Rewrite as equivalent rational expressions with denominator (3d−3)(d+7)(d−9).
53d2+18d−21,8d3d2−30d+27

Given:

The statement is, "The weight of a paper chip".

To find:

The most reasonable estimate.

Explanation:

As we know,

Since the weight of a paper chip is very little, so, the weight of the paper chip is measured using grams.

Thus, the most reasonable estimate of the weight of a paper chip is 1 gram.

Final answer: 1 gram

Answer:

85.50

Step-by-step explanation:

6 times 19 = 114 markers then times .75= 85.50

The vertices of the reflected square.

Let's calculate them:

A' = (-0.914, 3.914)

B' = (-2.828, 5.828)

C' = (-0.086, 7.086)

D' = (1.828, 5.172)

The vertices of the image of the square ABCD after reflecting it about the line through (0, 0) and (-2, 2), we can use the following steps:

Find the equation of the reflection line:

The reflection line passes through (0, 0) and (-2, 2).

We can calculate the slope (m) of the line using the formula (y2 - y1) / (x2 - x1):

m = (2 - 0) / (-2 - 0) = 2 / -2 = -1.

Using the point-slope form of a line (y - y1) = m(x - x1), we can use either of the given points to write the equation of the line:

y - 0 = -1(x - 0)

y = -x.

Find the midpoint of each side of the square:

The midpoints of the sides of a square are also the midpoints of its diagonals.

The midpoint of AB is ((4+6)/2, (3+4)/2) = (5, 3.5).

The midpoint of BC is ((6+5)/2, (4+6)/2) = (5.5, 5).

The midpoint of CD is ((5+3)/2, (6+5)/2) = (4, 5.5).

The midpoint of DA is ((3+4)/2, (5+3)/2) = (3.5, 4).

Reflect the midpoints about the line:

To reflect a point (x, y) about the line y = -x, we can find the perpendicular distance (d) from the point to the line and use it to determine the reflected point.

The perpendicular distance d from the line y = -x to a point (x, y) is given by the formula:

d = (y + x) / √(2).

The coordinates of the reflected points can be found using the formula for reflection across a line:

x' = x - 2d / √(2)

y' = y - 2d / √(2).

Calculate the reflected vertices:

The coordinates of the reflected vertices are as follows:

A' = (4 - 2(3.5 + 5) / √(2), 3 - 2(3.5 - 5) / √(2))

B' = (6 - 2(5 + 5) / √(2), 4 - 2(5 - 5) / √(2))

C' = (5 - 2(5.5 + 5) / √(2), 6 - 2(5.5 - 5) / √(2))

D' = (3 - 2(4 + 5) / √(2), 5 - 2(4 - 5) / √(2))

Now we can plot the original square ABCD and its image A'B'C'D' on the same graph to visualize the reflection.

For similar questions on vertices

https://brainly.com/question/1217219

#SPJ8

Answer:

Step-by-step explanation:

Given Parmesan cheese was on sale for  $13.60 per pound

Welsey bought a piece of the parmesan cheese that weighted \frac{11}{8} pounds

we need to spend$13.60 for 1 pound

for 11/8 pound

11/8 x 13.60= 18.72

So Wesley need to spend $18.70 to get the Parmesan cheese.

Answer:

125 cm

Step-by-step explanation:

If you separate the shape, you get an area of 50, 50, and 25. you then add these together to get 125

The value of d in the image that shows the two parallel lines that are crossed by the transversal is determined as: 125°.

In geometry, a transversal is a line that intersects two or more other lines at distinct points. When a transversal intersects a pair of parallel lines, it creates various angles and relationships between those angles.

The image attached below shows the two parallel lines which are crossed by the transversal, where angle d and 125° are vertical angles.

Since they are vertical angles, they will be equal or congruent to each other. Therefore, the value of d = 125°

Learn more about Transversal on:

https://brainly.com/question/24607467

#SPJ1

Answer:

Dear user,

Answer to your query is provided below

2(al−1) is the expression equivalent for 2la+26−2−26

Answer:

x=-12  (BUT IS EXTRENUS)

Step-by-step explanation:

If u dont know what extraneous is, dont worry about it...

Answer:

Graph C.

*See attachment below

Step-by-step explanation:

A graph that shows a set of ordered pairs representing a function would have each x-value being plotted against only one y-value. That is, every x-value must have exactly one y-value. Every x-value must not have more than 1 y-value being plotted against it.

The graph that shows this is the graph in option as shown in the attachment below.

After answering the presented questiοn, we can cοnclude that The fοrmula tο find the area and perimeter οf a twο-dimensiοnal shape depends οn the type οf shape

An equatiοn in mathematics is a statement that states the equality οf twο expressiοns. An equatiοn is made up οf twο sides that are separated by an algebraic equatiοn (=). Fοr example, the argument "2x + 3 = 9" asserts that the phrase "2x Plus 3" equals the value "9." The purpοse οf equatiοn sοlving is tο determine the value οr values οf the variable(s) that will allοw the equatiοn tο be true.

The fοrmula tο find the area and perimeter οf a twο-dimensiοnal shape depends οn the type οf shape. Here are sοme cοmmοn fοrmulas:

1. Rectangle:

• Area: A = length x width

• Perimeter: P = 2(length + width)

2. Square:

• Area: A = side x side (οr A = side²)

• Perimeter: P = 4 x side

3. Circle:

• Area: A = π x radius²

• Circumference (perimeter): C = 2π x radius (οr C = π x diameter)

4. Triangle:

• Area: A = (base x height) / 2

• Perimeter: P = side1 + side2 + side3

5. Trapezοid:

• Area: A = ((base1 + base2) x height) / 2

• Perimeter: P = side1 + side2 + side3 + side4

To know more about Area and Perimeter visit:

https://brainly.com/question/11957642

#SPJ1

Answer:

28 m below the surface to catch its prey

On solving the provided question, we can say that triangle BIG and triangle FUN are similar to each other and are congruent, so angle N is congruent to angle G.

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

here,

we have been provided with that

triangle BIG and triangle FUN are similar to each other and are congruent.

Angle N is congruent to angle G.

To know more about triangle visit:

https://brainly.com/question/2773823

#SPJ1

Answer:

4.5 cups of lemonade is needed

Step-by-step explanation:

Answer:

-4 + -6 = 10

Step-by-step explanation:

The first point is 4 units below zero, so -4

The next point shows that it is 10 points below zero, so -10

-4 + blank = -10

-10 - (-4) = -10 + 4 = -6

blank = -6

Check:

-4 + (-6) = -10

-4 - 6 = -10

correct

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

The probability is  \(P(k) =0.07843\)

Step-by-step explanation:

From the question we are told that

   The total number of cards is  n  =  52

Generally the number of ace in a standard deck of cards is  k  =  4

Generally the the first card drawn is not an ace so the remaining number of ace after the first card is drawn is  k =  4

also the remaining total number of cards after the first card is drawn is

     N =  n- 1

=>  N =  52 - 1  

=>  N =  51

Generally the probability of drawing an ace on the second attempt if the first card (which you did NOT put back in the pack) was not an ace is mathematically represented as

        \(P(k) =\frac{k}{N}\)

=>      \(P(k) =\frac{4}{51}\)

=>      \(P(k) =0.07843\)

Answer:

18 T-shirts

Step-by-step explanation:

1gram = 1000milligrams

1gram × 156000milligrams ÷ 1000milligrams

The milligrams unit cancel out each other thus grams remains as the main unit.

=156grams

1 T-shirt = 156grams

1 T-shirt × 2808grams ÷156grams

The grams unit cancel out each other thus T-shirt remains as the main unit.

=18 T-shirts

Answer:

18

Step-by-step explanation:

The growth of the plant last year was 25 inches if the normal growth was ten inches more than twice the amount of last year.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

The normal yearly growth of a plant is 60 inches.

Let's suppose the growth of the plant last year was x

The normal growth was ten inches more than twice the amount of last year.

From the above statement:

10 + 2x = 60

2x = 50

x = 25 inches

Thus, the growth of the plant last year was 25 inches if the normal growth was ten inches more than twice the amount of last year.

Learn more about the linear equation here:

brainly.com/question/11897796

#SPJ1

Answer:

0.55% probability that exactly 5 out of the first 13 customers buy a magazine

Step-by-step explanation:

For each customer, there are only two possible outcomes. Either they buy a magazine, or they do not. The probability of a customer buying a magazine is independent of other customers. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

And p is the probability of X happening.

10% of his customers buy a magazine

This means that \(P = 0.1\)

What is the probability that exactly 5 out of the first 13 customers buy a magazine?

This is P(X = 5) when n = 13. So

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 5) = C_{13,5}.(0.1)^{5}.(0.9)^{8} = 0.0055\)

0.55% probability that exactly 5 out of the first 13 customers buy a magazine

Answer:

\( P(X=5) = (13C5) (0.1)^5 (1-0.1)^{13-5}= 0.00554\)

So then  he probability that exactly 5 out of the first 13 customers buy a magazine is 0.0554

Step-by-step explanation:

Let X the random variable of interest "number of customers that buy a magazine", on this case we can model the variable of interest with this distribution:

\(X \sim Binom(n=13, p=0.1)\)

The probability mass function for the Binomial distribution is given as:

\(P(X)=(nCx)(p)^x (1-p)^{n-x}\)

Where (nCx) means combinatory and it's given by this formula:

\(nCx=\frac{n!}{(n-x)! x!}\)

We want to find this probability:

\( P(X=5)\)

And using the probability mass function we got:

\( P(X=5) = (13C5) (0.1)^5 (1-0.1)^{13-5}= 0.00554\)

So then  he probability that exactly 5 out of the first 13 customers buy a magazine is 0.0554

The required length of AC in triangle ABC is b = 119.57 units.

In triangle ABC, we have:

\($\angle B = 85^\circ$\)

\($\angle C = 53^\circ$\)

\($BC = 85 units\)

AB = c

AC = b (we need to find the value of b)

We know that the sum of the interior angles of a triangle is \($180^\circ$\). Therefore:

\($\angle A = 180^\circ - \angle B - \angle C$\)

\($\angle A = 180^\circ - 85^\circ - 53^\circ$\)

\($\angle A = 42^\circ$\)

Using the law of sines, we have:

\($\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$\)

Substituting the given values, we get:

\($\frac{c}{\sin 85^\circ} = \frac{b}{\sin 53^\circ}$\)

Solving for $c$, we get:

\($c = b \cdot \frac{\sin 85^\circ}{\sin 53^\circ}$\)

We also know that:

\($\frac{a}{\sin A} = \frac{85}{\sin 42^\circ}$\)

Solving for a, we get:

\($a = 85 \cdot \sin 42^\circ$\)

Now we can use the law of cosines to find b:

\($b^2 = a^2 + c^2 - 2ac \cdot \cos B$\)

Substituting the known values, we get:

\($b^2 = (85 \cdot \sin 42^\circ)^2 + \left[b \cdot \frac{\sin 85^\circ}{\sin 53^\circ}\right]^2 - 2 \cdot 85 \cdot b \cdot \sin 42^\circ \cdot \sin 85^\circ/(\sin 53^\circ)$\)

Simplifying and solving for b, we get:

b = 119.57 units

Therefore, the length of AC in triangle ABC is b = 119.57 units.

To know more about Triangle visit:

brainly.com/question/2773823

#SPJ1

Answer: it’s C

Your welcome

Step-by-step explanation:

Answer: See below

Step-by-step explanation:

The first is a beaker, it's used to measure liquid volume

The second is a ruler, it's used to measure length.

Last is a thermometer, it's used to measure temperature.

Answer:

\(180\)

Step-by-step explanation:

\(216(5/6)\)

\(216(5)/6\)

\(1080/6\)

\(=180\)

Answer:

180

Step-by-step explanation:

Square Area = side x side = 3x3 = 9

Rectangle Area = side x side= 7x3= 21

9 + 21 = 30 square inches

Answer:

30 square inches

Step-by-step explanation:

   \(\boxed{\text{\bf Area of rectangle = length *width}}\)

Rectangle1:

     Area = 6 * 3

              = 18 square inches

Rectangle2:

Area = 4 * 3

          = 12 square inches

Area of the figure = area of rectangle1 + area of rectangle2

                             = 18 + 12

                             = 30 square inches

Answer:

Step-by-step explanation:

To linearize the function cos^5(x), we can use the following identity:

cos^5(x) = (cos^2(x))^2 * cos(x) = (1 - sin^2(x))^2 * cos(x)

Now, we can use the identity e^(ix) = cos(x) + i sin(x) to rewrite the expression as follows:

(1 - sin^2(x))^2 * cos(x) = ((1 - e^(ix) * e^(-ix))/2)^2 * (e^(ix) + e^(-ix))/2

= (1/16) * (e^(4ix) - 4e^(2ix) + 6 - 4e^(-2ix) + e^(-4ix))

This expression is now linear in terms of e^(ix) and e^(-ix). Therefore, we have linearized the function cos^5(x) as:

(1/16) * (e^(4ix) - 4e^(2ix) + 6 - 4e^(-2ix) + e^(-4ix))

Answer:

x=7

Step-by-step explanation:

3.5/3= 1.1666666666

6*1.16666666= 7

x=7

Answer:

a) \(P(X>106.11)=P(\frac{X-\mu}{\sigma}<\frac{106.11-\mu}{\sigma})=P(Z>\frac{106.11-106}{0.3})=P(z>0.37)\)

And we can find this probability with the complement rule:

\(P(z>0.37)=1-P(z<0.37) =1-0.644= 0.356\)

b) \( z =\frac{106.11- 106}{\frac{0.3}{\sqrt{44}}}=  2.431\)

And if we use the z score we got:

\( P(z>2.431) =1-P(z<2.431) =1-0.992=0.008\)

Step-by-step explanation:

Let X the random variable that represent the lengths of a population, and for this case we know the distribution for X is given by:

\(X \sim N(106,0.3)\)  

Where \(\mu=106\) and \(\sigma=0.3\)

Part a

We are interested on this probability

\(P(X>106.11)\)

And we can use the z score formula given by:

\(z=\frac{x-\mu}{\sigma}\)

And using this formula we got:

\(P(X>106.11)=P(\frac{X-\mu}{\sigma}<\frac{106.11-\mu}{\sigma})=P(Z>\frac{106.11-106}{0.3})=P(z>0.37)\)

And we can find this probability with the complement rule:

\(P(z>0.37)=1-P(z<0.37) =1-0.644= 0.356\)

Part b

For this case we select a sample of n =44 and the new z score formula is given by:

\(z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}\)

And if we find the z score we got:

\( z =\frac{106.11- 106}{\frac{0.3}{\sqrt{44}}}=  2.431\)

And if we use the z score we got:

\( P(z>2.431) =1-P(z<2.431) =1-0.992=0.008\)

The time Jack left Santa Clara is 1 : 55 pm

A word problem in math is a math question written as one sentence or more. These statements are interpreted into mathematical equation or expression.

The time for Jack to walk to lose Altos is 25 min and he uses another 25mins to work to Palo alto.

Therefore, the total time he spent is

25mins + 25 mins = 50 mins

He arrived Palo at 2 :45 pm, therefore the time he left Santa Clare will be ;

2:45 pm = 14 :45

= 14:45 - 50mins

= 13:55

= 1 : 55pm

Therefore he left at 1:55 pm

learn more about word problem from

https://brainly.com/question/21405634

#SPJ1

The sampling method used by the restaurant manager allows for efficient data collection and a representative sample, it may introduce bias and lacks randomization.

Based on the information provided, we can identify the following statements that are true about the sampling method used by the restaurant manager to evaluate customer satisfaction with the new smoothie:

1. The manager uses systematic sampling: The manager surveys every other customer who orders the new smoothie. This systematic approach involves selecting every second customer, providing a consistent and organized sampling method.

2. The sample is representative: By surveying every other customer who orders the new smoothie, the manager ensures that the sample includes a variety of customers, reflecting the customer population as a whole.

3. The sample size may be smaller than the total customer base: Since the manager surveys every other customer, the sample size may be smaller compared to surveying every customer. This allows for efficient data collection and analysis.

4.The sampling method may introduce bias: The manager may inadvertently introduce bias by only surveying every other customer. Customers who are skipped in the survey may have different preferences or opinions, leading to a potential bias in the results.

5. The sampling method lacks randomization: Randomization is not employed in this sampling method, as the manager systematically selects customers. This could potentially introduce bias or exclude certain types of customers from the sample.

for more such questions on sampling method

https://brainly.com/question/13219833

#SPJ8