The two boxes shown are cuboids.
20 cm
4 cm
30 cm
3 cm
50 cm
10 cm
Work out how many of the smaller boxes you would need
to completely fill the larger one.

So Nicole put together 1/10 of that puzzle more than Heather did.

1) Gathering the data

Heather on Saturday

2/5

Heather on Sunday

3/10

Nicole

4/5

2) Let's add those ratios up for Heather's work

Comparing to Nicole's work

3) So Nicole put together 1/10 more than Heather did.

Answer:

C.  5x(-x + 2)

Step-by-step explanation:

To factor the expression -5x² + 10x, we need to look for a common factor that can be factored out.

Finding a common factor involves identifying a term or expression that can be factored out from each term of a given expression.

Both terms have the common factor of 5x, so we can factor out 5x:

5x(-x + 2)

Therefore, the factored form of -5x² + 10x is -5x(x - 2).

\(\hrulefill\)

Additional notes:

If we expand the expressions in the given answer options, we get:

  A.  −5x(x + 2) = -5x² - 10x

  B.  5(−x² + 10x) = -5x² + 50x

  C.  5x(−x + 2) = -5x² + 10x

  D.  x(5x + 10) = 5x² + 10x

Hence confirming that the correct answer is option C.

To factor \(-5x^2+10x\), we can begin by factoring out the greatest common factor, which is \(-5x\):

We can check our answer by distributing \(-5x\) to the expression inside the parentheses:

\(\therefore\) The answer is \(-5x(x-2)\).

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Answer:

x(7+15) \(\leq\) -19

Step-by-step explanation:

Answer:

6 units

Step-by-step explanation:

the horizontal difference is the distance between the x values of both points. we know the distance between 4 and -2 is 6.

The ratios of y/x are the same for the graph of y = 3x

and the ratios of y/x are NOT the same for the graph of  y = 3x + 4

In this question, we have been given the graphs of lines y = 3x and y = 3x + 4.

Consider the ratios of y/x for the graph y = 3x

6/2 = 3

3/1 = 3

(-6)/(-2) = 3

Consider the ratios of y/x for the graph y = 3x + 4.

7/1 = 7

(1)/(-1) = -1

(-2)/(-2) = 1

We can observe that the ratios of y/x are the same for the graph of y = 3x

and the ratios of y/x are different for the graph of  y = 3x + 4.

Therefore, the ratios of y/x are the same for the graph of y = 3x

and the ratios of y/x are NOT the same for the graph of  y = 3x + 4

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The independent variable in this data is the speed of the car. This is because the congressman is trying to determine whether or not the gas mileage improves at lower speeds.

The dependent variable is the gas mileage, because it is the variable that is being measured and that is affected by the independent variable.

The other variables in this data are the weight of the car, the type of engine, and the year of the car. However, these variables are not being changed in this experiment, so they are not considered to be independent variables.

The data shows that the gas mileage of the Toyota Camry improves as the speed of the car decreases. This supports the claim of the supporters of the bill to reduce the speed limit.

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The polygon was translated 5 units left and 9 units up using the rule for (x, y) ⇒ (x - 5, y + 9)

Translation is the movement of a point in the coordinate plane either up, left, down or right. Translation is a type of rigid transformation because it preserves both the shape and size of the figure.

Other types of rigid transformations are reflection and rotation.

The points D(5, -10) and T(-9, -6) were translated to give D'(0,-1), T'(-14,3). This means that the translation was 5 units left and 9 units up.

The rule for this translation is (x, y) ⇒ (x - 5, y + 9)

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Answer:

data given

interest rate 12%

amount to be received 15ooo

time9years

Step-by-step explanation:

from

A=p[1+r/100]^n

where

A is amount

p is principal

r is rate interest

n number of interist period

now,

15000=p[1+12/100]^8

15000/1.12^8 =p×1.12^8/1.12^8

p=6058.24

p=6058)

: .you should invest 6,058

The amount to be invested initially if you want to have fifteen thousand dollars after nine years is $3947.18.

If n is the number of times the interested is compounded each year, and 'r' is the rate of compound interest annually, then the final amount after 't' years would be:

\(a = p(1 + \dfrac{r}{n})^{nt}\)

We are given that:

A=15000

r=0.12

t=9

We need to find P. You can do this by rearranging the formula:

P=ertA​

Then plug in the given values and use a calculator:

P=e0.12×915000​

P≈3947.18

Therefore, by the given interest rate the answer will be $3947.18.

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Understanding statistical questions and data distributions is an important concept in data analysis and statistics. A statistical question is one that can be answered by collecting and analyzing data.

These questions typically ask about a population or group of individuals and are often related to trends or patterns.

Data distributions refer to the way data is spread out or distributed within a dataset. This can include measures like the mean, median, and standard deviation. Understanding data distributions is important for making accurate interpretations and predictions based on the data.

To practice understanding statistical questions and data distributions, it's important to work with real-world datasets and ask questions that can be answered using statistical analysis.

This can involve looking at trends and patterns in the data and interpreting the results in a meaningful way. By building these skills, you can become better equipped to analyze and interpret data in a variety of settings.

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The functions and its domain are a representation of their dependance on one another.

function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable). In the given question, we have two functions and we are required to find the composite of which ever form of the functions as well as the domain of the said function.

\(f(x) = \frac{3}{x}, g(x) = 2x + 8;\\(f.g)(x) = \frac{3}{2x + 8}\)

The domain of the function is given as

\(domain = (-\infty , -4) U (-4, \infty)\\\)

In the second composition of the function,

\((g.f) = \frac{6}{x} + 8\\domain = (-\infty, 0) U (0, \infty)\)

The third composition of function

\((f.f) = x\\domain = (-\infty, \infty)\)

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Using the z-distribution, the sample size that will produce the widest confidence interval is given by:

D. 36.

A confidence interval of proportions is given by:

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which:

The margin of error is given by:

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

The widest interval has the highest margin of error, and since the margin of error is inversely proportional to the sample size, a lower sample size generates a higher margin of error, hence option D is correct.

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Answer:

By solving this equation for the variable ' d ', you learn how many days after you fill the tank you'll have to send somebody back to fill it again.

Step-by-step explanation:

An order-preserving function is one where x < y implies f(x) < f(y). An isomorphism is a one-to-one order-preserving function between two partially ordered sets, while an automorphism is an isomorphism of a set to itself.

In the given excerpt, it explains the concepts of order-preserving functions, isomorphisms, and automorphisms in the context of partially ordered sets.

Order-Preserving Function:

A function f: P -> Q, where P and Q are partially ordered sets, is said to be order-preserving if for any elements x and y in P, if x < y, then f(x) < f(y). In other words, the function preserves the order relation between elements in P when mapped to elements in Q.

Increasing Function:

If P and Q are linearly ordered sets, then an order-preserving function is also referred to as an increasing function. It means that for any elements x and y in P, if x < y, then f(x) < f(y).

Isomorphism:

A one-to-one function f: P -> Q is called an isomorphism of P and Q if it satisfies two conditions:

a. f is order-preserving: For any elements x and y in P, if x < y, then f(x) < f(y).

b. f is onto (surjective): Every element in Q has a pre-image in P.

When an isomorphism exists between (P, <) and (Q, <), it means that the two partially ordered sets have a structure that is preserved under the isomorphism. In other words, they have the same ordering relationships.

Automorphism:

An automorphism of a partially ordered set (P, <) is an isomorphism from P to itself. It means that the function f: P -> P is both order-preserving and bijective (one-to-one and onto). Essentially, an automorphism preserves the structure and order relationships within the same partially ordered set.

These concepts are fundamental in understanding the relationships and mappings between partially ordered sets, particularly in terms of preserving order, finding correspondences, and exploring the symmetry within a set.

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Answer:

3/4

Step-by-step explanation:

There are 13 hearts in a 52 deck.

52-13=39

39/52=3/4

The probability that you are not dealt a heart from the deck of cards is 3/4.

Probability determines the chances that an event would occur. The probability the event occurs is 1 and the probability that the event does not occur is 0.

The probability that you are not dealth with a heart = 1 - (number of hearts / total number of cards)

1 - 13/52 = 39/52 =  3/4

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The change in amount of water in the pool after 1 min is 2 gallons.

Since water enters the large pool at pool at 10 gallons every minute, the rate in = 10 gal/min.

Also, water drains from the pool at 12 gallons every minute, the rate out = 12 gal/min.

So, the net rate of change of water in the large pool is rate in - rate out = 10 gal/min - 12 gal/min = -2 gal/min(the negative indicates that the water is draining).

So, the net change in the amount of water after 1 min = net rate of change × 1 min = - 2 gal/min × 1 min = -2 gal.(negative since its draining)

So, the change in amount of water in the pool after 1 min is 2 gallons.

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Answer:

73

Step-by-step explanation:

Since DA is the diameter, this means that you can divide the circle into two half-circles.  You will solve with the right half-circle.  A half-circle has a 180 total degrees.  Add up the values given and solve for x.

(2x) + (7x - 4) + (85) = 180

2x + 7x - 4 + 85 = 180

9x - 4 + 85 = 180

9x + 81 = 180

9x = 99

x = 11

Now that you have the value of x, solve for m∠CZB.

m∠CZB = 7x - 4

m∠CZB = 7(11) - 4

m∠CZB = 77 - 4

m∠CZB = 73

Answer:

y=cos(x)

Step-by-step explanation:

since the period doesnt start at (0,0) it is cos.

the wave also starts at a positive (0,1) so it is positive

Answer:

7

Step-by-step explanation:

Just put the numbers in order the find the number in the middle in the case that there are to numbers add the together then divide by 2

Answer:

A = 70 meters squared

Step-by-step explanation:

The area of a rectangle is given by length time width.

A = l*w

A = 7*10

A = 70 meters squared

Answer:

area of shaded region =15²-5²=200mm²

perimeter of outside edge =4×15=60mm

Answer:

Area of the shaded region:

Perimeter of outside edges:

Answer: 2x²-4x-16

Step-by-step explanation:

\((2x+4)(x-4)=\\2x(x)+2x(-4)+4(x)+4(-4)=\\2x^2-8x+4x-16=\\2x^2-4x-16\)

Answer:

Send the question please. You can send in the comments or in a separate question.

Answer:

100%?

Step-by-step explanation:

Answer:

6.8

Step-by-step explanation:

27 / 4 = 6.75, which rounded to the nearest tenth, is 6.8.

Answer:

X= 110/7 or 15.7 or rounded to 16

Answer:

x=15.714285

Step-by-step explanation:

-0.35x=-3-2.5

-0.35x=-5.5

-0.35/-0.35= -5.5/0.35

X=-5.5/-0.35

X=15.714285

Answer:

\(\left[\begin{array}{cc}x&y&-2&-9&0&-1&2&7&4&15\end{array}\right]\)

Step-by-step explanation:

Given

\(y = 4x - 1\)

Required

Create a function table for inputs -2, 0, 2 and 4

When x = -2

\(y = 4*-2 - 1 = -9\)

When x = 0

\(y = 4*0 - 1 = -1\)

When x = 2

\(y = 4*2 - 1 = 7\)

When x = 4

\(y = 4*4 - 1 = 15\)

So, the table is:

\(\left[\begin{array}{cc}x&y&-2&-9&0&-1&2&7&4&15\end{array}\right]\)

Hiker travels \(\frac{5}{2} km\) in \(\frac{2}{3}hours\) with speed of \(3\frac{3}{4} km/hr\).

Defining speed as the speed at which an object's location changes in any direction.

The distance traveled in the context of the time it took to travel that distance is how speed is defined. Since speed simply has a direction and no magnitude, it is a scalar quantity.

The speed formula is provided as:

\(v=\frac{d}{t}\);

where d is distance travelled, t is time taken and v is speed or velocity.

Average speed determined by the ratio of the total distance traveled by an object to the entire amount of time it took to travel that distance.

Given;

Average speed=\(3\frac{3}{4}=3+\frac{3}{4}=\frac{15}{4}\);

Average speed=\(\frac{d}{t}=\frac{15}{4}\);

Given total time \(\frac{2}{3}hours\);

⇒\(d=\frac{2}{3}*\frac{15}{4}=\frac{5}{2} km\);

Hiker travels \(\frac{5}{2} km\) in \(\frac{2}{3}hours\) with speed of \(3\frac{3}{4} km/hr\).

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Answer:

-6.28576e+81

Step-by-step explanation: