5 lollipops and 12 toffees have a mass of 61 grams and 10 lollipops and 13 toffees have a mass of 89 grams . Calculate the mass of one lollipop and one toffee

Answer:  The correct option is (D) (x - 3).

Step-by-step explanation:  Given that a polynomial function has a zero at x = 3.

We are to select the correct expression that must be a factor of the polynomial.

FACTOR THEOREM :   The theorem states that if x = a is a zero of a polynomial p(x), then (x - a) will be a factor of the polynomial p(x).

In case of our given polynomial, since x = 3 is a zero of the polynomial, so by factor theorem, we can say that

(x - 3) is a factor of the given polynomial.

Thus, the required factor is (x - 3).

Option (D) is CORRECT.

The number of houses left to be sold is 9, calculated from the initial total and the proportions sold each month.

The number of houses left to be sold is 9.

Initially, 1/3 of the 84 new houses were sold, which is 84 × (1/3) = 28 houses sold.

There were 84 - 28 = 56 houses remaining.

From these remaining houses, 5/7 were sold this month, which equates to 56 × (5/7) = 40 houses sold. Thus, 56 - 40 = 16 houses are left to be sold.

Answer:

[tex]\frac{3}{4}[/tex]

Step-by-step explanation:

the simplified form of the quantity of x plus 8, all over 4 − the quantity of x plus 5, all over 4

[tex]\frac{x+8}{4} -\frac{x+5}{4}[/tex]

To simplify the expression , we check the denominator.

When the denominators are same then we subtract the numerators, we put denominator only once

[tex]\frac{x+8-(x+5)}{4}[/tex]

Multiply negative inside the parenthesis and combine like terms

[tex]\frac{x+8-x-5}{4}[/tex]

[tex]\frac{3}{4}[/tex]

Answer:

B. [tex]12^{\circ}[/tex]

Step-by-step explanation:

We have been given an image of a circle. We are asked to find the measure of angle U.

We have been given that measure of angle 's' is 30 degrees, so the measure of arc RT will be 2 times the measure of angle 's' as angle 's' is inscribed angle of arc RT.

[tex]\text{Measure of arc RT}=2\times 30^{\circ}[/tex]

[tex]\text{Measure of arc RT}=60^{\circ}[/tex]

We know that the measure of angle formed by intersecting secant and tangent outside a circle is half the difference of intercepted arcs.

Using Secant-tangent theorem, we can set an equation to find the measure of angle U as:

[tex]m\angle U=\frac{1}{2}\times (\text{Measure of arc RS}-\text{Measure of arc RT})[/tex]

Substituting the given values in above equation we will get,

[tex]m\angle U=\frac{1}{2}\times(84^{\circ}-60^{\circ})[/tex]

[tex]m\angle U=\frac{1}{2}\times(24^{\circ})[/tex]

[tex]m\angle U=12^{\circ}[/tex]

Therefore, the measure of angle U is 12 degrees and option B is the correct choice.

Answer:

kf(x)

Step-by-step explanation:

I got it right.

Final answer:

701.5 is equal to 701.50 because in decimals, trailing zeroes after the decimal point do not change the value of the number; they only indicate precision.

Explanation:

The question is about whether 701.5 is equal to 701.50. In mathematics, when comparing numbers with different numbers of decimal places, it's important to understand the significance of trailing zeroes in the decimal part.

A zero after the decimal point but at the end of a number (trailing zero) does not change the value of the number.

Therefore, 701.5 is exactly equal to 701.50

This is because the trailing zero in 701.50 does not add any value but merely serves as a placeholder, indicating precision to the hundredth place without changing the number's value.

To round off or add zero to the calculated answer of 0.00001258 L and give a final answer with three significant figures, round up the last significant figure to 6.

In order to round off or add zero to the calculated answer and give a final answer with three significant figures, follow these steps:

To round off or add zero to the calculated answer to give a final answer with three significant figures, consider the following: For the value 0.00001258 L, the third significant figure is 5. Since the digit after the third significant figure (8) is greater than or equal to 5, we round up the third significant figure. Therefore, the final answer is 0.0000126 L.

To round off or add zero to the calculated answer to give a final answer with three significant figures, consider the following:

For the value 0.00001258 L, the third significant figure is 5. Since the digit after the third significant figure (8) is greater than or equal to 5, we round up the third significant figure. Therefore, the final answer is 0.0000126 L.

Answer:

29

Step-by-step explanation:

29 is only divisible by 1 and itself.

The 70 represents the no of people in the line at the time when the ticket booth is opened.

Given that,

Based on the above information, the 70 shows that the number of people at the time when the ticket booth is opened.

Therefore, the other options are wrong.

Thus we can conclude that the 70 represents the no of people in the line at the time when the ticket booth is opened.

Learn more: brainly.com/question/22401678

Answer:

The probability that a ticket that is randomly chosen will award a larger prize is:

                        1/5=0.2

Step-by-step explanation:

Let A denote the event that the ticket is a winning ticket.

B denote the event that there is a larger prize.

A∩B denote the event that there is a larger prize on the winning ticket.

Let P denote the probability of an event.

Now according to the given information we have:

[tex]P(A)=\dfrac{6}{10}[/tex]

Also, [tex]P(B|A)=\dfrac{1}{3}[/tex]

Hence, we are asked to find: P(A∩B)

We know that:

[tex]P(B|A)=\dfrac{P(A\bigcap B)}{P(A)}\\\\\\\dfrac{1}{3}=\dfrac{P(A\bigcap B)}{\dfrac{6}{10}}\\\\\\P(A\bigcap B)=\dfrac{1}{3}\times \dfrac{6}{10}\\\\P(A\bigcap B)=\dfrac{2}{10}=\dfrac{1}{5}=0.2[/tex]

            The probability is:

              1/5=0.2

The overall probability that a randomly chosen ticket will award a larger prize is 0.2, or 20%, obtained by multiplying the probability of drawing a winning ticket (0.6) with the probability of winning a larger prize if the ticket is a winner (0.333).

For the probability that a ticket randomly chosen will award a larger prize, given that 6 out of every 10 tickets are winners and of those, 1 out of every 3 is a larger prize.

First, we calculate the probability of drawing a winning ticket, which is 6/10 or 0.6.

Then we compute the probability of the winning ticket awarding a larger prize, which is 1/3 or approximately 0.333.

To find the overall probability of a randomly chosen ticket awarding a larger prize, we multiply these two probabilities together:

Overall probability = Probability of winning ticket×Probability of larger prize on winning ticket

Overall probability = 0.6 ×0.333

Overall probability ≈ 0.2

So, the probability that a ticket awards a larger prize is 0.2, or 20%.

The number of strawberries Sameer ate is 6.

Given that, Sameer ate a plum with 32 calories and several strawberries with 4 calories each. The total number of calories in Sameer’s snack was 56.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Now, remaining calories=Total number of calories - Number of calories in plum

=56-32=24

Number of strawberries=24/4 =6

Therefore, the number of strawberries Sameer ate is 6.

To learn more about a unitary method visit:

https://brainly.com/question/22056199.

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The function f(x) = xe⁻ˣ is concave down for intervals where the second derivative f''(x) is negative, which occurs when x > 0.

To determine the intervals where the function f(x) = xe⁻ˣ is concave down, we need to find the second derivative of the function and identify where it is negative. The first derivative of the function f'(x) = e⁻ˣ - xe⁻ˣ is obtained using the product rule. Then, we take the second derivative: f''(x) = -e⁻ˣ - e⁻ˣ + xe⁻ˣ = -2e⁻ˣ + xe⁻ˣ.

To find where the function is concave down, we need to find the intervals where f''(x) < 0. By analyzing the second derivative, we can see that the term -2e⁻ˣ is always negative, while the term xe⁻ˣ can be either positive or negative depending on the value of x.

For x > 0, the term xe⁻ˣ is positive, making f''(x) more negative, therefore, the function is concave down for x > 0.

Answer:

m(h)= 5.25h; 11.81

11.81 is the answer