 64 cm²

Using the given slant height of 15 cm, we can plug in the values into the formula for SA: SA = 64 cm² + (1/2)(32 cm)(15 cm) = 64 cm² + 240 cm² = 304 cm².

Therefore, the surface area of the square pyramid is 304 cm².

Learn more about the Surface Area of a Square:

https://brainly.com/question/22744289
#SPJ4

Answer:

3

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

Answer:

the answer of this question is number D. 2

HOPE IT HELPED YOU !!!

Answer:

D. x = 2

Step-by-step explanation:

Rearrange so that the variable is on one side and the rest are on the other

0.6x = 2.4 - 1.2

0.6x = 1.2

To make x on its own, you divide 0.6 from both sides

x = 2