What is the value of c?
a)4 units
b)5 units
c)6 units
d)7 units

P(A and B) is equal to 6.

To find P(A and B), we can use the formula:

P(A and B) = P(A) + P(B) - P(A U B)

Given the information:

P(A U B) = 32 (the probability of either event A or event B occurring)

Universal set contains 52 elements (total number of possible outcomes)

P(A intersection B) = 6 (the probability of both event A and event B occurring)

P(A) = 12 (the probability of event A occurring)

P(B) = 26 (the probability of event B occurring)

We can substitute the known values into the formula:

P(A and B) = P(A) + P(B) - P(A U B)

P(A and B) = 12 + 26 - 32

Simplifying the expression:

P(A and B) = 38 - 32

P(A and B) = 6

Therefore, P(A and B) is equal to 6.

The result indicates that the probability of both event A and event B occurring simultaneously is 6 out of the total number of possible outcomes in the universal set. It means that out of the 52 elements in the universal set, 6 of them satisfy the conditions of both A and B.

For more question on  equal visit:

https://brainly.com/question/29301106

#SPJ8

Answer:

the expected monthly payment is approximately $212.47, the total payment over the 60-month term is $12,748.20, and the total interest paid is $2,748.20.

Step-by-step explanation:

To calculate the monthly payment, total payment, and interest paid for an installment loan, we can use the loan payment formula:

Monthly Payment = P * (r * (1 + r)^n) / ((1 + r)^n - 1)

Where:

P = Principal amount (loan amount)

r = Monthly interest rate (annual interest rate divided by 12)

n = Total number of months

Given:

Principal amount (loan amount) = $10,000

Annual interest rate = 17%

Loan term = 60 months

First, we need to calculate the monthly interest rate and the total number of months:

Monthly interest rate = Annual interest rate / 12

r = 17% / 12 = 0.017 / 12 = 0.0014167

Total number of months = Loan term = 60 months

n = 60

Now, we can calculate the monthly payment using the loan payment formula:

Monthly Payment = $10,000 * (0.0014167 * (1 + 0.0014167)^60) / ((1 + 0.0014167)^60 - 1)

Using a calculator or spreadsheet software, the monthly payment comes out to be approximately $212.47.

To calculate the total payment, we can multiply the monthly payment by the total number of months:

Total Payment = Monthly Payment * Total number of months

Total Payment = $212.47 * 60

Total Payment = $12,748.20

To calculate the interest paid, we can subtract the principal amount from the total payment:

Interest Paid = Total Payment - Principal amount

Interest Paid = $12,748.20 - $10,000

Interest Paid = $2,748.20

Therefore, the expected monthly payment is approximately $212.47, the total payment over the 60-month term is $12,748.20, and the total interest paid is $2,748.20.

We can rewrite log2(4) as log2(2^2) x = 2 Theerefore, the solution to the equation 2^x - 4 = -4^x + 4 is x = 2.

To solve the equation 2^x - 4 = -4^x + 4 for x, we'll first simplify the equation and then proceed with solving it.

Let's start by simplifying the equation:

2^x - 4 = -4^x + 4

Rearranging the equation, we have:

2^x + 4^x = 8

Now, let's rewrite 4^x as (2^x)^2:

2^x + (2^x)^2 = 8

We can now combine the terms with the same base, 2^x:

2^x + (2^x * 2^x) = 8

Applying the laws of exponents, we can simplify the equation further:

2^x + 2^(2x) = 8

Now, let's substitute a variable, say y, to represent 2^x:

y + y^2 = 8

Rearranging the equation, we have a quadratic equation:

y^2 + y - 8 = 0

To solve this quadratic equation, we can factorize it:

(y + 2)(y - 4) = 0

Setting each factor equal to zero, we have two possible solutions:

y + 2 = 0 OR y - 4 = 0

Solving each equation, we find:

y = -2 OR y = 4

Now, let's substitute y back into the original variable:

2^x = -2 OR 2^x = 4

The equation 2^x = -2 doesn't have a real solution because raising any positive number (2 in this case) to a real power will always yield a positive result.

However, for the equation 2^x = 4, we can solve it by taking the logarithm base 2 of both sides:

log2(2^x) = log2(4)

x * log2(2) = log2(4)

x * 1 = log2(4)

x = log2(4)

Using the logarithm properties, we can rewrite log2(4) as log2(2^2):

x = 2

Therefore, the solution to the equation 2^x - 4 = -4^x + 4 is x = 2.

for such more question on equation

https://brainly.com/question/17482667

#SPJ8

The number of 90° angles formed by the intersections of EF and the parallel lines AB and CD is two.

When a line EF is perpendicular to lines AB and CD, it forms a total of two 90° angles. One 90° angle is formed at the intersection of EF and AB, and the other 90° angle is formed at the intersection of EF and CD.

The reason for this is that when a line is perpendicular to another line, it forms a right angle or a 90° angle at the point of intersection. Since EF is perpendicular to both AB and CD, it creates two such intersections, resulting in two 90° angles.

So, in this scenario, the number of 90° angles formed by the intersections of EF and the parallel lines AB and CD is two.

for such more question on angles

https://brainly.com/question/25716982

#SPJ8

Answer:

x = 15 , y = 21

Step-by-step explanation:

using Pythagoras' identity

in Δ ABD

x² + 8² = 17²

x² + 64 = 289 ( subtract 64 from both sides )

x² = 225 ( take square root of both sides )

x = [tex]\sqrt{226}[/tex] = 15

in Δ ADC

8² + DC² = 10²

64 + DC² = 100 ( subtract 64 from both sides )

DC² = 36 ( take square root of both sides )

DC = [tex]\sqrt{36}[/tex] = 6

then

y = x + DC = 15 + 6 = 21

Answer:

look at attachment

Step-by-step explanation:

The side length of the cube is [tex]s = \sqrt[3]{V}[/tex]

From the question, we have the following parameters that can be used in our computation:

V = s³

Where

Using the above as a guide, we have the following:

V = s³

Take the cube root of both sides

[tex]s = \sqrt[3]{V}[/tex]

Hence, the side length of the cube is [tex]s = \sqrt[3]{V}[/tex]

Read more about volume at

https://brainly.com/question/30849227

#SPJ1

The journal entry necessary to record the sale of goods on account includes debiting the Accounts Receivable and crediting the Sales Revenue account.

1. Identify the transaction details: Determine the amount and nature of the goods sold on account, including the sales price and any applicable taxes.

2. Debit the Accounts Receivable account: Increase the Accounts Receivable account by the total amount of the sale. This represents the amount owed to the company by the customer.

3. Credit the Sales Revenue account: Increase the Sales Revenue account by the total amount of the sale. This records the revenue generated from the sale of goods.

4. Include any applicable tax accounts: If taxes are involved, debit or credit the corresponding tax accounts accordingly. For example, if sales tax is collected, credit the Sales Tax Payable account.

5. Record any discounts or allowances: If the customer is entitled to any discounts or allowances, adjust the Accounts Receivable and Sales Revenue accounts accordingly.

6. Include any other relevant accounts: Depending on the specific circumstances of the sale, you may need to include additional accounts such as Cost of Goods Sold or Inventory.

7. Provide a brief description: Add a brief description of the transaction in the journal entry to provide clarity and reference for future accounting purposes.

Remember to consult with an accounting professional or refer to the specific accounting guidelines and policies of your organization to ensure accurate recording of journal entries.

For more such questions on journal entry, click on:

https://brainly.com/question/28390337

#SPJ8

The inequality "x ≤ 1" has infinitely many negative integer solutions as any negative integer value for x satisfies this condition.

The inequality that has infinitely many negative integer solutions is "x ≤ 1".

To understand why this is the case, let's break down the inequality and consider its implications. The inequality x ≤ 1 means that x is less than or equal to 1. In other words, any value of x that is smaller than or equal to 1 satisfies this inequality.

Now, when it comes to negative integers, they are numbers less than zero. Since negative integers are smaller than 1, any negative integer value for x will fulfill the condition x ≤ 1. For example, if we take x = -1, -2, -3, and so on, they are all less than or equal to 1, thereby satisfying the inequality.

Moreover, there are infinitely many negative integers (-1, -2, -3, and so on), meaning that there is no limit to the number of negative integer solutions that satisfy x ≤ 1. Hence, the inequality has infinitely many negative integer solutions.

On the other hand, the inequalities "x > 5" and "0 < x" do not have infinitely many negative integer solutions. "x > 5" implies that x must be greater than 5, excluding negative integers. "0 < x" states that x must be greater than zero, also excluding negative integers. Finally, "x ≥ 8" requires x to be greater than or equal to 8, which again does not include negative integers.

for such more question on inequality

https://brainly.com/question/17448505

#SPJ8

Step-by-step explanation:

Slope intercept form is

[tex]y = mx + b[/tex]

So you need to isolate the y variable

For the first equation

[tex]2x + y = - 3[/tex]

[tex]y = - 2x - 3[/tex]

For the second equation,

[tex]y = - 3 - 2x[/tex]

Notice that this system will have infinite solutions

Answer:

6 = 2 × 3

12 = 2 × 2 × 3

18 = 2 × 3 × 3

LCM of 6, 12, and 18 = 2 × 2 × 3 × 3 = 36

The smallest number of eggs that can be packed is 36.

i) U is a subspace of ℝ⁴.

(ii) V is not a subspace of ℝ⁴.

(iii) W is not a subspace of ℝ⁴.

To determine which of the given subsets are subspaces of ℝ⁴, we need to check if they satisfy three conditions:

The zero vector is in the subset.

The subset is closed under addition.

The subset is closed under scalar multiplication.

Let's analyze each subset:

(i) U = {(a, b, c, d) | a + 2b = c + 2d}

To check if U is a subspace, we need to verify the three conditions:

Zero vector: The zero vector in ℝ⁴ is (0, 0, 0, 0).

Substituting the values into the equation, we have 0 + 2(0) = 0 + 2(0), which is true.

So the zero vector is in U.

Addition: Suppose we have two vectors (a₁, b₁, c₁, d₁) and (a₂, b₂, c₂, d₂) in U. We need to check if their sum is also in U.

Adding the vectors component-wise, we get (a₁ + a₂, b₁ + b₂, c₁ + c₂, d₁ + d₂).

Substituting these values into the equation, we have (a₁ + a₂) + 2(b₁ + b₂) = (c₁ + c₂) + 2(d₁ + d₂), which holds true.

Hence, U is closed under addition.

Scalar multiplication:

Let (a, b, c, d) be a vector in U, and let k be a scalar. We need to show that k(a, b, c, d) is also in U.

Multiplying each component of the vector by k, we get (ka, kb, kc, kd). Substituting these values into the equation, we have ka + 2kb = kc + 2kd, which is also true.

Therefore, U is closed under scalar multiplication.

Since U satisfies all three conditions, it is a subspace of ℝ⁴.

(ii) V = {(a, b, c, d) | a + 2b = c + 2d + 1}

Let's analyze V using the three conditions:

Zero vector:

Substituting (0, 0, 0, 0) into the equation, we have 0 + 2(0) = 0 + 2(0) + 1, which is not true.

Therefore, the zero vector is not in V, and V fails the first condition.

Since V fails the first condition, it cannot be considered a subspace of ℝ⁴.

(iii) W = {(a, b, c, d) | ab = cd}

Now let's apply the conditions to W:

Zero vector:

Substituting (0, 0, 0, 0) into the equation, we have 0 [tex]\times[/tex] 0 = 0 [tex]\times[/tex] 0, which is true.

Therefore, the zero vector is in W.

Addition: Take two vectors (a₁, b₁, c₁, d₁) and (a₂, b₂, c₂, d₂) in W.

Their sum is (a₁ + a₂, b₁ + b₂, c₁ + c₂, d₁ + d₂).

Substituting these values into the equation, we have (a₁ + a₂)(b₁ + b₂) = (c₁ + c₂)(d₁ + d₂), which holds true.

Hence, W is closed under addition.

Scalar multiplication: Let (a, b, c, d) be a.

For similar question on subspace.

https://brainly.com/question/29891018  

#SPJ8

The value of the variable is 26

To determine the value of the variable, we have to know the following;

From the information shown in the diagram, we have;

3w - 1 and 77 are Corresponding angles, we have;

equate the angles, we get;

3w -1 = 77

collect the like terms, we have;

3w = 77 + 1

3w = 78

Divide by the coefficient

w =26

Learn more about angles at: https://brainly.com/question/25716982

#SPJ1

Answer:

10/3 cup  , 1 cup quarter cup

The solution set to inequality |x + 2| > 2 is equal to x < - 4 or x > 0, whose interval notation is x ∈ (- 4, 0).

In this problem we find the definition of the following inequality, whose solution set must be found:

|x + 2| > 2

First, use the definition of absolute value to eliminate bars:

x + 2 < - 2 or x + 2 > 2

Second, clear x on each expression:

x < - 4 or x > 0

Third, write the solution set in interval notation:

x ∈ (- 4, 0)

To learn more on inequalities: https://brainly.com/question/29792808

#SPJ1

The expression that represents the total amount of change Alexis should receive is:

20 - 3x

Cereals are the grains belonging to the grain family. Wheat, rice, corn, millet, rye, and many others. These are rich in carbohydrates.

The cereals most commonly cultivated are wheat, rice, rye, oats, barley, corn (maize), and sorghum.

The expression that represents the total amount of change Alexis should receive is:

20 - 3x

For such more questions on Cereal change

https://brainly.com/question/28340244

#SPJ8

Answer:

A. 20 – 3x

Step-by-step explanation:

The x-intercepts and y-intercepts of the graph are x = 5 and y = 2

From the question, we have the following parameters that can be used in our computation:

The graph

The x-intercepts are when y = 0

In this case, it is

x = 5

The y-intercepts are when x = 0

In this case, it is

y = 2

Read more about intercepts at

https://brainly.com/question/24363347

#SPJ1

Answer: c=24

Step-by-step explanation:

To isolate C, move 3 to the other side. C=3x8, 3x8 is 24 so C is 24. You can check this by dividing 24 (C) by 3 to check if it’s 8.

The answer is:

c = 24

Work/explanation:

To solve for c, multiply each side by 3. I'm doing this to get rid of the fraction on the left side.

[tex]\sf{\dfrac{c}{3}=8}[/tex]

[tex]\sf{c=8\cdot3}[/tex]

[tex]\sf{c=24}[/tex]

The value of tan(60°) is √3, and option C is correct.

In order to find the value of tan(60°) using the given diagram, we need to use the tangent formula which is:tan(x) = opposite / adjacentIn the case of the given diagram, we can see that the angle we're interested in is 60°, and the side opposite the angle is the length of the line marked "√3" and the side adjacent to the angle is the length of the line marked "1".Thus, we can plug in these values into the formula:tan(60°) = opposite / adjacenttan(60°) = √3 / 1tan(60°) = √3.

The value of tan(60°) is √3, and option C is correct.

for more such questions on  adjacenttan

https://brainly.com/question/28394984

#SPJ8

The perimeter of the trapezoid with sides measuring 23in., 19in., 22in., and 21in. is 85 inches.

To find the perimeter of a trapezoid, we need to add the lengths of all its sides. Let's calculate the perimeter step by step using the given side lengths:

Identify the sides: The given side lengths of the trapezoid are 23in., 19in., 22in., and 21in.

Add the side lengths: To find the perimeter, we sum up all the side lengths.

Perimeter = 23in. + 19in. + 22in. + 21in.

Perimeter = 85in.

Therefore, the perimeter of the trapezoid is 85 inches.

In the trapezoid, the sides measuring 23in. and 19in. are parallel to each other, as well as the sides measuring 22in. and 21in. The side lengths provided in the question correspond to the lengths of the respective sides.

By summing up all the side lengths, we obtain a perimeter of 85 inches.

Hence, the perimeter of the trapezoid with side lengths 23in., 19in., 22in., and 21in. is 85 inches.

For more such questions on trapezoid , click on:

https://brainly.com/question/1410008

#SPJ8

At the beginning of the 17th day of the experiment, the mass of the radioactive sample would be approximately 508.4 grams.

To determine the mass of the radioactive sample at the beginning of the 17th day, we need to calculate the successive decay of the mass over the 16-day period.

Given that the mass is decreasing by 5% per day, we can use the following formula to calculate the mass at the beginning of each day:

Mass_n = Mass_(n-1) * (1 - 0.05)

Where Mass_n represents the mass at day n and Mass_(n-1) represents the mass at the previous day.

Let's calculate the mass at the beginning of each day:

Day 1:

Mass_1 = 900 grams (given)

Day 2:

Mass_2 = Mass_1 * (1 - 0.05) = 900 * 0.95 = 855 grams

Day 3:

Mass_3 = Mass_2 * (1 - 0.05) = 855 * 0.95 = 812.25 grams

Similarly, we can continue calculating the mass for each subsequent day.

Day 17:

Mass_17 = Mass_16 * (1 - 0.05) = 508.3697481 grams (rounded to the nearest tenth)

Consequently, the radioactive sample would weigh about 508.4 grammes at the start of the experiment's 17th day.

for such more question on radioactive isotope

https://brainly.com/question/23118328

#SPJ8

slope/m=1

y-intercept/b=-11

. Figures 2 and 10 also demonstrate the same relationship, further supporting the proof of the theorem through visual representation.

I have chosen Image 4 to answer the questions.

A. In Image 4, the change from the previous image (Image 3) involves a translation of figure 5. The figure is shifted horizontally to the right, aligning its right side with the right side of figure 3. The transformation used is a horizontal translation.

B. I will choose figure 9 in Image 4. Figure 9 is a square located at the rightmost side of the image. Its side length is the same as the hypotenuse of the right triangle formed by figures 5, 7, and 8.

In relation to the figure in Image 1, the side length of figure 9 is equal to the square of the hypotenuse.

C. The length of figure 9, which represents the square of the hypotenuse, relates to the Pythagorean Theorem. According to the Pythagorean Theorem, the square of the hypotenuse (c^2) is equal to the sum of the squares of the other two sides (a^2 + b^2).

The length of figure 9, being a square, represents the square of the hypotenuse, confirming the relationship stated in the Pythagorean Theorem.

The visual proof demonstrates the Pythagorean Theorem by showing the relationship between the squares constructed on the sides of a right triangle.

Figures 5 through 9 depict different squares that relate to each other. The squares of the legs (a and b) in the triangle are shown in figures 5 and 7, and their areas are combined to form the square of the hypotenuse (c^2) in figure 9.

The visual proof visually illustrates that the sum of the areas of the squares constructed on the legs equals the area of the square constructed on the hypotenuse, which aligns with the Pythagorean Theorem.

For more questions Visual:

https://brainly.com/question/28028820

#SPJ8

Answer:

f(g(x)) = x + 11

g(f(x)) = √(x² + 11)

Step-by-step explanation:

f(x) = x² + 5

g(x) = √(x + 6)

f(g(x)) = f(√(x + 6))

= (√(x + 6))² + 5

= x + 6 + 5

f(g(x)) = x + 11

g(f(x)) = g(x² + 5)

= √(x² + 5 + 6)

g(f(x)) = √(x² + 11)

The vector subtraction for the given values of vectors, ⇀ – ⇀ is ⟨9, –12⟩.

To find the vector subtraction ⇀ – ⇀ , then subtract the corresponding components of the two vectors.

Given that the vectors ⇀ = ⟨3, –2⟩ and ⇀ = ⟨–6, 10⟩, the vector subtraction is calculated as follows:

⇀ – ⇀ = ⟨3, –2⟩ – ⟨–6, 10⟩

= ⟨3 - (–6), –2 - 10⟩

= ⟨3 + 6, –2 - 10⟩

= ⟨9, –12⟩

Therefore, the vector subtraction ⇀ – ⇀ is ⟨9, –12⟩.

Find out more on vector subtraction here: https://brainly.com/question/14920537

#SPJ1

Let [tex]x[/tex] be the number of bags of chips Bonnie bought.

Then, the number of cans of pop she bought is [tex]x + 10[/tex].

The total cost is [tex]\$17.50[/tex], so we can write an equation:

[tex]\qquad\qquad 0.5x + 1(x + 10) = 17.50[/tex]

Simplifying and solving for x:

[tex]\qquad\qquad\begin{gathered}0.5x + x + 10 = 17.50 \\ 1.5x + 10 = 17.50 \\ 1.5x = 7.50 \\ \fbox{x = 5}\end{gathered}[/tex]

[tex]\therefore[/tex] Bonnie bought 5 bags of chips and 5 + 10 = 15 cans of pop.

To check:

[tex]\blue{\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}[/tex]

(ノ^_^)ノ [tex]\large\qquad\qquad\qquad\rm 06/21/2023[/tex]

SOLUTION: 5 bags of chips and 15 pops

Solving by substitution, choose your variables. In this case, let “c” represent the number of chips, and “p” the number of pop

Make your equations:

1.00p + 0.50c = 17.50

c + 10 = p

In the first equation, substitute “p” for the second equation:

1.00(c + 10) + 0.50c = 17.50

Distribute 1.00 to everything within the brackets:

1.00c + 10.00 + 0.50c = 17.50

Solve for “c”.

1.00c + 0.50c + 10.00 = 17.50

1.50c = 17.50 - 10.00

1.50c = 7.50

c = 5

Now, since we know that “p” is 10 more then “c”, we can substitute “c” for 5 in the second equation:

5 + 10 = p

15 = p

5 chips, 15 pops

The volume of the rectangular tank is:

V = l × w × h = 40 cm × 30 cm × 35 cm = 42,000 cm³

The initial volume of water in the tank is:

V1 = l × w × h1 = 40 cm × 30 cm × 15 cm = 18,000 cm³

When 4800 cm³ of water is poured into the tank, the new volume of water becomes:

V2 = V1 + 4800 cm³ = 18,000 cm³ + 4800 cm³ = 23,800 cm³

Let's assume that the new water height is h2 cm. We can use the formula for the volume of a rectangular tank to find the new height:

V = l × w × h2

h2 = V / (l × w) = (23,800 cm³) / (40 cm × 30 cm) ≈ 19.83 cm

Therefore, the new height of the water in the tank is approximately 19.83 cm.

In a case whereby a groups of students are travelling together . One group consists of 40 bays and 25girls, in another group consists of 50 bays and 35 girls. percentage of boys and girls in the combined group​ is 60 and 40% respectively.

No.of girls that are in the group A = 25

No. of girls in group B = 35

Total no.of girls = 60 girls

No.of boys in Group A = 40

No.of boys in group B = 50

Total boys = 40boys

Total children = (60 + 90)

= 150 children

Percentage of girls = [tex]\frac{60}{150} *100[/tex] = 40 percent

Percentage of boys = [tex]\frac{90}{150} *100[/tex]= 60 percent

Learn more about  percentage  at;

https://brainly.com/question/24877689

#SPJ1

Based on the analysis and the given right triangle, option B, cos(90° - A), is equal to 3/4.

To determine which of the given expressions is equal to 3/4, let's analyze each option:

A. cosB: The cosine function is defined as the ratio of the length of the adjacent side to the hypotenuse in a right triangle. In this case, we are not given any information about angle B or the sides of the triangle, so we cannot determine if cosB is equal to 3/4.

B. cos(90° - A): Using the identity cos(90° - A) = sin(A), we can substitute sin A = 3/4 into the expression. Therefore, cos(90° - A) = sin(A) = 3/4.

C. sin(90° - B): This expression represents the sine of the complement of angle B. Since angle B is not given, we cannot determine its value or if sin(90° - B) is equal to 3/4.

Learn more about Right Triangle on:

https://brainly.com/question/29869536

#SPJ1

Answer:

D) All of the above.

Step-by-step explanation:

In right triangle ABC, we are told that:

As angle C is the right angle, and since the interior angles of a triangle sum to 180°, the other two angles, A and B, are complementary angles (sum to 90°). Therefore, we can say that:

For two complementary angles, the sine of one equals the cosine of the other. Therefore, in our right triangle ABC, the sine of A equals the cosine of B, and the sine of B equals the cosine of A:

Therefore, we can write sin A in three ways:

If sin A = 3/4, then:

So the correct answer option is D) All of the above, since all answer options equal 3/4.

2 on division by 3/7 yields 14/3.

For the division of two fractions, we need to multiply the first fraction with the reciprocal of the second. Reciprocal of a fraction means interchanging the numerator and denominator ie, the reciprocal of a is 1/a, the reciprocal of p/q = q/p, and so on.

For example, if a/b and c/d are the fractions the a/b ÷ c/d = a/b x d/c =ad/bc.

Implementing the same method to solve this question,

We have 2/1 = 2 as the first and 3/7 as the second fraction. Thus,

2 ÷3/7 =2 x 7/3 = 14/3. So 14/3 is the answer.

For further reading on fractions refer to,

brainly.com/question/8482939