Angelica’s bouquet of a dozen roses contains 5 white roses. The rest of the roses are pink. What fraction of the bouquet is pink roses? There are 12 roses in a dozen.

Answer: Niko needs 9 marshmallows and 6 graham crackers to make 3 s'mores.

Step-by-step explanation:

Let x be the number of marshmallows , y be the number of graham crackers and z be the number of s'mores.

Then according to given question

Niko uses 12 marshmallows and 8 graham crackers to make 4 s'mores

gives the equation 12x+8y=4z

If we divide whole equation by 4 , we get the quantity of x and y to make z such that

[tex]\frac{1}{4}(12x+8y)=\frac{1}{4}(4z)\\\Rightarrow3x+2y=z[/tex]

Now to make 3 s'mores, we need to multiply the equation by 3 such that

[tex]3\times(3x+2y)=3\times\ z\\\Rightarrow\ 9x+6y=3z[/tex]

Thus Niko needs 9 marshmallows and 6 graham crackers to make 3 s'mores.

For a real number a, a + 0 = a.  TRUE

For a real number a, a + (-a) = 1.  FALSE

For a real numbers a and b, | a - b | = | b - a |.  TRUE

For real numbers a, b, and c, a + (b ∙ c) = (a + b)(a + c).  FALSE

For rational numbers a and b when b ≠ 0, is always a rational number. TRUE

This comes from the identity property for addition that tells us that zero added to any number is the number itself. So the number in this case is [tex]a[/tex], so it is true that:

[tex]a+0=a[/tex]

This is false, because:

[tex]a+(-a)=a-a=0[/tex]

For any number [tex]a[/tex] there exists a number [tex]-a[/tex] such that [tex]a+(-a)=0[/tex]

This is a property of absolute value. The absolute value means remove the negative for the number, so it is true that:

[tex]\mid a-b \mid= \mid b-a \mid[/tex]

This is false. By using distributive property we get that:

[tex](a + b)(a + c)=a^2+ac+ab+bc \\ \\ a^2+ab+ac+bc \neq a+(b.c)[/tex]

A rational number is a number made by two integers and written in the form:

[tex]\frac{u}{v} \\ \\ v \neq 0[/tex]

Given that [tex]a \ and \ b[/tex] are rational, then the result of dividing them is also a rational number.

Answer:

A) True

B) False

C) True

D) False

E) True

Step-by-step explanation:

We are given the following statements in the question:

A) True

For  every real number, a, a + 0 = a. 0 is known as the additive identity.

B) False

For a real number a, a + (-a) = 0.

C) True

For a real numbers a and b, [tex]|a-b| = |b-a|[/tex]

D) False

For real numbers a, b, and c, a + (b ∙ c) = (a + b)(a + c).

Counter example: For a = 2, b =  1, c = 3

[tex]a + (b.c) = (a + b)(a + c)\\2 + (1.3) \neq (2+1)(2+3)\\5\neq 15[/tex]

E) True

For rational numbers a and b, b is not equal to zero, [tex]\frac{a}{b}[/tex] is always a rational number.

Answer:

The factored form of [tex]4a^3b^5-16a^5b^2+12a^2b^3[/tex] is [tex]4a^2b^2\left(ab^3-4a^3+3b\right)[/tex].

Step-by-step explanation:

To find the factored form of [tex]4a^3b^5-16a^5b^2+12a^2b^3[/tex] you must:

Apply exponent rule: [tex]a^{b+c}=a^ba^c[/tex]

[tex]a^2b^3=a^2b^2b,\:a^5b^2=a^2a^3b^2,\:a^3b^5=a^2ab^2b^3[/tex]

So, we can write our expression as [tex]4a^2ab^2b^3-16a^2a^3b^2+12a^2b^2b[/tex].

Next, rewrite 12 as [tex]3\cdot \:4[/tex] and -16 as [tex]4\cdot \:4[/tex]

[tex]4a^2ab^2b^3+4\cdot \:4a^2a^3b^2+3\cdot \:4a^2b^2b[/tex]

Factor out common term: [tex]4a^2b^2[/tex]

Therefore,

[tex]4a^3b^5-16a^5b^2+12a^2b^3= 4a^2b^2\left(ab^3-4a^3+3b\right)[/tex]

Answer: Parallel.

Step-by-step explanation:

Given: Lines a and c intersect at point S, creating 4 angles.

To Prove: Corresponding angles are congruent.

We are given that lines a and c intersect at point S.

Translate line a down line c until point S reaches point Q.

Call the new line through Q line b.

We know that translations preserve orientation then every point on line b is equidistant from every points on line a.

Therefore,  lines a and b are parallel by the definition of parallel lines.

Hence, the complete statement is Because translations preserve orientation, lines a and b are parallel.

The rates of 7 inches per 9 hours and 42 inches per 54 hours do form a proportion, as demonstrated by cross-multiplying the two ratios which resulted in equal cross products (378 inch-hours on both sides).

To determine if the two rates form a proportion, we need to compare the ratios of inches to hours for both scenarios. For the first rate, we have 7 inches in 9 hours, and for the second rate, we have 42 inches in 54 hours. A proper proportion exists when two ratios are equivalent.

Let's set up our two ratios:

Now, we will test if these ratios form a proportion by creating a fraction out of each ratio and then cross-multiplying.

(7 inches / 9 hours) = (42 inches / 54 hours)

Cross multiply:

7 inches * 54 hours = 378 inch-hours

42 inches * 9 hours = 378 inch-hours

Since the cross products are equal, the two rates indeed form a proportion.

Answer:

FALSE

Step-by-step explanation:

The amount of interest paid depends on the method adopted by the lender. There are several methodologies for applying interest, so that each sector will adhere to the most convenient modality. The interest paid by you will be the result of this choice and may for example have a daily, monthly, semi-annual or annual impact. Obviously all interest charged must be clearly described in a contract and must be considered legal in the state legal apparatus.

Answer:

The cost would be $ 5.38.

Step-by-step explanation:

Given,

The price of 5 pounds of cheese = $ 13.45,

So, the price of 1 pounds of cheese = [tex]\frac{\text{Price of }5\text{ pounds of cheese}}{5}[/tex]

[tex]=\frac{13.45}{5}[/tex]

[tex]=\$ 2.69[/tex]

Thus, the price of 2 pounds of cheese = 2 × price of each pound of cheese

= 2 × 2.69

= $ 5.38

The probability of rolling a 6 exactly twice in 8 rolls of a fair die is approximately 33.5%.

The situation describes a binomial distribution where we have:

The binomial probability formula is given by:

[tex]P(X = k) = \binom{n}{k} \times p^k \times (1-p)^{n-k}[/tex]

First, calculate (n choose k) which is given by:

[tex]\binom{n}{k}= n! / [k! \times (n-k)!][/tex]

For our problem:

[tex]\binom{n}{k} = 8! / [2! \times (8-2)!] = 28[/tex]

Next, calculate the probability:

[tex]P(X = 2) = 28 \times (1/6)^2 \times (5/6)^6[/tex]

Evaluating the above:

P(X = 2) = [tex]28 \times (1/36) \times (15625/46656)[/tex] ≈ 0.335

Therefore, the probability that the die comes up a 6 exactly twice in 8 rolls is approximately 0.335 or 33.5%.

The answer is f(n) = 60 + 10n.

The composite function rule (also called the chain rule) Has taken a look at the characteristic f(x)=(x2 + 1)17. we will think about this function as being. the end result of mixing features. If g(x) = x2 + 1 and h(t) = t17 then the result of.

A function rule along with value = p + zero.08p is an equation that describes a useful relationship. If p is the charge you pay for an object and 0.08 is the income tax, the feature rule above is the value of the item. in case you are given a desk, usually, you need to cautiously study the desk to peer what the function rule is.

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The dimensions that give the minimum surface area are a radius of approximately 2.83 cm and a height of approximately 0.64 cm.

To find the dimensions of the closed cylinder that give the minimum surface area, we need to express the surface area of the cylinder in terms of one variable.

Let's use the radius, r, as the variable.

The surface area of a closed cylinder is given by the formula: A = 2πr² + 2πrh, where h is the height of the cylinder.

Since we are given that the volume of the cylinder is 40 cm³, we can use the formula for the volume of a cylinder to express h in terms of r: V = πr²h = 40 cm³.

Substituting this expression for h in terms of r into the surface area formula, we get:

A = 2πr² + 2πr(40 / (πr²)) = 2πr² + (80 / r).

To find the dimensions that give the minimum surface area, we need to find the value of r that minimizes A.

To do this, we take the derivative of A with respect to r and set it equal to zero:

A' = 4πr - (80 / r²) = 0. Solving this equation, we find that r = √(20/π) ≈ 2.83 cm.

So, the radius that gives the minimum surface area is approximately 2.83 cm.

We can then use the volume formula to find the corresponding height: h = 40 / (π(2.83)²) ≈ 0.64 cm.

Therefore, the dimensions giving the minimum surface area are a radius of approximately 2.83 cm and a height of approximately 0.64 cm.

40 hours regular pay

8 hours at 1.5 = 8*1.5 = 12

40+12 = 52

1248/52 = 24

A) $24 per hour

B) 14*1.5 = $36 per hour for overtime

a)  

           His hourly rate= $ 24

b)

         His hourly overtime rate= $ 36

Jim worked 40 regular hours last week, plus 8 overtime hours at the time and a half rate.

This means if he is paid $ x per hour working in regular hours.

Then he will be paid $ (1.5x) per hour working overtime.

( Since it is given that: he is paid time and a half rate for overtime)

Now, his gross pay is: $ 1248

i.e.

Amount working at regular hours for 40 hours+ Amount obtained for working 8 hours overtime= $ 1248

i.e.

40x+8(1.5x)=1248

i.e.

40x+12x=1248

i.e.

52x=1248

i.e.

x=24

a)

Hence, his hourly rate is:$ 24

b)

His hourly overtime rate is: $ (24×1.5)

i.e.

His hourly overtime rate is:  $ 36

The unknown numbers are 11.5 and 11.5

Let the unknown numbers be x and y

If the sum of the numbers is 23, hence;

x +  y = 23

x = 23 - y ............. 1

If the product is at maximum, hence;

xy = maximum ......... 2

Substitute equation 1 into 2

(23 - y )y = maximum

23y - y² = maximum

maximum = -y² + 23y

A(y) =  -y² + 23y

Since the product A(y) is at maximum, hence dA(y)/dy = 0 as shown:

dA(y)/dy= -2y + 23 = 0

-2y + 23 = 0

2y = 23

y = 23/2

y = 11.5

Since x + y = 23

x = 23 - y

x = 23 - 11.5

x = 11.5

Hence the unknown numbers are 11.5 and 11.5

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