a
22 degrees

b
3 degrees

c
40 degrees

d
20 degrees

The greatest number of arrangements using every balloon is an illustration of the highest common factors (HCF).

The greatest number of arrangements you can make using every balloon is 8.

Given that:

[tex]White = 16[/tex]

[tex]Red = 24[/tex]

To determine the greatest number of arrangements, we simply calculate the HCF of 16 and 24.

We have:

[tex]16 = 2\times 2\times 2 \times 2[/tex]

[tex]24 = 2\times 2\times 2 \times 3[/tex]

The highest common factor is:

[tex]HCF =2 \times 2 \times 2[/tex]

[tex]HCF =8[/tex]

Hence, the greatest number of arrangements you can make using every balloon is 8.

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Using the concept of similar triangles to calculate the scale factor, the height of the streetlight is 3 times the height of the person.

Length of shadow cast = 10 feets

Height of person = 6 feets

Distance of person from streetlight light = 20 feets

Since the triangles are similar :

Comparing the length of both triangles :

The scale factor is :

Using the scale factor ; the height of the streetlight will be :

Height of streetlight = 18 feets

Height of person = 6 feets

Therefore, the streetlight is (18/6 = 3) 3 times the height of the person.

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Answer: B

Step-by-step explanation: B

The correct statement is B) The hypothesis is 'a number is a square number greater than 1.' This correctly identifies the 'if' part of the logical statement, whereas A), C) and D) are incorrect interpretations.

The given logical statement is 'If a number is a square number then it has at least one factor other than 1 and itself.' In examining the answer choices, 'B) The hypothesis is "a number is a square number greater than 1." correctly identifies the hypothesis or the 'if' part of the logical statement. A) is incorrect as it reverses the conditions and conclusions. C) is incorrect as the conclusion is the part following 'then' and D) is incorrect as 49, being a square number, upholds the conditions stated in the logical statement, and thus cannot be a counterexample.

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The coat would cost $0.60 more in Delaware County than in Fairfield County.

To determine how much more the coat would cost in Delaware County compared to Fairfield County, we need to calculate the total cost of the coat in both counties, including their respective sales tax rates, and then find the difference between these two amounts.

First, let's calculate the total cost of the coat in Delaware County:

1. Original price of the coat: $80

2. Sales tax rate in Delaware County: 7.25%

The sales tax amount in Delaware County is calculated as:

[tex]\[\text{Sales tax} = \text{Original price} \times \left(\frac{\text{Sales tax rate}}{100}\right) = 80 \times \left(\frac{7.25}{100}\right) = 80 \times 0.0725 = 5.80\][/tex]

So, the total cost in Delaware County is:[tex]\[\text{Total cost} = \text{Original price} + \text{Sales tax} = 80 + 5.80 = 85.80\][/tex]

The sales tax amount in Fairfield County is calculated as:

[tex]\[\text{Sales tax} = \text{Original price} \times \left(\frac{\text{Sales tax rate}}{100}\right) = 80 \times \left(\frac{6.5}{100}\right) = 80 \times 0.065 = 5.20\][/tex]

So, the total cost in Fairfield County is:

[tex]\[\text{Total cost} = \text{Original price} + \text{Sales tax} = 80 + 5.20 = 85.20\][/tex]

Now, let's find the difference in total costs between Delaware County and Fairfield County:

[tex]\[\text{Difference} = \text{Total cost in Delaware County} - \text{Total cost in Fairfield County} = 85.80 - 85.20 = 0.60\][/tex]

By using algebra to model the problem, we find that the pharmacist had 36 prescriptions for tranquilizers.

In the given problem, we need to find out the number of prescriptions for tranquilizers. We know that the pharmacist has 4/3 as many prescriptions for antibiotics as tranquilizers. We also know that the total number of prescriptions for both the drugs is 84. We can make a mathematical model out of this information and solve for the number of tranquilizer prescriptions.

Let us suppose the number of tranquilizer prescriptions is x. Then the number of antibiotic prescriptions would be 4/3*x. Together, these prescriptions add up to 84.

So, we can write the equation: x + 4/3*x = 84

To make the equation simpler we can multiply the entire equation by 3 which transforms the equation into: 3x + 4x = 252

Combining like terms gives us: 7x = 252

Finally, dividing both sides of the equation by 7 gives us the solution: x = 252 / 7

So, x = 36

Therefore, we conclude that the pharmacist had 36 prescriptions for tranquilizers.

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Answer:

Cost:$ 920 each or $5,520

Total annual interest: $65 per bond and $390 total

Yield: 7.06%

Step-by-step explanation:

The cost of the bonds is given by the multiplication of the value of the bonds by 92 and divided by 100:

1000*92/100=920

So the cost of each bond would be $920

Then the interest that is payed by the bonds is based on its value which is $1000, so he receives 65 dollars per bond a year, that multiplied by the 6 bonds is equal to $390.

The yield is the real money paid to return interest rate relation, so you just have to take the percentage if 5,520 is the 100, how much is $390=

5520/100=390/x

x=39000/5520=7.06%

The freezer's temperature decreased by 30 degrees Celsius from its original temperature of 18 degrees Celsius to reach -12 degrees Celsius.

The temperature change in the freezer is calculated by finding the difference between the final temperature and the initial temperature.

In this case, the freezer started at 18 degrees Celsius and cooled down to -12 degrees Celsius.

To determine the difference, subtract the initial temperature from the final temperature:

-12 degrees Celsius (final temperature) - 18 degrees Celsius (initial temperature) = -30 degrees Celsius.

The negative sign indicates a decrease in temperature.

Therefore, the temperature of the freezer decreased by 30 degrees Celsius.

This temperature change represents the amount by which the freezer's internal temperature dropped during the cooling process.

It's crucial to note that the negative value signifies a colder temperature than the initial state.

The cooling process might be influenced by factors such as the freezer's capacity, insulation, and cooling mechanism.

Temperature changes is essential for various applications, including food preservation and scientific experiments where precise temperature control is crucial.

The freezer experienced a temperature decrease of 30 degrees Celsius, resulting in a colder temperature of -12 degrees Celsius from its initial state of 18 degrees Celsius.

C) If the measures of two angles add up to 180 degrees, then they form a linear pair.

The statement below be rewritten as a conditional statement If the measures of two angles add up to 180 degrees, then they form a linear pair. Option C is correct.

Trigonometry deals with the relationship between the sides and angles of a right-angle triangle.

Rewrite the following sentence into a conditional statement. A linear pair is created when the measurements of two angles sum up to 180 degrees.

Hence,option C is correct.

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Final answer:

To find the perimeter of Jill's room in the scale drawing, convert the actual room measurements using the scale and then calculate the perimeter based on the scaled dimensions. The perimeter on the drawing is 12 inches.

Explanation:

The question asks us to calculate the perimeter of a room in a scale drawing. Jill's room measurements are 12.5 feet in length and 11.5 feet in width, with a scale of 0.5 inch equals 2 feet. To find the perimeter on the drawing, we first convert the actual measurements into scale measurements:

Scale for Length: 12.5 feet / 2 feet = 6.25; then 6.25 × 0.5 inch = 3.125 inches.

Scale for Width: 11.5 feet / 2 feet = 5.75; then 5.75 × 0.5 inch = 2.875 inches.

Next, we calculate the perimeter of Jill's room on the drawing:

Perimeter = 2 × (Length + Width) in the drawing.

Perimeter = 2 × (3.125 inches + 2.875 inches) = 2 × 6 inches = 12 inches.

Therefore, the perimeter of Jill's room on the drawing is 12 inches.

The product of the numbers will be 120. And the product 3 × 40 = 3 × 4 tens.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

PEMDAS rule means the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.

According to the commutative property of integer multiplication, changing the order of something like the operands or the integers has no impact on the outcome of the multiplication.

a x b = b x a

Similarly, the product of the numbers 3 and 40 can be written as,

3 × 40 = 3 × 4 tens

The product of the numbers will be

3 × 40 = 120

The product of the numbers will be 120.

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first number is x , second number is y

 y = x-6

 so answer is B 22-6 = 16

B (22,16)

The value of y is 1.

Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.

Let's simplify the left-hand side first:

4y - 7 + 2y = 6y - 7

Now let's simplify the right-hand side:

-3(y - 1) - 1 = -3y + 2

Now we can substitute these simplified expressions back into the original equation and solve for y:

6y - 7 = -3y + 2

Adding 3y to both sides, we get:

9y - 7 = 2

Adding 7 to both sides, we get:

9y = 9

Dividing both sides by 9, we get:

y = 1

Therefore, the solution is y = 1.

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We have that   1.888 as a mixed number is

[tex]\frac{9}{5}=1\frac{4}{5}[/tex]

From the Question we are told that

1.888 is given

Generally

[tex]1.8888 \approx\frac{9}{5}[/tex]

Therefore

the Mixed number is given as

[tex]\frac{9}{5}=1\frac{4}{5}[/tex]

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The student is asking about fractions. In a fraction, the denominator (bottom number) represents the total number of equal parts the whole is divided into, while the numerator (top number) signifies the parts we're considering. When multiplying, the numerators and denominators multiply separately to form the new fraction.

The student is referring to the concept of fractions. In a fraction, the number on the bottom (the denominator) is the total number of equal parts into which a whole is divided, and the number on the top (the numerator) is the number of those parts we are considering. To clarify by using an example, let’s take 2/4. In this scenario, the denominator is 4, which means our whole is divided into 4 equal parts. The numerator is 2, which shows that we're referring to 2 out of those 4 parts. When multiplying fraction, the numerators multiply to create the new numerator and denominators multiply to create the new denominator. Hence, 2/4 multiplied with 3/4 would produce 6/16.

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